supervisory hybrid control of a wind energy … · wind energy conversion and battery storage...

SUPERVISORY HYBRID CONTROL OF A WIND ENERGY CONVERSION AND

BATTERY STORAGE SYSTEM

by

Muhammad Shahid Khan

A dissertation submitted in conformity with the requirements

for the degree of Doctor of Philosophy

Graduate Department of Electrical and Computer Engineering

University of Toronto

© Copyright by Muhammad Shahid Khan, 2008

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SUPERVISORY HYBRID CONTROL OF A WIND ENERGY CONVERSION AND

BATTERY STORAGE SYSTEM

Doctor of Philosophy

2008

Muhammad Shahid Khan

Graduate Department of Electrical and Computer Engineering

University of Toronto

ABSTRACT

This thesis presents a supervisory hybrid controller for the automatic operation and control of a

wind energy conversion and battery storage system. The supervisory hybrid control scheme is

based on a radically different approach of modeling and control design, proposed for the subject

wind energy conversion and battery storage system.

The wind energy conversion unit is composed of a 360kW horizontal axis wind turbine

mechanically coupled to an induction generator through a gearbox. The assembly is electrically

interfaced to the dc bus through a thyristor-controlled rectifier to enable variable speed operation

of the unit. Static capacitor banks have been used to meet reactive power requirements of the

unit. A battery storage device is connected to the dc bus through a dc-dc converter to support

operation of the wind energy conversion unit during islanded conditions. Islanding is assumed to

occur when the tiebreaker to the utility feeder is in open position. The wind energy conversion

unit and battery storage system is interfaced to the utility grid at the point of common coupling

through a 25km long, 13.8kV feeder using a voltage-sourced converter unit. A bank of static

(constant impedance) and dynamic (induction motor) loads is connected to the point of common

coupling through a step down transformer.

A finite hybrid-automata based model of the wind energy conversion and storage system has

been proposed that captures the different operating regimes of the system during grid-connected

and in islanded operating modes. The hybrid model of the subject system defines allowable

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operating states and predefines the transition paths between these operating states. A modular

control design approach has been adapted in which the wind energy conversion and storage

system has been partitioned along the dc bus into three independent system modules. Traditional

control schemes using linear proportional-plus-integral compensators have been used for each

system module with suitable modifications where necessary in order to achieve the required

steady state and transient performance objectives. A supervisory control layer has been used to

combine and configure control schemes of the three system modules to suite the requirements of

system operation during any one operating state depicted by the hybrid model of the system.

Transition management strategies have been devised and implemented through the supervisory

control layer to ensure smooth inter-state transitions and bumpless switching among controllers.

It has been concluded based on frequency domain linear analysis and time domain

electromagnetic transient simulations that the proposed supervisory hybrid controller is capable

of operating the wind energy conversion and storage system in both grid-connected and in

islanded modes under changing operating conditions including temporary faults on the utility

grid.

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Dedicated to my mother who passed away during the course of this work.

May Allah rest her gentle soul in eternal peace.

Aameen.

v

ACKNOWLEDGEMENTS

I would like to express my gratitude to Prof. M.R. Iravani for his guidance and support in

bringing this work to completion. Thanks are also due to those friends and faculty support staff

who made my stay at the University of Toronto more comfortable and pleasant. Financial

support from Prof. M. R. Iravani and from the School of Graduate Studies in the form of research

grants, open fellowship awards and Roger fellowship awards are gratefully acknowledged.

Continuous encouragement and support from my parents and other family members has been

instrumental in completing this work.

vi

TABLE OF CONTENTS

ABSTRACT ................................................................................................................................................. ii ACKNOWLEDGEMENTS.......................................................................................................................... v TABLE OF CONTENTS............................................................................................................................. vi LIST OF TABLES....................................................................................................................................... ix LIST OF FIGURES ...................................................................................................................................... x NOMENCLATURE ................................................................................................................................xviii

ABBREVIATIONS ................................................................................................................................... xix

1. INTRODUCTION ................................................................................................................................. 1

1.1 BACKGROUND...................................................................................................................... 1 1.2 PROBLEM STATEMENT ...................................................................................................... 2 1.3 STUDY SYSTEM.................................................................................................................... 3 1.4 RESEARCH OBJECTIVES..................................................................................................... 7 1.5 LIMITATIONS ........................................................................................................................ 9 1.6 THESIS OUTLINE ................................................................................................................ 10

2. OPERATION AND CONTROL ......................................................................................................... 12

2.1 OPERATION OF THE STUDY SYSTEM ........................................................................... 12 2.1.1 Power Management ......................................................................................................... 13

2.1.1.1 Steady State Power Management .......................................................................................13 2.1.1.2 Transient Power Management ............................................................................................14

2.1.2 Load Management ........................................................................................................... 14 2.2 STATE TRANSITION DIAGRAM....................................................................................... 15 2.3 CONTROL DESIGN ............................................................................................................. 17

2.3.1 Modular Design Philosophy ............................................................................................ 19 2.3.2 Supervisory Control......................................................................................................... 21

2.4 PERFORMANCE SPECIFICATIONS.................................................................................. 23 2.4.1 Steady State Specifications.............................................................................................. 23 2.4.2 Transient Specifications................................................................................................... 23

2.5 METHODOLOGY................................................................................................................. 24 2.6 SUMMARY ........................................................................................................................... 25

3. MODELING AND CONTROL OF SYSTEM MODULES................................................................ 26

3.1 MODULE: WIND ENERGY CONVERSION UNIT............................................................ 26 3.1.1 Modeling and Control...................................................................................................... 26

3.1.1.1 Control Structure ................................................................................................................27 3.1.2 Sensitivity Analysis ......................................................................................................... 29

3.1.2.1 Operating Point Sensitivity.................................................................................................29 3.1.2.2 Parametric Sensitivity.........................................................................................................32

3.1.3 Simulation Studies........................................................................................................... 38 3.1.3.1 Response to Step Changes..................................................................................................38

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3.1.3.2 Performance under Dynamic Wind Conditions..................................................................41 3.2 MODULE: VSC-UTILITY GRID ......................................................................................... 43

3.2.1 Control Structure ............................................................................................................. 43 3.2.2 Sensitivity Analysis ......................................................................................................... 46


3.2.3 Simulation Studies........................................................................................................... 55 3.2.3.1 Steady State Performance...................................................................................................55 3.2.3.2 Dynamic Performance........................................................................................................55

3.3 MODULE: BATTERY STORAGE AND DC-DC CONVERTER....................................... 59 3.3.1 Modeling and Control...................................................................................................... 59 3.3.2 Sensitivity Analysis ......................................................................................................... 60


3.3.3 Simulation Studies........................................................................................................... 67 3.4 SUMMARY AND CONCLUSIONS..................................................................................... 69

3.4.1 Module: Wind Energy Conversion Unit.......................................................................... 69 3.4.2 Module: VSC-Utility Grid............................................................................................... 71 3.4.3 Module: Battery Storage and DC-DC Converter............................................................. 72

4. SUPERVISORY HYBRID CONTROL .............................................................................................. 74

4.1 HYBRID CONTROL SYSTEMS.......................................................................................... 74 4.2 HYBRID MODEL OF THE STUDY SYTEM...................................................................... 75

4.2.1 Finite Hybrid Automata................................................................................................... 76 4.3 SUPERVISORY HYBRID CONTROL OF THE STUDY SYSTEM................................... 79

4.3.1 Supervisory Control Requirements.................................................................................. 79 4.3.2 Supervisory Hybrid Control Philosophy.......................................................................... 80 4.3.3 Hybrid Control of VSC: Valve Switching Control.......................................................... 82 4.3.4 Control Transition Management...................................................................................... 87

4.3.4.1 State Initialization...............................................................................................................88 4.3.4.2 Parameter Scheduling.........................................................................................................90

4.3.5 Mode Transition Management......................................................................................... 90 4.3.5.1 Synchronization..................................................................................................................91

4.3.5.1.1 Signal Transfer ....................................................................................................92 4.3.5.2 On-grid to Off-grid Transition............................................................................................92

4.4 FLOW CHART ...................................................................................................................... 93 4.5 SUMMARY ........................................................................................................................... 94

5. SYSTEM OPERATION UNDER NORMAL CONDITIONS............................................................ 95

5.1 STUDY CASES ..................................................................................................................... 95 5.2 WIND ENERGY CONVERSION UNIT-UTILITY GRID................................................... 96

5.2.1 Control Scheme ............................................................................................................... 96 5.2.2 Simulation Studies........................................................................................................... 98

5.2.2.1 Steady State Performance...................................................................................................99

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5.2.2.2 Dynamic Performance........................................................................................................99 5.3 WIND ENERGY CONVERSION UNIT-STORAGE......................................................... 108

5.3.1 Control Scheme ............................................................................................................. 108 5.3.2 Simulation Studies......................................................................................................... 110

5.4 STORAGE-UTILITY GRID................................................................................................ 111 5.4.1 Control Structure ........................................................................................................... 111 5.4.2 Simulation Studies......................................................................................................... 113

5.5 STORAGE-VSC-LOAD...................................................................................................... 117 5.5.1 Control Structure ........................................................................................................... 117 5.5.2 Simulation Studies......................................................................................................... 120

5.6 WIND ENERGY CONVERSION UNIT-STORAGE-UTILITY GRID ............................. 123 5.6.1 Control Structure ........................................................................................................... 123 5.6.2 Simulation Studies......................................................................................................... 126

5.7 SUMMARY AND CONCLUSIONS................................................................................... 130

6. SYSTEM OPERATION INVOLVING STATE TRANSITIONS .................................................... 132

6.1 STUDY CASES ................................................................................................................... 133 6.2 SYSTEM STARTUP AND STANDBY.............................................................................. 135 6.3 STATE TRANSITIONS ...................................................................................................... 137

6.3.1 Off-Grid Mode of Operation ......................................................................................... 137 6.3.2 On-Grid Mode of Operation .......................................................................................... 141

6.3.2.1 State Transitions during Normal Operation......................................................................141 6.3.2.2 State Transitions during Temporary Fault Conditions.....................................................145

6.4 MODE TRANSITIONS ....................................................................................................... 149 6.4.1 Pre-planned Transitions................................................................................................. 149

6.4.1.1 Synchronization................................................................................................................149 6.4.1.2 On-Grid to Off-Grid Transitions ......................................................................................153

6.5 SUMMARY AND CONCLUSIONS................................................................................... 159

7. CONCLUSIONS................................................................................................................................ 161

7.1 OVERVIEW......................................................................................................................... 161 7.2 CONCLUSIONS.................................................................................................................. 163 7.3 CONTRIBUTIONS.............................................................................................................. 164 7.4 FUTURE WORK ................................................................................................................. 165

APPENDIX A........................................................................................................................................... 166 APPENDIX B........................................................................................................................................... 170 APPENDIX C........................................................................................................................................... 175 APPENDIX D........................................................................................................................................... 189 APPENDIX E ........................................................................................................................................... 206

REFERENCES ......................................................................................................................................... 223

ix

LIST OF TABLES

TABLE Page Table 3.1-1: WECU; Steady state operating points .................................................................... 29

Table 3.1-2: WECU; Eigenvalues corresponding to the steady state operating conditions in

Table 3.1-1. .......................................................................................................... 30

Table 3.1-3: WECU; Mode association of state variables and participation factors for ‘case 2’32

Table 3.2-1: VSC-Utility Grid; Steady state operating points.................................................... 46

Table 3.2-2: VSC-Utility Grid; Eigenvalues corresponding to the steady state operating points

identified in Table 3.2-1....................................................................................... 47

Table 3.2-3: VSC-Utility Grid; Eigenvalues and mode association for ‘case 2’........................ 49

Table 3.2-4: VSC-Utility Grid; Dominant modes, mode association of state variables and

participation factors for ‘case 2’ .......................................................................... 49

Table 3.3-1: Battery Storage and dc-dc converter (Boost mode of operation); Poles and RHP

zeros at different steady state operating points .................................................... 61

Table 3.3-2: Battery Storage and DC-DC Converter (Buck mode of operation); Eigenvalues at

different steady state operating points ................................................................. 62

Table 5.1-1: Study Cases and Objectives of the Performance Investigation; System Operation

Under Normal Conditions.................................................................................... 95

Table 6.1-1: Study Cases; System Operation Involving State Transitions............................... 133

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LIST OF FIGURES

FIGURE

Page

Figure 1.3-1: Wind energy conversion and battery storage system.............................................. 6

Figure 2.2-1: State Transition Diagram (STD) of the wind energy conversion and storage

system .................................................................................................................. 17

Figure 2.3-1: Supervisory hybrid control structure..................................................................... 18

Figure 2.3-2: Schematic diagram of system module ‘Wind Energy Conversion Unit’.............. 21

Figure 2.3-3: Schematic diagram of system module ‘VSC-Utility Grid’................................... 21

Figure 2.3-4: Schematic diagram of system module ‘Storage and dc-dc converter’.................. 21

Figure 3.1-1: WECU; Proposed current-controlled speed regulation scheme............................ 28

Figure 3.1-2: WECU; Root loci corresponding to different steady state operating points......... 31

Figure 3.1-3: WECU; Close-up of the root loci near to the origin; sensitivity with respect to the

steady state operating point.................................................................................. 31

Figure 3.1-4: WECU; Root locus of mode 1 for variations in the values of the control

parameters between 0 and 2 per unit in steps of 0.1 per unit [0: .1: 2] ................ 33

Figure 3.1-5: WECU; Root locus for mode 2 for variations in the values of the control


Figure 3.1-6: WECU; Root locus for mode 3 for variations in the values of the control


Figure 3.1-7: WECU; Root locus of mode 4 for variations in the values of the control


Figure 3.1-8: WECU; Sensitivity of mode 1 and 4 with respect to the LPF time constant iwτ

(from 3.0ms to 75.0ms in steps of 3.0ms)............................................................ 37

Figure 3.1-9: WECU; Response to step changes in wind speed, 1) wind speed 2) dc output

current and rectifier current limitation 3) optimum, reference and actual speed of

the generator......................................................................................................... 39

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Figure 3.1-10: WECU; Response to step changes in wind speed, 1) generator reactive power

consumption and excitation capacitor bank switching event 2) generator output

power 3) angular displacement between the generator and the turbine rotors.... 39

Figure 3.1-11: WECU; Response to step changes in the dc bus voltage, 1) dc bus voltage 2)

rectifier output current 3) angular displacement of the generator with respect to

the wind turbine ................................................................................................... 40

Figure 3.1-12: WECU; Operation during dynamic wind speed conditions, 1) wind speed 2)

optimum, reference and actual speed of the generator and capacitor bank

switching events 3) Reference and actual output dc current............................... 42

Figure 3.2-1: VSC-Utility Grid; Single line schematic and control structure ............................ 45

Figure 3.2-2: VSC-Utility Grid; Plot of the eigenvalues (32, 33) corresponding to operating

conditions from full load in rectifier mode (dI = -1.0 p.u.) to full load in inverter

mode ( dI = 1.0 p.u.) ............................................................................................ 48

Figure 3.2-3: VSC-Utility Grid; Loci of the eigenvalues corresponding to mode 1 for variations

in pdK and idK of the outer dc regulator ............................................................ 50

Figure 3.2-4: VSC-Utility Grid; Loci of mode 1 for variations in piK and iiK of the inner

current regulators ................................................................................................. 51

Figure 3.2-5: VSC-Utility Grid; Plot of the positive eigenvalues corresponding to Mode 2 for

variations in the parameters of the current and dc voltage regulators ................. 52

Figure 3.2-6: VSC-Utility Grid; Plot of the eigenvalue of mode 2 for variations in the

parameters vfbτ and ivK ....................................................................................... 53

Figure 3.2-7: VSC-Utility Grid; Traces of the eigenvalue of mode 2 for variations in piK and

iiK of the inner current regulators ....................................................................... 53

Figure 3.2-8: VSC-Utility Grid; Trace of the eigenvalue associated with mode 3..................... 54

Figure 3.2-9: VSC-Utility Grid; Response to load switchings and step changes in reference

voltages of the dc bus and the load bus, 1) dc current (disturbance) 2) & 3)

‘active’ and ‘reactive’ terminal currents of the VSC ........................................... 57

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Figure 3.2-10: VSC-Utility Grid; Response to load switchings and step changes in reference

voltages of the dc bus and the load bus, 1) reference and actual three phase rms

voltage at the load bus 2) reference and actual dc bus voltage........................... 58

Figure 3.3-1: Battery Storage and DC-DC Converter; Control structure and schematic diagram

.............................................................................................................................. 60

Figure 3.3-2: Battery Storage and DC-DC Converter; Loci of the eigenvalues λ2 and λ3,4

corresponding to the steady state operating points given in Table 3.3-2............. 62

Figure 3.3-3: Battery Storage and DC-DC Converter (Boost Mode); Eigenvalue trace with

respect to the proportional gain pdcK .................................................................. 63

Figure 3.3-4: Battery Storage and DC-DC Converter (Boost Mode); Eigenvalue trace with

respect to the integral gain idcK .......................................................................... 64

Figure 3.3-5: Battery Storage and DC-DC Converter (Buck Mode); Root loci with respect to the

proportional constant pdcK ................................................................................. 65

Figure 3.3-6: Battery Storage and DC-DC Converter (Buck Mode); Root locus with respect to

the integral constant idcK .................................................................................... 66

Figure 3.3-7: Battery Storage and DC-DC Converter (Boost Mode), 1) dc output and inductor

current 2) dc bus voltage..................................................................................... 67

Figure 3.3-8: Battery Storage and DC-DC Converter (Buck Mode), 1) injected at the dc bus

and inductor current 2) dc bus voltage................................................................ 68

Figure 3.3-9: Battery Storage and DC-DC Converter, 1) reference and actual dc bus voltage in

boost mode 2) reference and actual dc bus voltage in buck mode...................... 69

Figure 4.2-1: Finite Hybrid Automata (FHA) of the wind energy conversion and storage system

.............................................................................................................................. 78

Figure 4.3-1: Hybrid switching control of the VSC ................................................................... 84

Figure 4.3-2: Operation of the VSC with only SPWM and with hybrid valve switching control,

1) a phase voltage at the PCC, instantaneous value and amplitude 2) fault current

3) reference and actual phase ‘a’ converter current ............................................. 86

Figure 4.3-3: Operation of the VSC under hybrid valve switching control, 1) cycle-to-cycle

based instantaneous duty ratio and the average duty ratio over a power cycle 2)

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instantaneous switching frequency and the average frequency over a power cycle

.............................................................................................................................. 87

Figure 4.3-4: Re-initialization of inner current regulators for smooth transition from HSVM to

SPWM based valve-switching control................................................................. 89

Figure 4.3-5: Re-initialization of inner current regulators, 1) duration of the OCC operation and

orthogonal components of the converter terminal voltage for resetting of inner

current regulators 2) duration of the OCC operation and the orthogonal

components of the terminal current of the converter ........................................... 90

Figure 4.3-6: Frequency control during synchronization ........................................................... 91

Figure 4.4-1: Simplified flow chart for software implementation of the supervisory hybrid

control scheme ..................................................................................................... 93

Figure 5.2-1: Single line schematic and control structure of the study system in the operating

state #7 consisting of the two system modules i) WECU and ii) VSC – Utility

Grid ...................................................................................................................... 97

Figure 5.2-2: Operating State # 7; System Dynamic Performance for Step Changes in Wind

Speed, 1) wind speed 2) rotor optimal, reference and actual speed................. 101

Figure 5.2-3: Operating State # 7; System response to step changes in wind speed, 1) rectifier

output current and active current output of the VSC 2) VSC reactive current

output 3) VSC total current output and HSVM on duration............................. 101

Figure 5.2-4: Operating State # 7; System response to step changes in wind speed, 1) dc bus

voltage 2) load bus rms voltage ........................................................................ 102

Figure 5.2-5: Operating State # 7; System Operation under Load Transients, 1) load bus rms

voltage 2) dc bus voltage load 3) rectifier output current ................................ 103

Figure 5.2-6: Operating State # 7; Control performance under load transients, 1) VSC ‘active’

current 2) VSC ‘reactive’ current 3) VSC total current and HSVM on duration

............................................................................................................................ 104

Figure 5.2-7: Operating State # 7; System response during dynamic wind speed and load

transients, 1) wind speed 2) generator optimum, reference and actual speed.. 106

Figure 5.2-8: Operating State # 7; System Control during dynamic input wind speed and load

transients, 1) load bus rms voltage 2) dc bus voltage ...................................... 107

xiv

Figure 5.2-9: Operating State # 7; System response to dynamic wind conditions and load

transients, 1) & 2) VSC ‘active’ and ‘reactive’ current components 2) space

vector magnitude of the VSC current ................................................................ 107

Figure 5.3-1: Single line diagram and control schematic of the study system in the operating

state #4 consisting of the two system modules of (a) wind energy conversion unit

(b) battery storage and dc-dc converter.............................................................. 109

Figure 5.3-2: Operating State # 4; System response to changes in wind speed, 1) dc bus voltage

2) generator L-L terminal voltage and capacitor switching events 3) wind speed

............................................................................................................................ 111

Figure 5.4-1: Single line diagram and control schematic of the study system in operating state

number #9 consisting of the two system modules of (a) battery storage and dc-dc

converter (b) VSC-Utility Grid ......................................................................... 112

Figure 5.4-2: Operating State # 9; Response to load switching events, 1) dc bus voltage 2) 3

phase rms voltage at the load bus....................................................................... 114

Figure 5.4-3: Operating State # 9; Response to load switching events, VSC terminal currents,

1) ‘active’ current component 2) ‘reactive’ current component 3) maximum

current limit and actual output current of the VSC and OCC duration.............. 114

Figure 5.4-4: Operating State # 9; Response to step changes in the dc current, 1) dc current 2)

dc bus reference and actual voltage 3) reference and actual rms voltage at the

load bus .............................................................................................................. 116

Figure 5.4-5: Operating State # 9; Response to step changes in reference voltage signals, 1)

reference and actual dc bus voltages 2) reference and acutal rms voltages of the

load bus .............................................................................................................. 117

Figure 5.5-1: Single line diagram and control schematic of the study system in the operating

state number #3 consisting of the battery storage and dc-dc converter module

interfaced to the load through the VSC.............................................................. 119

Figure 5.5-2: Operating State # 3; Response to load switching and step changes in external dc

current , 1) reference and actual dc bus voltage 2) reference and actual rms

voltage at the PCC 3) reference and actual rms voltage at the load bus .......... 120

xv

Figure 5.5-3: Operating State # 3; Response to load switching and step changes in the external

dc current, 1) external dc source current 2) active current component of the VSC

3) reactive current component of the VSC 4) total output current of the VSC. 121

Figure 5.5-4: Operating State # 3; Response to step changes in reference signals, 1) reference

and actual voltages of the dc bus 2) reference and actual rms voltages at the PCC

3) reference and actual rms voltages at the load bus ......................................... 122

Figure 5.6-1: Single line schematic and control structure of the study system in the operating

state #6 (WECU + Storage + Utility) where all the three system modules are in

service ................................................................................................................ 125

Figure 5.6-2: Operating State # 6; Response to variations in wind speed, 1) wind speed 2)

optimum, reference and actual speed of the generator 3) output current of the

thyristor-controlled rectifier............................................................................... 128

Figure 5.6-3: Operating State # 6; Response during load switching, wind speed changes and

step changes in the reference voltage signals, 1) dc bus voltage 2) rms voltage at

the load bus ........................................................................................................ 128

Figure 5.6-4: Operating State # 6; Response to load switching and step changes in reference

signals, 1) active current components 2) reactive current components 3)

converter limit, total output current and HSVM on duration............................. 129

Figure 5.6-5: Operating State # 6; Response of the storage element to load switching and

reference step changes, 1) battery terminal voltage 2) battery terminal current

............................................................................................................................ 129

Figure 6.2-1: Startup and Standby Operation, 1) dc bus voltage 2) reference and actual rms

voltage at the PCC 3) phase voltages at the PCC ............................................. 136

Figure 6.2-2: Startup and Standby Operation, 1) orthogonal current components of the VSC 2)

battery terminal voltage 3) reference and inductor current............................... 137

Figure 6.3-1: Off-grid operation; Inter-state transitions among state #2 (Standby), state #3

(Storage + VSC) and state #4 (WECU + Storage), 1) dc bus reference and actual

voltage 2) reference and actual rms voltage at the PCC and ITI performance

limits 3) reference and actual rms voltage at the load bus and ITI performance

limits 4) Operating state of the system.............................................................. 139

xvi


(Storage + VSC) and state #4 (WECU + Storage), 1) orthogonal current

components of the VSC 2) orthogonal current components of the load bus 3)

rectifier output current, total instantaneous current of the load branch and the

output current of the VSC.................................................................................. 140


(Storage + VSC) and state #4 (WECU + Storage), 1) battery terminal voltage 2)

reference and actual battery terminal currents ................................................... 140

Figure 6.3-4: State transitions during on-grid mode of operation, 1) reference and actual dc bus

voltage 2) reference and actual rms voltage at the PCC 3) reference and rms

voltage at the load bus 4) system operating state and OCC operation intervals142

Figure 6.3-5: On-grid mode of operation; transitions during normal operation, 1) reference and

actual active current component of the converter 2) reference and actual reactive

current component of the converter 3) rectifier output current and total current of

the load branch and the VSC ............................................................................. 144

Figure 6.3-6: On-grid mode of operation; transitions during normal operation, 1) battery

terminal voltage 2) reference and actual battery current................................... 144

Figure 6.3-7: On-grid operating mode; state transitions caused by single line to ground fault, 1)

dc bus and thyristor-controlled rectifier output voltage 2) three phase rms

voltage at the PCC and the upper and lower limits defined by the ITI curve 3)

single phase rms voltage at the PCC and the ITI curve 4) control signals used for

state transition management............................................................................... 147

Figure 6.3-8: On-grid operating mode; State transitions caused by single line to ground faults,

1) VSC ‘active’ current output 2) VSC ‘reactive’ current output 3) rectifier

output current, total current of the load branch and output current of the VSC 148

Figure 6.3-9: On-grid operating mode; State transitions caused by single line to ground faults,

1) battery terminal voltage 2) reference and inductor current ......................... 149

Figure 6.4-1: Mode transitions; synchronization, 1) ‘a’ phase voltage waveforms at the two

sides of the TCB and the synchronization interval 2) reference frequency and

xvii

PLL outputs for the two sides of the TCB 3) reference and actual rms voltages

on the utility side of the TCB, at the PCC and at the load bus .......................... 151

Figure 6.4-2: Mode transitions; synchronization, 1) reference and actual dc bus voltage 2)

reference and actual rectifier current, reference and actual ‘active’ current

component of the converter 3) reference and actual ‘reactive’ current of the

converter 4) system operating state and duration of the OCC operation .......... 152

Figure 6.4-3: Mode transitions; no load synchronization, 1) control signals 2) wind energy

conversion and storage system operating states................................................. 152

Figure 6.4-4: Pre-planned on-grid to off-grid mode transition, 1) reference and actual dc bus

voltage 2) reference and actual rms voltage at the PCC 3) reference and actual

rms voltage at the load bus 4) operating state................................................... 153

Figure 6.4-5: Pre-planned on-grid to off-grid mode transition, 1) active current component of

the VSC 2) reactive current component of the VSC 3) space vector magnitude

of the load branch and the VSC output current.................................................. 154

Figure 6.4-6: Pre-planned on-grid to off-grid mode transition, 1) battery terminal voltage 2)

battery terminal current...................................................................................... 154

Figure 6.4-7: Un-planned on-grid to off-grid mode transition, 1) reference and actual dc bus

voltage 2) reference and actual rms voltage at the PCC 3) reference and actual

rms voltage at the load bus 4) operating state and OCC operation duration .... 156

Figure 6.4-8: Un-planned on-grid to off-grid mode transition, 1) active current component of

the VSC 2) reactive current component of the VSC 3) space vector magnitude

of the load branch and the VSC output current.................................................. 157

Figure 6.4-9: Un-planned on-grid to off-grid mode transition, 1) battery terminal voltage 2)

battery terminal current...................................................................................... 157

xviii

NOMENCLATURE

• Instantaneous quantities are represented by lower case letters e.g., x

• Space vector quantities are represented with an underscore e.g., tv

• Average and DC quantities are represented by upper case letters e.g., dcV

• Small perturbations in a signal are represented by a tilde over the instantaneous symbol

for the signal e.g., dcv~

xix

ABBREVIATIONS

WECU:

VSC:

IGBT:

BES:

SPWM:

HSVM:

CPM:

RHP:

LHS:

RHS:

OLD:

STD:

FHA:

FOS:

SOS:

OCC:

Wind Energy Conversion Unit

Voltage-Sourced Converter

Insulated-Gate Bipolar Transistor

Battery Energy Storage

Sinusoidal Pulse-Width Modulation

Hysteresis Space Vector Modulation

Current Programmed Mode

Right Hand Plane

Left Hand Side

Right Hand Side

Operating Logic Diagram

State Transition Diagram

Finite Hybrid Automata

Fault Operating State

Synchronization Operating State

Over Current Control

1

CHAPTER 1

INTRODUCTION

his chapter introduces the research work reported in this thesis. General background of

the subject has been presented first which is followed by the problem statement. A

description of the study system used in the research reported in this thesis has been presented and

research objectives are outlined. Limitations of the reported work have been pointed out

followed by an outline of the thesis given at the end of the chapter

1.1 BACKGROUND

The depletion of conventional energy sources e.g. oil and gas and the desire to limit their use

due to environmental concerns has led to the search for increased utilization of renewable energy

sources to meet the ever-growing demand of electrical power [1], [2]. Wind is one of the most

promising among the different types of available renewable energy sources [1]-[3]. During the

past decade considerable research has been carried out to improve wind turbine design and

control for increased power conversion efficiency and availability. Recently, the deregulated

electricity market has also opened the doors for customers owned distributed generation due to

perceived economic and technical benefits [4], [5]. Distributed generators are commonly

connected to the system at distribution voltage levels [6]-[8]. To date, distributed generators are

not operated in islanded conditions due to safety concerns of both personnel and equipment, and

are required to disconnect and shutdown in response to disturbances on the utility grid [9]. The

diversified and distributed nature of the supply system, due to increased penetration of

distributed generators and distributed storage devices, has the potential to increase overall

security and reliability of power supply [10]-[11]. Customized power quality and reliability

levels can be achieved according to the individual needs of the customers by using power

electronic based power processing units [12]-[13]. The diversified nature of the power system

together with the use of power electronics based power processing units can result in a power

system capable of providing the desired level of service under a variety of operating conditions.

Using conventional control methods commonly used in power systems, the control of a

system with limited energy capabilities in the off-grid operating mode is a difficult task [14]. The

T

2

situation becomes even more complex if the system contains a renewable energy source such as

wind energy power conversion unit(s), since this type of primary energy source is often

intermittent in availability. It becomes necessary to include a dispatchable energy source, such as

a storage device, in the scheme [15]. The control design of such a system also requires a

radically different approach when operation of these systems is required to weather changes in

operating conditions over a wide range. The operating conditions may include on-grid and off-

grid mode of operation and changes in the combination of the internal energy sources supplying

the load during the two operating modes [16].

In this research work the automatic control and management problem of a wind energy

conversion and battery storage system has been tackled from a supervisory hybrid control point

of view. Hybrid control systems are composed of both discrete and continuous state variables

[17], provide superior performance as compared to conventional control schemes [18]-[20] and

allow the pursuit of multiple control objectives [21]. Hybrid control has found widespread

applications from automotive, manufacturing and process industries to aerospace industry [22]-

[25]. Hybrid control has also found limited application in drives control and power systems [26],

[27].

The supervisory hybrid control scheme presented in this thesis for the wind energy

conversion and battery storage system provides automatic control of the system in islanded and

in grid-connected modes of operation under steady state as well as during transient operating

conditions including accidental state transitions caused by faults in the external supply system.

1.2 PROBLEM STATEMENT

Connection of the wind energy conversion units to the utility system through power electronic

converters has the advantage that the units can be operated at variable speeds to maximize

energy capture from the prevailing wind conditions and to alleviate stresses in the drive train

[28]. The converter interface to the utility also shields these units from normal disturbances on

the utility side and provides the ability to transfer the wind-generated power to the utility side

with improved power quality [29]. However, conventional control schemes employed for the

interfacing power electronic converters do not provide satisfactory operation during temporary

faults on the utility systems and these may also be taken out of service due to the operation of the

switch overload protection during such faults. The majority of faults on the utility system are

3

temporary single line to ground faults [30] and these can contribute considerably to the

downtime of these wind conversion systems.

As wind is stochastic in nature therefore permanent faults on the system also cause

shutdown of the wind conversion units even if sufficient wind power is available to serve local

loads. It is therefore desirable that the wind conversion system is capable of operation during

islanded conditions. This can be a particularly useful feature in case of rural communities or far-

flung areas with abundant wind energy potential and which are supplied through long radial

feeders. A low cost system in terms of initial investment and environmental impacts besides low

maintenance and operational requirements would be the desirables of a distributed energy system

in such communities.

The following are the desirable characteristics of operation of the subject wind energy

conversion and battery storage system to provide economical, reliable and acceptable quality

electrical power:

1. Automatic system operation

2. Fault ride through capability for temporary faults on the utility feeder

3. Protection and control integration for the power converters

4. Ability to operate in on-grid and off-grid modes

5. A control scheme based on available local system information

6. Control performance that conforms to specifications provided in section 2.4.

There is no available literature on wind energy conversion systems that addresses all the above

desirable control and operational requirements. The research presented in this thesis is focused

on the design of a control scheme for a wind energy conversion and battery storage system that

incorporates the above-mentioned desirable economic, control and operating features.

1.3 STUDY SYSTEM

Figure 1.3-1 shows the wind energy conversion and battery storage system used for the research

reported in this thesis. The study system is composed of a Wind Energy Conversion Unit

(WECU) and a battery storage element connected to a common dc bus. The system is interfaced

to the load and the utility grid at the Point of Common Coupling (PCC) through a Voltage-

Sourced Converter (VSC) unit. The complete system parameters are given in appendix A.

The WECU itself consists of a horizontal axis, three-blade wind turbine mechanically

coupled through a gearbox to an induction generator with a squirrel cage rotor construction. The

4

wind turbine has a maximum output capability of 360kW (1.2 per unit based on 300kVA base).

The generator has a matching maximum rating of 1.2 per unit and a rated voltage of 690V. The

generator unit is connected to the dc bus through a six-pulse thyristor-controlled rectifier and

delivers wind generated power at 1000 volts on the dc side. Static capacitor banks connected at

the generator terminals meet the reactive power demand of the generator and the thyristor

rectifier. The thyristor based rectifier interface gives the wind energy conversion unit the

capability of variable speed operation for maximum energy capture from the prevailing wind

conditions [31], [32].

The storage element is composed of series and parallel combination of battery banks, which

are connected to the dc bus through a dc-dc converter. The wind energy conversion and battery

storage system is connected to the utility grid and to the load at the PCC through the VSC

interface. The VSC is assumed to be composed of three legs, each containing a pair of Insulated-

Gate Bipolar Transistors (IGBTs). The utility grid has been represented by its Thevenin

equivalent at 132kV level and a long (25km) radial feeder at 13.8kV has been assumed for

connection to the wind energy conversion and battery storage system. The local load is served at

480 volts and is connected to the PCC through a step-up transformer. The load consists of both

constant impedance static and dynamic induction motor loads.

The storage device shown in Figure 1.3-1 can be used for transient power support of the

wind energy conversion unit during islanded operation. The storage can be used in combination

with the wind energy conversion unit or on its own to cater to the local load demand in the

absence of the utility supply. The presence of the storage device gives the system the desirable

characteristic of dispatchability. The use of a squirrel cage induction machine reduces system

initial cost and subsequent operational and maintenance requirements [33]. The use of a battery

storage device is environmentally benign and apart from some initial investment has no

significant operational and maintenance costs. The study system therefore provides a very

attractive solution to the power quality and reliability problems of isolated rural communities.

The following are the main features of the proposed system configuration:

1. Use has been made of an induction generator with squirrel cage construction. The output of

the generator is regulated through a thyristor-controlled rectifier. This means less initial

investment and low operation and maintenance costs of the wind energy conversion unit

making it economically more attractive.

5

2. The inclusion of a storage element on the dc bus side has a number of advantages than if it

is connected to the system at some other location:

a. The same power electronic interface to the utility grid is utilized for the wind energy

conversion unit and the battery storage element thus reducing the overall cost of the

system.

b. Simple system control: Active and reactive power sharing control has been avoided

which would have been required if the storage were connected at some other point to

the system. This would have been necessary in order to control system frequency and

to regulate node voltages in the system, respectively [33].

6

Figure 1.3-1: Wind energy conversion and battery storage system

7

1.4 RESEARCH OBJECTIVES

As described in chapter 2, section 2.1, the wind energy conversion and battery storage system

has two operating modes i) on-grid and ii) off-grid. Within these two basic operating modes a

number of ‘operating states’ could be identified in which the system has different state space

compositions based on the traditional definition of a state space involving state variables of the

system.

The primary objective of this thesis is to present a simplified approach based on hybrid

control theory to tackle the control design and analysis problem of the study system. Based on

the proposed approach a supervisory hybrid control scheme for the wind energy conversion and

battery storage system shown in Figure 1.3-1 has been presented. The supervisory hybrid

controller will operate the wind energy conversion and storage system in both on-grid and in off-

grid mode of operations, in steady state and during transient system operating conditions as

described in section 2.3.2. The supervisory controller for the study system will use local

information to steer its operation along pre-specified transition routes in response to different

system events. The transition routes are given by the hybrid automata shown in Figure 4.2-1.

The following tasks have been identified to achieve the above stated objective:

1. To develop a systematic approach towards the hybrid automata based hybrid modeling and

control of the wind energy conversion and battery storage system.

The hybrid automata of a system describes the allowable operating states of the system and

transition paths between these operating states that the system will follow in response to some

discrete events. An ‘operating state’ of the system will be based on the possible combinations of

the energy sources in the system (and not based on its state space composition). This point is

further elaborated in Appendix B in which a ‘State Transition Diagram’ (STD) has been

developed from the ‘Operating Logic Diagram’ (OLD) of the study system. The STD depicts

only those operating states in which the system is capable of steady state operation. The STD

will be complemented with ‘transient states’ as described in CHAPTER 4, to develop the final

‘Finite Hybrid Automata’ (FHA) for the wind energy conversion and battery storage system. The

‘transient states’ are the temporary operating states of the system during its transition from one

stable operating state in the on-grid operating mode to another in the off-grid mode of operation

and vice versa.

8

2. To devise control schemes based on the traditional control techniques using Proportional-

plus-Integral (PI) compensators for the three system modules i.e. the wind energy

conversion unit, the battery storage and dc-dc converter and the VSC-utility grid

independent of each other as described in section 2.3. The operation of the three system

modules under the proposed control schemes will be investigated separately for stability

and performance evaluation. Operational stability and selection of proper control

parameters for the three system modules will be based on eigenvalue sensitivity analysis

with respect to operating point and with respect to control parameters, respectively [35]-

[43].

3. To combine and configure the control schemes developed for the three system modules of

WECU, the battery storage and dc-dc converter and the VSC-utility grid respectively, to

control operation of the wind energy conversion and battery storage system during the

permissible operating states as depicted by the state transition diagram developed in

Appendix B.

4. To devise control schemes for operation of the wind energy conversion and storage system

during the ‘transient operating states’ depicted in the hybrid automata of the system which

is shown in Figure 4.2-1.

5. To develop suitable transition management strategies to minimize system transients caused

by state transitions and switching of the associated control schemes.

6. To develop supervisory control scheme for the wind energy conversion and storage system

to perform the following actions:

a. Oversee control transfer between different candidate controllers and control

schemes in response to changing operating states.

b. Manage transitions between different operating states. In other words to

reconfigure the wind energy conversion and storage system according to the

system events.

c. Provide suitable reference and feedback signals to the active controllers.

d. Provide control reset and initialization signals to the candidate controllers.

e. Perform power and load management in the wind energy conversion and storage

system.

f. Implement state and control transition management strategies.

9

The supervisory controller will infer the changing operating states of the system based on

information from selected indicators. Referring to Figure 1.3-1, the open or closed state of the

TCB (tiebreaker) will indicate the operating mode of the wind energy conversion and storage

system (i.e., on-grid or off-grid mode). The availability of the utility grid will be decided based

on the single phase rms voltages on the utility side of the TCB when these are within the normal

operating range specified by ANSI C84.1- 1995 [44]. Islanding detection algorithms have not

been implemented and islanding has been assumed as a known event. Availability of the battery

storage is assumed to be known a priori (this information could come from an energy

management system for the battery storage). Availability of the wind energy conversion unit will

be inferred from the dc output current of the thyristor-controlled rectifier. Fault on the utility side

will be determined from the peak value of the phase voltages on the utility side of the TCB. For

this purpose the algorithm described in reference [45] will be implemented. Status of the load

(connected or disconnected) will be inferred from the load breaker (LCB) shown in Figure 1.3-1.

In the absence of any theoretical guarantees for the control stability of the wind energy

conversion and storage system, digital time domain simulations of the nonlinear system will be

performed using PSCAD/EMTDC to investigate system operation under the proposed

supervisory hybrid control scheme both for stability and for performance evaluation [46]. This

will also require that suitable performance criteria be specified for the performance assessment

of the study system. Performance specifications have been described in section 2.4.

1.5 LIMITATIONS

The following are the main limitations of this thesis:

1. Linear integral and proportional-plus integral compensators have been used.

2. Parametric sensitivity analysis has been performed with respect to a single control variable

at a time; no inter-parametric sensitivity analysis has been attempted.

3. Aspects concerning economics of the system management have not been treated in this

research.

4. System protection issues are not of primary concern.

5. Neither system nor control parameters have been optimized.

10

1.6 THESIS OUTLINE

Chapter 2 gives details of operation of the wind energy conversion and storage system and

describes management of the system from a hybrid control point of view. Different possible

operating states are enumerated. Load and power management strategies are described and

performance criteria are presented. The chapter also gives a methodology for the control design

of the wind energy conversion and storage system and provides a strategy for evaluating stability

and performance of the system in its different operating states.

Chapters 3 provides control schematics and results of the linear and nonlinear analysis of the

three system modules of the study system i) the wind energy conversion unit consisting of the

wind turbine, the induction generator, static capacitor banks and the thyristor-controlled rectifier

ii) the storage element consisting of the battery storage and the dc-dc converter and iii) the VSC-

utility grid system module, respectively. Each system module contains one energy source and is

treated in the following order:

1. Module: Wind Energy Conversion Unit

2. Module: VSC-Utility Grid

3. Module: Battery Storage and DC-DC Converter

In this chapter associated control schemes for the three system modules have been elaborated

whereas mathematical models have been presented in the appendices.

Chapter 4 deals with the subject of the hybrid supervisory control of the wind energy

conversion and battery storage system. It provides background information into the hybrid

control systems. In this chapter a finite hybrid automata of the wind energy conversion and

storage system has been presented which depicts system operating states and the uni- and bi-

directional links between these states which the system is required to follow while moving from

one state to another. The chapter introduces the concept of ‘transition management’ used for the

supervisory hybrid control of the wind energy conversion and battery storage system.

Chapter 5 provides stability and performance evaluation of the operation of the study system

during all the operating states under ‘normal operating conditions’ as depicted by the hybrid

automata of the system shown in Figure 4.2-1. In all these operating states two or more of the

system modules are interacting with each other under normal load switching conditions. Control

schemes have been developed for the operation of the wind energy conversion and battery

storage system in each of the ‘normal operating state’. These control schemes have been derived

11

from the control schemes proposed for the three system modules of the study system and also

incorporate elements of transition management strategies described in chapter 4. Results of the

stability and performance evaluation of the study system using digital time domain simulations

of the nonlinear system in PSCAD/EMTDC have been presented in this chapter. The following

‘normal operating states’ have been considered:

1. Operating State: Wind Energy Conversion Unit-Utility Grid

2. Operating State: Storage-Utility Grid

3. Operating State: Storage-VSC-Load

4. Operating State: Wind Energy Conversion Unit -Storage

5. Operating State: Wind Energy Conversion Unit -Storage-Utility Grid

Chapter 6 provides simulation results for the operation of the wind energy conversion and

storage system during state transitions under the proposed supervisory hybrid control scheme.

The operation of the study system has been investigated for stability and performance, during

state transitions, through time domain simulations in PSCAD/EMTDC environment. Worst case

scenarios for transitions between the permissible operating states of the study system given by

the proposed hybrid automata have been considered.

Chapter 7 concludes the research reported in this thesis. It provides conclusions based on the

reported work and lists thesis contributions. Future research opportunities have been identified at

the end of the chapter.

Appendices are given at the end of the thesis:

1. System parameters are given in appendix A.

2. Appendix B provides a method to determine ‘operating states’ of the system using simple

Boolean logic to arrive at a State Transition Diagram (STD) for the study system.

3. Appendix C gives modeling details of the wind energy conversion unit.

4. Appendix D provides modeling details of the VSC-Utility grid system.

5. Appendix E details modeling of the battery storage and dc-dc converter.

References are provided at the end of the thesis.

12

CHAPTER 2

OPERATION AND CONTROL

n this chapter issues concerning the operation and hybrid control of the wind energy

conversion and storage system have been treated. Methodology for the control design,

selection of control parameters, criterion for performance evaluation and a methodology for

performance verification have been the main subjects of this chapter.

2.1 OPERATION OF THE STUDY SYSTEM

Referring to Figure 1.3-1, the wind turbine driven by the lifting force of the wind blowing across

the blades drives the mechanically coupled induction generator thereby converting the kinetic

energy of the wind into electrical energy. The electrical output power of the generator is

controlled and delivered at the dc bus through the thyristor rectifier. The generated power could

be delivered to the grid, used for battery charging, or else it could be partly delivered to the grid

and partly stored in the battery storage device for later use.

In the grid-connected mode, the load in the wind energy conversion and storage system can

be served by the energy sources internal to the system as well as by the external utility supply.

The load can be supplied with power from the utility feeder with or without any contribution

from the local energy sources and proper system operation can be ensured during both steady

state and dynamic operating conditions. In the isolated mode of operation, the VSC alone

transfers the available power from the wind energy conversion unit and the battery storage at the

desired voltage level and frequency. Power management is required in both grid connected and

during islanded operation in order to control power contribution from the energy sources in the

wind energy conversion and storage system and to direct it to proper sinks.

The two energy sources in the wind energy conversion and battery storage system are

limited in capacity and also a maximum capacity of 1.3 per unit has been assumed for the VSC,

therefore during islanded operation quality power can be assured only with a limited amount of

dynamic motor load connected at the load bus. Some load management is therefore required for

proper off-grid operation regardless of the level of availability of the energy sources in the wind

energy conversion and battery storage system.

I

13

The objective of the load management and the power management strategies is to achieve power

balance between the energy sources and the loads at any given time. However power

management is also concerned with the load sharing among the active energy sources in the

system and achieves the objective by continuously controlling power contributions from the

different energy sources in the system. Load management on the other hand, is provided to assist

in power management by ensuring that only that much power is demanded that can be supplied

by the available energy sources within the power quality constraints. Load management is a

discrete phenomenon while power management may involve discrete actions in that one or the

other energy source in the system may be taken in or out of service.

2.1.1 POWER MANAGEMENT

The power management strategy is based on the assumption that the storage will be used as a

backup supply and to provide steady state and transient power support during islanded mode of

operation. Provisions will be made to use the battery storage while the system is operating on-

grid for maintaining the dc bus voltage during severe disturbances including faults on the utility

feeder. Also the wind energy conversion unit will be operated to follow the maxim output curve

of the turbine for maximum power extraction from the prevailing wind.

2.1.1.1 Steady State Power Management

The steady state power management is concerned with power delivery from the energy sources

in the wind energy conversion and battery storage system over longer periods of time usually

called energy management, in both grid connected and in isolated mode of operation.

The following strategy will be used during the grid-connected mode of operation:

1. The WECU will be operated to extract maximum power from the prevailing wind

conditions at all times.

2. All the wind-generated power will be transferred directly to the utility side when the storage

element is fully charged.

3. All or part of the wind-generated power will be used for charging the battery storage when

required.

4. In the absence of wind-generated power, utility supply will be used for charging the storage

element if necessary.

The following strategy will be used in the islanded mode of operation:

14

1. Battery storage will be used to cater to the load demand together with WECU when the

power output of the latter is not enough to meet the load demand.

2. When the power output of the WECU exceeds the load demand then the excess power will

be used for charging the batteries.

3. In the absence of wind power generation, storage alone will meet the load power demand.

The case where the batteries are fully charged and the power output of the wind energy

conversion unit exceeds load demand has not been treated in this thesis. One solution in such a

scenario would be to operate the wind energy conversion unit at sub optimal level to match its

output to that of the load demand. Another strategy however is to use some dummy load (for

example some heating load) preferably connected to the dc bus to be able to extract maximum

power from the wind at all times.

2.1.1.2 Transient Power Management

Transient power management is concerned with the momentary power imbalance in the system

during the course of its operation.

During grid-connected mode of operation, variations in power from the wind energy

conversion unit caused by variations in wind speed as well as variations in load power demand

will be reflected in the amount of power delivered by the utility feeder. In other words, utility

supply will be relied upon for transient power support during grid-connected operation of the

wind energy conversion and storage system. Battery storage support during grid-connected

operation will only be used when dc bus voltage variations exceed certain limits in order to

ensure control stability of the system. This point is further explained in section 4.3.2.

In the isolated mode of operation, power transients from WECU and load power variations

will be absorbed by the storage element. In the absence of wind power generation, storage alone

will provide the required transient power support besides meeting steady state power demand.

2.1.2 LOAD MANAGEMENT

The amount of dynamic load that the wind energy conversion and storage system is able to

supply, in the islanded mode of operation without compromising power quality depends on the

capacity of the energy sources internal to the system. Also the VSC, which will transfer the

available energy from the internal sources to the load side, has a limited capacity (1.3 per unit).

Therefore a limited amount of load could be supplied during islanded operation of the system.

15

The inrush current at startup of a motor load (predominantly induction motors) which contains a

large reactive component causes voltage dips which in turn causes these loads to lose rotational

speed and in turn demand increased reactive current. This situation slows down the system

voltage recovery and may exceed converter rating and the available power capability of the

energy sources in the wind energy conversion and storage system. A similar situation exists

when motor load is subjected to transient voltage disturbances.

In this thesis a simple load management strategy has been adapted in which the higher rated

motor load ML2 (Figure 1.3-1) will be disconnected following system transition from grid-

connected to islanded mode of operation. The transients caused by the rest of the load are within

the handling capability of the VSC and the energy sources in the system.

2.2 STATE TRANSITION DIAGRAM

Referring to Figure 1.3-1, the wind energy conversion and storage system has two basic

operating modes:

1. Grid Connected Mode

2. Islanding Mode

The system has the following two possible operating conditions in each mode of operation:

1. Steady State

2. Transient

In steady state conditions, load and generation are in perfect balance. Under transient conditions

however, there exists a transitory imbalance between the load and generation and the system

settles down to a new equilibrium condition if it remains stable. System transients can be broadly

classified as:

1. Pre-planned Transients

2. Accidental Transients

Pre-planned transients are those resulting from intentional switching e.g. shutting down of the

utility feeder for maintenance work. Accidental transients on the other hand are random in nature

and are caused by system faults and switching in or out of the load as well as the power factor

correction capacitors, among others.

16

Both pre-planned and accidental transients can cause the combination of active energy sources in

the system to change leading to a change of the system ‘operating state’. Transient system

conditions accompanied by a change in the system operating state will be called a ‘transition’

while the dynamic conditions where the operating state of the system remains unchanged will

simply be called ‘transients’. A transition may be a result of a permanent system fault e.g. on the

utility feeder, followed by a disconnection from the utility (accidental transition) in which case

the system will switch from the grid connected mode to the isolated mode of operation. The

transition from one mode to the other may also be a pre-planned event e.g. due to maintenance

work on the feeder.

The wind energy conversion and storage system can have finitely many operating states and

in the absence of any analytical tool, in the context of hybrid control systems, the hybrid control

design for the wind energy conversion and storage system and its evaluation for stability and

performance is a very difficult task. It is therefore necessary to curtail the number of states that

the supervisory hybrid control scheme has to manage. Figure 2.2-1 gives the State Transition

Diagram (STD) of the study system with a limited set of operating states for which a supervisory

hybrid control scheme will be devised. Appendix B gives a systematic procedure for determining

the possible operating states of a system with multiple energy sources.

Referring to the STD in Figure 2.2-1, during grid connected mode when storage needs to be

built up, the system enters into the state ‘WECU + Storage + Utility’ and falls back to the state

‘WECU + Utility’ when the storage element is toped up to a pre-specified level. In the ‘VSC +

Utility’ operating state where only utility is supplying the load; the VSC will be used only for

voltage support at the PCC. Full converter capacity could be utilized for reactive power support

during this mode of operation. During islanding operation, there are three steady state operating

conditions namely:

1. The ‘standby’ state in which the dc bus is energized using the battery storage but the load

bus is kept disconnected.

2. The ‘storage’ operating state where the battery storage alone is supplying the load.

3. The ‘WECU + Storage’ operating state where the output from the wind energy conversion

unit and the storage are used together to meet the load demand.

During the latter two operating states load may or may not be present. The operating state in the

off-grid mode where only wind energy conversion unit is active is not sustainable due to the

17

absence of external transient power support and is therefore not represented. In the ‘start up’

operating state, the dc bus voltage will be energized in a controlled manner using the battery

storage and its voltage will be stabilized at the nominal value of 1.0 per unit (1000V).

Figure 2.2-1: State Transition Diagram (STD) of the wind energy conversion and storage system

2.3 CONTROL DESIGN

Control of the wind energy conversion and storage system using linear compensators and

Sinusoidal Pulse-Width Modulation (SPWM) based switching of the VSC necessarily cannot

provide for adequate control during accidental state transitions caused by faults on the utility

feeder and may not ensure performance requirements during transient operating conditions (e.g.

motor load switching) within each operating state. Considering that a reasonable limit has been

imposed on the output current of the VSC (1.3 p.u. = 1.2 p.u from WTU + 0.1 p.u. margin for

transient conditions as also for reactive power support; combined load is rated at 1.0 p.u.), it will

not be possible to contain its output current below the limit (1.3 p.u.) during a fault (particularly

a close up fault) on the utility feeder (also possibly during motor load switching) and the over

current protection of the VSC associated with its switching elements will take the unit out

causing interruption in service. It is therefore necessary to handle the management of the wind

energy conversion and storage system from a hybrid control perspective [19], [47] and [48].

The hybrid control problem is usually concerned either with switching between a number of

18

controllers for a single plant for optimum operation under changing operating conditions or

control of a plant whose state space composition is subject to change due to some discrete time

events or both. In a hybrid control structure the supervisory controller is at the top level of the

hierarchy and interacts both with the unit level regulators as well as the regulated plant(s). Figure

2.3-1 adapted from [49], illustrates the supervisory control structure. The thick solid lines

represent all the external inputs to the plant and all the outputs of the plant while thin solid lines

represent a subset of the plant outputs and the set of (control signal) inputs from the primary

regulators. The dotted lines represent information flow (monitoring and control signals) to and

from the supervisory control layer.

Figure 2.3-1: Supervisory hybrid control structure

The control action by the supervisory layer on the primary regulator may involve switching

between different controllers or updating control parameters for a single regulator or may

involve a combination of the two. Control action on the plant itself may include taking in or out a

subsystem (module) of the plant.

The control of the wind energy conversion and storage system will involve all the above-

mentioned aspects of a supervisory hybrid control scheme. Control action on the plant will

involve taking in or out one or more of the energy sources in the wind energy conversion and

battery storage system including the utility supply. The different operating states given by the

19

STD of the wind energy conversion and storage system (the plant) correspond to different state

space compositions as a result of the supervisory control actions on the system. This is further

explained in the subsequent sections and in CHAPTER 4 in the context of supervisory hybrid

control of the study system.

2.3.1 MODULAR DESIGN PHILOSOPHY

The wind energy conversion and storage system is a Multiple-Input-Multiple-Output (MIMO)

system and the control design could be tackled as such. As explained in section 2.2, the wind

energy conversion and battery storage system has two possible operating modes (on-grid and off-

grid). There are a number of possible operating states within the two basic modes of operation of

the system. Control design for each operating state using MIMO control approach represents a

considerably difficult design task. As pointed out in the previous section, control and mode

transitions will still have to be considered under a supervisory control layer (section 2.3.2).

The complexity associated with the control design of the study system using MIMO control

philosophy can be avoided by following the approach proposed in [50]. According to the

proposed approach the problem of modeling and control design for a complex system can be

simplified if the system could be partitioned along a suitable axis. The STD of Figure 2.2-1

points to such a partitioning axis i.e., the dc bus. It can be seen from Figure 2.2-1 that both the

battery storage supplying local load in islanded operation through the dc-dc converter interface,

and the utility interactive VSC unit are also two of the desirable operating states of the system

for wihc control schemes have to be designed. Any control scheme of the system in these two

operating states will have a dc voltage regulation loop as an integral component of the scheme. It

is also evident that the wind energy conversion unit will be operating only in combination with

either the storage element connected to the dc bus through the dc-dc rectifier unit (WECU +

Storage) or in the grid-connected mode through the VSC interface (WECU + Utility) or together

with both units (WECU + Storage + Utility). Based on these considerations and the assumption

that the dc bus voltage is tightly regulated, the wind energy conversion and battery storage

system can be partitioned into three modules as shown in Figure 2.3-2 through Figure 2.3-4, each

containing one energy source.

The dc capacitor is the common element to all the system modules shown in Figure 2.3-2

through Figure 2.3-4. For the system module consisting of the wind energy conversion unit, the

20

dc capacitor has been replaced with a constant voltage source. This is because the unit as such

cannot operate without an external support. Control design for each module will be carried out

independently of the other two system modules which will be represented as known disturbance

and hence will be taken care off in the control scheme of each module. Coupling between the

three modules will be minimized by tightly regulating the dc bus voltage. For this purpose dc

regulation loops will be designed for the two modules shown in Figure 2.3-3 and Figure 2.3-4 in

which the external dc current source represents the rest of the system as a known disturbance.

Only one of the two dc voltage regulators will be active during any one operating state of the

wind energy conversion and battery storage system in a mutually exclusive fashion. Control

schemes for the study system in each of the operating states given by the STD of Figure 2.2-1,

will be devised by combining and configuring the control schemes of the three system modules

to achieve control objectives of the system during that particular operating state. The supervisory

controller will select the proper regulator depending on the current operating state and the

implemented power management strategy.

The VSC will be operated as a current-regulated voltage source during grid-connected

operation of the system to achieve fast transient response [51]. In the grid-connected mode the

utility grid dictates the operating frequency of the system. In the isolated mode of operation the

load is served by the energy sources in the system through the VSC interface alone. The VSC

therefore cannot be operated as a current regulated voltage source since the objective is to supply

the load while maintaining the rms voltage at the PCC or at the load bus. The two objectives of

limiting the current output of the converter and at the same time to maintain the system rms

voltages using converter control alone are not possible without additional measures. In the

isolated operating mode, the converter therefore will be operated as a fixed frequency, directly-

controlled voltage source. The VSC control design, during grid-connected operation, will be

based on the decoupling of the qd current components through cross feedback of the controlled

variables as proposed in [52]. The VSC will be controlled using Proportional-plus-Integral (PI)

compensators during both grid-connected and in islanded modes of operation. The various

control schemes for the wind energy conversion and battery storage system during islanded and

in grid-connected mode are explained in CHAPTER 5.

21

Figure 2.3-2: Schematic diagram of system module ‘Wind Energy Conversion Unit’

Figure 2.3-3: Schematic diagram of system module ‘VSC-Utility Grid’

Figure 2.3-4: Schematic diagram of system module ‘Storage and dc-dc converter’

2.3.2 SUPERVISORY CONTROL

The supervisory controller will be managing the interaction of the controllers designed for the

three system modules shown in Figure 2.3-2 through Figure 2.3-4 when these modules are

combined to represent any one operating state given by the STD of the wind energy conversion

and battery storage system. The supervisory control layer will be required to manage the

following operating states during ‘normal operating conditions’:

22

1. Grid-connected Mode

a. Wind energy conversion unit –Utility grid

b. Wind energy conversion unit–Storage–Utility grid

c. Storage–Utility grid

d. VSC–Utility grid

2. Islanding Mode

a. Wind energy conversion unit–Storage

b. Storage

The ‘normal operating conditions’ include steady state operation as also the transient conditions

caused by load and capacitor switching. Switching between the above two modes i.e. grid-

connected and islanding operations and between any two operating states as depicted by the STD

in Figure 2.2-1 are the mode and state transitions respectively that will also be managed by the

supervisory controller. A mode transition will always involve a state transition however the wind

energy conversion and battery storage system can also transition between two different operating

states while in the same operating mode.

During each operating state the wind energy conversion and storage system will be managed

through a different control scheme. Each control scheme will combine the unit level controllers

designed for the three modules (Figure 2.3-2 through Figure 2.3-4) in the wind energy

conversion and storage system in a suitable fashion to achieve the objectives formulated for that

particular operating state. Furthermore, each control scheme will be designed to meet the

performance specifications outlined in the following sections. Each operating-state transition

therefore will be accompanied by a transition between the corresponding control schemes. The

STD will be expanded to include transitory operating states. This is necessary from the point of

view of system stability and quality of power supply and/or continuity of supply during faults in

the utility supply system as well as when the system undergoes transitions between the two

operating modes as explained in CHAPTER 4.

23

2.4 PERFORMANCE SPECIFICATIONS

Operating specifications will be required for the performance evaluation of the supervisory

hybrid controller during steady state and transient system operating conditions as also during

state transitions specified by the STD shown in Figure 2.2-1. For this purpose power quality at

the PCC and the load bus will be used as a means for performance evaluation of the wind energy

conversion and battery storage system under the proposed supervisory hybrid control scheme.

2.4.1 STEADY STATE SPECIFICATIONS

Reference [53] defines ‘power quality’ as ‘the concept of powering and grounding sensitive

equipment in a manner that is suitable to the operation of that equipment’. In the industry there is

however no broader consensus on the definition of power quality [54]. Harmonic current

distortion is one measure of the power quality and may also cause voltage waveform distortion.

Steady state performance of the wind energy conversion and storage system will be evaluated

based on the harmonic limits specified by reference [55], which covers the permissible harmonic

distortions of voltage and currents on the utility feeders as well as load contributed current

harmonics. The steady state harmonic limits will influence the choice of suitable duty-cycle

modulation scheme for the VSC during normal operation of the system.

2.4.2 TRANSIENT SPECIFICATIONS

Most of the power quality related issues are associated with momentary voltage disturbances.

While there is a general agreement on the steady state operating voltage ranges both at service

and utilization voltage levels specified by [44], there is no general agreement for the duration and

magnitude of the momentary voltage disturbances defined by [56], of various electrical

equipments for ride through capabilities. However electronic equipments are by far the most

sensitive load components. ITI (Information Technology Industry council formerly known as

Computer and Business Equipment Manufacturers Association ‘CBEMA’) curve describes the

ride through capabilities of electronic equipment based on a composite of the depth and duration

of the voltage disturbances. There are three fundamental regions identified in the ITI curve:

1. No Interruption in Function Region

2. No Damage Region

3. Prohibited Region.

These regions encompass various line-to-neutral voltage disturbances.

24

The limits specified by the ITI curve will be used as a basis for performance evaluation of the

system during dynamic operating conditions. The control objective will be to drive the wind

energy conversion and storage system to operate within the ‘no interruption in function’ region

without violating the maximum current output limit [1.3 p.u.] imposed on the VSC. For this

purpose the three phase rms and single phase instantaneous voltages at the PCC will be

monitored together with the instantaneous output current of the converter in each phase.

2.5 METHODOLOGY

The systematic development of analytical small-signal model and formal linear analysis of the

wind energy conversion and battery storage system is not the intention of this thesis. For this

purpose useful information could be found in [57], [58].

In this thesis nonlinear fundamental frequency model of each system module shown in

Figure 2.3-2 through Figure 2.3-4, complemented with the associated control scheme, will be

developed. These nonlinear models will be solved using the MATLAB/SIMULINK software to

obtain steady state operating points for the three system modules, for stability investigations and

for eigenvalue sensitivity analysis. Using linear analysis tools also available in the

MATLAB/SIMULINK software, eigenvalue analysis for linearized model of each system

module will be carried out. The sensitivity analyses are with respect to the operating points and

control parameters [35]-[39]. Performance of the three system modules, with the selected control

parameters based on eigenvalue sensitivity analysis, will be verified through simulations of the

detailed nonlinear models of the three system modules in PSCAD/EMTDC environment. These

tasks have been covered in CHAPTER 3.

Supervisory hybrid control of the wind energy conversion and battery storage system will be

investigated for transient performance and stability using time domain digital simulations of the

nonlinear model(s) in PSCAD/EMTDC simulation software. For this purpose system operation

will be considered under ‘normal conditions’ including steady state operation and for conditions

involving state transitions. Operation of the system under ‘normal conditions’ will involve

interaction of the control schemes developed for the three system modules as also supervisory

control actions described in CHAPTER 4. State transitions will also involve switching of control

schemes and both pre-planned and accidental transitions caused by faults on the utility side (as

explained in CHAPTER 4) will be considered. System operation under ‘normal conditions’ has

25

been covered in CHAPTER 5 while operation involving state transitions is the subject of

CHAPTER 6.

2.6 SUMMARY

In this chapter the following main aspects of the hybrid control of the wind energy conversion

and battery storage system have been covered:

1. Power and load management strategies have been presented for the grid-connected and

autonomous operation of the study system.

2. A State Transition Diagram (STD) for the study system with a limited set of permissible

operating states has been presented.

3. The need for a hybrid control approach for the study system has been established.

4. A modular control design philosophy for the study system has been given.

5. The principal requirements of the supervisory hybrid control scheme for the study system

have been described.

6. Steady state and transient specifications for the performance evaluation of the hybrid

control of the study system have been presented.

7. A methodology has been proposed for the hybrid control design and performance

verification of the wind energy conversion and storage system during steady state and

dynamic operating conditions including state transitions. According to this methodology

MATLAB/SIMULINK software will be used for linear (eigenvalue) analysis for stability

with respect to operating point and for selection of control parameters whereas the

PSCAD/EMTDC software will be used for verification of performance compliance during

large system transients.

26

CHAPTER 3

MODELING AND CONTROL OF SYSTEM MODULES

his chapter presents control schemes of the three system modules i.e. the wind energy

conversion unit, the battery storage and dc-dc converter and the VSC-Utility grid.

The control schemes utilize linear PI compensators. Fundamental frequency nonlinear models of

the three system modules are given in Appendix C, D and E respectively. In this chapter results

of the linear analysis of the modules with the associated control schemes are provided. For the

linear analysis MATLAB/SIMULINK software has been used. The linear analysis has been

substantiated by results from simulation studies of the detailed nonlinear model in

PSCAD/EMTDC software environment.

3.1 MODULE: WIND ENERGY CONVERSION UNIT

In this section control objectives have been given for the operation of the wind energy

conversion unit shown in Figure 2.3-2. A current-controlled speed regulation of the unit has been

proposed. Results of the eigenvalue sensitivity analysis with respect to control parameters and

operating points have been presented together with simulation results of the detailed nonlinear

model of the module using electromagnetic transients simulation software PSCAD/EMTDC.

3.1.1 MODELING AND CONTROL

The first step in the control design problem is to determine the functions required of the

controller(s) and the performance specifications [59]. The second step is control synthesis i.e. to

select suitable control laws that can achieve the required performance specifications. The

objectives established for the control of the wind energy conversion unit are the following:

1. Drive the unit to track performance curve of the turbine for maximum power generation

from the prevailing wind conditions with minimum overshoot and oscillations.

2. Obtain smooth output power.

3. Ensure that component power ratings are respected by limiting the amount of output power

to the generator rating, during both steady state and transient system operating conditions.

T

27

3.1.1.1 Control Structure

Figure 3.1-1 shows the proposed control scheme for the wind energy conversion unit that can be

used to achieve the objectives listed above. Conventional speed regulation of the unit based on

linear compensator and using only rotor speed as feedback does not provide the ability to contain

the amount of power from the unit during transient operation because of the generator terminal

voltage variations with speed. The conventional speed regulation loop has been augmented with

an inner current control loop to enable transient output power control of the wind energy

conversion unit. A constant voltage source represents the dc bus since it has been assumed that

the dc bus voltage is held relatively constant due to the dc voltage regulation loops associated

with the control schemes of the VSC (Figure 3.2-1) and the dc-dc converter (Figure 3.3-1). In

these control schemes the WECU is represented as a known disturbance.

Referring to Figure 3.1-1, the optimal turbine rotational speed corresponding to the input

wind speed is calculated using the performance curve of the turbine given in section C.1 in

Appendix C. A first order low pass filter has been used to filter out the high frequency

components of the reference optimal speed. The filtering of the reference optimal speed helps to

reduce the control activity and therefore unwanted torsional mechanical stresses in the system.

The outer speed regulation loop provides reference current signal to the inner current regulator,

the output of which gives the firing angle of the thyristor rectifier. By placing limits on the

current regulator the output power of the generator can be limited during both steady state and

transient operations. The transient conditions may be caused by variations in wind speed or it

may be a result of the switching of the excitation capacitors.

Mathematical modeling of the wind energy conversion unit and associated control scheme

shown in Figure 3.1-1 has been described in details in appendix C. The unit has 14 state

variables out of which 4 describe the electrical dynamics of the induction generator, 4 state

variables are associated with the mechanical system, 1 state variable describes the dynamics of

the generator terminal node, 1 state variable is associated with the dc link and 4 state variables

describe the dynamics of the control scheme. The dc bus voltage variations have been neglected

in the small signal model as it has been assumed tightly regulated. Another reason for neglecting

variations in the dc bus voltage is the fact that the inner current control loop (Figure 3.1-1) in the

speed regulation of the wind turbine unit provides adequately fast control of the output dc current

28

Figure 3.1-1: WECU; Proposed current-controlled speed regulation scheme

29

of the thyristor rectifier unit thereby isolating the generator side of the rectifier from variations in

the dc bus voltage. This has been verified through time domain simulations of the detailed

nonlinear model of the WECU module in PSCAD/EMTDC (section 3.1.3). The effects of the

variations in the dc bus voltage, however, can be included in the analysis of the system by

considering the small signal model with an additional input signal representing small

perturbations in the dc bus voltage.

3.1.2 SENSITIVITY ANALYSIS

In the following sections results of the eigenvalue sensitivity analysis of the wind energy

conversion unit are presented. Sensitivity analysis has been performed with respect to control

parameters and with respect to operating point of the unit. A linear model of the wind energy

conversion unit is developed and analyzed in MATLAB/SIMULINK environment. The steady

state operating points listed in Table 3.1-1 have been obtained using equation solving features of

MATLAB/SIMULINK and have been considered for the sensitivity analysis of the operation of

the unit. These operating points represent the entire speed range of the wind energy conversion

unit for a constant excitation capacitance of 750µF (delta connection). Table 3.1-1 also identifies

three steady state cases i.e. case 1, case 2 and case 3, used in the subsequent sections for

sensitivity analysis with respect to control parameters.

Table 3.1-1: WECU; Steady state operating points

Wind Speed

Vw (m/s)

ωoptimal

(p.u.)

Turbine Output

Torque (p.u.)

Generator Terminal

Voltage ‘Vqg’ (p.u.)

DC Current

Id (p.u.)

Firing Angle

α (deg)

5.2 (Case 1) 0.85 -0.65025 1.0992 0.50669 11.175

6.0 0.91667 -0.75625 1.1895 0.66041 24.784

6.5 0.95833 -0.82656 1.2521 0.7504 30.316

7.0 (Case 2) 1.0 -0.9 1.314 0.8623 34.571

7.5 1.0417 -0.97656 1.3749 0.9906 38.012

8.0 (Case 3) 1.0833 -1.0562 1.4321 1.1428 40.751

3.1.2.1 Operating Point Sensitivity

Table 3.1-2 gives the eigenvalues λ’s of the wind energy conversion unit corresponding to the

steady state operating conditions listed in Table 3.1-1. The steady state operating points have

30

been marked 1 to 6 in Table 3.1-2. Examination of this table shows that all the eigenvalues

pertaining to each steady state operating point are in the left half of the complex plane with one

eigenvalue for each operating point located at the origin (referred to as mode 0 in Table 3.1-2).

Figure 3.1-2 gives the root loci of all the eigenvalues while Figure 3.1-3 gives loci of the

dominant eigenvalues of the unit corresponding to the steady state operating points 1 to 6 (Table

3.1-1). The numerals 1 to 6 in these figures associate system poles with the corresponding steady

state operating points. For steady state point 1, the induction generator is operating near to the

knee point on the magnetization curve and one of the eigenvalue pair (referred to as mode 1 for

‘case 2’ in Table 3.1-2) corresponding to that steady state operating point moves close to the

right half plane. This mode is associated with the mechanical system (Table 3.1-3) and is also

influenced by the state variable of the dc side (in other words by the power level delivered at the

dc bus). It is concluded that with the selected control parameters and given sufficient excitation

capacitance such that the machine operates along the saturated portion of its magnetic

characteristics, the operation of the unit remains stable for the entire speed range corresponding

to that excitation level.

Table 3.1-2: WECU; Eigenvalues corresponding to the steady state operating conditions in Table 3.1-1.

STEADY STATE OPERATING POINT

1 Vw=5.2 m/s

(Case 1)

2 Vw=6.0 m/s

3 Vw=6.5 m/s

4 Vw=7.0 m/s

(Case 2)

5 Vw=7.5 m/s

6 Vw=8.0 m/s

(Case 3)

0.0 0.0 0.0 0.0

(mode 0) 0.0 0.0

-0.36288 -0.3659 -0.36792 -0.37026 -0.37281 -0.37564 -3.2551 -3.002 -3.0119 -3.0247 -3.0275 -2.9894 -4.8828 -4.6078 -4.3583 -4.1064 -3.8601 -3.6263

-5.0 -5.0 -5.0 -5.0 -5.0 -5.0

-6.5368 ± 123.68i -16.654 ± 119.86i -18.864 ± 113.64i -17.709 ± 108.01i

(mode 1) -15.533 ± 104.22i -13.475 ± 101.42i

-295.83 -216.72 -30.698 -28.144 -26.826 -26.01

-38.737± 426.84i -36.065 ± 416.15i -33.512 ± 408.6i -31.146 ± 401.85i

(mode 2) -28.684± 395.94i -26.443 ± 391.32i

-44.284 ± 958.87i -46.324 ± 967.6i -46.076 ± 975.59i -46.204 ± 983.2i

(mode 3) -46.372± 990.39i -46.864 ± 996.38i

-18.566 ± 25.051i -71.136 -151.2 ± 69.662i -159.03 ± 117.74i

(mode 4) -167.87 ± 147.78i -177.03 ± 169.66i

λ

-40.236

31

Figure 3.1-2: WECU; Root loci corresponding to different steady state operating points

Figure 3.1-3: WECU; Close-up of the root loci near to the origin; sensitivity with respect to the steady state operating point

32

3.1.2.2 Parametric Sensitivity

The control parameters considered for the sensitivity analysis are piwK , iiwK of the inner current

regulator and pwK , iwK of the outer speed regulator as shown in Figure 3.1-1. In all figures

from Figure 3.1-4 to Figure 3.1-8, the numerals accompanying any pole location also indicate the

value of the parameter in per unit. The variations in all the control parameters are from 0 per unit

to 2 per unit in steps of 0.1 per unit (shown in the figures as [0: .1: 2]) of their initial values. The

steps have been consecutively numbered from 1 to 21 and marked in the following figures. In

addition to the control parameters of the compensator, the effect of time constant iwτ of the first

order LPF in the feedback loop of the inner current regulator has also been investigated. Unless

otherwise stated, the eigenvalue sensitivity analysis has been performed at the steady state

operating conditions referred to as ‘Case 2’ in Table 3.1-1 and in Table 3.1-2 (rated power

output).

Table 3.1-3 identifies system components whose state variables have a dominant influence

on each (pair of) eigenvalue(s) and gives normalized participation factor of each dominant state

variable. Participation factors for each eigenvalue have been normalized based on the magnitude

of the participation factor of the most dominant state variable. Only state variables with a

participation factor greater than 0.05 per unit have been included. The symbols (q,d) represent

the orthogonal variables associated with the component and the symbols (ω,θ) indicate the

variables associated with the speed and position respectively, of the generator and turbine rotors.

Table 3.1-3: WECU; Mode association of state variables and participation factors for ‘case 2’

Mode Number and Participation Factors Component/State Variable 0 1 2 3 4

Inner Regulator - 0.08 - - 0.14

Inner LPF - 0.14 - - 1.0 Controller

Outer Regulator - - - - -

DC Link - 0.20 - - 0.99

Stator (q,d) - - 0.41 , 0.17 1.0 , 0.36 - , 0.15 Generator

Rotor (q,d) - 0.07 , 0.05 1.0 , 0.13 0.394 , 0.06 - , 0.09

Excitation Branch - - 0.262 0.32 0.054

Generator (ω,θ) - 0.633 , 1.0 0.096, - - 0.08 , - Mechanical System Trubine (ω,θ) - , 1.0 0.2 , - - - -

33

Mode 0 is associated with the state variable representing the angular position of the turbine rotor.

This mode responds only to the unidirectional accelerating (decelerating) torque on the turbine

(and not to any oscillating torque). In this mode the turbine and the generator rotors move in

synchronism [60].

Mode 1 is associated with the mechanical system of the wind energy conversion unit and is

affected by the amount of the active power delivered to the dc side. It is influenced to a lesser

degree by the inner regulator. Figure 3.1-4 gives the loci of the eigenvalue for this mode. There

are three traces of the same eigenvalue corresponding to variations in the control parameters

piwK , iiwK of the inner current regulator and pwK of the outer speed regulator. The mode

frequency and damping are both affected by the variations in the proportional constants piwK and

pwK of the inner and outer compensators respectively. Integral constant iwK of the outer

compensator has a negligible influence on this mode and has therefore been omitted from the

plot in Figure 3.1-4.

Figure 3.1-4: WECU; Root locus of mode 1 for variations in the values of the control parameters between 0 and 2 per unit in steps of 0.1 per unit [0: .1: 2]

34

From the eigenvalue traces in Figure 3.1-4, it is concluded that for a given loading condition, this

mode will cause instability when only integral control is exercised in the inner current

compensator. With only integral action in the outer compensator (pwK = 0) the mode exhibits

extremely low damping, which increases (together with reduced frequency of the mode) with

increasing values of the proportional constant. The integral constant iwK in the outer loop does

not influence this mode as predicted by state association of the mode given in Table 3.1-3.

Figure 3.1-5 gives the eigenvalue loci for Mode 2. This mode is predominantly associated

with the electrical dynamics of the machine and the excitation branch. Integral constants of the

compensators in both the outer and inner control loops do not affect this mode as is evident from

state association of this mode (Table 3.1-3). This mode is affected by the proportional constants

pwK and piwK of the outer and the inner regulators respectively. Increasing values of the

proportional constants pwK and piwK tend to increase the frequency and reduce the damping of

the mode.

Figure 3.1-5: WECU; Root locus for mode 2 for variations in the values of the control parameters between 0 and 2 per unit in steps of 0.1 per unit [0: .1: 2]

35

Mode 3 is the highest frequency mode of the system. It is associated with the electrical dynamics

of the generator and the excitation branch. The sensitivity of the mode to variations in control

parameters pwK and piwK is shown in Figure 3.1-6 through the trace of the eigenvalue associated

with this mode. Influence of the state variables associated with the controllers (and hence of the

integral constants iwK , iiwK of the outer and inner regulators respectively) on this mode is not

significant since these variables do not have any appreciable participation in the make up of this

mode. The proportional constants pwK and piwK influence this mode in a similar way however

the effect is insignificant. Both frequency and damping are reduced with reducing values of these

constants.

Figure 3.1-6: WECU; Root locus for mode 3 for variations in the values of the control parameters between 0 and 2 per unit in steps of 0.1 per unit [0: .1: 2]

Mode 4 is associated with the dynamics of the inner control loop and is influenced by the

state variable associated with the dc side. It is a highly damped mode. Sensitivity of this mode to

variations in the control parameters piwK , iiwK of the inner regulator and to pwK of the outer

36

regulator is shown in Figure 3.1-7. Integral constant iwK of the outer regulator (Figure 3.1-1)

does not exercise any influence on this mode as predicted by the state association of the mode

given in Table 3.1-3. Figure 3.1-7 reveals that mode 4 is affected mostly by the proportional

constant piwK of the inner compensator. It degenerates into two real poles at lower values of the

constant piwK . Increasing values of iiwK (integral constant of the inner compensator) causes both

the frequency and the damping to decrease as shown in Figure 3.1-7. The proportional constant

pwK of the outer compensator also affects the frequency and the mode damping, both of which

increase with increasing values of the constant.

Figure 3.1-7: WECU; Root locus of mode 4 for variations in the values of the control parameters between 0 and 2 per unit in steps of 0.1 per unit [0: .1: 2]

Figure 3.1-8 shows the effect of changes in the time constant iwτ of the LPF in the inner

feedback loop on mode 1 and 4, for all the three steady state cases i.e., Case1, Case2 and Case3

identified in Table 3.1-1 and in Table 3.1-2. The time constant is varied from 1 per unit (3ms) to

37

25 per unit (75ms) in steps of 1 per unit. Higher values of the time constant lead to instability of

the unit through mode 1.

Figure 3.1-8: WECU; Sensitivity of mode 1 and 4 with respect to the LPF time constant iwτ (from

3.0ms to 75.0ms in steps of 3.0ms)

The foregoing sensitivity analysis reveals that parameters of the inner control loop affect the

stability of the system. Only integral action in the inner compensator is not able to provide stable

operation of the wind energy conversion unit as mode 1 moves to the positive half of the

complex plane. Also a slower inner control loop due to lower cut-off frequency of the inner LPF

will cause instability due to mode 4 movement into the positive half plane. It is concluded that

relatively higher values (7.85 for inner loop in kA) should be used for the variable piwK and

lower values (3.0ms) for the time constant iwτ . Fine tuning of the control parameters needs to

take into account factors such as transient variations in angular displacement between the

generator and turbine rotors (torsional stresses) besides overshoot and response time for step

changes in the reference speed.

38

3.1.3 SIMULATION STUDIES

Analysis results given in the preceding sections have been verified (not reported) through

simulations of the detailed nonlinear model of the unit in PSCAD/EMTDC simulation software.

The operating point of the induction generator along the saturation curve affects the eigenvalues

of the system which in turn is dependent on the excitation level of the machine. The excitation

level has also a bearing on the power factor of the machine. In the following sections simulation

results (from PSCAD/EMTDC) of the wind energy conversion unit with the proposed speed

regulation scheme are presented with different levels of excitations.

3.1.3.1 Response to Step Changes

1. Step Changes in Wind Speed

Figure 3.1-9 and Figure 3.1-10 show response of the wind energy conversion unit for step

changes in wind speed. Initially the unit is running with a constant wind speed of 6.0 m/s. Two

excitation capacitor banks (450µF each, delta configured) are connected at the generator

terminals. One capacitor bank is permanently connected to the generator.

Figure 3.1-9 shows the rectifier output current and the generator speed in response to step

changes in wind speed from 6.0 m/s to 7.5 m/s in steps of 0.5 m/s at t = 4.5s, t = 12.0s and t =

18.0s. Downward step change in wind speed is also shown. The output power of the unit is

limited during the downward step change in the wind speed from 7.5 m/s to 7 m/s at t = 24.0s.

The unit is therefore able to track the reference speed under the proposed control scheme both for

upward and downward step changes in the wind speed within the steady state output power limit

of the rectifier.

Figure 3.1-10 shows a capacitor switching event (one bank is taken out) used to control

excitation of the induction generator in order to control the power factor and also to prevent

saturation of the controller for the simulation case shown in Figure 3.1-9. The turbine-generator

mechanical system is well damped even though losses in the system have been neglected.

Switching of the capacitor bank connected at the generator terminal excites the torsional mode of

the mechanical system (mode 1 in Table 3.1-2) which however, is sufficiently damped (plot 3,

Figure 3.1-10).

39

Figure 3.1-9: WECU; Response to step changes in wind speed, 1) wind speed 2) dc output current and rectifier current limitation 3) optimum, reference and actual speed of the generator

Figure 3.1-10: WECU; Response to step changes in wind speed, 1) generator reactive power consumption and excitation capacitor bank switching event 2) generator output power 3) angular displacement between the generator and the turbine rotors

40

4. Step Changes in DC Bus Voltage

In practice step changes in the dc bus voltage will not occur, however this case is presented to

demonstrate the ability of the porposed control scheme to limit output power of the generator

during transient disturbances on the dc bus when its voltage is supported by a battery storage in

the islanded operation or when it is supported by the VSC in the grid connected mode.

Figure 3.1-11 shows system response (continuation of the previous simulation case) to step

changes in the dc bus voltage with constant wind speed of 7 m/s at the turbine hub, and one

excitation bank connected to the generator terminals (450µF, delta configured). The dc source

voltage is step changed from 1.0 per unit to 1.05 per unit at t = 30.0s and back to 1.0 per unit at t

= 31.0s. At time t = 32.0s, the dc source voltage is step changed from 1.0 per unit to 0.95 per unit

and back to 1.0 per unit at time t = 33.0s. After each disturbance in the dc source voltage the unit

attains a new steady state operating point. The control scheme is able to maintain the output

power of the unit despite disturbances on the dc side. The step changes in the dc bus voltage also

excites torsional mode of the system (plot 3) which decays out quickly.

Figure 3.1-11: WECU; Response to step changes in the dc bus voltage, 1) dc bus voltage 2) rectifier output current 3) angular displacement of the generator with respect to the wind turbine

41

3.1.3.2 Performance under Dynamic Wind Conditions

Figure 3.1-12 shows system operation for dynamic conditions of the wind speed which has the

following characteristics:

0.6=meanV m/s, 0.1=gustV m/s, 5.0=rampV m/s together with noise components [61].

Figure 3.1-12 (plot 2) also shows switching events of the two capacitor banks at time t =

4.25s, 13.6s, 14.0s, 16.4s, 18.35s and 19.6s. One capacitor bank (450µF, delta configured) is

permanently connected to the system while two other capacitor banks of the same rating (delta

configured 450µF capacitors) are switched in and out based on a hysterises band around the

generator speed thresholds. A hysterises band has been used in order to reduce switching events

during the course of operation of the wind energy conversion unit. At higher speed above 0.97

per unit, both capacitor banks are taken out and only the permanently connected bank (number 1)

of equal rating provides for the excitation requirements of the generator. The two capacitor banks

(number 2 and 3) are connected back as the generator speed passes thresholds while coming

down towards the lower end of the operating speed range of the unit. The capacitor banks have

been sized to meet the excitation requirements of the generator while keeping the power factor

reasonably high to reduce internal losses in the machine.

Referring to Figure 3.1-12 (plot 2), at t = 4.25s, the third capacitor bank is taken out and the

unit operates with one fixed capacitor bank connected to the generator terminal. At t = 13.6s, the

bank is connected back as the generator speed drops below 0.96 per unit and taken out again as it

passes the 0.97 per unit threshold. The bank is connected back at t = 16.4s and remains

connected thereafter. The second capacitor bank (number 2) is connected to the generator

terminals at t = 18.35s when its speed falls below 0.9 per unit and remains connected as long the

generator speed remains below 0.91 per unit (till the time t = 19.6s).

It is concluded that the proposed regulator gives acceptable speed tracking within the output

power limits of the generator and the rectifier. The fast acting current-controlled speed regulation

scheme also provides adequate damping of the mechanical oscillations caused by capacitor

switching events (plots 2 & 3).

42

Figure 3.1-12: WECU; Operation during dynamic wind speed conditions, 1) wind speed 2) optimum, reference and actual speed of the generator and capacitor bank switching events 3) Reference and actual output dc current

43

3.2 MODULE: VSC-UTILITY GRID

Control objectives of the system module ‘VSC-Utility grid’ (shown in Figure 2.3-3) and a

control scheme utilizing PI compensators are presented in the following sections. This is

followed by eigenvalue sensitivity analysis of the system. Modeling details of the module are

given in Appendix D wherein the PLL and the sensor dynamics have been included. A PLL is

used to track the phase angle of the system voltage space vector [62]. The VSC has been

operated as a current regulated voltage source [52].

3.2.1 CONTROL STRUCTURE

The following objectives are identified for the control of the VSC:

1. Transfer available power at the dc side to the utility grid and thus regulate the dc bus

voltage

2. Provide reactive power support to achieve rms voltage control at the PCC or the load bus

(based on the feedback signal which could come from the PCC or the load bus rms

voltage). In this section the load bus rms voltage has been controlled since no other load on

the feeder has been assumed.

Figure 3.2-1 shows a single line schematic and the control structure proposed for the VSC-Utility

grid system module. The diagram also shows the sign convention (used in appendix D for

modeling of the system). The VSC control has been adopted from [52] where the effects of the

cross coupling between the orthogonal components of the VSC output current have been

minimized by adding forward compensating terms (cross feedback) corresponding to the voltage

drop across the utility network. An outer PI compensator based dc voltage regulation loop

provides reference signal to the inner active current controller while the reference to the reactive

current controller comes from the outer rms voltage regulation loop.

The dc current injected at the dc bus, which is assumed as a (known) disturbance is forward

fed to the inner q axis current controller thereby bypassing the slow dynamics of the dc voltage

regulator. The converter interfacing reactor and the power factor correction capacitors at the PCC

provide the necessary current and voltage harmonic suppression. To minimize interaction

between the active and reactive current regulators to a minimum during transient system

operation, the control loop that supplies reference for the inner reactive current controller will be

designed to have adequately slow dynamics as compared to the dc voltage regulation loop and

44

the inner current control loops. For this purpose the time constant of the LPF in the rms voltage

control loop has been selected large enough (10ms) such that during fast transient voltage

disturbances the reactive current reference output of the regulator remains essentially constant

i.e. the variations in the reactive current reference are of much slower frequency than that of the

active current reference. Also the maximum reactive current supplied by the converter will be

dependent upon the value of the active current component being delivered by the converter at

any given time during its operation.

A fundamental frequency nonlinear model of the ‘VSC-Utility Grid’ system module

together with the associated control scheme shown in Figure 3.2-1 has been developed in

appendix D. The ‘VSC-Utility Grid’ system model has 33 state variables whereas 2 control

variables namely the dc bus reference voltage and the three-phase rms reference voltage of the

load bus make up the input vector of the closed loop system. Of the 33 state variables, 11 state

variables belong to the VSC component and its associated control scheme, 16 state variables

make up the load including the load network of which 5 state variables belong to each of the two

induction motor loads, 4 state variables are associated with the utility supply and 2 state variables

belong to the PLL device.

45

Figure 3.2-1: VSC-Utility Grid; Single line schematic and control structure

46


A linear model of the system module (based on the nonlinear model given in appendix D) has

been developed and analyzed in MATLAB/SIMULINK environment. In this section results of

the eigenvalue sensitivity analysis with respect to operating point and control parameters are

presented.

Parametric sensitivity analysis has been carried out with respect to control parameters at the

steady state operating points given in Table 3.2-1. Sesitivity with respect to operating point has

also been considered for operating conditions other than those given in Table 3.2-1 (explained

below). During all the steady state operating conditions the load connected to the system remains

unchanged as also the capacitors connected to the PCC and the load bus. Static load (SL1),

which has a constant lagging power factor of 0.81 and the load torques TL1 and TL2, have been

kept at 0.5 per unit each. Two capacitor banks each of 1.5µF capacity (at 13.8kV) are connected

to the PCC and the load bus.

Table 3.2-1: VSC-Utility Grid; Steady state operating points

DC Source VSC Utility Supply Load

Id[p.u.] P [p.u.] P [p.u.] Q [p.u.] P [p.u.] Q [p.u.] P [p.u.] Q [p.u.]

Case 1 -1.0 1.0 1.0 1.31 1.66 -1.34 0.64 0.31

Case 2 0.0 0.0 0.0 0.94 0.65 0.97 0.64 0.31

Case 3 1.0 -1.0 -1.0 0.35 0.34 0.39 0.64 0.31


The steady state conditions considered for the operating point sensitivity of the system

eigenvalues correspond to different level of dc current injection at the dc bus (Figure 3.2-1). The

steady state operating conditions (total 13) cover the full range of operation of the VSC from full

load in the rectifier mode (case 1 in Table 3.2-1) to full load in the inverter mode (case 3).

Table 3.2-2 gives eigenvalues of the system module for the steady state operating conditions

namely; case 1, case2 and case 3 which are identified in Table 3.2-1. All the eigenvalues in Table

3.2-2 remain in the negative half of the complex plane indicating that the system remains stable

for full load in the rectifier mode to full load operation in the inverter mode.

47

Referring to Table 3.2-2, real poles 32 and 33 are associated with the outer dc compensator (PI 1

in Figure 3.2-1) and the PLL respectively, each with a participation factor of 1.0 per unit. The

dominant eigenpair (32, 33), for the noload condition and full load condition in the inverter

mode, is associated with the PLL dynamics (participation factors of 1.0 and 0.16 per unit for the

two state variables of the PLL). The same eigenpair has significant but diminishing contribution

(<0.9 per unit) from the state variable associated with the outer dc compensator for higher

loading conditions in the inverter mode of operation. It is concluded that the PLL has a greater

influence in the inverter mode of operation of the VSC.

Table 3.2-2: VSC-Utility Grid; Eigenvalues corresponding to the steady state operating points identified in Table 3.2-1

λ Number

CASE 1 CASE 2 CASE 3

1, 2 -13.066 ± 87887i -13.047 ± 87887i -13.039 ± 87887i 3, 4 -13.041 ± 87133i -13.040 ± 87133i -13.040 ± 87132i 5, 6 -102.39 ± 6298.3i -102.20 ± 6298.8i -102.04 ± 6299.2i 7, 8 -101.01 ± 5545.5i -100.70 ± 5544.9i -100.41 ± 5544.4i 9, 10 -211.15 ± 620.31i -226.35 ± 618.04i -241.23 ± 616.07i 11, 12 -514.67 ± 376.68i -514.67 ± 376.74i -514.67 ± 376.76i 13, 14 -297.04 ± 293.08i -297.04 ± 293.14i -297.05 ± 293.17i 15, 16 -23.736 ± 376.46i -23.718 ± 376.49i -23.701 ± 376.48i 17, 18 -70.468 ± 226.42i -74.659 ± 231.99i -78.315 ± 237.09i 19, 20 -77.448 ± 95.669i -77.439 ± 95.797i -77.426 ± 95.876i

21 -130.05 -130.06 -130.12 22 -99.608 -88.855 23 -77.055 -81.763

-82.637 ± 8.6815i

24, 25 -6.4776 ± 37.16i -6.4834 ± 37.19i -6.488 ± 37.213i 26, 27 -31.661 ± 23.381i -31.134 ± 23.607i -30.459 ± 23.712i

28 -20.608 -20.567 -20.539 29 -7.2181 -7.1974 -7.1888 30 -7.1434 -7.1299 -7.1143 31 -14.228 -14.168 -14.113 32 -10.25 33 -11.587

-11.26 ± 0.1081i -11.644 ± 0.41263i

Figure 3.2-2 gives a graphical presentation of the movement of the two eigenvalues ‘32’ and

‘33’ (Table 3.2-2) for steady state conditions with dc bus loading from -1.0 per unit (case 1 in

Table 3.2-1) through 0.0 (case 2) to 1.0 per unit (case 3) in steps of 0.167 per unit (50A). A total

of 13 steady state operating points have been considered including those for which the

eigenvalues are given in Table 3.2-2. The eigenvalues (Figure 3.2-2) are numbered for steady

state conditions with numeral ‘1’ referring to the full load rectifier mode (case 1) while numeral

48

‘13’ indicates the full load inverter mode of operation (case 3) and numeral ‘7’ indicates the

noload condition (case 2, real power exchange between the dc and ac side is zero).

Figure 3.2-2: VSC-Utility Grid; Plot of the eigenvalues (32, 33) corresponding to operating conditions from full load in rectifier mode (dI = -1.0 p.u.) to full load in inverter mode (dI = 1.0 p.u.)


Parametric sensitivity analysis has been performed initially at the steady state operating point

pertaining to ‘case 2’ in Table 3.2-1. Table 3.2-3 gives system eigenvalues for ‘case 2’ and

identifies components that have major or minor contribution in each (pair) of the eigenvalues.

Major contribution has been defined based on a participation factor of 1.0 per unit while minor

contribution has been defined as a participation factor greater than 0.05 per unit. Major

contribution has been identified by the letter ‘X’ while minor contribution is idicated by the letter

‘x’. Dominant modes affected by the VSC and its associated control scheme have also been

noted in Table 3.2-3. It should be noted that the load in Table 3.2-3 also includes the interposing

transformer and feeder between the load bus and the PCC whereas the PCC itself has been

considered as part of the Utility Grid.

49

Table 3.2-3: VSC-Utility Grid; Eigenvalues and mode association for ‘case 2’

Dominant System Components λ VSC Utility Grid Load PLL

-13.985 ± 9669.7i - - X - -14.119 ± 8915.8i - - X - -104.47 ± 4348.6i x X x - -102.51 ± 3595i x X - - -224.78 ± 622.22i X x - - -508.88 ± 376.33i - - X - -300.82 ± 292.31i - - X - -23.714 ± 376.42i - - X - -76.48 ± 229.48i [Mode 3] X x - x -75.925 ± 109.4i - - X - -130.03 X - - - -85.122 ± 6.4713i [Mode 4] X - x x -7.0019 ± 36.022i - - X - -30.982 ± 23.242i [Mode 2] X - x x -7.1885 X - - - -7.1324 X - - - -15.286 - - X - -13.114 x - X x -11.309 ± 0.12524i [Mode 1] x - x X

Table 3.2-4 gives state association with corresponding participation factors for the dominant

modes identified in Table 3.2-3, in which (q,d) represents the orthorgonal components and LPF1,2

refers to the first order low pass filters ‘LPF 1’ and ‘LPF 2’ in Figure 3.2-1.

Table 3.2-4: VSC-Utility Grid; Dominant modes, mode association of state variables and participation factors for ‘case 2’

Mode Number and Participation Factors Component/State Variable Mode 1 Mode 2 Mode 3

DC Capacitor 0.11 0.04 0.400

Terminal Currents (q,d) - - , 0.100 0.395, 0.577

Inner Regulators (q,d) 0.038 , - - -

Inner LPFs (q,d) - - , 0.153 0.536 , 1.0

Outer Regulators (q,d) 0.845 , - - , 1.0 -

VSC and Control Scheme

Outer LPF1,2 - 0.487 , 0.499 0.059

x1pll 1.0 0.040 - PLL

x2pll 0.132 0.123 0.054

Currents (q,d) - - 0.057 , 0.075 Utility Network

PCC voltage (q) - - -

- - - Load Network

Induction Motors (LM1,2) - , 0.082 - , 0.436 -

50

For all the subsequent figures in this section, variations in a control parameter are indicated as

[x i; s; xf] meaning that the parameter value is varied from ‘xi’ per unit to ‘xf’ per unit in steps of

‘s’ per unit. The numerals accompanying an eigenvalue on the root locus indicates the step

number with ‘xi’ marked as 1.

Table 3.2-4 indicates that mode 1 is mostly influenced by the PLL and the dc bus voltage

regulator. Figure 3.2-3 gives loci of the eigenvalue for mode 1 for variations in the proportional

and integral constants pdK , idK of the dc voltage regulator (PI 1) repectively. Referring to

Figure 3.2-3, the complex eigenpair of mode 1 gives rise to two real poles when the value of the

proportional constant pdK of the dc bus voltage regulator (PI 1) is either increased or decreased

from its initial value. The parameter idK has a similar but opposite effect. The root locus

suggests the use of lower values for the proportional constant pdK and higher values for the

integral constant idK .

Figure 3.2-3: VSC-Utility Grid; Loci of the eigenvalues corresponding to mode 1 for variations in pdK

and idK of the outer dc regulator

51

Figure 3.2-4 gives the loci of the eigenvalues pertaining to mode 1 for variations in the

proportional and integral constants piK , iiK of the inner current regulators (PI 2 and PI 4 in

Figure 3.2-1). Referring to Figure 3.2-4, increasing the proportional gain piK results in the

complex pole pair of mode 1 to degenerate into two real poles while decreasing the integral gain

iiK gives rise to the same effect. The proportional and integral gains of the inner current

regulators have opposing effects on the behaviour of this mode. Control of mode 1 is lost for

higher and lower values of piK and iiK respectively. This mode is sufficiently damped and does

not affect system stability.

Figure 3.2-4: VSC-Utility Grid; Loci of mode 1 for variations in piK and iiK of the inner current

regulators

Mode 2 is highly influenced by the dynamics of the rms voltage control loop, induction

motor ML2 and the PLL. Effects of the proportional and integral constants pvK and ivK of the

outer rms voltage regulator (PI 3 in Figure 3.2-1) are shown in Figure 3.2-5. This mode exhibits

52

higher frequency and reduced damping for higher values of ivK . The proportional constant pvK

has the opposite but much less significant effect on the movement of mode 2. As confirmed from

the participation of the state variables in this mode (Table 3.2-4), variations in the integral

constant idK of the dc voltage regulation loop do not have any significant effect on either the

frequency or the damping of the mode 2. This is also true for the proportional constant pdK of

the dc voltage regulator.

Figure 3.2-5: VSC-Utility Grid; Plot of the positive eigenvalues corresponding to Mode 2 for variations in the parameters of the current and dc voltage regulators

Figure 3.1-6 gives root loci for mode 2 for variations in the time constant vfbτ of the LPF 2

in the feedback loop of the rms voltage regulator (Figure 3.2-1). This parameter has a relatively

significant and opposing effect as that of the proportional constant pvK . Since the two low pass

filters LPF 1 and LPF 2 are in series these exerts similar effect on mode 2 as confirmed by their

participation factors given in Table 3.2-4.

53

Figure 3.2-6: VSC-Utility Grid; Plot of the eigenvalue of mode 2 for variations in the parameters vfbτ

and ivK

Figure 3.2-7: VSC-Utility Grid; Traces of the eigenvalue of mode 2 for variations in piK and iiK of the

inner current regulators

54

Root loci of mode 2 corresponding to variations in the proportional and integral constants piK ,

iiK are given in Figure 3.2-7. The proportional constant piK exerts relatively significant

influence on the damping and the frequency of mode 2 which diminishes with higher value of the

constant piK .

Mode 3 is caused by the interaction of the low pass filters in the feedback paths of the inner

current control loops and the terminal currents of the VSC. Traces of the eigenvalue associated

with mode 3 in Figure 3.2-8, indicates that this mode will cause instability for very low values of

the proportional gain piK of the inner current regulators (PI 2 and PI 4). The constant piK has

significant effect on both frequency and damping of this mode. The integral constant iiK has a

relatively insignificant effect on this mode. A typical value (3.0ms) has been used for the time

constants of the low pass filters in the inner current regulators.

Figure 3.2-8: VSC-Utility Grid; Trace of the eigenvalue associated with mode 3

55

From the operating point sensitivity analysis it has been established that the dominant

eigenvalues of the system are relatively independent of the steady state operating conditions

(from full load in the rectifier mode to full load in the inverter mode of operation of the VSC).

Selection of the VSC control parameters can thus be carried out by considering the no-load case

alone (VSC real power exchange is zero).

From parametric sensitivity analysis it is concluded that of all the control parameters, the

proportional gain piK of the inner current regulators has a significant effect on the dominant

modes of the system. A higher value should be selected for this parameter. System and control

parameters are given in appendix A. Fine tuning of the control parameters generally needs to be

performed in PSCAD/EMTDC digital simulation environment where factors such as overshoot,

harmonic content of the converter delivered current and the PCC (and/or the load bus) voltage

would need to be considered.


In the following sections results are presented from digital simulations of the detailed nonlinear

model of the VSC-Utility Grid system module performed in PSCAD/EMTDC software

environment. A switching frequency of 3.96 kHz (66x60Hz) has been used for the VSC gating

control in the PSCAD/EMTDC simulation software.

3.2.3.1 Steady State Performance

The system is operating in steady state and the converter is delivering 0.97 per unit of ‘active’

and 0.4 per unit of ‘reactive’ current with a dc current injection of 1.0 per unit on the dc side.

Both the individual harmonic magnitudes as well as the THD for the current and the voltage are

less than the limits recommended by [55]. THD is less than 0.05% for the converter terminal

current and less than 0.02% for the PCC voltage. These results have been achieved with a

capacitor of 1.5µF at the PCC (at 13.8kV). The results (not shown) are also within limits for a

capacitor value of 0.75µF at the PCC.

3.2.3.2 Dynamic Performance

The following should be noted about the simulation results presented in this section:

1. The base power used is 300kVA with the converter rated at 1.3 per unit.

56

2. The instantaneous ‘abc’ reference frame variables have been expressed in per unit based on

their maximum values corresponding to their nominal rms values.

3. The per-unitized (induction motor) load torques are based on the respective machine rating.

4. The VSC switching method is based on SPWM at the switching frequency of 3960Hz

(66x60 Hz).

Figure 3.2-9 and Figure 3.2-10 shows response of the system to load transients and to step

changes in the reference signals for the dc bus voltage and the rms voltage at the load bus. The

two figures have been drawn for the same time duration.

Initially the system is running under no-load conditions with a 1.5µF capacitor connected at

the PCC (at 13.8kV). A dc current id = 0.66 per unit is injected at the dc bus by a constant

current source. The injected power into the dc bus is transferred to the utility side by the

converter together with a reactive power import to maintain the rms voltage at the load bus at 1.0

per unit. At time t = 1.5s, a lagging power factor (0.81) static load (SL1 in Figure 3.2-1) of 0.28

per unit rating is connected to the system at the load bus. At t = 2.5s an induction motor load

(ML1 rated at 0.127 per unit or 38kW) is connected to the load bus while running at synchronous

speed with zero load at its shaft. A second capacitor bank of 1.5µF is connected to the PCC

(13.8kV) at time t = 3.75s. At time t = 4.5s another static load (SL2) rated at 0.28 per unit (power

factor of 0.81 lagging) is switched on and at t = 5.5s full load torque is applied on motor ML1.

At time t = 6.0s the dc current injection is step increased to 1.0 per unit. At t = 7.0s another

induction motor load (ML2) is connected to the system while running at synchronous speed with

zero load torque. The motor load ML2 is rated at 0.273 per unit (82kW). The load torque on

motor ML2 is then step increased to 1.0 per unit at t = 8.0s. At time t = 8.5s the dc reference

signal is step changed from 1.0 per unit to 1.03 per unit and back to 1.0 per unit at time t = 9.5s.

At t = 10.5s the reference rms voltage signal is step changed from 1.0 per unit to 0.98 per unit

and back to 1.0 per unit at time t = 11.5s.

Figure 3.2-9 and Figure 3.2-10 show that after each event mentioned above, the system

returns to a stable operating state. Also the rms voltage of the load bus remains within the

performance bounds of the ‘no interruption in function’ region specified by the ITI curve during

all load switchings and dc side disturbances. The dc bus voltage remains tightly regulated despite

disturbances (in the form of external dc current injection) at the dc bus.

57

Figure 3.2-9: VSC-Utility Grid; Response to load switchings and step changes in reference voltages of the dc bus and the load bus, 1) dc current (disturbance) 2) & 3) ‘active’ and ‘reactive’ terminal currents of the VSC

58

Figure 3.2-10: VSC-Utility Grid; Response to load switchings and step changes in reference voltages of the dc bus and the load bus, 1) reference and actual three phase rms voltage at the load bus 2) reference and actual dc bus voltage

59

3.3 MODULE: BATTERY STORAGE AND DC-DC CONVERTER

The assumed storage medium consists of a bank of lead-acid batteries. Control objectives have

been given first, followed by results of stability and parametric sensitivity analysis. The results

from the eigenvalue analysis of the system have been verified using detailed nonlinear model in

the PSCA/EMTDC simulation software. Selection of the module components and the details of

modeling these components are given in appendix E.

3.3.1 MODELING AND CONTROL

The dc-dc converter control is to:

1. Facilitate bidirectional power flow control for battery charging and discharging purposes.

2. Provide dc bus voltage regulation.

During islanded operation of the wind energy conversion and battery storage system, the storage

device will be used for steady state and transient power support as per the power management

strategy described in section 2.1.1. An adequately fast control response is therefore desirable.

Current Programmed Mode (CPM) control using peak inductor current has been used for the

converter duty ratio control which has the inherent characteristic of over-current protection of the

switching devices [132].

Figure 3.3-1 shows control schematic of the system module. A controlled current source

connected to the dc bus represents power contribution to or from the other two system modules

namely the wind energy conversion unit and the VSC-Utility grid. A small signal model of the

battery storage and dc-dc converter module with CPM based control of the dc-dc converter is

given in Figure E-6.

Referring to Figure 3.3-1, the load current on the dc bus is forward fed to the dc bus voltage

control loop which regulates the output current of the battery storage to meet load demand while

maintaining the dc bus voltage. This arrangement bypasses the dynamics of the voltage control

loop resulting in a relatively faster response time. The control scheme given in Figure 3.3-1 will

be suitably modified when the battery storage and dc-dc converter system module is used to

support the dc bus voltage while it is operated with the VSC unit as shown in Figure 5.4-1 and

Figure 5.6-1 as also when the storage alone is used to meet load demand in the system through

the VSC unit as shown in Figure 5.5-1.

60

Modeling details of the module with the control structure shown in Figure 3.3-1 are given in

appendix E. The battery storage and dc-dc converter model has 4 state variables of which 1 each

is associated with the battery storage, the dc-dc converter and the dc bus and 1 state variable is

associated with the dc voltage regulator. The dc bus reference voltage makes up the input vector

of the closed loop system.


Results of the eigenvalue sensitivity analysis with respect to control parameters and with respect

to steady state operating points are presented in the following sections. Predictions from linear

analysis have been verified using the detailed nonlinear model of the system module in the

PSCAD/EMTDC simulation environment.

Figure 3.3-1: Battery Storage and DC-DC Converter; Control structure and schematic diagram


1. Boost Mode of Operation

Table 3.3-1 gives the eigenvalues and the location of the corresponding RHP zero of the system

module at different steady state operating points in boost mode of operation. The equilibrium dc

61

loading conditions at nominal dc bus voltage (1.0 per unit) are also listed in the table. There is no

oscillatory mode during moost mode of operation and all the eigenvalues of the system are in the

left half of the complex plane.

Referring to Table 3.3-1, the dominant eigenvalues exhibit little shift from one equilibrium

operating point to another thereby indicating a relatively uniform operation of the module over

the operating range, in boost mode. The effect of the RHP zero which gives the system a non-

minimum phase nature, is more pronounced at higher loadings and has negligible influence at

low loading conditions because of the fact that the capacitor terminal voltage will drop relatively

quickly at higher loading during the period that the inductor current is being built up. During this

period the dc capacitor alone supports the load and as such its value has a bearing on the location

of the RHP.

Table 3.3-1: Battery Storage and dc-dc converter (Boost mode of operation); Poles and RHP zeros at different steady state operating points

I o [p.u] 0.167 0.333 0.500 0.667 0.833 1.00

λ1 -4369.3 -3822.8 -3264.4 -2689.7 -2090.9 -1445.7

λ2 -26.896 -26.416 -25.954 -25.508 -25.075 -24.652

λ3 -86.608 -98.092 -112.56 -132.78 -164.82 -228.29

λ4 -62.481 -61.052 -60.095 -59.37 -58.778 -58.269

RHP Zero 1019.2 484.98 306.34 216.57 162.32 125.8

2. Buck Mode of Operation

Table 3.3-2 gives the eigenvalues of the system module at different steady state operating points

in buck mode of operation. The equilibrium dc loading conditions at nominal dc bus voltage are

also listed in Table 3.3-2. The system remains stable with all the eigenvalues in the left half of

the complex plane. There is only one oscillatory mode (λ3,4) during buck mode of operation of

the dc-dc converter. The oscillatory mode is considerably damped. It is noted that the damping of

the mode increases while its frequency is reduced for higher loading conditions.

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Table 3.3-2: Battery Storage and DC-DC Converter (Buck mode of operation); Eigenvalues at different steady state operating points

I o

[p.u] -0.167 -0.333 -0.500 -0.667 -0.833 -1.00

λ1 -10312 -9894.2 -9453.8 -8988 -8493.9 -7968

λ2 -31.245 -30.479 -29.782 -29.141 -28.544 -27.984

λ3,4 -56.769±12.182i -58.429±12.108i -60.235±11.787i -62.239±11.096i -64.5± 9.7864i -67.141±7.1648i

Figure 3.3-2 gives loci of eigenvalue loci λ2 and λ3,4 when the dc-dc converter is operating

in buck mode corresponding to the steady state operating points listed in Table 3.3-2. The steady

state dc loadings are at nominal dc bus voltage (1000V or 1.0 per unit).

Figure 3.3-2: Battery Storage and DC-DC Converter; Loci of the eigenvalues λ2 and λ3,4 corresponding to the steady state operating points given in Table 3.3-2

63


Figure 3.3-3 through to Figure 3.3-6 show eigenvalue loci for the boost and the buck mode of

operation of the dc-dc czonverter, as the proportional constant pdcK and integral constant idcK of

the dc voltage regulator are varied from 0.0 per unit to 1.8 per unit of their initial values, in steps

of 0.15 per unit ([0.0: 0.15: 1.8]). The following steady state points have been considered:

Boost Mode: oI = 0.5 per unit; dcV = 1.0 per unit

Buck Mode: oI = -0.5 per unit; dcV = 1.0 per unit.

1. Boost Mode of Operation

Referring to Figure 3.3-3, the two dominant real poles (λ2,4) given in Table 3.3-1 give rise to an

oscillatory mode at lower values of the proportional constant pdcK . The constant pdcK is varied

from 0.0 per unit to 1.8 per unit in steps of 0.15 per unit.

Figure 3.3-3: Battery Storage and DC-DC Converter (Boost Mode); Eigenvalue trace with respect to the

proportional gain pdcK

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At extremely low values (approaching zero) for the proportional constant pdcK , the system

exhibits very low damping while higher values (≥10) for pdcK result in a stable and well

damped system response during the boost operating mode of the dc-dc converter.

Figure 3.3-4 shows root locus of the dominant eigenvalues of the system for variations in the

integral constant idcK in the boost mode of operation. At higher values of the integral constant

the two most dominant real eigen values (λ2,4) give rise to an oscillatory mode. The resultant

mode however has sufficient damping and is not of any concern.

Figure 3.3-4: Battery Storage and DC-DC Converter (Boost Mode); Eigenvalue trace with respect to the

integral gain idcK

2. Buck Mode of Operation

Figure 3.3-5 gives the root loci of the dominant eigenvalues (λ2 and λ3,4 in Table 3.3-2) of the

storage and dc-dc converter module in the buck mode of operation for variations in the

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proportional constant pdcK . The proportional constant pdcK is varied from 0.8 per unit to 1.2

per unit in steps of 0.001 per unit.

Referring to Figure 3.3-5, mode (λ3,4) degerates into two real poles for one particular value

of the of pdcK (0.917 p.u.) with λ2 lying in the middle between the two. For higher values of

pdcK , the real pole λ2 is located on the RHS of the locus for the mode (λ3,4) while for lower

values of the constant the real eigenvalue λ2 is located farther along the real axis on the LHS of

the of the eigenvalue locus of the oscillatory mode. Extremely low values of pdcK (~ 0) will

result in a low frequency sustained oscillatory response of the module. A higher value (≥10) of

the proportional constant pdcK is therefore suggested for a fast and adequately damped response.

Figure 3.3-5: Battery Storage and DC-DC Converter (Buck Mode); Root loci with respect to the proportional constant pdcK

66

Figure 3.3-6 shows locus of the eigenvalue for the oscillatory mode (λ3,4) of the dc-dc converter

in the buck operating mode for variations in the integral constant idcK . The integral constant

idcK is varied from 0.8 per unit to 1.5 per unit in steps of 0.001 per unit. The root locus plot in

Figure 3.3-6 shows that a high value (≥200) for the integral constant idcK would result in an

adequately fast and well damped response.

Figure 3.3-6: Battery Storage and DC-DC Converter (Buck Mode); Root locus with respect to the integral constant idcK

Final selection of the two constants pdcK and idcK should take into account the frequency

variations of the oscillatory modes in the other two system modules so that undesirable mutual

interaction between the three system modules can be avoided when these are operated

interactively.

67


Digital simulation results of the nonlinear detailed system model developed in the

PSCAD/EMTDC environment are presented below. A converter switching frequency of 3.0 kHz

has been used.

1. Step Changes in Current

Figure 3.3-7 shows response to step changes in dc side injected current while the dc-dc converter

is operating in the boost mode. Referring to the first graph, initially a 0.5 per unit current is being

drained from the dc bus (representing the VSC as a known disturbance) and the system operates

in a quasi steady state condition. At time t = 0.6s the dc current drain is step changed from 0.5

per unit to 0.67 per unit and back to 0.5 per unit at t = 0.9s. At time t = 1.2s the load current is

reduced in one step from 0.5 per unit to 0.33 per unit and back to 0.5 per unit at time t = 1.5s.

The dc-dc converter response is almost immediate due to forwarding feeding of the disturbance

current.

Plot 2 in Figure 3.3-7 shows the dc bus voltage during step changes in the output current

from the dc bus side. The response of the dc-dc converter system is adequately damped and

stable and the dc bus remains regulated within a narrow band of ±1.0% around the nominal value

of 1.0 per unit.

Figure 3.3-7: Battery Storage and DC-DC Converter (Boost Mode), 1) dc output and inductor current 2) dc bus voltage

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The sequence of events shown in Figure 3.3-7 is repeated in Figure 3.3-8, however the

disturbance current is now injected into the dc bus and the dc-dc converter is operating in the

buck mode. Here also operation of the system module is stable and the dc bus voltage is tightly

regulated within a very narrow band of ±0.4% around the nominal value.

Figure 3.3-8: Battery Storage and DC-DC Converter (Buck Mode), 1) injected at the dc bus and inductor current 2) dc bus voltage

2. Step Changes in Reference Voltage

Figure 3.3-9 gives system response to step changes in the dc bus reference voltage. Plot 1 shows

system response when the dc-dc converter is operating in a boost mode with a constant current

load of 0.5 per unit at the dc bus.

Initially the reference voltage signal is set at 1.0 per unit. At time t = 1.8s the reference

voltage is step changed to 1.05 per unit and back to 1.0 per unit at t = 2.5s. At time t = 2.4s the

reference is again step changed from 1.0 per unit to 0.95 per unit and back to 1.0 per unit at time

t = 2.7s. In each case the dc bus voltage is maintained at the reference level within a settling time

of less than 100ms with an overshoot of less than 20%. The nonminimum phase nature of the

system in the boost mode is evident from plot 1 in which the initial system response is opposite

to that of the commanded step change in the dc bus voltage.

Plot 2 in Figure 3.3-9 gives the system response to step changes in the reference dc bus

voltage during a buck mode of operation. A constant dc current of 0.5 per unit is being injected

during these step changes. The sequence of events in the buck mode of operation is the same as

that in the first plot for the boost mode of operation. During both the boost and the buck mode of

69

operation the module is able to track the reference signal for the dc bus voltage with acceptable

overshoots (less than 20%) and with adequately fast settling times (less than 100ms).

Figure 3.3-9: Battery Storage and DC-DC Converter, 1) reference and actual dc bus voltage in boost mode 2) reference and actual dc bus voltage in buck mode

3.4 SUMMARY AND CONCLUSIONS

In this chapter control schemes and linear analysis results of the three system modules namely

the wind energy conversion unit, the VSC-Utility grid system and the Storage and dc-dc

converter system have been presented. Control performance for the three system modules has

been verified through simulations using detailed nonlinear models of these systems in

PSCAD/EMTDC simulation software.

3.4.1 MODULE : WIND ENERGY CONVERSION UNIT

1. Control scheme for the system module ‘wind energy conversion unit’ has been presented. A

new current-controlled speed regulation scheme for the unit has been proposed. The control

scheme is a modification of the conventional linear PI compensator based speed regulator

with generator speed as the feedback signal, using a thyristor-controlled rectifier. The

conventional regulation scheme has been augmented with an inner current control loop to

provide transient and steady state output power control of the unit as shown in Figure 3.1-1.

2. A complete mathematical model of the wind energy conversion unit with the proposed

control scheme has been developed which is given in Appendix C. The model takes into

70

account magnetic nonlinearity of the induction generator using the commonly available no-

load terminal voltage verses current characteristics of the machine.

3. Eigenvalue sensitivity analysis with respect to operating point and with respect to control

parameters has been presented. The analysis has been performed with the linear analysis

tools available in MATLAB/SIMULINK using the numerical, linear state space models

extracted from the fundamental frequency nonlinear model given in Appendix C.

4. Time domain simulation results from PSCAD/EMTDC of the detailed nonlinear model of

the wind energy conversion unit have been presented to substantiate results from the linear

system study.

The following conclusions have been arrived at, based on the results of the linear and nonlinear

analysis:

1. The proposed current-controlled speed regulation of the wind turbine unit ensures that the

generator and rectifier power limits are respected under all steady state and common

transient operating conditions by imposing limits on the inner current regulator. The

transient operating conditions may include upward and downward step changes in the

reference speed and switching of the excitation capacitor banks among others.

2. The proposed control scheme provides robust and uniform performance over the entire

operating speed range of the wind energy conversion system using three parallel connected

static capacitor banks. The level of excitation is step changed during operation of the unit

over its speed range.

3. The current-controlled speed regulation of the wind turbine unit provides rejection

capabilities for the dc bus voltage disturbances and provides sufficient damping of the

turbine-generator torsional mode for the otherwise lossless mechanical system. It reduces

mechanical oscillations caused by switching of the excitation capacitors and by the

variations of the dc bus voltage.

4. The turbine-generator torsional mode is affected by the proportional constants of both the

outer and the inner compensators. Higher values of these control parameters result in

increased damping and reduced frequency of the mode. Integral action in the inner current

control loop alone does not provide any damping of the torsional mode and will result in

mechanical instability of the system. On the other hand simple gain in the inner

compensator can ensure system stability however this results in excessive control activity

71

and poor step response. Integral constant in the outer compensator does not affect the

torsional mode of the mechanical system.

5. The time constant of the LPF in the inner compensator of the wind turbine speed regulation

scheme can also affect system performance and stability. Higher values of the time constant

will result in instability of the system due to modes associated with both electrical and

mechanical systems.

6. Tuning of the control parameters of the wind energy conversion unit should be carried out

at higher loadings (higher operating speeds) since variations in control parameters cause

significant movements of the system eigenvalues at higher loadings of the unit.

3.4.2 MODULE : VSC-UTILITY GRID

1. A control scheme for the VSC-Utility grid system module has been presented based on the

traditional control approaches using linear PI compensators.

2. A synchronous reference frame based model of the VSC-Utility grid module with the

associated control scheme has been developed and is presented in appendix D. The model

takes into account dynamics associated with the PLL, network and the sensors.

3. Eigenvalue sensitivity analysis of the system module with the proposed control scheme has

been presented with respect to steady state operating point and with respect to control

parameters.

4. Results from linear analysis have been verified through digital simulations of the detailed

model of the VSC-Utility grid module in PSCAD/EMTDC (given in Appendix D).

The following conclusions are drawn based on the results of the linear analysis in

MATLAB/SIMULINK and the simulations results from PSCAD/EMTDC:

1. The proposed model of the VSC-Utility grid system in the synchronous reference frame

captures the dynamics of the module in sufficient details and therefore provides accurate

results, which have been validated using results from the detailed system model in

PSCAD/EMTDC. Stability issues therefore can be investigated with confidence using the

linearized model obtained from the proposed fundamental frequency nonlinear model of the

system module.

2. PLL dynamics play an important role in the stability investigation of the system particularly

in the inverter mode of operation.

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3. Sensor dynamics represented by an LPF in the feedback loops with a sufficiently small time

constant (3ms) do not affect stability properties of the system.

4. The VSC-Utility grid system is stable in both the rectifying and in the inverter mode of

operation with the control scheme utilizing linear PI compensators.

5. THD of the PCC voltage and the injected current by the VSC are within the limits

recommended by [55] (<0.02% and <0.05% respectively).

6. The rms voltage of the regulated load bus remains within the performance bounds specified

by the ‘no-interruption in function region’ of the ITI curve for all load-switching

conditions.

7. Parametric analysis of the system module shows that mode 3 will cause instability for low

values of the proportional constant in the inner current regulators of the VSC-Utility grid

system.

8. Of all the control parameters in the VSC-Utility grid system module, the proportional

constant of the inner current regulators has the greatest influence on the dominant

oscillatory modes. Higher values for the proportional constants of the compensators in both

the outer dc and the inner current regulation loops are suggested to increase damping of the

dominant oscillatory modes.

9. Tuning of controllers for the VSC-Utility grid system could be done while in no load

operation (active power exchange is zero or minimal) as suggested by the operating point

and parametric sensitivity analysis of the eigenvalues of the linearized system.

3.4.3 MODULE : BATTERY STORAGE AND DC-DC CONVERTER

1. Control scheme for the storage and dc-dc converter system using CPM duty ratio control

and linear PI compensator has been presented.

2. A detailed mathematical model of the module with the associated control scheme has been

developed and is given in appendix E.

3. Eigenvalue sensitivity analysis with respect to operating point and with respect to control

parameters has been presented for both buck and boost mode of operation of the dc-dc

converter.

4. Results from the linear analysis have been confirmed through digital simulations of the

detailed nonlinear model of the unit in PSCAD/EMTDC.

The following conclusions are based on the results of the linear and nonlinear analysis:

73

1. The battery storage and dc-dc converter system module is stable under the proposed control

scheme in both buck and in boost modes of operation.

2. DC bus voltage is tightly regulated (within ±0.3% of the nominal) with the selected control

parameters (given in appendix A) in both modes of operation of the dc-dc converter for

large step changes in the load current at the high voltage dc bus.

3. It is concluded that selection of the proportional constant pdcK and the integral constant

idcK requires careful considerations and should take into account possible interactions with

the oscillatory modes in the VSC-Utility grid system.

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CHAPTER 4

SUPERVISORY HYBRID CONTROL

his chapter presents a supervisory hybrid control strategy for the automatic control of

the wind energy conversion and storage system. It gives an overview of the hybrid

control systems and the mathematical formalisms that have been developed for modeling such

systems. Hybrid automata based model of the wind energy conversion and storage system has

been presented and a supervisory hybrid control scheme for the system has been proposed. This

is followed by an overview of the transition management required in the satisfactory operation of

such a hybrid control system. Details of the management strategies for operating state and mode

transitions used in conjunction with the proposed supervisory hybrid control scheme are given at

the end of the chapter.

4.1 HYBRID CONTROL SYSTEMS

A hybrid control system consists of both continuous and discrete valued states. Both these states

influence the dynamic behavior of the system. Hybrid systems embrace a wide range of

applications from process control to aerospace to power systems [22]-[27]. Such a control

paradigm of real world systems is appealing from several perspectives, some of which are:

1. Performance that exceeds any fixed classical or nonlinear smooth controller e.g.

• Optimality

• Adaptation

• Stability

2. Performance that reflects multiple objectives e.g.,

• Response speed

• Accuracy

• Robustness

• Disturbance rejection

3. Performance that respects state and control constraints

For a detailed discussion of the above, the reader is referred to reference [19].

T

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While classical control represents a balanced trade off between multiple performance objectives

using a single feedback function, a hybrid control is used to achieve multiple objectives by

utilizing a set of a priori specified family of feedback functions. Neither a linear nor a nonlinear

control law can guarantee performance objectives over the entire range of operation of a large

number of nonlinear physical systems.

Besides the growing complexity of physical systems, modeling and control complexity of

such systems make modular and decentralized control architecture also more appealing. The

complex system is thus divided into smaller pieces that easily lend themselves up for treatment

with classical modeling and control tools. The different pieces are then put together to form the

larger control system. Coordination among the different pieces of a complex system or different

controllers of a single system is achieved through a supervisory control layer. There is a large

body of literature available on the subjects, both hybrid systems and supervisory control, some of

which are given in the references [63]-[71].

4.2 HYBRID MODEL OF THE STUDY SYTEM

Development of a comprehensive mathematical formalism for hybrid systems is still an active

field of research [20], [71], [72]. There are basically three types of frameworks available for the

study of hybrid control systems [20]:

1. Equation based models

2. Models based on Finite State Machines (FSM)

3. Petri Nets formalism

The first modeling framework has roots in system science while second and third are graph

theoretic models from computer science. A recent development is the hybrid automaton, which is

an extension of the FSM and has found widespread acceptance [20]. Varying version of this

framework have been reported in the literature, however both discrete events and continuous

time dynamics are given in sufficient detail such that the resultant model captures most of the

properties of a hybrid system.

In this research work a formal representation of the system has not been attempted since our

objective is the validation of operation of the wind energy conversion and storage system under

the proposed supervisory hybrid control scheme through nonlinear time domain simulations.

Consequently hybrid modeling of the subject wind energy conversion and storage system is not

76

explicitly given in mathematical terms, rather through graphical representation in the form of

hybrid automata.

4.2.1 FINITE HYBRID AUTOMATA

In developing the system STD shown in Figure 2.2-1, it had been assumed that the operating

state changes instantaneously. This however is a gross simplification. Consider the Finite Hybrid

Automata (FHA) of the wind energy conversion and battery storage system shown in Figure

4.2-1, which has been developed from the STD of the system by incorporating two transient

operating states of FOS (Fault Operating State) and SOS (Synchronization Operating State) and

an Over Current Control scheme (OCC). The OCC operation will involve control of the VSC as

a current source using Hysteresis Space Vector Modulation (HSVM) for gating signal

generation. The hybrid switching and control of the VSC has been described in section 4.3.3.

Appendix B describes the process of arriving at the FHA of the system shown in Figure 4.2-1.

The wind energy conversion and storage system has two operating modes as discussed in

CHAPTER 2. While in grid-connected mode, in any operating state, the system may experience

transient operating conditions as a result of either some load switching or due to some fault. Both

these transients may either be internal or external to the wind energy conversion and battery

storage system and may cause violations of performance bounds or violation of the VSC rating

limit or both.

Violation of the performance bounds and/or VSC rating limit due to normal disturbances in

the system will result in the activation of the OCC operation of the VSC. If performance

violations are a result of a utility side fault disturbance (D = 1) then the system will immediately

transition to the transient operating state FOS (operating state #10). During FOS operating state

the VSC will also be controlled using the OCC scheme. If the disturbance is persistent and the

rms voltage at the PCC crosses the preset bounds within the upper and lower voltage bounds

given by the ITI curve, then the system will go into the off-grid mode of operation otherwise

after a short stay in the FOS will return to the original operating state in the grid-connected mode

with an active OCC control scheme of the VSC.

A situation similar to the FOS in the grid-connected mode can be described by defining a

fault operating state in the off-grid mode of operation caused by an internal disturbance (ID).

That case however, is outside the scope of this work.

77

Mode transition from on-grid to off-grid operation may either be direct (pre-planned) or due to

some disturbance (accidental). The system will change operating modes through the transient

operating state FOS when mode transition is triggered by a disturbance i.e. by a fault on the

utility feeder. The wind energy conversion and storage system can transition to any of the

operating state #2 (Standby), #3 (Storage) or #4 (WECU + Storage) while changing operation

from on-grid to off-grid mode. Pre-planned transitions from on-grid to off-grid mode (S = 0, D =

0) will be direct and will not involve the transient fault operating state #10 (FOS).

Mode change from off-grid to on-grid is a controlled transition in which the system will go

through the transient operating state SOS (operating state #5). The wind energy conversion and

storage system can proceed to any of the two operating states #6 (WECU + Storage + Utility) or

state #9 (Storage + Utility) depending on the availability of the wind energy conversion unit

(WECU). Any disturbance internal or external during such a controlled transition through the

transient operating state SOS that may result in violation of performance bounds will cause the

system to fall back into the off-grid mode of operation and immediately to proceed to shutdown

if the disturbance is permanent and internal to the wind energy conversion and storage system.

However no internal faults have been simulated.

78

Figure 4.2-1: Finite Hybrid Automata (FHA) of the wind energy conversion and storage system

79

4.3 SUPERVISORY HYBRID CONTROL OF THE STUDY SYSTEM

Supervisory control is required to coordinate the application of the control schemes meant for the

operation of the wind energy conversion and storage system in the various operating states

depicted by the FHA in Figure 4.2-1. Supervisory control is also needed to steer the system from

grid-connected mode to the off-grid mode of operation and vice versa according to the route plan

given by the FHA and to ensure that power quality remains within the steady state and transient

specifications given in section 2.4. The supervisory control will not only be acting on the

primary and secondary regulators but also the control plant itself, in this case the wind energy

conversion and storage system, to ensure proper system performance during preplanned and

accidental state transitions.

4.3.1 SUPERVISORY CONTROL REQUIREMENTS

To achieve coordination among the different possible control schemes and to ensure that the

system performance remains within the specified limits, the supervisory control is required to

manage the following based on the available local information in the wind energy conversion

and battery storage system:

1. Provide steady state and transient power management as outlined in section 2.1.1

2. Provide load management during islanded operation according to the available capacity of

the energy sources in the wind energy conversion and storage system as outlined in section

2.1.2.

3. Provide suitable input reference signals to the primary regulators.

4. Provide system ride-through capability and switch-overload protection during temporary

faults on the utility system by switching between Sinusoidal Pulse-Width Modulation

(SPWM) and Hysteresis Space Vector Modulation (HSVM) based gating and control of the

VSC. The hybrid switching and control of the VSC has been described in section 4.3.3.

5. Manage switching among the different candidate controllers (or control schemes) suitable

for the control objective at hand, for all the solid state switching devices.

6. Provide suitable actions to keep PCC or load bus voltage excursions within the performance

specifications outlined in section 2.4. The supervisory actions may either be on the

regulators (or control schemes) or on the plant itself, e.g. opening of the tie circuit breaker

to isolate the wind energy conversion and battery storage system from the utility grid in the

case of an external fault.

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4.3.2 SUPERVISORY HYBRID CONTROL PHILOSOPHY

As outlined in the power management strategy in section 2.1.1, the storage element will act both

as a sink and a source for the wind energy conversion and battery storage system during steady

state as well as in transient operating conditions during off-grid mode of operation. In higher

wind conditions when storage element is full up to its capacity, instead of operating the wind

turbine at suboptimum level, a dc or ac side dummy load could be switched in. If this

arrangement is followed and a dc dummy load is implemented then both the VSC and the dc-dc

converter could have lower MVA capacities with respect to the maximum power generation limit

from the wind turbine. System optimization aspects however have been ignored in this thesis and

no dummy load is considered. It is assumed that the wind energy conversion unit has a maximum

rating corresponding to the turbine power curve i.e. 1.2 per unit while both the storage and the

VSC are rated at 1.3 per unit.

In grid-connected mode of operation all the generated power will be transferred to the utility

side as and when available except for the conditions where the storage element needs to be

topped up. Thus during charging, or discharging in the case of overcharge (an assumption),

storage element will become interactive with the rest of the system. All power transients during

this mode of operation will be dumped onto the utility grid except when the instantaneous power

rating of the utility-side converter may exceed its limit or when the dc bus voltage moves outside

of the band between the maximum and the minimum allowable values. In that case, part of the

generated power will be diverted to the storage element. This may happen during initial start-up

of the wind turbine or during peak generation periods as also during system transient conditions.

With the normal capacity factor of 42% or less for the present generation of wind turbines, this

situation will arise infrequently except for the start-up periods where it is still possible to

formulate a control strategy that brings down the wind energy conversion unit to the optimum

speed level while limiting its power output levels to those manageable during the particular

operating conditions. This again will involve some sort of hybrid control where possibly the

control reference speed is increased to reduce the output power and then gradually decreased to

the optimum level to contain the amount of power extracted from the WECU. In this thesis

control of the WECU has not been configured to add into the transient stability management of

the wind energy conversion and storage system.

81

The following points have been kept in mind while designing a supervisory hybrid control

scheme for the wind energy conversion and storage system:

1. System is started up using storage element alone

2. After startup the system should be able to serve the load or connect to the grid directly as

the case may be

3. Various component ratings should be respected during normal or abnormal operation of the

wind energy conversion and storage system (e.g., during a fault on the utility feeder)

4. The wind energy conversion and storage system should be able to follow the FHA with

minimal transients during movement from one operating state to another in both on-grid

and off-grid mode of operation including transitions between the two modes

5. The wind energy conversion and storage system should be able to hookup with the utility

grid during load switching and other normal system disturbances e.g. voltage dips on the

utility or the wind energy conversion and storage side of the tiebreaker, during and

immediately after synchronization

6. The system should have fault ride-through capability during utility side temporary faults

provided performance limits are not violated in which case the wind energy conversion and

storage system will be disconnected from the main utility feeder and will continue

operation in the islanded mode

7. The outer dc voltage regulation loop of the VSC will be used for regulating the dc bus

voltage during on-grid mode of operation

8. Storage support during on-grid operation will be utilized only for limiting terminal current

of the VSC and to maintain the dc bus voltage during such conditions. When the dc bus

voltage is within the desirable operational limits then the storage support will come in the

form of charging or discharging during transient disturbances. Storage based dc bus voltage

regulation will take over in case the upper and lower limits of the dc bus voltage have been

violated. The decision to hand over dc bus voltage regulation to the control loop associated

with the storage element will be based on an inner and outer hysteresis band around the

nominal value of the dc bus voltage. Control will be transferred to the storage based

regulation loop when the outer band is violated and handed back over to the VSC based

control scheme once the dc bus voltage falls back to within the limits of the inner band.

82

Using a single control law, whether based on linear or nonlinear control techniques, to achieve

the above stated objectives is not possible. Even linear control becomes nonlinear when various

control limitations are considered e.g. rating limitations of the various components. The strategy

adapted here is to analyze various operating regimes of the system and devise a suitable

mechanism to switch between candidate controllers and/or shape their reference inputs such that

the wind energy conversion and storage system takes the desired route and operates within the

limits of the prescribed performance criteria.

The state of the art in the hybrid control systems at this stage of its development does not

provide any analytical tools to synthesize hybrid supervisory control for the wind energy

conversion and storage system nor does it provide any analytical means for investigating system

stability and performance under such a supervisory control scheme. In the absence of any

analytical means and theoretical guarantees, therefore the only viable alternative to ensure proper

system operation is to imagine all possible operating conditions that may be encountered while

the system follows the proposed hybrid automata given in Figure 4.2-1 using time domain

simulations of the detailed nonlinear system and to devise suitable supervisory control action that

will be taken during such conditions. In this thesis electromagnetic transients simulation software

PSCAD/EMTDC has been used for the purpose.

A crafted transition management strategy based on the analysis of the time domain

simulation results will be required for proper system operation under the proposed FHA model of

the wind energy conversion and storage system. In the following paragraphs various control and

transition management strategies have been described which have been used in conjunction with

the proposed supervisory hybrid control scheme for the automatic control of the study system.

4.3.3 HYBRID CONTROL OF VSC: VALVE SWITCHING CONTROL

A hybrid control and gating scheme is proposed for the control of the VSC to impart fault ride-

through capability to the wind energy conversion and battery storage system during grid-

connected mode of operation. This objective is achieved by operating the VSC as a controlled

current-source with Hysteresis Space Vector Modulation (HSVM) based control scheme. Under

‘normal operating conditions’ however, the VSC will be operated as a current regulated voltage-

source with Sinusoidal Pulse-Width Modulation (SPWM) based control scheme.

In the grid connected mode during normal operating conditions, SPWM based control of the

VSC is preferred for the following reasons:

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1. Higher converter efficiency due to relatively low switching frequency requirements

2. adequately fast control response

3. Low amplitude sideband harmonics around the switching frequency and its integral

multiples which are, in the frequency domain, separated by a large distance from the

fundamental frequency and are easily filtered out if required to achieve steady state

performance objectives [74].

Under transient fault operating conditions however, stability of the converter operation takes

precedence over steady state considerations. In the FOS operating state during fault conditions

on the utility side (D = 1) and during OCC operation for limiting converter output current during

normal system disturbances, the VSC will be driven as a controlled current source with HSVM

based control scheme. Control of the VSC using HSVM has the following advantages [74]:

1. Fast transient response

2. Immunity to dc bus voltage ripple

3. Insensitivity to system parameters

4. does not require system phase information

5. Inherent overcurrent protection

To achieve transient performance objectives as outlined in section 2.4.2, a simple hysteresis

based valve switching, which drives the converter as a controlled current source could be used.

Conventional hysteresis control however causes unnecessary switching operations resulting in

high switching frequency. The high switching frequency gives rise to concerns for thermal

stability of the VSC and its associated gate-driving circuitry [75]. Besides, operating frequency

of the present generation of IGBT switches is limited to about 10 kHz for up to 1 MW power

handling capacity [76]. HSVM based switching has been shown to have considerably lower

operating frequency than conventional hysteresis based switching control for the same width of

the hysteresis band [77]. Different valve switching techniques based on Space Vector

Modulation (SVM) have been proposed for improved response with reduced switching

frequency [78].

Figure 4.3-1 shows the proposed hybrid switching and control scheme for the VSC in which

the two gating strategies employed are:

1. Sinusoidal Pulse-Width Modulation

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Figure 4.3-1: Hybrid switching control of the VSC

85

2. Space Vector Modulation

Details of the SPWM based control scheme are provided in section D.1.6 in appendix D, while

implementation details of HSVM are given in reference [73]. In this thesis, the converter

switching frequency has been restricted to10 kHz during HSVM based gating control.

The proposed hybrid switching and control of the VSC will utilize the two switching

strategies interchangeably to ensure proper system operation during both steady state and

transient system operating conditions. SPWM based control will be used to satisfy steady state

operating requirements while HSVM based control will be used to provide stability and

continuity of operation during and after the temporary transient fault conditions.

Transition management involving re-initialization and parameter scheduling for switching

between SPWM and HSVM based control schemes has been described in sections 4.3.4.1 and

4.3.4.2. Reactive power support will be suspended during transient fault conditions to limit

reactive current contribution by the converter. This will be achieved by resetting the PI

compensator (in Figure 4.3-1) in the rms voltage control loop to zero during such conditions.

This strategy will make sure that the VSC would cause minimum or no interference with the

operation of the feeder protection system.

The switching decision between the two control schemes will be based on the following

events:

1. Violation of single phase peak voltage limits

2. VSC capacity violation

The single-phase peak voltage will be determined using the ‘Voltage Envelop’ tracking of the

individual phases by utilizing the concept of ‘energy operator’ outlined in [44].

Figure 4.3-2 illustrates the need for hybrid control and switching scheme as outlined above.

The case study presents simulation results obtained using PSCAD/EMTDC in which the system

is initially operating in the operating state # 7 (WECU + Utility). Two capacitor banks (each

0.75µF, delta configured) are connected at the PCC. A 0.76 per unit static load with a power

factor of 79% lagging and one induction motor load (0.2 per unit with rated load torque) are

connected to the load bus. The initial dc output current of the WECU is 0.76 per unit and the rms

voltage at the PCC is being regulated at 1.0 per unit.

86

Referring to Figure 4.3-2, three successive single line to ground faults are applied on phase ‘a’

(A-G fault) at three different locations along the utility feeder. The first fault event occurs at the

PCC at time t = 0.26s, the second event occurs at mid point along the utility feeder at time t =

0.97s and third event happens at the start of the utility feeder at time t = 1.67s. In each case the

fault duration is 5 cycles with a fault resistance of 2Ω. The three fault events are marked on plot

2 as 1, 2 and 3. Plots on the Left Hand Side (LHS) represent the case when only SPWM based

control and gating scheme is used while plots on the Right Hand Side (RHS) give results for the

case when hybrid control of the VSC is excersized.

Figure 4.3-2: Operation of the VSC with only SPWM and with hybrid valve switching control, 1) a phase voltage at the PCC, instantaneous value and amplitude 2) fault current 3) reference and actual phase ‘a’ converter current

Plot 3 in Figure 4.3-2 shows that the reference is faithfully tracked during fault condition

with HSVM based control scheme of the VSC and hence it is possible to limit the output current

of the converter in such operating conditions. The control scheme based on SPWM on the other

hand fails to track the reference signal during such single line to ground fault operating

conditions and hence fails to restrict the output current of the converter. The situation is much

worse for phase faults and multiple phases to ground faults.

Figure 4.3-3 shows duty ratio and gating frequency of the upper switch connected to ‘a’

phase in the three-leg VSC converter before, during and after the temporary A-G fault at the

PCC as shown in Figure 4.3-2, with a corresponding converter switching control sequence of

SPWM-HSVM-SPWM. The duration of OCC operation (HSVM) is about 140ms.

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Figure 4.3-3: Operation of the VSC under hybrid valve switching control, 1) cycle-to-cycle based instantaneous duty ratio and the average duty ratio over a power cycle 2) instantaneous switching frequency and the average frequency over a power cycle

4.3.4 CONTROL TRANSITION MANAGEMENT

During transition between any two permissible operating states as allowed by the FHA, the

system variables may evolve undesirably due to the sudden change in the control action due to a

change in the control laws accompanying the state change. This is almost always the case due to

accidental transitions caused by system faults. A transition management strategy is therefore

required to keep the state variables within permissible operating bounds during such transient

conditions [79]. These bounds are defined based on the stability margins, the ratings of the

system components and operating philosophy of the system among other considerations. Lastly

the duration of such a transitional stage, in this research work, is governed by the ITI (formerly

CBEMA) curve defined for the ride through capabilities of sensitive electronic equipment.

Transition management is required both for pre-planned and accidental state transitions. A

useful reference for transition management is provided in [79]. Various means of bumpless

transfer between different regulators have been used in practice [80], [81] e.g.:

1. Output blending

2. Parameter blending

3. Transient management

4. Gain scheduling

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5. State initialization

In the research work presented in this thesis, gain scheduling and state initialization have

been used, besides input reference shaping and forward fed signal transfer, as means for a

smooth transfer between the active and the latent controllers.

4.3.4.1 State Initialization

The VSC control uses the same control laws but different switching techniques for situations

where regulation error or other performance and control objectives are violated (e.g. maintaining

PCC rms voltage level). Referring to Figure 4.3-1, for a smooth transition from HSVM to

SPWM based switching control of the converter, the output of the PI compensators in the inner

current loops (PI 2 and PI 4) are reinitialized when valve switching control is transferred from

the former to the latter. For this purpose the terminal voltage of the converter could be monitored

to provide the required resetting values. However beside a delayed reponse of the sensors,

accurate determination of the qd components of the converter terminal voltage space vector is

difficult due to large harmonic content of the VSC terminal voltage. This arrangement also

requires an additional set of voltage sensors at the converter terminals.

The qd components of the terminal voltage space vector can be accurately estimated from

the (known) gating signals to the converter. The converter gating signals can be used to

determine the αβ composition of the space vector commanded of the converter [77]. The qd

components can then be calculated from the αβ composition of the terminal space vectors of the

VSC, using the following transformation:

−=

β

α

θθθθ

v

v

v

v

d

q

cossin

sincos

3

2 (4-1)

where θ is the PLL derived angle of the voltage space vector at the PCC.

The qd reference frame based voltage signals are then passed through a LPF to obtain a

smooth initializing signal. A time constant of 10ms has been used for the LPF for a smooth and

reasonably fast response. Figure 4.3-4 schematically shows the arrangement for obtaining the

resetting values of the inner current regulators during the OCC based operation of the VSC.

Referring to Figure 4.3-1, inverse transition between the two types of switching strategies

i.e. from SPWM to HSVM based switching does not involve any reinitialization since the same

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outer control loops provide reference signals to the inner current regulators of the SPWM based

control scheme and to the space vector generator of the HSVM based gating control.

Figure 4.3-4: Re-initialization of inner current regulators for smooth transition from HSVM to SPWM based valve-switching control

Referring to Figure 4.3-4, the reference current signals are transformed back to the abc

coordinates using the PLL estimated phase information of the PCC voltage space vector. The

reference currents in the abc refrence frame are then compared with the feedback signals from

the converter terminal current sensors. The error signal is fed to a space vector generator, the

details of which are provided in reference [73], for gating signal generation during HSVM

operation. In this thesis, the maximum switching frequency during HSVM operation has been

restricted to 10 kHz. To achieve this limit the input to the space vector generator is sampled at

the minimum required samping frequency of 20 kHz (Sampling Theorem1).

Figure 4.3-5 shows simulation results corresponding to the first fault event (single line to

ground fault at PCC) shown in Figure 4.3-2. The first plot shows orthogonal components of the

reference voltage which are the output of the inner current regulators while the second plot

shows orthogonal components of the converter output currents. The duration of the OCC

operation (HSVM on duration) is shown on both plots. With the start of the OCC operation, the

inner regulators are initialized to follow the signals vqt(reset) and vdt(reset) which are the output of

the initialization scheme shown in Figure 4.3-4. At the end of the OCC operation, SPWM based

control scheme takes over and at the same time rms voltage control of the PCC voltage is

resumed. It can be seen that control transition from HSVM based control scheme to the SPWM

based control scheme is transient free with the proposed re-initialization scheme. 1 Also known as Whittaker–Nyquist–Kotelnikov–Shannon sampling theorem

90

Figure 4.3-5: Re-initialization of inner current regulators, 1) duration of the OCC operation and orthogonal components of the converter terminal voltage for resetting of inner current regulators 2) duration of the OCC operation and the orthogonal components of the terminal current of the converter

4.3.4.2 Parameter Scheduling

Referring to Figure 4.3-1, adaptation of the first order LPF in the rms voltage control loop

consists of reducing the filter time constant during HSVM based switching control (1.0 ms used

in the subsequent simulations). At the end of the HSVM based control event, the time constant of

the LPF is adjusted back to a relatively high value (10 ms) to contain control activity in order to

achieve (quasi) steady state harmonic limits imposed during normal system operation. This

action on the LPF in the rms control loop makes sure that the feedback signal to the control loop

is the current value of the PCC rms voltage when the voltage regulation loop becomes active

again.

4.3.5 MODE TRANSITION MANAGEMENT

Mode transition management becomes necessary when the transition is caused by a fault on the

utility side in the case of on-grid to off-grid transition and also when the wind energy conversion

and storage system goes from off-grid mode to on-grid mode of operation. The former is an

accidental transition and has been taken care of by introducing the additional transient operating

state of FOS while the latter is a controlled (pre-planned) transition, which requires proper

synchronization procedure during the SOS operating state.

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4.3.5.1 Synchronization

The procedure given in [82] has been used for synchronization control and is shown in Figure

4.3-6. Referring to Figure 4.3-6, the q components of the voltage space vector on either side of

the (open) tiebreaker are used by a PI compensator to alter the reference operating frequency of

the wind energy conversion and storage system (islanded mode of operation) in order to align the

voltage space vector of the PCC with that of the utility feeder at the PCC.

In order to minimize transients the difference between the d components of the PCC voltage

space vectors on either side of the tiebreaker is brought to within 3%. For this purpose the

auxiliary loop in the reference input containing an integrator as shown in Figure 5.5-1 is disabled

by initializing the integrator to zero and the reference signal is switched to the measured rms

voltage signal at the PCC from the utility side of the tiebreaker. Regulation of the load bus

voltage is delayed for 100ms after closing of the tiebreaker to allow for any transients caused by

the synchronization to subside.

Figure 4.3-6: Frequency control during synchronization

As soon as the wind energy conversion and storage system is successfully synchronized with

and connected to the utility grid, HSVM based valve switching control scheme will take over

control of the VSC gating signals. This is done to make sure that performance remains within

limits in the presence of temporary transient disturbances caused by load switching and/or

temporary utility side disturbances immediately after the wind energy conversion and storage

system is latched on to the utility feeder. Also during the HSVM based control immediately after

synchronization, the transition between the forward fed signals in the two dc regulation loops is

completed. This is further explained below:

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4.3.5.1.1 Signal Transfer

The PI compensators in the dc regulation loops belonging to the battery storage and dc-dc

converter and the VSC-Utility grid modules, are initialized to zero when they are switched

among themselves. However, the forward fed signals used for power transfer are controlled in a

manner that they are gradually transferred from zero to maximum from the storage based

regulator to the VSC based regulation loop when the latter is required to take over after

synchronization. At the end of the signal transfer event control is handed over to the VSC based

regulator. On the other hand no special transition management is required when VSC based dc

regulator hands over control to the storage based dc regulator since the latter has a much faster

response. In this case forward fed signals are directly transferred to the storage based dc

regulation loop.

4.3.5.2 On-grid to Off-grid Transition

During normal on-grid mode of operation with SPWM valve switching control, the VSC is

controlled as a current-regulated voltage source. In the off-grid mode of operation however, the

VSC is operated as a constant frequency, controlled voltage source whose magnitude is directly

controlled based on the feedback signal from the PCC rms voltage. For transition between on-

grid to off-grid mode of operation, the PI compensator of the PCC rms voltage regulator (Figure

5.5-1) is re-initialized. The initialization value comes from the output of the active current

regulator ( qtrv in Figure 4.3-1) used in the grid-connected mode of operation after passing it

through a first order LPF with a time constant of 50ms.

Pre-planned transition will cause the wind energy conversion and storage system to switch

operation directly from on-grid to off-grid mode. In the situation where the transition is caused

by faults on the utility side the wind energy conversion and storage system will go through the

transient operating state of FOS in which HSVM based gating control of the VSC will be active

to contain the amount of current contributed by the VSC. The decision to disconnect the utility

feeder during fault operation will be based on the violation of the steady state operating limits of

the three phase rms voltage at the PCC (±10% of nominal) or the peak voltages of any two

phases being simultaneously lower than 70% of the nominal. This is necessary in order to be able

to keep the rms voltage within limits specified by the ‘no interruption in service’ region of the

ITI curve.

93

4.4 FLOW CHART

The proposed supervisory hybrid control is inevitably a software enabled control scheme.

Software implementation of the supervisory hybrid control scheme will vary depending on the

implementation platform and the software development philosophy. A simplified, self-

explanatory flow chart of the supervisory control scheme is given in Figure 4.4-1.

Figure 4.4-1: Simplified flow chart for software implementation of the supervisory hybrid control scheme

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4.5 SUMMARY

This chapter describes the supervisory hybrid control scheme for the wind energy conversion and

battery storage system. After reviewing the state of the art in hybrid control system, the chapter

gives details of the hybrid automata based model of the study system and provides strategies for

control and operating state transitions of the system.

The following are the main contributions of this chapter:

1. Finite hybrid-automata based model of the wind energy conversion and storage system has

been presented.

2. Supervisory hybrid control requirements have been defined.

3. Based on the specified requirements, a supervisory hybrid control scheme has been

proposed.

4. Control scheme and operating state transition management strategies have been developed,

which include:

a. Hybrid switching and control of the VSC utilizing SPWM and HSVM based

gating signal generation during normal and transient fault operating states of the

study system, respectively

b. Compensator initialization mechanisms for bumpless transfer between the active

and latent controllers

c. A simple adaptation mechanism for the time constant in the LPF of the rms

voltage control loop during on-grid mode of operation

d. Strategy for the transfer of reference control signals during switching between the

dc voltage regulators associated with the VSC and the dc-dc converter control

schemes

e. Transition management strategy for accidental mode transitions

f. Transition management strategy for off-grid to on-grid mode transition

5. A simplified flow chart for the software implementation of the supervisory hybrid control

scheme has been presented.

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CHAPTER 5

SYSTEM OPERATION UNDER NORMAL CONDITIONS

n this chapter operation of the wind energy conversion and storage system has been

investigated for performance and stability through digital time domain simulations

studies of the detailed nonlinear model(s) in PSCAD/EMTDC. The chapter deals with only those

operating states that are described by the FHA of Figure 4.2-1 and which involve a combination

of the three system modules that have been investigated for stability and performance in

CHAPTER 3. The objective is to study the interaction of the control laws that have been devised

for the individual system modules and which have been configured to achieve stability and

performance objectives of the wind energy conversion and storage system in the various

operating states shown in Figure 4.2-1, under normal operating conditions. The normal operating

conditions refer to operating scenarios which may involve load switching and switching of

control schemes but these do not involve transitions between operating states and do not involve

any fault scenarios.

5.1 STUDY CASES

Table 5.1-1 lists the operating states which have been investigated in this chapter. It also lists the

objectives of the reported study cases.

Table 5.1-1: Study Cases and Objectives of the Performance Investigation; System Operation Under Normal Conditions

Operating State

# System Configuration Objectives of the Performance Study

7 WECU + UTILITY

Steady state operation, hybrid valve switching control,

parameter scheduling, reactive power control with dynamic

limits2, step responses, switching events, stochastic wind

conditions

4 WECU + STORAGE (off-

grid)

Steady state operation, step responses, load and capacitor bank

switching events, battery charging and discharging operations

2 Based on the instantaneous active output current of the converter in order to be able to limit total output current of the VSC

I

96

9 STORAGE + UTILITY Steady state operation, load switching, response to external dc

current disturbances, step responses (various)

3 STORAGE + VSC

Steady state operation, load switching events, response to

external dc current disturbances, step responses, reference

shaping

6 WECU + STORAGE +

UTILITY

Steady state operation, step responses, load and capacitor bank

switching events, stochastic wind conditions, battery charging

and discharging operations, reactive power control with dynamic

limits (VSC)

5.2 WIND ENERGY CONVERSION UNIT-UTILITY GRID

This section provides simulation results of the operation of the wind energy conversion and

storage system in the operating state #7 (WECU + Utility, Figure 4.2-1). Control structure of the

wind energy conversion and storage system in this operating state is a combination of the control

schemes used for the two system modules namely; i) wind energy conversion unit and ii) VSC-

Utility Grid which are given in Figure 3.1-1 and in Figure 4.3-1 respectively.

5.2.1 CONTROL SCHEME

Figure 5.2-1 gives the single line schematic and control structure of the wind energy conversion

and storage system during operating state #7 (Figure 4.2-1) in which the wind generated power is

delivered to the utility grid through the VSC interface. The load may or may not be present

which constitutes different operating conditions within this operating state. Figure 5.2-1 also

shows the hybrid switching and control strategy used for the VSC as explained in section 4.3.3.

Referring to Figure 5.2-1, the external current signal in Figure 4.3-1 has been replaced with

the actual output current from the thyrsitor rectifier unit. Proper operation of the WECU and the

VSC is ensured by the dc bus voltage regulator which is part of the VSC control scheme. The

wind generated power is transferred to the utility grid as and when available using the inner

current regulator of the grid side converter. The objective is to minimize dc bus voltage

variations in order to provide power tracking and maintain stability of WECU.

The decision to switch between SPWM and HSVM based control and gating schemes is

based on the amount of the total current delivered by the converter. When the converter total

current output exceeds 1.29 per unit, HSVM based gating and control scheme is enabled which

97

Figure 5.2-1: Single line schematic and control structure of the study system in the operating state #7 consisting of the two system modules i) WECU and ii) VSC – Utility Grid

98

remains active till the converter output current drops to 1.28 per unit with an off delay time of

100ms. Reactive power support is enabled as long as the converter active current output is less

than 85% of the converter current limit which has been set at 1.3 per unit. The reactive current

limit of the converter is dynamically adjusted based on the active current output of the converter.

Once disabled, reactive power support is not resumed until active current output of the converter

drops to 75% of its maximum limit. During the period when reactive power support is suspended

(by reseting the rms voltage compensator to zero) the LPF time constant is changed from 10.0ms

to 1.0ms so that control activity can resume with respect to the most recent value of the rms

voltage feedback signal.

In practical applications, converters are usually oversized since their controls are generally

not designed (or unable) to restrict their output currents during severe system disturbances e.g.,

during closeup faults in the utility system. With a lower capacity of 1.3 per unit assumed for the

converter in the study system it will be shown that the practice of oversizing converters can be

abandoned by using the hybrid control and gating scheme for the VSC proposed in section 4.3.3,

allowing for more economical solutions to power system problems that require the use of

switching converters. It however will be noticed in the subsequent sections and in CHAPTER 4,

that the selection of suitable converter capacity needs to take into account not only the active

power requirements in the system but also needs to take into account reactive power support that

the converter would be required to deliver during maximum wind power generation periods

under noload conditions. This is effectively an optimization problem requiring solution in the

form of montecarlo simulations in which multiple variables are changed simultaneously to find

optimum sizing of the converter. The optimization problem relating to component sizing has not

been addressed in this thesis.


In the following sections simulation results are presented for different operating scenarios to

evaluate the performance of the wind energy conversion and storage system in the subject

operating state. The following points are common to all these scenarios:

• A permanent capacitor bank of 450µF (39.1kVAR star configured at 480 volts) is

connected to the load bus

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• Two capacitor banks of equal rating (53.85kVAR, 0.25 µF delta connected capacitors

at 13.8kV) have been used at the PCC. One capacitor bank is permanently connected

while the second bank is connected to the PCC as the load increases to reduce reactive

power demand from the VSC.

• Three capacitor banks of equal rating (300µF delta configured) have been used for

excitation control of the induction generator. One capacitor bank is permanently

connected while the other two capacitor banks are connected to the generator terminal

according to a hysteresis based control strategy using generator operating speed as

explained in CHAPTER 3.

• Initially the system is operating at no-load with the VSC delivering 0.64 per unit of

active current qtmri and -0.89 per unit of reactive current dtmri with a total VSC output

current of 1.1 per unit. The initial dc output current of the wind energy conversion unit

is 0.66 per unit with a constant average wind speed of 6.0 m/s at the turbine hub.

5.2.2.1 Steady State Performance

The steady state operating conditions are the same as the initial conditions described above. With

the SPWM based control scheme, the THD for the converter current is less than 0.06% while that

for the PCC voltage is less than 0.03%. These values are well below the steady state performance

limits specified in section 2.4.1.

5.2.2.2 Dynamic Performance

1. Step Changes in Wind Speed

Figure 5.2-2 through Figure 5.2-4 shows system operation for step changes in the input wind

speed. Initial conditions are the same as described in section 5.2.2. Referring to Figure 5.2-2, at

t=7.0s wind speed is step changed from 6.5 m/s to 7.0 m/s. Output power from the WECU

initially decreases to allow for the turbine to accelerate to the higher optimum operating speed.

The active current output of the converter shown in Figure 5.2-3 (plot 1) also decreases with a

corresponding decrease in the reactive current (plot 2). As the output power from the WECU

increases so does the total output current of the VSC (plot 3). When the converter output current

reaches the threshold (1.29 p.u.), HSVM based control and gating scheme of the VSC is enabled

(OCC operation, Figure 4.2-1) in order to limit its output current. Reactive power support from

100

the converter is also suspended as the active current component has reached 85% of the converter

maximum limit. After a preset duration of 100 ms, the converter again starts operation with

SPWM gating and control scheme while reactive power contribution from the converter remains

suspended.

Referring to Figure 5.2-2, at time t = 13.0s, wind speed is further increased in step from 7.0 m/s

to 7.5 m/s. The initial decrease in the WECU output current causes the active current output of

the VSC to fall below the minimum level (75% of the VSC maximum current limit) which

enables reactive power support from the VSC. However the sudden increase in the converter

reactive current causes violation of the converter current limit again enabling OCC operation of

the VSC and at the same time reactive power support is disabled once again. The reactive power

support remains suspended for the rest of the simulation time as the converter active current

output remains above the minimum specified threshold (75% of converter limit) below which

reactive power support is set to resume. Plot 3 in Figure 5.2-3 shows events of the converter

maximum current violation. It also shows the duration of the OCC operation.

Figure 5.2-4 shows the dc bus voltage and the rms voltage at the load bus during step

changes in the wind speed described above. The dc bus voltage is regulated within a very narrow

band (±0.5%) while the rms voltage at the load bus remains within the ‘no-interrruption in

function’ region of the ITI curve.

During the time when a higher reactive current output is demanded of the converter but the same

is limited due to the dynamic limitation on its reactive current output, unwanted interaction arises

(results not shown) between the active and reactive current regulators. This unwanted interaction

is magnified (however contained) due to cross coupling between the two current components and

due to limited response speed of the converter under SPWM based switching scheme. It is

therefore necessary to suspend reactive current contribution during high wind speed regimes. It is

also pointed out that the current control speed regulation scheme is able to shield the wind

energy conversion unit from the effects of the dc bus voltage variations arising out of the

unwanted interaction described above.

101

Figure 5.2-2: Operating State # 7; System Dynamic Performance for Step Changes in Wind Speed, 1) wind speed 2) rotor optimal, reference and actual speed

Figure 5.2-3: Operating State # 7; System response to step changes in wind speed, 1) rectifier output current and active current output of the VSC 2) VSC reactive current output 3) VSC total current output and HSVM on duration

102

Figure 5.2-4: Operating State # 7; System response to step changes in wind speed, 1) dc bus voltage 2) load bus rms voltage

This case study confirms that the proposed hybrid control scheme is stable and enables

system operation within the specified performance limits during operating conditions involving

step changes in wind speed. The dc bus voltage is tightly regulated within ±0.5% of the nominal

value. The VSC can exert direct control on the PCC voltage and using rms voltage signal of the

load bus to to control the PCC voltage gives rise to large transients which however are limited

due to higher time constant of the first order LPF in the feedback loop. A better strategy is

proposed in section Figure 5.5-1 in which the reference signal to the voltage control loop for

regulating rms voltage at the PCC is shaped to provide indirect regulation of the load bus

voltage. This strategy has also been used later in CHAPTER 4 which investigates stability and

performance of the supervisory hybrid control scheme for large transients involving transitions

of the operating state of the study system.

2. Load Switching

Figure 5.2-5 and Figure 5.2-6 give simulation results when the system is operating under load

switching conditions with a constant wind speed at the turbine hub. Initial operating conditions

are the same as given in section 5.2.2. Wind speed is held constant at 6.0 m/s. The various load

switching events are marked on plot 1 in Figure 5.2-5. Switching event of the second capacitor

103

bank at the PCC has also been identified in Figure 5.2-5. It is pointed out that induction motor

loads are connected to the load bus while these are running at almost synchronous speed with

zero load torque.

Figure 5.2-5: Operating State # 7; System Operation under Load Transients, 1) load bus rms voltage 2) dc bus voltage load 3) rectifier output current

Referring to Figure 5.2-5, plot 1 shows the rms voltage at the load bus. At time t = 20.0s the

load bus reference rms voltage signal is step changed from 1.0 per unit to 0.98 per unit and back

to 1.0 per unit at t = 22.0s. As the converter has a higher reactive power support capability due to

low active power delivery from the WECU therefore the load bus voltage is well regulated and

remains within the steady state limits of ±10%. Referring to Figure 5.2-6, HSVM based control

of the VSC is activated due to the connection of motor load ML2 at t = 15.0s (event marked on

plot 1 in Figure 5.2-5) and is caused by a sudden increase in the reactive power demand from the

converter.

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Plot 2 in Figure 5.2-5 shows the dc bus voltage which remains within ±1.0% of the nominal. Step

changes in the dc reference voltage are applied at time t = 24.0s from 1.0 per unit to 1.03 per unit

and back to 1.0 per unit at t = 26.0s. The downward step in the reference dc bus voltage causes

converter output current to reach above 1.29 per unit which invokes HSVM based control of the

VSC for a preset minimum period of 100ms (plot 3 in Figure 5.2-6). Plot 3 of Figure 5.2-5 shows

the rectifier output current which is tightly controlled by the speed regulation scheme of the

generator and provides a constant output power corresponding to the constant wind speed level at

the turbine.

Figure 5.2-6: Operating State # 7; Control performance under load transients, 1) VSC ‘active’ current 2) VSC ‘reactive’ current 3) VSC total current and HSVM on duration

This case also demonstrates the need for hybrid switching and control scheme for the VSC.

HSVM based gating and control of the VSC is invoked when the large induction motor load is

switched in and when a downward step change is commanded in the dc bus voltage. The results

presented in Figure 5.2-5 and Figure 5.2-6 confirm that the proposed control scheme shown in

Figure 5.3-1 is stable and that transient performance of the system remains within the ‘no-

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interruption in function’ region given by the ITI curve. This case also shows that the wind

turbine control provides robust speed tracking and effectively isolates the WECU from the

disturbances on both the dc and the ac side of the VSC. The dc bus voltage remains tightly

regulated which validates the philophosy of the decoupled control design for the wind energy

conversion and storage system.

3. Load Switching and Stochastic Wind

Figure 5.2-7 through Figure 5.2-9 gives simulation results of the operation of the system during

stochastic wind conditions accompanied by load switching events. Initial conditions are the same

as in the previous two cases. Load switching events and step changes in the reference signals of

the rms voltage at the load bus and the dc bus voltage follow the same sequence with the same

time interval between successive events as in the previous case. However unlike the previous

case the sequence of load switching events starts at time t = 3.0s.

The stochastic wind conditions are:

Mean wind speed at the turbine hub: Vmw = 3.5 m/s

Gust component of the wind speed: Vgw = 1.0 m/s with a gust period of 5.0s,

Ramp component of the wind speed: Vrw = 0.5 m/s and a ramp period of 2.0s.

The stochastic wind speed also contains randomly generated noise components [61].

Figure 5.2-7 shows the wind speed level and the corresponding regulated speed of the

generator. At time t = 1.0s wind speed is allowed to change stochastically with the above

mentioned disturbance components. Generator (and hence the turbine) rotor speed follows the

commanded reference speed which is obtained by filtering the high speed components of the

optimal turbine speed corresponding to the wind speed at the turbine hub. It is noted that during

the period when the turbine is accelerating the reference speed is closely followed while during

decelaration this is not the case. The reason is that the generator output power is restricted to 1.2

per unit during its operation. The operation of the WECU over the speed range shown in Figure

5.2-7 also involves switching of the excitation capacitors however these events have not been

shown.

Figure 5.2-8 shows the rms voltage at the load bus and the dc bus voltage during wind

conditions shown in Figure 5.2-7 and with load switching events mentioned earlier. Load bus

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rms voltage remains within the transient specification limits and also within the steady state

limits of ±10% however entails sever variations due to frequent enabling and disabling of the rms

voltage regulator which is caused by large variations in the active output power from the wind

energy conversion unit. The dc bus voltage has relatively large variations however remains

within ±1.5% of the nominal. The large variations in the dc bus voltage are partly due to frequent

enabling and disabling of the reactive power support from the VSC due to its capacity limitation.

It is therefore concluded that within the assumed limitations on the output current of the VSC, a

better control strategy would be to disable rms voltage regulation during stochastic wind

conditions with sever disturbances. This would avoid frequent use of OCC operation in case of

violations of the output current limit of the VSC and would also avoid any unwanted interaction

between the active and reactive current components (caused by the dynamic limit on the reactive

power support as explained in section 5.2.1).

Figure 5.2-7: Operating State # 7; System response during dynamic wind speed and load transients, 1) wind speed 2) generator optimum, reference and actual speed

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Figure 5.2-8: Operating State # 7; System Control during dynamic input wind speed and load transients, 1) load bus rms voltage 2) dc bus voltage

Figure 5.2-9: Operating State # 7; System response to dynamic wind conditions and load transients, 1) & 2) VSC ‘active’ and ‘reactive’ current components 2) space vector magnitude of the VSC current

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The operation of the WECU shown in Figure 5.2-7 through Figure 5.2-9, does not involve OCC

operation of the VSC since the total output current of the converter remains below its maximum

limit of 1.3 per unit (plot 3, Figure 5.2-9). This however may not be true for all wind conditions.

This case study shows that the proposed control scheme for the grid-interactive wind energy

conversion system is stable when the system is operating under the simultaneous wind speed and

load switching conditions. The SPWM based control scheme is capable of tracking the reference

signals under such operating conditions. The dc bus voltage is maintained within 1.5% of its

nominal value and the rms voltage of the load bus remains within the transient performance

limits specified in section 2.4.2.

Referring to the case studies presented above, it is concluded that the proposed control

scheme shown in Figure 5.2-1 devised for the operating state #7 (WECU + Utility) is stable

under all operating conditions and can ensure performance targets specified in 2.4.2.

5.3 WIND ENERGY CONVERSION UNIT-STORAGE

This section presents operation of the wind energy conversion and storage system in the

operating state #4 (WECU + Storage, Figure 4.2-1). In this operating state operation of the wind

energy conversion unit is supported by the battery storage through the bi-directional dc-dc

converter. The objective is to investigate interaction of the control schemes developed for the

WECU system module and the battery storage and dc-dc converter module through time domain

simulations in PSCAD/EMTDC. In this section therefore, the load and the VSC interface are not

part of the system.

5.3.1 CONTROL SCHEME

Figure 5.3-1 shows single line schematic and control structure of the wind energy conversion and

battery storage system. The control structure has been obtained by combining the control

schemes developed for the ‘WECU’ system module which is shown in Figure 3.1-1 and the

‘battery storage and dc-dc converter’ module shown in Figure 3.3-1. Referring to Figure 5.3-1,

the battery storage absorbs the wind-generated power while providing dc bus voltage regulation

to enable proper operation of the wind energy conversion unit. Simulations have been carried out

using the detailed nonlinear model in PSCAD/EMTDC and the results are presented in the

following paragraphs.

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Figure 5.3-1: Single line diagram and control schematic of the study system in the operating state #4 consisting of the two system modules of (a) wind energy conversion unit (b) battery storage and dc-dc converter

110


Figure 5.3-2 shows simulation results when the system is operating under constant and stochastic

wind speed conditions. The initial conditions are given below:

Mean wind speed at the turbine hub: Vmw = 6.0 m/s

Excitation Capacitance: 600 µF (two equal banks of 300 µF, each delta configured)

Id = 0.66 per unit (198A), Vdc = 1.0 per unit (1000V), ωT = ωg = 0.917 per unit

Generator line-line terminal voltage; V g (L-L) = 1.163 per unit (802.47V)

Turbine output torque; TT = -0.746 per unit

Initially the unit is operated with a constant wind speed of 6.0 m/s. At time t = 9.0s the wind

speed is step changed from 6.0 m/s to 6.5 m/s and back to 6.0 m/s at t = 16.0s.

Stochastic wind speed is simulated at time t = 22.0s and onward with wind speed properties as in

section 5.1. The dc reference voltage signal is step changed from 1.0 per unit to 0.95 per unit at t

= 30.0s and back to 1.0 per unit at time t = 32.0s, during stochastic wind operation of the unit. In

Figure 5.3-2 switching events of the excitation capacitor banks are also identified (plot 3, 1=on,

0=on) which occur during variable speed operation of the WECU under the dynamic wind

conditions. Switching in of the capacitor banks causes mechanical oscillations between the

turbine and the generator rotors which can be observed in plot 1 and in the output current of the

rectifier (plot 3) at around time t = 30.5s and t = 33.6s. The mechanical oscillations however

damp out quickly.

This case study shows that the dc-dc converter provides tight regulation of the dc bus

voltage (within ±0.4%) while transferring the wind generated power to the battery storage both

during constant wind speed involving step changes and during dynamic wind conditions. No

appreciable mechanical oscillations occur due to step changes in the reference dc bus voltage or

due to switching of excitation capacitor banks during dynamic wind conditions due to current

controlled speed regulation scheme of the WECU and tight regulation of the dc bus voltage

around its nominal value. The case study confirms stability of the control scheme for the wind

energy conversion and battery storage system in the operating state #4 (WECU + Storage).

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Figure 5.3-2: Operating State # 4; System response to changes in wind speed, 1) dc bus voltage 2) generator L-L terminal voltage and capacitor switching events 3) wind speed

5.4 STORAGE-UTILITY GRID

In this section operation of the wind energy conversion and storage system has been considered

in the operating state #9 (Storage + utility, Figure 4.2-1). In this operating state the two system

modules shown in Figure 2.3-3 and in Figure 2.3-4 are interacting with each other.


Since the hybrid control strategy presented in CHAPTER 4 also envisages the use of the storage

element for dc voltage regulation during periods of temporary disturbances on the utility as also

on the dc bus, therefore dc bus voltage regulator associated with the dc-dc converter control has

been used in the control scheme shown in Figure 5.4-1. The proposed control structure is a

combination of control schemes shown in Figure 3.2-1 and in Figure 4.3-1. To confirm stability

and performance of the system under large transients, the storage is required to meet the active

power demand of the load in the storage-utility grid system (operating state #9). At times utility

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Figure 5.4-1: Single line diagram and control schematic of the study system in operating state number #9 consisting of the two system modules of (a) battery storage and dc-dc converter (b) VSC-Utility Grid

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supply will also be used for charging the batteries; therefore the control scheme also includes a

charging-current control input to the active current regulator of the VSC. To facilitate external dc

source other than the storage element, a controlled current source has been connected to the dc

bus, which acts as a known disturbance. Any surplus or deficiency in power supply from the

external dc source vis-à-vis load demand will be met by the storage element.


Figure 5.4-2 through Figure 5.4-5 shows system response under the proposed control scheme

during load switching conditions and during conditions involving reference step changes.

1. Load Switching

Figure 5.4-2 and Figure 5.4-3 show response of the storage-utility grid system for conditions

involving load switching only. The switching events are marked on plot 2 in Figure 5.4-2.

Initially the system is running at no load with the storage supporting the dc bus voltage. A 450µF

capacitor bank (star configured) provides reactive power support at the load bus (at 480 V) and a

0.25µF capacitor bank (delta configured) is connected at the PCC (at 13.8kV). The dc bus

voltage and the rms voltage of the load bus are at 1.0 per unit. The active and reactive currents of

the VSC are 0.0 per unit and -0.73 per unit, respectively. The external dc current representing the

WECU as a known disturbance is 0.0 per unit.

Referring to Figure 5.4-2, the following switching events have been simulated:

A 0.5 per unit charging current is drawn from the utility side at time t = 1.5s. The charging

process is terminated at t = 2.5s. At time t = 3.0s motor load (ML1) rated at 51 hp (38 kW or

0.127 p.u.) is connected to the load bus while it is running at no load at almost synchronous

speed. At time t = 4.0s a static load (SL1, 0.28 per unit) with a power factor of 0.81 lagging is

connected to the load bus. At t = 5.0s full rated torque is applied to the motor ML1 running at no

load. At time t = 6.0s another induction motor load (ML2) rated at 107 hp (0.273 p.u. or 82 kW)

is connected to the bus while it is running at no load at synchronous speed. Another static load

(SL2, rating equivalent to that of SL1) is connected to the load bus at time t = 7.0s and at time t =

8.0s full load torque is applied on the induction motor ML2.

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Figure 5.4-2: Operating State # 9; Response to load switching events, 1) dc bus voltage 2) 3 phase rms voltage at the load bus

Figure 5.4-3: Operating State # 9; Response to load switching events, VSC terminal currents, 1) ‘active’ current component 2) ‘reactive’ current component 3) maximum current limit and actual output current of the VSC and OCC duration

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The converter output currents are shown in Figure 5.4-3 corresponding to the events given in

Figure 5.4-2. Plots 1 and 2 show the active and reactive current components respectively while

plot 3 shows the total current output of the converter. Over current control mechanism (OCC,

Figure 4.2-1) is activated twice due to the large and sudden fluctuations in the converter output

currents caused by the connection of the motor load ML2. It should be noted that the control

scheme is configured to follow load demand as explained in section 5.4.1.

This case study shows that the storage-utility grid system under the proposed control scheme

remains stable during operation involving load switching events. The control scheme is able to

track the active current demand of the load branch while maintaining the dc bus voltage and the

rms voltage of the load bus within the specified transient operating limits. The dc bus voltage is

maintained within ±4.0% while the rms voltage at the load bus remains within ±7.0% of its

nominal value. The over current control mechanism (HSVM control and gating scheme of the

VSC) is also able to contain the converter output current below its maximum limit.

2. Step Changes in DC Current

Figure 5.4-4 gives simulation results for step changes in the external dc current source

(disturbance) for initial conditions where full load is connected to the load bus. This case is a

continuation of the previous simulation case which involved load switching events.

Referring to Figure 5.4-4, a 0.35 per unit dc current is injected into the dc bus at time t =

10.0s. At time t = 12.0s the dc injected current is step changed from 0.35 per unit to 0.5 per unit

and to 1.0 per unit at time t = 14.0s. The dc current is reduced from 1.0 per unit to 0.5 per unit at

time t = 16.0s and held constant thereafter.

This case study illustrates the robustness of the proposed control scheme to the presence of

the external disturbances on the dc bus and shows that both the dc and the rms voltage of the

load bus are tightly regulated. The dc bus voltage and the rms voltage of the load bus remain

within ±2.0% and ±0.1% of their nominal values, respectively. The system remains stable during

these events and the ac side remains virtually isolated from the disturbances on the dc side.

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Figure 5.4-4: Operating State # 9; Response to step changes in the dc current, 1) dc current 2) dc bus reference and actual voltage 3) reference and actual rms voltage at the load bus

5. Step Changes in Reference Signals

Figure 5.4-5 gives control response to step changes in the dc and the rms voltage reference

signals. Initially full load is connected to the load bus and all the load demand is met by the

battery storage (continuation of the previous case #2). A constant dc current of 0.5 per unit is

being injected at the dc bus.

Referring to Figure 5.4-5, at time t = 18.5s the reference dc bus voltage is step changed from

1.0 per unit to 1.03 per unit and back to 1.0 per unit at time t = 20.0s. The reference rms load bus

voltage is step changed from 1.0 per unit to 0.98 per unit at time t = 21.0s and back to 1.0 per

unit at t = 22.0s. Operation of the system remains stable and the signals are tracked within

reasonable settling times and overshoots. Settling time and overshoot in case of the dc voltage

regulation is (<) 102ms and (<) 12% respectively while these are (<) 75ms and (<) 4%

respectively for the rms voltage regulation.

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From the simulation cases presented above, it is concluded that operation of the study system in

the operating state #9 (Storage + Utility, Figure 4.2-1) remains stable and within the performance

limits (specified in section 2.4) under the propsed control scheme shown in Figure 5.4-1.

Figure 5.4-5: Operating State # 9; Response to step changes in reference voltage signals, 1) reference and actual dc bus voltages 2) reference and acutal rms voltages of the load bus

5.5 STORAGE-VSC-LOAD

In this section operation of the study system is considered in the operating state #3 (Storage +

VSC, Figure 4.2-1). In this operating state, the system is composed of the battery storage

interfaced to the load through the dc-dc converter and the VSC interface. The system is in the

islanded mode of operation and all the load demand is met by the storage element alone. As

outlined in CHAPTER 4, during islanded operation the VSC is operated as a directly controlled

voltage source


The single line schematic and control structure of the system in the operating state #3 is given in

Figure 5.5-1. The control structure is composed of the control scheme for the system module

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‘storage and dc-dc converter’ shown in Figure 3.2-1 and a propsed control scheme for the VSC

unit for its operation during islanded conditions. The large induction motor load (ML2) is

disconnected from the load bus during islanded operation according to the power management

strategy given in section 2.1.1, in order to limit the amount of the dynamic load to within the

handling capability of the battery storage.

Referring to Figure 5.5-1, the external dc current source represents the WECU as a known

disturbance. Any surplus or deficiency in power supply from the external dc source is met by the

storage element. The active current drawn by the load is forward fed to the dc bus voltage

regulation scheme for rapid response to variations in load demand. The VSC generates a

balanced set of constant frequency sinusoidal three phase voltages to achieve the commanded

rms voltage at the PCC. A tuned oscillator provides the constant reference frequency signal.

A simple PI compensator has been used to control the voltage magnitude at the PCC. The

proportional and the integral constants of the PI compensator have been set at 0.3 and 15.0

respectively. To control the rms voltage at the load bus a correction term corresponding to the

voltage drop between the PCC and the load bus is added to the external reference signal. The

modified reference signal is then used to control the output voltage of the VSC corresponding to

the feedback signal of the rms voltage at the PCC. For this purpose an integral compensator with

a time constant of 0.1s has been used. It has been shown in the simulation studies given in the

following paragraphs that with the proposed reference shaping, the load bus voltage can be

controlled indirectly to meet the performance specifications given in section 2.4. The proposed

reference shaping method does not require knowledge of the parameters of connecting branch

and the interposing transformer between the PCC and the load bus. This method of indirect

control of the rms voltage at the load bus has also been used in CHAPTER 4 for grid-connected

operation of the study system as opposed to the direct control scheme given in the previous

sections.

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Figure 5.5-1: Single line diagram and control schematic of the study system in the operating state number #3 consisting of the battery storage and dc-dc converter module interfaced to the load through the VSC

120


This section presents simulation results in which the following events have been considered.

1. load switching

2. step changes in dc current

3. step changes in reference signals

1. Load Switching and Step Changes in DC Current

Figure 5.5-2 and Figure 5.5-3 give system response for load switching and step changes in the

external dc current. Each figure covers the time duration involving both load switching and step

changes in the external dc current. Initially the system is running at no-load. Only one capacitor

bank (0.25µF, delta configured) is permanently connected to the PCC (at 13.8kV). A 450µF

capacitor bank (star configured) is permanently connected to the load bus. The VSC is absorbing

0.3 per unit of reactive current and there is no current contribution from the external dc current

source.

Figure 5.5-2: Operating State # 3; Response to load switching and step changes in external dc current , 1) reference and actual dc bus voltage 2) reference and actual rms voltage at the PCC 3) reference and actual rms voltage at the load bus

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Figure 5.5-3: Operating State # 3; Response to load switching and step changes in the external dc current, 1) external dc source current 2) active current component of the VSC 3) reactive current component of the VSC 4) total output current of the VSC

Referring to Figure 5.5-2, motor (ML1) is connected to the load bus at time t = 2.0s while it

is running at synchronous speed with zero load torque. This is followed by connection of the

static load (SL1) at time t = 3.0s. At time t = 4.0s, full load torque is applied on the motor ML1.

Another static load (SL2, of rating equivalent to that of SL1) is connected to the load bus at time

t = 5.0s. The system returns to a stable steady state operation after initial transients caused by

each load switching event. The rms voltages at the load bus and at the PCC remain within the

transient operating limits given by the ITI curve and the dc bus voltage remains tightly regulated

to within ±1.5% of the nominal value.

Referring to Figure 5.5-3, the external dc current disturbance is step changed at time t = 6.0s

from 0.0 per unit to 0.1 per unit, from 0.1 per unit to 0.15 per unit at t = 8.0s, from 0.15 per unit

to 0.3 at t = 10.0s and from 0.3 per unit to 0.0 per unit at time t = 12.0s. The step changes in the

external dc current representing WECU as a know disturbance does not affect the output current

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of the VSC and the dc bus voltage remains within ±1.5% of the nominal. Plot 4 in Figure 5.5-3

gives the total current output of the VSC which remains below its maximum limit (1.3 per unit)

and remains unaffected by the step changes in the external dc current injected at the dc bus.

The dc bus voltage is regulated within ±1.5% and the rms load bus voltage remains within

the bounds of the ‘no-interruption in function’ region of the ITI curve. This case study shows

that the proposed control scheme is stable and ensures that the load demand is met within the

performance constraints outlined in CHAPTER 2.

2. Step Changes in Reference Signals

Figure 5.5-4 gives simulation results for step changes in the references for the dc bus voltage and

the rms voltage at the load bus. The simulation results are a continuation from the previous case

study shown in Figure 5.5-2 and Figure 5.5-3. Initially load demand from the static loads (SL1

and SL2) and the motor load (ML1, with full load torque) is being served by the battery storage.

Figure 5.5-4: Operating State # 3; Response to step changes in reference signals, 1) reference and actual voltages of the dc bus 2) reference and actual rms voltages at the PCC 3) reference and actual rms voltages at the load bus

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Referring to Figure 5.5-4, the dc reference voltage is step changed from 1.0 per unit to 1.03 per

unit at time t =14.0s and back to 1.0 per unit at t = 15.5s. The reference rms voltage is step

changed from 1.0 per unit to 0.98 per unit at time t = 16.0s and back to 1.0 per unit at time t =

17.0s. The step change in the dc bus reference signal causes considerable variations in the rms

voltage at the PCC and the load bus. The integral term in the control loop adjusts the reference

PCC rms voltage signal to achieve the desired rms voltage at the load bus which is kept within

the steady state voltage limits and the transient performance bounds dictated by the ITI curve, for

step changes in the dc bus reference voltage and also for step changes in the reference signal for

the rms voltage at the load bus.

The case studies presented above confirm that the dc-dc converter control scheme provides

sufficiently fast response to achieve transient performance targets. The VSC output current

remains well below the maximum limit of 1.3 per unit and load demand is met within the

performance constraints given in section 2.4. The proposed control scheme provides stable

system operation during operating conditions involving load switching, step changes in the dc

disturbance current and during step changes in the reference signals for the dc bus voltage and

the rms voltage at the load bus.

5.6 WIND ENERGY CONVERSION UNIT-STORAGE-UTILITY GRID

In this section operation of the wind energy conversion and storage system has been considered

in the operating state #6 (WECU + Storage + Utility, Figure 4.2-1). All the three system modules

namely i) the wind energy conversion unit, ii) the battery storage and dc-dc converter, and iii) the

VSC-Utility Grid are interacting during this operating state of the wind energy conversion and

battery storage system. The three system modules are shown in Figure 2.3-2 through Figure

2.3-4. In the following sections a control structure has been proposed using control scheme of the

individual system modules given in Figure 3.1-1, Figure 3.3-1and in Figure 4.3-1. Performance

and stability of the proposed control scheme have been investigated using the detailed nonlinear

model of the system in PSCAD/EMTDC.


The control scheme for the wind energy conversion and storage system in the operating state #6

(WECU + Storage + Utility) has been designed to achieve the following objectives:

1. Active power demand of the load will be met by the utility feeder.

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2. Reactive power support will be provided to regulate PCC (or load bus) rms voltage.

3. The bidirectional dc-dc converter will be used for regulating the dc bus voltage.

4. All the available wind generated power will be transferred to the utility side except during

charging of the storage batteries.

Figure 5.6-1 shows single line schematic and control structure for the operation of the wind

energy conversion and storage system in the operating state #6.

Referring to Figure 5.6-1, a control signal for the charging current has been added to the

scheme which is forward fed to the current regulator of the dc-dc converter for fast control

response. The current from the WECU is also forward fed to the VSC active current regulator for

the same purpose. During charging period output from the VSC will be reduced by the amount of

the charging current. Thus if sufficient power is not available from the WECU, then the

remaining amount of the charging current will be imported from the utility grid. The VSC gating

control is based on the hybrid switching control strategy in order to keep its current output within

the allowable limit of 1.3 per unit (OCC operation, Figure 4.2-1). The HSVM based VSC control

(OCC operation) is enabled when either converter current limit exceeds 1.29 per unit or when the

individual phase rms voltage of the load bus falls below 95% of the nominal value in order to

keep rms voltage variations within the bounds given by the ITI curve. The HSVM based gating

and control scheme (OCC operation) remains active for a minimum of 150ms after the initial

disturbance which has caused its activation, is over.

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Figure 5.6-1: Single line schematic and control structure of the study system in the operating state #6 (WECU + Storage + Utility) where all the three system modules are in service

126


The case study presented below takes into account the following operating conditions:

1. Steady state operation of the WECU during no-load condition

2. Storage charging operation during constant wind speed

3. Dynamic wind conditions with:

a. Load switching events

b. Step changes in reference signals for rms voltage at the load bus and the dc

bus voltage

c. Capacitor switching events both at the generator and at the load side

Initially the wind energy conversion and storage system is operating under the following steady

state conditions:

Vdc = VLrms = Vbt = 1.0 per unit, wG = 0.9166 per unit,

Id = 0.655 per unit, Iqtmr = 0.655 per unit, Idtmr = -0.9 per unit,

IqLmr = 0.0 per unit, IdLmr = -0.13 per unit, Ib = 0.0 per unit,

where Vbt is the battery terminal voltage and Iqtmr, Idtmr are the orthogonal components of the

converter output current measured with respect to the relative reference frame (sensor outputs) as

explained in appendix D. The variables IqLmr, , IdLmr are the orthogonal current components of the

load branch in the relative reference frame. The VSC total output current is 1.114 per unit. A

0.25µF, delta configured capacitor bank is connected to the PCC. Two capacitor banks each

300µF (delta configured) are connected at the generator terminal. Three capacitor banks have

been used, all of equal rating, for the excitation control of the generator with one permanently

connected while the other two capacitor banks are switched in and out depending on the

generator speed.

Referring to Figure 5.6-2, the constant input wind speed to the turbine model is step changed

from 6.0 m/s to 6.5 m/s at time t = 9.0s and back to 6.0 m/s at t = 16.0s. Random wind speed

operation is simulated at time t = 22.0s with the stochastic wind speed characteristics the same as

in section 5.2.2.2. Switching events of the excitation capacitor banks are also marked on plot 2 in

the same figure.

Figure 5.6-3 shows the dc bus voltage and the three phase rms voltage at the load bus. Step

changes in the reference signal are from 1.0 per unit to 0.98 per unit and back to 1.0 per unit for

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the rms voltage at the load bus at time t = 32.0s and t = 34.0s. Step changes in the reference

signal for the dc bus voltage are from 1.0 per unit to 1.03 per unit and back to 1.0 per unit at t =

36.0s and t = 38.0s. The dc bus voltage is regulated within a narrow band of ±2.0% while the rms

voltage at the load bus satisfies the operating performance limits of the ‘no-iterruption in

function’ region of the ITI curve.

Referring to Figure 5.6-4 and Figure 5.6-5, a charging current of 0.15 per unit is requested at

t = 14.0 s while the system is operating at no load with a constant wind speed at the turbine hub.

The charging current is dropped to 0.0 per unit at t = 15.0s. The different switching events at the

utility side are as follows:

ML1 connection at t = 23.0s; full shaft-load application at t = 24.0s; SL1 connection at t = 25.0s;

ML2 connection at t = 27.0s wilth full shaft-load applied at t = 28.0s; Additional capacitor bank

of 0.25 µF (delta configured) is connected at PCC at time t = 30.0s; SL2 is connected at time t =

31.0s. It is pointed out here that the induction motors (ML1 and ML2) are connected to the load

bus while these are running at almost synchronous speed with zero load torque. Figure 5.6-4 also

shows the time intervals during which HSVM based VSC control is active (OCC operation,

Figure 4.2-1). It should be noted that the second event of OCC operation is caused by the

switching event of the capacitor bank at the PCC.

In this case study both constant wind speed operation with step changes and stochastic wind

regime operation of the system with load switching and step changes in reference signals have

been simulated. The system returns to steady state operation after each transient condition. It is

concluded that the operation of the wind energy conversion and storage system in the grid-

connected mode, where all the three system modules are in service, is stable and the performance

of the system remains within the specified steady state and transient limits.

128

Figure 5.6-2: Operating State # 6; Response to variations in wind speed, 1) wind speed 2) optimum, reference and actual speed of the generator 3) output current of the thyristor-controlled rectifier

Figure 5.6-3: Operating State # 6; Response during load switching, wind speed changes and step changes in the reference voltage signals, 1) dc bus voltage 2) rms voltage at the load bus

129

Figure 5.6-4: Operating State # 6; Response to load switching and step changes in reference signals, 1) active current components 2) reactive current components 3) converter limit, total output current and HSVM on duration

Figure 5.6-5: Operating State # 6; Response of the storage element to load switching and reference step changes, 1) battery terminal voltage 2) battery terminal current

130


In this chapter control schemes have been presented for the operation of the wind energy

conversion and storage system in the operating states where two or more of the system modules

are interactive. Normal system conditions have been considere which include:

1. Steady state operation

2. Step and dynamic wind speed changes

3. Switching of capacitor banks on the generator side as also on the utility side

4. Load switching events

In all the operating states of the wind energy conversion and storage system considered in this

chapter, stability and performance of the control schemes have been investigated through digital

time domain simulations of the detailed nonlinear models of the system using PSCAD/EMTDC

simulation software.

The following conclusions are based on the results presented in the preceding sections:

1. Modular control approach for the wind energy conversion and storage system, presented in

section 2.3.1, has been validated through time domain simulations.

2. It has been shown that different control structures developed for the individual system

modules of the wind energy conversion and storage system shown in Figure 2.3-2 through

Figure 2.3-4 can be combined together to suit operational requirements of the system in its

different operating states (as depicted in Figure 4.2-1).

3. In all the operating states considered in section 5.1 through section 5.6, operation of the

wind energy conversion and storage system conforms to the steady state and transient

performance criteria given in section 2.4. The control schemes provide stable system

operation in each operating state of the wind energy conversion and storage system.

4. In sections 5.1 and 5.6 it has been shown that the VSC output current can be contained

below the maximum allowable (1.3 p.u.) limit using HSVM based control and gating

scheme during grid interactive mode under normal operating conditions, with a restricted

switching frequency of 10 kHz. Transition management for switching between HSVM and

SPWM based control and gating schemes of the VSC provides a relatively bumpless

transfer between the two.

5. In the operating state #7 (WECU + Utility) in section 5.1, it has been shown that the

dynamic limitation on the reactive power support of the VSC should be employed with

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care. To avoid unwanted interaction between the real and reactive current controllers of the

VSC (results not shown), the reactive power support from the converter should be disabled

during system operation under sever disturbances in wind speed while no load is connected

to the load bus.

6. It is concluded that SPWM based control scheme of the VSC is not able to contain the

converter output current during interaction of the active and reactive current regulators

caused by dynamic limitations on the reactive current component of the VSC (results not

shown). If reactive current is not restricted to a lower percentage of the maximum converter

limit as has been done in section 5.1, the dynamic limitation on the reactive current control

may cause system operation to become unstable.

132

CHAPTER 6

SYSTEM OPERATION INVOLVING STATE TRANSITIONS

n the previous chapter it was shown that operation of the wind energy conversion and

storage system under the proposed control schemes for the individual operating states of

the system (Figure 4.2-1) is stable and conforms to the steady state and transient performance

specifications given in section 2.4. Control schemes for the system configuration in each

particular operating state were obtained by combining and reconfiguring the control schemes

given in Figure 3.1-1, Figure 3.2-1 and Figure 4.3-1 of the individual system modules (Figure

2.3-2 through Figure 2.3-3) using the modular control design philosophy proposed in section

2.3.1.

In this chapter stability and performance of the supervisory controller is investigated under

system operating conditions which involve inter-mode transitions and transitions among

operating states as represented by the FHA of Figure 4.2-1 within each operating mode of the

study system. It should be noted that a transition between two operating states connected by a

particular (directional) transition path shown in Figure 4.2-1 is also accompanied by a transition

between the control schemes corresponding to the particular system configurations (composition

of active energy sources in the system) in the two operating states.

As proposed in section 2.5, stability and performance characteristics of the supervisory

controller (given in section 4.3) will be evaluated using time domain digital simulations of the

detailed nonlinear model of the study system in PSCAD/EMTDC.

Results of the simulation studies are presented in the following sections in which the

‘startup’ process (transient operating state #1) has been described first. The following should be

noted:

1. All the circuit breakers including breakers connecting load to the load bus and the capacitor

banks to the load bus and to the PCC have been modeled as nonideal which can interrupt

current only at zero crossing.

2. Two capacitor banks (each 0.25µF, delta configured) have been used for reactive power

support at the PCC.

3. Capacitor bank switching is blocked during mode transitions and during OCC operation

I

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until after the system has stabilized.

4. To allow for proper re-initialization of the inner current regulators of the SPWM based

control scheme and for separating the control switching event from the transients

subsequent to the fault event, the OCC operation of the VSC when enabled remains active

for a minimum duration of 150ms.

6.1 STUDY CASES

Table 6.1-1gives a summary of the operating-state transitions considered in this chapter. All the

transition cases have been simulated and clearly illustrate the stability of the supervisory control

of the wind energy conversion and battery storage system.

Table 6.1-1: Study Cases; System Operation Involving State Transitions

Ope

ratin

g

Mod

e

Tra

nsiti

ons

System Configuration3 Cause of Transition

1 2 START UP STANDBY Start up operation of the system

2 3 STANDBY STORAGE Load switching

3 4 STORAGE WECU + STORAGE Start up of the wind energy conversion unit

4 3 WECU + STORAGE STORAGE Blocking of thyristor rectifier unit

OF

F-G

RID

MO

DE

3 2 STORAGE STANDBY Disconnection of load bus

7 6 WECU+UTILITY

WECU+STORAGE+UTILITY Storage charging operation

6 9 WECU+STORAGE+UTILITY

STORAGE+UTILITY Blocking of thyristor rectifier unit

9 8 STORAGE+UTILITY VSC+UTILITY Termination of the charging process

8 7 VSC+UTILITY WECU+UTILITY Unblocking of thyristor rectifier unit

PR

E-P

LAN

NE

D T

RA

NS

ITIO

NS

ON

-GR

ID M

OD

E

7 8 WECU+UTILITY VSC+UTILITY Loss of wind power due to low wind level

3 Refer to Figure 4.2-1

134

OF

F-G

RID

O

N-G

RID

4 5

6

(OCC)

6

WECU + STORAGE SOS

WECU+STORAGE+UTILITY (OCC)

WECU+STORAGE+UTILITY

WECU+UTILITY

Synchronization

PR

E-P

LAN

NE

D T

RA

NS

ITIO

NS

ON

-GR

ID

OF

-GR

ID

8 3 VSC+UTILITY STORAGE Pre-planned mode transition, motor load ML2

is kept disconnected from the load bus

7 10

7

WECU+UTILITY FOS

(WECU+STORAGE+UTILITY)

WECU+UTILITY

State transition due to temporary single-line-to-

ground fault at the PCC, employs storage

support during the transient operating state of

FOS, no-load operation

ON

-GR

ID M

OD

E

7 10

7

WECU+UTILITY FOS

(WECU+UTILITY) WECU+UTILITY

State transition due to temporary single-line-to-

ground fault at the PCC, no-load operation

AC

CID

EN

TA

L T

RA

NS

ITIO

NS

ON

-GR

ID

OF

-GR

ID M

OD

E

9 10

3

STORAGE+UTILITY FOS

(STORAGE+UTILITY) STORAGE

Single-line-to-ground fault at the PCC, full

load operation

135

6.2 SYSTEM STARTUP AND STANDBY

The startup process and standby operation (states #1 and #2 respectively, Figure 4.2-1) of the

wind energy conversion and storage system is shown in Figure 6.2-1 and Figure 6.2-2. The

control structure shown in Figure 5.5-1 has been used. In line with the control philosophy and the

FHA given in CHAPTER 4, the wind energy conversion and storage system is started with the

help of the storage element. A breaker with a 0.5Ω pre-insertion resistor has been used to contain

the inrush current when the storage element is connected to the fully discharged dc bus capacitor.

In the absence of the pre-insertion resistor the battery is shorted for the period during which the

dc bus voltage is less than the battery terminal voltage due to the anti-parallel diode (switch S2,

Figure 3.3-1) in the dc-dc chopper circuit. Under such conditions the chopper control will not be

able to contain the battery output current. The pre-insertion resistance is chosen such that the

maximum battery current remains within its rating limit (1.3 per unit current at the dc bus side)

and is applied for a period of 40ms during which time the dc capacitor is charged to a sufficiently

high level (approximately 0.47 p.u.) after which chopper control dictates the battery output

current.

Initially the dc capacitor is in a completely discharged state. The dc bus is isolated from both

the wind energy conversion unit and from the PCC (Figure 1.3-1). The tie circuit breaker (TCB,

Figure 1.3-1) is in open position. One capacitor bank (0.25 µF, delta configured and completely

discharged) is connected to the PCC. The load bus is kept disconnected.

Referring to Figure 6.2-1, the breaker connecting the dc bus to the battery storage is closed

at time t = 0.02s with a pre-insertion resistance of 0.5 Ω, during the ‘startup’ operating state

(state #1, Figure 4.2-1). The pre-insertion resistance is bypassed at time t = 0.06s. The dc bus

voltage is stabilized by the time t = 0.16s. After completion of the ‘startup’ process the VSC

control is activated at time t = 0.37s and at the same time the reference signal is ramped up from

0.0 per unit to 1.0 per unit in about 100ms. The rms voltage at the PCC is then stabilized at 1.0

per unit by the time t = 0.5s and the system thereafter starts operation in the ‘standby’ operating

state.

Plots 1 and 2 in Figure 6.2-1 show the dc bus voltage and the rms voltage at the PCC

respectively. The time instant at which the pre-insertion resistance is bypassed is marked on plot

1. The overshoot in the dc bus voltage during the startup process is below 10% which settles

down to the nominal value of 1.0 per unit in about 210ms. Plot 3 in Figure 6.2-1 shows the

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instantaneous voltage at the PCC in the ‘abc’ reference frame. Due to the ramping up (reference

shaping) of the input reference signal to the VSC voltage control loop the overshoot in the rms

voltage at the PCC is only 2.5% since this procedure avoids the inrush currents caused by the

step-up transformer and the capacitor banks connected to the PCC (Figure 1.3-1).

Figure 6.2-1: Startup and Standby Operation, 1) dc bus voltage 2) reference and actual rms voltage at the PCC 3) phase voltages at the PCC

Plot 1 in Figure 6.2-2 shows the orthogonal components of the VSC terminal current in the

relative reference frame (appendix D, section D.1.5). Plot 2 in Figure 6.2-2 shows the battery

terminal voltage which drops to around 0.84 per unit during full load on the storage element. Plot

3 in Figure 6.2-2 shows the terminal current of the battery storage which is restricted to below

the maximum current limit of the dc-dc converter unit (assumed 1.3 per unit at the high voltage

side). Nominal duty ratio at no load (2.5) has been used for per unitizing the battery current at the

lower voltage side (battery side).

137

Figure 6.2-2: Startup and Standby Operation, 1) orthogonal current components of the VSC 2) battery terminal voltage 3) reference and inductor current

6.3 STATE TRANSITIONS

In the following sections worst case transitions of the study system between operating states

given by the FHA (Figure 4.2-1) of the system are presented in order to assess stability and

performance of the proposed supervisory controller.

6.3.1 OFF-GRID MODE OF OPERATION

In the off-grid mode of operation there are three normal operating states of the system namely

state #2 (Standby), state #3 (Storage) and state #4 (WECU + Storage) in which the system can

operate for extended periods of time. Control structures for the operation of the system in the off-

grid mode are shown in Figure 5.3-1 and in Figure 5.5-1. In Figure 5.5-1 the wind energy

conversion unit has been represented as a known disturbance. It should be noted that there is no

change in the system control structure between the three operating states except that the rms

voltage at the PCC is regulated rather than the rms voltage of the load bus during the time when

it is disconnected from the PCC. No supervisory control actions on the regulators are required

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during the off-grid mode operation of the system. The load bus could be connected while the

system is in operation in any of the three operating states (#2, #3 or #4).

Figure 6.3-1 to Figure 6.3-3 give simulation results for the inter-state transitions during

islanded operation of the study system. Initially the system is running in the standby operating

state (#2, Figure 4.2-1) in which the PCC is energized and the rms voltage is stabilized at

nominal value. A single capacitor bank (0.25µF, delta configured) is connected to the PCC.

Referring to Figure 6.3-1, at time t = 1.87s the load bus is energized by closing the circuit

breaker LCB (Figure 1.3-1) with a capacitor bank (450 µF, star configured) permanently

connected to it. The system then starts operation in state #3. Till that point in time no load is

connected to the load bus. Regulation of the load bus voltage is enabled after a delay of 200ms

and its rms voltage is stabilized at the nominal value in about 240ms. At time t = 2.25s full load

consisting of the two static loads SL1, SL2 and one induction motor load ML1 with rated torque

and running at rated speed (0.944 p.u.) is connected to the load bus simultaneously. The rms

voltage of the load bus drops to 0.986 per unit after the load connection event and recovers

rapidly. Wind energy conversion unit is brought into the scheme at time t = 2.55s by enabling

gating control of the thyristor rectifier. Before the thyristor rectifier is turned on, the induction

generator was energized and it was running above the optimal speed (reference speed) of 1.033

per unit corresponding to a wind speed of 7.4m/s. The start of this event causes the study system

to move to operating state #4 from its previous operating state #3. Reffering to plots 3 in Figure

6.3-1 and in Figure 6.3-2, the system moves from operating state #4 to state #3 when the WECU

is disabled by blocking the thyrisotr rectifier unit at time t = 2.88s. The load bus is then

disconnected at time t = 3.16s which causes the system to change operating state from state #3 to

state #2 (Standby).

Plots 2 and 3 in Figure 6.3-1 also show the envelope of the ‘no-interruption in function’

region of the ITI curve. At the start of the first event at time t = 1.87s and immediately after the

occurrence of the event at time t = 3.16s it is the rms voltage of the PCC that is being regulated

and the ITI voltage envelope for the ‘no-interruption in function’ region has been shown for the

PCC voltage. During the connection of the full load it is the rms voltage of the load bus which is

being regulated (enabled after 200ms of the load bus connection to the PCC) and the ITI voltage

envelope is shown for that particular event. The rms voltages at the PCC as well as at the load

bus remain within the ITI performance limits for the electronic equipments sensitive to voltage

disturbances. It should be noted that connection and disconnection of the load bus at no load

139

causes interactions between the orthogonal current controllers, and is a result of the low losses in

the system during no load operation. The dc bus voltage remains within ±5% of the nominal

value during the full load switching and during the various state transitions (Figure 4.2-1) in the

off-grid mode of operation of the system. Referring to Figure 6.3-3, it should be noted that the

rapid response of the dc-dc converter and the controlled current-source nature of the WECU unit

results in low amplitude variations (±1% of the nominal) in the dc bus voltage to events

corresponding to the state transitions involving the WECU module.

Figure 6.3-1: Off-grid operation; Inter-state transitions among state #2 (Standby), state #3 (Storage + VSC) and state #4 (WECU + Storage), 1) dc bus reference and actual voltage 2) reference and actual rms voltage at the PCC and ITI performance limits 3) reference and actual rms voltage at the load bus and ITI performance limits 4) Operating state of the system

140

Figure 6.3-2: Off-grid operation; Inter-state transitions among state #2 (Standby), state #3 (Storage + VSC) and state #4 (WECU + Storage), 1) orthogonal current components of the VSC 2) orthogonal current components of the load bus 3) rectifier output current, total instantaneous current of the load branch and the output current of the VSC

Figure 6.3-3: Off-grid operation; Inter-state transitions among state #2 (Standby), state #3 (Storage + VSC) and state #4 (WECU + Storage), 1) battery terminal voltage 2) reference and actual battery terminal currents

141

The above case study shows that the control scheme of the system in the off-grid mode is stable

during its operation involving state transitions under the most severe operating conditions.

Referring to Figure 5.2-5 and Figure 5.4-2 it is concluded that with the proposed control scheme,

the wind energy conversion unit could be considered as a constant current source during transient

operation of the system. Therfore a constant current source could be used instead of the WECU,

for transient performance and stability evaluation of the control scheme of the study system,

since with the dc bus voltage tightly regulated, the WECU dynamics are almost decoupled from

the rest of the system.

6.3.2 ON-GRID MODE OF OPERATION

In the following sections state transitions of the study system during on-grid mode of operation

are considered. Both ‘normal’ and temporary fault conditions have been taken into account.

6.3.2.1 State Transitions during Normal Operation

Figure 6.3-4 through Figure 6.3-6 give simulation results for state transitions during on-grid

mode of operation under normal operating conditions. Two capacitor banks (each 0.25µF, delta

configured) are connected to the PCC. Full load and two capacitor banks (each 450µF, star

configured) are connected to the load bus. The load (Figure 1.3-1) is composed of two equally

rated static loads SL1, SL2 and two induction motor loads ML1, ML2 with rated load torques.

The wind speed at the hub of the wind turbine is held constant at 7.4 m/s. The system is initially

operating in state #7 (WECU + Utility, Figure 4.2-1) with the wind turbine running above the

optimal reference speed of 1.033 per unit. The following initial conditions are noted:

Id = 1.0 per unit, Iqt = 0.97 per unit, Idt = 0.36 per unit

Vrmspcc = 1.013 per unit, VLrms = 1.0 per unit, Vbt = 1.0 per unit (with Vb = 1.0 per unit = 400V)

The total output current of the VSC is 1.03 per unit while total load current is 0.91 per unit. All

the wind generated power is being transferred to the utility side.

Referrring to Figure 6.3-4, constant current charging of the battery storage is initiated by

reducing the the voltage of the constant dc source (Vb) in the equivalent model of the battery

storage from the nominal 1.0 per unit (400V) to 0.9 per unit (360V) at time t = 2.95s. The system

therefore transitions from its initial operating stat #7 to the operating state #6 (WECU +Storage +

Utility). During this operation the battery storage is being charged with a constant current (Ib

[HV side] = 0.86 per unit) by directing part of the wind generated power to the storage element

142

through the forward feed scheme shown in Figure 5.6-1. Under these operating conditions the

VSC has still enough capacity to meet the reactive power demand in order to maintain the rms

voltage of the load bus at 1.0 per unit. It should be noted that instead of directly controlling the

rms voltage at the load bus as shown in Figure 5.6-1, the reference shaping scheme introduced in

section 5.5 (Figure 5.5-1) has been used for indirect control. This permits voltage regulation

scheme to be active during OCC operation (D = 0, Figure 4.2-1) as also during transient system

operation under utility side fault contitions (D = 1).

Figure 6.3-4: State transitions during on-grid mode of operation, 1) reference and actual dc bus voltage 2) reference and actual rms voltage at the PCC 3) reference and rms voltage at the load bus 4) system operating state and OCC operation intervals

Referring to plot 3 in Figure 6.3-5, the system is forced to transition to operating state #9

(Storage + Utility) by blocking gating control of the thyristor rectifier unit at time t = 3.4s. In the

absence of the wind power generation the required battery charging-power is now imported from

the utility side. Referring to plot 3 in Figure 6.3-5, the sudden loss of wind power generation and

143

the constant charging current load on the VSC results in the total converter current to hit the

level of 1.29 per unit at time t = 3.42s which initiates OCC operation (HSVM based control and

gating scheme of the VSC) in order to limit the converter output current below 1.3 per unit. At

the same time reference shaping of the rms voltage control loop is disabled (to avoid frequent use

of the OCC operation due to limited capacity of the converter, assumed to be 1.3 per unit). The

disabling of the reference shaping is obtained by reseting the output of the integrator in the

auxiliary loop of the rms voltage regulator to zero. This results in the regulation of the rms

voltage at the PCC at the nominal level (rather than the rms voltage at the load bus). Once

initiated, the OCC based operation of the VSC continues for a minimum of 150ms after which

SPWM based control and gating scheme of the converter takes over again. Reference shaping is

resumed 100ms after the SPWM based control scheme of the converter is enabled.

Referring to plot 3 in Figure 6.3-5, at the end of the first OCC operation the converter total

current is still at the threshold level of 1.29 per unit causing another cycle of the OCC operation.

In the meanwhile charging process is terminated at time t = 3.6s and the system switches to the

operating state #8 (VSC + Utility) with the OCC based control scheme of the converter. In the

operating state #8, the VSC is only supplying reactive power to the system. The converter has

therefore adequate capacity to meet the reactive power demand at the end of the second OCC

operating cycle and also when the reference shaping of the rms voltage regulator resumes at time

t = 3.82s (plot 2, Figure 6.3-4). The rms voltage at the load bus is therefore again stabilized at the

nominal level while in operating state #8.

The firing angle control of the thyristor rectifier is enabled again at time t = 4.1s and the

speed regulation scheme of the WECU tries to extract maximum power from the unit to bring

down its speed to the reference value of 1.033 per unit. With the chosen parameters of the inner

current regulator in the speed regulation scheme and the relatively slow response of the rectifier

unit, there is an overshoot of approximately 0.395 per unit in the output current of the recitifier

which is about 0.295 per unit above the rating of the VSC. Over current control (OCC) of the

VSC is therefore enabled to restrict the output current to below 1.3 per unit. At the same time

reference shaping of the rms voltage regulator is disabled. During this time the reactive current

output of the converter is reduced since it is dependent on the active current output of the

converter at any given time during its operation. The reactive power support is suspended at time

t = 4.17s when the active current output of the converter reaches the level of 1.2 per unit and

144

would not be resumed until the active current drops below 1.0 per unit. This causes the rms

voltage at the load bus to increase momentarily to about 1.01 per unit.

Figure 6.3-5: On-grid mode of operation; transitions during normal operation, 1) reference and actual active current component of the converter 2) reference and actual reactive current component of the converter 3) rectifier output current and total current of the load branch and the VSC

Figure 6.3-6: On-grid mode of operation; transitions during normal operation, 1) battery terminal voltage 2) reference and actual battery current

145

After the OCC operation the wind generated power is within the handling capability of the VSC

and normal operation resumes whit the rms voltage of the load bus being regulated at 1.0 per unit

again. As the turbine speed falls below the reference value, the output of the unit gradually

reduces to zero at which point the system moves on to state #8 (VSC + Utility) at time t = 5.05s.

In this operating state the active power output of the converter falls near to zero and its reactive

current output increases to about 0.95 per unit to hold the rms voltage at the load bus at the

nominal value.

This case study confirms the stability of the supervisory control scheme for state transitions

under normal operating conditions during on-grid mode of operation of the study system.

Though the VSC capacity is not enough (with the chosen capacity values of the static capacitor

banks) to pursue rms voltage regulation of the load bus, the rms voltage at the laod bus as also at

the PCC remains within the transient performance limits. The case study highlights the fact that

individual system components should be adequately rated for adverse operating conditions of the

system. It also shows that given proper capacity of the VSC, the reference shaping scheme of the

rms voltage regulator can be successfully employed to indirectly control the voltage at the load

bus without sacrificing control response of the VSC as was done using the direct rms voltage

control scheme for the load bus (Figure 5.6-1).

6.3.2.2 State Transitions during Temporary Fault Conditions

Figure 6.3-7 through Figure 6.3-9 show state transitions of the study system from operating

states within the normal operating regime during the on-grid operating mode (D = 0) to the

transient operating state FOS (D = 1) and back to the normal operation. Two such transitions,

representing worst case scenarios, have been shown with the transition sequence of state #7 to

state #10 and back to state #7. The first transition cycle illustrates the transient storage support

strategy outlined in section 4.3.2.

Initially the system is operating with the load bus connected to the PCC under a no-load

condition. A capacitor bank (450µF, delta configured) is permanently connected to the load bus.

For the simulation period considered, both capacitor banks at the PCC are connected to the

system. At the start of the simulation period at time t = 2.0s, the recitifier is delivering 1.06 per

unit current at the dc bus with the turbine running at a slightly higher speed above the reference

speed of 1.033 per unit (corresponding to a constant wind speed of 7.4 m/s). The VSC is

delivering the wind generated power to the utility side with an active current ouput of

146

approximately 1.01 per unit. The rms voltage regulation is suspended for the time being since the

active current output of the converter previously after crossing the threshold of 1.2 per unit

remains above 1.0 per unit. It is recalled that the voltage regulation scheme is disabled when the

active current output of the VSC increases above 1.2 per unit and is not resumed until it drops

below 1.0 per unit.

Referring to Figure 6.3-7, a single phase line to ground (A-G) fault is applied at the PCC at

time t = 2.09s. The fault resistance is 0.001Ω. The fault is applied for a duration of 3 cycles.

Immediately after the fault, the converter current shoots to above the threshold level causing

activation of the OCC and simultaneously the system moves to the FOS operating state (state

#10). It is mentionead here that during FOS operation the VSC uses the HSVM based control

and gating scheme in order to ensure continuity of system operation. From plots 1 and 3 in

Figure 6.3-9, it is noted that the converter current actually shoots above the converter current

limit of 1.3 per unit and that the HSVM based swiching of the converter seems not to be able to

restrict output current of the converter to below its rating. This however is not the case and can

be explained in terms of the modeling of the HSVM based switching scheme in

PSCAD/EMTDC wherein interpolation of the switching instances has been ignored. Another

factor is the bandwidth of the inner and outer bands for the generation of the switchsing patrons

for HSVM based gating signal generation. A bandwidth of 30A has been used for the outer band

and 22.5A has been used for the inner band [77]. In the absence of interpolated switching

instances the HSVM based control is affected by the simulation time step (5µs used for

simulations in PSCAD/EMTDC).

Referring again to Figure 6.3-7, during the single line to ground fault the dc bus voltage

exceeds the threshold of 1.08 per unit. This causes storage support to be called in (plot 3) and the

excess current (reference ‘active’ current – converter limit of 0.6634) is diverted to the storage

by enabling dc-dc converter control. Storage provides support until the dc bus drops to below

1.04 per unit. Figure 6.3-9 shows the battery terminal voltage and current for the time interval

shown in Figure 6.3-7. The rapid control action of the dc-dc converter prevents further voltage

rise of the dc bus and quickly brings down the voltage to within the range for normal system

operation. It is pointed out that storage control scheme is not used for dc bus voltage regulation

during on-grid operation of the system whether under normal or during transient fault conditions.

Plots 2 and 3 in Figure 6.3-7 show that rms voltages at the load and at the PCC remain within the

ITI ‘no-interrruption in function’ region during and after the temporary fault operating conditions

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as also when full load is connected to the load bus at time t = 2.48s. The full load is composed of

the two static loads SL1, SL2 and the two induction motor loads ML1, ML2 with rated load

torques and running at rated speeds. Connection of the full load brings down the reactive power

support requirement from the VSC and OCC operation is not invoked during normal on-grid

operation thereafter until the initiation of another fault. Reference shaping is resumed again at

time t = 3.14s.

Another A-G fault at the PCC is applied at time t = 3.3s with identical fault characteristics.

This time the dc bus voltage rise remains below 1.08 per unit and storage support is therefore not

utilized. After cycling through the FOS operating state the system starts normal operation again

in state #7. Transient performance limits are not violated and the system remains stable during

and after the temporary single line to ground fault at the PCC.

Figure 6.3-7: On-grid operating mode; state transitions caused by single line to ground fault, 1) dc bus and thyristor-controlled rectifier output voltage 2) three phase rms voltage at the PCC and the upper and lower limits defined by the ITI curve 3) single phase rms voltage at the PCC and the ITI curve 4) control signals used for state transition management

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This case study confirms that the supervisory control scheme developed for the study system is

able to provide stable system operation during temporary faults at the worst location on the

feeder (PCC) even during high wind power generation periods. The case study also illustrates the

transient power management strategy used in connection with over/under voltage of the dc bus.

It is confirmed that the performance of the supervisory controller remains within the transient

speicifications provided by the ITI curve.

It should be mentioned here that an alternate transient support scheme could be used in

which the WECU is allowed to over speed for the fault duration to reduce its output power such

that storage element would not need to be involved during voltage rise on the dc bus. The stored

energy in the wind turbine and generator system in the form of kinetic energy could then be

recovered by steering the wind turbine down to the optimal speed corresponding to the prevailing

wind conditions. The control scheme for the wind energy conversion unit however has not been

configured for transient power management during grid side disturbances.

Figure 6.3-8: On-grid operating mode; State transitions caused by single line to ground faults, 1) VSC ‘active’ current output 2) VSC ‘reactive’ current output 3) rectifier output current, total current of the load branch and output current of the VSC

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Figure 6.3-9: On-grid operating mode; State transitions caused by single line to ground faults, 1) battery terminal voltage 2) reference and inductor current

6.4 MODE TRANSITIONS

6.4.1 PRE-PLANNED TRANSITIONS

In the following sections simulation results are presented for the pre-planned mode transitions of

the study system. The transitions are from off-grid mode to on-grid mode of operation and vice

versa.

6.4.1.1 Synchronization

The worst case scenario of the WECU delivering the maximum current and the system catering

to the maximum load while in operating state #4 in the off-grid mode has been considered. In

this case the forward fed signal (dc current from the rectifier) requires gradual transfer from the

storage control scheme to the VSC based control scheme in order to divert wind generated power

from the storage to the utility side of the VSC with minimum transients. The following should be

noted:

1. Variations (for the synchronization process) in the oscillator output frequency (for VSC

control in islanding conditions) have been limited to ±2% of the nominal.

2. Regulation of the rms voltage scheme is not resumed until 400ms after successful

completion of the synchronization process to separate synchronization transients from the

control switching transient.

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During synchronization period, reference shaping is disabled and the reference signal in the inner

loop of the VSC output voltage control scheme shown in Figure 5.5-1 comes from the actual rms

voltage of the utility side of the TCB (Tie Circuit Breaker, Figure 1.3-1). The TCB is only closed

once the voltage space vectors at the two sides of the TCB are aligned with each other and the

difference between the rms voltages at the two sides is within 1%. Immediately after connection

to the utility, the VSC is operated as a controlled current source with HSVM based switching and

control scheme (OCC) for a minimum duration of 100ms. Also the active and reactive currents

supplied by the storage during islanded operating state (before connection to the utility when the

VSC has been operated as a directly controlled voltage source) are ramped down to zero. In a

similar fashion the rectifier output current is diverted to the utility side by ramping up the dc

current forward fed signal in the VSC control scheme from zero to 100%. Storage support of the

system is dropped after the successful synchronization and control transition process.

Figure 6.4-1 gives simulation results before, during and after the synchronization process.

Figure 6.4-2 and Figure 6.4-3 illustrate the transition management strategy used for minimizing

transients that would result because of switching between two different control schemes. Initially

a current of 1.2 per unit is being drawn from the induction generator since the wind turbine is

running at a slightly higher speed than the reference optimal speed (1.033 per unit)

corresponding to the reference wind speed of 7.4m/s. Full load (SL1, SL2 and ML1 with full

load torque) is connected to the load bus. A capacitor bank (0.25µF, delta configured) is

connected to the PCC and one capacitor bank (450 µF, star configured) is connected to the load

bus. The converter is delivering a total current of 0.64 per unit with nominal voltage at the load

bus (rms voltage of the load bus is being regulated).

Referring to Figure 6.4-1, the synchronization process starts at time t = 2.74s and

simultaneously voltage regulation is switched from the rms voltage at the load bus to that at the

PCC. The control scheme of the oscillator which is generating the reference frequency for the

VSC control in the islanding operation varies its frequency (plot 2 in Figure 6.4-1) in order to

align the voltage space vector at the PCC with voltage space vector at the utility side of the TCB.

After a 4ms synchronized operation, the PCC is connected to the utility feeder by closing the

TCB at time t = 2.88s.

Plot 3 in Figure 6.4-2 shows that immediately after the SOS operating state (#5, Figure

4.2-1) the system moves on to the operating state #6 (WECU + Storage + Utility) with OCC

operation of the VSC (HSVM based control and gating scheme). After the wind generated power

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is diverted to the utility side and the storage support is dropped, the system moves on to the

operating state #7 (WECU + Utility). The dc bus voltage shown in plot 2 indicates a slight

increase of less than 3% above the nominal value during diversion of the wind generated power

to the utility side.

Figure 6.4-3 shows the supervisory control actions on the primary regulators. Plot 1 shows

the command signal for changing control of the VSC as directly controlled voltage source to the

current controlled voltage source. It also shows the control signal for transferring dc regulation

control from the control scheme associated with the storage and dc-dc converter module (Figure

5.6-1) to the control scheme associated with the VSC (Figure 5.2-1). Plot 3 shows that the

forward fed signal (rectifier output current) is transferred between the two control schemes

mentioned above in a ramped fashion and at the end of the HSVM operation the VSC is used to

deliver the whole output power from the wind energy conversion unit to the utility side. The

discrepancy between the forward fed signals to the two control schemes, due to the static gains

(Gd2a and Gdc), primarily results in a slight increase in the dc bus voltage (plot 1 in Figure 6.4-2).

Figure 6.4-1: Mode transitions; synchronization, 1) ‘a’ phase voltage waveforms at the two sides of the TCB and the synchronization interval 2) reference frequency and PLL outputs for the two sides of the TCB 3) reference and actual rms voltages on the utility side of the TCB, at the PCC and at the load bus

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Figure 6.4-2: Mode transitions; synchronization, 1) reference and actual dc bus voltage 2) reference and actual rectifier current, reference and actual ‘active’ current component of the converter 3) reference and actual ‘reactive’ current of the converter 4) system operating state and duration of the OCC operation

Figure 6.4-3: Mode transitions; no load synchronization, 1) control signals 2) wind energy conversion and storage system operating states

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The case study shows that the study system can transition from any of the three states namely

state #2 (Standby), state #3 (Storage) and state #4 (WECU + Storage) in the off-grid mode with

minimum transients to the two designated operating states namely state #6 (WECU + Storage +

Utility) and state #9 (Storage + Utility) through the intermediate synchronization operating state

SOS (state #5) while meeting transient performance requirements.

6.4.1.2 On-Grid to Off-Grid Transitions

1. Pre-planned Transitions

Figure 6.4-4 through Figure 6.4-6 illustrate a representative pre-planned transition from

operating state #8 (VSC + Utility) in the on-grid mode to operating state #3 (Storage + VSC) in

the off-grid mode. It represents the most severe operating conditions for pre-planned transition in

which the storage element is required to pickup the entire load after disconnection from the grid

(except ML2 which is disconnected when the TCB is in open position).

Figure 6.4-4: Pre-planned on-grid to off-grid mode transition, 1) reference and actual dc bus voltage 2) reference and actual rms voltage at the PCC 3) reference and actual rms voltage at the load bus 4) operating state

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Figure 6.4-5: Pre-planned on-grid to off-grid mode transition, 1) active current component of the VSC 2) reactive current component of the VSC 3) space vector magnitude of the load branch and the VSC output current

Figure 6.4-6: Pre-planned on-grid to off-grid mode transition, 1) battery terminal voltage 2) battery terminal current

Initially the system is operating in the grid-connected mode in operating state #8 wherein the

VSC is only supplying reactive power for regulation of the rms voltage at the load bus. The load

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bus is indirectly regulated at the nominal value by regulating the PCC voltage at 1.013 per unit

using reference shaping in the rms voltage regulation scheme as described earlier. Full load is

being served with two capacitor banks (0.25µF, each delta configured) connected to the PCC and

two capacitor banks connected at the load bus (450µF and 600µF, each star configured). The

VSC is supplying 1.07 per unit reactive current.

Referring to Figure 6.4-4 through Figure 6.4-6, opening of the circuit breaker TCB is

initiated at time t = 1.6s which completes in about 10ms at time t = 1.612s. With the opening of

the TCB, the second capacitor bank (600µF, star configured) is disconnected and the induction

motor load ML2 is dropped by opening their respective controlling breakers. With the complete

disconnection of the utility feeder the study system switches operation to state #3 in the off-grid

mode and simultaneously dc bus voltage control is handed over to the storage based control

scheme (Figure 5.5-1) and battery storage picks up the load (Figure 6.4-6). After initially

dropping to about 0.927 per unit the dc bus voltage recovers back to the nominal value at around

t = 1.74 per unit (in about 128ms). Referring to plots 2 and 3 in Figure 6.4-4, the rms voltages at

the PCC and at the load bus remains within the transient performance limits while plot 3 in

Figure 6.4-5 shows that the VSC output current remains within its maximum capacity (1.3 p.u.)

before, during and after the pre-planned mode transition.

The case study shows that the supervisory control provides stable operation of the study

system for worst case pre-planned transition from state #8 in the grid-connected mode to state #3

in the off-grid moperating mode while maintaining performance within the specified limits.

2. Accidental Transitions

Figure 6.4-7 through Figure 6.4-9 illustrate worst case scenario of an un-planned mode transition

from operating state #9 (Storage + Utility) in the grid-connected mode to the operating state #3

(Storage + VSC) in the off-grid operating mode. Before transition in the grid-connected mode,

full load was being served with two capacitor banks connected to the PCC and two capacitor

banks connected at the load bus as in the previous case.

Initially the VSC is supplying a constant charging current of 0.38 per unit (HV side) to the

storage element. The VSC is also supplying reactive power to the system with a reactive current

at 1.07 per unit to regulate the load bus voltage at the nominal value and the PCC voltage at 1.01

per unit. A single line to ground fault (A-G) is applied for a 3-cycle duration at the PCC on the

utility side of the TCB. The fault resistance is 0.001 Ω and the fault is applied at time t = 2.0s.

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The system changes operating state to state #10 (FOS) as soon as the fault condition is detected.

The single line to ground fault causes the three phase rms voltage at the PCC to go below 0.8 per

unit at which time induction motor load (ML2) is shed and the capacitor bank (600µF, star

configured) connected to the load bus is disconnected by initiating opening of their circuit

breakers. Opening of the TCB is initiated when the rms voltage at the PCC drops further to

below the level of 0.74 per unit. At the completion of the breaker opening operation at time t =

2.03s system control is handed over to the storage based control scheme shown in Figure 5.5-1 in

its operating state #3 (Storage + VSC) in the off-grid mode of operation. After the load is picked

up by the storage element, the dc bus voltage initially drops to about 0.85 per unit and recovers

to nominal value at around t = 2.189s. Plots 2 and 3 in Figure 6.4-7 also show the voltage

envelope of the ‘no-interruption in function’ region for the electronic equipment given by the ITI

curve. It is concluded that the rms voltage at the load bus and at the PCC remains within the

transient performance limits.

Figure 6.4-7: Un-planned on-grid to off-grid mode transition, 1) reference and actual dc bus voltage 2) reference and actual rms voltage at the PCC 3) reference and actual rms voltage at the load bus 4) operating state and OCC operation duration

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Figure 6.4-8: Un-planned on-grid to off-grid mode transition, 1) active current component of the VSC 2) reactive current component of the VSC 3) space vector magnitude of the load branch and the VSC output current

Figure 6.4-9: Un-planned on-grid to off-grid mode transition, 1) battery terminal voltage 2) battery terminal current

The supervisory controller provides a stable operation for the on-grid to off-grid mode

transition through the intermediary fault operating state FOS (state #10). It will be noticed from

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Figure 6.4-9 that the VSC output current however exceeds the limit of 1.3 per unit immediately

after the system starts operation in the islanding mode. The explanation to this lies in the

behaviour of the induction motors under fault conditions. The induction motor load (particularly

ML2 rated at 0.27 per unit or 82 kW) draws a large amount of reactive power during the period,

suppressing further the voltage at the load bus and hence at the PCC. After disconnection from

the utility, the battery storage and the dc capacitor are the only sources of energy supply within

the system to meet the load demand (including ML1) through the VSC interface. This causes

converter current limits to be exceeded. The motor load ML2 will need to be disconnected at an

earlier stage during the fault conditions (or during voltage sags under normal operation) than the

level of 0.8 per unit used in the simulation case presented in this section. It is mentioned here that

the VSC current remains within limits (results not shown) when the same fault is applied with

only SL1, SL2 and ML1 with rated load torque and a single capacitor bank (450µF, star

configured) connected to the load bus.

This case highlights the importance of proper sizing of the system components for

uninterrupted system operation during unplanned transition from on-grid to off-grid mode.

Proper coordination of the protection scheme of the induction motor load ML2 is required if the

system is to make a successful transition from on-grid to off-grid mode through the intermediary

fault operating state (FOS) during operating conditions depicted in the foregoing simulation case

with the assumed rating of the VSC (1.3 per unit). The case however indicates that control

remains stable for the state transition caused by the single line to ground fault at the PCC.

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This chapter considers large transients causing transition of the study system from one operating

state to another (shown in Figure 4.2-1). Each state transition requires switching between the

corresponding control schemes. The state and control scheme transitions are managed by the

supervisory control layer. The objective is to demonstrate stability and performance of the

supervisory control scheme through time domain digital simulations of the nonlinear detailed

model of the study system in PSCAD/EMTDC software environment. Besides transitions among

operating states in which the system can operate for extended periods of time, system operation

during startup (state #1) and during standby operating state (state #2) have also been described

and demonstrated.

The following conclusions are based on the simulation results presented in the preceding

sections:

1. The proposed supervisory control scheme is stable and drives the study system along the

specified route given by the FHA (Figure 4.2-1) of the system without exceeding transient

performance limits proposed in section 2.4.2.

2. The wind energy conversion and storage system can be imparted ride through capabilities

for temporary single phase faults on the utility side by using the hybrid control and gating

scheme for the VSC proposed in section 4.3.3.

3. The WECU module with the proposed control scheme (Figure 3.1-1) can be represented as

a constant current source for transient performance and stability evaluation of the study

system.

4. Transients associated with the pre-planned mode transitions and those caused by switching

of control schemes within each operating mode have been minimized by using transition

management schemes proposed in CHAPTER 4.

5. Proper coordination of the protection scheme for the motor load ML2 will be required if the

system is to successfully transition from grid-connected mode to off-grid mode due to a

single line to ground fault at the PCC, without exceeding converter maximum current limit

(assumed 1.3 per unit).

6. System components, particularly the VSC and the capacitor banks at the PCC and at the

load bus need to be properly sized for the converter to be able to regulate the rms voltage at

the load bus under all normal operating conditions.

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It should be noted that transient performance with respect to the single phase rms voltage at the

PCC cannot be maintained for faults at the utility feeder close to the PCC unless the wind energy

conversion and storage system goes into the off-grid mode of operation immediately after the

occurrence of fault. Therefore to ensure temporary fault ride-through capability of the wind

energy conversion and storage system, the single phase sensitive load if any would need to be

moved either on to the dc side or changes would be required in the configuration of the wind

energy conversion and storage system to ensure that operation of the sensitive single phase

equipment remains uninterrupted during operation of the system in the FOS (state #10).

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CHAPTER 7

CONCLUSIONS

7.1 OVERVIEW

Operation and control of a wind energy conversion and battery storage system has been

presented in this thesis. A practical, radically different modeling and control design approach has

been proposed for the study system composed of a wind energy conversion unit and a battery

storage element with power electronic based converters which interface the two units to each

other and to the utility power system. A survey of the literature on the subject shows that so far

all of the published research has been focused on the individual control aspects of a wind energy

conversion system in either grid-connected mode or in the islanded mode of operation. There is

no published work that describes both operational and control aspects of a wind energy

conversion system in both modes of operation.

The modeling framework proposed in this thesis for the wind energy conversion and battery

storage system borrows its characteristics from the Finite Hybrid Automata (FHA) representation

of hybrid control systems. The original FHA framework is suitable for systems with relatively

few state variables. It therefore has found fewer applications to practical control problems

encountered in power systems where the control problem can be associated with a large number

of state spaces each with relatively large number of dimensions. The FHA modeling framework

also does not address the issue of transition management when a configurable hybrid system,

such as a power system, moves from one state space to another. Also the state transitions are

assumed to be instantaneous. This assumption generally is not valid for control problems

concerning power systems. The FHA framework in its present form therefore becomes

impractical for a large number of control problems relating to power systems.

Control design of the wind energy conversion and battery storage system is another issue

which is related to the modeling of the system. The study system presents a complex Multiple-

Input-Multiple-Output (MIMO) control problem. The control design problem has been simplified

by using a modular control design approach suggested by the State Transition Diagram (STD) of

the study system. A careful analysis of the operation of the system using the STD, which is the

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basis for the proposed modified FHA model of the system given in Figure 4.2-1, reveals that the

system can be partitioned along the dc bus into three independent system modules based on

certain assumptions. Control design for each module has then been carried out in isolation from

the rest of the system, with assuming that the three system modules are decoupled when the dc

bus voltage is tightly regulated. The modified FHA of the system has then been used to devise

suitable schemes for the system when the individual system modules are operated in various

combinations as depicted by the FHA in Figure 4.2-1, in order to meet the steady state and

transient performance specifications outlined in CHAPTER 2.

Modularization is the underlying principle of the practical approach of modeling and control

design presented in this thesis, in the context of the wind energy conversion and battery storage

system. Unlike the original FHA which is based on the state space composition of a system, the

proposed modified framework represents operation of the wind energy conversion and storage

system based on the allowable combinations of the energy sources in the system. The modified

FHA of the system also reveals partitioning axes for modularization of the system and thus

provides a basis for a modularized control design. Each allowable combination of the energy

sources in the system (defined in this thesis as an ‘operating state’) requires a different control

scheme for the system. Within an operating state, changes in state space of the system due to

changes in control scheme are represented by multiple substates within that operating state. This

allows for the building block modules to be considered on their own in each operating state of

the system and suitability of one control scheme or another can be assessed and envisioned with

respect to steady state and transient response objectives. This also allows for considerations of

suitable transition management of control schemes according to the different system

configurations when a supervisory layer is considered for the overall control management of the

system.

A supervisory control mechanism designed on the basis of the proposed modified FHA of

the system provides coordination among the different control schemes designed for individual

operating states in order to drive the wind energy conversion and battery storage system along

the prespecified routes given by the FHA of the system. The proposed supervisory hybrid

controller of the study system uses power and load management strategies for transient and

steady state power balance in the system and implements transition management strategies for

bumpless transfers between control schemes (regulators) as also for smooth transitions from one

operating state to another.

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The control design and operation management principles developed for the supervisory hybrid

control of the wind energy conversion and battery storage system presented in this thesis could

also be applied to other control problems of similar nature where coordinated operation and

control of a system with several local generation sources is required. Steps involved in the design

process are given at the end in appendix B.

7.2 CONCLUSIONS

The following conclusions are presented based on the research reported in this thesis:

1. It is concluded that the complex control problem of a wind energy conversion and storage

system can be handled using hybrid control techniques and a modular control design

approach.

2. The successful operation of the wind energy conversion and storage system requires

formulation of suitable power and load management strategies. Transition management

strategies are also required for smooth transition between the two operating modes (on-grid

and off-grid operation) and between the various possible operating states of the system

within each operating mode.

3. It is concluded that control schemes based on simple linear control laws together with the

hybrid switching scheme for the VSC, could be combined and coordinated through a

supervisory control layer for the automatic operation of the wind energy conversion and

battery storage system in an operating space that consists of many different possible

operating conditions. Apart from steady state and normal dynamic operating conditions, the

operating space may also include state transitions caused by a change in the system control

structure alone or due to a change in the configuration of the wind energy conversion and

storage system accompanied by a change in the control scheme.

4. The proposed supervisory hybrid control scheme of the study system provides flexibility in

the control of the system to suite different operating requirements under different operating

conditions. It allows for the pursuit of multiple control objectives for the system, e.g.

maintaining operation within transient performance specifications and limiting converter

output current during utility side faults in order to impart temporary fault ride-through

capability to the wind energy conversion system.

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7.3 CONTRIBUTIONS

The following are the main contributions of this thesis:

1. A modified modeling and control design approach based on the finite hybrid automata

framework of hybrid control systems has been proposed for the representation of the

operation and for the design of a supervisory hybrid control scheme for the wind energy

conversion and storage system.

2. Automatic operation and control of the wind energy conversion and storage system has

been demonstrated, using a supervisory hybrid controller which drives the system along a

pre-specified route represented by a modified FHA of the system. It has been shown that

the supervisory hybrid controller can be synthesized using traditional control schemes and

simple linear compensators in conjunction with suitable transition management strategies.

3. A hybrid control and gating scheme for the VSC has been presented which gives the wind

energy conversion system the capability of fault ride-through during grid-connected mode

of operation for temporary faults originating on the utility side. The proposed hybrid control

and gating scheme provides integrated protection and control of the VSC. It also avoids

over sizing of the converter which is otherwise a common practice to ensure continuous

system operation.

4. A novel current controlled speed regulation of the wind driven induction generator has been

presented. The proposed control scheme provides robust and uniform performance over the

entire speed range within the constraints imposed on the system operation. These

constraints include:

• Operating speed range of the generator

• Limitations on the output of the generator and thyristor-controlled rectifier

• Limitations on the mechanical oscillations of the generator-wind energy conversion

unit

The proposed speed regulator provides robust performance in the face of internal and

external system disturbances. The internal system disturbances may originate on:

• the dc side of the thyristor-controlled rectifier due to dc bus voltage fluctuations or

• on the generator side of the system due to capacitor switching which may also cause

extreme mechanical stresses in the system

External disturbance comes in the form of wind speed variations.

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5. The concept of transition management has been introduced in the context of the supervisory

hybrid control of the wind energy conversion and storage system for a smooth transition

among the various operating states given by the FHA of the system. It should be noted that

a transition in the operating state of the study system also involves switching between the

associated control schemes of the system in the pre and post-transition operating states.

6. A reference shaping technique has been introduced for the indirect control of the rms

voltage of the load bus to achieve transient performance specifications by exercising direct

control over the PCC voltage using the VSC. The proposed technique has the advantage

that it does not require knowledge of the parameters of the load branch between the load

bus and the PCC and can be used both in grid-connected and in islanded operation of the

wind energy conversion and battery storage system.

7.4 FUTURE WORK

The following potential research areas are identified:

1. Hardware and software implementation of a scaled down wind energy conversion and

battery storage system with the proposed supervisory hybrid control scheme reported in this

thesis.

2. Hybrid control of an expanded wind energy conversion and battery storage system

containing other forms of distributed generation e.g. a micro turbine connected at some

node other than the PCC, in a micro grid configuration.

3. Operation of the reported wind energy conversion and storage system with an expanded

FHA model which accounts for transient fault operating states due to internal faults within

the wind energy conversion and storage system itself.

4. Application of the proposed hybrid modeling and control design approach suggested in this

thesis towards systems containing multiple energy sources in a micro grid configuration.

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APPENDIX A

SYSTEM PARAMETERS

Parameters of the wind energy conversion and battery storage system are given in Table A-2, in

per unit. Base values are given in Table A-1 while Table A-3 gives control parameters for the

system.

Table A-1 Base values

Name and Description Base Value4

Vdc : DC Bus Voltage 1000 V

Vb : Battery Voltage 400 V

Id : DC Current 300 A

Ib : Battery Current 750 A

Iqd : qd reference frame Currents 510.31 A

Vqd : qd reference frame Voltages 391.92 V

Table A-2 System parameters

Component Parameter Symbol Value

Inertia Constant tH 2.5 p.u. Wind Turbine5

Mechanical damping - 0.0

Inertia Constant gH 0.48 p.u. Induction Generator6


4 The base values on the AC and the DC side of the converter are based on a power base of 300 MVA with rated base voltages on either side of the converter. A nominal duty ratio of 2.5 has been used for base values on the battery side of the dc-dc converter. 5 Dynamic characteristics are given in Figure C-3 6 Magnetizing characteristics are given in Figure C-5

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Component Parameter Symbol Value

Stator Reactance lsX 0.119 p.u.

Rotor Reactance lrX 0.119 p.u.

Stator Resistance sr 0.012 p.u.

Rotor Resistance rr 0.0085 p.u.

Induction Generator

Reactance of the magnetizing branch mX 4.366 p.u.

capacitance dcC 40.0mF

inductance dcL 0.05H DC Bus

Resistance dcR 0.0318Ω

Series Resistance bsR 30.0mΩ

Resistance of the parallel branch bpR 25.0mΩ

Capacitance in the parallel branch bpC 0.6F

Constant voltage source bV 400 V

Battery Storage and dc-dc

converter

Inductance bL 0.003H

Reactance of the (ideal) transformer (13.8kV/480V, 0.5MVA) LL 0.08 p.u.

Resistance of the (ideal) transformer (13.8kV/480V, 0.5MVA) LR 0.0

Inertia Constant 1mH 0.5 p.u.

Stator Reactance 1lsX 0.065 p.u

Rotor Reactance 1lrX 0.049 p.u.

Stator Resistance 1sr 0.078 p.u.

Load7

Induction Motor

Load

ML1

Rotor Resistance 1rr 0.044 p.u.

7 Core and winding magnetic saturation has been neglected for both induction motor loads

168

Reactance of the magnetizing branch 1mX 2.67 p.u. Induction

Motor Load

ML1 Mechanical damping - 0.0

Inertia Constant 2mH 0.48 p.u.

Stator Reactance 2lsX 0.119 p.u.

Rotor Reactance 2lrX 0.119 p.u.

Stator Resistance 2sr 0.012 p.u.

Rotor Resistance 2rr 0.0085 p.u.

Reactance of the magnetizing branch 2mX 4.366 p.u.

Induction

Motor Load

ML2


Resistance slr 2.89 p.u.

Load

Static Load

(SL1, SL2) Reactance slx 2.09 p.u.

Reactance 21.01 p.u. Feeder

Resistance 12.58 p.u.

Reactance of the (ideal) transformer (132kV/13.8kV, 25MVA) - 0.08 p.u.

Reactance - 29.87 p.u.

Utility

Network Thevenin

Equivalent

(Power Grid) Constant Voltage V∞ 132.0kV

Table A-3 Control parameters

Controller Parameter Symbol Value

Proportional constant (inner current loop) piwK 0.00785 rad A-1

Integral constant (inner current loop) iiwK 0.1745 rad A-1

Time constant (LPF, inner feedback loop) iwτ 3.0ms

Wind Energy

Conversion System

Proportional constant (outer speed

regulator) pwK 24.0 rad s-1 A-1

169

Integral constant (outer speed regulator) iwK 8.0 rad s-1 A-1

Wind Energy

Conversion System Time constant (LPF, reference speed)

wτ 0.20s

Proportional constant (inner current loop) piK 0.20 VA-1

Integral constant (inner current loop) iiK 1.43 VA-1

Proportional constant (outer dc regulator) pdK 10.0 AV-1

Grid-connected

operation

Integral constant (outer dc regulator) idK 100.0 AV-1

Reference Shaping Integral constant - 0.10s

Proportional constant - 0.30 p.u.

VSC

Islanded operation Integral constant - 15.0 p.u.

Proportional constant pdcK 10.0 AV-1

Battery storage and

dc-dc converter Integral constant idcK 200.0 AV-1

170

APPENDIX B

MODIFIED HYBRID MODELING FRAMEWORK

A hybrid system consists of continous and discrete state variables. In power systems, elements

such as generators and loads exhibit continous dynamics while the actions of protection elements

for example; constitute discrete events [83]. A number of different frameworks have been

suggested for modeling general hybrid dynamical systems [20]. Attempts have been made to

provide a suitable hybrid modeling framework for power systems [69], [83] and [84]. None of

these hybrid modeling frameworks however, provides for a systematic modeling and control

design approache. Apart from specific hybrid systems with a few state variables, there are no

analytical means for analysis and stability investigation of a switched hybrid system.

In the following sections an attempt has been made to provide for an integrated modeling

and control design approach for small scale power systems (micro-grids) in the context of the

wind energy conversion and battery storage system. Modularization is the underlying principle

for the proposed approach which borrows characteristics from the general FHA modeling

framework. However unlike the original FHA modeling paradigm, operation of the system is not

depicted based on the state space composition of the system, rather it is based on the allowable

composition of the energy sources in the system (defined as an ‘operating state’ of the system).

The basic philosophy behind this approach is the consideration that a different control scheme

will be required for satisfactory operation of the system in each operating state corresponding to

each allowable combination of the energy sources in the system. The modified FHA of the

system thus not only reduces modeling complexity but also provides for a basis for a modular

control design. Transition between different possible control schemes for the system in each

operating state can be depicted by substates corresponding to each control scheme. The modified

FHA of the system thus depicts system operation with a reduced number of operating states

where the transition paths among the allowable operating states of the system are prespecified. A

supervisory control layer is then used to combine the control schemes which have been devised

for system operation during each individual operating state, for the integrated control of the

171

system.

The hybrid control scheme with a hierarchical supervisory control layer offers the possibility

of combining and reconfiguring the individual control schemes of the system in order to pursue

multiple control objectives under varying operating conditions. This has been demonstrated with

respect to the study system reported in this thesis.

In the modified FHA representation, operation of the system is divided into two basic

modes:

1. Grid Connected Mode (on-grid operation)

2. Islanded Mode (off-grid operation)

The modified FHA of a system can be developed from the STD of the system. The STD of the

system is a graphical illustration of the operating logic for the system and is based on the

assumption that transition between the two modes (on-grid and off-grid) and between different

operating states within each mode is instantaneous.

Consider a generic small power system (micro-grid) consisting of three energy sources A, B

and C, besides the energy source in the form of the external power grid. Generally, operational

and control considerations will be the basis for the possible operating states of the system (e.g. a

wind energy conversion system cannot operate on its own without an external support due to the

intermittent nature of the wind). A STD for the system is shown in Figure B-1 where it is

assumed that all the desireable ‘normal’ operating states of the system are represented. The

assumption of an instantaneous transition between the two operating modes is in general a gross

simplification and as such not valid. A transient operating state in which the system is first

synchronized with the external power grid before it switches operation from islanded mode to

grid-connected mode is required. Similarly, a transient fault operating state need to be considered

when fault rid-through capability for the system is desireable.

System configuration together with the STD of the system will generally provide clues to the

suitable axes along which the system could be partitioned for modular control design. The STD

of Figure C-1 could be augmented with the transient operating states mentioned above together

with the assumed two different possible control schemes for the system operating state in which

the energy source C is in service, to arrive at the modified FHA of the system shown in Figure C-

2.

172

Figure C- 1: State Transition Diagram (STD) for a generic system with three energy sources A, B and C

Figure C- 2: Finite Hybrid Automata for the generic system with three energy sources A, B and C

173

The STD of a system with relatively fewer energy sources could be directly determined.

However, this may be relatively tedious when possible combinations of more than a few energy

sources are considered. Boolean logic could be used for obtaining the STD of a system from the

Operating Logic Diagram (OLD) in such situations. The OLD is a graphical representation of the

truth table for the energy sources (and the load) in the system. Figure C-3 gives the OLD for the

study system, as an example. Here two levels of the availability of the energy sources in the wind

energy conversion and storage system have been assumed, 1) low and 2) high. This may be the

case for low and high winds or low and fully charged storage batteries.

Figure C- 3: OLD for the wind energy conversion and storage system reported in this thesis

Figure C-3 gives only one side of the OLD in the off-grid mode of the system, the other is

similar with the system in the on-grid mode. The non allowable states could be striked out to

obtain the STD shown in Figure 2.2-1.

174

The supervisory control design process of a system with multiple operating states and multiple

generation sources can be divided into the following steps:

1. Formulate control objectives and modes of operation (on-grid, off-grid or both) and specify

performance requirements (for steady state and dynamic system operation).

2. Formulate load and power management strategies.

3. Obtain the Operation Logic Diagram (OLD) of the system.

4. Determine the State Transition Diagram (STD) of the system from the OLD developed in

the previous step by eliminating operating states that are not feasible and not desirable.

5. Obtain the FHA of the system by suplementing the STD with suitable transient operating

states such as Fault Operating State (FOS) if needed and Synchronization Operating State

(SOS) if both on-grid and off-grid mode of operation is required and by determining uni

and bi-directional transition paths among the various operating states of the system.

6. Carefull analysis of the system STD and/or FHA which depends on the particular system

configuration, suitable partition axis (axes) should be located.

7. Determine suitable control structures for the system in each of its operating state with the

objective to minimize control scheme transitions as the system will move from one

operating state to another following the proposed FHA for the particular system.

8. Determine suitable monitoring and control signals used by the supervisory control layer that

will be used for decision making regarding control and/or system configuration changes.

9. Verify control performance using established control techniques e.g., linear analysis and

using time domain simulations.

175

APPENDIX C

MODELING OF WIND ENERGY CONVERSION UNIT

A schematic representation of the wind energy conversion unit is shown in Figure C-1, which

also shows the sign convention used for developing a mathematical model of the system in a qd

reference frame where the q axis is aligned along the stator ‘a’ phase voltage vector and leading

the d axis.

Figure C- 1: Schematic of the wind energy conversion unit and sign convention used for modeling

Referring to Figure C-1, the wind mass flowing across the turbine creates a lifting force on

the blades resulting in a rotational torque on the turbine. The turbine drives the mechanically

coupled squirrel cage induction generator, the electrical output power of which is regulated

through the thyristor-controlled rectifier bridge. A constant dc voltage source supports operation

of the wind energy conversion unit.

A control scheme for the unit is shown in Figure 3.1-1 which has been reproduced in Figure

C-2. In the following sections detailed description of the component-by-component modeling of

the wind energy conversion unit has been presented.

176

Figure C- 2: Single line control schematic of the wind energy conversion system

177

C.1 AERODYNAMIC MODEL OF THE WIND TURBINE

The wind turbine used in this thesis is a three-blade, horizontal axis stall regulated machine. The

input to the aerodynamic wind turbine model, wind speed, is generally a random variable both in

magnitude and direction and depends on many factors such as spatial distribution across the

plane of the rotor blades among others [85]. For the dynamic wind speed the following

expression is generally used [86], [87]:

nwgwrwmww VVVVV +++= , (C-1)

where wV is the measured wind speed, mwV is the average wind speed at the hub height, rwV

and gwV are the ramp and the gust components and nwV is the noise component present in the

wind.

A simplified model of the wind turbines used for power system stability studies generally

assumes a mean wind speed at its input with the output rotor power given by the following

expression [85]-[88]:

( ) 3

2

1, wpT AVCP ρβλ= , (C- 2)

where ρ is the air mass density, A is the rotor swept area and pC is a dimensionless power

coefficient whose value depends on the type and operating conditions of the wind turbine i.e. the

pitch angle β and the tip speed ratioλ . The ratio of the blade tip speed to wind speed is given

by:

w

T

V

Rωλ = . (C- 3)

Here R is the radius of the wind turbine rotor and Tω is its angular speed. For a constant pitch

wind turbine pC varies as a function of λ alone. The power coefficient has a maximum value

for a specific optimum rotor speed of the turbine at any specific wind speed.

The dynamic model of the wind turbine can be constructed by using a family of power

verses rotational-speed curves of the turbine for the operating range of the wind speed. The

178

dynamic wind turbine model used in this thesis consists of a family of normalized power verses

speed curves, shown in Figure C-3.

Figure C- 3: Wind turbine output power verses speed characteristics

C.2 INDUCTION GENERATOR

For an induction generator, magnetic saturation model in the machine plays a vital role in the

stable operation of the unit [89]. Also the machine model needs to take into account both stator

and rotor electrical dynamics. There are two fundamental circuit models used for the study of an

induction machine [90]. In one approach, which considers a symmetrical induction machine,

loop impedance method or the nodal admittance method is employed to come up with a per-

phase equivalent circuit model [91]. In the second approach, which is not restricted to the

symmetrical machine alone, fundamental machine theory is used to derive an orthogonal axis

model in the arbitrary reference frame [92]. The former approach is suitable only for steady state

studies while the later can be used for all possible operating conditions including asymmetries

both in the stator and the rotor circuits and nonlinearities such as magnetic saturation and

frequency effects [90]. A detailed discussion on induction machine modeling is provided in [91].

Magnetic nonlinearity of the machine core needs to be incorporated into the machine model for

excitation and sustained operation of the induction machine. Main flux saturation can be

represented in the machine model with both currents and flux linkages as state variables. In the

former cross coupling effect between the orthogonal circuits of the machine caused by the time

varying nature of the magnetizing inductance, is explicitly expressed while in the latter the effect

179

is implicitly accounted for [93]. A number of approaches have been suggested for incorporating

cross coupling effect for the study of saturated induction machines [93]-[96].

In this thesis the 4th order so-called ‘T’ model of the machine has been used in which both

the rotor and the stator leakage reactances are assumed equal [91]. Modeling of the main flux

saturation is based on the approach given in [97], [98]. The following points should be noted

about the machine model used in this thesis:

1. Currents have been used as state variables for the machine model in the qd reference frame.

2. Main flux saturation has been taken into account by using an assumed no-load terminal

voltage verses current characteristics of the machine.

3. The resistance of the magnetizing branch representing hysteresis and eddy current losses

has been neglected. The implication of this assumption is that the magnetizing flux is in

phase with the magnetizing current.

The equivalent orthogonal circuit model of a squirrel cage induction machine in the synchronous

reference frame rotating at ω rad/s is given in Figure C-3 in which all quantities are referred to the

stator side [95].

Figure C- 4: Synchronous reference frame equivalent circuit of a three phase induction machine

The voltage equations of the machine are given by:

180

qsgdsgqsgsqg pirv λλω ++= , (C- 4)

dsgqsgdsgs pir λλω +−=0 , (C- 5)

qrgdrgrqrgr pir λλωω +−+= )(0 , (C- 6)

qsgdsgrqsgr pir λλωω +−−= )(0 , (C- 7)

where sr , rr are the resistances of the stator and rotor windings, lsL , lrL are the stator and rotor

leakage inductances and dt

dp = is the differential operator. The stator flux linkages qsgλ , dsgλ and the

rotor flux linkages qrgλ , drgλ can be written as:

)( qrgqsgqsglsqsg iiMiL ++=λ , (C- 8)

)( drgdsgdsglsdsg iiMiL ++=λ , (C- 9)

)( qrgqsgqrglrqrg iiMiL ++=λ , (C- 10)

)( drgdsgdrglrdrg iiMiL ++=λ . (C- 11)

In the above equations M represents the mutual inductance between the stator and the rotor

windings.

C.2.1 Representation of Saturation

Only the nonlinearity of the mutual coupling between the stator and rotor windings has been

taken into account since saturation of the stator leakage reactance can be neglected as it is in

general much smaller compared to the air gap reactance [91]. Figure C-5 shows the assumed

magnetizing characteristics (reference) and the no-load test results on the symmetrical induction

machine implemented in PSCAD/EMTDC with the same reference characteristics. For accurate

linear analysis it is imperative that the machine model presented in these sections is a faithful

representation of the machine model implemented in PSCAD/EMTDC. For this purpose the

saturation characteristics of the machine in PSCAD/EMTDC (and not the reference

characteristics) have been approximated with a continuous function, as shown in Figure C-5.

181

Figure C- 5: No-load magnetizing characteristics of the machine (terminal voltage verses magnetizing current)

The no-load saturation curve has been approximated with the following continuous function

using nonlinear regression (curve fitting) techniques as opposed to the common approach of

using polynomial and trigonometric functions that does not provide for a good fit of the assumed

characteristics.

)tanh( 2mpumpumputpu iiiv δγβα ++= , (C- 12)

where tpuv , mpui are the per unit terminal voltage and the magnetizing current, respectively. The

coefficients of the nonlinear function have been determined as:

202613043.0,44582632.6,0689323.59,063543125.1 =−=== δγβα .

Neglecting the voltage drop component of the stator winding resistance, the nonlinear

relationship of the mutual inductance M (in actual units) with the per unit magnetizing current

mpui is then given by:

baselspumpub

mpumpumpu ZLi

iiiM ]

)tanh([

2

−++

=ω

δγβα. (C- 13)

182

Here baseZ and bω are the base impedance and frequency respectively, and lspuL is the stator

leakage inductance in per unit.

The magnetizing current mi for the machine circuit in Figure C-3, is given as:

22 )()( drgdsgqrgqsgm iiiii +++= . (C- 14)

The derivatives of the flux linkages given in equations C-5 to C-8 are then given by:

pMipiMpiLp qmqrgqsgsqsg ++=λ , (C- 15)

pMipiMpiLp dmdrgdsgsdsg ++=λ , (C- 16)

pMipiLpiMp qmqrgrqsgqrg ++=λ , (C- 17)

pMipiLpiMp dmdrgrdsgdrg ++=λ , (C- 18)

where;

qrgqsgqm iii += , (C- 19)

drgdsgdm iii += , (C- 20)

MLL lss += , (C- 21)

MLL lrr += . (C- 22)

The derivative of the mutual inductance can be written in terms of partial derivatives as:

][ drgdrg

mqrsg

qrg

mdsg

dsg

mqsg

qsg

m

m

pii

ipi

i

ipi

i

ipi

i

i

di

dMpM

∂∂

+∂∂

+∂∂

+∂∂

= . (C- 23)

The partial derivatives in the above equation are given as:

m

qm

qrg

m

qsg

m

i

i

i

i

i

i=

∂∂

=∂∂

, (C- 24)

m

dm

drg

m

dsg

m

i

i

i

i

i

i=

∂∂

=∂∂

. (C- 25)

For equation C-13, the derivative of M with respect to mi (in actual units) is given as:

183

base

mpub

mpumpumpu

mpub

mpumpumpu

m

Vi

iii

i

iii

di

dM]

])[(tanh(])2()tanh(1[[

2

222

ωδγβα

ωδγβγβα ++

−+++−

= ,

(C- 26)

where baseV is the base voltage.

Substitution of the stator and rotor flux linkages and their derivatives into the voltage equations

of the machine given in C-4 to C-7 gives the following equation:

,

)(0)(

)()(0

0

0

0

0

0

+

−−−−

−−=

drg

qrg

dsg

qsg

drqddqd

qdqrqdq

dqddsqd

qdqqdqs

drg

qrg

dsg

qsg

rrgg

rgrg

ss

ssqg

i

i

i

i

p

LMMM

MLMM

MMLM

MMML

i

i

i

i

rLM

LrM

MrL

MLrv

ωωωωωωωω

ωωωω

(C- 27)

where:

mm

dmsds

mm

qmsqs di

dM

i

iLL

di

dM

i

iLL

22

, +=+= , (C- 28)

mm

dmrdr

mm

qmrqr di

dM

i

iLL

di

dM

i

iLL

22

, +=+= , (C- 29)

and

mm

dmd

mm

qmq

mm

dmqmqd di

dM

i

iMM

di

dM

i

iMM

di

dM

i

iiM

22

,, +=+== . (C- 30)

The set of equations from C-27 to C-30 gives the model of the induction generator. The per unit

electrical torque produced by the induction machine is [95]:

)(.).( qrgdsgdrgqsgbasebase

bupe iiii

IV

MT −=

ω. (C- 31)

184

C.3 MECHANICAL DYNAMICS

The mechanical coupling of the wind turbine-generator has been represented by its torsional

model with two lumped masses connected through an elastic shaft. The following should be

noted:

4. An ideal gearbox has been assumed and all the variables have been referred to the

generator side.

5. Both mutual and self-damping of the generator and the turbine rotors have been neglected.

The equivalent two-mass-spring torsional model adequately represents the dynamics of the wind

turbine and the generator mechanical system for most power system studies [86], [87]. The

model used in this thesis is shown in figure C-6. This model also reflects the effects of the

dynamic interactions between the turbine and the generator shafts, which in turn affect the

electrical quantities of the induction generator.

Figure C- 6: Turbine-generator mechanical coupling

The mechanical coupling between the turbine and the generator can be written as [60].

−+

−

−

=

.).(

.).(

.).(.).(

.).(.).(

002

0

00

02

01002

02

0

00012

02

0

upT

upe

T

b

g

b

T

T

g

g

upT

bup

T

b

upg

bup

g

b

T

T

g

g

T

T

H

H

KH

KH

KH

KH

dt

dω

ω

θωθω

ωω

ωω

θωθω

. (C- 32)

185

Here gθ , Tθ are the angular displacements of the generator and the turbine rotors, gω and Tω

are their angular speeds, and .).( upeT and .).( upTT are the generator electrical and the turbine

mechanical torque respectively, in per unit. The constant .).( upK represents the shaft stiffness in

per unit.

C.4 EXCITATION

In the presence of appropriate valued terminal capacitors and due to residual magnetism in the

machine core together with nonlinear magnetic characteristics as mentioned in the earlier

sections, an induction machine when driven by a prime mover, will have induced emf causing

leading current circulation between the machine and the terminal capacitors [99]-[101]. This is

the excitation phenomenon of the induction generator which has erroneously been termed as

‘self-excitation’. Excitation of the induction generator using static capacitors is caused by the

presence of a pair of unstable eigenvalues which causes terminal voltage of the machine to

increase exponentially until the machine operating point moves on to the saturated portion of the

curve [100].

The excitation phenomenon begins at a particular speed for a particular value of the terminal

capacitance and depends on the machine parameters and saturation characteristics [99]. For a

particular machine the value of the excitation capacitance lies within a range bounded by a

minimum and a maximum value. If the excitation capacitance lies outside this range then the

machine will fail to have induced emf.

Transformation into the qd reference frame of the nodal equation at the generator terminal

node with an ideal excitation capacitor branch, results in the following equations:

( )e

qrqsgqg C

iiv

dt

d +−= , (C- 33)

qge

drdsg

vC

ii +=ω , (C- 34)

where qri , dri are the active and reactive components of the lagging current drawn by the

thyristor rectifier bridge, ω is the rotational speed of the synchronous reference frame and

eC is the excitation capacitance.

186

C.5 THYRISTOR RECTIFIER AND DC BUS

With suitable excitation the terminal voltages of the machine will be almost sinusoidal and the

machine will draw lagging sinusoidal currents, the magnitude of which will depend on the value

of the excitation capacitance and the power delivered by the machine. Since the six-pulse Graetz

bridge is connected to the machine terminal with an ideal isolating transformer, therefore

commutation inductance is nonexistent. The current drawn by the rectifier with a dc side inductor

and a constant dc voltage source will be of rectangular periodic form, the fundamental of which

will be displaced by an angle equal to the firing angle α of the bridge rectifier measured with

respect to the natural commutation of the bridge [102]. This is shown in figure C-7.

The thyristor-controlled rectifier can therefore be represented by the fundamental frequency

average-value model [102]-[104] where:

απ

cos33

qgd vV = . (C- 35)

Figure C- 7: Waveforms for a six-pulse thyristor-controlled rectifier with a constant dc source

And from the power balance on the ac and the dc side of the rectifier, neglecting the bridge

internal losses:

απ

cos32

dqr ii = , (C- 36)

απ

sin32

ddr ii = . (C- 37)

187

The dc side of the rectifier is described by the following differential equation:

dcd

dd

dqg

dd V

Li

L

Rv

Li

dt

d 1cos

331 −−= απ

. (C- 38)

C.6 CONTROL OF THE THYRISTOR RECTIFIER

Proportional-plus-Integral compensators have been used for regulators. Figure C-8 shows the

variables associated with a generic PI compensator. Referring to Figure C-8, the PI compensator

of the form ‘s

kk i

p + ’ can be written in the state space form as:

)( fbrefipi xxkxdt

d −= , (C- 39)

)( fbrefppipi xxkxy −+= . (C- 40)

Figure C- 8: Proportional plus Integral (PI) compensator

With reference to Figure C-2, the equations for the outer speed regulation loop are then given as:

)( refgiwpiw kxdt

d ωω −= , (C- 41)

)( refgpwpiwdref kxi ωω −+= , (C- 42)

where pwk , iwk are the proportional and integral constants of the outer speeder regulator and drefi

is the reference to the inner current control loop. With wτ as the time constant of the LPF, the

reference speed refω is given as:

)(1

optimalrefw

refdt

d ωωτ

ω +−= . (C- 43)

188

The equations for the inner current regulator can be written similarly and are given below:

)( drefdfbiiwpiiw iikxdt

d −= , (C- 44)

)( drefdfbpiwpiiw iikx −+=α , (C- 45)

)(1

ddfbiw

dfb iiidt

d +−=τ

, (C- 46)

where piwk and iiwk are the proportional and integral constants of the inner current controller, iwτ

is the time constant of the LPF in the feedback path and α is the firing angle of the thyristor

rectifier.

Equations C-12 to C-46 give the complete mathematical model of the wind energy conversion

unit. The model has 14 state variables out of which 4 describe the electrical dynamics of the

induction generator, 4 state variables are associated with the mechanical system, 1 state variable

describes the dynamics of the generator terminal node, 1 state variable is associated with the dc

link and 4 state variables describe the dynamics of the controllers.

The above system model can be linearized around an operating point and the small signal model

can be expressed as:

uBxAxdt

d ~~~ += ,

uDxCy ~~~ += .

The state vector is TpiiwdfbpiwrefdqgTTggdrgqrgdsgqsg xixiviiiix ]~~~~~~~~~~~~~~

[~ ωθωθω= , and the input

vector is ToptimalTTu ]~~

[~ ω= . A variable pertaining to the dc bus voltage could also be used in the

input vector u~ to study the effects of dc bus voltage variations on the different oscillatory modes

of the system. This exercise however has not been carried out as tight regulation of the dc bus

voltage has been assumed.

189

APPENDIX D

MODELING OF VSC – UTILITY GRID SYSTEM

In the following, a synchronous reference frame based nonlinear system model has been

presented that takes into account the dynamics of the Phase Locked Loop (PLL) together with

the network dynamics. The component models have been developed in state space form in a

complementary input-output relationship basis that are easily put together to form the overall

model of the VSC- Utility grid system. The choice of the reference node (PCC) makes it easier to

represent the system containing the VSC in either a grid-connected mode of operation or in an

isolated operating mode.

Reference [52] provides a mathematical modeling and control approach for a VSC

connected to a stiff utility system. However, for accurate analysis of the interactions of the VSC

with the utility system, network dynamics need to be taken into account [105]. Also, dynamics of

the PLL can play an important role in the stability of the system [106] and therefore need to be

included in the system model.

The model developed in the following sections includes both network as well as PLL

dynamics. Sensor dynamics are also taken into account. A distinction has been made between a

sensor, which is generally represented as a low pass filter, and the low pass filter itself.

The following points should be noted about the model:

1. The nonlinear model of the VSC-Utility Grid system is in the synchronous reference frame

with the q axis aligned along the PCC ‘a’ phase voltage and the d axis is lagging the q axis.

2. The VSC has been operated as a current regulated voltage source.

3. The PCC has been used as a reference point for modeling the VSC-Utility grid system and

is particularly useful in reducing modeling complexity in that few changes are required in

the system model, apart from the VSC control as shown in Figure 5.5-1, to represent the

grid-connected and isolated mode of operation of the system. Referring to Figure D-3, in

the isolated mode 0ω is associated with the voltage space vector tV of the VSC.

4. Various network components have been incorporated into the model as linear components.

5. The PLL has been taken into account as a linear device [106].

190

Figure 3.2-1 shows the single line control schematic of the VSC-Utility grid system repeated in

Figure D-1 for ease of reference. With reference to Figure D-1 and D-2, the following device and

control equations are derived:

D.1 MODELING

Figure D-1 gives the equivalent single line diagram of the VSC-Utility grid system. The

subscripts ‘q’ and ‘d’ indicate that the variable is in the orthogonal synchronous reference frame.

The additional subscript ‘r’ in the variable names in the subsequent paragraphs highlights the fact

that the quantity referred to is in the synchronous reference frame as determined by the PLL, e.g.

the orthogonal voltage components qtrv and dtrv shown in Figure D-2 are relative to the

synchronous reference frame qmdm. To avoid confusion, the reference frame determined by the

PLL would be called simply the ‘relative’ synchronous reference frame.

The space vector representation of the VSC-Utility grid system in the synchronous reference

frame is shown in Figure D-3. The angle θ in Figure D-3 is the displacement of the relative

reference frame qmdm with respect to the synchronous qd reference frame. Angle srθ is the

position of the utility voltage space vector sV with respect to the relative reference frame axis qm

and tθ gives the angular position of the converter terminal voltage space vector tV while Lθ

gives the position of the load bus voltage space vector LV in the synchronous reference frame.

The subscript ‘m’ in a variable name signifies a measured quantity, e.g. the output of a sensor.

D.1.1 Converter

The governing equations for the converter in the actual synchronous reference frame can be

written as:

−+

−

−−=

dt

qpccqt

dt

qt

dt

qt

v

vv

Li

i

L

RL

R

i

i

dt

d 1

ω

ω, (D-1)

)(2

3dtdtqtqtddcdcdcdc viviivv

dt

dvC +−= . (D-2)

191

Figure D- 1: Single Line Schematic and Control Structure of the VSC-Utility grid Subsystem

192

Figure D- 2: Single line equivalent diagram of the system module ‘VSC-Utility grid’

Figure D- 3: Space Vector Representation of the VSC-Utility Grid system

193

Variables qti and dti represent the orthogonal components of the converter terminal current ti

while qtv and dtv are the orthogonal components of its terminal voltage tv . Equation D-2 comes

from the instantaneous power balance between the ac and the dc sides and takes into account the

instantaneous power of the interface reactor (step-up transformer).

D.1.2 Network Dynamics

The dynamics of the utility network are given by the following matrix equation:

−+

−

−−=

ds

qpccqs

sds

qs

s

s

s

s

ds

qs

v

vv

Li

i

L

RL

R

i

i

dt

d 1

ω

ω. (D-3)

where qsi and dsi are the active and reactive current components supplied by the utility, and qsv

and dsv are the qd components of the utility voltage at the PCC.

The dynamics of the load network (including the step down transformer) are similarly defined by

the following equation:

−−

+

−

−−=

dL

qLqpcc

LdL

qL

L

L

s

L

dL

qL

v

vv

Li

i

L

RL

R

i

i

dt

d 1

ω

ω. (D-4)

Here qLi and dLi are the qd components of the load current, and qLv and dLv represent the qd

components of the load bus voltage.

D.1.3 PLL

The linearized PLL dynamics are given by [106] as:

θ

+

−−

=

ppll

ipll

pll

pll

ppll

ipll

pll

pll

k

k

x

x

k

k

x

x

dt

d

2

1

2

1

1

0, (D-5)

pllsr x2=θ , (D-6)

where

194

+=

)(1

1 θ

θ

ppllpll

ipll

pll

kxs

s

k

x and srs θθθ −= .

D.1.4 Node with a Capacitor Branch

The qd components of a node voltage, with a capacitor branch connected to the node, are related

to the sum of the currents at the node in the following general manner:

+

−=

∑∑

d

q

d

q

d

q

i

i

e

eC

e

e

dt

dC

0

0

ωω

. (D-7)

Variables qe and de in equation D-7 are the q and d components of the node voltage ‘e ’, ω

is the angular speed of the node voltage space vector, and qi and di are the active and reactive

current components entering the node.

From equation (D-7) the following relations are obtained at the PCC:

)(1

qLqsqtpf

qpcc iiiC

vdt

d −+= , (D-8)

)(1

dLdsdtpf

iiiC

−+−=ω . (D-9)

Similarly at the load bus the following relation holds:

−

−

+

−=

∑

∑

∑

∑

dMLj

qMLj

dSLj

qSLj

dL

qL

LdL

qL

dL

qL

i

i

i

i

i

i

Cv

v

v

v

dt

d 1

0

0

ωω

. (D-10)

Subscript ‘ ...2,1=j ’ represents the number of the connected Static Load (SL ) and/or the Motor

Load (ML ) at the load bus, as shown in Figure D-1.

In a grid-connected mode as in the case of the VSC-Utility grid system, the actual reference

frame qd is associated with the voltage space vector of the utility voltage source, i.e. sV . The

relative position of sV with respect to pccV (or the q axis) can be determined from the following

relationship:

195

ωωθ −= 0sdt

d. (D-11)

Angular speed 0ω of the voltage space vector at the infinite bus is a constant and has a value of

fπ2 rad/s wheref is the system operating frequency.

D.1.5 Sensor and Low Pass Filter Dynamics

Figure D-4 shows how the input and output of a sensor represented by a low pass filter and that

of a low pass filter itself in the two synchronous reference frames qd and qmdm have been

distinguished.

Figure D- 4: Representation of the dynamics of a Sensor and a Low Pass Filter (LPF)

Referring to Figure D-4, dynamic model of a sensor represented by an LPF

+ τs1

1 with the

time constant τ , in state space form is given by:

)(1

rmrmr xxxdt

d +−=τ

, (D-12)

where rx is the input and mrx is the output of the LPF. The additional subscript ‘ m ’ denotes

the ‘measured’ (output) value of an orthogonal component of the variable x and the subscript

‘ r ’ indicates that it is in the relative reference frame.

The output of the current sensors at the converter terminals are then given as:

+

−−

=

dtr

qtr

idtmr

qtmr

idtmr

qtmr

i

i

i

i

i

i

dt

d

ττ1

10

011. (D-13)

196

Equation D-13 can also be written as:

+

−−

=

−

dt

qt

idtmr

qtmr

idtmr

qtmr

i

i

i

i

i

i

dt

d 1R1

10

011

ττ. (D-14)

The transformation matrix R is given as:

−=

θθθθ

cossin

sincosR . (D-15)

Using the space vector magnitude of a node voltage for determining the rms voltage at that node,

the rms voltages at the PCC and at the load bus are given as:

+

−−

=

L

qpcc

vrmsL

rmspcc

vrmsL

rmspcc

v

v

v

v

v

v

dt

d

2

3110

011

ττ, (D-16)

where vτ is the time constant of the voltage sensor represented as a first order low pass filter and

qpccv is the magnitude of the voltage space vector at the PCC. The space vector magnitude of the

load bus voltage Lv is given by:

22

dLqLL vvv += ,

where qLv and dLv are the q and d components of the voltage space vector LV .

D.1.6 Converter Control

Referring to Figure D-5, the equations for the dc voltage control loop could be written as:

)( dcfbdcrefidpid vvkxdt

d −= , (D-17)

)( dcfbdcrefpdpiddqtref vvkxii −+−= . (D-18)

Similarly the rms voltage control loop in the state space domain is given by:

)(1

rmsfbrmsmvfb

rmsm vvvdt

d −=τ

, (D-19)

)( rmsmrmsrefivpirms vvkxdt

d −= . (D-20)

)( rmsmrmsrefpvpirmsdtref vvkxi −+= . (D-21)

197

Figure D- 5: Outer voltage regulators

The equations for the current regulators are similarly given by:

( )qtmrqtrefiipiUq iikxdt

d −= , (D-22)

( )qtmrqtrefpipiUqq iikxu −+= , (D-23)

qpccdtmrqqtr vLiuv ++= 0ω , (D-24)

( )dtmrdtrefiipiUd iikxdt

d −= , (D-25)

( )dtmrdtrefpipiUdd iikxu −+= , (D-26)

qtmrddtr Liuv 0ω−= , (D-27)

where qtrv and dtrv are the voltages demanded of the converter by the current regulators in the

reference frame qmdm.

Referring to Figure D-6, the converter actual output voltages qtv and dtv are given as:

=

dtr

qtr

dt

qt

v

v

v

vR . (D-28)

198

Figure D- 6: Converter terminal voltage components in the actual qd and relative qmdm synchronous reference frames

D.1.7 Passive Load

The static load connected to the load bus can be written in a state space domain as:

+

−

−−=

dL

qL

jdSLj

qSLj

j

j

j

j

dSLj

qSLj

v

v

Li

i

L

RL

R

i

i

dt

d 1

ω

ω, (D-29)

where ‘ ...2,1=j ’ is the number of the parallel connected static load as shown in Figure D-1, qSLi

and dSLi are the static load q and d current components.

D.1.8 Induction Motor Load

The nonlinear induction machine model with fluxes as state variables is given by [95]:

+

−−

−−−

−

−−

=

0

0

0

0

0

0

0

'

'

'

0

'0

''

'

0

0

'

0

'

'dL

qL

drj

qrj

dsj

qsj

j

ssjrjrj

j

mjrj

rj

j

ssjrj

j

mjrj

j

mjsj

j

rrjsj

j

mjsj

j

rrjsj

drj

qrj

dsj

qsj

v

v

D

Xr

D

Xr

D

Xr

D

Xr

D

Xr

D

Xr

D

Xr

D

Xr

dt

d ω

ψψψψ

ωωω

ωωω

ωω

ωω

ω

ψψψψ

, (D-30)

199

2'mjrrjssjj XXXD −= . (D-31)

The algebraic relationships between machine fluxes and currents are:

−−

−−

=

drj

qrj

dsj

qsj

ssjmj

ssjmj

mjrrj

mjrrj

j

drj

qrj

dsj

qsj

XX

XX

XX

XX

D

i

i

i

i

'

'

'

'

00

00

00

00

1

ψψψψ

, (D-32)

where qsji and dsji are the machine terminal currents ‘ ...2,1=j ’ represents a number assigned to

the motor load as shown in Figure D-1 and Figure D-2.

The mechanical dynamics for a lumped mass machine shaft are governed by the following

equation [95]:

( )Ljejj

rj TTHdt

d −=2

0ωω , (D-33)

( )qMLrjdMLjdMLrjqMLjbasej

mjej iiii

P

XT −=

2

3 . (D-34)

where ‘ ...2,1=j ’ is the number of the parallel connected induction motor load at the load bus,

eT and LT are the machine electrical and mechanical load torques respectively, in per unit based

on the machine rating. Variables qMLji and dMLji are the stator currents, and qMLrji and dMLrji are

the rotor currents of the induction machine in the stator reference frame.

The set of equations from (D-1) to (D-34) gives a detailed model of the system module

‘VSC-Utility grid’ which takes into consideration not only the network but also the PLL and the

sensor (voltage and current) dynamics. This modeling approach can be extended to a system

containing a VSC, with any number of nodes, for a detailed analysis of the system.

D.2 MODEL VALIDATION

The nonlinear model of the VSC-Utility Grid system described by equations D-1 through D-34

has been implemented in MATLAB/SIMULINK environment using its GUI based equation-

solving features. A comparison of the simulation results from the nonlinear model in

MATLAB/SIMULINK with simulation results from the detailed system model developed in the

200

PSCAD/EMTDC simulation package is presented below. All the variables have been plotted in

per unit values.

The following should be noted:

5. The base power used is 300kVA with 1.3 per unit as the assumed maximum current limit

of the converter.

6. The instantaneous ‘abc’ reference frame variables have been expressed in per unit based on

their maximum values corresponding to their nominal rms values.

7. The per-unitized (induction motor) load torques are based on the respective machine rating.

8. The VSC switching control in PSCAD/EMTDC is based on SPWM and a switching

frequency of 3960 Hz (66x60 Hz) has been used.

Table D-1 gives control parameters used for simulations while base values for per

unitization are given in Table A-1 in appendix A. Figure D-7 through Figure D-9 shows system

response for load transients from the nonlinear model in MATLAB/SIMULINK and the system

model in PSCAD/EMTDC. All these figures have been drawn for the same time duration. The

various points along the time line when a particular load is connected (disconnected) from the

feeder have been marked in Figure D-7.

Table D-1: Control parameters

Name and Description Value

piK : Proportional gain of the inner current regulators 0.2 [p.u.]

iiK : Integral gain of the inner current regulators 1.428 [p.u.]

pdK : Proportional gain of the dc voltage regulator 10.0 [AV-1]

idK : Integral gain of the dc voltage regulator 100.0 [AV-1]

pvK : Proportional gain of the rms voltage regulator 2.0 [AV-1]

ivK : Integral gain of the rms voltage regulator 1000.0 [AV-1]

201

Initially the system is running under no-load conditions with a 1.5µF capacitor connected at the

PCC (at 13.8kV). A dc current id = 0.66 per unit is injected into the dc bus by a constant current

source. The injected power into the dc bus is transferred to the utility side by the converter with a

reactive power import to maintain the load rms voltage at 1.0 per unit. At 1.5s a 0.81 lagging

power factor static load (SL1), 0.28 per unit rating is connected to the system. The system after

small transients attains a new steady state operating point. At t=2.5s a small 0.127 per unit (38

kW) induction motor load (ML1) is connected to the load bus while running at synchronous

speed with zero load at its shaft. A second capacitor bank of 1.5µF is connected to the PCC (at

13.8kV) at 3.75s while another static load (SL2) rated at 0.28 per unit (with a power factor of

0.81 lagging) is connected at 4.5s. At 5.5s full load torque is applied to the motor load ML1. At

t=6.0s the dc current injection is increased to 1.0 per unit. At t=7.0s another induction motor load

(ML2) is connected to the system while running at synchronous speed with zero load torque. The

motor load ML2 is rated at 0.273 per unit (82 kW). The load torque (TLM2) is then increased to

1.0 per unit at t=8.0s. At t=8.5s the dc reference signal is changed from 1.0 per unit to 1.03 per

unit and back to 1.0 per unit at t=9.5s. At t=10.5s the reference rms voltage signal is changed

from 1.0 per unit to 0.98 per unit and back to 1.0 per unit at t=11.5s. The active and reactive

components of the load current from the nonlinear model in MATLAB/SIMULINK and the

system model in PSCAD/EMTDC of the VSC-Utility Grid system are shown in Figure D-8.

Figure D-7 through Figure D-9 shows that the system response to load and reference step-

changes for the nonlinear MATLAB/SIMULINK model given by equations D-1 to D-34 closely

matches the response of the detailed system model in PSCAD/EMTDC. Also, the rms voltage of

the load bus remains within the performance bounds of the ‘no interruption in function’ region

specified by the ITI curve. It should be noted that the PSCAD/EMTDC based nonlinear model of

the module also takes into account switching phenomena of the power converters.

202

Figure D- 7: Response comparison of the VSC-Utility Grid system from the nonlinear model in MATLAB/SIMULINK and the system model in PSCAD/EMTDC

203

Figure D- 8: DC bus voltage and rms voltage at the load bus obtained from nonlinear system responses in MATLAB/SIMULINK and PSCAD/EMTDC for step changes in load

204

Figure D- 9: Load current components in the synchronous reference frame obtained from nonlinear system responses in MATLAB/SIMULINK and PSCAD/EMTDC for step changes in load

205

D.2.1 Response Comparison

In the following section a comparison of the simulation results in MATLAB/SIMULINK from

the nonlinear and the linear system models is presented. The linear system has been obtained at

the following steady state operating point:

FCFCupTupT

upVupVlaggingfactorpowerupSL

IIupI

LpfLmLm

dcLrms

dtqtd

µµ 5.1,5.1.,.5.0.,.5.0

..0.1.,.0.1,81.0.,.357.0

13.0,1495.0.,.5.0

21

1

========

−===

Figure D-10 shows the nonlinear and the linearized system responses. The two responses are

more or less identical which validates the linear analysis reported in this thesis.

Figure D- 10: Response comparison of the linear and nonlinear models of system module ‘VSC-Utility grid’ in MATLAB/SIMULINK

206

APPENDIX E

SELECTION AND MODELING OF BATTERY STORAGE AND DC-DC CONVERTER

E.1.1 PREAMBLE

In the following sections general characteristics of a Battery Energy Storage (BES) system have

been described followed by an overview of the various approaches that are in use for modeling

lead-acid batteries. This is followed by a discussion on the selection of battery parameters

suitable for the application in this thesis and the basic thoughts that went into the selection of the

dc-dc converter topology. Modeling of the battery storage and the dc-dc converter has been

described in section E.1.5.

E.1.2 STORAGE BATTERY

Storage batteries have applications in both generating systems as well as transmission and

distribution systems [107]. Based on time duration, two main applications of Battery Energy

Storage (BES) in power systems are [107], [108]:

1. Power Quality Control:

a. Compensation of Voltage Sags/Swells

b. Short Duration Temporary Outages

2. Energy Management:

a. Load Catering

b. Peak Shaving

c. Block Loading/Discharge (Full output power for a specific amount of time)

d. Voltage Regulation

e. Spinning Reserve

Characteristics of the storage batteries are different for each of the above two main applications.

207

For a multifunctional application involving both power quality and power management, the BES

needs to possess characteristics common to both applications. In power quality management

(high power application, duration in seconds to minutes), high charge/discharge rate capability

within the voltage limits is desirable while in energy management mode (higher energy

application) the battery is discharged over a longer period of time typically in hours. In the

former case battery capability is specified in kW or MW along with the kWhr or MWhr capacity

(Ampere hour at a specified voltage) that is usually specified in the latter case. A detailed study

about utility applications of battery energy storage is described in [109].

Lead-acid batteries can provide both power and energy requirements of the two broad areas of

application mentioned above by staking individual cells in series and in parallel combinations.

Some basics of lead-acid batteries are provided in [110] while references [111]-[116] provide

utility examples of the application of this storage technology.

In the analysis of systems with lead-acid battery storage, the particular mathematical model

used depends on the type of studies carried out. There are a number of battery models available

as far as the terminal electrical behavior is concerned [116]-[121]. Detailed battery models take

into account the chemistry of the battery cell, state of charge together with environmental effects

such as temperature etc., [122]. Parameter identification of these higher order models is

particularly difficult [123]. The detailed models are suitable for such purposes as battery

management systems for example. For power system analysis two different dynamical models

have been suggested [121], [124]:

• Long-term model

• Short-term model

Both models are represented in terms of the electrical components to emulate battery terminal

behavior, with the long-term model also incorporating non-electrical parameters. The 2nd model

is independent of battery chemistry and is suitable for system studies with short to medium time

applications (high power applications).

Two variations of the short-term model are shown in Figure E-1. In (a) same parameters are

used for both charging and discharging purposes while in (b) [117] the charging and discharging

resistances are different and this fact has been determined from experimental tests. The short-

208

term dynamical model is particularly suitable for control design purposes in isolated power

systems where fast control response is desirable.

Figure E- 1: Short-term battery models

E.1.3 SELECTION OF BATTERY PARAMETERS

A nominal battery voltage of 400 volts has been chosen for the battery bank. The response time

of the battery bank is dependent on its electrical parameters. The nominal voltage can be

obtained by series combination of individual battery cells (200units x 2volts/unit) while the

desired electrical parameters can be obtained by the parallel combination of strings containing a

number of series connected battery cells. Model (a) in Figure E-1 has been used for the research

reported in this thesis. Table E- 1 gives battery parameters for two BES systems reported in the

literature. System 1 parameters are from [121] while those for system 2 are from [125]. For the

voltage levels selected for the dc bus (1000 V) and for the battery storage (400 V), system 2 will

be able to deliver the maximum load for about 10s after which battery terminal voltage will drop

to the extent that the dc-dc converter will not be able to deliver the maximum load at the nominal

dc bus voltage level since the duty ratio will saturate. For system 2, therefore a higher nominal

battery voltage will be required. This system will be suitable for power quality applications

however not for energy management purposes where the battery system will be in operation for

extended periods of time.

Several IEEE standards describe procedures for determining battery capacity for different

applications. Two such documents of interest in cases like the study system are ANSI/IEEE Std.

484 and 485. This subject is however outside the scope of this thesis.

209

Table E- 1: 300 kW Battery Parameters

Parameter System 1 System 2 Study System

bsR [mΩ] 52 53.847 30

bpR [mΩ] 80 4.142 25

bpC [F] 250 0.2414 0.6

pτ [ms] 20,000 1 15

Min. Terminal Voltage at Full Load [%]

84.9 83 84.00

Figure E-2 shows battery terminal voltages of the three systems tabulated above, for a constant

step current discharge. Time constant associated with system 2 is relatively small while that of

system 1 is too long for the purposes of our study. System 1 response is effectively that of a

constant voltage source behind a series resistance as far as fast system transients are concerned.

A compromise between the two is the system with a time constant equal to about a cycle of the

fundamental frequency as reported in [125]. In this case battery dynamics are adequately

represented and the time constant falls within the range of most dc-dc converters [125].

Figure E- 2: Battery terminal voltage for a step discharge current

210

E.1.4 DC-DC CONVERTER

The dc-dc converter for use in conjunction with the battery storage devices needs to have the

capability of bi-directional current (power) flow between the dc bus and the battery storage.

According to the sign convention adopted in this thesis, the converter operates in the fourth

quadrant of the VI plane during the charging mode of operation. During operation in this mode

the battery storage absorbs the excess energy available at the dc bus to maintain the bus voltage.

In charging the battery, the converter operates in buck mode transferring power to the lower

voltage level. In the discharging mode, power flows from the battery storage to the dc bus. The

converter operation is in the first quadrant in boost mode, transferring power to the high voltage

dc bus side.

There are numerous converter topologies available to achieve dc-dc conversion [126]. The

basic buck and the boost converters have higher efficiency, lowest switch count and lowest

component stresses among the fundamental converters available for the two types of operations

[127]. The converter dynamics are also well understood in both these modes. Figure E-3 shows a

current-bidirectional buck-boost converter [127]. When the two switches are controlled in a

complimentary fashion, the converter is then referred to as a synchronous converter.

Synchronous control of the converter reduces switching losses when the switching devices have

lower ‘on’ resistance than the anti-parallel diodes.

Referring to figure E-3 and assuming that duty ratio D is associated with switch 1S ; under

steady state conditions the following relations hold [127]:

Boost Mode: D

VV Ti

To = , (E-1)

Buck Mode: ToTi VDV )1( −= , (E-2)

where TiV and

ToV are the average values of the input and the output voltages and

DD −= 1 . Each switch is assumed to be composed of an IGBT with an anti-parallel connected

diode.

211

Figure E-3: Two-quadrant Buck-Boost Converter

E.1.5 MODELING OF THE BATTERY STORAGE AND DC-DC CONVERTER

In the sections that follow, modeling of the battery storage and the dc-dc converter is described.

For the duty ratio control of the converter Current Programmed Mode (CPM) control will be

employed. The single line schematic of the battery storage and dc-dc converter is shown in

Figure 3.3-1, which has been reproduced in Figure E-4 for convenience.

E.1.6 AVERAGE VALUE CONVERTER MODEL

Average value model of the converter system shown in Figure E-3 and in Figure E-4 is obtained

using state space averaging method [127]:

During the interval dT switch 1S is closed and 2S open. During this interval the circuit can be

described by:

UBXAXdt

d11 += , (E-3)

XCY 1= . (E-4)

During the interval TdTTd →= switch 1S is open and 2S is closed. The system is then given

by:

UBXAXdt

d22 += , (E-5)

XCY 2= . (E-6)

212

Figure E-4: Control structure and system schematic for the system module consisting of the battery storage and dc-dc converter

Where:

−

−−

=

000

011

01

1bpbpbp

bb

bs

CRC

LL

R

A ,

−=

01

00

10

1

dc

b

C

LB ,

=100

010

001

1C ,

−

−−−

=

001

011

11

2

dc

bpbpbp

bbb

bs

C

CRC

LLL

R

A ,

−=

01

00

10

2

dc

b

C

LB ,

=100

010

001

2C ,

213

=

dc

bp

b

v

v

i

X ,

=

b

o

v

iU , XY = .

The low frequency state space average model of the converter is then given as:

TTTUBXAX

dt

d += , (E-7)

TTXCY = . (E-8)

where T

X is the average value of X over a switching cycle. The state space average model of

the converter in equilibrium is then given by:

oo

oo

CXY

BUAX

=+=0

(E-9)

where 0X , 0U and 0Y are the state, input and the output vectors corresponding to the

equilibrium operating point. The averaged system matrices are:

−

−−−

=+=

00

011

1

21

dc

bpbpbp

bbb

bs

C

D

CRC

L

D

LL

R

ADDAA ,

−=+=

01

00

10

21

dc

b

C

LBDDBB ,

=+=100

010

001

21 CDDCC ,

where D is the duty ratio at the equilibrium operating point.

E.1.7 SMALL SIGNAL CONVERTER MODEL

The small signal system model can be obtained from the state space average model using small

signal perturbations. The linear model can be expressed as:

214

( ) Sus

xs

xdt

d BA ~~~ += , (E-10)

xs

y C ~~ = . (E-11)

where

[ ]dXAABus

B ˆ)21( 0−+= ,

=

dc

bp

b

v

v

i

x~

~

~

~ ,

=

b

o

v

iu ~

~,

=d

v

i

u b

o

S~~

~

~ ,

−

−−−

=

00

011

1

dc

bpbpbp

bbb

bs

C

D

CRC

L

D

LL

R

sA ,

−−=

dc

b

dc

b

dc

b

C

I

C

L

V

L

sB

01

000

10

,

=100

010

001

sC ,

and 0X represents the system variables at the equilibrium operating point.

E.1.8 CURRENT PROGRAMMED MODE CONTROL

References [128]-[132] provide a detailed treatment of the subject of the large and small signal

modeling of the CPM control. Referring to Figure E-5, under transient conditions ( ) ( )Tii bb ≠0 .

Under these conditions the peak and average values of the inductor current waveform differ by

the average value of the inductor current ripple, which is given by:

22

2

2

2

1_

Tdm

Tdmi

Trippleb += . (E-12)

The average inductor current over a switching cycle is then given by the expression:

22

2

2

2

1

Tdm

TdmdTmii aTCTb −−−= , (E-13)

where for boost mode of operation:

b

bt

L

vm =1 ,

b

btdc

L

vvm

−=2 ,

215

Figure E- 5: Current waveforms in CPM Control

and for buck mode of operation:

b

btdc

L

vvm

−=1 ,

b

bt

L

vm =2 .

In both the buck and the boost modes of operation the following relations hold true:

bsbbpbbt Rivvv −−= , (E-14)

2mmm fa = : 10 ≤< fm . (E-15)

where fm is a multiplying factor.

For 0=fm , the CPM buck and/or boost converter has the well-known instability problem

for 5.0≥D [127]. The higher the value of fm the lower the number of switching periods it

takes to attain a new steady state value after a small initial disturbance in the inductor current bi .

The controller is able to correct for the small disturbance in the same cycle when 0.1=fm . This

is then referred to as the deadbeat control [127], which has been used in this thesis.

Assuming constant slope of the artificial ramp, the linear model of the current controller, in

both boost and buck mode of operation, is given by:

~2

~2

)~~(1~

2

2

1

2

mTD

mTD

iiTM

d bca

−−−= . (E-16)

216

Since 1m and 2m are functions of the converter voltages, the above expression may be written as:

~~)~~

(~

dcdbtbbcm vFvFiiFd −−−= . (E-17)

In terms of state and input variables the duty cycle can be expressed as:

[ ] [ ]

−+−−=

b

cbmmdmbmbsbm

v

iFFFxFFFFRFFd ~

~~)1(

~, (E-18)

[ ]

+=

b

cvdod

v

ibbxAd ~

~~~

, (E-19)

where:

( )dmbmbsbmd FFFFRFFA −−= )1( , mo Fb = and bmvd FFb −= .

E.1.9 VOLTAGE COMPENSATOR

Figure E-6 shows the complete small signal system model of the battery storage and dc-dc

converter module with CPM control (Figure E-4). The state variable associated with the linear PI

compensator for the external voltage regulation loop can be expressed as:

[ ] dcrefidcidcpidc vkxkxdt

d ~~00~ +−= , (E-20)

dcrefidccpidc vkxAxdt

d ~~~1 += . (E-21)

The control current is then given by:

[ ] dcrefpdcodcpdcpidcc vkiGxkxi ~~~00~~ ++−+= , (E-22)

dcrefpdcodccpidcc vkiGxAxi ~~~~~2 +++= . (E-23)

The set of equations E-10, E-11 and E-20, E-21 together with equation E-23 gives the complete

closed loop small signal model of the dc-dc converter and the battery storage with CPM duty

ratio control.

217

Figure E- 6: Linear system model of the dc-dc converter and the battery storage

E.1.10 MODEL VALIDATION

The closed loop small signal model of the the battery storage and dc-dc converter module given

above has been implemented in MATLAB/SIMULINK for validation against the system model

in PSCAD/EMTDC. The following should be noted:

1. In PSCAD/EMTDC a converter switching frequency of 3.0 kHz has been used.

2. The control parameters are: 200,10 == idcpdc KK .

3. The slope 2m of the artificial ramp ai is held constant at the steady state operating point for

the linear model in MATLAB/SIMULINK but is varied on a cycle to cycle basis for the

nonlinear model in PSCAD/EMTDC.

218

Figure E-7 shows the current waveforms in close-up for CPM control implemented in

PSCAD/EMTDC, in both buck and boost modes of operation: plot a) is for boost mode while

plot b) gives current waveforms in the buck mode of operation whereas plot c) gives the ramp

current in the two operating modes.

Figure E- 7: Waveforms for CPM control in PSCAD/EMTDC environment for buck and boost operating modes, 1) boost operating mode 2) buck operating mode 3) ramp reference current component

E.1.11 BOOST MODE OF OPERATION

Figure E-8 through Figure E-10 gives a comparison of the linear system response from

MATLAB/SIMULINK with the response from the detailed system model in PSCAD/EMTDC

with the converter operating in boost mode at a constant loading of 0.5 per unit (150A) at the dc

bus. The step change in load is ±0.167 per unit (50A). The difference in the control currents is

due to the averaging used for linear model of the current programmed controller together with

the fact that the slope of the artificial ramp is held constant in MATLAB/SIMULINK model but

is varied on a cycle by cycle basis according to the slope 2m in PSCAD/EMTDC environment.

219

Figure E-8 gives comparison of the converter control reference current ci and the inductor

current bi for the linear and the nonlinear models in response to step changes in the load

connected to the dc bus. Figure E-9 shows response comparison for the two models for the dc

bus voltage dcv and the battery terminal voltage btv for the same step changes in the load. Figure

E-10 gives a response comparison of the linear and the nonlinear systems for step changes of

±0.03 per unit (±30V) in the reference dc bus voltage while the dc load current is kept constant at

0.5 per unit.

Figure E- 8: Current Waveforms in Boost Mode of Operation; comparison between linear MATLAB/SIMULINK based and nonlinear PSCAD/EMTDC based simulations for step changes of ±0.167 per unit (±50A) in dc bus load Io, 1) dc load current 2) reference control current 3) inductor current

220

Figure E- 9: Voltage Waveforms in Boost Mode of Operation; comparison between linear MATLAB/SIMULINK based and nonlinear PSCAD/EMTDC based simulations for step changes of ±0.167 per unit (±50A) in dc bus load Io, 1) dc load current 2) dc bus voltage 3) battery terminal voltage

Figure E- 10: Voltage Waveforms in Boost Mode of Operation; comparison between linear MATLAB/SIMULINK based and nonlinear PSCAD/EMTDC based simulations for step changes in dc bus reference voltage with constant dc bus load of 0.5 per unit (150A), 1) dc bus voltage 2) battery terminal voltage

221

E.1.12 BUCK MODE OF OPERATION

Figure E-11 and Figure E-12 show a comparison of the linear system response from

MATLAB/SIMULINK with the response from the system model in PSCAD/EMTDC with the

converter operating in buck mode at a constant loading of -0.5 per unit (-150A) at the dc bus.

The step change in load is ±0.167 per unit.

Figure E-11 gives comparison of the converter control reference current ci and the inductor

current bi for the linear and the nonlinear models in response to step changes in the load

connected to the dc bus. Figure E-12 shows responses of the two models for the dc bus voltage

dcv and the battery terminal voltage btv for the same step changes in load. It can be seen from

Figure E-8 through Figure E-12 that the linear and the nonlinear model responses are in close

agreement with each other and therefore validates the small signal system model.

Figure E- 11: Current Waveforms in Buck Mode of Operation; comparison between linear MATLAB/SIMULINK based and nonlinear PSCAD/EMTDC based simulations for step changes of ±0.167 per unit (±50A) in dc bus load Io, 1) dc load current 2) reference control current 3) inductor current

222

Figure E- 12: Voltage Waveforms in Buck Mode of Operation; comparison between linear MATLAB/SIMULINK based and nonlinear PSCAD/EMTDC based simulations for step changes of ±0.167 per unit (±50A) in dc bus load Io, 1) dc load current 2) dc bus voltage 3) battery terminal voltage

223

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