windenergyconversion.pdf

Rotor Side Control of Grid-Connected Wound Rotor Induction Machine

and its Application to Wind Power Generation

A Thesis

Submitted for the degree of Doctor of Philosophy

in the Faculty of Engineering

by

Rajib Datta

Department pf Electrical Engineering

INDIAN INTITUTE OF SCIENCE

Bangalore-560 012, (INDIA)

FEBRUARY, 2000

Acknowledgements

I am grateful to Prof. V.T.Ranganathan for his guidance and help during the course of my

research work. Many of the ideas presented in the thesis are results of numerous sessions of lively

discussions with him. His instructive suggestions and encouragement are deeply acknowledged.

I thank Prof. V.Ramanarayanan for all that I have learnt from him, including power

electronics. I gratefully acknowledge his efforts in providing an excellent laboratory infrastructure.

I sincerely thank Prof. Indraneel Sen for his advice and careful review of the thesis.

Acknowledgements are due to Mr. T.Chouridas and other members of the Electrical

Engineering Workshop for their help in fabricating the experimental setup.

I thank Mrs. Silvi Jose for maintaining the Power Electronics Store and helping in purchase of

components.

I also appreciate the assistance and cooperation provided by Mr. D.M.Channe Gowda and his

colleagues in the Electrical Engineering Office.

Prof. Jamadagni gladly extended the various facilities available at the Centre for Electronic

Design and Technology, whenever required. His useful suggestions during the design of the DSP

hardware are duly acknowledged.

I sincerely thank Prof. Giri Venkataraman of University of Wisconsin, Madison, for his keen

interest in my work and, for ensuring a steady flow of many critical hardware components to our lab.

The DSP-based hardware activities in the Power Electronics Group have been made possible

due to the excellent cooperation of Mr.Sanjeev Das Mahapatro of Texas Instruments, India.

Thanks are due to the members of the Power Electronics Lab, ER&DC, Trivandrum, for their

help in providing valuable information and data regarding a practical wind energy conversion system.

I owe a great deal to my lab mates G.Narayanan, Debiprasad Panda and Parthasarathi Sen

Sharma for their help, support and constant motivation. Ebenezer Vidyasagar has been equally

involved with me in the design of the TMS320F240 board. Enlivening discussions with Souvik and

Gautam has helped my understanding of various technical issues. It has been a pleasure to work with

Rajapandian, Giridharan, Venkatesh, Mahesh, Biju, Ramananurthy and other members of the Power

Electronics Group. The synergetic atmosphere in the lab has truly been an inspiring and educative

experience for me.

iii

Abstract

This thesis deals with modeling, simulation and implementation of rotor side control

strategies for a grid-connected wound rotor induction machine. In the system under consideration, the

stator is directly connected to the constant frequency three phase grid and, the rotor is supplied by two

back-to-back three phase voltage source inverters with a common dc link. Such a configuration is

attractive in large power applications with limited speed range of operation. The rotor currents are

controlled at any desired phase, frequency and magnitude to control the active and reactive powers of

the machine independently.

A stator flux oriented model of the doubly-fed wound rotor induction machine is presented.

The front-end converter is similarly modeled in the stator voltage reference frame. The current

controllers are designed in the field coordinates. Simulation waveforms exhibit excellent transient

response of the current loops; the dynamics of the direct and quadrature axes are also observed to be

decoupled.

Two position sensorless algorithms for grid-connected wound rotor induction machine are

proposed. In the first method the field oriented current controllers are retained; the rotor position is

estimated by using simple transformations between the stator and rotor coordinates. The second

algorithm directly controls the active and reactive powers by instantaneous control of the rotor flux. It

uses a novel strategy to update the sector information of the rotor flux. The salient features for both

these methods are starting on-the-fly, stable operation at zero rotor frequency and minimal

dependence on machine parameters.

An experimental setup consisting of IGBT inverters and a TMS320F240 DSP based digital

controller is developed in the laboratory to implement the control algorithms. Relevant experimental

waveforms are presented; they are observed to be in good agreement with the simulation results.

Application of rotor side control of doubly-fed induction machine to wind energy conversion

systems is studied. The scheme is compared against the existing systems using cage rotor induction

machine. Peak power point tracking algorithm in the conventional torque control mode is first

implemented. A dc motor driven by a commercial thyristor drive is used to simulate the turbine

characteristics. Subsequently, a method is proposed to track the peak power point locus which

operates in the speed control mode. Unlike the previous case, here precise information about the

turbine characteristics is not required. This strategy is also implemented and verified experimentally.

v

Contents

Acknowledgements iii

Abstract v

List of Symbols xiii

1 Introduction 1

1.1 General 1

1.2 Basic Concept of Rotor Side Control 2

1.3 Background 3

1.4 Rotor Side Control with Back-to-back Inverter Configuration 7

1.5 Rotor Side Control: Modes of Operation 8

1.5.1 Mode 1: Subsynchronous Motoring 9

1.5.2 Mode 2: Supersynchronous Motoring 11

1.5.3 Mode 3: Subsynchronous Generation 12

1.5.4 Mode 4: Supersynchronous Generation 13

1.6 Present Status 14

1.7 Scope of the Thesis 16

2 Modeling and Simulation 19

2.1 Introduction 19

2.2 Machine Model in Field Coordinates 20

2.3 Field Oriented Control 25

2.3.1 Rotor Equation in Field Coordinates 25

2.3.2 Design of Rotor Current Controller in Field Coordinates 28

2.4 Simulation Results - Rotor Side Control 32

2.5 Front end Converter 43

2.6 System Description 44

2.7 Principle of Operation and Control 45

2.8 Modeling of the Power Circuit 47

2.9 Front end Converter Controller Design 50

vii

2.9.1 Design of the Current Controller 50

2.9.2 Design of the Voltage Controller 52

2.10 Simulation Results - Front end Converter 53

2.11 Conclusion 61

3 Hardware Organization and Experimental Results for Conventional Field Oriented Rotor

Side Control and Front end Converter Control 63

3.1 Introduction 63

3.2 Organization of the Power Circuit 65

3.2.1 IGBT Converter 65

3.3 DSP Based Control Hardware 67

3.3.1 TMS320F240 - A Brief Overview 68

3.3.2 TMS320F240 Based Digital Control Platform 68

3.4 Software Organization 72

3.4.1 Task Scheduling 72

3.4.2 Program Flow 73

3.4.3 Description of Tasks 74

3.4.5 Generation of Unit Vectors Synchronized to the Supply Voltage 77

3.4.6 Generation of Unit Vectors from Incremental Position Encoder Pulses 78

3.4.7 Scaling and Signal Monitoring through DAC 80

3.5 Experimental Results 80

3.5.1 Rotor Side Control 81

3.5.2 Front end Converter Control 87

3.6 Conclusion 90

4 Rotor Side Field Oriented Control without Position Sensors 91

4.1 Introduction 91

4.2 Review of Existing Schemes 92

4.3 Proposed Algorithm for Position Sensorless Control 94

4.3.1 Computation of 96ims

4.3.2 Starting 97

4.3.3 Speed Estimation 97

Contents

viii

4.4 Simulation 99

4.5 Implementation and Experimental Results 106

4.6 Conclusion 111

5 Direct Power Control - Concept and Implementation 113

5.1 Introduction 113

5.2 Concept of Direct Power Control 114

5.3 Voltage Vectors and their Effects 116

5.3.1 Effect of Active Vectors on Active Power 117

5.3.2 Effect of Active Vectors on Reactive Power 119

5.3.3 Effect of Zero Vector on Active Power 119

5.3.4 Effect of Zero Vector on Reactive Power 120

5.4 Control Algorithm 120

5.4.1 Measurement of Stator Active and Reactive Power 121

5.4.2 Defining References and Errors 121

5.4.3 Switching Vector Selection 122

5.5 Sector Identification of Rotor Flux 124

5.6 Starting 127

5.7 Simulation Results 128

5.8 Implementation and Experimental Results 133

5.9 Conclusion 138

6 Using Doubly-fed Wound Rotor Induction Machine for Wind Power Generation

- Design Considerations and Control Strategies 139

6.1 Introduction 139

6.1.1 Wind Turbines 139

6.1.2 Isolated and Grid-connected WECS 140

6.1.3 Choice of Wind Electric Generators 141

6.2 Conventional Fixed Speed System 143

6.2.1 Wind Turbine Characteristics 143

6.2.2 Conventional Fixed Speed System 144

6.3 Variable Speed System using Cage Rotor Induction Machine 147

Contents

ix

6.3.1 Design Example 147

6.3.2 Operating Region and Control 150

6.4 Variable Speed System using Wound Rotor Induction Machine 152

6.4.1 Design Example 152

6.4.2 Operating Region and Control 154

6.5 Simulation of WECS 156

6.5.1 Fixed Speed System 157

6.5.2 Variable Speed System using Cage Rotor Induction Machine 160

6.5.3 Variable Speed System using Wound Rotor Induction Machine 164

6.6 Detailed Simulation of Variable Speed System WECS using

Wound Rotor Induction Machine with Rotor Side Current Control 164

6.7 Practical Implementation of Variable Speed System using

Wound Rotor Induction Machine in Torque Control Mode 168

6.7.1 Simulation of the turbine characteristics 172

6.7.2 Experimental Results 172

6.8 Peak Power Tracking in Speed Control Mode 175

6.8.1 Peak Power Tracking Algorithm 177

6.8.2 Selection of Sampling Frequency 179

6.8.3 Selection of Kt 180

6.8.4 Experimental Results 181

6.9 Conclusion 183

7 Conclusion 185

7.1 General 185

7.2 Summary of the Present Work 185

7.3 Scope for Further Research 187

References 189

A Machine Model in Stationary Coordinates 195

B Details of Major Power Circuit Components 201

B.1 Wound Rotor Induction Machine 201

Contents

x

B.2 IGBT Power Converters 202

B.3 Front end Converter 202

B.4 Position Encoder and Mounting Arrangement 203

B.5 DC Motor and Drive 204

C MATLAB Data Files 205

C.1 Machine and Controller Parameters used for Simulation and

Implementation of Rotor side Control 205

C.2 Power Circuit and Controller Parameters used for Simulation and

Implementation of Front end Converter Control 208

D Relevant Data of Vestas V-27 Wind Turbine 211

E Calculation of DC Bus Capacitance 213

Contents

xi

List of Symbols

Instantaneous values of stator phase currents is1, is2, is3

Instantaneous values of rotor phase currentsir1, ir2, ir3

Instantaneous values of front end converter phase currentsife1, ife2, ife3

Instantaneous values of grid phase currentsig1, ig2, ig3

Instantaneous values of capacitor current, dc bus current and load current ic, idc, il

respectively for the front end converter

Instantaneous values of stator phase voltagesus1, us2, us3

Instantaneous values of rotor phase voltagesur1, ur2, ur3

Instantaneous values of transformer secondary phase voltages for the uac1, uac2, uac3

front end converter

Instantaneous values of the front end converter phase voltagesufe1, ufe2, ufe3

Instantaneous value of the dc bus voltageudc

Instantaneous values of the -axis and -axis stator currents respectivelyisa, isb a b

Instantaneous values of the -axis and -axis rotor currents respectivelyira, irb a b

Instantaneous values of the a-axis and b-axis rotor currents respectivelyira, irb

Instantaneous values of the -axis and -axis front end converter currents ifea, ifeb a b

respectively

Instantaneous values of the -axis and -axis stator flux imsa, imsb a b

magnetizing currents respectively

Instantaneous values of the -axis and -axis stator voltages respectivelyusa, usb a b

Instantaneous values of the -axis and -axis rotor voltages respectivelyura, urb a b

Instantaneous values of the -axis and -axis transformer secondary uaca, uacb a b

voltages for the front end converter respectively

Instantaneous values of the -axis and -axis front end converter voltages ufea, ufeb a b

respectively

Instantaneous values of the -axis and -axis stator flux respectivelyysa, ysb a b

xiii

Instantaneous values of the -axis and -axis rotor flux respectivelyyra, yrb a b

Instantaneous values of the d-axis and q-axis stator currents respectivelyisd, isq

Instantaneous values of the d-axis and q-axis rotor currents respectivelyird, irq

Instantaneous values of the d-axis and q-axis front end converter currents ifed, ifeq

respectively

Instantaneous values of the d-axis and q-axis rotor current references ird& , irq

&

respectively

Instantaneous values of the d-axis and q-axis front end converter current ifed& , ifeq

&

references respectively

Instantaneous values of the d-axis and q-axis stator voltages respectivelyusd, usq

Instantaneous values of the d-axis and q-axis rotor voltages respectivelyurd, urq

Instantaneous values of the d-axis and q-axis transformer secondary uacd, uacq

voltages for the front end converter respectively

Instantaneous values of the d-axis and q-axis front end converter voltages ufed, ufeq

respectively

Instantaneous values of the d-axis and q-axis rotor voltage references urd& , urq

&

respectively

Instantaneous values of the d-axis and q-axis front end converter voltage ufed& , ufeq

&

references respectively

Space phasor of rotor currents in rotor reference frameir

Space phasor of rotor currents in stator reference framesir

Space phasor of stator currents in stator reference frameis

Reference space phasor of rotor currents in rotor reference frameir&

Space phasor of stator flux magnetizing current in stator reference frame ims

Instantaneous magnitude of the stator flux magnetizing current space phasorims

Space phasor of stator voltages in stator reference frameus

Space phasor of rotor voltages in rotor reference frameur

Space phasor of rotor flux yr

List of Symbols

xiv

Space phasor of stator fluxys

Space phasor of air gap fluxym

Resistances of the stator and rotor phase windings respectivelyRs, Rr

Self-inductances of the stator and rotor phase windings respectivelyLs, Lr

Magnetizing inductanceLo

Leakage factors of the stator and rotor phase windings respectivelyrs, rr

Total leakage factorr

Stator and rotor time constants respectivelyTs, Tr

Machine torquemd

Load torqueml

Torque constant Kc

Moment of inertiaJ

Ac side inductance per phase for the front end converter Lfe

Ac side coil reactance per phase for the front end converterXfe

Ac side coil resistance per phase for the front end converterRfe

Time constant of the ac side coil in the front end converterTfe

Time constant of the current loops in rotor side controlTir

Time constant of the current loops in the front end converter controlTife

Time constant of the voltage loop in the front end converter controlTvfe

Proportional gain for PI controller used in rotor side current controlKpir

Proportional gain for PI controller used in front end converter current controlKpife

Proportional gain for PI controller used in front end converter voltage controlKpvfe

Peak of triangular carrier waveform for sine-triangle modulationutri

Gain of the rotor side converterGr

Gain of the front end converterGfe

Gain of the current sensors used for rotor side controlKir

Gain of the current sensors used for front end converter controlKife

Angle between the stationary axis and the stator flux space phasor l

Angle between the stationary axis and the rotor axise

List of Symbols

xv

Angle between the stationary axis and the stator voltage space phasorh

Angle between the stationary axis and the rotor current space phasorq1

Angle between the rotor axis and the rotor current space phasorq2

Angle between the stator flux and rotor flux space phasorsdp

Angular velocity of the stator voltage zs

Angular velocity of the stator flux zms

Angular rotor velocity in electrical rads.s-1ze

Estimated angular velocity rotor velocity in electrical rads.s-1zest

Angular rotor velocity in mechanical rads.s-1z

Total power P

Stator powerPs

Rotor powerPr

Wind turbine powerPt

Target power in peak power trackingPt arg et

Power coefficient of the wind turbineCp

Swept area of the wind turbine bladesA

Air-densityq

Wind velocityv

Radius of the wind turbine bladesR

Angular velocity of the wind turbine bladeszt

Tip-speed ratio of the wind turbinek

Proportional gain used in peak-power tracking algorithm in torque control Kopt

mode

Proportional gain used in peak-power tracking algorithm in speed control modeKt

List of Symbols

xvi

Chapter 1

INTRODUCTION

1.1 General

Efficient control of electric power, both at the generation and utilization ends, has been an

important contributing factor for industrial growth in the twentieth century. Bulk of this power is

generated and utilized through electromechanical energy conversion. Variable speed operation of

electrical machines enables this conversion of power in a controlled manner. With the availability of

power semiconductor devices the efficiency of conversion is high and, if desired, fast dynamic

response can also be achieved.

Even though, dc machines can be easily controlled and are inherently suitable for high

dynamic performance, several disadvantages associated with the mechanical commutator have

restricted their usage in the recent past. On the other hand, squirrel cage induction machines have

become increasingly popular due to their rugged construction and maintenance-free operation. Using

field oriented control techniques, the flux and torque of an induction machine can be controlled in a

decoupled manner and hence, fast dynamic performance, similar to that possible with dc machines,

can also be achieved.

While cage rotor induction machines are mainly used for medium power drive applications,

the wound rotor or slip-ring induction machines are commonly used in large power drives having

limited range of operating speeds. The increased cost of a slip-ring machine is justified by the reduced

size of power electronic converter in the rotor circuit. So far, such machines were used as slip power

recovery drives with pump or fan type of mechanical loads. However, with the emergence of variable

1

speed constant frequency (VSCF) generation applications such as wind power generation, there is an

increased attention towards wound rotor induction machines controlled from the rotor side.

1.2 Basic Concept of Rotor Side Control

The speed of a cage rotor induction machine is primarily determined by the supply frequency.

The short circuited rotor offers very low resistance and the nominal slip is within 5%. A small part of

the power fed from the stator ( ) is lost in the rotor circuit (due to rotor resistive loss) ( ) and thePs Pr

rest appears as mechanical output ( ). The power flow diagram is shown in Fig.1.1. The rotorPm

power loss, being proportional to the slip speed, is commonly referred to as the slip power.

In case of a wound rotor induction machine it is possible to introduce additional resistance in

the rotor circuit (Fig.1.2). Thereby the rotor power loss increases with a corresponding decrease in the

shaft output power. For the same load torque this results in an increased slip and a reduction in the

shaft speed. Using variable rotor resistance it is, therefore, possible to vary the slip power and, hence

the rotor speed.

Fig.1.2 Speed control of wound rotor induction motor

with external rotor resistance

Ps Pr

Pm

Fig.1.1 Power flow in cage rotor

induction motor

InputPower

SlipPower

Wound Rotor

Induction Motor

ResistorBank

With the availability of thyristors this concept was utilized to introduce a dynamically varying

resistance in the rotor circuit [1] as shown in Fig.1.3. It is shown that the torque produced by the

machine is approximately proportional to the dc link current. Therefore, a speed controlled drive can

be designed whose inner loop controls the dc link current by adjusting the duty ratio of the switch.

High starting torque is available at low starting current. Also improved power factor is possible over a

Chapter 1 Introduction

2

wide range of speed. However, the method is inefficient because of the power lost in the external

resistors and, is only used in intermittent speed control applications where the efficiency penalty is

not of great concern.

If the slip power is absorbed by an appropriate electrical source instead of being wasted in the

resistive elements, the same objective can be achieved. The rotor power, in this case, is regenerated

back in electrical form. It is possible to control the amount of power absorbed by the source and

hence the shaft speed can be varied. If the source has both sourcing and sinking capabilities, power

can be absorbed from or injected into the rotor circuit. The slip can therefore, be positive or negative

enabling subsynchronous and supersynchronous operation.

Fig.1.3 Wound rotor induction machine control with dynamic rotor resistance

Input

Power

Slip Power

DC Link Choke

Chopper

Wound RotorInductionMotor

1.3 Background

Historically the controllable electrical source in the rotor circuit was another auxiliary

machine. The slip power was recovered back either in mechanical form or in electrical form. The

former was proposed by Kramer and the latter by Scherbius in the same year (1906). These schemes

can be viewed in simplified forms as in Fig.1.4(a) and Fig.1.4(b). In Kramer drive the torque

contribution of the dc motor reduces the mechanical load taken by the induction motor. On the other

hand, electrical recovery by Scherbius scheme uses another induction generator which feeds back the

slip power to the grid at power frequency. In both cases slip is controlled by controlling the field of

the dc machine.


3

Fig.1.4 Slip power recovery schemes using auxiliary machines

Input

Power

Slip Power

Diode BridgeDCMotor

Input

Power

Slip Power

Diode BridgeDCMotor Cage Rotor

Induction Generator

(b) Scherbius system

(a) Kramer System

Wound Rotor

Induction Motor

WoundRotor

Induction

Motor

With the advent of controllable power devices like SCRs, it was possible to dispense with the

additional machines. The variable frequency slip power could be recovered by introducing a

phase-controlled converter at the grid interface. This was proposed by several researchers in the

1960s. Erlicki [2] proposed a scheme in 1965 where the rotor circuit was fed by an inverter operating

at a frequency greater than the grid frequency. The inverter is the power source of the drive and part

of the slip power is fed back from the stator to the grid. A phase-controlled rectifier is provided

between the inverter and the network, which permits continuous voltage control of the dc inverter


4

supply. However, the rating of the inverter and the rectifier in the rotor circuit has to be more than

the mechanical output obtained from the drive.

The more conventional scheme where the rotor power is rectified and fed back to the grid by a

phase-controlled inverter (Fig.1.5) was subsequently proposed by Lavi and Polge [3], and Shepherd

and Stanway [4]. This method of control became popularly known as the Static Scherbius system. A

large dc link choke is used to interface the diode bridge output with the grid-side inverter. This

ensures that the rotor current is continuous and proper control over the speed can be exercised by

varying the inverter firing angle. However, the inverter consumes reactive power because of phase

control and the overall system power factor is poor. The reactive power demand of the inverter also

depends on the slip range, being ideally zero when the rotor runs at the synchronous speed. To

improve the system power factor a transformer with proper turns ratio is connected between the

inverter and the grid. The drive is started through external resistors in the rotor circuit which are

subsequently cut-off when the designed slip range is reached.

Fig.1.5 Static slip power recover scheme

Input

Power

Slip Power Diode Bridge

Wound Rotor

Induction Motor

DC Link Choke

Phase ControlledInverter

Transformer

With the diode bridge and inverter arrangement, a commutatorless Kramer drive for large

capacity induction machines was proposed by Wakabayashi et.al.[5] in 1976. In this scheme the

inverter in the rotor circuit drives a synchronous motor whose shaft is coupled to the main motor

shaft; hence the slip power adds to the mechanical output. The inverter is load commutated; hence

control at low speeds is not possible because of insufficient back emf.


5

In all these schemes the rotor power can flow in one direction only; so the machine can

operate either at subsynchronous or at supersynchronous speeds. However, instead of the dual

converter system, use of a cycloconverter in the rotor circuit permits power flow in both directions.

This was proposed by Long and Schmitz [6], Weiss [7], Chattopadhyay [8] and Mayer [9]. The

cycloconverter permits a reversible power flow naturally and speed control is possible for

subsynchronous as well as supersynchronous operation by controlling the injected rotor voltage. Long

and Schmitz described cycloconverter control of a doubly-fed induction motor giving speed torque

characteristics similar to that of a dc series motor. Weiss reported the application and performance of

an ac drive using a cycloconverter and a doubly-fed wound rotor motor for pump and compressor

applications. In [8], a simple rotor position-detector is used to switch the thyristor configuration in a

sequential manner to generate an output voltage having a predominant slip-frequency component. The

speed-torque characteristics obtained are similar to that of a dc shunt motor, and the drive is reported

to be inherently stable. A 15000 hp cycloconverter-fed wound rotor induction motor drive with high

dynamic response of stator active and reactive powers is presented in [9]. An orthogonal control

scheme is employed to determine the rotor voltages. However, in the absence of proper current

control loops, the stator power flow can be smoothly controlled only above 35% slip. However, the

use of cycloconverters in industrial drives has been restricted because of the large number of

thyristors used in the power circuit, the complexity involved in the firing and commutation circuits

and the complex interaction with the grid.

Wind energy recovery using Static Scherbius induction generator was proposed by Smith

et.al. [10]. In their scheme a current source inverter is used on the rotor side and a fully-controlled

rectifier on the line side. A novel signal generator concept, which is locked in phase to the rotor emf

controls the secondary power to provide operation over a wide range of subsynchronous and

supersynchronous speeds. The VA rating of the current source is determined as a function of the gear

ratio and the operating range. However, the need for a large dc link choke and commutation

capacitors were the major disadvantages. Subsequently, Holmes et.al. [11] proposed a

cycloconverter-excited divided-winding doubly-fed machine as a wind power converter. The system

was conceptually similar to the previous scheme, except that, the current source inverter was replaced

by a cycloconverter in the rotor circuit.


6

1.4 Rotor Side Control with Back-to-back Inverter Configuration

Presently, there is an increased attention towards rotor side control of wound rotor induction

machine for VSCF wind power generation. Voltage source inverters using IGBTs have become the de

facto choice for variable speed drives in the nineties. The diode bridge and thyristor inverter

combination in the Static Scherbius system is replaced by two back-to-back IGBT inverters with a

capacitive dc link (Fig.1.6). Standard three phase bridge topology is employed for the converters.

With a PWM converter in the rotor circuit, the rotor currents can be controlled in a desired phase,

frequency and magnitude. This enables reversible flow of active power in the rotor and the system

can operate in subsynchronous and supersynchronous speeds, both in motoring and generating modes.

The dc link capacitor acts as a source of reactive power and, it is possible to supply the magnetizing

current, partially or fully, from the rotor side. The stator side power factor can thus be controlled.

Using vector control techniques, the active and reactive powers can be controlled independently and

hence fast dynamic performance can also be achieved.

Fig.1.6 Rotor side control scheme with back-to-back PWM converters with capacitive dc link

Slip Power

Wound Rotor

Induction Machine

DC Bus

Transformer

Rotor sideConverter

Front endConverter

Series Inductors

The converter used at the grid interface is termed as the line-side converter or the front end

converter (FEC). Unlike the rotor side converter, this operates at the grid frequency. Flow of active

and reactive powers is controlled by adjusting the phase and amplitude of the inverter terminal

voltage with respect to the grid voltage. Active power can flow either to the grid or to the rotor circuit


7

depending on the mode of operation. By controlling the flow of active power, the dc bus voltage is

regulated within a small band. Control of reactive power enables unity power factor operation at the

grid interface. In fact, the FEC can be operated at a leading power factor, if it is so desired. Since, the

inverter operates at a high frequency, usually between 1 kHz to 5 kHz, the harmonics in input current

are largely reduced.

It should be noted that, since the slip range is limited, the dc bus voltage is lesser in this case

when compared to stator side control. A transformer is therefore necessary to match the voltage levels

between the grid and the dc side of the FEC.

This arrangement presents enormous flexibility in terms of control of active and reactive

powers in variable speed applications. In the following section, the concept of controlling the power

flow in the machine by injecting currents in the rotor circuit is explained by deriving suitable phasor

diagrams and power flow diagrams.

1.5 Rotor Side Control : Modes of Operation

Fig.1.7 Operating region of the doubly fed induction machine with rotor side control

MODE1

MODE2

MODE3

MODE4

0

Tor

que

Speed

ωs

The operating region of the system in the torque-speed plane is shown in Fig.1.7. As stated

earlier, the rotor side control strategy is advantageous within a limited slip range. Hence the operating

region is spread out on both sides of the synchronous speed implying both subsynchronous andzs

supersynchronous modes of operation. Moreover, the machine can operate in the motoring and

generating modes irrespective of the speed. Thus four distinct modes of operation can be achieved

through rotor side control corresponding to the four quadrants in the torque-speed plane.

In Fig.1.7 mode 1 refers to positive torque and subsynchronous speed; this is termed as

subsynchronous motoring (i.e. normal motoring) operation. Mode 2 corresponds to positive torque


8

and supersynchronous speed; this mode is called supersynchronous motoring. Similarly mode 3

corresponds to subsynchronous generation and mode 4 corresponds to supersynchronous

generation. The following sections describe how these different modes of operation can be achieved

through rotor side control.

1.5.1 Mode 1: Subsynchronous Motoring

Fig.1.8 Approximate equivalent circuit with rotor side control

ψsLo

isr

us

is

sσ Lo

A simplified equivalent circuit of the doubly-fed wound rotor induction machine controlled

from the rotor side is shown in Fig.1.8. It is assumed that the rotor currents can be injected at any

desired phase, frequency and magnitude. Therefore, the rotor circuit can be represented by a

controllable current source. The equivalent circuit is drawn in the stator reference frame; hence the

rotor current is represented as . The steady-state phasor diagram and power flow diagram for thesir

subsynchronous motoring mode of operation are shown in Fig.1.9.

Neglecting the stator resistance, it may be assumed that the stator flux remains constant inys

magnitude and frequency since the stator is connected to the power grid. has two components; theys

stator leakage component and the magnetizing component. The former is due to the stator current

alone, while the latter is due to both the stator and the rotor currents. An equivalent current canims

be defined in the stator reference frame, which is responsible for the stator flux. This is termed as the

stator flux magnetizing current [12]. The direction of (which is in phase with ) is defined asys ims

the d-axis and, the direction of the stator voltage, which is at quadrature to , is termed as theys

q-axis. It is possible to resolve and along and perpendicular to . (The components of theis sir ims

currents along the d-axis are represented with subscript 'd', and those along the q-axis with subscript

'q'.) The mathematical relations between the currents in this stator flux reference frame is derived in

Chapter 2 where the field oriented model is presented. Here, a qualitative approach is taken to

understand the effect of current injection in the rotor circuit.


9

(a)

d-axis

q-axis

imsisd

isq is

irq

uses

isσs Loωs

er

d-axis

B'

Airq

isq is

ir

isd ird ims

q-axis

A'

B

(c) (d)

Fig.1.9 Phasor diagram and power flow diagram during subsynchronous motoring

(b)

d-axis

q-axis

imsisd

isq is

uses

isσs Loωs

er

ird

irirq

ψs

ψm

ψs

ψm

Ps

Pr

Pm

Since is constant, it implies that is also constant and equals the sum of and .ys ims isd ird

With current control being exercised in the rotor circuit, an injection of positive will naturallyird

result in a lesser value of being drawn from the stator terminals. The stator power factor is therebyisd

improved. This feature is clearly depicted in Fig.1.9(a) and Fig.1.9(b). Fig.1.9(a) shows beingims

fully supplied from the stator side, as in the case of a cage rotor induction machine, whereas in

Fig.1.9(b) it is partially supplied from the rotor side and partly from the stator side. It may be noted

here that will never be made negative. This would mean that the stator has to supply theird


10

magnetizing energy of the machine, as well as the reactive energy demand of the rotor circuit,

bringing down the stator power factor to a very low value.

Along the q-axis, the magnitude of the active component of stator current is directlyisq

proportional to , but opposite in sign. In fact, the induction machine can be looked upon as airq

current transformer as far as the active power flow in the stator and rotor circuits are concerned.

Hence, to produce a motoring torque (i.e. positive torque), has to be negative. This is evidentirq

from Fig.1.9; a negative induces a positive , implying flow of active power into the statorirq isq

circuit. Below the synchronous speed the rotor falls behind the air-gap flux and the rotor induced emf

lags the mutual flux by 900 as shown in Fig.1.9(a) and Fig.1.9(b). er ym

The locus of and for constant active power flow is shown in Fig.1.9(c). As the tip of theis ir

rotor current phasor is moved from B to A, the stator current phasor locus moves in the opposite

direction from B’ to A’. From this phasor diagram it may be appreciated that some amount of reactive

power can as well be delivered to the source from the stator side, when the reactive power supplied

from the rotor side is more than the machine requirement. This is, however, possible when the active

load demand is low and there is adequate current margin in the rotor coils. In order to utilize the

copper in the stator and rotor circuits effectively, it is advisable to divide the reactive power demand

between the two ports.

Under the condition of subsynchronous motoring the stator voltage phasor leads theus

air-gapd voltage under all conditions of load which indicates power flowing into the stator.es(= −er )

Also the rotor current makes an angle less than 900 with , the rotor induced emf, implying thatir er

active power is being extracted from the rotor circuit. This rotor power, or the slip power, is

recovered from the rotor circuit and fed back to the mains, thereby increasing system efficiency. The

mechanical power output is roughly the difference between the stator and rotor powers. This is

illustrated in Fig.1.9(d).

1.5.2 Mode 2: Supersynchronous Motoring

With remaining negative if the machine runs above synchronous speed, it enters theirq

supersynchronous motoring mode of operation. The rotor now moves ahead of the air-gap flux ym

and, therefore, leads by 900. The phase relations between the stator and rotor currents remainer ym

as in mode 1; only the direction of rotor power reverses as now makes an angle more than 900 with ir

. This is shown below in Fig.1.10. er


11

It may be noted that in this mode of operation, if the stator input power is 1 p.u. and the motor

is running at a slip of s p.u., the mechanical output that can be obtained is (1+s) p.u. which is more

than the apparent power rating of the machine.

(a)

d-axis

q-axis

imsisd

isq is

uses

isσs Loωs

ird

irirq

= er

Fig.1.10 Phasor diagram and power flow diagram during supersynchronous motoring

(b)

Ps Pr

Pm

ψs

ψm

1.5.3 Mode 3: Subsynchronous Generation

(a)

d-axis

q-axis

ims

isd

irq

is

uses

isσs Loωs

ird

ir

isq

er

Fig.1.11 Phasor diagram and power flow diagram during subsynchronous generation

Pm

Ps Pr

(b)

ψs

ψm


12

If a positive is injected into the rotor circuit, changes direction and becomes negative.irq isq

Therefore, the active power flow into the stator becomes negative indicating that the machine is

generating. This can also be appreciated from the fact that the stator terminal voltage vector nowus

lags the stator induced emf. The phase angle between and exceeds 900, implying that power isir er

fed into the rotor circuit. The power flow and phasor diagrams are given in Fig.1.11.

1.5.4 Mode 4: Supersynchronous Generation

With remaining positive the machine can go over to the supersynchronous generatingirq

mode. As far as the stator circuit is concerned everything remains the same as in mode 3; only the

rotor power flow changes its direction. With the rotor induced emf leading the air-gap flux, theer

angle between and becomes less than 900 indicating power flow out of the rotor. It is interestingir er

to note that in supersynchronous generation mode the shaft power is recovered from both the stator

and rotor ends. Therefore, if 1 p.u. power is extracted from the stator while the machine is running at

a slip s, the total power generated will be (1 + s) p.u. Hence in the supersynchronous generation mode

it is actually possible to generate power more that is than the rating of the machine. The phasor and

power flow diagrams for this mode are given in Fig.1.12.

Fig.1.12 Phasor diagram and power flow diagram during supersynchronous generation

(a)

q-axis

ims

isd

irq

is

ψm

uses

ψs

isσs Loωs

ird

ir

isq

er=

d-axis

(b)

Pm

PrPs


13

1.6 Present Status

In order to control the rotor currents in the desired manner, field oriented control is employed.

Stator flux oriented control of doubly-fed wound rotor induction machine has been described by

Leonhard [12] and Vas [13]. Motoyoshi et.al. [14] used a reference frame fixed to the air-gap flux to

control the active and reactive powers of the machine independently. In the schemes used in [12, 14]

cycloconverters were used to interface the rotor side to the grid. Motoyoshi also presented a detailed

analysis of the current harmonics drawn from the supply due to the use of a cycloconverter. However,

the use of PWM converters, as discussed in section 1.5, reduces the complexity of the power circuit

and allows the system to operate at any desired power factor. With high switching frequency the

current drawn from or injected into the grid is also sinusoidal.

Leonhard’s approach of field orientation in the stator flux reference frame became popular

because of its close resemblance to rotor-flux orientation in cage rotor machines. A flexible active

and reactive power control strategy using field oriented control was reported by Xu et.al. [15]. Apart

from controlling the active power flow to optimally track the torque-speed profile of the turbine for a

VSCF generating system, the reactive power is also controlled to minimize the machine copper

losses. Similar strategies for variable speed wind power generation has been presented by Asher et.al.

[16]. Experimental results presented in [16] show that the scheme is suitable for closely tracking the

desired torque-speed trajectory in either a speed control or current control mode.

For decoupled control of active and reactive power, the instantaneous position of the rotor

with respect to the stator is required. In conventional field oriented control schemes, this is derived

from an incremental or absolute encoder fitted to the machine shaft. A high resolution position

encoder, apart from being expensive, reduces system reliability. Moreover, in doubly-fed machines

the mounting of the encoder on the rotor shaft is not straightforward. The encoder has to be oriented

in such a way that the angle between the stator and rotor coil axes can be read-off directly. Quite

naturally a major challenge to researchers in this area has been to eliminate the use of this encoder

and yet, obtain similar dynamic performance.

Position sensorless control of ac machines have attracted a lot of attention in recent times [13,

33, 34]. However, the major focus of activity has been restricted to cage rotor induction machine and

permanent magnet synchronous machine due to their higher usage in industrial vector controlled

drives. A few techniques have been proposed by different research groups for rotor position


14

estimation of doubly-fed wound rotor machines [17, 18, 19]. The fact that, both the stator and rotor

currents are directly measurable quantities in this case, provides interesting options for accurate

position estimation, even at zero rotor frequency. In [17] the desired angle of the rotor current in the

rotor reference frame, is compared with the angle of the rotor current vector in the stator reference

frame, to generate the rotor frequency. Torque angle estimation is proposed in [18]. The algorithm

uses rotor voltage integration; hence estimation at or near synchronous speed is difficult. In [19]

transformations between the rotor reference frame and the stator flux reference frame are employed

for estimating the rotor position. However, the algorithms proposed in the literature so far do not

address to all the requirements of a VSCF generating system.

In order to control the active and reactive power flow in the machine without position sensors,

an alternative approach may be considered where, instead of the rotor current, the rotor flux is directly

controlled. Direct self control (DSC) of induction motor has been proposed [20] where the stator flux

is controlled to track a hexagonal trajectory. The switching scheme is such as to control the torque

within a defined band. Subsequently direct torque control (DTC) schemes [13, 21, 22, 23] have been

reported; the primary difference from the earlier method being a circular trajectory of the stator flux.

So far, the application of direct torque control has been primarily addressed to cage rotor induction

motors and permanent magnet synchronous motors [13]. However, it is possible to extend the concept

of DTC to directly control the stator active and reactive powers in case of a wound rotor induction

machine.

The implementation of such control algorithms demands fast real-time computations. Apart

from the transformations and current control loops associated with field oriented control, most of the

sensorless algorithms require the machine model to be computed parallelly within the controller.

Microprocessor-based digital controllers have been effectively used to implement field oriented

control techniques for ac machines [24]. However, in order to improve the dynamic performance, the

need for faster computation was felt. The recent availability of high-speed digital signal processors

(DSP) has enabled easy implementation of computationally intensive algorithms in real time with

high sampling frequencies [25]. The current trend is to incorporate application-specific peripheral

hardware along with the processor in the same silicon package. PWM generation engines are also

provided internally. This simplifies the design and minimizes chip count. Therefore, the hardware

cost and the software overhead are reduced to a great extent.


15

1.7 Scope of the Thesis

The present work aims at modeling, design and development of rotor side control strategies

for grid connected slip ring induction machines for VSCF generation systems, with particular

reference to wind power generation.

The thesis is organized in the following chapters.

Chapter 2 deals with the modeling and simulation of the scheme using field-orientation and

rotor position feedback. Firstly, the machine model is developed in the stator flux reference frame.

Field oriented control equations are derived and design of active and reactive current controllers are

discussed in detail. The system is simulated using MATLAB-SIMULINK platform. Simulation

results for both motoring and generating modes of operation under dynamic and steady-state

conditions are presented. Next, the modeling and simulation of the three phase front end converter

used at the grid interface are discussed. The principle of operation and control philosophy are

explained. The dynamic equations for the power circuit are derived in stationary and synchronous

reference frames. The controller comprises an outer voltage loop and two inner current loops

(corresponding to active and reactive components of the line current). The current loops are designed

in the synchronous reference frame. Simulation results for transient and steady-state operations are

given.

The development of the power hardware and the DSP-based digital controller is discussed in

detail in Chapter 3. Experimental results for conventional field oriented control with rotor position

feedback and the front end converter control are also presented. The laboratory setup consists of a

3.5kW slip-ring induction machine with its stator connected to the 415V, 50 Hz, 3 phase power grid,

and the rotor being fed by two back-to-back IGBT-based PWM converters. The power converters are

developed in-house for this purpose. In order to simulate the torque-speed characteristics of the prime

mover (i.e. the wind turbine), a 5 hp dc motor driven by a commercial four-quadrant thyristor drive is

used. A TMS320F240 DSP based digital control board is designed and, employed for implementing

the control algorithms. This hardware platform is aimed at a generalized solution for motor control

applications and is equipped with the required analog and digital interfaces. It is powerful enough to

execute all the control loops associated with the rotor side control and front end converter control

algorithms at a sampling frequency of 2.9 kHz. The software is assembly coded for fast real-time

execution. The organization of the software with different modules and, task scheduler is explained.


16

Finally, relevant experimental results to demonstrate the steady-state and dynamic performance are

presented. The actual experimental responses are found to be consistent with the simulation results.

Chapter 4 deals with position sensorless vector control of the wound rotor machine. The

requirements of a position sensorless algorithm when used in VSCF operation are clearly brought out.

A novel control strategy based on transformations between the stator and rotor coordinates is

proposed. The algorithm is simple to implement, can be started on the fly (an important consideration

for wind power generation) and, can run stably at zero rotor frequency (i.e. at synchronous speed). It

is also independent of any critical system parameter and does not involve any dynamic angle

controller. The performance of the algorithm under different conditions, e.g. during starting, transient

in active power and parameter variation is studied through exhaustive simulation. It is observed that

the scheme exhibits excellent dynamic and steady-state performance. Details of implementation along

with relevant experimental results are provided. The experimental and simulation results are found to

be in good agreement.

In Chapter 5, a method for direct decoupled control of active and reactive power is presented.

The algorithm extends the switching logic of direct torque control (DTC) (normally used in cage

rotor induction machine) to rotor side control of doubly-fed wound rotor induction machine. By

selecting the appropriate vectors in the rotor circuit the stator active and reactive powers are

controlled within narrow hysteresis bands. But unlike DTC, the exact position of the rotor flux is not

calculated. It is observed that the information of the sector in which it resides is sufficient for

switching the correct inverter state. A novel method for updating the sector information, based on the

direction of change of reactive power in the stator circuit is proposed. The direct power control

algorithm uses only stator quantities for active and reactive power measurement and is inherently

position sensorless. It is computationally simple and does not incorporate any machine parameter.

The algorithm can start on the fly and operates stably at synchronous speed. Simulation and

experimental results to validate the concept are presented.

Chapter 6 deals with application of rotor side control of grid connected slip ring induction

machine to wind power generation. A brief review of wind-turbines and their characteristics is first

presented. The proposed VSCF system is compared with the existing systems using cage rotor

induction machines (both fixed speed and variable speed). Characteristics of a practical turbine are

considered to design the major electrical components used in the three systems. It is observed that, in

spite of a higher machine cost, the proposed overall system employing rotor side control is


17

economically competitive. The performances of these systems are compared through extensive

simulation. The proposed scheme is seen to be superior in terms of energy output. The motivation of

variable speed operation is to maximize the generator energy output by tracking the peak power point

locus of the turbine. This is first demonstrated with the more conventional torque control mode of

operation. Since, the control law in this case depends on the mechanical characteristics of the turbine

and air-density, it is felt that an alternative approach of speed control can be used to make the peak

power point tracking method more robust and parameter-independent. An algorithm is proposed

which searches the zero slope on the power-speed characteristics of the turbine. The generator is run

in the speed control mode with the speed reference being generated as a function of the change in

active power. Both these algorithms are implemented on the laboratory experimental setup and

relevant experimental results are furnished.

Chapter 7 concludes the thesis with suggestions for further work.


18

Chapter 2

MODELING AND SIMULATION

2.1 Introduction The rotor side control scheme for doubly-fed wound rotor induction machine, introduced in

Chapter 1, shows that independent control of active and reactive powers can be accomplished through

current injection in the rotor circuit in a desired manner. In order to design such a current controller,

field oriented control is employed. Stator flux orientation, as proposed by Leonhard [12], is a natural

choice for decoupling the dynamics of the active and reactive current loops. Contrary to the cage rotor

induction machine, there is an uncontrolled voltage source connected to the stator of a doubly-fed

wound rotor induction machine. This acts as a disturbance variable in the plant model. The current

controller, therefore, needs to be designed in such a way that the effect of the disturbance terms are

nullified [26].

The control of the front end converter has attracted major attention of researchers over the last

decade. Several current control techniques have been proposed for high power factor PWM rectifiers

used in single phase and three phase utilities [27-31]. A hyteresis current controller has been

discussed in [27], whereas, fixed frequency switching controllers are proposed in [28, 30, 31]. The

intensive whistling noise in the ac side reactor due to fixed frequency switching can be reduced by

using a multiple-frequency carrier [29]. In [32], a direct power control strategy is reported which

selects the optimum switching state of the converter by measuring the instantaneous active and

reactive powers. Even though most of these control methods promise satisfactory performance, the

selection of a particular strategy is based on the ease of implementation. It is observed that if the front

end converter is modeled in the synchronous reference frame with stator voltage orientation, the

structure of the active and reactive current loops closely resembles the corresponding current loops

19

for rotor side control. Similar software modules can, therefore, be used for simulating and

implementing the machine side and the front end converter control.

The objective of this chapter is to formulate a mathematical model of the doubly-fed

grid-connected wound rotor induction machine and the front end converter. A design methodology is

evolved for developing the current controllers. Simulation results are presented to confirm the design

and modeling. The implementation of field oriented control and experimental results are given in the

next chapter.

2.2 Machine Model in Field Coordinates

In a doubly-fed wound rotor induction machine, control is exerted on the rotor side while the

stator remains connected to a constant voltage constant frequency source. In order to formulate the

dynamic modeling in the field coordinates, it is assumed that the rotor side converter is equipped with

fast-acting current loops. Hence, given a reference , the rotor current space phasor follows itir& ir

within a finite but extremely short interval of time. The rotor voltage equation is used for designing

the rotor current controller, as discussed in a later section. For the present, the rotor side can be

simply represented by a controllable current source [Fig.2.1] and the rotor current phasor can be taken

as an input to the machine model. It is the stator voltage equation, which determines the dynamic

behavior of the machine. This equation, in the stationary reference frame, is furnished below.

Rs is + (1 + rs ) Loddt is + Lo

ddt ir eje = us

or, (2.1)Rs is + Loddt

(1 + rs ) is + ir eje = us

Fig.2.1 Equivalent circuit in stator reference frame

Lo

Rs

isr

is

sσ Lo

us ψs Loims=

Chapter 2 Modeling and Simulation

20

The magnetizing current vector, which is qualitatively explained in Chapter 1, is defined as

ims = (1 + rs ) is + ir eje

(2.2)= (1 + rs ) is + sir

is the equivalent current vector in the stator reference frame responsible for producing the statorims

flux as depicted in the equivalent circuit of Fig.2.1. Hence it may be called the stator fluxys

magnetizing current. In terms of , Eq.(2.1) can be written as ims

(2.3)Rsis + Loddt ims = us

Since the quantity over which direct control can be exercised is (and not ), Eq.(2.3) needsir is

to be expressed in terms of the rotor currents. Substituting for in Eq.(2.3) using Eq.(2.2), we getis

Rsims − ir e je

1 + rs+ Lo

ddt ims = us

or, (2.4)Tsddt ims + ims =

(1+ rs )Rs

us + ir eje

where is the electrical time-constant of the stator circuit.Ts = Lo(1 + rs )Rs

= Ls

Rs

The above equation Eq.(2.4) is defined in the stator reference frame. It can now be expressed

in terms of a coordinate system fixed to the stator flux or equivalently to the current . In orderys ims

to do this is first expressed in polar form with respect to stator coordinates asims

(2.5)ims = ims ejl

where is the instantaneous magnitude of the current space phasor and, is its instantaneousims ims l

position with respect to the stationary axis. The various phase relationships are shown in Fig.2.2.

Now Eq.(2.4) can be written as

Tsddt ims ejl + ims ejl = 1 + rs

Rsus + ir eje

or, (2.6)Tsdims

dt ejl + Tsims jdldt ejl + imsejl = 1 + rs

Rsus + ir eje


21

Field Axis

µε

Rotor Axis

Stator Axis

ird

irq

ri

ωe

ω ms

Fig.2.2 Angular relations of current vectors for doubly fed induction machine

The above equation can be transformed into field coordinates by multiplying both sides with

the operator e−jl

(2.7)Tsdims

dt + j Ts imsdldt + ims = 1 + rs

Rsus e−jl + ir ej(e − l)

In the field coordinates, the stator voltage and rotor current space phasors can be represented

as

, us e−jl = usd + j usq

and (2.8)ir ej(e − l) = ird + j irq

Substituting this in Eq.(2.7) and separating the real and imaginary parts yields the following

equations.

(2.9)Tsdims

dt + ims = 1 + rs

Rsusd + ird

(2.10)dldt = zms = 1

Ts ims

1 + rs

Rsusq + irq

Eq.(2.9) and Eq.(2.10) represent the dynamics of the field vector magnitude and angle

respectively. The stator voltage and rotor current vectors are the two inputs to the system, of which

the former is not controllable (hence a disturbance variable) and the latter is the control variable.

The electromagnetic torque developed can also be expressed in terms of the field current

vector. In the stationary coordinates the torque equation is given by

(2.11)md = 23

P2 Lo Im is ir eje &


22

Substituting for using Eq.(2.2), we getis

md = 23

P2 Lo Im

ims − sir

1 + rs

sir&

= 23

P2

Lo

1 + rsIm ims sir

&

= 23

P2

Lo

1 + rsIm imsejl ird + j irq ejl &

(2.12)= − 23

P2

Lo

1 + rsims irq

The complete set of equations that describe the machine dynamics in the field coordinates can

be therefore, written as

(2.13 a)Tsdims

dt + ims = 1 + rs

Rsusd + ird

(2.13 b)dldt = zms = 1

Ts ims

1 + rs

Rsusq + irq

(2.13 c)J dzdt = − 2

3P2

Lo

1 + rsims irq − ml

(2.13 d)dedt = P

2 z = ze

The simulation block diagram of the doubly-fed wound rotor induction machine modeled in

the field coordinates is given in Fig.2.3. The inputs to the system are the stator voltage and the rotor

currents. It is assumed that there is a controlled current source in the rotor circuit which is capable of

injecting currents at appropriate phase, frequency and magnitude. The rotor currents are first

transformed to the stator reference frame using the operator . Subsequently the stator voltages andeje

rotor currents (in the stator reference frame) are transformed to the field coordinates by multiplying

with . The angle µ is derived by solving the q-axis equation Eq.(2.13b). The magnitude of ise−jl ims

computed using the d-axis equation Eq.(2.13a). It may be noted that the alternating quantities in the

stationary coordinates, when transformed to the field coordinates appear as dc quantities.


23

3/2

3/2

++

++

X

**

+

_

u s1

u s2 u s3u s βu s

αu sd

u sq

i r1 i r2 i r3

i ra i rbi rdi rq

e-j (µ−

ε)

µe-j

Rs

sσ

+1

Rs

sσ

+1

i ms

T sT s

ωm

s

ωm

s

+_

md

ml

J1s

σ+

132

2PL

0-

µ µ−ε

Fig.

2.3

Blo

ck d

iagr

am o

f th

e do

ubly

-fed

wou

nd r

otor

indu

ctio

n m

achi

ne m

odel

in th

e fi

eld

coor

dina

tes

2Pω

e


24

2.3 Field Oriented Control

The rotor circuit consists of a three phase voltage source inverter operating in the

current-controlled mode. The stator is connected to a constant magnitude, constant frequency source

which has ideally infinite capacity for sourcing and sinking active and reactive powers. It may also be

assumed for the time being that the dc source for the inverter can supply or sink the active and

reactive powers handled by the rotor without affecting the dc bus voltage. (In practice the FEC

interfaces the dc bus with the ac grid, which is discussed in a later section). The schematic block

diagram of this arrangement is shown in Fig.2.4.

3 phaseconstantvoltage

constantfrequency

3 phasevariablevoltagevariable

frequency

Controllerirq

*rd

*i

Feedback signals

Fig.2.4 Schematic block diagram of the system arrangement for doubly-fed SRIM

2.3.1 Rotor Equation in Field Coordinates

For designing the rotor current controller the rotor voltage equation has to be considered. This

equation repeated here,

(2.14)Rr ir + Lrddt ir + Lo

ddt is e−je = ur

is in the rotor reference frame and needs to be transformed to the field coordinates for field-oriented

control. Moreover, the equation has to be expressed only in terms of , the variable to be controlled,ir

and , the field variable.ims


25

From Eq.(2.2)

(2.15)is =ims − ir e je

1 + rs

Substituting for using Eq.(2.15), Eq.(2.14) may be expressed asis

(2.16)Rrir + Lrddt ir + Lo

ddt

ims e−je − ir

1 + rs= ur

Now, Lo

1 + rs=

L02 Lr

Ls Lr= (1 − r) Lr

and .ims = imsejl

Therefore, Eq.(2.16) can be written as

(2.17)Rr ir + r Lrddt ir + (1 − r)Lr

ddt ims ej(l − e) = ur

Writing in terms of the direct and quadrature axis components of rotor current and voltage vectors

Rr ird + jirq ej(l − e) + rLrddt ird + jirq ej(l − e)

+ (1 − r) Lrddt ims ej(l − e)

= urd + jurq ej(l − e)

or, Rr ird + jirq ej(l − e) + rLrddt ird + jirq ej(l − e)

+ rLr jd(l − e)

dt ird + jirq ej(l − e) + (1 − r) Lrdims

dt ej(l − e)

+ (1 − r) Lr ims jd(l − e)

dt ej(l − e)

(2.18)= urd + jurq ej(l − e)

In order to transform this equation to the field-oriented reference frame, both sides have to be

multiplied by . Thereby the following complex equation can be derived.e−j(l − e)

Rr ird + jirq + rLrddt ird + jirq + j (zms − ze )rLr ird + jirq


26

+ (1 − r) Lrdims

dt + j (zms − ze )(1 − r)Lr ims

(2.19)= urd + jurq

where, is the slip frequency. (2.20)d(l − e)

dt = zms − ze

Finally, the real and the imaginary parts are separated to get the d-axis and q-axis equations

respectively as given below.

(2.21)rTrdird

dt + ird = urd

Rr+ (zms − ze ) rTr irq − (1 − r)Tr

dims

dt

rTrdirq

dt + irq =urq

Rr− (zms − ze ) rTr ird − (zms − ze ) (1 − r)Trims

(2.22)

These equations represent the dynamics of the rotor currents in the field coordinate system. It

is observed that due to the presence of the rotational emf terms, there is some amount of

cross-coupling between the d and q axes. However, the current-loop dynamics in the two axes can be

made independent of each other by compensating for these cross-coupling terms.

It is interesting to note the connotations of the terms underlined in these two equations.

Multiplying these terms with gives the corresponding voltages, which can be interpreted asRr

follows.

(a) : This is the rotational emf induced in the d(zms − ze ) r Tr irq % Rr = (zms − ze ) r Lr irq

axis due to the q axis rotor current. Since the relative speed of the rotor with respect to the field

axis is , the frequency term involved in this equation corresponds to the slip(zms − ze )

frequency.

(b) : This denotes the transformer induced voltage in−(1 − r) Trddt ims % Rr = −(1 − r) Lr

ddt ims

the d-axis due to the field current . Obviously this term will not appear in the q-axis.

(c) : This term gives the rotationally induced−(zms − ze ) r Tr ird % Rr = − (zms − ze ) r Lr ird

emf in the q-axis due to the d-axis current, similar to the first term.

(d) : This denotes the speed emf(zms − z) (1 − r )Tr ims % Rr = (zms − ze ) (1 − r ) Lr ims

induced in the q-axis due to the field. The frequency term involved in this equation is again the

slip frequency.


27

Due to the presence of these terms, there exists some coupling between the two axes.

However, as the slip range is limited, the contribution of the terms (a) and (c) is relatively small

compared to the speed emf term (d). The transformer emf term (b) also does not exist after the flux

has built up, provided the stator voltage is constant in magnitude and frequency. While designing the

rotor current controller it is possible to compensate for these terms and make the loop dynamics in the

two axes independent of each other. This is discussed in the following section.

2.3.2 Design of Rotor Current Controller in Field Coordinates

It is obvious that if the rotor current needs to be controlled in the field coordinates, two

independent controllers are needed; one for the d-axis and the other for the q-axis. The design method

is same for both; only the feedforward terms differ in each case. Design of a proportional (P)

controller, and a proportional-integral (PI) controller are presented here.

(a) Proportional Controller

Let the desired current loop dynamics in the d-axis be given by

(2.23)Tirdird

dt + ird =ird

&

K ir

where is the desired current-loop time constantTir

and, is the current sensor gain.Kir

The task is now to find out the d-axis component of the instantaneous inverter terminal

voltage required to produce the current dynamics given by Eq.(2.23).

Substituting for from Eq.(2.23) in Eq.(2.21) givesdird

dt

urd = rLr

T irK irird& − Kir ird + Rr ird + (1 − r) Lr

dims

dt − (zms − ze ) r Lr irq

(2.24)

The inverter can be modeled as a gain block . For sine-triangle modulation the inverter gainGr

depends on the dc bus voltage and the peak of the triangle . udc utri

(2.25)Gr = udc

2$u tri

In order to make the inverter gain constant, the peak of the carrier triangular waveform is madeutri

proportional to .udc


28

Therefore, the reference for the d-axis component of rotor voltage is given by

urd& = urd

Gr

= rLr

T irK irGrird& − Kir ird + Rr

Grird +

(1−r) Lr

Gr

dims

dt −(zms − ze ) r Lr

Grirq

(2.26)

Assuming same current loop dynamics for the q-axis the reference for the q-axis component

of the rotor voltage can be expressed as

urq& =

urq

Gr

= rLr

T irK irGrirq& − Kir irq + Rr

Grirq

(2.27)+(zms − ze ) (1−r) Lr

Grims +

(zms − ze ) r Lr

Grird

If the impressed rotor voltages are in accordance with Eq.(2.26) and Eq.(2.27), the field and

quadrature axes rotor currents can be controlled independently. The rotor current controller, therefore,

does not contribute significantly to the dynamics of the system. It only ensures that the rotor currents

track the reference signals produced by the outer loops. It may be appreciated that the current loop

dynamics can be made much faster than the rotor time constant. However, a practical limitation to the

bandwidth of the current controller is imposed by the switching frequency. Since the controller is

designed in the field coordinates, all the quantities are dc and implementation of the controller

becomes simpler.

The simulation block diagram of the rotor current controller is shown in four parts. Fig.2.5

shows the computation of the flux vector and transformation of the rotor currents to the field

coordinates. Assuming that at , the rotor and stator axes are aligned, the rotor position can bet = 0 e

directly obtained in the simulation by integrating the shaft speed. The rotor currents are first

transformed to the stationary coordinates with this angle information . The angle , which the fielde l

axis makes with the stator coordinates, as well as the magnitude of , can be calculated from theims

stator and rotor currents as follows.

In the stator coordinates,

imsejl = (1 + rs)(isa + jisb) + (ira + jirb)(cos e + j sin e)


29

= [(1 + rs) isa + ira cos e − irb sin e]

(2.27)+ j [(1 + rs) isb + ira sin e + irb cos e]

Therefore, ims = [{(1 + rs)isa + ira cos e − irb sin e}2

(2.28)+ {(1 + rs)isb + ira sin e + irb cos e}2]1/2

(2.29)l = arctan{(1+rs)isb + ira sin e + irb cos e}{(1+rs)isa + ira cos e − irb sin e}

Fig.2.5 Flux computation and rotor current transformation blocks

µ

ims

+

-ε

ε

dims

dt

ωms−

Eq.(2.28)

Eq.(2.29)

ir1ira

irbir2ir3

is1

is3

is2 isβ

isα

3/2

3/2

ird

irq

d/dt

d/dt ωe

µe-jejε

The d-axis controller block diagram along with the plant is given in Fig.2.6(a). All the

parameters necessary for constructing the feedforward terms have already been computed in the

previous stage. After generation of the reference voltages and , they are again transformedurd& urq

&

back to the rotor reference frame by multiplying with the inverse transformation operator .ej (l−e)

However, for the sake of simplification, transformation of from the field coordinates to the rotorurd&

reference frame in the controller, and the corresponding forward transformation in the machine model

are not shown in the diagram. The plant model in the d-axis is shown with shaded blocks. It is evident

from this diagram that the controller just adds or subtracts the disturbance inputs to the machine

model reducing the plant to merely an integrator. Hence, the closed loop system behaves like a

first-order lag circuit whose time-constant can be modified by changing the proportional gain of the

system, as in Fig.2.6(b) and Fig.2.6(c). The q-axis current controller can be similarly modeled; the

compensating terms will only be different in this case. In the controller block diagram the current

sensor gain Kir is assumed to be unity for simplifying the diagrams.


30

The implementation of this controller is discussed in Chapter 4. The details for the practical

implementation vary slightly from the theoretical design of the controller, even though the overall

concept remains the same.

(b)

(c)

Fig.2.6 Block diagram of d-axis proportional rotor current controller

(a)

(b) Proportional Integral Controller

In the proportional controller, the steady-state error in the rotor currents will depend on the

accuracy of computation of the feedforward terms. Any error in the compensation terms would result

in slight modification of the dynamic response. In the practical implementation, it is extremely

difficult to perfectly nullify the disturbance terms owing to measurement and computational errors.

Therefore, a proportional integral controller needs to be incorporated. This is particularly important

when the machine is run in the torque-control mode without any outer speed loop. The flux

computation and transformations shown in Fig.2.5 remain identical. The plant is modeled as a

first-order lag system with the two rotational emfs as disturbance inputs as shown in Fig.2.7(a). These

two terms are canceled through feedforward compensation as before. In the controller, the PI


31

ird&

ird

rLr

GrT ir

Rrird

Gr

(1−r)Lr

Gr

dims

dt

(1 − r)Lrdims

dt

Rrird

(zms−ze )Gr

rLrirq

(zms − ze )rLrirq

Gr 1rLr

1s

ird

1rLr

1s

rLr

T irird&

ird

irdird& 1

1 + sT ir

+ − + + +

+

+ − −+

+

+ +

−

+−

time-constant is made equal to , so that the dynamics of the system is decided by the proportionalrTr

gain, as shown in Fig.2.7(b) and Fig.2.7(c).

The choice of proportional gain follows from the equation , where is theKpir = rTr

T irRr Tir

desired effective time constant of the current loop.

(b)

(c)

Fig.2.7 Block diagram of d-axis proportional-integral rotor current controller

(a)

2.4 Simulation Results - Rotor Side Control

The entire system is simulated on the MATLAB-SIMULINK platform. The simulation model

comprises different functional modules or subsystems. Each of these modules, in turn have several

levels of subsystems which are developed using the standard SIMULINK library.


32

ird&

ird

Kpir

Gr

(1 + rTrs)rTr

(1−r)Lr

Gr

dims

dt

(1 − r)Lrdims

dt(zms−ze )

GrrLrirq

(zms − ze )rLrirq

1Rr(1 + rTrs)

Gr+

− −

+ +

+

+ +

−

ird

ird& irdKpir

(1 + rTrs)rTr

1Rr(1 + rTrs)

11 + T irs

ird& ird

+−

Rotor toStator 7

Ml

Torque Converter

7

W

6

Ir3

2

Is23

Is34

Ir1 5

Ir2

1

Is1

CurrentInspection

Block

*

We

P/2

Pole Pair

Sin E, Cos E

MechanicalSubsystem

1

Vsa 2

Vsb 3

Vsc 3ph to 2phStator Side

6

Vrc

5

Vrb

4

Vra

3ph to 2phRotor Side

ElectricalSubsystem

Fig.2.8 SIMULINK model of the doubly-fed SRIM

As an example, the modeling of the doubly-fed SRIM may be considered. The machine model

consists of the transformation blocks, electrical subsystem, torque converter block and, the

mechanical subsystem. This is shown in Fig.2.8. The transformation blocks include 3 phase to 2

phase transformation, rotor coordinate to stator coordinate transformation and, the corresponding

inverse transformations (used in the current inspection block). The electrical subsystem is modeled in

the stationary coordinate system. The state space equations (Eq.(A32)) to compute the stator and rotor

currents in the stator reference frame are derived in Appendix A. The torque equation, given by

Eq.(A33), is executed in the torque converter block. Finally, the mechanical subsystem computes the

machine speed from the mechanical dynamics, as given by Eq.(A22d). The position of the rotor with

respect to the stator is obtained through integration of the shaft speed in the block. Thesesin e, cos e

modules with appropriate interconnections are grouped together to form the SRIM block in the

system simulation model of Fig.2.9. In a similar manner, the other functional modules of Fig.2.9 are

developed.


33

8

w*

1

Us1

2

Us2

3

Us3

7

Load Torque

6

Control Enable

5

Ird*

Controller Inverter SRIM

4

DCBus

Sensors

Sine PWM

Fig.2.9 SIMULINK block diagram of a speed-controlled drive using doubly-fed SRIM

A speed controlled drive using grid-connected doubly-fed SRIM is simulated. Stator flux

orientation, as discussed in the earlier sections, is employed. The d-axis and q-axis current controllers

are designed in the field reference frame. For the speed loop, a PI controller is employed which

generates the q-axis / active current reference . The d-axis reference is set in open loop. Theirq& ird

&

machine parameters, sensor gains and, controller gains are given in Appendix B and Appendix C. In

order to emulate the implementation of the controller in the DSP-based hardware platform, the

controller module is modeled in per unit. The base values are selected appropriately as given in the

MATLAB data file of Appendix C. The results are presented in per unit terms for the sake of

uniformity.

The speed response of the drive under no load is given in Fig.2.10(a). The motor is started

DOL with the rotor shorted. At t=0.25s, the rotor side control is released with a speed reference z&

=0.75 p.u. At t=1.25s, the speed reference is given a step change from 0.75 p.u. to 1.25 p.u. The

corresponding motor torque and are given in Fig.2.10(b) and Fig.2.10(c) respectively. The speedirq

controller time constant is set to 100 ms. At t=1.75s, is given a step change to 0.75 p.u. Thisird&

results in transfer of the reactive power from the stator to the rotor side. However, a change in ird

does not affect , as can be seen from these plots.irq


34

0 0.5 1 1.5 20

0.5

1

1.5

secs

Spe

ed (

p.u.

)

Fig.2.10(a) Simulated speed response of the speed-controlled grid-connected SRIM drive

0 0.5 1 1.5 2-1.5

-1

-0.5

0

0.5

1

1.5

secs

Mot

or T

orqu

e (p

.u.)

Fig.2.10(b) Simulated torque response of the speed-controlled grid-connected SRIM drive


35

0 0.5 1 1.5 2-1.5

-1

-0.5

0

0.5

1

1.5

secs

irq (

p.u.

)

Fig.2.10(c) Simulated response of the speed-controlled grid-connected SRIM driveirq

0 0.5 1 1.5 2-1.5

-1

-0.5

0

0.5

1

1.5

secs

ird (

p.u.

)

Fig.2.10(d) Simulated response of the speed-controlled grid-connected SRIM driveird


36

0.7 0.72 0.74 0.76 0.78 0.8-1

-0.5

0

0.5

1

secs

irq (

pu)

Fig.2.11(a) Simulated step response of for the grid-connected SRIMirq

0.7 0.72 0.74 0.76 0.78 0.8-1

-0.5

0

0.5

1

secs

ird (

pu)

Fig.2.11(b) Corresponding simulated response of for the grid-connected SRIMird


37

Fig.2.11(c) Corresponding simulated response of along with for the grid-connected SRIMis us

Fig.2.11(d) Corresponding simulated response of along with for the grid-connected SRIMsir us


38

1 1.02 1.04 1.06 1.08 1.1-1

-0.5

0

0.5

1

secs

ird (

pu)

Fig.2.12(a) Simulated step response of for the grid-connected SRIMird

1 1.02 1.04 1.06 1.08 1.1-1

-0.5

0

0.5

1

secs

irq (

pu)

Fig.2.12(b) Corresponding simulated response of for the grid-connected SRIMirq


39

Fig.2.12(c) Corresponding simulated response of along with for the grid-connected SRIMis us

Fig.2.12(d) Corresponding simulated response of along with for the grid-connected SRIMsir us


40

0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

secs

spee

d (p

.u.)

Fig.2.13(a) Simulated response of speed through the synchronous speed for the grid-connected SRIM

0.8 1 1.2 1.4 1.6 1.8 2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

secs

ir (p

.u.)

Fig.2.13(b) Corresponding simulated response of for the grid-connected SRIMir


41

0.8 1 1.2 1.4 1.6 1.8 2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

secs

Ps

(p.u

.)

Fig.2.13(c) Corresponding simulated response of stator power for the grid-connected SRIM

0.8 1 1.2 1.4 1.6 1.8 2-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

secs

Pr

(p.u

.)

Fig.2.13(d) Corresponding simulated response of rotor power for the grid-connected SRIM


42

The dynamic response of the current loops are given in Fig.2.11 and Fig.2.12. The q-axis

current loop time constant is designed for 1ms and, the d-axis loop time constant is designed for 4ms.

(The d-axis reference is not required to be varied dynamically; so the dynamic response of needird

not be very fast.) The actual stator currents and, the rotor currents in the stator reference frame are

also shown. In Fig.2.11 is zero, so the stator supplies the reactive power and the rotor powerird

factor is unity. In Fig.2.12, the reactive power is transferred from the stator to the rotor side, resulting

in an improvement in the stator power factor.

The transition through synchronous speed is shown in the plots of Fig.2.13(a) through

Fig.2.13(d). With an initial speed of 0.6 p.u., the simulation is run with p.u. and a loadirq& = 0.5

torque of -0.88 p.u. (i.e. driving torque). Therefore, the stator power remains constant, while the rotor

power goes from positive to negative. The transition of the rotor phase current through synchronous

speed is also shown.

Using the aforestated method of rotor current control the four modes of operation as described

in chapter 1 can be achieved. During subsynchronous motoring and supersynchronous generation, the

direction of rotor power flow is from the rotor circuit to the grid. Therefore, an ordinary diode bridge

rectifier cannot be employed as the line side converter. A current controlled IGBT based PWM

converter is used instead. In the following sections, the method of control for this front end converter

and relevant simulation results are presented.

2.5 Front end Converter

A conventional phase-controlled rectifier has several serious disadvantages. Firstly, with the

dc bus polarity remaining constant, power flow can be in one direction only. Secondly, it draws

reactive power from the line, which is substantial at large firing angles. Lastly, the current drawn

from the mains is far from sinusoidal. Obviously, a four-quadrant drive or generating system cannot

be implemented with a phase-controlled converter in the line side.

The front end converter employs a three-phase inverter bridge topology and is controlled to

enable power flow in both directions, keeping the dc bus voltage within good regulation. It can be

operated at any desired power factor, and hence, can even act as a reactive power source as far as the

grid is concerned. The converter is operated as a PWM voltage source inverter in the

current-controlled mode; so, the harmonics in the line current waveform are substantially reduced.

43

It is understood that by employing stator voltage orientation, the active and reactive currents at

the input of the front end converter can be controlled in the synchronous reference frame. The control

essentially has the same structure as the rotor side controller. The objectives of control and, modeling

of the power and control circuit are described in the following sections.

2.6 System Description

Fig.2.14 Schematic block diagram of the front end converter

Transformer Inductor

+_

PWM Signals

FeedbackSignals

Inverteruac1

uac2

uac3

ufe1

ufe2

ufe3

ife1

ife3

ife2

udc i l

us1

us2

us3

ife1 ife2,

uac1 uac2,udc

i l

udc*

Digital

Controller

The schematic block diagram of the front end converter is shown in Fig.2.14. The transformer

in the input side is used to match the voltage levels between the dc bus and the ac side. The rotor side

converter operates within a limited frequency range. Hence, the dc bus voltage requirement is less

when compared to the stator side control schemes of cage rotor induction machine. The saving in the

converter rating in the rotor side is achieved due to reduction in voltage rating of the power devices.

With a reduced dc bus voltage it, however, becomes necessary to use a transformer at the input of the

front end converter. Since the rotor side need not be isolated from the ac grid, an autotransformer can

be used instead. This reduces the cost and weight of the equipment considerably.

The PWM switching converter is connected to the secondary side of the transformer through

series chokes. These inductors act as buffers between the two voltage sources. The choice of the

values for these inductors depends on the switching frequency, allowable harmonics in the input

current waveform and the reactive power requirement.


44

The objectives for the control of the converter are,

i) Voltage regulation of the dc bus,

ii) bi-directional power flow,

iii) operation at any desired power factor, and

iv) low current harmonics.

2.7 Principle of Operation and Control

The front end converter requires closed-loop control to meet the stated objectives. The basic

strategy for control and resulting circuit behavior can be explained easily by means of the phasor

diagrams given in Fig.2.15.

uac ufe

i fexfe

(a) Ac side equivalent circuit

i fe uac

ufe

i fe xfe

(b) Forward power flow at upf

i fe

uac

ufe

i fe xfe

(c) Forward power flow at leading power factor

ufe

uac

i fe xfe

(d) Reverse power flow at upf

ufe

uac

i fe xfei fe

i fe

(e) Reverse power flow at leading power factor

Fig.2.15 Equivalent circuit and phasor diagrams for the front end converter

The primary objective of control is dc bus voltage regulation. A change in the dc bus voltage

can be attributed to an imbalance between the active powers between the ac and dc sides. (The effect

of reactive power on the dc bus is to produce ripples in the voltage even though the average value

remains the same.) Hence, the voltage error in the dc side is an indication of the active power demand

in the ac side. If the demand is positive, active power drawn from the grid needs to be increased; if


45

the demand is negative, it has to be fed back to the grid. Since the converter has bidirectional

switches, current flow can be in either direction and it is possible to source or sink active power in the

ac side.

Fig.2.15(a) shows the single phase equivalent circuit of the ac side of the front end converter.

If the load current in the dc side for a given dc bus voltage is known, the current drawn from the ac

side at any desired power factor can be calculated applying power balance between the ac and dc

sides. Consequently, subtracting the reactive drop from the source voltage, the magnitude and phase

of the inverter terminal voltage with respect to the source can be computed. The inverter, therefore,

acts as a fixed frequency source with controllable phase and magnitude. Fig.2.15(b) and Fig.2.15(d)

represent steady-state phasor diagrams at unity power factor operation when power is flowing from ac

to dc side and vice versa. The corresponding phasor diagrams for leading power factor operation are

illustrated in Fig.2.15(c) and Fig.2.15(e). It is observed that the magnitude of the inverter terminal

voltage increases in this case. The amount of reactive power that can be injected into the grid depends

on the available dc bus voltage and the value of per unit inductance in the ac side.

The terminal voltage of the inverter will also contain switching harmonics apart from the

fundamental. As far as the harmonics are concerned the ac source acts as a short-circuit and the

effective impedance to the harmonic current is . For high frequency switching (more than 1kHz),nXfe

the harmonic impedance is quite high resulting in very low distortion of the ac side current waveform.

With the above scheme of control it is possible to achieve the desired objectives as stated

earlier. The salient features of the control strategy can be summed up as the following.

4 Employs an outer voltage control loop to regulate the dc bus voltage and an inner current control

loop to control the ac side inductor current.

4 Outer voltage loop decides the value of inductor current to meet the active power balance between

the two dc and ac sides.

4 The current loop tracks this reference by adjusting the inverter terminal voltage so that proper

phase relationship between the supply voltage and the inductor current is maintained for a given

power factor operation.

4 Employs current-controlled sinusoidal PWM for current tracking.

4 The current controller is designed in synchronously rotating reference frame with orientation

being done with respect to the supply voltage space phasor.


46

Fig.2.16 shows the schematic block diagram of the control structure of the front end

converter. The voltage controller is a proportional-integral controller with feed-forward of the load

current and generates or the reference for the active component of current. The reference for theifeq&

reactive component of current , is set in open loop; e.g. it is set to zero for unity power factorifed&

operation. The current controller operates in the synchronous reference frame and generates and ufed&

for the inverter terminal voltage. These references are first transformed back to the stationaryufeq&

reference frame, and then from two phase to three phase quantities. Finally, the three phase references

are compared with a triangular carrier to generate the PWM signals for the inverter switches. The

modeling of the power circuit and design of the controllers are discussed in detail in the following

sections.

Fig.2.16 Schematic block diagram of the control structure of the front-end converter

D-Axis

Contrl

Q-Axis

Contrl

PowerCircuit

VoltageContrl

PWMGenr.

Tranf.&

+

_

udc*

udc

+

_

ifed*

ifed

ifeq*

+ _ifeq

uac1 uac2 uac3

ufe1

ufe3

ufe2

udc

udci fe1i fe2i fe3

Unit VectorGenr.

Tranf.

i fe1i fe2i fe3

uac1uac2uac3

sin θ

cosθ

sin θ cosθ

2.8 Modeling of the Power Circuit

In the stationary reference frame, the ac side voltage equations for the three phases can be

written as follows.


47

(2.30)uac1 = ufe1 + Lfeddt ife1



The above equations can also be represented in terms of space phasors as

(2.33)uac = ufe + Lfeddt ife

where, (2.34)uaca = ufea + Lfeddt ifea

(2.35)uacb = ufeb + Lfeddt ifeb

θα

β

q

d

Fig.2.17 Stationary and synchronous reference frame

Stator voltage space phasor

The stationary reference frame equations are transformed to synchronously rotating reference

frame; the orientation being done with respect to the supply voltage space phasor as indicated earlier.

The relative orientation of the stationary and synchronous reference frames is shown in Fig.2.17. To

maintain compatibility with the d-axis and q-axis definitions used in rotor side control, the supply

voltage phasor axis is taken as the q-axis in this case. The unit vectors and can be directlycos h sin h

obtained from and respectively. In terms of the d-axis and q-axis variables Eq.(2.34) anduaca uacb

Eq.(2.35) can be rewritten as follows.

uacq ejh = ( ufeq + j ufed) ejh + Lfeddt ifeq + j ifed ejh

or, uacq ejh = ( ufeq + j ufed) ejh + Lfeddt ifeq + j ifed ejh

(2.36)+ j dhdt Lfe ifeq + j ifed ejh


48

Eq.(2.36) describes the system dynamics in the stationary coordinates in terms of the

synchronous reference frame variables. Since the orientation is done with respect to the grid voltage,

is zero. Transforming this to the rotating reference frame by multiplying both sides with uacd e−jh

and separating the real and imaginary parts the following d-axis and q-axis equations can be obtained.

(2.37)ufed + Lfeddt ifed + zsLfeifeq = 0

(2.38)ufeq + Lfeddt ifeq − zsLfeifed = uacq

Due to the transformation, rotational emf terms appear in the voltage equations in the

synchronous reference frame, giving rise to cross-coupling between the two axes. These rotational

emf terms are required to be compensated by appropriate feedforward signals in order to

independently control the active and reactive components of current.

Fig.2.18 DC Bus Model

i feq

idc

i l

ic

Cudc

uacq

udc

23

.

The dynamics of the dc bus voltage can be modeled by considering the balance between the

active power flow between the ac and the dc sides. If the series inductor is lossless,

(2.39)23 uacq $ ifeq = udc idc

where is the dc bus current as indicated in Fig.2.18. This current can be written in terms of theidc

capacitor charging current and, the load current as ic il

(2.40)idc = ic + il = Cdudc

dt + il

Substituting from Eq.(2.40) in Eq.(2.39) the following equation can be derived.idc

(2.41)Cdudc

dt = 23

uacq

udc$ ifeq − il

Since the dc bus voltage is regulated within a narrow band and, the ac side voltage is

nominally constant, the factor may be considered as a constant ratio to transform theuacq

udc


49

synchronous reference frame current to the dc link current. The model is schematically shown in

Fig.2.18.

2.9 Front end Converter Controller Design

2.9.1 Design of the Current Controller

The design of the current controller is similar to that discussed in rotor side control. Two

independent controllers are used for controlling the d-axis and q-axis currents. For the sake of

completeness design of proportional controller and proportional-integral controller are discussed in

detail.

a) Proportional Controller

Let the desired current loop dynamics in the q-axis be given by

(2.42)Tifedi feq

dt + ifeq =i feq

&

K ife

where is the desired current-loop time constantTife

and, is the current sensor gain.Kife

Substituting from Eq.(2.42) in Eq.(2.38) gives the q-axis component of the instantaneousdi feq

dt

inverter terminal voltage required to produce the desired current dynamics.

(2.43)ufeq = uacq + zs Lfe ifed − L fe

T ifeK ifeifeq& − Kife ifeq

The inverter can be modeled as a constant gain block as explained in SectionGfe = udc

2$u tri

2.3.2(a). The reference for the q-axis component of rotor voltage is, therefore, given by

ufeq& =

u feq

G fe

(2.44)=uacq

G fe+ zs L fe i fed

G fe− L fe

T ifeK ifeG feifeq& − Kife ifeq

The plant along with the controller for the q-axis is shown in Fig.2.19. The current sensor gain

is taken as unity to simplify the diagram.Kife

Assuming same current loop dynamics for the d-axis, the reference for the d-axis component

of the rotor voltage can be expressed as the following.

ufed& = u fed

G fe


50

(2.45)= −zs L fe i feq

G fe− L fe

T ifeK ifeG feifed& − Kife ifed

If the impressed inverter voltages are in accordance with Eq.(2.44) and Eq.(2.45), the active

and reactive components of the ac side current can be controlled independently.

(a)

(b)

(c)

Fig.2.19 Block diagram of q-axis proportional front end current controller

So far it has been assumed that the resistive drop for the inductor is negligible, which in

practice is a valid assumption. However, if a proportional controller is used, the inclusion of the

resistive drop as compensating terms in (2.44) and (2.45) minimizes the steady-state error.

b) Proportional Integral Controller

The design of the proportional-integral controller is similar to that discussed in Section

2.3.2(b). The resistive drop is taken into consideration and the plant is represented by a first-order lag

along with the cross-coupling and input voltage terms. The q-axis plant and controller are given in


51

ifeq&

ifeq

L fe

T ifeG fe

uacq

G fe

zsL fei fed

G fe

Gfe

uacq

zsLfeifed

1L fe

1s

ifeq

+−

+

− ++

+

−

+ −

L fe

T ife

1L fe

1s ifeqifeq

&

+−

ifeq&

ifeq1

1 + T ifes

Fig.2.20. The PI time-constant is made equal to and the proportional gain Tpife Tfe(= Lfe/Rfe) Kpife

is selected as , where is the effective current-loop time constant.T fe

T ifeRfe Tife

Fig.2.20 Block diagram of q-axis proportional-integral front end current controller

(b)

(c)

(a)

+ _

_ +

++

+_

+ _

+_

2.9.2 Design of the Voltage Controller

Since the primary objective of the controller is to regulate the dc bus voltage within a narrow

band, a proportional integral controller is the obvious choice. It may be appreciated that the response

of the voltage controller need not be very fast. It is, however, desirable that the transient undershoot

or overshoot in the dc bus voltage due to sudden variations of load in the dc side is limited to a

minimum, nominally within 5%. This is achieved by using the dc-side load current as a feed-forward

term to the voltage controller. The structure of the controller, along with the plant is shown in

Fig.2.21(a). It is assumed that the current control loop is much faster than the outer voltage loop. So


52

ifeq&

ifeq

Kpife

G fe

(1 + T fes)T fes

uacq

G fe

zsL fei fed

G fe

Gfe

uacq

zsLfeifed

1R fe(1 + T fes)

ifeq

ifeqifeq& Kpife

(1 + T fes)T fes

1R fe(1 + T fes)

11 + T ifes

ifeq& ifeq

the dynamics of the current loop can be neglected while designing the voltage controller. The forward

path transfer function of the system becomes

(2.46)Kpvfe

CTvfe

1+sTvfe

s2

From the bode plot of the system, shown in Fig.2.21(b), it can be inferred that has to be1/Tvfe

selected slightly lower than the desired bandwidth. The gain is then adjusted to make the phaseKpvfe

margin close to 90o.

Fig.2.21(a) Structure of PI controller

Fig.2.21(b) Magnitude and Phase plot of the voltage loop

+ _

++

+_

dB

Frequency (logscale)

Frequency (logscale)

2.10 Simulation Results - Front end Converter

The SIMULINK model of the front end converter power circuit is shown in Fig.2.22. The

three phase inverter block generates the inverter terminal voltages taking the gating signals as its

input. The ac side dynamic equations in the stationary reference frame i.e. Eq.(2.30) through

Eq.(2.31) are modeled in the subsequent block. The outputs from this block are the inductor currents,

which are then multiplied with the switch status to form the dc side current in the demodulator block.


53

udc&

udc

Kpvfe(1+Tvfes)

Tvfes

il

32

udcuacq

1ifeq& ifeq 2

3uacq

u fe

il

1sC

udc

1/Tvfe

00

−900

−1800

Finally, the dynamics of the capacitor voltage, given by Eq.(2.41), is modeled to get the dc bus

voltage.

The modeling of the entire system along with the feedbacks and controllers is given in

Fig.2.23. The individual functional modules can be identified clearly from this diagram.

1Iload

6U2*

4Vs3

3Vs2

7U3* AC Side3 Ph Inverter

4Is3

3Is2

2Is1

2Vs1

5U1*

Demodulator DC Side

1Vc

Fig.2.22 SIMULINK model of the three phase front end converter power circuit

Load

Sensors

VoltageController

Uref

Uref

Power Circuit

3ph Source

PWMGenerator

Current Controller

Fig.2.23 SIMULINK system model of the three phase front end converter

The simulation results for the three phase front end converter under various transient

conditions are given in Fig.2.24 through Fig.2.28. The parameters for the power circuit and the

controller used in this simulation are taken to be the same as in the experimental setup. These are

listed in a MATLAB file in Appendix C. The controller module is modeled in per unit in order to

emulate the actual implementation of the controller.


54

The current loop dynamics is first investigated. The output of the voltage loop is disconnected

and, step changes in the current references are given. The initial dc bus voltage is set to the rated

value of 300V. The value of the capacitor is made much higher than the actual value of 4000 µF to

keep the bus voltage constant during the forced transients in the active and reactive current loops. The

true response of the current loops can, therefore, be determined. It may be noted here that such

decoupling of the voltage and current loops is not possible during the implementation.

In Fig.2.24(a), responses of and for step change in from 0 to 0.5 p.u. withifeq ifed ifeq&

, are shown. The designed current loop time constant is 2ms. The corresponding response ofifed& = 0

the ac side current is given in Fig.2.24(b) along with the supply voltage. Since , the inputifed& = 0

power factor is observed to be unity. The reversal of active current from 0.5 p.u. to -0.5 p.u. under

unity power factor operation is shown in Fig.2.25. Current responses for step change in from 0 toifed&

0.25 p.u. with p.u. are plotted in Fig.2.26. The input current waveform shows that the frontifeq& = 0.5

end operates at a leading power factor, thereby supplying reactive power to the source. There is, of

course, a limit to the reactive current that can be injected. This depends on the dc bus voltage and the

line side inductance value. Since the reactive voltage drop adds to the line voltage in the same phase,

the maximum value of can be written by the following equation.ifed

(2.47)ifed,max = ª2. 32 .

udc2„2

mmax − us

zL

The decoupling of the dynamics of the d-axis and q-axis current loops is clearly evident form these

plots.

The initial charging of the dc bus voltage from 178V (i.e. ) to 300V and, transient dueª2.125

to application of positive load of 0.75 p.u. is shown in Fig.2.27. The response of the dc bus voltage

when the load is reversed from 0.35 p.u. to -0.35 p.u. is plotted in Fig.2.28. The voltage loop time

constant is designed to be 100 ms.


55

Fig.2.24(a) Response of and ifeq ifed

Fig.2.24(b) and response of uac ife

Fig.2.24 Simulation results for step change in from 0 to 0.5 p.u. with .ifeq& ifed

& = 0


56

Fig.2.25(a) Response of andifeq ifed

Fig.2.25(b) and response ofuac ife

Fig.2.25 Simulation results for step change in from 0.5 p.u. to -0.5 p.u. with .ifeq& ifed

& = 0


57

Fig.2.26(a) Response of andifeq ifed

Fig.2.26(b) and response ofus ife

Fig.2.26 Simulation results for step change in from 0 to 0.25 p.u. with p.u.ifed& ifeq

& = 0.5


58

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

1.2

secs

udc

(p.u

.)

Fig.2.27(a) Response of udc

0 0.5 1 1.5 2 2.5-1.5

-1

-0.5

0

0.5

1

1.5

secs

ifeq

(p.u

.)

Fig.2.27(b) Response ofifeq

Fig.2.27 Simulation results of response of dc bus voltage when a positive

load of 0.75 p.u. is suddenly applied on the dc side


59

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

1.2

secs

udc

(p.u

.)

Fig.2.28(a) Response of udc

0 0.5 1 1.5 2 2.5 3-1.5

-1

-0.5

0

0.5

1

1.5

secs

ifeq

(p.u

.)

Fig.2.28(b) Response ofifeq

Fig.2.28 Simulation results of response of dc bus voltage when the dc side

load is reversed from 0.35 p.u. to -0.35 p.u.


60

2.11 Conclusion

A stator flux oriented model has been derived for the wound rotor induction machine. Current

controllers designed in the field reference frame comprise proportional or proportional-integral

controllers with subsequent addition or subtraction of the compensating terms. The design method is

simple as it directly follows from the rotor voltage equations. Simulation results show that the

dynamics of the active and reactive current loops are decoupled as required. The front end converter

is modeled in the stator voltage reference frame. The structure of the current loops is similar to that

for the rotor side control. The front end converter has been exhaustively simulated for forward and

reverse power flow conditions. It is shown that leading power factor operation is possible upto a

certain limit. The voltage controller exhibits excellent transient response during sudden impact of

load on the dc bus.


61

Chapter 3

HARDWARE ORGANIZATION AND EXPERIMENTAL

RESULTS FOR CONVENTIONAL FIELD ORIENTED

ROTOR SIDE CONTROL AND FRONT END CONVERTER

CONTROL

3.1 Introduction

A major emphasis of the present work is to develop a generalized hardware platform for

high-performance ac drives. The system organization for rotor side control of doubly-fed wound rotor

induction machine presents a versatile case where both the machine side and line side converters are

necessary. In order to demonstrate the application of such a system to wind power generation, the

wind turbine characteristics also need to be simulated with a dc drive. In this chapter a detailed

description of the experimental setup is provided. The DSP-based software implementation of

conventional field-oriented rotor side control with position sensors and, control of the front end

converter are discussed. Finally, typical experimental results are furnished. The transient responses of

the control loops are compared with those obtained through simulation to verify the system modeling

and controller design.

63

Fig.

3.1

Org

aniz

atio

n of

the

expe

rim

enta

l set

up

{{

{

Lin

e si

de

Co

nve

rter

Mac

hin

e si

de

Co

nve

rter

Wou

nd r

otor

indu

ctio

n m

achi

neD

C

mac

hine

i s1

i s2

i s3

i r1 i r2 i r3

S1S2

S3S1

'S2

'S3

'

u dc

+ -

i fe1

i fe2

i fe3

i g1

i g3

i g2

u s1

u s3

u s2

TM

S32

0F24

0 D

SP

bas

ed

Dig

ital C

ontr

olle

r

Con

trol

ler

DC

Driv

e

Enc

oder

u ac1

u ac2

u ac3

Chapter 3 Hardware Organization and Experimental Results

64

3.2 Organization of the Power Circuit

The organization of the experimental setup is schematically shown in Fig.3.1. The power

circuit essentially consists of two three phase IGBT converters with a common capacitive dc link, a

step down transformer at the input of the front end converter and ac side series inductors. The

machines comprise a three phase wound rotor induction machine and a separately excited dc motor

coupled to the same shaft. The details of the components used in the power hardware are listed in

Appendix B. A brief overview of the power converters, which have been developed as a part of the

present work, is included in this section.

3.2.1 IGBT Converter

The IGBT converters use the conventional three phase bridge topology. The converters are

fabricated in-house in a modular fashion. Physically, the machine side and front end converters are

housed in two different cabinets with the dc bus connected together through cables. In order to

minimize the parasitic leakage inductance of the dc bus, a sandwiched arrangement of the positive

and negative buses have been designed. The electrolytic capacitors are seated directly on the bus and,

are physically close to the device terminals. Apart from these electrolytic capacitors, polypropylene

capacitors with low ESR are connected directly at the device terminals. The inverter design is,

therefore, snubberless; the polypropylene capacitors only absorb the small switching spikes that

appear on the dc bus. The devices are mounted on an appropriate heat sink and, forced air-cooling is

employed. The other hardware subsystems of the inverter are described below.

(a) Gate Drive Card

Each gate drive card houses the drive circuits for two devices, corresponding to one leg. The

input gating signal for each device is optically isolated with high-bandwidth HP3101 optocoupler

[36]. The gate-emitter voltage is clamped by two back-to-back zeners for protection. Short circuit

protection is also incorporated by collector voltage sensing. A fast-response diode, PFR818, is used to

sense the collector voltage. It is compared with a zener reference to generate an enabling signal for

the gate drive. This signal is brought out of the gate drive card through another HP3100 optocoupler

as a status signal. In the event of a short-circuit, the status signal goes low and, the pulses to all

devices are blanked out. The driver card also houses an SMPS to supply the un-isolated side of the

circuit. The gate drive circuit is schematically shown in Fig.3.2.


65

Fig.3.2 Schematic block diagram of IGBT gate drive circuit

Status Signal

Gate Pulse

HP3101

HP3101

Sht ckt protectionlogic

PFR 818

Buffer Driver

Collector

Gate

Emitter

SMPS

+15V+15V

(b) Current Sensor Card

Hall effect low profile current transformer Telcon HTP50 is used for current sensing [37].

Two current sensors are mounted on a single card. The sensor output is scaled by a linear amplifier to

10V. Extensive measurements are performed to evaluate the performance of the sensors. The sensor!

circuit offers very low non-linearity (maximum of 0.2%) and, high bandwidth (100 kHz).

(c) Voltage Sensor Card

A precision ac/dc voltage transducer is fabricated with a high CMR isolation amplifier

HCPL-7800 [36, 38]. The isolated output of the transducer is scaled to 10V by using a differential!

amplifier stage. The measured non-linearity of the card is within 0.5% and, -3dB bandwidth is 20

kHz.

(d) Protection and Delay Card

This card accepts the gating pulses for the top devices in each leg of the converter from the

digital controller. It then generates the complementary gating signals for the bottom devices and,

introduces the dead-time between the two. The different sensor outputs and gate drive status signals

are also routed to this board. Comparator logic is used to generate relevant protection signals like

overcurrent, overvoltage, undervoltage etc. All these signals are then AND-ed using wired logic. The

final ‘enable’ signal is used for blanking out the base drive pulses under any fault condition.


66

(e) Indicator Card

The various protection signals from the protection and delay card are routed to this board. Any

fault condition is indicated by switching on a particular LED in the front panel of the cabinet.

The feedback signals for the control of the front end converter consist of the ac side currents,

ac side voltages, the dc side load current and, the dc bus voltage. Apart from the ac side voltage

transducers, all the other sensors are integrated within the front end converter cabinet. In the case of

machine side converter, the rotor current sensors and the dc bus voltage transducer are integrated

within the rotor side converter cabinet. However, the stator side voltages and currents also need to be

measured. The ac side voltage for the front end converter differs from the stator voltage by the

transformer turns ratio. In practice, a suitable tapping from the input transformer is used for

measuring the ac side voltage. The stator voltage is then derived by scaling this signal appropriately

within the software.

The rotor side converter and the front end converter operate from 300V dc bus. This allows a

maximum rotor induced voltage of i.e. 106V for . The maximum allowableudc

2ª2mmax mmax = 0.85

slip is therefore, 0.375 p.u. To ensure that the rotor circuit is open when the slip exceeds this limit, a

contactor is introduced between the converter and the rotor terminals. This contactor opens the rotor

circuit if the slip exceeds this limit or, the dc bus voltage exceeds 325V.

3.3 DSP Based Control Hardware

In the implementation of the present scheme, it was felt that a single processor would be

convenient to execute the control algorithms for the front end as well as the machine side converter.

Several control loops, therefore, need to be executed in real-time at a high sampling rate. This has

prompted the use of computationally powerful digital signal processor (DSP) for the present

application.

The current trend of DSP manufacturers is to incorporate application-specific peripheral

hardware along with the processor in the same silicon package. This simplifies the design, minimizes

chip count and, reduces the hardware cost. The TMS320F240 DSP from Texas Instruments has the

architectural features necessary for digital control functions and, the peripherals needed to provide a

single-chip solution for motor control applications. The present digital control hardware is built

around the 'F240 processor. The software implementation is closely linked to the processor


67

architecture. In this section, a brief overview of the 'F240 DSP and the digital control board is first

presented, so as to make the implementation details more clear later.

3.3.1 TMS320F240 - A Brief Overview

The TMS320F240 is a 16-bit, fixed point DSP which can execute 20 million instructions per

second (MIPS) [39, 40]. The core CPU consists of a 32-bit central arithmetic logic unit (CALU), a

32-bit accumulator and a 16-bit X 16-bit parallel multiplier with 32-bit product capability. Apart from

these, there are eight 16-bit auxiliary registers with a dedicated arithmetic unit for indirect addressing

of data memory.

The internal memory consists of 544 words X 16-bit dual-access RAM which can be used as

data or program memory. In order to function as a stand-alone controller, 16K X 16-bits of flash

EEPROM is provided on-chip. Hence, at power-on, the processor can boot from the internal ROM.

This internal memory is sufficient for most digital motor control applications. However, external

memory modules can be interfaced and appropriately mapped in the 224K words of addressable

memory space.

The TMS320F240 houses several advanced peripherals, optimized for motor control

applications. The most important peripheral is the event manager (EV) module, which provides

general-purpose timers and compare registers to generate up to 12 PWM outputs. Efficient usage of

the EV timers reduces software overhead for PWM generation drastically. The EV incorporates a

quadrature encoder pulse (QEP) circuit which can be interfaced directly to an incremental position

encoder. The peripherals also include a dual, 10-bit analog-to-digital converter (ADC), which can

perform two simultaneous conversions within 7µs; an internal PLL clock module; a serial

communication interface; and a serial peripheral interface.

3.3.2 TMS320F240 Based Digital Control Platform

A generalized digital control platform has been designed using TMS320F240. It comprises

four hardware modules; (i) an analog signal conditioning board, (ii) a DSP board, (iii) a position

encoder interface and (iv) a power converter interface. All these modules are developed in-house and

the integrated platform is being used for different motor control applications.

The schematic block diagram of the control hardware is given in Fig.3.3.


68

Fig.

3.3

Org

aniz

atio

n of

the

digi

tal c

ontr

ol h

ardw

are

R-C

Filte

rPA

L Pow

er-o

nre

set

4 M

Hz

Buf

fer

Buf

fer

Buf

fer

Buf

fer

TM

S320

F240

JTA

G32

K S

RA

M

Qua

d

DA

C

Scal

ing

and

Shif

ting

Cir

cuit

FEC

Ana

log

Sign

als

Rot

or s

ide

Ana

log

Sign

als

Stat

or s

ide

Ana

log

Sign

als

Dig

ital I

/O

FEC

PWM

Rot

orsi

dePW

M

Enc

oder

Puls

es

XD

S510

Sign

alM

onito

ring

Scal

ed

Ana

log

Sign

als


69

(a) Analog Signal Conditioning Board

The internal ADCs of the 'F240 are unipolar and operate between 0 to 5V. Since the sensor

outputs (from the power circuit) are in the range of 10V, these signals need to be properly scaled!

before feeding them to the ADCs. This scaling is done in the analog signal-conditioning board. First,

the 10V signals are scaled down to 2.5V; then they are shifted by adding a reference voltage of! !

+2.5V. Finally, the signals are clamped between 0 and 5V with appropriate zeners for protection of

the ADCs. A total of 10 analog channels can be handled by the signal conditioning board.

(b) Processor Board

The sensor outputs, appropriately scaled, are routed to the ADC inputs of the DSP in the

processor board. First order R-C filters are provided for the purpose of noise elimination and

anti-aliasing. For signal monitoring and debugging, a quad-channel 12-bit digital-to-analog converter

(DAC) DAC4815 [41] is used. DAC4815 is bilpolar and operates between 10V. The variables of!

interest are properly scaled and output through the DAC.

The PWM outputs and other digital I/Os from the 'F240 are buffered using 74ALS245. The

PWM signals are routed to the inverter interface board. The QEP signals, after similar buffereing, are

terminated on a connector, which interfaces to the external circuit associated with the incremental

position encoder.

The board has a total of 64K words of external, on-board memory. The memory is partitioned

in the following manner: 32K words of EEPROM as external program memory and 32 K words of

SRAM as external data memory. Since this digital hardware platform is targeted towards system

development, provision of onboard RAM makes it convenient to modify the software and directly

download on to the external memory. If the internal flash EEPROM is used the memory needs to be

erased and burnt every time the software is modified; this is extremely inconvenient and

time-consuming. However, the external memory needs to be fast so that the number of wait-states

introduced can be reduced. In the design, 15 ns CY7C199 SRAM from Cypress [42] is used; hence

additional wait-states need not be introduced. The use of high speed external memory, of course,

necessitates the printed circuit board (PCB) to be mutilayered. (The present board is 4-layered; the

two internal layers being the power plane and the ground.)


70

A 4 MHz reference crystal is used externally, which in conjunction with the on-chip oscillator

circuit generates the input clock to the internal PLL module. The PLL can be programmed to generate

the required CPU clock.

A power-on reset circuit is also included to drive the DSP into a pre-defined state after the

power supply is switched on. Apart from the 5V supply required for the processor and buffers, the

onboard DAC operates from 15V. A power supply unit of appropriate rating is designed for the!

processor board, analog signal conditioning board and, the incremental encoder circuit.

The processor communicates with the PC through an emulator (XDS510). The emulator card

is seated on the PC mother board and connects to the DSP hardware via the JTAG port.

(c) Power Converter Interface

The interface board provides a single-point connection between each converter unit and the

digital control platform. The power circuit and the DSP hardware communicate through an FRC

cable, which carries the PWM signals generated by the DSP and the analog feedback signals from the

converter. There is also provision for transmitting the PWM signals through optical fiber links;

however, in the present work this is not used.

(d) Position encoder interface

For determining the rotor position with respect to the stator, an incremental position encoder

is mounted on the machine shaft. An encoder having 2500 pulses/rev from Stegmann is used. The

encoder generates two trains of pulses through its two quadrature pulse channels and an index pulse

through the third channel. It is mounted in such a way that, when the rotor a-phase coil axis coincides

with the stator a-phase coil axis, the index pulse is generated. The test procedure for determining the

coil axes and, accordingly, orienting the encoder is given in Appendix B.

The quadrature encoder pulses and the index pulse have to be routed to the encoder interface

connector in the processor board. However, it is observed that due to long length of the cable, the

signals are prone to pick-up noises. Hence, at the encoder end, these signals are fed to 75172 current

drivers [43]. The corresponding receivers 75173 [43] are physically located close to the processor

board. These receivers convert the current signals into TTL voltage levels which can be directly

interfaced to QEP channels of the 'F240.


71

3.4 Software Organization

The requirement for fast real-time control demands that the software has to be efficient in

terms of execution time. This has prompted the use of Assembly Language for programming the DSP.

The power of a DSP mainly lies in single-cycle execution of most instructions (even if they involve

several mathematical steps e.g. multiply, accumulate, data move (MACD)). Hence, very compact and

efficient Assembly Language code can be written. However, compact codes tend to be cryptic in

nature and, hence, difficult to be debugged and modified. Moreover, in the present scheme, the

software has to execute several control loops, axis transformations, and management of the different

internal peripherals. A modular approach is, therefore, necessary to organize the software.

All the functions that the processor needs to execute are first broadly grouped into different

tasks. Each task comprises several subroutines. The tasks are arranged in an appropriate sequence in

time, so that the required bandwidths of the different control loops can be achieved. This is done by a

task scheduler, as described in the following subsection.

3.4.1 Task Scheduling

Fig.3.4 Organization of the different software tasks

TransfRotor Side

Rotor CC,

Volt LoopTurbine

SimulationFEC

Curr LoopFEC

Curr LoopFEC

Curr Loop

56.8 µs340.8

FECCurr Loop

µs

Timer Interrupt

The execution of the different tasks are driven by a timer interrupt. A general purpose timer of

the 'F240 (Timer1) is initialized to generate an interrupt at every 56.8µs (2048 X 27.7ns) (The 'F240

PLL is set to produce a CPU clock of 36 MHz, corresponding to a time period of 27.7 ns.) Each

individual task gets executed in this time slot of 56.8µs. To complete all the tasks, six time slots are

required, corresponding to a time period of 340.8µs.

The FEC current control is executed in every alternate time slot. Therefore, the sampling rate

of the FEC current loop is 56.8 X 2µs i.e. 113.6µs. The rotor side current control and FEC voltage

control are executed once in 340.8µs. The manner in which the tasks are actually organized in the

different time slots are shown in Fig.3.4. The task scheduler keeps track of the present task that is


72

being executed and switches to the subsequent one at the next Timer1 interrupt. This is implemented

by using a software counter.

3.4.2 Program Flow

A main software module controls the flow of the program. The processor and the internal

peripherals are first initialized before the task scheduler is called into operation. The initialization

process is divided into several subroutines. These routines are listed below along with their functions.

Subroutine INITIALIZE:

Initialize internal PLL to set the CPU clock to 36 MHz.

Initialize general purpose timer Timer2 in directional up-down count mode (QEP

circuit)

Initialize general purpose timer Timer3 in up count mode (tracking line frequency

for FEC control)

Configure PWM and I/O ports

Initialize internal ADC module

Subroutine READ_OFFSET:

Read all ADC channels with zero inputs

Subroutine INIT_PWM:

Initialize general purpose timer Timer1 in up-down count mode

(generation of sampling frequency interrupt at every 56.8µs and, generation of

carrier for sine-triangle comparison at 4.4 kHz (4 X 56.8µs) )

Subroutine INIT_INT:

Initialize interrupt due to Timer1 (sampling frequency generation)

After the initialization process is over, the program goes into an idle loop waiting for the first

interrupt to occur. The first interrupt triggers the program to the task scheduler, from where it

branches off to TASK1. After completion of TASK1 (which takes around 50µs), the wait loop is

again invoked. The subsequent interrupt again passes on the control to the task scheduler. In this

manner, the execution of the different tasks are carried out in a loop.


73

3.4.3 Description of Tasks

It is observed from Fig.3.4 that TASK1, TASK3 and TASK5 are the same, namely execution

of the FEC current control. The transformations needed for rotor side current control are performed in

TASK2 and, the current control loop along with the FEC voltage control are executed in TASK4.

TASK6 executes the simulation of the turbine characteristics, which is discussed in a later chapter. In

this subsection, a brief description of the routines included in these tasks (except TASK6) is

furnished.

(a) TASK1, TASK3, TASK5

Subroutine SOC_Uac :

Start of Conversion for ADC channels connected to the .uac1, uac2

Subroutine READ_Uac:

Read ADC FIFO to get , adjust for channel offset and, scale data. uac1, uac2

Subroutine SOC_Ife:

Start of Conversion for ADC channels connected to the .ife1, ife2

Subroutine GET_UVECT:

Generates and unit vectors synchronized to the line voltage waveform. (Theuacq sin h, cos h

analog-to-digital conversion takes about 7µs on the 'F240. Hence, wherever possible, this conversion

time is spent in executing other routines.)

Subroutine READ_Ife:

Read ADC FIFO to get , adjust for channel offset and, and scale data.ife1, ife2

Subroutine GET_Ifed_Ifeq:

Compute .ife3

Compute (3 phase to 2 phase transformation)ifea, ifeb

Compute (Stationary to synchronous reference frame transformation using ifed, ifeq

)sin h, cos h

Subroutine CURRENT_LOOP:

Execute FEC current control loop (using PI control) and generate . ufed& , ufeq

&


74

Subroutine GET_Uref:

Compute ( Synchronous to stationary reference frame transformation using ufea& , ufeb

&

)sin h, cos h

Compute ( 2 phase to 3 phase transformation)ufe1& , ufe2

& , ufe3&

Subroutine UPDATE_PWM_FE:

Update compare registers (of Full Compare Units) for PWM signal generation for FEC.

(b) TASK2

Subroutine SOC_Is:

Start of Conversion for ADC channels connected to the .is1, is2

Subroutine GET_POS:

Read internal timer associated with QEP circuit (Timer2).

Scale timer value to get .e

Get .sin e, cos e

Compute rotor speed.

Subroutine READ_Is:

Read ADC FIFO to get , adjust for channel offset and, and scale data.is1, is2

Subroutine SOC_Ir:

Start of Conversion for ADC channels connected to the .ir1, ir2

Subroutine READ_Ir:

Read ADC FIFO to get , adjust for channel offset and, and scale data.ir1, ir2

Subroutine GET_Ims:

Compute .is3

Compute (3 phase to 2 phase transformation)isa, isb

Compute .ir3

Compute (3 phase to 2 phase transformation)ira, irb

Compute (Rotor to stator reference frame transformation using )ira, irb sin e, cos e

Compute imsa, imsb

Compute ims2

Compute (using stored square root table)ims


75

Compute sin l, cos l

Subroutine FLD_ORIENT:

Compute (Stationary to stator flux reference frame transformation using ird, irq

)sin l, cos l

(c) TASK4

Subroutine SOC_UIdc:

Start of Conversion for ADC channels connected to the .udc, il

Subroutine GET_FF_TERMS:

Compute feed-forward terms for rotor side control.

Subroutine ROT_CURR_CONTRL:

Execute rotor side current control loop (using PI control) and generate .urd& , urq

&

Subroutine GET_Uref_R:

Compute ( Stator flux to stationary reference frame transformation using ura& , urb

&

)sin l, cos l

Compute ( Stationary reference frame to rotor reference frame transformation using ura& , urb

&

)sin e, cos e

Compute ( 2 phase to 3 phase transformation)ur1& , ur2

& , ur3&

Subroutine UPDATE_PWM_RE:

Update compare registers (of Simple Compare Units) for PWM signal generation for rotor

side control.

Subroutine READ_UIdc:

Read ADC FIFO to get , adjust for channel offset and, and scale data.udc, il

Subroutine VOLT_LOOP:

Execute FEC voltage control loop (using PI control) and generate .ifeq&

The subroutines of related functionalities are included in the same file so that they can share

the common variables locally. However, there are a few variables which need to be accessed by a

large number of routines. These are defined globally in one place and referenced in the other files. All

these files are assembled and linked together to form the executable file (.out file), which can be


76

directly downloaded into the internal and external RAMs in the processor board. The memory

allocation and mapping are defined in a command file (.cmd file) and are done through the linker.

The implementation of the routines is a matter of coding detail and is not presented in the

thesis. However, the generation of the unit vectors for the FEC and, for the rotor shaft position is

slightly involved. The algorithm for these routines are briefly explained in the following subsections.

3.4.5 Generation of Unit Vectors Synchronized to the Supply Voltage

<θ

GP Timer3

PositiveZCD

CountRegister

Reset

Read Count

+

Ts / TCLK

CountValue

No. ofSamples

360 ) +

+

+

<θ

θ[k-1]θ[k] Look-up

Table

sin θ[k]

cosθ[k]

CLK

us1

Fig.3.5 Algorithm for generation of unit vectors synchronized to the grid

In order to generate the unit vectors synchronized to the grid voltage, the 'F240sin h, cos h

general purpose timer (Timer3) is made use of. The CPU clock, suitably prescaled, acts as the clock

to the timer and, it is programmed in continuous up-count mode. At every positive zero crossing of

, the timer value is read off and the timer is reset to zero. This count is, therefore, proportional touac1

the time period of the supply voltage for the previous cycle and, is used to compute the increment in h

i.e. at every sampling instant over the present cycle. With this estimated value of the unit vectorsDh h

are then read off from a sine lookup table in the memory. This is schematically shown in Fig.3.5. To

take an example, it may be assumed that the grid frequency was exactly 50 Hz in the previous cycle.

Therefore, number of samples taken for the present cycle is 177 with a sampling period of 57µs. This

means that at the 177th sample, the pointer points to the extreme end of the lookup table. If the grid

frequency slightly reduces, the duration of the present cycle will be more than 20 ms. Therefore, in

the subsequent sampling interval the value of calculated would be more than 3600 and the pointerh


77

would try to access a location beyond the table. This is not allowed. The value of is checked ath

every sampling interval and, when it exceeds 3600, is forced to zero and is forced to -1. Ifcos h sin h

on the other hand, the frequency increases over the present cycle, the zero crossing detection will

occur before the pointer goes to the end of the table. In that case, there will be a small discontinuity in

the unit vectors at positive zero crossing. Since the variation of the grid frequency is extremely slow,

the number of samples gained or lost in every cycle is observed to be not more than 1 or 2. Hence, the

error in the unit vectors near the positive zero crossing is negligible and, proper interlocking of the

unit vectors with the supply voltage is ensured. It may be noted that if the unit vectors are derived

directly from the phase voltages, the presence of harmonics results in their distortion in turn leading

to distortion of the line current waveforms. The line voltage and are shown in Fig.3.6.uac1 cos h

Fig.3.6 Experimental results showing and uac1 cos h

3.4.6 Generation of Unit Vectors from Incremental Position Encoder

Pulses

The pulses from the incremental encoder act as the inputs to the QEP module of the 'F240.

Once initialized, the QEP circuit detects the rising and falling edges of the inputs and generates a train

of pulses whose frequency is four times the frequency of the individual QEP channels. The pulse train

is internally routed to the clock input of the general purpose timer Timer2, which is set in the

directional up-down count mode. This implies that if the pulse train in QEP channel 1 leads that of

QEP channel 2, the timer will operate in up-count mode; if channel 2 lags channel 1, it will operate in

down-count mode. If the timer is reset at the point when the rotor and stator axes coincide i.e. when


78

the index pulse is generated, then the timer count value is proportional to the rotor shaft position at

any instant of time. However, this is implemented in a slightly different manner.

Fig.3.7 Resetting logic of the timer in QEP circuit

Timer2count

T1

T2-T1

T2

Index Pulse

Sampling interupt

Stored inCAPFIFO3

The index pulse from the encoder is connected to the capture input of the QEP module. The

capture unit is also associated with Timer2. When a signal undergoes a desired transition at the

capture input, the count value of Timer2 gets stored in a FIFO register (CAP3FIFO). This is

illustrated in Fig.3.7. As shown in this diagram, CAPFIFO3 now contains the value T1. In the

software, this event is signaled by setting a corresponding interrupt flag (EVIFRC), though the actual

interrupt is disabled. At the subsequent sampling interrupt, the setting of EVIFRC is detected and the

Timer2 counter is reset to the value (T2 - T1). The capture module is also reset simultaneously. This

ensures that when the position information is read, the Timer2 count is always proportional to .e

Subsequently, the timer value is appropriately scaled and, the unit vectors are read off fromsin e, cos e

the sine lookup table in the memory. In Fig.3.8, the rotor position and the unit vectors are given.e


79

Fig.3.8 Experimental results showing and e sin e

3.4.7 Scaling and Signal Monitoring through DAC

While implementing an involved control scheme it is important that easy access to

intermediate computed variables is available. The DAC provided in the DSP hardware is utilized for

this purpose. In this thesis, all the experimental results that are presented, are DAC outputs captured

on a HP5601 digital storage oscilloscope.

The entire computation within the processor is done on a per unit scale. The base values for

the various quantities are given in Appendix B. For a 16-bit processor the (signed) maximum and

minimum numbers vary from 7FFFh to 8000h. This is taken as +2 p.u. to -2 p.u. Therefore, +1 p.u. is

represented by 3FFFh, and -1 p.u. by 4000h.

For outputting the different variables through the DAC (which is 12-bit), appropriate scaling

of the variables is, therefore, necessary. In practice, the scaling is done in such a way that +10V

presents 2 p.u. scale. (Hence, most variables appear to be within +5V).

3.5 Experimental Results

The experimental results for the transient and steady-state operation of the rotor side and front

end converter are presented in this section. Appendix C lists the details of the controller parameters

that are used in the implementation as well as in the simulation. The machine rating and hardware

details are available in Appendix B.


80

3.5.1 Rotor Side Control

The step response of from 0 to 0.5 p.u. with held constant at 0.75 p.u. is shown inirq ird

Fig.3.9(a). The designed active current loop time-constant is 1 ms. The corresponding stator current

and, the rotor current in the stator reference frame , are given in Fig.3.9(b) and Fig.3.9(c)is sir

respectively. It is observed that when is zero, the stator current is close to zero and, the rotorirq

supplies the reactive power for the machine. With the application of positive , the stator instantlyirq

goes into generating mode (negative ) at almost unity power factor. The rotor current increases inisq

magnitude as it now handles both the active and the reactive powers.

The dynamics of the reactive current loop is made slightly slower than the active loop. The

reactive current reference is normally keep constant and is not decided by any outer loop. So, the

reactive loop is mostly regulatory in nature and need not be as fast as the active loop. In Fig.3.10(a)

the response of , when a step change in is given from 0 to 0.75 p.u, is presented. The activeird ird&

current reference is kept at zero. Fig.3.10(b) and Fig.3.10(c) show that the stator initially suppliesirq&

only the reactive power of the machine, and the rotor current is zero. With the application of theird

reactive power is transferred to the rotor circuit and, the stator current falls close to zero.

The transient responses of these current loops obtained through simulation are also presented

in Fig.3.11(a) and Fig.3.11(b). It is observed that the simulation and experimental results are in good

agreement thereby validating the machine modeling and design of the controller.

The relationship between the stator and rotor currents in the d-axis and q-axis is shown clearly

in Fig.3.12(a) and Fig.3.12(b). Along the q-axis, and are proportional to each other differingirq isq

by a factor , but of opposite polarity. However, along the d-axis, when is zero, equals (1 + rs ) ird isd

. With the application of , the reactive power is transferred to the rotor circuit and, ims/(1 + rs) ird isd

falls down to zero. The steady-state relation between and is shown in Fig.3.12(c). It isusa imsa

obvious that lags the supply voltage component by 900. The steady-state value of is alsoimsa ims

shown in the same plot.

The stator and rotor currents in their own reference frames, for subsynchronous and

synchronous operations are shown in Fig.3.13(a) and Fig.3.13(b). The rotor current under

synchronous condition is dc and, the operation is observed to be perfectly stable. The ride through

synchronous speed is illustrated in Fig.3.13(c). The rotor current waveform passes through zero

frequency from one phase sequence to the other.


81

(a) Channel 1- channel 2-ird, irq

(b) Channel 1- channel 2- , channel 3-us, is irq&

(c) Channel 1- channel 2- , channel 3-us, sir irq&

Fig.3.9. Experimental results showing the transient response of the q-axis current control loop. A

step in is given from 0 to 0.5 p.u. and is maintained at 0.75 p.u.irq& ird

&


82

(a) Channel 1- channel 2-ird, irq

(b) Channel 1- channel 2- , channel 3-us, is ird&

(c) Channel 1- channel 2- , channel 3-us, sir ird&

Fig.3.10. Experimental results showing the transient response of the d-axis current control loop. A

step in is given from 0 to 0.75 p.u. and is maintained at zero.ird& irq

&


83

Fig.3.11(a) Simulated response of and for step change of from 0 to 0.5 p.u. with held ird irq irq& ird

&

constant at 0.75 p.u.

Fig.3.11(b) Simulated response of and for step change of from 0 to 0.75 p.u. with ird irq ird& irq

&

held constant at zero.


84

Fig.3.12(a) Experimental results showing relationship between irq, isq

Fig.3.12(b) Experimental results showing relationship between ird, isd

Fig.3.12(c) Experimental results showing relationship between usa, imsa


85

Fig.3.13(a) Experimental results showing steady-state waveforms for at irq& = 0.75, ird

& = 0.5

1275 rpm (subsynchronous operation)

Fig.3.13(b) Experimental results showing steady-state waveforms for irq& = 0.75, ird

& = 0.5

at 1435 rpm (synchronous operation)

Fig.3.13(c) Experimental results showing transition through synchronous speed.


86

3.5.2 Front end Converter Control

In order to evaluate the dynamics of the front end converter without the influence of the rotor

side control loops, it is tested with step loads for positive power and negative power flow. The

experimental test setup is shown in Fig.3.14. For power flow from the grid to the dc load, S1 is closed

and S2 is kept open. To test the regenerative mode of operation, S2 is also closed. The criterion for

negative power flow can be easily derived as

. (3.1)udiode−udc

Rse> udc

R l

R l

R se

udiode

S2

S1

udc

Front end

Converter

DiodeBridge

Rectifier

udc = 300V udiode = 360V

Rl = 66W Rse = 9W

Fig.3.14 Experimental setup for testing the front end converter

The steady-state ac side voltage and current waveforms for forward power flow is given in

Fig.3.15(a). The same plots for regenerative mode of operation are given in Fig.3.15(b). In both these

cases, is kept at zero to demonstrate unity power factor operation. Leading power factorifed&

operation with kept at 0.25 p.u. is shown in Fig.3.15(c). The current waveforms are observed toifed&

be smooth without any perceptible ripple. This is because of the high value of the series inductors

(0.66 p.u.) used in the experiment.

The transient response of the dc bus voltage due to application of positive and negative loads

is shown in Fig.3.16(a) and Fig.3.16(b) respectively. The designed voltage loop response of 100 ms is

reflected in the observed waveforms. In Fig.3.16(c), the input side current waveform is shown due to

reversal of dc load. Since, is zero, and goes from positive to negative through zero, the acifed ifeq

side current also has to go down to zero before changing its phase.


87

(a) Forward power flow at unity power factor (S1 on and S2 off)

(b) Reverse power flow at unity power factor (S1 on and S2 on)

(c) Forward power flow at leading power factor (S1 on, S2 off and p.u.)ifed& = 0.25

Fig.3.15 Experimental results showing steady-state waveforms uac1, ife1


88

(a) Sudden application of forward load (instant of closing S1 with S2 off)

(b) Sudden reversal of load (instant of closing S2 with S1 on)

(b) Sudden reversal of load (instant of closing S2 with S1 on)

Fig.3.16 Experimental results showing dc bus voltage and currents during transient loading


89

Fig.3.17 Simulated transient response of and for sudden application of positive loadudc ifeq

The simulation plots of dc bus voltage and active current transients due to similar positive

loading are given in Fig.3.17 respectively. The experimental and simulation results show close

resemblance establishing the validity of the system modeling and design of the controllers.

3.6 Conclusion

A power hardware platform for implementing the rotor side control strategies has been built.

The hardware is designed in a modular fashion and has been standardized in the laboratory for

general motor control applications. A TMS320F240 DSP based digital control board is also designed

and developed. This platform is powerful enough to execute all the control loops associated with

rotor side control and front end converter control. Conventional field oriented control using shaft

position sensor and front end converter control is first implemented. Experimental results presented in

this chapter show decoupled response for the active and reactive current loops. They are also in close

agreement with the simulated waveforms. Several control algorithms are developed subsequently and

are presented in the following chapters. All these algorithms are implemented using the same

hardware setup.


90

Chapter 4

ROTOR SIDE FIELD ORIENTED CONTROL WITHOUT

POSITION SENSORS

4.1 Introduction

For field oriented control of ac machines the position of the rotor with respect to the stator is

necessary. This information is usually derived by mounting a suitable position encoder on the shaft of

the machine. The performance of a vector controlled drive depends on the accuracy of the position

information and hence on the accuracy and resolution of the position encoder. The use of a position

encoder (incremental/ absolute/ resolver) introduces additional interfacing hardware between the

instrument and the controller. These factors while adding to the cost simultaneously reduce the

reliability of the drive.

In doubly-fed induction machines, it is moreover necessary to mount the encoder in a specific

orientation with respect to the stator. The preferred orientation would be such that an index pulse is

generated when the rotor and stator 'a' phase coil axes coincide. This would ensure that the rotor

position is directly derived by counting the quadrature encoder pulses (discussed in Chapter 3).e

Hence, apart from the higher component cost, the cost of having precise mounting arrangement also

needs to be considered. Quite naturally a major challenge to researchers in this area has been to

eliminate the use of this encoder and, yet obtain similar dynamic performance.

91

Position sensorless control of ac machines have attracted a lot of attention in recent times [13,

33, 34]. However, the major focus of activity has been restricted to cage rotor induction machines and

permanent magnet synchronous machines due to their higher usage in industrial vector controlled

drives. Doubly-fed wound rotor induction machines being mostly used in conventional slip-power

recovery schemes, fast dynamic response is not so far required. Currently, the requirement for VSCF

operation in applications like wind power generation has led to the use of field oriented control of

such machines to independently control the active and reactive powers (discussed in earlier chapters).

Hence, the rotor position information needs to be acquired. In wind power generation, there is a large

physical separation between the generator (which is coupled to the turbine shaft through gears) and

the power electronic equipment (which is at ground level). It is, therefore, desirable that there is

minimum interface between the two and, for higher reliability, a control scheme without shaft

position sensors.

There are two major challenges in designing a position sensorless scheme for a doubly-fed

wound rotor induction machine. The foremost requirement is that the algorithm should work stably at

or near synchronous speed. The synchronous speed operation corresponds to zero rotor frequency;

hence this is analogous to zero speed operation in case of cage rotor induction machine. The second

criterion is that the algorithm should be able to start on the fly. It is understood that the rotor side

control strategy operates over a restricted speed range. The rotor circuit is closed and the control is

initiated when the speed rises above a minimum threshold. Hence, the position estimation algorithm

should start while the rotor is already in motion, without the knowledge of any initial condition.

The literature available on sensorless control of doubly-fed wound rotor induction machines is

rather sparse and algorithms proposed do not address the aforementioned requirements

simultaneously. A position sensorless algorithm, capable of starting on the fly and stable operation at

or near synchronous speed has been developed and presented in this chapter.

4.2 Review of Existing Schemes

It is well-known that most of the sensorless strategies for cage rotor induction motors use

stator voltage integration to compute the stator flux. This approach gives rise to usual low-frequency

integration problems due to offset and saturation. Performance of sensorless schemes at very low

frequency or at zero speed is therefore not satisfactory. In case of cage rotor induction machine, the

Chapter 4 Rotor Side Control Without Position Sensors

92

only variables that one can access are the stator currents and voltages whereas, in case of doubly-fed

wound rotor induction machine, the rotor currents can also be measured directly. Thus precise

information about another state variable is available. However, most of the earlier publications tend

to overlook this fact and, relatively complicated schemes based on angle controllers have been

proposed.

In [17], the desired angle of the rotor current in the rotor reference frame is computed from the

active and reactive powers in the stator circuit. The actual angle of the rotor current vector in the

stator reference frame is simultaneously computed. These two variables are fed to an angle controller

which generates the rotor frequency. The actual rotor currents are subsequently used for current

control. The details of the angle controller and the rotor current control method are not presented in

[17]; hence it becomes difficult to access the dynamic behavior of such an angle control method.

The method proposed in [18], on the other hand, uses the rotor voltages and currents to design

a torque angle controller. The torque of the induction machine can be expressed as a cross-product of

the rotor flux and rotor current vectors. From the measured rotor currents and voltages, the rotor flux

is first computed by integrating the PWM rotor voltage. Subsequently, the angle between the rotor

flux vector and rotor current vector ( ) is estimated. The reference angle is set by the torqued d&

demand decided by an outer speed control loop. The error between the reference and estimated torque

angles drives a voltage controlled oscillator (VCO) to generate the slip frequency. The VCOd& − d

output is simultaneously integrated to generate an angle ; this is used for transformation of the rotorhs

currents to the synchronous reference frame. Finally, the rotor current controller is designed in the

synchronous reference frame. The major drawback of this scheme is the method employed for

computation of rotor flux. The integration of rotor voltage at or near synchronous speed, is analogous

to the integration of the stator voltage at or near zero speed in case of a cage rotor induction machine.

Hence, similar problems of integrator saturation resulting in incorrect estimation of the rotor flux is

inevitable. Use of this algorithm has to be restricted upto a certain minimum slip and operation

through synchronous speed is not possible.

The scheme proposed in [19] is by far the most comprehensive one available in the literature.

The system developed (ROTODRIVE) is a commercial product aimed at the variable speed high

power drive market (>300 kW). The objective is mainly to provide a wide speed range with a reduced

size of the converter. The system is started with the stator circuit shorted and the rotor being fed from


93

a PWM converter (Mode I). After the speed has reached 0.5 p.u., the stator is opened (Mode II) and,

subsequently connected to the grid (Mode III). After this, rotor side field oriented control is employed

upto a maximum speed of 1.5 p.u. With the stator flux remaining constant it is possible to maintain

rated torque capability upto this maximum speed. The sensorless method proposed for Mode III uses

coordinate transformations for estimating the rotor position. The stator voltage vector is taken as the

synchronous reference frame. The stator currents are measured and the rotor current vector in the

synchronous reference frame is estimated using the machine parameters. The rotor current vector is

directly measured in the rotor coordinates. From this information, the angle between the stator and

rotor axes is determined. This algorithm provides stable operation at or near synchronous speed and,

can be started on the fly. However, the accuracy of the estimation process depends on machine

parameters like and the supply frequency. Ls, Rs

The proposed algorithm is also based on axis transformations. However, it is more direct and

does not involve the synchronous reference frame. The dependence on machine parameters is also

largely reduced.

4.3 Proposed Algorithm for Position Sensorless Control

Fig.4.1 Location of different vectors in stationary coordinates

θ ρ1

ρ2

ε

θ- 900

Stator axis

Rotor axis

d-axis

q-axis

Stator voltage

Rotor current

Stator flux

ω ms

ω e

The proposed sensorless algorithm can be explained with the help of Fig.4.1. Here, the rotor

current vector is shown along with the stator and rotor axes. Seen from the stator coordinate system,

makes an angle . The same vector makes an angle with the rotor axis. The problem, therefore,ir q1 q2

is to compute and , so that can be determined. With the knowledge of the statorq1 q2 e = (q1 − q2)


94

flux and the stator currents, the rotor current in the stator reference frame i.e. can be computed. Insir

the rotor reference frame can be directly measured. From this information, the angle between their

two reference frames can be computed by using simple trigonometric relations.

In Fig.4.1, the stator voltage vector is also shown. Assuming that the stator resistance dropus

is negligible, the stator flux axis i.e. the d-axis is at quadrature to it. Hence, the stator flux

magnetizing current vector makes an angle ( - 900 ) with the stator axis. It is also assumed thatims h

the magnitude of vector (denoted as ) is already known. (The estimation of is presentedims ims ims

later). Therefore, the components can be written as follows. a, b

(4.1)imsa = ims $ sin h

(4.2)imsb = − ims $ cos h

Using this value of and the measured value of , the rotor currents can be computed inims is

the stationary coordinates as

(4.3)ira = imsa − (1 + rs)isa

(4.4)irb = imsb − (1 + rs)isb

(4.5)|sir | = ira2 + irb

21/2

The unit vectors for are given by sir

(4.6)cos q1 = ira / |sir |

(4.7)sin q1 = irb / |sir |

The rotor currents are directly measured in the rotor circuit and, the unit vectors for can beir

derived as

(4.8)cos q2 = ira / |ir |

(4.9)sin q2 = irb / |ir |

Equations (4.6), (4.7) and equations (4.8), (4.9) represent the unit vectors in the two reference

frames; the former rotating at synchronous speed and, the latter at slip frequency. The unit vectors

pertaining to the rotor position can be now easily computed.e = (q1 − q2)


95

(4.10)sin e = sin(q1 − q2) = sin q1 $ cos q2 − sin q2 $ cos q1

(4.11)cos e = cos(q1 − q2) = cos q1 $ cos q2 + sin q1 $ sin q2

It may be noted here that the unit vectors and corresponding to the rotor positionsin e cos e

suffice for executing the vector control algorithm. The actual angle need not be computed through

inverse functions, as in [19].

4.3.1 Computation of ims

The accuracy of this computation depends on the value of , since the other quantities areims

directly measured. The stator flux can be calculated directly by stator voltage integration so that the

variations in the grid voltage and frequency are taken into account. However, in order to estimate ,ims

the magnetizing inductance is required. If there is a substantial boost in the grid voltage or, a dipLo

in the grid frequency, is most likely to saturate. This will lead to an incorrect estimation of .Lo ims

Also, the presence of distortion components in the grid voltage normally gives rise to integration

problems. The objective is, therefore, to make the estimation process minimally dependent on any

machine parameter and if possible, avoid integration of the stator voltage.

Any change in the magnitude of the stator flux being much slower than the sampling

frequency (2.9 kHz), can be correctly estimated by adopting the following method ofims

recomputation. First, for the present sampling interval is computed by transforming the presentims

rotor current sample to the stator coordinates using the unit vectors computed in the previous interval.

This is formulated as follows.

(4.12)ira∏

[k] = ira[k] $ cos e[k − 1] − irb $ sin e[k − 1]

(4.13)irb∏

[k] = irb[k] $ cos e[k − 1] + ira $ sin e[k − 1]

(4.14)imsa∏

[k] = (1 + rs ) $ isa[k] + ira∏

[k]

(4.15)imsb∏

[k] = (1 + rs ) $ isb[k] + irb∏

[k]

(4.16)ims∏

= imsa∏ 2 + imsb

∏ 21/2

The superscript ' indicates intermediate variables used in the computation. as calculated fromims∏

Eq.(4.16) is passed through a low-pass first-order filter with a time-constant of 1 ms. This ensures


96

that even if there is any small error in the previous sample of and , it is not directly reflectedsin e cos e

in the present estimate. The estimation of is the first step in the position estimationims ims

algorithm. With this value of , the algorithm proceeds from Eq.(4.1) till Eq.(4.11).ims

4.3.2 Starting

It is understood that the algorithm has to start with a known value of in order to compute e ims

by using Eq.(4.12) through Eq.(4.16). Since the rotor side control needs to be started on the fly, it is

not possible to assign an initial value of . Instead, the algorithm starts with an initial value of ,e ims

which is the same as its nominal value given by . The position of is computed fromus/(zsLo ) ims

the stator voltage phasor as before. After a few sampling intervals, the algorithm switches over to the

recomputation method.

The estimation process thus becomes independent of variations in the stator voltage and

frequency. The only machine parameter on which the algorithm depends is the stator leakage factor

. The leakage is only a small percentage of the stator inductance and is not subjected to anyrs

saturation. Even a significant error in the value of does not introduce any appreciable error in thers

estimation of and . This is verified through extensive simulation. The instantaneous naturesin e cos e

of computation also ensures jitter-free estimation during transients in the active and reactive power.

4.3.3 Speed Estimation

The decoupling terms associated with the rotor current controller being slip dependent it is

necessary to compute the speed of the machine. Apart from regular motor drive applications the speed

information is also necessary for generation applications like wind-energy conversion systems where

the active power reference is made to vary as a function of the rotor speed to achieve maximum

power transfer. The speed can be estimated by using the following equation.

(4.17)zest = cos e $ ddt sin e − sin e $ d

dt cos e

The usual method of differentiation of rotor position would require to be computed from thee

unit vectors using inverse trigonometric functions. This is avoided in this method of speed estimation.

Moreover, the unit vectors are smoothly varying continuous functions unlike (which ise

discontinuous at ) and, are easier to differentiate without checking for discontinuity. However,e = 2o

the differential terms contribute to some noise which is eliminated by employing a first-order

low-pass filter. The position and speed estimation block diagrams are shown in Fig.4.2.


97

Fig.

4.2

Sche

mat

ic b

lock

dia

gram

of

the

posi

tion

sens

orle

ss a

lgor

ithm

X X

d/dt

- d/

dt

Σω

est

sin ε

cos ε

1/

i r__|

|i rbi ra i ra i rb

sin

ρ2

cosρ

2

u s α

u s β

Z-1

i r__|

|s

1 __Σ Σ

ε =

ρ1 −

ρ2

sin

ρ1

cos ρ

1

i sβ

(1+

σs)

-

sin

ε

cos ε

i sα

(1+

σs)

-

i ms α

i ms β

Com

pute

an

gle

of

Com

pute

mag

nitu

de

ofi s α i s β

Com

pute

i ms α

i ms β

i ms

sin θ

cos θ

i ms

i ms


98

4.4 Simulation

The simulation of the system is carried out in MATLAB-SIMULINK platform to study the

starting and, the effect of parameter variation on the proposed algorithm. The simulation block

diagram is the same as given in Chapter 2; the controller now incorporates a position estimation block

as shown in Fig.4.3. The same machine and controller parameters are selected as used in the

laboratory experimental setup [Appendix C].

The plots of estimated and actual during starting are given in Fig.4.4 through Fig.4.5. Thesin e

rotor side control is released with an active current reference of p.u. and, with differentirq& = 0.5

initial speeds. In these runs, the speed is held constant by increasing the system inertia. It is observed

that the estimated position catches up with the actual position almost instantaneously irrespective of

the initial speed.

The steady-state relations between and for p.u. and p.u. aresin q1 sin q2 z = 0.75 z = 1.0

shown in Fig.4.6(a) and Fig.4.6(b) respectively. At synchronous speed is perfectly dc, implyingsin q2

that the rotor currents in the rotor reference are also dc. This illustrates the stable steady-state

operation at synchronous speed.

4Ir2f

1Us1f

2Us2f

5Is1f

6Is2f

3Ir1f

11Isqf

10Isdf

8Usdf9

Usqf

3ph to 2ph Flux Estimator

3Imsf

Wms-WEstimator

Stator toField

Speed and Position Estimator

7Speed

1Irdf

2Irqf

Rotor toField

4Wms-W

5sin(M-E)

6cos(M-E)

Fig.4.3 SIMULINK block diagram of the position estimation module


99

0.8 0.82 0.84 0.86 0.88 0.9-1.5

-1

-0.5

0

0.5

1

1.5

secs

sinE

_est

Fig.4.4(a) Estimated sin e

0.8 0.82 0.84 0.86 0.88 0.9-1.5

-1

-0.5

0

0.5

1

1.5

secs

sinE

Fig.4.4(b) Actual sin e

Fig.4.4 Estimated and actual at starting with p.u.and p.u. The initial speed sin e irq& = 0.5 ird

& = 0.75

is set to 1 p.u. and, the inertia is made high so that the shaft speed does not change during this

transient.


100

0.4 0.42 0.44 0.46 0.48 0.5-1.5

-1

-0.5

0

0.5

1

1.5

secs

sinE

_est

Fig.4.5(a) Estimated sin e

0.4 0.42 0.44 0.46 0.48 0.5-1.5

-1

-0.5

0

0.5

1

1.5

secs

sinE

Fig.4.5(b) Measured through encodersin e

Fig.4.5 Estimated and actual at starting with p.u.and p.u. The initial speed sin e irq& = 0.5 ird

& = 0.75

is set to 1.25 p.u. and, the inertia is made high so that the shaft speed does not change during

this transient.


101

Fig.4.6(a) , at subsynchronous speedsin q1 sin q2

Fig.4.6(b) , at synchronous speedsin q1 sin q2

Fig.4.6 Steady-state waveforms of , at subsynchronous (0.75 p.u.) and synchronous sin q1 sin q2

speed (1 p.u.) for p.u.and p.u.irq& = 0.5 ird

& = 0.75


102

0.25 0.255 0.26 0.265 0.27-1.5

-1

-0.5

0

0.5

1

1.5

secs

sinE

, sin

E_e

st

Fig.4.7(a) Estimated (solid lines) and actual (dotted lines)sin e

0.31 0.315 0.32 0.325 0.33-1.5

-1

-0.5

0

0.5

1

1.5

secs

sinE

, sin

E_e

st

Fig.4.7(b) Estimated (solid lines) and actual (dotted lines)sin e

Fig.4.7 Estimated and actual when (a) value of used in computation equals 1.5 times the sin e rs

actual and, (b) value of used in computation equals 0.5 times the actual valuers


103

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.550

0.2

0.4

0.6

0.8

1

1.2

secs

W_e

st (

befo

re fi

lter)

(p.

u.)

Fig.4.8(a) Estimated speed before low-pass filter

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.550

0.2

0.4

0.6

0.8

1

1.2

secs

W_e

st (

afte

r fil

ter)

(p.

u.)

Fig.4.8(b) Estimated speed after low-pass filter

Fig.4.8 Estimated speed before and after the low-pass filter when the estimation algorithm is started

with an actual rotor speed of 1 p.u.


104

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.550.6

0.65

0.7

0.75

0.8

secs

ims

(p.u

.)

Fig.4.9(a) Actual during startingims

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.550.6

0.65

0.7

0.75

0.8

secs

ims_

est (

p.u.

)

Fig.4.9(b) Estimated during startingims

Fig.4.9 Actual and estimated during starting with p.u. and p.u.ims irq& = 0.5 ird

& = 0.75


105

Fig.4.7(a) and Fig.4.7(b) shows the effect of variation in in the estimation process. In thers

first case, used in the estimation algorithm is 1.5 times the actual value and, in the second case, itrs

is 0.5 times. The plots show almost negligible errors in the computation of the unit vectors, even at

starting.

The estimation of speed is shown in Fig.4.8. The estimated speed signals before and after the

low-pass filter are given in Fig.4.8(a) and Fig.4.8(b). The filter time constant is set to 25 ms.

In Fig.4.9(a) and Fig.4.9(b), the actual and estimated waveforms of are plotted duringims

starting with an active current reference of p.u. and initial speed of 1 p.u. The increase in irq& = 0.5

magnitude is attributed to the stator resistive drop. (It may be appreciated that for a smallims

laboratory scale machine the stator resistance drop is relatively high; however, in a practical case,

rotor side control is only employed for wound rotor machines of ratings greater than 100 kW where

the stator resistance drop can be neglected.)

4.5 Implementation and Experimental Results

The position sensorless algorithm is implemented on the same hardware setup as discussed in

Chapter 3. The same software organization is retained; only a subroutine POS_EST is introduced.

The position estimation algorithm is implemented in this routine. The controller details associated

with the sensorless implementation of field-oriented control also remain the same as given in

Appendix C.

The steady-state relations between , and, are given in Fig.4.10. It is observedsin q1 sin q2 sin e

from these plots that the frequency of is the difference of the frequencies of and .sin e sin q1 sin q2

A comparison between the unit vector generated using an incremental position encodersin e

with computed employing the proposed sensorless algorithm is given in Fig.4.10. The plotssin e

given in Fig.4.11(a) and Fig.4.11(b) correspond to synchronous and, supersynchronous modes of

operation. The instantaneous tracking of the position (when the rotor side control is activated) and

accurate steady-state operation are observed.

In Fig.4.12, the impact of sudden active load on the estimation algorithm is shown. A step

change of from 0 to 0.5 p.u. does not produce any transient in the estimation of .irq& sin e


106

Fig.4.10 Experimental waveforms showing , and for rpmsin q1 sin q2 sin e z = 1190

Fig.4.11(a) Experimental waveforms showing estimated and actual at starting for rpmsin e z = 1460

Fig.4.11(b) Experimental waveforms showing estimated and actual at starting for rpm sin e z = 1600


107

Fig.4.12 Experimental waveforms showing estimated and actual for step in from 0 to 0.5 p.usin e irq&

Fig.4.13(a) Experimental waveforms showing estimated and actual at starting before filteringz

Fig.4.13(a) Experimental waveforms showing estimated and actual at starting after filteringz


108

Fig.4.14(a) Experimental results showing step in from 0 to 0.5 p.u. with = 0.75 p.u.irq& irq

&

Fig.4.14(b) Experimental results showing step in 0 to 0.75 p.u. and = 0ird& irq

&

Fig.4.15 Experimental results showing steady-state before and after filteringims


109

Fig.4.16(a) Experimental results showing steady-state with p.u. and us1, is1, ir1 ird& = 0.75

p.u. at 1620 rpm (supersynchronous operation)irq& = 0.5

Fig.4.16(b) Experimental results showing steady-state with p.u. and us1, is1, ir1 ird& = 0.75

p.u. at 1428 rpm (synchronous operation)irq& = 0.5

Fig.4.17 Experimental results showing during transition through synchronous speedir1, z


110

The estimated speed signals (from and before and after filtering are shown insin e cos e)

Fig.4.13(a) and Fig.4.13(b). During the initial period there is a large error in the estimated speed due

to the filter time-constant. If this incorrect value of estimated speed is used to determine the

slip-dependent cross-coupling terms in the rotor current control, it will give rise to undesired

transients and, in turn, erroneous estimation. In practice, the estimated position would not be able to

catch up with the actual position. Hence, during starting the computed slip is forced to zero for about

100 ms; after this the estimated speed signal is used to calculate the slip.

The transient response of the q-axis and d-axis rotor current loops are shown in Fig.4.14(a)

and Fig.4.14(b) respectively. The responses are observed to be identical to those shown in Chapter 3,

thereby establishing the fact that, with the position estimation algorithm the same dynamic

performance can be achieved. In Fig.4.14(b), the response is taken during switching on of the rotor

converter; hence a small transient is observed in the rotor currents (before the estimated position

catches up with the actual one).

Fig.4.15 shows the estimated before and after the low-pass filter. ims

In Fig.4.16(a) and Fig.4.16(b), the steady-state stator and rotor currents in their own reference

frames are shown along with the stator voltage waveform for supersynchronous and synchronous

modes of operation. The reactive power is supplied from the rotor side; hence the stator power factor

is unity. In Fig.4.16(b), the rotor currents are dc showing that the estimation algorithm operates stably

at zero rotor frequency. The transition through synchronous speed is also observed to be smooth, as is

illustrated in Fig.4.17.

4.6 Conclusion

Position sensorless control of wound rotor induction machine is a desirable feature of VSCF

generation systems like wind power generation. The proposed position sensorless algorithm meets the

requirements for such applications. The algorithm can be started on the fly without the knowledge of

the initial rotor position. Operation at synchronous speed, corresponding to zero rotor frequency, is

stable; also it can ride through synchronous speed smoothly. The proposed method of computation of

stator flux magnetizing current makes the estimation process independent of critical machine

parameters. The simulation and experimental results show that the dynamic performance of the

system compares with that using position sensors.


111

Chapter 5

DIRECT POWER CONTROL -

CONCEPT AND IMPLEMENTATION

5.1 Introduction

In field oriented control technique, the transient response of the active and reactive powers is

dependent on the degree of decoupling between the direct and the quadrature axes. This, in turn,

depends upon the accuracy of computation of the stator flux magnetizing current and accuracy of

rotor position information. As proper alignment of the position encoder is difficult in doubly-fed

machine, sensorless methods as discussed in chapter 4 are employed. These methods which make use

of field oriented control require mathematical computations involving coordinate transformation and

parameter estimation.

An alternative approach may be considered where, instead of the rotor current, the rotor flux

is directly controlled to control the active and reactive power flow in the machine. Direct self control

(DSC) of induction motor has been proposed [20] where the stator flux is controlled to track a

hexagonal trajectory. The switching scheme is such as to control the torque within a defined band.

Direct torque control (DTC) schemes have also been proposed [21-23]; the primary difference from

the earlier method being a circular trajectory of the stator flux. Two hysteresis controllers, namely a

torque controller and a flux controller, are used to determine the switching states for the inverter. The

method of control is computationally simple and, does not require the rotor position information.

However, the problem associated with low frequency sensorless operation exists.

113

So far, the application of direct torque control has been primarily restricted to cage rotor

induction motors and, permanent magnet synchronous motors [13]. In this chapter, an algorithm is

proposed which extends the switching concepts of DTC to rotor side control of doubly-fed wound

rotor induction machine. Here the directly-controlled quantities are the stator active and reactive

powers; hence, the algorithm is referred to as direct power control in this text. The sector in which

the rotor flux is presently residing is identified and the switching vectors are selected to control its

trajectory in a desired manner with respect to the stator flux. The sector information is updated in a

novel way based on the direction of change of the reactive power due to the application of a switching

vector. This method is inherently position sensorless and does not use any machine parameter in the

computation. The concept of direct power control is first introduced. The details of the control

strategy are subsequently presented with relevant simulation and experimental results.

5.2 Concept of Direct Power Control

The basic concept of direct control of active and reactive power can be appreciated from the

phasor diagrams based on the equivalent circuit of the doubly-fed machine as shown in Fig.5.1.

From the phasor diagram in Fig.5.2 it is noted that the component of the stator current hasisq

to be controlled to control the stator active power and has to be controlled to control the statorPs isd

reactive power . This is achieved in turn by controlling the rotor currents and respectively,Qs irq ird

as discussed in the previous chapters.

d-axis

q-axis

imsisd

isq is

us

ird

irirq

Fig.5.2 Phasor DiagramFig.5.1 Approximate Equivalent Circuit

ψs

is

us L0

sσ L0 rσ L0

ur

is r

ψr ψs

ψr

ψm

Chapter 5 Direct Power Control

114

d-axis

q-axis

imsisd

isq is

irq

us

A

B d-axis

q-axis

ims

isq

irq

us

ird

C D

=

(a) (b)

Fig.5.3 Phasor diagrams showing variations in rotor flux with change in active and reactive powers

ψs

ψm

ψr

ψs

ψmψr

δ pδ p

The effect of injection of these rotor currents on the air-gap and rotor fluxes can be derived by

subtracting and adding the respective leakage fluxes. The variation of the rotor flux with variations in

the active and reactive power demand is shown in Figs.5.3(a) and Fig.5.3(b). In Fig.5.3(a) ,ird = 0

i.e. the reactive power is fed completely from the stator side. Under this condition if is variedirq

from 0 to full load, the locus of varies along A-B which indicates a predominant change in angle yr

between and , whereas the magnitude of does not change appreciably. In other words, adp ys yr yr

change in the angle would definitely result in a change in the active power handled by the stator indp

a predictable fashion. For example, in Fig.5.3(a) which indicates motoring mode of operation, the

active power can be increased by decelerating the rotor flux with respect to the stator flux. Conversely

it can be reduced by accelerating the rotor flux. In Fig.5.3(b) the stator active power demand is

maintained constant so that is constant and is varied from 0 to the rated value of . Here theirq ird ims

locus of varies along C-D, resulting in a predominant change in magnitude of , whereas theyr yr

variation of is small. Therefore, the reactive power drawn from the grid by the stator can bedp

reduced by increasing the magnitude of the rotor flux and vice-versa. It may be noted that the phasor

diagrams as indicated in Figs.5.3(a) and 5.3(b) remain the same irrespective of the reference frame;

the frequency of the phasors merely changes from one reference frame to the other. It can be

concluded from the above discussion that;


115

i) The stator active power can be controlled by controlling the angular position of the rotor flux

vector.

ii) The stator reactive power can be controlled by controlling the magnitude of the rotor flux vector.

These two basic derivations are used to determine the instantaneous switching state of the

rotor side converter to control the active and reactive power as discussed in the following section.

5.3 Voltage Vectors and their Effects

S3

(0 1 0)

S4

(0 1 1)

S0

(0 0 0)

S7

(1 1 1)

Fig.5.4 8 possible switching states of a three phase VSI

S1

(1 0 0)

S2

(1 1 0)

S5

(0 0 1)

S6

(1 0 1)


116

Fig.5.4 shows the 8 possible switching states of a three phase VSI of which six are active

states (S1, S2,....S6) and two are zero states (S0, S7). Assuming that the orientation of the three phase

rotor winding in space at any instant of time is as given in Fig.5.5(a), the six active switching states

would correspond to the voltage space vectors U1, U2 ....U6 [Fig.5.5(b)] at that instant. In order to

make an appropriate selection of the voltage vector the space phasor plane is first subdivided into six

600 sectors I,II..VI. The instantaneous magnitude and angular position of the rotor flux space phasor

can now be controlled by selecting a particular voltage vector depending on its present location. The

effect of the different vectors as reflected on the stator side active and reactive powers, when the rotor

flux is positioned in Sector 1 is illustrated in the following subsections.

Phase a

Phase b

Phase c

S1(100)

S2 (110)S3 (010)

S4(011)

S5 (001) S6 (101)

Sector 1

Sector 2Sector 3

Sector 4

Sector 5 Sector 6

U1

U2U3

U4

U5 U6

Fig.5.5(a) Orientation of the rotor winding in

space with respect to which the voltage

space phasors are drawn

Fig.5.5(b) Voltage space phasors

5.3.1 Effect of Active Vectors on Active Power

Considering anti clockwise direction of rotation of the flux vectors in the rotor reference

frame to be positive, it may be noted that is ahead of in motoring mode of operation and isys yr ys

behind in generating mode. This is illustrated in Fig.5.6(a) and Fig.5.6(b) respectively. In the rotoryr

reference frame the flux vectors rotate in the positive direction at subsynchronous speeds, remain

stationary at synchronous speed and start rotating in the negative direction at supersynchronous

speeds.


117

ψs

ψr ψs

ψr

U1

U2U3

U4

U5 U6

U1

U2U3

U4

U5 U6

subsyn

supersyn

subsyn

supersyn

(a) (b)

δ p δ p

Fig.5.6 Flux vectors in (a) motoring mode and (b) generating mode

In the motoring mode of operation in Sector I, application of voltage vectors U2 and U3

accelerates in the positive direction. This reduces the angular separation between the two fluxesyr

resulting in a reduction of active power drawn by the stator. At subsynchronous speeds, U2 and U3

cause to move in the same anti clockwise direction as ; hence the effect on depends on theyr ys Ps

difference between the angular velocities of the two fluxes. The factors effecting the angular

velocities of the fluxes and are the slip speed and the dc bus voltage respectively. In the rotorys yr

reference frame, rotates at slip speed and the rate of change of depends on the dc bus voltageys yr

and the applied inverter state. So, for a given bus voltage, higher the slip lesser is the relative angular

velocity between the two flux vectors, thereby effecting a slower change in and vice-versa. AtPs

supersynchronous speeds the relative velocity is additive and change in is faster.Ps

In the generating mode of operation, application of vectors U2 and U3 result in an increase in

angular separation between the two and thereby an increase in the active power generated by the

stator. ( being negative for generation, U2 and U3 still results in a reduction of positive activePs

power). The relative speeds of the vectors in subsynchronous and supersynchronous generation are

same as in motoring operation; hence the same conclusions can be drawn. Similarly it can be seen


118

that the effect of U5 and U6 on the active power would be exactly opposite to that of U2 and U3 in

both the motoring and generating modes.

Power drawn by the stator being taken as positive and power generated being taken as

negative, it may be concluded that, if the rotor flux is in the kth sector, application of vectors U(k+1)

and U(k+2) would result in a reduction in the stator active power and application of vectors U(k-1)

and U(k-2) would result in an increase in the stator active power.

5.3.2 Effect of Active Vectors on Reactive Power

From the phasor diagrams Fig.5.3(a) and Fig.5.3(b) it can be seen that the reactive power

drawn by the stator depends upon the component of along i.e. . The angle between andyr ys yrd ys

i.e. being small, the magnitude of is approximately equal to . Therefore, when the rotoryr dp yr yrd

flux vector is located in Sector I, voltage vectors U1, U2, and U6 increase its magnitude whereas

vectors U3, U4, and U5 reduce its magnitude. This holds good irrespective of whether the machine is

operating in motoring or generating mode. An increase in magnitude of indicates an increasedyr

amount of reactive power being fed from the rotor side and hence, a reduction in the reactive power

drawn by the stator resulting in an improved stator power factor. A decrease in magnitude of yr

amounts to lowering of the stator power factor.

As a generalization it can be therefore said that if the rotor flux resides in the kth. sector,

where k = 1,2,3..6, switching vectors U(k), U(k+1), and U(k-1) reduce the reactive power drawn from

the stator side and U(k+2), U(k-2), U(k+3) increase the reactive power drawn from the stator side.

5.3.3 Effect of Zero Vector on Active Power

The effect of the zero vectors is to stall the rotor flux without affecting its magnitude. This

results in an opposite effect on the stator active power in subsynchronous and supersynchronous

modes of operation.

In subsynchronous motoring, application of a zero vector increases as keeps rotating indp ys

the positive direction at slip speed. Above the synchronous speed, rotates in the counter clockwiseys

direction thereby reducing . Hence active power drawn by the stator increases for subsynchronousdp

operation and decreases for supersynchronous operation. Active power generated being negative, the


119

same conclusion holds true for the generating modes as well. The rate of change of depends on thePs

slip speed alone as remains stationary in the rotor reference frame. yr

5.3.4 Effect of Zero Vector on Reactive Power

Since a zero vector does not change the magnitude of the rotor flux its effect on the reactive

power is rather small. Nevertheless, there is some small change in ; its effect being dependent onQs

whether the angle between the stator and rotor fluxes increases or decreases due to the application of

a zero vector. An increase in angular separation between the two fluxes reduces resulting in anyrd

increment of drawn from the stator side. The converse is true when reduces. Qs dp

It is observed that the change in due to the application of U0 or U7 is different in all the 4Qs

modes of operation. This is summarized in Table 5.1. (The effect on is also included in this tablePs

for the sake of completeness.)

Table 5.1 Effect of zero vector on active and reactive power

dp m e yrd o e Qs m, Ps m

dp o e yrd m e Qs o, Ps o

Supersynchrnous

dp o e yrd m e Qs o, Ps o

dp m e yrd o e Qs m, Ps mSubsynchronous

GeneratingMotoringSpeed

Note: denotes increase, denotes decreasem o

5.4 Control Algorithm

With the inferences drawn in the previous section it is possible to switch an appropriate

voltage vector in the rotor side at any given instant of time to increase or decrease the active or

reactive power in the stator side. Therefore, any given references for stator active and reactive powers

can be tracked within a narrow band by selecting proper switching vectors for the rotor side

converter. This is the basis of the direct power control strategy. The details of the control algorithm

are discussed in the following subsections.

It should be noted that in a VSCF system, the outer loop will decide the reference for the

overall active power generated or absorbed by the machine. This includes both the stator and rotorP


120

powers ( and ). From this set value and the present speed, the reference torque can bePs Pr md&

computed. The reference for the stator power can, therefore, be calculated as

(5.1)Ps& = md

& $ zs

is set according to the desired power factor at the stator terminals.Qs&

5.4.1 Measurement of Stator Active and Reactive Power

The active and reactive power on the stator side can be directly computed from the stator

currents and voltages. Assuming a balanced three phase three wire system, only two currents and two

voltages need to be measured. The active and reactive powers can be expressed as

(5.2)Ps = 23 usa isa + usb isb

(5.3)Qs = 23 usb isa − usa isb

where (5.4)usa = 32 us1

(5.5)usb =32 us1 + 2us2

and, (5.6)isa = 32 is1

(5.7)isb =32 is1 + 2is2

5.4.2 Defining References and Errors

Let the references for the stator active and reactive powers be and respectively, andPs& Qs

&

the respective allowable bands of excursion of and on either side of their reference values be Ps Qs

and . This is illustrated in Fig.5.7. It is desired that when crosses and hits thePband Qband Ps Ps&

upper band the switching vectors which reduce the active power are selected and consequently isPs

brought down until it hits the lower band. To accomplish this a modified reference is definedPs&&

which is toggled between and depending on the sign of .Ps& + Pband Ps

& − Pband (Ps&& − Ps )

As shown in Fig.5.7, at instant A, is and is positive. When Ps&& Ps

& + Pband (Ps&& − P) Ps

crosses at instant B, this error becomes negative and instantaneously is brought down to Ps&& Ps

&&

. This continues till instant C when the error again becomes positive and isPs& − Pband Ps

&&

modified to . This can be formulated as follows.Ps& + Pband


121

Perr = Ps&& − Ps

if (Perr > 0)

Ps&& = Ps

& + Pband

else

(5.8)Ps&& = Ps

& − Pband

In a similar manner the error and reference for the reactive power can be written as

Qerr = Qs&& − Qs

if (Qerr > 0)

Qs&& = Qs

& + Qband

else

(5.9)Qs&& = Qs

& − Qband

A

B

C

bandP

Ps

P**s

P*s

Fig.5.7 Ps, Ps&, Ps

&&

5.4.3 Switching Vector Selection

In order to determine the appropriate switching vector at any instant of time, the errors in Ps

and , and the sector in which the rotor flux vector is presently residing are taken into consideration.Qs

Thus the following two switching tables for active vector selection can be generated. Table 5.2(a) and

Table 5.2(b) correspond to negative and positive respectively.Perr Perr

Table 5.2(a) Selection of active switching states when (Perr <= 0)

S1S6S5S4S3S2Qerr <= 0

S2S1S6S5S4S3Qerr > 0

Sector 6Sector 5Sector 4Sector 3Sector 2Sector 1


122

Table 5.2(b) Selection of active switching states when (Perr > 0)

S5S4S3S2S1S6Qerr <= 0

S4S3S2S1S6S5Qerr > 0

Sector 6Sector 5Sector 4Sector 3Sector 2Sector 1

If the rotor side converter is switched in accordance to these tables it is possible to control the

active and reactive powers in the stator side within the desired error bands. But the use of active

vectors alone would result in non-optimal switching of the converter and also a higher switching

frequency.

The effect of the zero vectors on and has been summarized in Table 1. Since the zeroPs Qs

vectors affect both these parameters the usual logic for zero vector selection to enhance/reduce the

torque as used in direct torque control cannot be applied here. The algorithm for incorporating the

zero vector logic is as follows.

if (Ps& m 0) {

if (z [ zs) {

;subsynchronous motoringif (Qerr m 0 && Perr m 0)

Sn = Sz

else Sn = Sa }

;supersynchronous motoringelse { if (Qerr < 0 && Perr < 0)

Sn = Sz

else Sn = Sa } }

else {if (z [ zs) {

;subsynchronous generationif (Qerr < 0 && Perr m 0)

Sn = Sz

else Sn = Sa }

;supersynchronous generationelse {if (Qerr m 0 && Perr < 0)

Sn = Sz

else Sn = Sa } }

Here, represents the switch state to be selected, represents a zero state and an activeSn Sz Sa

state.


123

It has already been mentioned that the effect of zero vector is primarily on the active power;

the effect on reactive power is minimal. Also, it is observed that the effect on is opposite in thePs

subsynchronous and supersynchronous modes of operation. This criterion is used in detecting the

transition from subsynchronous to supersynchronous operation and vice-versa. It can be illustrated

with an example. It is assumed that the machine is operating in subsynchronous generation mode.

Therefore, the use of a zero vector increases and consequently should decrease. The amountPs Perr

of reduction in depends on the slip speed (for a constant dc bus voltage). When the slip becomesPerr

negative, will start increasing (instead of reducing) with the application of a zero vector. ThisPerr

direction of change of is detected and it is inferred that the mode of operation has now changedPerr

to supersynchronous generation. The zero vector logic is then modified accordingly.

The choice between S0 and S7 is done depending on the minimum inverter switching. For

example while switching to a zero vector from S1, S0 is selected. On the other hand if the transition

to the zero vector is from S2, S7 is selected. Both these transitions then would result in switching of

only one arm of the inverter.

It may be concluded that these switching strategies would result in close tracking of and Ps&

within the prescribed error bands using near-optimum switching of the rotor side converter.Qs&

5.5 Sector Identification of Rotor Flux

In order to implement the switching algorithm the present sector of the rotor flux has to be

identified. The exact position of the rotor flux space phasor is not of importance as far as the selection

of the switching vectors are concerned. This is because of the fact that the choice of the rotor voltage

vectors is based upon errors in the stator quantities (and not the rotor flux) which are directly

measurable.

The proposed method of sector identification is based on the direction of change in when aQs

particular switching vector is applied. The concept is illustrated by the following example. Let us

assume that the present position of the rotor flux is in Sector 1 and it is moving in the anti clockwise

direction (corresponding to subsynchronous operation). Therefore, application of switching states S2

and S6 results in a reduction of and application of S3 and S5 results in an increment of . WhenQs Qs

the rotor flux vector crosses over to Sector 2, the effect of states S3 and S6 on would reverse.Qs

Vector U3 would now act to reduce instead of increasing it. Similarly the effect of vector U6 on Qs


124

would also be opposite. These reversals in the direction of change of , when a particular vectorQs Qs

is applied, can be detected and a decision of sector change may be taken on this basis. Similarly, if the

flux vector is rotating in the clockwise direction (supersynchronous operation) the effect of states S2

and S5 on would change in direction when changes over from Sector 1 to Sector 6. Thus inQs yr

any particular direction of rotation there are two vectors which can provide the information for sector

change. Since the rotor flux vector cannot jump through sectors the change will always be by one

sector, either preceding or succeeding. In this method, even though the exact position of the flux is

unknown, the sector information can be updated just by observing the changes in due to theQs

applied vectors. It may be noted that the effect of the vectors on would not provide a conclusivePs

inference about the change in sector.

The expected direction of change in due to the application of any switching vector in theQs

different sectors can be summed up in the following table.

Table 5.3 Expected direction of change in . Qs

0--+++-0Sector 6

0---+++0Sector 5

0+---++0Sector 4

0++---+0Sector 3

0+++---0Sector 2

0-+++--0Sector 1

S7S6S5S4S3S2S1S0

Note: + indicates increment in , - indicates decrement in , 0 indicates no change (however,Qs Qs

application of the zero vectors will result in some small changes, but zero vectors are not taken into

consideration to infer sector changes).

It may, however, be noted that in a particular sector not all vectors will be applied. For

example, in sector k, vectors U(k) and U(k+3) will never be applied. These vectors would have

predominant effect on the reactive power, but their effect on the active power would depend on the

actual position of the rotor flux vector in the sector. In most applications there is hardly any

requirement for fast transient changes in reactive power; so it is not necessary to apply the strongest

vector to effect any change in . In the switching logic, therefore, only those vectors are selectedQs


125

which have uniform effects on and in terms of their direction of change irrespective of thePs Qs

position of the rotor flux in a particular sector.

For any given vector applied in a particular sector the expected direction of change in canQs

be read off from Table 5.3. The actual direction of change can be computed from the present value of

and its previous value. If they are in contradiction then a decision on change of sector is taken.Qs

Whether the sector change has to be effected in the clockwise or anti clockwise direction depends on

the applied vector and the observed change in . This information is stored in another lookup tableQs

as furnished below.

Table 5.4 Direction of change of sector

00+ 1- 10+ 1- 10Sector 6

0- 10+ 1- 10+ 10Sector 5

0+ 1- 10+ 1- 100Sector 4

00+ 1- 10+ 1- 10Sector 3

0- 10+ 1- 10+ 10Sector 2

0+ 1- 10+ 1- 100Sector 1

S7S6S5S4S3S2S1S0

Note: 0 indicates no change, + 1 indicates the sector has to be updated to its next value in the anti

clockwise direction, -1 indicates the sector has to be updated to its previous value.

To illustrate the algorithm with an example it may be assumed that the rotor flux vector is

presently residing in Sector 1 and rotating in the anti clockwise direction (corresponding to

subsynchronous speed operation). As long as the flux vector is within the boundary of Sector 1, the

direction of change in will be as expected and the computed direction will match with that storedQs

in Table 5.3. The quantitative change in due to the effect of the vectors will obviously depend onQs

the position of in the sector but the direction of change should be in accordance with this table. Inyr

this example, since is rotating in the anti clockwise direction the most widely used active states inyr

Sector 1 will be S2 and S3. When the flux vector has crossed over to Sector 2, S2 will have a more

pronounced effect on in the same direction as in Sector 1, but the effect of S3 will reverse itsQs

direction. The application of S3 will cause a decrement in whereas in Sector 1 it is expected toQs

increase. Hence, the computed direction of change will be opposite to that stored in Table 5.3. When


126

this is detected the corresponding entry in Table 5.4 is looked at. For Sector 1 and switch state S3 the

entry in Table 4 indicates a positive change in sector. Hence it is updated to Sector 2.

Similarly it can be verified that if the flux vectors are rotating in the clockwise direction

(corresponding to supersynchronous speed) the most commonly used active states will be S6 and S5.

When crosses over to Sector 6, S6 will have a predominant effect on in the same direction asyr Qs

in Sector 1, but S5 will cause to reduce instead of increasing it. This direction of change in isQs Qs

detected from Table 5.3, and the corresponding entry in Table 5.4 indicates a change in sector in the

negative direction. Hence the sector information is updated from Sector 1 to Sector 6.

For reliable detection of the direction of change of a minimum switching period of 6Qs

sampling periods (336 µs) of a particular switching state is maintained. This also puts a maximum

switching limit of 4.5 kHz for the rotor side converter.

This method of sector identification is independent of any machine parameter but relies on

directly measurable fixed frequency quantities. It is also independent of the rotor frequency and can

work stably at or near synchronous speed.

5.6 Starting

Before the rotor side converter is switched on, the entire reactive power is drawn from the

stator side. Initially is set to the computed value of after passing it through a low-pass filterQs& Qs

with a time constant of 100 ms. Thereby it is ensured that at the instant of switching the rotor

converter, is within and the sector estimation algorithm can be used for correcting to theQerr Qband

appropriate sector. Since, the minimum switching period on the basis of which a definite decision

about sector change is made is about 336 µs, the algorithm locks onto the correct sector within 1 ms (

336x3) even if the actual sector is opposite to the computed sector at switch-on. The system can bej

thus, started on-the-fly without any appreciable transient in rotor or stator currents. is then slowlyQs&

ramped down to zero (or any other reference) so that the sector updating logic can function properly.

It may be noted here that the sector correction logic will give improper inferences for a sudden step

change in . However, a transient demand of reactive power is not a practical requirement for theQs&

present system, and a gradual change in is acceptable. Qs


127

5.7 Simulation Results

The direct power control algorithm is simulated on the MATLAB-SIMULINK platform. The

field oriented controller block is replaced by the direct power control module. Since the outputs of

this block are directly the switching signals for the rotor side converter, the PWM generation block is

omitted. The main modules used to model the direct power algorithm and the interconnections

between them are illustrated in Fig.5.8. This simulation is done with the same machine parameters as

given in Appendix C. For uniformity of presentation, per unit representation with the same base

values is also maintained in this case.

The transient response due to a step change in active power command from 0 to 0.5 p.u.,Ps&

while is maintained at 0 is shown in Fig.5.9(a) and Fig.5.9(b). and are kept at 0.05Qs& Pband Qband

p.u. in this case. It is observed that response time of to reach its set value is approximately 2 ms.Ps

This can be the fastest possible response at a given speed because only the desired active vector is

used during the transient. Similar transient response for generating condition is given in Fig.5.10(a)

and Fig.5.10(b). The response of the stator current corresponding to these step changes in active

power are presented in Fig.5.11(a) and Fig.5.11(b). Since the reactive power reference is held atQs&

zero, unity power factor operation is clearly observed at the stator terminals.

3

S3

2

S2

2

Q*

delP, delQPs, Qs

1

P*

P**, Q**

3

Usa 4

Usb 5

Isa 6

Isb

1

S1

Sector Update

Switching pattern

generation

Fig.5.8 SIMULINK block diagram of the direct power algorithm


128

0.34 0.35 0.36 0.37 0.38 0.39 0.4-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

secs

P (

p.u.

)

(a) Response of Ps

0.34 0.35 0.36 0.37 0.38 0.39 0.4-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

secs

Q (

p.u.

)

(b) Response of Qs

Fig.5.9 Simulation results showing transient responses of and due to step change in from 0 Ps Qs Ps&

to 0.5 p.u. with at = 0.9 p.u.Qs& = 0 z


129

ss

0.25 0.26 0.27 0.28 0.29 0.3-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

secs

P (

p.u.

)

(a) Response of Ps

0.25 0.26 0.27 0.28 0.29 0.3-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

secs

Q (

p.u.

)

(b) Response of Qs

Fig.5.10 Simulation results showing transient responses of and due to step change in from Ps Qs Ps&

0 to -0.5 p.u. with at = 0.9 p.u.Qs& = 0 z


130

ss

0.34 0.35 0.36 0.37 0.38 0.39 0.4-1.5

-1

-0.5

0

0.5

1

1.5

secs

us, i

s (p

.u.)

(a) Response of for motoringis

0.25 0.26 0.27 0.28 0.29 0.3-1.5

-1

-0.5

0

0.5

1

1.5

secs

us, i

s (p

.u.)

(b) Response of for generationis

Fig.5.11 Simulation results showing transient responses of along with due to step change in is us Ps&

(a) from 0 to 0.5 p.u. (b) from 0 to -0.5 p.u., with at = 0.9 p.u.Qs& = 0 z


131

0.5 0.55 0.6 0.65 0.7 0.75 0.8-1.5

-1

-0.5

0

0.5

1

1.5

secs

Psi

_ra

(p.u

), S

ecto

r

Fig.5.12 Simulation waveform showing identification of sector with rotor flux component yra

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2-1.5

-1

-0.5

0

0.5

1

1.5

secs

ir (p

.u),

Sec

tor

Fig.5.13 Simulation waveform showing and sector information during transition through ir

synchronous speed


132

The rotor flux along with the sector information is given in Fig.5.12. The sector information is

shown in the form of steps; there are 6 steps corresponding to the six sectors. The rotor current during

transition through synchronous speed is plotted in Fig.5.13. As the rotor passes through the

synchronous speed, the slope of the steps change from positive to negative, thereby indicating that the

rotor flux changes its direction of rotation.

5.8 Implementation and Experimental Results

The direct power control algorithm is implemented on a laboratory experimental setup. The

software is organized in a similar manner as discussed earlier. The modules which implement the

algorithm are listed below with brief descriptions.

Subroutine COM_POWER

Computes stator active and reactive powers from and .usa, usb isa, isb

Subroutine COM_ERR

Compute errors in active and reactive powers

Subroutine UPDATE_SECTOR

Implements the sector updating logic

Subroutine SELECT_PATTERN

Selects switching state for the inverter depending on the sector of the rotor flux.

Subroutine UPDATE_PATTERN

Outputs switching pattern depending on the selected switching state.

It may be noted that the lookup tables which are used in the routines UPDATE_SECTOR,

SELECT_PATTERN and, UPDATE_PATTERN are compact and occupy a small part of the data

memory space. Execution of the assembly code is fast and, it is possible to have a loop-time of 50 µs

if the processor executes only the direct power algorithm. Experimental results to validate the direct

power control algorithm are presented here.


133

Fig.5.14(a) Experimental waveforms showing transient response of and due to step change in Ps Qs

from 0 to -0.5 p.u. and = 0Ps& Qs

&

Fig.5.14(b) Experimental waveforms showing transient response of due to step change in from is Ps&

0 to -0.5 p.u. and = 0Qs&

Fig.5.14(c) Experimental waveforms showing steady-state waveforms of and is us


134

Fig.5.15(a) Experimental results showing steady-state waveforms for = -0.5 p.u., =0us, is, ir Ps& Qs

&

at 1300 rpm (subsynchronous operation)

Fig.5.15(b) Experimental results showing steady-state waveforms for = -0.5 p.u., =0us, is, ir Ps& Qs

&

at 1430 rpm (synchronous operation)

Fig.5.16 Experimental results showing steady-state , for = -0.25 p.u., =0yra yrb Ps& Qs

&


135

Fig.5.17(a) Experimental results showing and sector information during startingQs

Fig.5.17(b) Experimental results showing , and sector information during steady-state Ps Qs

operation with = -0.5 p.u., =0 at 1300 rpmPs& Qs

&

Fig.5.17(c) Experimental results showing and sector information during transition through ir

synchronous speed


136

Transient in active power for a step change in from 0 to -0.5 p.u. is shown in Fig.5.14(a). Ps&

is maintained at 0. As is changed goes out of the prescribed band of 0.05 p.u.. ThisQs& Ps

& Perr

results in the selection of only the active vectors thereby effecting the fastest possible change in .Ps&

The slope of change of P is decided by the rate of change of rotor current which in turn depends on

the dc link voltage. It may be noted from these waveforms, that, the transient responses in and Ps& Qs

&

are perfectly decoupled. The steady-state ripple in and due to switching between the positivePs& Qs

&

and negative error bands can also be observed. Fig.5.14(b) illustrates the effect of the active power

transient as reflected in the stator current waveform. The steady-state current waveform in Fig.5.14(c)

clearly shows unity power factor operation.

The steady-state stator voltage and current waveforms for subsynchronous and synchronous

operations are given in Fig.5.15(a) and Fig.5.15(b) respectively. The synchronous speed operation is

observed to be perfectly stable. In Fig.5.16, the steady-state rotor flux waveforms and areyra yrb

presented.

One of the important requirements of the wind power generators is that the machines have to

be "cut-in" when the turbine speed crosses a given limit. The method of "on-the-fly" starting has been

discussed in section 5.6. The relevant waveforms of and the computed sector are given inQs

Fig.5.17(a). (The sector information is scaled and output through DAC such that the analog output

voltage is 1V multiplied by the sector number.) Before the rotor converter is switched on, the sector

information as can be seen from the plot is erroneous. However, the computed sector locks onto the

actual sector instantaneously as the rotor circuit is excited. is gradually ramped down to zero.Qs

Fig.5.17(b) shows the steady-state waveforms of and along with the sector information for Ps Qs Ps&

= -0.5 p.u. and =0. Fig.5.17(c) gives the rotor current waveform along with the sector informationQs&

for transition through synchronous speed. During subsynchronous speed operation, the flux vectors

rotate in the anti clockwise direction in the rotor reference frame; hence the sector number increases

from 1 to 6 and resets back to 1. This is represented by the ascending staircase waveform. As the rotor

moves over to supersynchronous speed the flux vectors start rotating in the clockwise direction.

Therefore, the sector number changes in the reverse order as seen by the descending staircase. The

changeover from subsynchronous to supersynchronous speed is observed to be smooth without any

transients in and .Ps Qs


137

5.9 Conclusion

A method of direct power control for doubly-fed, slip ring induction machine is presented.

The stator active and reactive powers are controlled within hysteresis bands by adopting a switching

algorithm on the rotor side. It is proposed that instead of estimating the exact position of the rotor

flux, the information of the sector in which it resides is sufficient for switching the correct inverter

state. A novel method for sector identification based on the direction of change of reactive power is

proposed. The control algorithm uses only stator quantities for active and reactive power

measurement and is inherently position sensorless. It is computationally simple and does not

incorporate any machine parameter. Relevant simulation and experimental results to validate the

concept are presented. The direct power control method can be an attractive proposition for slip-ring

induction generators in wind-energy application.


138

Chapter 6

DOUBLY-FED WOUND ROTOR INDUCTION MACHINE

FOR WIND POWER GENERATION - DESIGN

CONSIDERATIONS AND CONTROL STRATEGIES

6.1 Introduction

Harnessing wind power by means of windmills can be traced back to about four thousand

years from now, when they were used for milling and grinding grains and, for pumping water. Even

today there are over one million windmills in operation around the world used for traditional

applications. However, there has been a renewed interest in wind energy in recent years as it is a

potential source for electricity generation with minimal environmental impact [44, 45]. With the

advancement of aerodynamic designs, wind turbines which can capture hundreds of kilowatts of

power, are readily available. When such wind energy conversion systems (WECS) are integrated to

the grid, they produce a substantial amount of power, which can supplement the base power generated

by thermal, nuclear or hydro power plants.

6.1.1 Wind Turbines

Modern wind turbines can be broadly categorized into two basic configurations: horizontal

axis wind turbine (HAWT) and vertical axis wind turbine (VAWT).

The former, as the name suggests, has its axis aligned parallel to the wind direction. The

present low-solidity (two or three blades) HAWTs have evolved from developments in aircraft wing

and propeller design. The axis of an HAWT needs to be continually oriented along the changing wind

139

direction. This is accomplished by yaw control (slow rotation by gear arrangement) of the nacelle

(assemblage comprising wind turbine, gears, generator, bearings, control gear etc. mounted in a

housing). These turbines are commercially available with ratings upto 1650 kW [50] and are

universally employed in the generation of electricity.

VAWTs have an axis of rotation perpendicular to the wind direction; so they can harness wind

from any direction without the need to reposition the rotor when the wind direction changes. The

Darrieus VAWT, which is the earliest VAWT, has a huge egg-beater like structure with curved blades

attached at the top and bottom of the same vertical shaft. This shape is structurally suitable for

withstanding relatively high centrifugal forces. It is however, difficult to manufacture, transport and

install. This led to the proposition of straight-bladed VAWTs, the H-type VAWT and V-type VAWT.

Due to higher manufacturing costs, VAWTs have not become economically competitive with

HAWTs. In the present work, the system design and control has been proposed with a standard a

three-bladed HAWT. However, the same methods can be applied to VAWTs also.

6.1.2 Isolated and Grid-connected WECS

A WECS consists of a wind turbine coupled to the generator shaft by means of a suitable

gearbox. The generator may be connected to the constant frequency power grid, or it may supply an

isolated load. On this basis, WECS can be broadly classified as grid-connected or isolated systems.

While use of isolated WECS is restricted to small scale power generation in remote areas,

grid-connected systems are more popular and much higher power capacities are commercially

available.

Power extracted from wind is of intermittent nature depending on the wind velocity. It is not

guaranteed that the power demand of the load can always be met by a WECS. Therefore, in case of

isolated systems the power captured by the turbine either has to be temporarily stored (usually by

means of batteries) [46] or it has to be supplemented by other means, such as, diesel-electric

generation, batteries etc. [47]. The latter is referred to as the hybrid energy system. In such a scheme

reported by Nayar et.al.[48], the diesel engine always delivers a certain amount of load so that its fuel

efficiency is high. The battery is normally charged through a wind electric generator. The inverter

either shares the load with the diesel generator (during peak load condition) or accepts power from

the same and operates as a battery charger (during medium load condition). Under light load

conditions the diesel engine is shut down and the entire power is supplied from the battery bank. Even

Chapter 6 Wound Rotor Induction Machine for Wind Power Generation

140

though the initial investment is high, the advantages are higher efficiency and smaller size of the

diesel generator. Hybrid energy systems using wind power have not become popular because of high

cost, control complexity and requirement of large battery banks.

Rather than serving a localized load WECS can be integrated to large power grids. The energy

generated from wind is readily absorbed without affecting the supply quality. (The amount of

intermittently generated power which a grid can absorb depends on the grid condition; typically 10%

power penetration is within permissible limits [49].) Wind turbines used for grid connected systems

are of larger size, normally rated above 100 kW (typical ratings being 225 kW, 600 kW, 660 kW,

1650 kW [50]). In locations of continuous favorable wind conditions, several such WECS are

connected to the grid forming a wind-farm. Very large scale WECS (>1 MW) have been installed in a

few places (e.g. a 3 MW unit was installed in 1982 in Maglap, Sweden) on experimental basis.

However, such large units are very expensive and uncommon.

6.1.3 Choice of Wind Electric Generators

The common electric generators used for isolated WECS are the dc generator, field wound or

permanent magnet synchronous alternator and the capacitor-excited induction generator [46]. Of

these, the induction generator is most attractive because of its ruggedness, low cost and, low

maintenance requirement. The magnetizing current is obtained from the capacitors connected across

its output terminals. As the turbine drives the rotor, the residual magnetism helps in building up the

terminal voltage; its magnitude and frequency being dependent on the shaft speed, capacitance value

and, the system load.

The cage rotor induction machine is also the most frequently used generator for grid

connected WECS [57]. When connected to the constant frequency network, the induction generator

runs at near-synchronous speed drawing the magnetizing current from the mains, thereby resulting in

constant speed constant frequency (CSCF) operation. However, if there is flexibility in varying the

shaft speed, the power capture due to fluctuating wind velocities can be substantially improved. This

is explained in the later sections. The requirement for variable speed constant frequency (VSCF)

operation led to several developments in the generator control of WECS.

Variable speed wind turbine control using cage rotor machine is reported by Muljadi et.al.

[51]. The generator is run in V/f mode by a voltage source inverter. The frequency command is

decided by the present rotor speed and the target power. The turbine speed is measured, and the target


141

power is determined based on a cubic function of speed. The required frequency is then computed

depending on the machine parameters. The annual energy production of the system was estimated

using Raleigh annual wind distribution. It is reported that for a 5m radius turbine, the annual energy

production was 49.6 MWH, compared to 37.2 MWH for a corresponding fixed speed system.

Vector controlled squirrel cage induction generators for VSCF wind power systems are also

commercially available [52]. Instantaneous control over the machine torque can be exercised leading

to smoother variations in generator power and speed. The front end converter is simultaneously

controlled for unity power factor operation under all wind conditions. Direct torque control (DTC)

algorithm can also be employed for decoupled control over the generator flux and torque. Recently a

225 kW prototype using DTC on the machine side and similar switching logic for the FEC has been

successfully implemented and tested [53].

In spite of the disadvantages associated with slip-rings, the wound rotor induction machine

has been a potential candidate as wind electric generator. By suitable integrated approach towards

design of a WECS, use of a slip-ring induction generator is found to be economically competitive.

Control of both grid-connected and isolated variable speed wind turbines with doubly fed induction

generator has been implemented by Pena et.al. [16], [54]. Conventional vector control using a

position sensor has been employed from the rotor side in both the cases for independent control of

active and reactive power. For the isolated WECS, control of an auxiliary load in parallel with the

main load, allows the system to track the optimal wind turbine speed for maximum energy capture. In

case of the grid-connected system the generator is run in speed-control mode with the help of a torque

observer for optimum operating point tracking. Implementation of a torque observer is, however,

difficult. Beyond the rated operating point, the algorithm tries to reduce the shaft speed to limit the

generator power. This requires sufficient torque capability of the generator to overcome the

instantaneous turbine torque and, may not be a feasible solution in practice.

In this chapter a comprehensive study on variable speed grid-connected WECS using wound

rotor induction machine as the wind electric generator is presented. The motivation for variable speed

control is explained and the proposed scheme is compared against the existing fixed speed and

variable speed systems using cage rotor machines. The turbine characteristics are generated by a dc

drive in the laboratory setup. Peak power point tracking algorithm in the conventional torque control

mode is first implemented. A dc motor driven by a commercial thyristor drive is used to simulate the

turbine characteristics. Subsequently, a novel technique for tracking the peak power points using


142

speed controlled operation is proposed. The technique searches the zero slope point on the

power-speed characteristics of the turbine. The peak power tracking is made independent of turbine

characteristics, air density etc. in this method. This strategy is also implemented and verified

experimentally.

Note: In this chapter, the sign convention adopted for active power is different from that of the earlier

chapters. Since only generator operation is being considered, active power is taken as positive if it

flows out of the induction machine terminals, both at the stator as well as the rotor. The power

developed by the turbine is always taken to be positive.

6.2 Conventional Fixed Speed System

In order to appreciate the need for variable speed control in wind power generation, the wind

turbine characteristics and, the limitations of the fixed speed system have to be understood. This is

explained in the following subsections.

6.2.1 Wind Turbine Characteristics

A wind turbine is characterized by its power-speed characteristics. The amount of power Pt

that a turbine is capable of producing depends upon its dimensions, blade geometry, air density and

the wind velocity. For a HAWT it is given by

(6.1)Pt = 0.5 $ Cp $ q $ A $ v3

where is the air density, A is the swept area (cross-sectional area) of the turbine and v is the windq

velocity. Cp is called the power coefficient and is dependent on the ratio between the linear velocity

of the blade tip ( ) and the wind velocity (v). This ratio, known as the tip-speed ratio, is definedR $ zt

as

(6.2)k = z t$Rv

where R is the radius of the turbine.

An idealized Cp Vs. curve, taken from [56], is shown in Fig.6.1. It is observed that thek

power coefficient is maximum for a particular tip-speed ratio. This implies that for any wind velocity

there is a particular rotor rpm for which maximum power transfer takes place. The prime motivation

for variable speed control of WECS is to track this rotor speed with changing wind velocity so that

Cp is always maintained at its maximum value. Using the Cp- curve of Fig.6.1, the power-speedk


143

characteristics are plotted for a commercially available turbine (Vestas V27) by using a Mathcad

program. In the following sections these power curves, as shown in Fig.6.2 and Fig.6.3, are used for

comparison between the different control schemes and designs.

.

0.5

5 10

0.2

0.4

02 15

λ

Cp

Fig.6.1 characteristicsCp Vs. k

6.2.2 Conventional Fixed Speed System

Most of the wind turbines now in operation are fixed-speed systems. The turbine is coupled to

a cage rotor induction generator through a gearbox and the stator of the generator is tied to the three

phase grid through a transformer. The grid frequency therefore, determines the mechanical speed of

the generator/turbine shaft, the slip being nominally of the order of 5%. This system, even though,

apparently simple and reliable, severely limits the quantity of power generated and has several

associated disadvantages that require major attention.

In order to understand the implications of using a variable speed system, the design and

operation of a fixed-speed system is to be investigated in a more detailed manner. A practical system

is considered where a Vestas V27 turbine is coupled to a 225 kW, 50 Hz induction generator

[Appendix D]. The machine has two stator windings; one with 6 poles with a rated shaft speed of

1008 rpm and the second with 8 poles corresponding to a shaft speed of 750 rpm. The maximum

speed of the turbine shaft is 43 rpm. This requires a gearbox with a ratio of 43:1008 i.e. 1:23.4. Once

the rated power of the generator is reached, the turbine goes into pitch control mode (where the pitch

angle of the blade is mechanically adjusted to limit the turbine power transfer). The implication of

pitch control is that for a given tip-speed ratio, the value of Cp decreases with a corresponding

reduction in the turbine power.

In Fig.6.2, power-curves of the turbine are plotted for wind velocities from 5 m/s to 14 m/s

against the turbine shaft rpm and Fig.6.3 shows the same curves against the generator shaft rpm with

the gear-ratio of 1:23.4. The operating locus for the constant speed system is given by the line A-B.


144

From these characteristics it is observed that at a wind-speed of around 14 m/s the rated power of the

machine (225 kW) is reached at 43 rpm (corresponding to approximately 1008 rpm of the rotor shaft).

This is indicated by the point B. It can also be seen that the maximum power that the turbine can

actually generate at a wind-speed of 14 m/s is about 460 kW, provided the turbine shaft speed is

allowed to vary upto 85 rpm and a generator of adequate capacity is used.

The fixed speed system in this case is designed to operate at 1000 rpm, whereas operation at

1500 rpm would result in substantially higher generation. The reason is as follows. It may be

observed from the turbine characteristics that at 1000 rpm the change in turbine power for a large

change in wind velocity is not significant. Even for a wind velocity of 20 m/s the power generated can

only be 250 kW. This ensures that the generator is not overloaded to a great extent even if there is a

sudden gust of wind. Pitch control comes into operation once the rated power is reached; but this

hydraulically operated mechanism being sluggish, transient overshoot of the generator power cannot

be prevented. So operating at 1000 rpm ensures that the generator is not overloaded under sudden

high wind conditions. However, at 1500 rpm the rise in power with wind velocity is much sharper as

observed from Fig.6.3. Fixed speed systems are therefore, designed for lower shaft speeds where the

turbine power curves (for different wind velocities) are close to each other. Thus a natural protection

against overslip and overload is provided for the generator, but utilization of the turbine capability is

poor.

A cage rotor induction generator when connected to the grid draws the magnetizing current

from the line thereby reducing the stator power factor. Under low wind conditions, when the active

power generation is low, the machine mainly draws reactive power from the grid and the stator power

factor is extremely poor. The lagging reactive power is compensated by connecting capacitor banks

across the line. Depending on the active power generation, these capacitors are either cut-in or cut-out

to regulate the average power factor of the generator between 0.95 and 1. But the random switching

of the capacitor banks gives rise to undesirable transients in the line currents and voltages. In a grid,

where hundreds of such machines are installed, these capacitive switchings can cause severe

overvoltage problem.

From Fig.6.3 it may be noted that if the machine is always operated at 1000 rpm, then the

power generated for low wind velocities (<5 m/s) will be extremely small. In order to boost the

generated power under such circumstances another winding of reduced power capacity (50 kW) is

added to the motor with 4 pole pairs, with a synchronous speed of 750 rpm. The controller switches


145

over from one winding to the other depending upon the wind condition. This feature makes the

machine nonstandard and expensive. Design compromises are also associated with this addition of a

separate winding. It is seen that the no-load current for the main generator is about 235 A (about 0.59

p.u.) [Appendix D], which is unusually high for a machine of 225 kW rating.

0 20 40 60 80 100 1200

100

200

300

400

500

Turbine Shaft Speed (rpm)

Tur

bine

Pow

er (

kW)

A

B

S

T

Q

v1 v2 v3v4

v5

v6

v7

v8

v9

P

14 m/s

v10

12 m/s

11 m/s

8 m/s

Fig.6.2 Power curves of the wind turbine against turbine shaft rpm (v1=5m/s, v2=6m/s .. v10= 14m/s)

0 500 1000 1500 2000 25000

100

200

300

400

500

A

B

v1v2

v3

v4

v5

v6

v7

v8

v9

v10

Generator Shaft Speed (rpm)

Tur

bine

Pow

er (

kW)

Fig.6.3 Power curves of the wind turbine against generator shaft rpm with gear-ratio of 1:23.4


146

6.3 Variable Speed System using Cage Rotor Induction Machine

A variable speed WECS enables enhanced power capture as compared to a constant speed

constant frequency system. The rotor speed can be made to vary with the changing wind velocity so

that the turbine always operates with maximum Cp, within the power and speed limits of the system.

The power limit is governed by the choice of generator rating, while the speed limit is dictated by the

mechanical design of the turbine and the tower. Selection of the generator can be judiciously made

based on the average wind velocity during the peak wind season. To exploit the power transfer

capability adequately, turbines operating at higher speeds are being built; some of them being

commercially available as well.

In the following sections, two design examples for variable speed systems are furnished; the

first one uses a cage rotor induction machine as the wind electric generator, and the second one uses a

slip-ring induction generator. These systems are compared with the conventional fixed speed system

in terms of component size, ratings etc. In a later section, the energy captured by all the three systems

over a defined wind function is calculated through simulation. The results demonstrate the superior

performance of the variable speed systems.

6.3.1 Design Example

To present a comparative picture between fixed speed and variable speed systems the same

turbine characteristics (Vestas V27) are considered. It is assumed that the turbine shaft speed is

allowed to vary upto 120 rpm. (This implies a maximum tip speed of 170 m/s, which is reasonable for

a system of few hundred kW rating [57].) It is also assumed that the average wind velocity during the

peak wind season is 12 m/s.

Fig.6.4 Variable speed grid-connected WECS with cage rotor induction machine

3 PhaseTransformer

Front endConverter

3 Phase3 Phase

Inverter

Cage RotorInduction Machine

Gear box

Wind turbine


147

(a) Generator and Gearbox Selection

From Fig.6.2, it may be noted that the maximum power that can be delivered by the turbine at

the wind velocity of 12 m/s is about 290 kW corresponding to the shaft speed of 75 rpm. On this

basis, a 300 kW, 415V squirrel cage induction machine is selected. The synchronous speed of the

machine is kept at 1000 rpm by using a 6-pole machine. Assuming that the rated power is reached at

the rated frequency, the gear ratio works out to be 1000:75 i.e. 13.3:1. The cost of the gearbox can be

brought down by using a lower gear-ratio. This is possible by selecting a machine with higher pole

pairs. However, with increase in the number of pole pairs the machine frame size increases. The

magnetizing current requirement also increases significantly.

(b) Converter Rating

For variable speed control, the back-to-back PWM converter configuration as shown in

Fig.6.4 is used on the stator side. The stator side converter supplies the required reactive power and

also handles the full active power generated by the machine. The line side converter transfers the

generated active power to the grid at unity power factor and regulates the dc bus voltage. The size of

the converters, therefore, is dictated by the generator rating. With a provision for overloading, the

ratings of the converters can be taken as 375 kVA.

For this power rating, IGBT modules are ideally suited, so that a high switching frequency of

about 5 kHz can be employed to limit the current ripple in both the converters to less than 10%. The

device ratings can be computed as follows.

is,rms(max) = 375000/(ª3 $ 415) = 522A

is,peak = 738A

Allowing 10% peak-to-peak switching ripple, the peak current rating for the device may be taken as

5% more than .is,peak

is,peak(max) = 1.05 $ 738 = 775A

Using a maximum modulation index of 0.9 with sine-triangle modulation, the dc bus voltage that is

required is given by

udc = 2 $ (415 $ ª2/ª3) $ 0.9 = 753V

The dc bus can be designed for 750 V.


148

Two paralleled 1200V, 400A IGBT modules can be selected. The same devices may be used

for both the converters, even though the line side converter will be operating at upf and need not carry

any reactive current.

(c) DC Bus Capacitor

Assuming no-load current to be 15% of the rated current (i.e.62.6A) and allowing 0.5% dc bus

voltage ripple due to reactive loading, the dc bus capacitance can be computed [Appendix E] as

C = ª2 $ inl/ RPU $ udc $ 24 $ frated

= ª2 $ 62.55/(0.005 $ 750 $ 24 $ 50)

= 19658 lF

iripple,rms = ª2/ª3 $ inl

= ª2/ª3 $ 62.55 = 51A

The capacitors are divided in three banks corresponding to three phases. (Each phase consists

of two legs, one for the front end converter and the other for the machine side converter). The voltage

rating of 750V cannot be achieved with a single electrolytic capacitor in each parallel branch. 2,

3300µF, 450V capacitors may be used in series for each branch. 12 such parallel units (a total of 24

capacitors) need to be connected to meet the required capacitance value. Hence, each bank comprises

4 such units. The effective capacitor value becomes

.C = 12 $ 3300/2 = 19800lF

The rms ripple current in each branch is 4.25A, which is within allowable limits.

(d) Input Transformer

The line side converter is interfaced to the power grid through a transformer. Potential wind

sites are usually remote and the transmission grid is available at a higher voltage. (For example, in

south Tamil Nadu, India, the wind farms are connected to 6.6 KV power grid). The transformer can

be rated for 375 KVA with a turns ratio of 6.6KV:415V.

(e) Line Side Inductance

The line side series reactance decides the current ripple for the front end converter. Hence, a

very low value cannot be used. With 5 kHz switching frequency and 0.25 p.u. choke the switching

ripple is within the design limits of 10% (checked through simulation). Using this value,

Lfe = 0.25 $ (415/ª3)/ is,rms $ 2 $ o $ 50


149

= 0.25 $ (415/ª3)/(417 $ 2 $ o $ 50)

= 457.5lH

Therefore, 450µH series inductance per phase can be selected.

6.3.2 Operating Region and Control

With the designed gear ratio, the V27 power curves are plotted in Fig.6.5. The operating

region is also marked on the characteristics. Once the cut-in wind velocity (3-4 m/s) is reached, the

system is connected to the grid and it starts generation. Control over the machine torque is exercised

using field oriented control or direct torque control algorithms. Upto the rated operating point of the

generator corresponding to 300 kW, 1000 rpm, the system runs in peak-power tracking mode either

through torque control or through speed control. (These control algorithms are discussed in a later

section). Beyond this point, the power is kept constant with increasing speed. This is achieved by

reducing the torque through field weakening. With 33% reduction, the speed can be increased upto

1500 rpm, the corresponding shaft speed being 1500/13.3 i.e. 113 rpm (within the allowable limit). At

this speed the system goes into pitch-control mode which restricts further increase of speed and

power. The operating region is also illustrated in the torque-speed characteristics in Fig.6.6.

The advantages of this variable speed WECS with respect to the conventional system can be

summed up as follows.

(i) For the same turbine, it allows higher power capture, thereby increasing the annual energy output

significantly. The generator rating can be judiciously selected based on the wind potential of the

site.

(ii) The proposed system is capable of providing the required reactive power of the induction

generator from the dc bus capacitance. The front end converter is controlled to operate at unity

power factor at the grid interface irrespective of the active power generation. With the converter

switching at high frequency, the currents injected into the line are sinusoidal without any

undesirable transients

(iii)Variable speed operation also allows a standard single winding machine to be used over the entire

operating range of the turbine. Hence the machine cost is reduced and the complexities associated

with winding-switchovers are eliminated.

(iv)Since torque of the machine is controlled (either by field-orientation or DTC) the generator cannot

be overloaded at any point of time beyond the prescribed limits.


150

0 200 400 600 800 1000 1200 14000

100

200

300

400

500


Tur

bine

Pow

er (

kW)

Ptarget

v1 v2v3

v4

v5

v6

v7

v8

v9

v1014 m/s

12 m/s

Fig.6.5 Operating region of WECS with cage rotor induction machine in the planeP − z

0 200 400 600 800 1000 1200 1400

0

1000

2000

3000

4000

5000


Tur

bine

Tor

que

(Nm

)

Mdtarget

v1v2

v3v4

v5

v6

v7

v8

v9

v1014 m/s

12 m/s

Fig.6.6 Operating region of WECS with cage rotor induction machine in the plane m − z


151

6.4 Variable Speed System using Wound Rotor Induction

Machine

Rotor side control of slip-ring induction machine can be effectively used for variable speed

WECS because of its inherent VSCF operation capability. The same arrangement, as discussed in the

previous chapters, applies to WECS, the prime mover in this case being a wind turbine (Fig.6.7). In

order to bring out the relative merits of using the proposed scheme a similar design example is

presented with the same turbine characteristics.

6.4.1 Design Example

(a) Generator and Gear Ratio

With the same assumptions regarding wind conditions and speed range, a 6 pole slip-ring

induction machine of 300 kW is selected. One important design criterion for slip ring induction

machines is the choice of rotor and stator turns ratio. It is advantageous to put lesser number of turns

on the rotor side. However, this increases the current rating of the rotor winding. A compromise can

be achieved by using a delta-connected stator winding and a star-connected rotor winding. The rotor

turns can be made times the stator turns to make the effective turns ratio 1:1; the current rating1/ª3

for the rotor winding is also not largely enhanced. The synchronous speed being 1000 rpm and

assuming that rated stator power is reached at the rated frequency, the selected gear ratio remains

same, i.e.13.3:1.

Fig.6.7 Variable speed grid-connected WECS using doubly-fed wound rotor induction machine

3 PhaseTransformer

Front endConverter

3 Phase3 Phase

Inverter

Wound RotorInduction Machine

Gear box

Wind turbine


152

(b) Converter Rating

The converter rating in this case depends on the range of operating speed. Assuming 0.5 p.u.

slip on either side of the synchronous speed, the converter rating can be half the power rating of the

stator. Allowing the same amount of overloading as earlier, the converter can be rated for 375*0.5 i.e.

187.5 KVA.

It may be noted that the equivalent current ratings for the stator and rotor are same for the

selected turns ratio. So, the current rating of the devices, as selected in the previous case, also applies

here. However, the maximum voltage that needs to be applied to the rotor terminals is half the stator

voltage. Therefore, a dc bus of 375V (750/2) is sufficient in this case for the same maximum

allowable modulation index of 0.9.

For the rotor side converter and front end converter, 2 paralleled 600V, 400A IGBT modules

can be selected. If desired, the reactive power can be distributed equally between the rotor and the

stator sides, and the front end converter can be operated at leading power factor to compensate for the

lagging VAR drawn by the stator. This results in equal current loading for the rotor side and front end

converters. However, since the reactive current is only about 10-15% of the rated current, it does not

make a significant difference even if the rotor side converter supplies the full reactive power and the

front end converter is operated at unity power factor.

(c) DC Bus Capacitor

Since the reactive current requirement is almost the same for a cage rotor machine and a

wound rotor machine of 300 kW rating [67], the same capacitor value needs to be used. However, the

voltage rating is reduced by half. Using single 450V capacitors for each parallel branch may not

provide sufficient voltage margin when the bus is charged to 375V. A more realistic design would be

to use 2, 250V capacitors in series in each branch. The configuration of the capacitor banks remains

the same i.e. a total of 24, 250V, 3300 µF capacitors are required for the entire bank. The rms ripple

current rating in each branch remains at 4.25A as in the previous case.

(d) Input Transformer

The transformer connecting the system to a 6.6KV grid should have two secondaries; one

winding connecting the stator being rated at 415V and the second winding, connecting the front end

converter being rated at 415/2 i.e.208V. Without this voltage reduction on the rotor side, it is not

possible to operate the dc bus at 375V. Consequently the voltage ratings for the devices and the


153

capacitor bank cannot be optimized. The rating of the transformer also has to be boosted up by 50%

because of the extra power being generated from the rotor side during supersynchronous operation.

Therefore, a 375*1.5 i.e. 560 KVA transformer is to be used with two windings having turns ratio of

6.6KV:415V/208V.

(e) Line Side Inductance

The same per unit reactance of 0.25 can be used in this case. However, since base impedance

is reduced to half (due to reduction in input voltage), 225µH per phase inductance is sufficient for the

present scheme.

6.4.2 Operating Region and Control

The operating region of the WECS with rotor side control is shown in Fig.6.8. The speed of

operation is limited to the range 500 rpm-1500 rpm. When the wind velocity exceeds the cut-in value,

the system is allowed to accelerate until the generator shaft speed reaches 500 rpm. The system is

connected to the grid at this point and rotor side control is brought in. While in operation, if the

generator power falls below 40 kW (corresponding to 6 m/s of wind velocity), the rotor speed is

maintained at 500 rpm by operating in the speed control mode. Once the power exceeds 40 kW, the

system goes into peak-power tracking mode upto the synchronous speed of 1000 rpm. At this

operating point, the stator power has reached its limit and the rotor power is zero (zero slip). This also

corresponds to the rated torque condition. From 1000 rpm till 1500 rpm the machine operates at

constant rated torque with power being recovered from the rotor circuit as well. The total generated

power follows a straight line locus above the synchronous speed with an additional 150 kW being

regenerated from the rotor side at 1500 rpm. This is a distinct advantage as compared to cage rotor

induction machine because, in this case, the stator field is always constant and, the rated torque can be

maintained upto the maximum speed. Therefore, operation upto a higher wind velocity can be

achieved before the system goes into pitch control mode. The loci for the stator and rotor powers are

also shown in Fig.6.8. Fig.6.9 indicate the operating region in the torque-speed characteristics.

The advantages of a variable speed WECS using rotor side control of slip-ring induction

machine as compared to variable speed, cage rotor induction generator can be summed up as follows.

(i) The ratings of the converters are significantly reduced. This is manifested in the lower voltage

ratings required for the devices.


154


0 200 400 600 800 1000 1200 1400

0

-100

100

200

300

400

500

Tur

bine

Pow

er (

kW)

Pstator

Pgen

Protor

v1 v2v3

v4

v5

v6

v7

v8

v9

v10

14 m/s

12 m/s

6 m/s

Fig.6.8 Operating region of WECS with wound rotor induction machine in plane P − z

0 200 400 600 800 1000 1200 1400

0

1000

2000

3000

4000

5000


Tur

bine

Tor

que

(Nm

) Mdtargtet

v1v2

v3v4

v5

v6

v7

v8

v9

v10

14 m/s

12 m/s

6 m/s

Fig.6.9 Operating region of WECS with wound rotor induction machine in planem − z

(ii) The stator flux is constant over the entire operating region. Therefore, the torque can be

maintained at its rated value above the synchronous speed. This results in higher power above the

synchronous speed (i.e. at high wind velocities) when compared to a cage rotor induction

generator of the same frame size. Thus the machine utilization is substantially improved.


155

(iii)A lower dc bus voltage is required. This reduces the voltage rating of the capacitor bank and

significant saving in the cost of the capacitor.

(iv)The line side inductance value is also reduced.

Table 6.1 Summary of the design results for the three WECSs.

500 - 1500 rpm0 - 1500 rpmFixed1000 rpm/750 rpm

Speed Range(generator shaft)

450 kW300 kW225 kWMaximumPower Capture

560 kVA6.6KV:415V/208V

375 kVA6.6KV:415V

250 kVA, 6.6KV:415VTransformer

225 µH450 µHNoneFEC Inductance

19800 µF(2, 250V, 3300µF in series

in each branchX

12 parallel branches)

19800 µF(2, 450V, 3300µF inseries in each branch

X 12 parallel branches)

None(PF correction capacitor bank

connected to the ac mains)

DC BusCapacitance

375V750VNoneDC Bus Voltage

187.5 KVA,600V,400AX2 IGBT modules

375 KVA,1200V,400AX2 IGBT modules

NoneConverter

13.3:113.3:123.4:1Gear Ratio

Wound rotorinduction machine

415V, 300 kW,50Hz, 6-pole

Cage rotor induction machine415V, 300 kW,

50Hz, 6-pole

Two winding cage rotor induction machine

Main:415V, 225 kW, 6 poleAuxiliary:415V, 50 kW, 8 pole

Generator

V27V27V27Turbine

Variable Speed System withSlip Ring Induction

Machine

Variable Speed Systemwith Cage Rotor

Induction Machine

Constant Speed System withCage Rotor Induction Machine

6.5 Simulation of WECS

A simplified model of the electromechanical system is taken for simulation of the different

WECSs. The electrical and mechanical losses of the system are neglected. The limits of power and

speed are imposed. When the maximum power is reached it is assumed that pitch control comes into

operation. However, the dynamics associated with this is not considered. The basic objective of this


156

particular section is to determine the energy capture for the three systems under consideration. A wind

function is defined and, the turbine power and target power for the generator are determined. Current

controller dynamics are ignored for the time being and it is assumed that the actual generated power

tracks the reference instantaneously. A more detailed simulation including the rotor side current

controllers and a realistic wind profile is presented later where the rotor current control scheme is also

included.

Wind is a randomly fluctuating variable. Therefore, it is difficult to model and evaluate the

performance of a WECS theoretically without implementing it and subjecting it to actual

environmental conditions. Some theoretical predictions are possible with the statistical data of wind

variations at a particular location [60]. However, these are more appropriate for optimal planning of

WECS in terms of cost, overall energy output per unit land area etc. [61], rather than evaluating the

relative performances of the different generating schemes. For effective performance evaluation the

system has to be operated over the entire range of wind variations so that all the design limits are

reached. This is simulated by defining a wind function as

Vw = 10 - 2.cos(2.pi/20)t - 5.cos(2.pi/600)t (6.3)

Fig.6.10(a) shows the wind profile; it is observed that the wind varies between maxima and mimima

with a periodicity of 10 secs and these peaks and troughs are modulated over a longer period with a

periodicity of 10 mins. The minimum touches the cut-in speed of 3 m/s, whereas the global maximum

reaches 25 m/s. All the three systems are subjected to this wind function and the shaft speed,

generator power and generated energy are plotted.

6.5.1 Fixed Speed System

In this case, the generator shaft speed is kept constant at 1000 rpm (since the allowable slip is

only 8 rpm which can be neglected). When the turbine input power falls below 50 kW, the second

winding with 8 poles is brought into operation, in which case the speed is fixed at 750 rpm. Since the

turbine shaft speed is constant, there is no change in the stored energy of the system and the blade

inertia does not come into picture. Neglecting losses, the turbine and generator powers are the same.

The total energy output due to the defined wind function over a period of 10 minutes is found to be

21.5 kWh. The relevant simulated waveforms are given in Fig.6.10(a) through Fig.6.10(d).


157

0 100 200 300 400 500 6002

4

6

8

10

12

14

16

18

Time (secs)

Win

d V

eloc

ity (

m/s

)

Fig.6.10(a) Wind velocity function

0 100 200 300 400 500 6000

10

20

30

40

50

Time (secs)

Tur

bine

Sha

ft S

peed

(rp

m)

Fig.6.10(b) Turbine shaft speed for CSCF system


158

0 100 200 300 400 500 6000

50

100

150

200

250

secs

Gen

erat

or P

ower

(kW

)

Fig.6.10(c) Generator power for CSCF system

0 100 200 300 400 500 6000

5

10

15

20

25

30

35

40

secs

Gen

erat

ed E

nerg

y (k

WH

)

Fig.6.10(d) Generated energy for CSCF system


159

6.5.2 Variable Speed System using Cage Rotor Induction Machine

The system is designed to track the peak power by varying the rotor speed upto the rated

operating point corresponding to 300 kW, 1000 rpm. From 1000 rpm to 1500 rpm the power is kept

constant by reducing the generator torque through field weakening. Beyond this point the speed and

power are held constant through pitch control. The optimum operating point tracking can be achieved

by several algorithms, the simplest being operation in torque control mode. This method, as discussed

below, is employed in the present simulation for energy calculation.

In order to operate the system in the peak-power tracking mode, Cp has to be maintained at

. This corresponds to a certain tip-speed ratio λ opt. Therefore, for any wind velocity, theCp max

target power can be written as

(6.4)Pt arg et = 0.5 $ Cp max $ q $ A $ v3

Eliminating v from Eq.(6.4) using Eq.(6.2)

Pt arg et = 0.5 $ Cp max $ q $ A $z t $ Rkopt

3

= 0.5 $ Cp max $ q $ A $ Rkopt

3$ zt

3

(6.5)= Kopt $ zt3

It is seen that the target power varies as the cube of the rotor speed, other parameters being

dependent on the turbine characteristics and assuming air density to be constant. Hence the torque

corresponding to the peak-power locus varies as the square of the rotor rpm.

(6.6)md,t arg et = Kopt $ zt2

The generator torque is always set in accordance to this desired locus. The speed of the shaft

is free to vary and therefore, it settles at an operating point where the generated torque equals the

turbine torque. Since the intersecting points between the two curves correspond to the maximum

power points, it is ensured that the generator always extracts the maximum possible power from the

turbine irrespective of the wind speed. This can be explained with reference to Fig.6.2. Let the system

be operating at the point S, corresponding to a wind velocity of v4 (=8 m/s) and generating about

90kW. Under this condition if the wind velocity increases to v7 (=11 m/s), immediately the turbine

power rises to 200 kW as indicated by point P. Since the speed of the system cannot change

instantaneously, the generator still continues to deliver 90 kW. The driving power being more, the


160

system accelerates, and with increasing speed the generated power also rises until it reaches the stable

operating point T. When the wind speed falls the operating point for the turbine shifts to Q, but the

generator power does not immediately change. This gradually decelerates the system back to S. In this

process a part of the energy from the wind is stored by the inertia of the system during increasing

wind velocities; which is released during deceleration in a controlled manner.

From Fig.6.5 and Fig.6.6 it can be seen that, beyond the rated speed the generator torque is

varied as

(6.7)md,t arg et =Pg,rated

z t

The system is simulated with the same turbine data [Appendix D]. It is observed that due to

constant variation in the wind velocity the system is always in the transient state searching for the

optimum operating point. The large inertia of the rotating blades tend to reduce the fluctuations in

torque and power to a substantial extent. The relevant plots are given in Fig.6.11(a) through

Fig.6.11(d). The system is started with an initial speed of 10 rpm. (Before this point the turbine torque

is almost zero and the system fails to accelerate in the simulation model. In practice the pitch angle is

controlled to start the system.) The generator power is limited to 300 kW and the generator shaft

speed is limited to 1500 rpm. The corresponding turbine shaft speed is 113 rpm. It is assumed that the

pitch control comes into operation beyond these limits and restricts the operating region. However,

the dynamics related to the pitch control mechanism are neglected for simplification. It is seen that

the energy output for the defined wind function (Eq.6.3) over 10 minutes is 28.5 kWH, an increment

of 32.5% with respect to the previous case.

It is interesting to note that this control mechanism eliminates the need for measurement of

wind velocity to track the peak-power locus. Moreover, since the torque of the machine is directly

controlled the generator is never allowed to exceed its maximum torque capability; so the problem of

overloading or pulling out does not arise and the pitch control mechanism can operate more

effectively in this mode of operation.


161

0 100 200 300 400 500 6002

4

6

8

10

12

14

16

18

Time (secs)

Win

d V

eloc

ity (

m/s

)


0 100 200 300 400 500 6000

20

40

60

80

100

120

Time (secs)

Tur

bine

Sha

ft S

peed

(rp

m)

Fig.6.11(b) Turbine shaft speed for VSCF system using cage rotor induction machine


162

0 100 200 300 400 500 6000

50

100

150

200

250

300

350

secs

Gen

erat

or P

ower

(kW

)

Fig.6.11(c) Generator power for VSCF system using cage rotor induction machine

0 100 200 300 400 500 6000

5

10

15

20

25

30

35

40

secs

Gen

erat

ed E

nerg

y (k

WH

)

Fig.6.11(d) Generated energy for VSCF system using cage rotor induction machine


163

6.5.3 Variable Speed System using Wound Rotor Induction Machine

The same method of control to track peak power is used in this case. The generator speed is

restricted between 500 rpm and 1500 rpm (0.5 p.u. slip). Therefore, for wind velocities lower than

6m/s, the system is operated in constant speed mode at 500 rpm. The peak power point tracking

algorithm is effective from 500 rpm to 1500 rpm corresponding to wind velocities of 6 m/s to 12 m/s

respectively. Below 50 kW, the system is run in speed control mode at a constant speed of 500 rpm.

When the generator power exceeds this threshold value, it switches over to peak-power tracking by

torque control as discussed in the previous section. From 1000 rpm till 1500 rpm, the torque is kept

constant at the rated value, beyond which, pitch control becomes effective. Thus the stator power is

limited to 300 kW beyond 1000 rpm, whereas the rotor generates an additional amount depending on

the slip. The question of flux weakening does not arise in this case because the stator flux is dictated

by the grid voltage and frequency. The relevant simulated waveforms are shown in Fig.6.12(a)

through Fig.6.12(f). The energy output in this case for the same wind cycle for 10 minutes is found to

be 35 kWH, an increase of 22.8% with respect to the variable speed system using cage rotor machine

and 62.7% with respect to the conventional fixed-speed system. The improvement in energy capture

is due to the rated torque capability of the machine upto the maximum speed. Above the synchronous

speed, even though the stator power is saturated to 300 kW, the rotor in addition generates a

substantial amount of power, so that the net power captured is largely enhanced. The advantage of

this scheme lies in the fact that this excess power is obtained from the same frame size of the

generator.

6.6 Detailed Simulation of Variable Speed WECS using Wound

Rotor Induction Machine with Rotor Side Current Control

In this section simulation of the doubly-fed grid connected wound rotor induction generator

operating under with a realistic wind profile is presented. Generation of the wind profile using a

random function generator is shown in Fig.6.13. The function generator output is passed through a

first order filter to smoothen out sharp fluctuations. The output of the function generator varies from 0

to 2. This is scaled by the filter gain and added to an average value of 12. The variation in wind

velocity is thus in the range of 0 to 18 m/s.


164

0 100 200 300 400 500 6002

4

6

8

10

12

14

16

18

Time (secs)

Win

d V

eloc

ity (

m/s

)


0 100 200 300 400 500 6000

20

40

60

80

100

120

secs

Tur

bine

Sha

ft S

peed

(rp

m)

Fig.6.12(b) Turbine shaft speed for VSCF system using wound rotor induction machine


165

0 100 200 300 400 500 6000

50

100

150

200

250

300

350

secs

Sta

tor

Pow

er (

kW)

Fig.6.12(c) Stator power of wound rotor induction machine for VSCF system

0 100 200 300 400 500 600-200

-150

-100

-50

0

50

100

150

200

secs

Rot

or P

ower

(kW

)

Fig.6.12(d) Rotor power of wound rotor induction machine for VSCF system


166

0 100 200 300 400 500 6000

100

200

300

400

500

secs

Gen

erat

or P

ower

(kW

)

Fig.6.12(e) Total generated power for VSCF system using wound rotor induction machine

0 100 200 300 400 500 6000

5

10

15

20

25

30

35

40

secs

Gen

erat

ed E

nerg

y (k

WH

)

Fig.6.12(f) Generated energy for VSCF system using wound rotor induction machine


167

3

s+2*pi/20

FilterRandomFunction Generator

++

Sum

12

Average Speed

1

Wind Velocity

Fig.6.13 SIMULINK block diagram of the random wind profile generator

The torque reference is generated using the same torque control law as described in section

6.5. The q-axis current reference is derived from this torque reference assuming the stator flux isirq&

constant at the nominal value. The d-axis reference is kept at 0, so that, the stator supplies the total

reactive power required by the machine. The same rotor current controller is employed with rotor

position feedback. The simulation results are presented in Fig.6.14(a) through Fig.6.14(f). The speed

variations of the generator shaft (Fig.6.14(b)) tend to follow the pattern of the wind profile

(Fig.6.14(a)) to track the peak power. The generator torque (Fig.6.14(c)) and the stator generated

power (Fig.6.14(d)) differ by a scaling factor, which is the synchronous frequency. The generator

torque is saturated at its rated value so that the stator power is limited to its nominal rating of 300

kW. The rotor power varies between -40 kW (in the subsynchronous range) and 110 kW (in the

supersynchronous range) as seen from Fig.6.15(e). This is in agreement with the operating point locus

shown in Fig.6.8 The generator output power is the sum of the stator and the rotor powers and it is

observed that a substantial amount of power is generated from the rotor side even after the stator

power saturates to its rated value.

6.7 Practical Implementation of Variable Speed System using

Wound Rotor Induction Machine in Torque Control Mode

The peak power tracking algorithm is implemented on the experimental setup. The turbine

characteristics are simulated by a dc motor driven by a commercial drive. The system is run for

different wind velocities and the corresponding steady-state operating points are found to be close to

the peak power points in the curves. Transients due to step changes in wind velocity are alsoP − z

recorded and presented in this section.


168

0 100 200 300 400 500 6000

5

10

15

20

25

secs

Win

d V

eloc

ity (

m/s

)

Fig.6.14(a) Wind velocity profile

0 100 200 300 400 500 6000

200

400

600

800

1000

1200

1400

1600

secs

Gen

erat

or S

haft

Spe

ed (

rpm

)

Fig.6.14(b) Generator shaft speed


169

0 100 200 300 400 500 6000

500

1000

1500

2000

2500

3000

secs

Gen

erat

or T

orqu

e (N

m)

Fig.6.14(c) Generator shaft torque

0 100 200 300 400 500 6000

50

100

150

200

250

300

350

secs

Sta

tor

Pow

er (

kW)

Fig.6.14(d) Stator power


170

0 100 200 300 400 500 600-150

-100

-50

0

50

100

150

secs

Rot

or P

ower

(kW

)

Fig.6.14(e) Rotor Power

0 100 200 300 400 500 6000

50

100

150

200

250

300

350

400

450

secs

Gen

erat

or P

ower

(kW

)

Fig.6.14(f) Generator power


171

6.7.1 Simulation of the turbine characteristics

The V27, characteristics corresponding to four wind velocities v6, v7, v8 and v9 (10P − z

m/s, 11m/s, 12 m/s, 13 m/s) are expressed in per unit and are shown in Fig.6.15. These characteristics

are then stored in the form of lookup tables in the external memory of the DSP as 32 word arrays. The

generator shaft speed is computed, scaled to the resolution of the table and the corresponding turbine

power is then read from memory. The turbine torque is subsequently calculated. This is given as a

reference to the dc drive. The dc drive is a stand-alone unit with an independent analog controller. It

can be operated in either current control mode or speed control mode with external analog references.

In the present case, the torque reference for the dc drive, suitably scaled, is output via the DAC in the

processor board. It is then routed to the reference input of the torque controller. The dc motor is thus

made to emulate the characteristics of the chosen wind turbine.

The system is started in the following manner. Initially, a small constant torque reference is

given to the dc drive. Since the rotor side control is not yet released, the generator torque is zero. The

dc motor speed ramps up. When the speed crosses a threshold (1200 rpm in the present case) the

software ‘switches in’ the turbine characteristics. This further accelerates the motor. In the absence of

any generating torque, the torque controller for the dc drive saturates and the machine speed settles at

the maximum value depending on the input voltage and the field current (nominally at 1875 rpm).

The reference for the generator torque at this speed saturates at the rated value (since the rated speed

is exceeded). So, when the rotor side current control is enabled, the system decelerates and eventually

settles down to a steady-state operating point where the generator torque equals the prime mover

torque.

6.7.2 Experimental Results

The active current reference for the rotor side control is set in accordance with theirq&

computed speed. From Eq.(6.5) it can be inferred that in per unit scale (since 1 p.u. Kopt = 1

is reached at 1 p.u. speed).Pt arg et

Therefore, irq& (pu) =

md&(pu)$(1+rs )

Xo(pu) $ 1ims(pu)

(6.8)=md

&(pu)$(1+rs )ys(pu)

Since under rated condition of input voltage and frequency, is unity,ys


172

irq& (pu) = md

&(pu) $ (1 + rs )

(6.9)= z(pu)2 $ (1 + rs )

With such scaling, the software implementation of the peak power tracking algorithm in

torque control mode becomes very simple. The rotor side reactive current reference is set to zeroird&

for the present experiment. The software modules for the simulation of the turbine characteristics and

generation of the rotor current reference are executed in the 6th slot of the task schedule, as discussed

in Chapter 3. Therefore, the torque references are updated every 341 µs. The system was run for each

of the wind velocities and the operating points were recorded (Fig.6.15). It is seen that the results are

in close proximity to the peak power points in the characteristics. The small errors can beP − z

attributed to (i) the resolution of the turbine characteristics as stored in the memory and (ii) the losses

incurred in the system.

Generator Shaft Speed (p.u.) Experimentaloperating points

1.4

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2

Tur

bine

Pow

er (

p.u.

)

v6

v7

v8

v9

Fig.6.15 Turbine characteristics for experimental verification and operating points


173

Fig.6.16(a) Experimental result for transients in and due to change in wind velocity between v6z irq&

and v8 while operating in torque control mode

Fig.6.16(b) Experimental result for transients in and due to change in wind velocity between z irq&

v7 and v9 while operating in torque control mode

The transients in speed and active current reference for step changes in wind velocity fromirq&

v8 to v6 and vice versa are given in Fig.6.16(a). Similar responses are recorded for transitions

between v7 and v9 in Fig.6.16(b). The settling time between two operating points is decided by the

system inertia and the mechanical losses. Since, the actual system inertia cannot be scaled in the

laboratory setup, the responses do not match the practical dynamic behavior of a WECS.

Nevertheless, it can be concluded that with varying wind conditions, the torque control law works and

the reference torque is dynamically updated to follow the optimum operating point locus. It is also


174

observed from Fig.6.16(b) that beyond 1 p.u. speed (corresponding to 5V in the oscilloscope plot), the

system runs with constant torque with limited to its rated value.irq&

Note: For these experiments, the base power is taken as 3 kW (instead of 4.5 kW as considered in the

earlier chapters). With the base speed still at 1500 rpm, the base torque is 3/4.5 i.e. 0.67 times the

previous case. The scalings for the inner current control loops are not modified; therefore, isirq&

limited to .0.67 i.e. 0.738 p.u. In Fig.6.16(b) it can be seen that saturates at about 3.7 V(1 + rs ) irq&

(corresponding to 0.738 p.u.).

6.8 Peak Power Tracking in Speed Control Mode

In the torque control mode algorithm, the parameter depends on the turbineKopt

characteristics and air density. The terms depending on the turbine dimensions like the blade length

and swept area, and parameters like and are available with turbine manufacturers. TheCp,max kopt

term on the other hand, depends on the climatic conditions prevalent at a particular site. Theq

air-density may vary considerably over various seasons. As a result, the value of computed onKopt

the basis of some nominal air-density value will not result in optimal tracking of the peak power point

under all conditions. Fig.6.17 shows the V27 turbine characteristics when the air-density decreasesq

by 50%. The peak power point trajectory computed with is superimposed on the same curves.Kopt

With the reduction in air-density the turbine output itself reduces; at the same time the tracking

trajectory being incorrect there is considerable loss in output energy. Using the same wind function as

described by Eq.6.3 the simulation of section 6.5.3 is run with = 0.5*1.225 kg/m3 and the earlierq

value of for a period of 10 mins. It can be seen from Fig.6.18 that the output energy for theKopt

same value is 17 kWH, whereas with a correct value of (0.5 times the earlier one) theKopt Kopt

output energy is 19 kWH.

In the following section a method of tracking the peak power is proposed which is

independent of the turbine parameters and air-density. The algorithm searches for the peak power by

varying the speed in the desired direction. In [62], a fuzzy logic based controller is proposed to track

the optimum operating point locus. This system has been designed with a cage rotor induction

machine and, can possibly be extended to a doubly-fed machine. However, it is felt that similar

performance can be obtained even without the complication of implementing a fuzzy controller. In


175

the algorithm presented here, the generator is operated in the speed control mode with the speed

reference being dynamically modified in accordance with the magnitude and direction of change of

active power. The peak power points in the curve correspond to . This fact is madeP − z dP/dz = 0

use of in the optimum point search algorithm.

0 200 400 600 800 1000 1200 14000

100

200

300

400

500


Tur

bine

Pow

er (

kW)

Pgen

Fig.6.17 Turbine characteristics with = 0.5*1.225 kg/m3

0 100 200 300 400 500 6000

5

10

15

20

secs

Gen

erat

ed E

nerg

y (k

WH

)

Fig.6.18 Generated energy for = 0.5*1.225 kg/m3 with correct value of (continuous line) and q Kopt

earlier value of (dotted line)Kopt


176

6.8.1 Peak Power Tracking Algorithm

ω1 ω2

v1

v2

v3P8

P7

P4P3P2

P1 P6P5

Generator Shaft Speed

Tur

bine

Pow

er

Fig.6.19 Shift of operating points in the proposed peak power tracking algorithm

The proposed algorithm is explained with the help of Fig.6.19, where the curvesP − z

corresponding to two wind velocities are shown. Let the present wind velocity be v1. The generator is

run in the speed control mode with a speed reference of (which corresponds to the optimumz1

operating point P1 for v1). The generator output power and speed are sampled at regular intervals of

time. If the wind velocity is steady at v1 the difference between successive samples of active power P

i.e. will be very small and no action is taken. Now let there be a step jump in wind velocity fromDP

v1 to v2. Since the speed is constant, this would result in a change of operating point from P1 to P2.

Therefore, would be large and positive. Corresponding to this change in a positive change inDP DP

speed reference is commanded. The change in speed reference is made proportional to . ThisDz& DP

shifts the operating point from P2 to P3 resulting in a smaller positive change in . Since thisDP

change in is due to a positive change in it implies that the peak power point is further to theDP Dz&

right hand side of the curve. Thus a further positive change in is commanded in proportion to Dz&

. In this process when becomes very small (within some defined band) no further change inDP DP

speed command is given and the system keeps operating at P4. Now if the wind velocity again

changes from v2 to v1, the operating point shifts to P5 resulting in a large negative change in .DP


177

Thus a negative change in speed reference in proportion to is applied. However, this results in aDP

positive change in as the operating point shifts to P6. Since the positive change is due to aDP

negative change in speed command the peak power point is to the left of P6. Therefore, the speed

reference is further reduced. The algorithm continues until is within the pre-defined band and theDP

operating point again slides back close to P1.

The algorithm is implemented in the following manner. The active power is sampled at a

particular rate and the incremental change is computed as

(6.8)DP(k) = P(k) − P(k − 1)

The magnitude of is given byDz&(k)

(6.9)| Dz&(k) | = | DP(k) % Kt |

where is the proportional constant and needs to be selected judiciously. This is discussed later.Kt

However, the sign of has to be properly assigned. If is zero i.e the speedDz&(k) Dz&(k − 1)

reference was not changed in the previous sample then the sign of alone decides the sign of DP(k)

. If is non-zero, the product of the signs of and determines theDz&(k) Dz&(k − 1) Dz&(k − 1) DP(k)

sign of . This can be formulated as follows.Dz&(k)

if ( == 0 ) Dz&(k − 1)

S = Sign( )DP(k)

else

S = Sign( )* Sign( )DP(k) Dz&(k − 1)

= S . | * |Dz&(k) DP(k) Kt

The reference speed is sampled at the same frequency as the active power. If the magnitude of

is within some small defined band then the reference speed is not changed, otherwise it isDP(k)

changed by . Dz&(k)

if( <= )|DP(k)| Pband

z&(k) = z&(k − 1)

else

z&(k) = z&(k − 1) + Dz&(k)

With this reference, the machine is operated in the speed control mode. The controller block

diagram is given in Fig.6.20. A PI controller is employed for the speed loop. The output of the speed

controller is saturated at the rated torque of the machine. Therefore, beyond the rated operating point,

the operation is similar to that in the torque control mode. This is explained with the help of Fig.6.19.


178

Let P4 denote the rated operating point. Now, if the wind velocity increases to v3, the speed controller

will try to increase to generator torque so that the operating point shifts to P7. However, the rated

torque is already applied at P4; hence the prime-mover accelerates the system until a stable operating

point at P8 is reached. Hence, the control naturally ensures that the operating region remains the

same as indicated earlier in Fig.6.8.

Fig.6.20 Block diagram of the controller

P

PeakPowerTrack-ing

ω∗

ω

1/Kc

m*d irq*

ird*

RotorCurrentControl

S1

S2

S3

+ _

6.8.2 Selection of Sampling Frequency

The choice of sampling frequency is critical for the algorithm to work properly. This is related

to the speed loop response time. Let it be assumed that the system was initially operating at point P1

(Fig.6.19) for a wind velocity v1. If the wind velocity changes to v2, the higher motive power tends to

accelerate the system. The speed controller comes into operation and holds back the system by

increasing the generator torque. Hence, the active power generated increases, shifting the operating

point to P2. The peak power tracking logic now gives an increment in the speed command. In order to

accelerate the system the generator torque is instantaneously reduced. The driving torque being more,

the system accelerates. Finally, as the reference speed is approached the generator torque gradually

increases and becomes equal to the turbine torque. If the generator power is computed during the

period when the speed controller is active, it would provide a misleading information about . ADP

sample taken immediately after the increment of the speed command would show that the generator

power actually reduces. On this basis the peak power tracking algorithm will command a decrement

in speed. Therefore, the system will tend to oscillate about the initial operating point with the

machine torque fluctuating in the positive and negative direction. The correct execution of the

algorithm depends on the correct detection of the operating points on the characteristics of theP − z

turbine. Hence, the sampling period for this algorithm should be more than the response time of the


179

speed loop. It may be assumed that the speed loop settles down within 4 times the designed loop time

constant. Therefore, the sampling period is taken as 4 times the speed loop time constant of the

system.

The inertia of the system being high the speed loop time constant cannot be made very small;

this would require a machine of very high torque capability. It is noted that a fast speed controller also

gives rise to large transients in the machine torque, which is reflected in the generated power. This is

a disadvantage of employing speed control in generating systems. However, the dynamics of the

speed controller can be made slower so that the fluctuations in the machine torque can be reduced.

Also in a wind-farm where many such systems are connected to the grid there will be some averaging

effect in the overall power generated and, the power fluctuations of the individual machines would

not be directly reflected on the grid.

6.8.3 Selection of Kt

500 600 700 800 900 1000

100

150

200

0

50

250

300

350

0


Tur

bine

Pow

er (

kW)

∆ω

∆ P

Peak power point locus

Fig.6.21 characteristics in the region of operation of peak power tracking algorithmP − z

determines the change in speed reference for a given change in . Therefore, it depends onKt P

the slope of the characteristics. To choose a value of , an approximate idea of the turbineP − z Kt

characteristics is needed. The characteristics in the region of operation of the peak powerP − z

tracking algorithm are considered. This is shown in the V27 power curves of Fig.6.21. The wind


180

velocities over this region vary between 6 m/s and 12 m/s. The approximate changes in forDz

successive changes in wind velocities and hence are also shown. It is obvious that the isDP Dz/DP

more for lower wind velocities and vice-versa. If is set to the maximum value of in theKt Dz/DP

operating range then, for changes in wind velocities during high wind conditions, the increment in

speed reference would be more than desired. This would result in overshooting of the optimum

operating point. The system would oscillate about the peak power point before it settles down.

Therefore, the maximum value of is limited by the lowest value of . A large value of Kt Dz/DP Kt

will also result in a large transient in generator torque which is not desirable. Hence the value of Kt

selected is substantially lower than the limit imposed by the minimum value of . Dz/DP

From Fig.6.21 it can be seen that the curves are flat-topped near the peak power points.P − z

Therefore, the change in for an increment in speed would be very small in this region. The DP Pband

may be set at 5% of the nominal power rating of the generator. So the final operating point may not

move exactly to the peak power point, but may settle down close to it.

6.8.4 Experimental Results

The same experiment, as discussed in section 6.7, is repeated with the aforesaid algorithm.

The speed loop time constant is designed to be 250 ms, and the sampling period for the active power

is taken to be 1 sec. is selected as 0.25. With these parameters the algorithm is run for the differentKt

wind velocities. The resulting operating points are plotted in Fig.6.22 along with the optimum

operating points. The errors are found to be slightly more in this case compared to the torque control

mode of operation. However, due to the flat-topped nature of the curves of the turbine, thisP − z

does not result in appreciable reduction in the generated power.

The transient response of speed and for transitions between v6 and v8 are shown inirq&

Fig.6.23(a). At instant A, there is a step change in wind velocity from v8 to v6. The torque

instantaneously falls with a small drop in speed. This is because of the time constant associated with

the speed controller. At the subsequent sample (at instant B), this change in active power is detected

and a decrement in speed reference is commanded. The transient in (in the positive direction) isirq&

due to the action of the speed controller. The subsequent samples show insignificant change in active

power and, therefore, almost constant operating speed. The reverse operation is observed when the

wind velocity changes from v6 to v8. In Fig.6.23(b), similar waveforms of speed and areirq&


181

presented for changes in wind velocity between v7 and v9. The saturation of the torque beyond the

rated speed is clearly observed from the plot of .irq&

1.4

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2

Generator Shaft Speed (p.u.)

Tur

bine

Pow

er (

p.u.

)

v6

v7

v8

v9

Experimentaloperating points

Fig.6.22 Turbine characteristics for experimental verification and operating points

Fig.6.23(a) Experimental result for transients in and due to change in wind velocity between v6z irq&

and v8 while operating in speed control mode with proposed algorithm


182

Fig.6.23(b) Experimental result for transients in and due to change in wind velocity between z irq&

v7 and v9 while operating in speed control mode with proposed algorithm

6.9 Conclusion

A comprehensive study on the design and performance of WECS using wound rotor induction

machine with rotor side control has been presented. A comparison with the existing schemes shows,

that for a machine of similar rating, energy capture can be enhanced by using a wound rotor machine.

In this case, the rated torque is maintained even at supersynchronous speeds whereas, in a system

using cage rotor machine, field weakening has to be employed beyond synchronous speed, leading to

reduction of torque. It is therefore, possible to operate the proposed system upto higher wind

velocities. The voltage rating of the power devices and dc bus capacitor is substantially reduced. The

size of the line side inductor is also decreased. Hence, the use of wound rotor induction machine

promises to be economically feasible and attractive for wind power generation.

Peak power tracking using conventional torque control mode is implemented and

experimentally verified. An algorithm for searching the optimum operating point in speed control

mode is proposed. This technique makes peak power tracking independent of the turbine

characteristics and the air density. Experimental verification shows that the performance of the

control algorithm compares well with the conventional torque control method.


183

Chapter 7

CONCLUSION

7.1 General

Rotor side control of grid-connected wound rotor induction machine has shown considerable

promise for use in variable speed constant frequency applications with limited speed range. The

ratings of the power converters to be used are reduced and the machine utilization is improved. Use of

field oriented control technique provides effective control over the active and reactive powers

handled by the machine. The recent availability of high-performance DSPs with integrated peripheral

units for motor control applications, allows easy implementation of sophisticated control strategies.

The scheme has the potential of being a reliable and cost-effective solution to wind power generation

as well as industrial drives.

7.2 Summary of the Present Work

Modeling, simulation and experimental verification of rotor side control strategies are

presented in this thesis. Application of the same to wind energy conversion system is also

investigated. The effect of current injection in the rotor circuit has been first explained with

appropriate phasor and power flow diagrams. It is shown, that in supersynchronous mode of

operation, power is either absorbed or generated by both the stator and the rotor sides, leading to

better utilization of the machine rating.

185

The doubly-fed wound rotor induction machine is modeled in the stator flux oriented

reference frame and the front end converter in the stator voltage oriented reference frame. Direct and

quadrature axes current controllers, consisting of PI loops with appropriate compensating terms to

decouple the dynamics of the two axes, have been designed for both the converters. The design

procedure is direct and follows from the voltage equations derived in the field coordinates.

Simulation results show excellent dynamic response for the current loops. Steady-state unity power

factor operation at the stator terminals and at the grid interface of the front end converter is

demonstrated. The front end converter is shown to be capable of operating at a leading power factor

upto a certain limit.

The control algorithms are implemented on an experimental setup in the laboratory. The IGBT

based power converters are designed and fabricated in a modular way. They are subjected to rigorous

testing including short-circuiting of the dc bus. These power converters have become standard

modules for other drive applications in the laboratory. A generalized digital control platform is also

built using a TMS320F240 DSP. The hardware has sufficient number of digital and analog inputs/

outputs to interface with two converters and the computing power necessary to execute all the control

loops associated with the rotor side and front end converters at a fast sampling rate (8.85 kHz for the

fastest loop). The software is designed for multitasking with a task scheduler coordinating the

execution of the various modules. Firstly, the conventional rotor side field oriented control scheme is

implemented with position sensors. Transient responses for the active and reactive components of

rotor current are in close agreement with the corresponding simulation results. Unity power factor is

achieved both at the front end and stator terminals. The voltage control loop exhibits good regulation

and fast dynamic response. Even for step reversal of load on the dc side, the deviation of the bus

voltage from the set value is within 10%.

A position sensorless algorithm for field oriented control is proposed. The algorithm makes

use of simple transformations to estimate the rotor current in the stator reference frame. With the

rotor current being directly measured in the rotor reference frame, the angle between the two axes is

easily determined. A method of correctly estimating the stator flux without integration of the stator

voltage is employed. The proposed method can be started on-the-fly, i.e., when the rotor is already in

motion. It also operates stably at synchronous speed which corresponds to zero rotor frequency.

These features are verified through extensive simulation and subsequently demonstrated through

laboratory experiments.

Chapter 7 Conclusion

186

An algorithm for directly controlling the active and reactive powers in the stator circuit is

proposed. In this method, the instantaneous magnitude and angular velocity of the rotor flux vector

with respect to the stator flux is controlled by selecting an appropriate switching state of the rotor side

inverter. Instead of integrating the rotor PWM voltage to obtain the rotor flux (as practised in

conventional DTC techniques), a novel strategy to update the sector information is used. The

algorithm does not make use of any machine parameter but relies on the measured active and reactive

powers in the stator for controlling the rotor flux. Features like on-the-fly start and stable synchronous

speed operation are also obtained. The direct power control algorithm is simulated extensively and

verified experimentally. Excellent dynamic response for change in active power is demonstrated.

Application of rotor side control of doubly-fed induction machine to wind energy conversion

systems is studied. The scheme is compared with the existing fixed speed and variable speed systems

using cage rotor induction machine. Power circuit component cost decreases considerably with the

proposed scheme. A lower power rating of the converters also increases the reliability of the system.

The rated torque is maintained even beyond the synchronous speed and hence, energy capture is

improved at higher wind velocities. This additional power is generated through the rotor circuit

resulting in better utilization of the machine rating compared to systems with cage rotor machines.

An algorithm for the tracking the peak power points on the turbine characteristics in the

conventional torque control mode is first implemented. A dc motor driven by a commercial thyristor

drive is used to simulate the turbine characteristics. The machine is run in current control mode with

appropriate reference signals generated from the DSP. Experimentally obtained steady-state operating

points match closely with the optimum operating points on the turbine characteristics. Subsequently,

a novel method is proposed to track the peak power point locus which operates in the speed control

mode. Unlike in the previous case, precise information about the turbine characteristics is not

required. By intelligently varying the speed, the algorithm searches the zero slope locations on the

turbine power-speed curves. This method of tracking the peak power has also been experimentally

verified.

7.3 Scope for Further Research

This thesis successfully demonstrates the potential of doubly-fed wound rotor induction

machine for VSCF operation. Such schemes can also be advantageously used in high power drives.


187

The complete potential of these systems are yet to be fully exploited and there exists scope for further

research.

In case of a grid connected system, the rated torque of the machine can be maintained upto

twice the synchronous speed, provided a 1 p.u. converter is used in the rotor circuit. At the highest

speed, the machine, therefore, delivers 2 p.u. of power from the same frame size, 1 p.u. being drawn

from the stator and 1 p.u. from the rotor. However, with the stator connected to a constant frequency

source, the speed cannot be further increased. Moreover, it is not possible to obtain speed reversal

with the present arrangement. If, instead of connecting the stator to the grid, it is also fed from a

voltage source inverter, the speed range of the system can be further extended and speed reversal can

also be achieved. Such a scheme has been recently proposed by Kawabata [70] et. al., where, a

double-inverter-fed vector-controlled drive is implemented with a wound rotor induction machine

using position sensors.

This scheme will be attractive in high speed, high torque applications. The position sensorless

algorithms proposed in the thesis, can be directly applied to this system. It is possible to achieve

stable zero speed operation, which is still a problem in sensorless schemes for cage rotor induction

machines. Direct torque control algorithms can be developed for such doubly-controlled machines.

The flexibility to control both the stator and rotor flux can improve the dynamic performance of the

drive. It simultaneously opens many possibilities for selecting the switching states of the inverters.

There is a growing awareness that power electronic systems need be modularized, so that

systems of larger ratings can be developed by integrating low power modules. High frequency IGBT

inverters are now commercially available upto ratings of 250 kW. A doubly-controlled induction

machine may be designed with split-phase rotor and stator windings, each being fed from a standard

inverter module. The number of split phase windings used will depend on the required power rating

of the drive. Such an approach towards development of very high power drives can prove

advantageous compared to the current trend for using multilevel converters.


188

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193

Appendix A

MACHINE MODEL IN STATIONARY COORDINATES

is1

ir1

is2

ir2

is3

ir3

ε

Stator Axis

Rotor Axis

(a) (b)

Fig.A1 Three phase and equivalent two phase coil-systems

ira

irb

ε

Rotor Axis

Stator Axisisα

isβ

α−axis

β− axis

a-axis

b-axis

The doubly-fed wound rotor induction machine has symmetrical three phase coil systems both

on the stator and the rotor [Fig.A1(a)], which can be represented by two equivalent two phase coil

systems [Fig.A1(b)]. The rotor axis makes an angle ε(t) with respect to the stator axis.

The current space phasors defined for the stator and the rotor currents in their own reference

frames, namely and respectively can be written as is(t) ir(t)

(A1)is(t) = isa(t) + j isb(t)

(A2)ir(t) = ira(t) + j irb(t)

where (A3)isa = 32 is1

(A4)isb =32 is2 − is3

and (A5)ira = 32 ir1

195

(A6)irb =32 ir2 − ir3

It is assumed that both the stator and rotor windings have isolated neutrals so that

(A7)is1(t) + is2(t) + is3(t) = 0

(A8)ir1(t) + ir2(t) + ir3(t) = 0

The flux linkages of the stator coils along the ‘α’ and ‘β’ axes are given by

(A9)ysa = Ls isa + Lo ira cos e − Lo irb sin e

(A10)ysb = Ls isb + Lo ira sin e + Lo irb cos e

where is the self inductance of the stator coils and is the maximum value of the mutualLs Lo

inductance between the stator and rotor coils.

Equations (A9) and (A10) can be combined to get the stator flux linkage space phasor as

ys = ysa + j ysb

= Ls (isa + j isb) + Lo (ira + j irb) (cos e + j sin e)

(A11)= Ls is + Lo ir eje

Similarly the rotor flux linkage space phasor can be written as

yr = yra + j yrb

(A12)= Lr ir + Lo is e−je

where is the self inductance of the rotor coil. (It is assumed for the sake of simplicity that the rotorLr

coils have the same number of turns as the stator coils.)

The voltage equations for the stator and rotor coils can be written as

(A13)usa = Rs isa + ddt ysa

(A14)usb = Rs isb + ddt ysb

(A15)ura = Rr ira + ddt yra

Appendix A Machine Model in Stationary Coordinates

196

(A16)urb = Rr irb + ddt yrb

where is the stator resistance and is the rotor resistance. Combining Eq.(A13) with Eq.(A14)Rs Rr

and Eq.(A15) with Eq.(A16), the complex voltage space phasors can be derived.

(A17)us = Rsis + ddt ys

(A18)ur = Rrir + ddt yr

Substituting and from Eq.(A11) and Eq.(A12) into Eq.(A17) and Eq.(A18)ys yr

respectively gives

us = Rsis + ddt Ls is + Lo ir eje

(A19)= Rsis + Lsddt is + Lo

ddt ir eje

ur = Rrir + ddt Lr ir + Lo is e−je

(A20)= Rrir + Lrddt ir + Lo

ddt is e−je

Equations (A19) and (A20) represent the electrical dynamics of the stator and rotor circuits in their

respective coordinate systems.

The instantaneous electromagnetic torque developed by the machine is given by

(A21)md = 23

P2 Lo Im is ir eje &

represents the complex conjugate of the rotor current space phasor in the stator coordinateireje &

system. Therefore the complete set of equations that describe the behaviour of the machine is as

follows.

(A22a)Rsis + Lsddt is + Lo

ddt ir eje = us

(A22b)Rrir + Lrddt ir + Lo

ddt is e−je = ur

(A22c)J dzdt + B z = 2

3P2 Lo Im is ir eje &

− ml

(A22d)dedt = P

2 z = ze


197

The rotor current and rotor voltage space phasors in the stator reference frame can be written

as follows.

(A23)sir = ir eje

(A24)sur = ur eje

With the new representation of the rotor current vector in the stationary coordinates, the stator

and rotor voltage equations i.e. Eq.(A19) and Eq.(A20) may be rewritten as

(A25)Rsis + Lsddt is + Lo

ddt

sir = us

and, Rr sir e−je + Lrddt

sir e−je + Loddt is e−je = ur

or, Rr sir e−je + Lrddt

sir e−je − Lr sir j dedt e−je

(A26)+ Loddt is e−je − Lo is j de

dt e−je = ur

Even though Eq.(A26) is written in terms of the stator and rotor current space phasors in the

stationary coordinates, it is still in the rotor reference frame. To transform it to the stator reference

frame both sides have to be multiplied by .eje

Thus, (A27)Rr sir + Lrddt

sir − j ze Lr sir + Loddt is − j ze Lo is = sur

Now, Eq.(A25) and Eq.(A27) depict the electrical dynamics of the machine in the stationary

coordinates. The next step is to represent this machine model in the standard state-variable form

suitable for simulation using available software platforms.

Substitution of from Eq.(A27) in Eq.(A25) and, from Eq.(A25) in Eq.(A27)ddt (sir) d

dt is

and subsequent simplification results in the following.

rTsdis

dt =us

Rs− is − j ze (1 − r)Ts is − j ze

Ts

(1+rs)sir

(A28)+ Ts

Tr

1(1+rs)

sir − 1Rs(1+rr )

sur


198

rTrdsir

dt =sur

Rr− sir − j ze Tr sir − j ze

Tr

(1+rr)is

(A29)+ Tr

Ts

1(1+rr) is − 1

Rr(1+rs ) us

where (A30a)Ls = (1 + rs ) Lo

(A30b)Lr = (1 + rr ) Lo

(A30c)r = 1 − 1(1+rs )(1+ rr )

and are the defined as the leakage factors for the stator and the rotor respectively, and is thers rr r

total leakage factor.

These complex equations can be split into real and imaginary parts using the following

definitions.

(A31a)is = isa + jisb

(A31b)sir = ira + jirb

(A31c)us = usa + jusb

(A31d)sur = ura + jurb

After substitution and separation of the real and imaginary parts, we get the electrical circuit

equations in state-space form as given below.

Xÿ = A X + B U

where (A32a)X = isa isb ira irbT

(A32b)A =

− 1rTs

ze(1+r)r

1r(1+rs )Tr

ze

r(1+rs )

− ze(1−r)r − 1

rTs− ze

r(1+rs )1

r(1+rs )Tr

1r(1+rr )Ts

− ze

r(1+rr ) − 1rTr

− zer

ze

r(1+rr )1

r(1+rr )Ts

zer − 1

rTr


199

(A32c)B =

1rLs

0 − 1r(1+rr )Ls

0

0 1rLs

0 − 1r(1+rr )Ls

− 1r(1+rs )Lr

0 1rLr

0

0 − 1r(1+rs )Lr

0 1rLr

(A32d)U = usa usb ura urbT

The electromagnetic torque developed can be derived from Eq.(A21) as follows.

md = 23

P2 Lo Im isa + j isb ira + j irb

&

(A33)= 23

P2 Lo isb ira − isa irb

(The model of a squirrel cage induction machine becomes a special case of Eq.(A32) when ura = 0

and .)urb = 0


200

Appendix B

DETAILS OF MAJOR POWER CIRCUIT COMPONENTS

B.1 Wound Rotor Induction Machine

3 kW, 415V, 50 Hz, 4 pole, 3 phase

Stator : 415V, ∆ connected, 7.2 A

Rotor : 415V, Y connected, 6.6 A

Various Base and Per Unit Values are

Base voltage = V = 239.6 V415ª3

Base current = 6.26 A

Base impedance = = 239.66.26 W 38.34 W

Base power = W = 4500 W 3 $ 6.26 $ 239.6

Base angular frequency = = 314.16 rad/s2 $ o $ 50

Base torque = = 28.65 Nm.4500( 2

4 )$314.16

Electrical Parameters of the Machine

0.17610.1761Total Leakage Factor (r)

0.10170.1017Rotor Leakage Factor (rr )

0.10170.1017Stator Leakage Factor (rs )

1.4503177 mHMagnetizing Inductance (Lo )

1.5978195 mHRotor Inductance (Lr )

1.5978195 mHStator Inductance (Ls )

0.06832.62 WRotor Resistance (Rr )

0.04061.557 WStator Resistance (Rs )

Values in p.u.Values in SI UnitsNominal Parameters

201

B.2 IGBT Power Converters

Devices used: SEMIKRON SKM12350GB IGBT modules (50A, 1200V) [35]

Heat Sink: Afcoset 80AD with forced air cooling

Busbar: Sandwiched

DC Bus Capacitor for each unit:

2 X 1000 µF Electrolytic (350 V working, 400 V surge) from RESCON

3 X 0.47 µF Film (1000 V) from RS Components

Current sensor card:

Telcon HTP50 ( 50 A)!

Non-linearity 0.2%

Bandwidth 100 kHz

Gain: 1 V output corresponds to 3.55 A

Voltage sensor card:

Uses high CMR isolation amplifier HCPL-7800

Non-linearity 0.5%

-3 dB bandwidth 20 kHz

-450 bandwidth 12.6 kHz

Gain: 1V output corresponds to 32.7 V

B.3 Front end Converter

Transformer at the input of the front end converter:

2 KVA, 3 phase, 50 Hz with tappings on the primary and secondary sides

Primary: 380 V/ 400 V/ 415 V/ 440V

Secondary: 50 V/ 75 V/ 100 V/ 125 V/ 150 V/ 175 V

(In the experiments the underlined tappings are used.)

AC side inductor of front end converter:

Three separate cores; each core has two windings with tappings.

1st winding - 17 mH, 20 mH, 23 mH, 25 mH

2nd winding - 40 µH, 80 µH, 100 µH

Appendix B Power Circuit Components

202

(In the experiments 17 mH is connected in opposition to 100 µH tapping; however, the

actual measured value of inductance with LCR meter comes to 17.9 mH.)

Various base and per unit values for the front end converter are

AC side base voltage = V = 72.169 V125ª3

AC side base current = 8.5 A

Base impedance = = 72.1698.5 W 8.49 W

DC side base voltage = 300 V

DC side base current = 6.133 A

Base power = W = 1840 W3 $ 72.169 $ 8.5

Per unit ac side inductance = = 0.66242$o$50$17.9%10−3

8.49

B.4 Position Encoder and Mounting Arrangement

Type: Stegmann HD20 Incremental Position Encoder

Resolution: 2500 pulses per revolution

Maximum output frequency: 100 kHz

Maximum operating speed: 3000 rpm.

The encoder is mounted on the non-drive end of the machine shaft through a flexible

coupling. The orientation of the instrument is such that when the rotor ‘a’ phase coil aligns with the

stator ‘a’ phase coil, the index pulse is generated. The initial mounting was done in the following

manner.

The wound rotor induction machine was driven by the dc motor. The stator circuit is kept

open and a dc mmf is injected into the rotor circuit. The ‘b’ and ‘c’ phase terminals of the rotor are

shorted and a dc source is connected between this point and the ‘a’ phase terminal. Therefore, the

direction of the rotor mmf is along the ‘a’ phase axis. This induces a sinusoidal rotational emf in the

stator. At the instant the ‘a’ phase coil axes for the stator and the rotor coincide, the flux linkage

between them is maximum. This corresponds to the negative zero crossing of the voltage induced in

the stator ‘a’ phase. This induced voltage and the index pulse are observed in the oscilloscope and, by

repeated trials, the orientation of the encoder is adjusted so that the index pulse goes high exactly at

the negative zero crossing of the voltage.


203

B.5 DC Motor and Drive

5.6 kW, 1500 rpm separately excited dc motor

Armature: 220V, 31 A

Field: 220V, 1.36 A

Drive: 4 quadrant AUTOCON drive from Autodata

Three phase fully controlled anti parallel bridge for four quadrant operation.

Input 125V, 3 phase, 50 Hz input

Current rating 45 A.


204

Appendix C

MATLAB DATA FILES

C.1 Machine and Controller Parameters used for Simulation and

Implementation of Rotor side Control

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Data file for simulation of field oriented control %% of wound rotor induction motor with stator connected %% directly to 3 phase bus and rotor fed from a bidirect- %% ional converter. %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 3ph Source%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Supply to stator of WRIM (Primary to Transformer)Uspeak = 1.414*240

% Supply to front-end converter (Secondary of Transformer)Ucpeak = 125*(1.414/1.732)f = 50w = 2*pi*fr = 2*pi/3

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Wound Rotor Induction Machine Parameters%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

SigmaS = 0.1017SigmaR = 0.1017Sigma = 1 - 1/((1+SigmaS)*(1+SigmaR))Rs = 1.557Rr = 2.62Lo = 177e-3Ls = Lo*(1+SigmaS)Lr = Lo*(1+SigmaR)

205

P = 4Kc = -2/3*1/(1+SigmaS)*P/2B = 0.0161J = 0.1Ts = Ls/RsTr = Lr/RrTm = J/B

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Sensor Gains (machine end)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Ki = 1/3.55Kv = 1/32.7

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Inverter (machine end)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Vdc = 300

% Maximum modulation indexMImax = 0.85

% Maximum allowable slipSmax = ((Vdc/(2*1.414))*MImax)/240

% Gain-factor machine sideGr = MImax/Smax %Inverter Gain - trinagle peak is 1 p.u.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Sine Pulse Width Modulator%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

FreqTri = 4464T = 1/FreqTri

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Machine side Controller Parameters%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Rotor current controller time constantTir_d =0.004 %Desired d_axis time constantTir_q =0.001 %Desired q_axis time constant

Appendix C MATLAB Data Files

206

Kpir_d = (Sigma*Tr/Tir_d)*Rrpu %Proportinal gain - d_axisKpir_q = (Sigma*Tr/Tir_q)*Rrpu %Proportinal gain - q_axis

% Speed controller time constantTw = 100e-3

% Rotor current limits (25% margin)IrdMax = 1.25IrqMax = 1.25

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Base Quantities for machine side control%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Usbase = 1.414*240Isbase = 1.414*6.26Irbase = 1.414*6.26Zbase = Usbase/IsbaseWbase = 157.08*2Tbase = 20e-3

Rspu = Rs/ZbaseRrpu = Rr/ZbaseXspu = 2*pi*50*Ls/ZbaseXrpu = 2*pi*50*Lr/ZbaseXopu = 2*pi*50*Lo/Zbase

Imsrated = 1/(Xspu)*Isbase*1.5Mdbase = -Kc*Lo*Imsrated*(Irbase*1.5)

Tipu = Ti/Tbase

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% END FILE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


207

C.2 Power Circuit and Controller Parameters used for

Simulation and Implementation of Front end Converter

Control

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Data File for Simulation of Front-end Converter %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 3ph Source%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Vph = 125*(1.414/1.732) %peak of ac side pahse voltagef = 50w = 2*pi*fr = 2*pi/3

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Power Circuit %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Lfe = 17.9e-3Rfe = 0.64C = 4000e-6

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Sensor Gains (front end)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Kife = 1/3.55 %ac side current sensor gainKvfe = 1/32.7 %ac side voltage sensor gainKidc = 1/3.55 %dc side current sensor gainKvdc = 1/32.7 %dc side voltage sensor gain

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Base Quantities for front end converter control%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Uacbase = 125/1.732Isbase = 8.5*1.414Zbase = Uacbase*1.414/IsbaseVdcbase = 300


208

Idcbase = 6.133

Rpu = R/ZbaseTfe = Lfe/RfeTl = C*Vdcbase/Idcbase

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Front-end Controller Parameters%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Voltage ControllerTvfe = 110e-3Kpvfe = 1.516

%Current ControllerTpife = Tfe %PI time constantTife = 0.002 %Desired time constant of the current loopKpife = (Tfe/Tife)*Rpu %PI proportional gain

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Inverter (machine end)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Gfe = Uacbase*1.414/(Vdcbase/2) %Inverter Gain - trinagle peak is 1 p.u.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Sine Pulse Width Modulator%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

FreqTri = 4464T = 1/FreqTri

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% END FILE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


209

Appendix D

RELEVANT DATA OF VESTAS V-27 WIND TURBINE Rotor

Diameter: 27m

Swept Area: 573 m2

Rotational speed, generator 1: 43 rpm

Rotational speed, generator 1: 33 rpm

Number of blades: 3

Cut-in speed: 3.5 m/s

Rated wind speed (225 kW): 14 m/s

Cut-off wind speed: 25 m/s

Survival wind speed: 56 m/s

Gearbox

Nominal power: 433 kW

Ratio: 1:23.4

Generator1

225 kW, 400 V, 396 A, 50 Hz, 1008 rpm, 163 kVAR

Generator2

50 kW, 400 V, 101 A, 50 Hz, 760 rpm, 48 kVAR

211

Appendix E

CALCULATION OF DC BUS CAPACITANCE The reactive power drawn by the load is supplied by the dc link capacitor. The effect of this is

to produce ripple on the dc bus voltage. Practically, the ripple current handled by the dc link capacitor

decides its value.

Ip

-Ip

0

TsTs/12

Fig.E.1 Ripple current in the dc link capacitor

i (t)c

The reactive component of the fundamental load current, when reflected on the dc link,

appears as shown in Fig.E.1. In order to derive a simplified expression for the ripple in the dc bus

voltage, this current waveform can be approximated as a saw-tooth waveform (shown as dotted line

in the Fig.E.1). From to , the capacitor current can then be expressed ast = 0 t = Ts/12

(E.1)ic =Ip

Ts/12 t

where, is the peak of the current waveform and is the time period of the fundamental cycle.Ip Ts

The voltage ripple can therefore, be calculated asDudc

(E.2)Dudc =Ip.Ts

24C

If the allowable voltage ripple is (where RPU is the p.u. ripple in the dc voltage), then theRPU.udc

dc bus capacitance required can be derived by using Eq.(E.2). The value of C should be estimated for

the maximum reactive power which is drawn by the load at the rated frequency.

213

(E.3)C =Ip

RPU.udc

124.frated

For an induction machine, is approximately the peak of the no-load current. Therefore,Ip

(E.4)C = ª2.Inl

RPU.udc

124.frated

The rms value of the ripple current can be derived as

ic,rms = 1Ts

¶0Ts Ip

Tst

2dt

1/2

(E.5)=Ip

ª3

Appendix E Calculation of DC Bus Capacitance

214

windenergyconversion.pdf

Documents

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implementation of rotor

rotor currents

power electronics group

power electronics store

phase grid

wind power generation

large power applications