thesis - wind energy system
DESCRIPTION
grid connection systemTRANSCRIPT
Design of a Converter for Interfacing a High-
Speed Generator to the Grid
Prepared by:
Xiao Ming Hu
Student Number
HXXXIA001
Department of Electrical Engineering
University of Cape Town
Prepared for:
Professor M.A. Khan
****Electrical Engineering Department****
University of Cape Town
October 2014
Submitted to the Department of Electrical Engineering at the University of Cape Town in partial
fulfilment of the academic requirements for a Bachelor of Science degree in Electrical Engineering
Key Words: Machines, Power Electronics, Vector control, PWM, Matlab/Simulink
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Declaration 1. I know that plagiarism is wrong. Plagiarism is to use another's work and pretend that it is one's
own.
2. I have used the IEEE convention for citation and referencing. Each contribution to, and quotation
in, this final year project report from the work(s) of other people, has been attributed and has
been cited and referenced.
3. This final year project report is my own work. I have not allowed, and will not allow, anyone to
copy my work with the intention of passing it off as their own work or part thereof.
Name: Xiao Ming Hu
Signature: Date: 16 October 2014
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Terms of reference At the beginning of the project, Professor M.A. Khan instructed the researcher to achieve the
following objectives:
Perform a literature review concerning the possible topologies of power converters used for
interfacing a high speed permanent magnet generator to the grid.
The researcher must choose a suitable topology of power converters for implementation
based on the literature review.
Choose appropriate control and switching strategy for interfacing the permanent magnet
generator to the grid.
Choose and design the grid filter to be used.
Derive a mathematical model for the permanent magnet synchronous generator.
Implement the control strategy with the grid filter and the derived generator model in
Matlab/Simulink.
Perform analysis on the results obtained from the simulation for the viability and efficiency
of the implemented control strategy.
Determine the efficiency of the designed filter with respect to total harmonic distortion in
the grid current.
In addition, the researcher must:
Include all Simulink models used for the simulation
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Acknowledgements First and foremost I would like to thank my immediate family who is overseas for providing me with
guidance and support throughout my best and darkest moments.
I would like to thank and extend my sincere appreciation to the following individuals and groups of
people who guided me through the process of completing and submitting my thesis:
My supervisor, Dr. Azeem Khan for providing guidance and constantly pushing me to try
harder and complete the project.
Mrs. Shireen Sabodien for organizing meetings with my supervisor and keeping me on track
with general administration.
Post Graduate students Chetan Gajjar and Chris De Beer for helping me with my simulations.
Sarah Jane Newnham for setting time aside to proof read my thesis and correcting all
grammatical errors.
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Abstract Due to increasing power demands, the development of distributed power generation plants using
Micro-turbines has been fast growing in recent years. High-speed machines are typically used for
such applications, as they have the advantage of generating high-density power with reduced size.
However, they come with problems, such as higher loss density and cooling difficulties. The high
frequency AC output power of the high-speed generator needs to be converted into the AC power,
with constant frequency and constant voltage before power transmission at the grid side can take
place. This frequency conversion between the machine and the grid can be accomplished by
implementing appropriate power electronic converter topologies that are properly controlled.
The objective of this thesis is to develop a Matlab/Simulink-based system for interfacing the high-
speed generator with the grid. The system will serve as a tool for studying the machine and grid
behavior during load variations.
The main emphasis of the work presented in this thesis is the understanding of the fundamental
concepts developed in the past for similar high-speed generator systems. Furthermore, a step-by-
step approach used for designing a model suitable for simulation of such systems is demonstrated.
The machine under analysis is a surface mounted permanent magnet generator, which is connected
to the grid through an AC-DC-AC converter and an LCL filter. A mathematical model for the PM
machine, suitable for simulations, was developed for implementing the appropriate control scheme.
Vector control algorithm along with SVPWM switching strategies, are implemented on both the
machine-side and the grid-side. The LCL filter design is based on a systematic algorithm adapted
from past literatures. The controllers are designed using modulus optimum and symmetrical
optimum tuning techniques, along with approximated transfer functions derived from system
models. Further analysis and alteration was conducted on the controllers using Matlab/Sisotool for
improved performance.
Simulation for the designed system shows the correct operations of the control strategy and good
filter performance. The results from the simulation confirm the feasibility of the proposed design
structure.
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Table of Contents Declaration ............................................................................................................................................... i
Terms of reference .................................................................................................................................. ii
Acknowledgements ................................................................................................................................ iii
Abstract .................................................................................................................................................. iv
Table of Contents .................................................................................................................................... v
List of Figures ....................................................................................................................................... viii
List of Tables .......................................................................................................................................... xi
Nomenclature ....................................................................................................................................... xii
Chapter 1 - Introduction ......................................................................................................................... 1
1.1 Background to the study ............................................................................................................... 1
1.2 Objectives of this study ................................................................................................................. 1
1.2.1 Problems to be investigated .................................................................................................. 1
1.2.2 Purpose of the study .............................................................................................................. 2
1.3 Scope and limitations .................................................................................................................... 2
1.4 Plan of development ..................................................................................................................... 2
Chapter 2 - Literature review .................................................................................................................. 3
2.1 Permanent magnet synchronous machines (PMSM) ................................................................... 3
2.2 Converter topologies for micro-turbine generator....................................................................... 3
2.3 Machine-side control .................................................................................................................... 5
2.4 Grid-side control ........................................................................................................................... 6
2.5 Grid filter ....................................................................................................................................... 6
2.6 Modulation (switching) scheme ................................................................................................... 7
Chapter 3 - Theory development ............................................................................................................ 8
3.1 Reference frame theory ................................................................................................................ 8
3.1.1 Stationary reference frame (αβ frame/Clarke transformation) ............................................ 8
3.1.2 Synchronous reference frame (dq frame/Parke transform) .................................................. 9
3.1.3 Reference frame theory application .................................................................................... 10
3.2 Machine model ........................................................................................................................... 10
3.2.1 Electrical equations of PMSG ............................................................................................... 10
3.2.2 Mechanical equations of PMSG ........................................................................................... 11
3.2.3 Block diagram model for PMSG ........................................................................................... 12
3.3 Vector control ............................................................................................................................. 12
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3.3.1 Field Oriented Control for PMSG ......................................................................................... 12
3.3.2 Voltage oriented control for grid-tied converter ................................................................. 13
3.3.3 Control techniques for FOC .................................................................................................. 14
3.3.4 Control technique for voltage oriented control................................................................... 16
3.3.5 PI controller tuning techniques ............................................................................................ 17
3.4 Pulse Width Modulation (PWM) ................................................................................................. 19
3.4.1 Sinusoidal PWM (SPWM) ..................................................................................................... 19
3.4.2 Space vector PWM (SVPWM) .............................................................................................. 20
3.5 Grid filters ................................................................................................................................... 21
Chapter 4 - Modelling ........................................................................................................................... 24
4.1 Phase Locked Loop (PLL) ............................................................................................................. 24
4.2 Voltage source converter (VSC) .................................................................................................. 24
4.3 LCL filter ...................................................................................................................................... 25
4.4 Filter design ................................................................................................................................. 26
4.5 Grid model .................................................................................................................................. 29
4.6 DC link voltage ............................................................................................................................ 30
Chapter 5 - Controller design ................................................................................................................ 31
5.1 Machine-side controllers design ................................................................................................. 31
5.1.1 DQ-axis current controllers .................................................................................................. 32
5.1.2 Speed controller ................................................................................................................... 35
5.2 Grid-side controllers design ........................................................................................................ 39
5.2.1 DQ-axis current controllers .................................................................................................. 39
5.2.2 DC-link voltage controller .................................................................................................... 43
Chapter 6 - Simulation and analysis ...................................................................................................... 47
6.1 Model verification ....................................................................................................................... 47
6.2 Grid side simulations ................................................................................................................... 50
6.2.1 Current Step response of the grid side converter ............................................................... 50
6.2.2 Voltage step response of the grid-side converter ............................................................... 51
6.2.3 DC link control in relation with active/reactive power flow to the grid .............................. 52
6.3 Machine side simulations ........................................................................................................... 56
6.3.1 Current step response of the machine-side converter ........................................................ 56
6.3.2 Speed step response of the machine-side converter .......................................................... 57
6.3.3 Speed control in relation to applied shaft torque due to load demand variation .............. 59
6.3.4 DC-link voltage variation with respect to machine torque variation ................................... 64
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6.4 Complete system simulation....................................................................................................... 66
6.4.1 Back-to-Back Power flow ..................................................................................................... 69
6.5 Grid filter efficiency..................................................................................................................... 72
Chapter 7 - Conclusions ........................................................................................................................ 74
7.1 Converter topology chosen ......................................................................................................... 74
7.2 Model of the PMSG derived ........................................................................................................ 74
7.3 Filter analysis and design ............................................................................................................ 74
7.4 Control and switching strategy ................................................................................................... 74
7.4.1 Choosing the control method and switching strategy ......................................................... 74
7.4.2 Design and simulation of the system with control algorithm implemented ....................... 75
7.5 Assumptions made ...................................................................................................................... 75
Chapter 8 - Recommendations ............................................................................................................. 76
8.1 Improve machine model accuracy .............................................................................................. 76
8.2 Include micro-turbine model ...................................................................................................... 76
8.3 Introduce realistic operating conditions ..................................................................................... 76
8.4 Explore alternative converter topologies ................................................................................... 76
8.5 Explore alternative control strategies ......................................................................................... 76
8.6 Improve filter design methods .................................................................................................... 76
8.7 Implement the designed system ................................................................................................. 76
Chapter 9 - List of References ............................................................................................................... 77
Chapter 10 – Appendices ...................................................................................................................... 80
10.1 Appendix A: PLL Model ............................................................................................................. 80
10.2 Appendix B: PMSG model ......................................................................................................... 81
10.3 Appendix C: VSC model ............................................................................................................. 83
10.4 Appendix D: Adapted Simulink model for SVPWM ................................................................... 84
10.5 Appendix E: Simulink model used for PMSG model verification .............................................. 85
10.6 Appendix F: Independent grid-side Simulink model with control implemented...................... 86
10.7 Appendix G: Independent machine-side Simulink model with control implemented ............. 87
10.8 Appendix H: Simulink schematic for the complete system with full control strategy
implemented ..................................................................................................................................... 88
Chapter 11 – EBE Faculty: Assessment of Ethics in Research Projects ................................................. 89
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List of Figures Figure 3.1 Adapted from Relationship of stator current space vector and stator phase currents ........ 8
Figure 3.2 Adapted from [31] Relationship of current space vector components in stationary and
rotating reference frames ....................................................................................................................... 9
Figure 3.3 Block diagram of a permanent magnet synchronous machine ........................................... 12
Figure 3.4 Extracted from [13] Field Oriented Control Schematic Block .............................................. 13
Figure 3.5 Adapted from [16] Voltage oriented control for grid-tied inverter ..................................... 14
Figure 3.6 Adapted from [2] Phasor relationship between machine stator current and Torque angle α
using CTA ............................................................................................................................................... 14
Figure 3.7 Adapted from [2] Diagram of vectors and vector angles using UPF .................................... 15
Figure 3.8 Grid side voltage and current space phasor diagram .......................................................... 17
Figure 3.9 General Control loop ............................................................................................................ 17
Figure 3.10 Extracted from [37] Three-phase-two-level-full-bridge voltage source inverter .............. 19
Figure 3.11 State space hexagon resulting from SVPWM .................................................................... 20
Figure 3.12 Frequency response of L, LC and LCL filters ....................................................................... 22
Figure 3.13 Extracted from [38] Series resistor damped LCL filter ....................................................... 22
Figure 3.14 Series resistor Damped LCL filter with varying resistor values .......................................... 23
Figure 4.1 Extracted from [41] Generalized structure of PLL for grid applications .............................. 24
Figure 4.2 Extracted from [20] LCL filter circuit .................................................................................... 25
Figure 4.3 Extracted from [20] Single phase LCL model in s-plane ....................................................... 26
Figure 4.4 Relationship between attenuation and r ............................................................................. 27
Figure 4.5 Bode plot of LCL filter ........................................................................................................... 28
Figure 4.6 Bode plot of LCL filter after damping ................................................................................... 29
Figure 4.7 Extracted from [20] Grid voltage phasors ............................................................................ 30
Figure 4.8 Extracted from [41] DC link circuit of AC-DC-AC converter ................................................. 30
Figure 5.1 Adapted from [2] Machine-side full controller structure .................................................... 31
Figure 5.2 Q-axis current control loop .................................................................................................. 32
Figure 5.3 Root locus plot for the current controller ............................................................................ 33
Figure 5.4 Open loop bode plot for the current controller .................................................................. 34
Figure 5.5 Step response of the current loop ....................................................................................... 34
Figure 5.6 Improved current loop step response ................................................................................. 35
Figure 5.7 Speed control loop for the PMSG ........................................................................................ 35
Figure 5.8 Closed loop response comparison between actual current loop and approximated current
loop ....................................................................................................................................................... 36
Figure 5.9 Root locus plot for the speed controller .............................................................................. 37
Figure 5.10 Bode plot for the speed control loop ................................................................................. 38
Figure 5.11 Closed loop step response of the designed speed control loop ........................................ 38
Figure 5.12 Adapted from [20] Grid-side controller structure ............................................................. 39
Figure 5.13 Grid-side current loop ........................................................................................................ 39
Figure 5.14 Modulated sine wave input for the filter ........................................................................... 40
Figure 5.15 Comparison of filter response to an input at 50 Hz ........................................................... 40
Figure 5.16 Comparison of filter response to an input at 1000 Hz ....................................................... 41
Figure 5.17 Root locus plot for the grid-side current control loop ....................................................... 42
Figure 5.18 Open loop bode plot for the grid-side current control loop .............................................. 42
Figure 5.19 Step response of the designed grid-side current loop ....................................................... 43
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Figure 5.20 Grid-side voltage control loop ........................................................................................... 43
Figure 5.21 Root locus plot for the voltage controller .......................................................................... 45
Figure 5.22 Bode plot for the voltage control loop .............................................................................. 45
Figure 5.23 Closed loop step response of the designed voltage control loop ...................................... 46
Figure 6.1 Electromagnetic torque response comparison during motoring mode .............................. 47
Figure 6.2 Rotor angle comparison during motoring mode ................................................................. 48
Figure 6.3 Rotor speed comparison during motoring mode ................................................................ 48
Figure 6.4 dq-axis current comparison during motoring mode ............................................................ 49
Figure 6.5 Electromagnetic torque response during generating mode ................................................ 49
Figure 6.6 dq-axis current response compared to references .............................................................. 50
Figure 6.7 dq-axis current response zoomed in at t = 0.15s ................................................................. 51
Figure 6.8 DC voltage response compared to the reference voltage ................................................... 51
Figure 6.9 DC-link input power and current ......................................................................................... 52
Figure 6.10 Comparison between grid active/reactive power and input DC link power ..................... 53
Figure 6.11 dq-axis current during input power variation .................................................................... 53
Figure 6.12 DC-link voltage response due to DC-link current variation ............................................... 54
Figure 6.13 Grid currents and voltage behaviour for varying grid input power ................................... 54
Figure 6.14 Grid phase A voltage and current ...................................................................................... 55
Figure 6.15 dq-axis current step response............................................................................................ 57
Figure 6.16 dq-axis current step response (Zoomed in) ....................................................................... 57
Figure 6.17 Machine-side speed loop step response ........................................................................... 58
Figure 6.18 Machine-side speed loop step response (zoomed in) ....................................................... 58
Figure 6.19 Required power and torque from the machine at rated speed ........................................ 60
Figure 6.20 Torque response to the load demand variation at rated speed ........................................ 60
Figure 6.21 Rated machine speed response ......................................................................................... 61
Figure 6.22 dq-axis current response at rated speed ........................................................................... 61
Figure 6.23 Stator current and voltage response at rated speed ......................................................... 62
Figure 6.24 Output power response compared to the reference input power at rated speed ........... 63
Figure 6.25 Torque and power demand for half rated machine speed ................................................ 63
Figure 6.26 Stator current and voltage and half rated machine speed ................................................ 64
Figure 6.27 Shaft torque variation ........................................................................................................ 65
Figure 6.28 DC-link voltage variation .................................................................................................... 65
Figure 6.29 DC-link currents variation .................................................................................................. 66
Figure 6.30 Applied torque to the machine for the complete system ................................................. 67
Figure 6.31 DC-link current for the complete system ........................................................................... 67
Figure 6.32 DC-link current for the complete system ........................................................................... 68
Figure 6.33 Machine and grid-side active and reactive power ............................................................. 68
Figure 6.34 Machine-side voltages and currents .................................................................................. 69
Figure 6.35 Grid-side voltages and currents ......................................................................................... 69
Figure 6.36 Machine-side voltage and current during inverse operation ............................................ 70
Figure 6.37 Grid-side voltage and current during inverse operation ................................................... 70
Figure 6.38 DC-link voltage during inverse operation .......................................................................... 71
Figure 6.39 FFT analysis of grid-side current before filtering ............................................................... 72
Figure 6.40 FFT analysis of grid-side current after filtering .................................................................. 72
Figure 6.41 Grid current before filtering .............................................................................................. 73
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Figure 6.42 Grid current after filtering ................................................................................................. 73
Figure 10.1 PLL Matlab/Simulink Schematic diagram ........................................................................... 80
Figure 10.2 Electrical part of the PMSG model ..................................................................................... 81
Figure 10.3 Mechanical part of the PMSG model ................................................................................. 81
Figure 10.4 Complete PMSG model ...................................................................................................... 82
Figure 10.5 VSC simulink schematic ...................................................................................................... 83
Figure 10.6 Adapted simulink model for the SVPWM .......................................................................... 84
Figure 10.7 PMSG verification system in Simulink ................................................................................ 85
Figure 10.8 Independent grid-side simulink model .............................................................................. 86
Figure 10.9 Independent machine-side simulation .............................................................................. 87
Figure 10.10 Complete system simulation in simulink ......................................................................... 88
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List of Tables Table 3.1 Switching states of a 3-phase inverter implementing SVPWM ............................................ 20
Table 4.1 System Rated Parameters ..................................................................................................... 27
Table 4.2 Calculated filter parameters ................................................................................................. 29
Table 6.1 Machine parameters used for the simulation ....................................................................... 56
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Nomenclature PMSM Permanent Magnet Synchronous Machine IPMSM Interior Permanent Magnet Synchronous Machine SPMSM Surface Mounted Permanent Magnet Synchronous Machine MTG Micro-Turbine Generator IGBT Insulated Gate Bipolar Transistor PCS Power Conditioning System V/HZ Volt per Hertz Control FOC Field Oriented Control DTC Direct Torque Control PMSG Permanent Magnet Synchronous Generator SVPWM Space Vector Pulse Width Modulation PLL Phase Locked Loop VOC Voltage Oriented Control DPC Direct Power Control VSC Voltage Source Converter SPWM Sinusoidal Pulse Width Modulation THD Total Harmonic Distortion Stationery frame real and imaginary variables Space phasor of three phase currents Alpha and Beta current components of
d and q current components of
Space phasor of three phase voltage Alpha and Beta voltage components of
d and q voltage components of
Space phasor of stator flux linkage d and q flux components of
Flux linkage produced by the permanent magnet
Angle between d-axis and -axis Electromagnetic torque Pole pairs Synchronous inductance dq-axis inductance component of
CTA Constant Torque Angle control UPF Unity Power Factor control CSF Constant stator flux control MTPA Maximum Torque Per Ampere control Modulus Optimum transfer function Modulus Optimum time constant Damping ratio Frequency modulation index
Amplitude modulation index DC-link voltage L-filter transfer function LC-filter transfer function LCL-filter transfer function Electrical radian speed Mechanical radian speed Viscous Damping constant Inertia Mechanical torque
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MIMO Multiple Input Multiple Output system SISO Single Input Single Output system da, db, dc Converter upper switch control signals Converter upper switches Converter leg voltages Voltage between converter negative bus and capacitor
midpoint DC-link current Filter inverter side inductance Filter grid side inductance
Filter damping resistance Switching frequency
Resonant frequency Filter inverter-side inductor parasitic resistance Filter grid-side inductor parasitic resistance
Active power Reactive power Filter capacitance
PI controller proportional gain
PI controller integral gain PI controller integral time constant PI controller transfer function Converter transfer function Current loop transfer function Machine transfer function Sampling delay transfer function
Grid filter transfer function
DC-link capacitor transfer function
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Chapter 1 - Introduction
1.1 Background to the study Accelerating commercialization of distributed resources has brought up the development of micro-
turbine generators (MTG) as a viable technology to implement distributed power generation. An
MTG is usually a high-speed rotating machine that is capable of generating high-efficiency power on
the scale of kilowatts [1]. These electrical machines usually come in the form of synchronous
machines that have applications ranging from high power to low power [2]. Within this class of
machines, Permanent Magnet Synchronous Machines (PMSM) are especially suited for distributed
generation systems. The main advantage of a PMSM is its reduced size and higher density power
generation capabilities.
The increase in efficiency from using high-speed machines also introduces a proportional increase in
its grid connection complexity. A Highly efficient power conversion system is needed to convert the
high-frequency AC output power from the machine to the low-frequency AC power compatible with
the grid. The power conversion system usually consists of power electronic converters with
controllable switches, such as an Insulated Gate Bipolar Transistor (IGBT). These converters are
commanded by appropriate control and switching strategies in order to achieve efficient frequency
transformation between AC energy sources. They also have the responsibility to monitor the
operating conditions on both the machine and grid side.
MTG systems, together with a well-developed power conversion strategy, will realize all the benefits
of implementing high-speed machines and avoid negative impacts on system reliability and safety.
1.2 Objectives of this study
1.2.1 Problems to be investigated
This project will look into the design methodology for the power conversion system used to connect
a high-speed permanent magnet synchronous generator to the grid. The main problems to be
investigated include the control and switching strategy for a frequency converter, as well as the
design of a grid filter.
Possible converter topologies must be investigated and compared for an optimal solution. Different
control and switching strategies will be explored for the chosen converter topology. For the machine
side, the control scheme must be able to regulate the speed of the machine. For the grid side, the
control scheme, together with the grid filter, must regulate the grid voltage and eliminate high
frequency harmonics caused by the inverter switching operation. The filter design must take into
consideration the grid frequency, converter switching frequency, DC-link voltage as well as the
power requirements.
The final deliverable will be the complete Matlab/Simulink based system implementing all the
system requirements mentioned in the above paragraph.
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1.2.2 Purpose of the study
Distributed generation using high-speed machines is a relatively new concept which is becoming
more popular in recent years due to improving machine and power electronic technologies. By
integrating distributed plants into the utility grid, decentralized power supply can be realized, which
has proven to be more economical in many cases.
The PMSG is a popular, if not the best, choice for such systems. However, there is a trade-off
between efficiency and complexity when one must consider implementing this technology. There
are many different existing control strategies that can be used for this kind of system. This research
allows a good understanding of the fundamental concepts governing the above mentioned system
by presenting simulated results on the system behavior.
A good understanding of the system will provide increased efficiency for future development. The
design complexity can be greatly reduced based on past experiences.
1.3 Scope and limitations This project provides a solution to the design problem of a power conversion system for integrating
a high-speed permanent magnet synchronous generator into the grid. A Matlab/Simulink-based
model will be derived and used for simulation results. The proposed system is limited to a machine
rated at 5.5kw and 20000rpm, as specified by the project requirements. The proposed system does
not include the micro-turbine model and operates in stable conditions with only load demand
variations. Experimental implementations are not included in this project.
1.4 Plan of development The report begins with a brief description of the applications of high-speed machines. This is
followed by stating the objectives of this thesis with its scope and limitations.
A literature review of the most commonly used converter topologies, control and switching
strategies for integrating a high-speed permanent magnet generator to the grid is presented in
Chapter 2.
In Chapter 3, the relevant theories necessary for the development of this project are discussed; basic
analysis and comparison are performed for the different types of grid filters.
Chapter 4 presents a more specific analysis based on the machine and grid-side modelling.
Furthermore, this chapter also includes the grid filter design based on the theoretical discussion in
chapter 3.
Using all the information from the previous chapters, chapter 5 shows the step-by-step approach of
designing the system controllers.
The designed system is completely simulated in chapter 6. The results are presented with
accompanying discussions that explains the efficiency of the system.
Conclusions and recommendations are finally presented in chapter 7 and 8 respectively.
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Chapter 2 - Literature review This project is simulation-oriented, for a converter that connects a biogas turbine-driven high-speed
generator to the grid. The issues that need to be covered are mainly centered on meeting
requirements with regard to machine- and grid-side control. This section provides a brief review of
the literature that is applied to this project. The discussion evolves from very basic topologies to
complex topologies of converter design, including its associated control schemes and modelling. The
relevant theories are discussed further in chapter 3.
2.1 Permanent magnet synchronous machines (PMSM) A brief overview of PMSM was discussed in [2]. Different types of PMSM were categorized. The
machine that is relevant to the scope of this project is Sinusoidal type PMSM, which can be
separated into Surface Magnet (SPMSM) and Interior Magnet (IPMSM) types. The main difference
between the two structures is that SPMSMs have identical dq-axis inductances where IPMSMs have
different dq-axis inductances. The different usages, advantages and disadvantages for SPMSM and
IPMSM are mentioned in [2]. In [2], the high-speed machine is designed using IPMSM and in [3]
SPMSM was used. Comparing the two machine structures, it is seen that IPMSM is inherently suited
for high speed operation. However it introduces saliency and hence complicates the control of the
machine. On the other hand SPMSM has simple control algorithms due to its identical dq-axis
inductances. However for high-speed operation the rotor construction must be carefully carried out
to cater for high mechanical stress on the circumference of the rotor. For that reason, machines with
a low pole count are usually used. Control strategy for salient PMSM and flux weakening of the
machine were briefly discussed in [4]. From the literature, it is apparent that, for high-speed
operations of permanent magnet synchronous machines, the main issues are the mechanical stress
imposed on the machine as well as the impact of increasing temperature on the magnets. A
significant number of careful decisions must be made for the construction of the high-speed PMSM.
2.2 Converter topologies for micro-turbine generator The recent interest in distributed generation has brought up the need for generators that are
smaller in size with high efficiency in power generation. A micro-turbine-driven high-speed
generator (MTG) seems to be a promising solution. For most of these MTG units, the turbine shaft is
directly coupled to the generator rotor shaft, causing the output power frequency of the PMSM to
easily reach the range of kHz [5, 6, 7]. This high-frequency output must be converted to an output at
grid frequency, usually between 50 or 60 Hz, before interfacing. Appropriate generator model and its
associated converter topologies must be chosen for efficient operation for both machine- and grid-
side. The PMSM discussed in section 2.1 is most suited for such high-speed MTG systems as it is
much more compact for low volume operations compared to other magnetic machines. Hence a
converter topology will be chosen for the PMSM.
A dynamic model of an MTG system only suitable for transient analysis was developed in [5]. The
proposed model in [5] uses a brushless PMSG that is directly connected to a gas-driven turbine. The
converter used is an AC-DC-AC converter. The machine side is connected to a three-phase diode
bridge rectifier, and the grid side is connected to an Insulated Gate Bipolar Transistor (IGBT) based
power inverter. The high frequency ac current output from the PMSG is first converted to DC by the
rectifier and presented to the inverter as a voltage source by a DC link. However, simulations in [5]
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only presented the model’s time-domain dynamics while no stability analysis was done. This makes
the study inherently inaccurate with respect to industrial applications.
The diode bridge rectifier is commonly used in industry for the three-phase system described in [5].
However, the quality of output using such rectifiers is poor. The main problem is the significant
amount of harmonics and hence reactive power generated on the AC side. These poor quality power
output results in voltage distortion, poor power factor at power supply side and slowly varying
rippled DC output at DC side. This problem is investigated in [8] where an efficiency comparison was
analyzed between two IGBT-based power converter systems (PCS) for connecting an MTG to a grid.
The MTG in [8] was a two-pole machine, operating at 5000 rpm that generated three-phase AC
voltage at 400-900Hz and power up to 175KW. The PCS is responsible for converting the high
frequency generator output voltage to the gird voltage at 480V 60Hz. One PCS topology involved a
diode rectifier as well as a boost DC-to-DC converter and a PWM inverter while the other one
contained an active rectifier and a PWM inverter. Based on the dynamic simulation results in [8] for
the studied MTG, the PCS using the topology with an active rectifier and an inverter shows better
operating efficiency under heavy load conditions. These results are applicable to a MTG system with
higher operating speed as long as the frequency does not exceed the maximum switching frequency
of the power semiconductors used in the PCS.
The MTG models considered in [5] and [8] uses unidirectional converters for grid interfacing. In
reality, the micro-turbine does not have the ability to self-start [4]. Power is needed to operate the
PMSG as a motor for the startup of the turbine. Hence the converter design must have mechanism
put in place for the starting period of the MTG [9]. One way would be connecting an extra inversion
stage to the PMSG. However, a converter topology proposed in [6] offers bi-directional active power
flow without the extra inversion stage. This topology consists of two back-to-back active converters,
each controlled properly so that the generated energy was exchanged with the grid system under
unity displacement factor. The studied MTG model in [6] uses a two-pole PMSG with non-salient
rotor that operates at 1600 Hz, the machine output power is 30 kW and the terminal line-to-line
voltage is 480 V. The grid is represented by a balanced three-phase source, 480 V line-to-line, 60 Hz
frequency, having an internal per-phase impedance of 0.4 ohms resistance and 2 mH inductance.
Simulations performed in [6] provide good insight for operations of the MTG during its steady-state
and transient period. Comparing the converter topology used in [5] and [8] to the one used in [6], it
can be realized that for bi-directional converters the control requirement is much more
sophisticated.
In paper [10] [1] [11] alternative AC-AC converters were discussed. Studies in [10] [1] are based on
matrix converters and a high-frequency cyclone-converter was developed in [11]. In [10], a review
was conducted on developing AC-AC matrix converters by Fuji Electric. The paper discussed the
principle of an AC-AC matrix converter and its associated advantages when comparing to
conventional AC-DC-AC converters. The advantages include the realization of motor regeneration by
the matrix converter with almost no input current harmonics, reduction in size due to the
elimination of a filter capacitor or reactor, and reduced power loss. New technology, such as reverse
blocking IGBT, protection, and control, was discussed in [10] as these technologies have direct
implications on overcoming matrix converter practical limitations. Another AC-AC matrix converter
model, to interface a high-speed MTG connected to a utility grid, was presented in [1]. Specifics such
as switching strategy and control mechanism were shown. The simulation of the MTG system,
5 | P a g e
including the dynamic models of the MTG, generator, matrix converter, converter control, and MTG
control were performed on computer software for dynamic behavior analysis. The simulation results
in [1] showed the viability of using AC-AC matrix converters for interfacing MTG to the grid.
However, as the matrix converter is a recently developed concept, it has limitations that are not yet
solved. The construction of a matrix converter requires many more semiconductors than a
conventional AC-DC-AC converter. Furthermore, the switches require bi-directional capabilities
which must be realized by appropriated arrangements of semiconductor devices. A matrix converter
also requires very complex control schemes and its maximum output voltage cannot exceed 83
percent of its input voltage. From the above mentioned published papers, it is realized that the back-
to-back full bridge converter offers a full range of control options and is by far the most well
developed AC-AC converter as yet. For this project, control strategies for this type of converter are
explored.
2.3 Machine-side control The control of the machine side is needed for regulating the speed of the generator as well as
producing good sinusoidal current waveforms. The control methods for a PMSG are mainly divided
into scalar and vector control. Scalar control method monitors only the magnitude and frequency of
voltage, currents and flux linkage. The Volt/Hertz (V/HZ) control of the scalar control class is the
most popular and commonly used for electric drive system applications. This control strategy is also
one of the easiest methods amongst other types of control schemes. Vector control is based on the
concept of establishing a relationship between speed, torque and currents of the machine [12], it is
more complex than scalar control and implemented in the synchronous rotating reference frame.
From the literature, it can be concluded that although scalar control is a simple method for steady
state control of a PMSG. However, the superiority of vector control is obvious when dynamic
behaviors of the machine are concerned.
In [12], two methods from the vector control class were discussed; they are Field Oriented Control
(FOC) and Direct Torque control (DTC) specifically applicable for electric drive systems. In [13, 14],
implementation of the FOC algorithm was discussed. FOC is implemented by transforming machine
equations into the synchronous reference frame. This method uses the rotor speed in its feedback
control strategy, it also has two current control loops that allow independent control on the flux and
hence torque of the machine. Using FOC strategy there are a few requirements. The acquisition of
the three-phase stator currents and the rotor position are required. The disadvantage of FOC is its
complexity in having three control loops and hence the design of three separate PI controllers with
additional sensors. As a solution for easier control strategy for PMSG, DTC was developed to
eliminate the two current control loops whilst provide torque and flux control for the machine. The
disadvantages of DTC lie with its dependency on high end technology in terms of controller, variable
switching frequency, high torque pulsations and fast sampling time requirements.
In [6] and [15] both FOC and DTC were implemented for a PMSG. It can be seen from the simulation
results that DTC and FOC both yield similar results when efficiency is concerned. However, due to
dynamic behaviors in the PMSG, FOC turns out to be the better option as it does not produce high
torque pulsations. Both vector control methods are implemented in conjunction with space vector
pulse width modulation (SVPWM) as the switching scheme for the rectifier.
6 | P a g e
Different control techniques can be embedded in the vector control scheme to efficiently operate
the generator and hence reduce losses [16]. Different control techniques were discussed in [17] and
[4]. The most frequently used control techniques covered in literatures are constant torque angle,
constant stator flux, unity power factor and maximum torque per ampere control. The constant
torque angle method keeps the angle of torque produced by the machine at a constant value; it is
most suited for a surface mounted PMSM [17]. The constant stator flux method has superior steady
state performances; however torque capability of the machine is limited due to limitation on the
stator flux [17]. The unity power factor method keeps the stator voltage and current in phase to
minimize the volt-ampere rating, but the machine efficiency is reduced [18]. Maximum torque per
ampere method is the most complex control technique; it uses the machine reluctance torque to
maximize the torque-per-ampere ratio, this control method is most suited for interior magnet PMSM
control [19].
2.4 Grid-side control Grid side control aims to achieve low harmonic content in the grid currents, it requires the DC link
voltage and as well as the grid voltages and currents to be monitored [16]. Vector control with grid
filter and phase locked loop (PLL) is most frequently used [20].
The type of vector control used on the grid side converter are voltage oriented control (VOC) and
direct power control (DPC) [20]. These two methods are analogous to FOC and DTC with the
machine-side. VOC was discussed in literature [20], [21] and [22]. VOC orients the current along the
dq-axis voltages hence it consists two inner current loops and one outer voltage loop that monitor
the DC voltage. VOC has good transient and dynamic performances however this is limited to
balanced grid condition [20]. DPC is a simplified VOC strategy as it eliminates the two current control
loops, the reference voltage for the modulator is provided directly by power controllers via a look up
table [20]. Unity power factor technique should be embedded in the vector control scheme for the
grid side [16].
The PLL is used to synchronize the inverter output current to the grid voltage [20]. It is also used to
acquire grid information such as the grid frequency and phase [23].
2.5 Grid filter Voltage Source Converters (VSC) produces waveform with harmonic distortion at their switching
frequency [16]. It is important that these high frequency harmonics do not pollute the grid; hence an
effective filter must be implemented to eliminate these harmonics. Since the switching frequency is
well above the fundamental grid frequency, hence the harmonics can be removed by a low pass grid
filter. The topologies and design limitations for the grid filter are discussed in [16], [20] and [24]. L,
LC and LCL filters are most commonly used for grid connected inverters and they are compared for
performance analysis in [16] and [20]. The L and LC type filters are simply implemented; however
their application is limited for low power operations as the inductor size for these filters must be
increased for good current harmonic attenuation at higher frequencies. The LCL type filter achieves
high current harmonic attenuation even with small inductor values, however it requires damping as
it introduces resonance to the system. The damping for LCL filters can be done by passive damping
using resistors or active damping using active circuit components [16]. The design procedure and
limitations for an LCL filter was comprehensively dealt with in [24]. Filter characteristics such as
reactive power absorbed by the filter capacitor, resonant frequency, voltage drop across inductors
7 | P a g e
and passive damping losses must be carefully analyzed before designing the filter. In [16], [20] and
[24] the grid side inductance of the filter is lumped together with the grid impedance, this is correct;
however they should be separated for accurate grid voltage acquisition.
2.6 Modulation (switching) scheme Based on the above research for the converter topology and control, it is realized that for correct
implementation of active converters, good modulation techniques is vital for commanding the
controllable switching elements in the converter. As a result, good quality voltage and current
output at desired frequency and amplitude can be achieved for varying load types [25].
There are many types of modulation scheme; the two used most frequently for power converters
are the Sinusoidal PWM (SPWM) and Space Vector PWM (SVPWM) [25].
SPWM is the most commonly used pulse-width-modulation technique, its application ranges from
low power to high power systems. In most applications, the disadvantages of SPWM are overlooked
as it is relatively insignificant compared to the advantages and simplicity of SPWM [26]. The main
advantage of SPWM lies in that it is suitable for most modern digital technologies. The control and
implementation of SPWM switching based power converters are much less complex when compared
to the requirements of other switching techniques. However it has also some disadvantages that can
affect the quality of some systems. SPWM is well known for its attenuation of the fundamental
frequency amplitude, this behaviour is not acceptable for high power systems. Compromises must
be made when choosing the switching frequency, SPWM produces less THD at higher switching
frequencies but that also implies more switching losses will occur due to the switching transients of
the switching elements. These disadvantages can cause a significant amount of stresses on the
switching devices. Furthermore high frequency components with high amplitude may exist which
can greatly reduce the quality of the converter output [27].
Space vector modulation for a two-level three-leg voltage source converter is implemented based on
representation of three-phase quantities as a vector in a two-dimensional plane. 8 possible switching
states are imposed on the voltage source converter so as to have the output current always
continuous. The desired output line-to-line voltage of the voltage source converter is provided by a
reference vector rotating clockwise or anti-clockwise in the two-dimensional plane [28, 29, 30].
Comparing SPWM to SVPWM, the main advantage of the latter is that the output THD is much
lower. However, the complexity of SVPWM has steered away many from implementing it. It is not
hard to see the compatibility between SVPWM and vector control method discussed in section 2.3
and 2.4 since both uses similar transformation of three-phase quantities to a two-dimensional
vector.
The relevant theory for both SPWM and SVPWM is discussed further in chapter 3.
8 | P a g e
Chapter 3 - Theory development This section provides a brief discussion on the theory involved for the project development. The
project is of multidisciplinary nature, hence many aspects need to be studied and revised for good
analysis of the system. The fields of theory covered in this section include reference frame theory,
vector control, filter design and converter switching theories. Furthermore, the mathematical model
for the PMSG is presented in this section so that the vector control theory can be explained with
respect to the machine. A Simulink based model of the PMSG will be derived from the mathematical
model.
3.1 Reference frame theory This section is a brief summary of reference frame theory based on the material obtained from the
course EEE4014C and literature [31] and [32].
3.1.1 Stationary reference frame (αβ frame/Clarke transformation)
The three-phase stator currents of an AC machine or the three-phase currents of a grid-tied inverter
can be represented as a space phasor that rotates at the angular frequency of the currents in the
form:
(1)
Transforming from abc frame to αβ frame, the three-phase quantities can be represented as two
time varying quantities defined by equation (2):
(2)
The phasor diagram in Figure.3.1 below shows the relation between the stationary reference frame
(αβ frame) and the natural reference frame (abc frame).
Figure 3.1 Adapted from Relationship of stator current space vector and stator phase currents
9 | P a g e
The transformation from the abc frame to αβ frame and vice versa is done by using Clarke/Inverse
Clarke transforms:
[
]
[
√
√
] [
] (2)
[
]
[
√
√
]
[
] (3)
3.1.2 Synchronous reference frame (dq frame/Parke transform)
The stationary reference frame variables are time varying hence still in sinusoidal form. Using these
variables will complicate the control system design. The αβ frame variables can be projected on to
the synchronous reference frame (dq frame) that rotates at the same angular frequency as the
current space phasor. By intelligent placement of the real d-axis of the dq frame, the current space
phasor can be transformed into two dc quantities defined by equation (4).
(4)
The phasor relationship between αβ frame and dq frame is shown in figure.3.2 below.
Figure 3.2 Adapted from [31] Relationship of current space vector components in stationary and rotating reference frames
The transformation from αβ frame to dq frame and vice versa is done by using Parke /Inverse Parke
transforms:
[ ] [
] [
] (5)
[
] [
] [
] (6)
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3.1.3 Reference frame theory application
For an AC machine, the three-phase stator currents can be transformed into two dc currents in the
dq frame. Using these DC quantities, simple linear control algorithms can be derived for the
machine. For machine-side converter control, d-axis is aligned with the rotor pole axis of the
machine, this means the dq frame rotates at the same electrical angular speed as the rotor of the
machine, and hence the space phasor components are constant when observed from the dq frame.
The same principle can be applied to the grid-tied converter but the d-axis is aligned with the grid
voltage phasor.
3.2 Machine model The machine model can be separated into electrical and mechanical parts for the PMSG. The model
is derived in the synchronous rotating frame for less complex machine control.
3.2.1 Electrical equations of PMSG
The derivation of the model and relevant equations are based on EEE4014C course work and
literature [16, 2]. The following equations depict the voltage and flux linkage of the machine in dq
reference frame:
Voltage equations
(7)
(8)
(9)
Where
and = d and q-axes voltages
and = d and q-axes currents
= stator winding resistance
and = d and q-axes inductances
= flux produced by the permanent magnet
and = d and q-axes flux
= electrical rotating speed of the machine
The component voltages induced in the d and q-axis coils can be classified as “transformer emfs” or
“rotational emfs”. The transformer emf terms in equations (7) and (8) are
and
. They are
induced in the d and q-axis coils as a result of the rate of change of the total flux linking the
respective coils. The rotational emfs account for the remainder of the induced voltage terms in (7)
and (8). They are induced as a result of the relative movement between the stationary three-phase
stator winding and the total d and q-axes fluxes.
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3.2.2 Mechanical equations of PMSG
The instantaneous power produced by the machine can be expressed using rotor dq frame
variables as in equation (10):
(10)
The electromagnetic torque is derived from equation (10) in terms of dq-axis current as in equation
(11):
(11)
Where
electromagnetic torque produced by the machine
= number of pole pairs of the machine
Equation (11) can be expressed in terms of two components as:
(12)
Two components can be seen from equation (12), the field-alignment torque component
and the reluctance torque component
. The field alignment torque is produced as a
result of the tendency for two magnetic fields to align. The field produced by the permanent
magnets tends to align with the field due to the current in the rotating q-axis coil, thus producing a
field alignment torque on the rotor. The reluctance torque is produced as a result of the differences
in reluctance between the d and q-axis flux paths. For surface mounted PMSG, , hence the
electromagnetic torque is directly proportional to .
The electromagnetic torque can also be expressed in terms of its relationship with input mechanical
torque , electrical speed , rotor inertia and the viscous friction coefficient .
(
)
(13)
It should be noted that the difference between is used to accelerate or decelerate the
machine. This is analogous to the motoring and generating operation of the PMSG. If the difference
is negative then the machine is in generating mode.
It is also important to realise that d and q-axis voltages are linked by and . This cross
coupling effect complicates the control of the machine model as it becomes a multiple input
multiple output system (MIMO). However, it can be dealt with in the control loop by adding and
subtracting the coupled terms from their respective links. By using this technique, the system
becomes single input and single output (SISO), which allows simple control algorithm to be
implemented.
12 | P a g e
3.2.3 Block diagram model for PMSG
The block diagram for a permanent magnet synchronous machine is modelled by rearranging
equations (7), (8), (12) and (13). Figure.3.3 below shows the machine block diagram.
Figure 3.3 Block diagram of a permanent magnet synchronous machine
It can be seen that the machine has inherent cross coupling due to the and terms.
Based on the above mathematical model, a Simulink model of the PMSG is derived. The Schematic
diagram of the model is shown in Appendix B figure.10.2, 10.3 and 10.4.
3.3 Vector control For this project the converters on both the machine-side and grid-side are controlled using vector
control algorithm. Vector control is implemented in the synchronous reference frame discussed in
section 3.1.2 above. The types of vector control for the PMSG and the grid-tied inverter are chosen
as field oriented control and voltage oriented control respectively based on the literature review for
machine-side and grid-side control.
3.3.1 Field Oriented Control for PMSG
In [13, 14], implementation of the FOC algorithm was discussed. This strategy uses two-dimensional
vector oriented control. There are three feedback control loops which consist of two inner current
loops and an outer speed loop. The current loops control the dq-axis currents of the machine and
the speed loop regulates the speed of the machine. Each control loop needs a PI controller. Typically
the inner loop must react faster than the outer loop since currents are electrical quantities that vary
much faster than speed which is a mechanical quantity. Figure.3.4 below shows the block diagram
for a PM machine using FOC.
13 | P a g e
Figure 3.4 Extracted from [13] Field Oriented Control Schematic Block
From figure.3.4 it can be seen that the output of the speed loop PI controller provides the reference
value for the q-axis current control loop. Using FOC strategy there are a few requirements. The
acquisition of the three-phase stator currents and the rotor position are required. This brings about
the need for sensors that will accurately measure the necessary quantities. The permanent magnet
flux is fixed on the rotor d-axis hence its position can be obtained by measuring the speed of the
rotor. The rotor position θ is obtained by integrating the rotor speed ω. The stator currents
are transformed to the by Clarke transformation, then applying Park transform with θ are
obtained for the current feedback loop. The outputs of the two PI current controllers are the dq-axis
reference voltages
. The converter switching is directly commanded by
. Various control
techniques can be embedded within the vector control algorithm for optimal machine performance;
these techniques are discussed in section 3.3.3 below.
3.3.2 Voltage oriented control for grid-tied converter
The control for the grid-tied converter is similar to the control for the PMSG. Detailed
implementation was discussed in literature [33, 20, 6, 16]. The voltage oriented control consists of
three PI controllers just like the field oriented control, however, the outer loop regulates the DC link
voltage instead of speed hence the name “voltage oriented”. The grid phase voltage angle is
acquired by a phase locked loop (PLL); this angle is corrected (if out of phase) and used for abc to dq
transformation of the grid currents and voltage. This allows the grid voltage to be phase locked to
the grid-converter currents. The DC link voltage is fed back to the outer loop PI controller; together
with the reference DC link voltage the outer loop provides the d-axis current reference. Same as field
oriented control, the output of the dq-axis current PI controllers is used as reference voltages for the
switching of the grid-tied converter. In Figure.3.5, an overview of voltage oriented control for the
grid-tied converter is shown.
14 | P a g e
Figure 3.5 Adapted from [16] Voltage oriented control for grid-tied inverter
The control technique that can be embedded in the grid-side vector control is discussed in section
3.3.4 below.
3.3.3 Control techniques for FOC
There are various control techniques that can be used with FOC. These techniques have different
advantages and disadvantages, which result in varying machine performance. For a PMSG the most
important control techniques used are constant torque angle, unity power factor, constant stator
flux control and maximum torque per ampere control. This section briefly presents the above
mentioned control techniques based on the discussion of different control properties in [2].
3.3.3.a) Constant torque angle (CTA)
This method keeps the torque angle constant at 90° where the torque angle α is defined as the angle
between the stator current space vector and the rotor d-axis. The phasor relationship between
machine stator current and torque angle using CTA is shown in figure.3.6 below.
Figure 3.6 Adapted from [2] Phasor relationship between machine stator current and Torque angle α using CTA
15 | P a g e
From the phasor diagram we can see that and . Since α is kept at 90°,
this leads to being kept at 0 constantly. Using the above expressions of and , the torque
equation using constant torque angle control technique was derived in [2]:
(14)
Referring back to Equation (12) shows that only the field alignment torque component hence is
used to control the electromagnetic torque. It is easy to observe that this control technique should
be only used for a surface mounted PM machine where and that the dq-axis fluxes
produced by the machine are relatively small.
3.3.3.b) Unity power factor (UPF)
In this method, power factor is maintained at unity. This means the angle φ between and is
kept at 0. This allows the volt-ampere rating to be minimized but the maximum torque and
efficiency will be reduced. The vector diagram for power factor control is shown in figure.3.7 below.
Figure 3.7 Adapted from [2] Diagram of vectors and vector angles using UPF
From figure.3.7, since φ is kept at 0, then the stator current space vector is in quadrature with the
stator flux linkage space vector . This leads to the current expressions [2]:
| | | | (15)
| | | | (16)
Where is the angle of stator flux linkage vector. Using the above equations the unity power factor
expression is found as:
(17)
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3.3.3.c) Constant stator flux control (CSF)
This technique restricts the flux of the machine below the saturation point and hence voltage is
maintained low. The magnitude of the stator flux linkage space vector is expressed as [2]:
√
√( ) ( )
(18)
Constant stator flux control has the best steady state performance characteristic compared to the
other control techniques shown above. However, the torque capability is limited as a result of
limitation on the stator flux linkage.
3.3.3.d) Maximum torque per ampere control (MTPA)
This is the most complex method from the above mentioned control techniques. The reluctance
torque is used to maximize the torque-to-ampere ratio hence the efficiency of the motor can be
increased. The following equations are taken from [2] which determine the reference dq-axis current
values for the current control loops:
√ ( )
( ) (19)
√
(20)
The advantage for the MTPA strategy is the usage of reluctance torque. Since in an interior
permanent magnet machine is smaller than , this results in non-zero reluctance torque
component for equation (20). Thus MTPA is suitable for controlling the IPMSM.
MTPA can be used for SPMSM in a way similar to the constant torque angle control technique. Since
and are equal for a SPMSM, this means the electromagnetic torque is directly proportional to
the q-axis current as defined by equation (14). The maximum torque per ampere condition will be
satisfied when:
(21)
This can be achieved by forcing the d-axis current to 0 hence the stator current equals to the q-axis
current.
3.3.4 Control technique for voltage oriented control
Control for the grid side should be focused on the active and reactive power flow from DC link to the
grid. The unity power factor (UPF) control technique discussed in 3.2.3.b) can be used to ensure
efficient active power monitoring by the grid-tied inverter. UPF for the grid side control differs to the
same technique used for the machine side in such a way that the d-axis of the synchronous rotating
frame is aligned with the grid voltage space phasor as shown in figure.3.8 below.
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Figure 3.8 Grid side voltage and current space phasor diagram
From figure.3.8, it can be seen that UPF can be achieved if θ = 0, thus the q-axis component of the
grid current must be set to zero to satisfy the UPF condition.
3.3.5 PI controller tuning techniques
The PI controllers used in the vector control are tuned using two commonly used techniques
described in literature [34, 4] for similar systems.
3.3.5.a) Modulus Optimum
Figure.3.9 below shows a general control system loop.
Figure 3.9 General Control loop
Modulus Optimum method tunes the parameter of controllers so that the following rules are
complied with [16]:
1.
2. | |
Following the above two rules, the magnitude of the closed loop transfer function will equal to 1
from a frequency of zero to as high a frequency as possible. Note is the closed loop transfer
function of the system in Figure.3.9. The method starts with realizing the order of the closed loop
transfer function of the system. Then it is compared to the modulus optimum equation of the same
18 | P a g e
order to solve for the controller values. For the purpose of this project, only second and third order
modulus optimum transfer functions are needed [16]:
√
(22)
( )( )
(23)
is the time constant of the feedback control system designed by this control method.
3.3.5.b) Symmetrical Optimum
The general equation of symmetrical optimum design procedure is presented below:
∑
(24)
represent the number of controller parameters that can be adjusted. Since a PI controller has two
adjustable parameters, equation (24) can be used to derive the following equations:
(25)
(26)
Equation (25) and (26) can be modified to achieve maximum phase margin, this is done by Preitl and
Precup in [35]:
√ (27)
√ (28)
The variable β should be set between 4 and 16. If β smaller than 4 the system’s phase margin will be
too small. If β is set to larger than 16 the system’s phase margin will be too large. In [36], the
characteristic equation was derived using the fact that a value of β 9 results in one real pole and
two which form a conjugate pair:
(
) (
) (29)
The real pole position is determined by and hence must be set to greater than 1 so that the
real pole is faster than the conjugate pair and ζ is the damping factor [36]. The controller parameters
are determined by comparing equation (29) to a third order characteristic equation of the form
shown in equation (30).
(30)
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3.4 Pulse Width Modulation (PWM) PWM voltage source converters are used to operate as either inverters or rectifiers. The modulation
method used to command the converter is vital for the output quality of the converter. There are
various modulation techniques. For a two-level-full-bridge voltage source converter two modulation
schemes, namely sinusoidal PWM (SPWM) and space vector PWM (SVPWM), are commonly used
[28]. This section serves as a theoretical review and comparison of the above mentioned two
methods based on the theory developed in literature [37, 4, 25].
3.4.1 Sinusoidal PWM (SPWM)
SPWM is generated by comparing modulating sinusoidal signals (with amplitude and frequency
) to triangular carrier wave forms (with amplitude and frequency ). and are the
fundamental amplitude and frequency of the desired output. is the switching frequency of the
converter. To explain the generation of SPWM, A three-phase-two-level-full-bridge voltage source
inverter is shown in figure.3.10 below.
Figure 3.10 Extracted from [37] Three-phase-two-level-full-bridge voltage source inverter
SPWM is generated by using the condition if then the upper switch for a single leg of the
converter will turn on and the lower switch will turn off resulting in the leg voltage to equal either
the dc voltage or 0 respectively. This is applied to all three legs of the converter. The frequency and
amplitude of the fundamental component of the inverter output can be controlled by and
where is the amplitude modulation index defined as the ratio between and . The switching
frequency of the inverter can be controlled by the frequency modulation index defined as the
ratio between and . The modulating signal can be synchronized to the carrier signal which
results in synchronous SPWM, else it results in asynchronous SPWM. For synchronous PWM the
output harmonics are at multiples of the fundamental frequency and for asynchronous PWM the
output harmonics are at frequencies that’s not a multiple of the fundamental frequency. For SPWM
the maximum line-to-line output voltage has the magnitude of √
√ [26].
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3.4.2 Space vector PWM (SVPWM)
Space vector PWM uses the reference frame theory where the reference voltage is given in the
space vector form. For a three-phase system, the space voltage vector can be defined using equation
(1). For a three phase inverter as shown in figure.3.10, the three phase output from each leg can be
described in binary as either on or off. SVPWM implements such a method that 8 possible switching
combinations are possible for the inverter so that no two switches from the same leg will be turn on
or off at the same time. This results in 8 states of the inverter and is illustrated in table.3.1 below.
Table 3.1 Switching states of a 3-phase inverter implementing SVPWM
Inverter output line voltages Inverter output leg voltages Inverter switches state
Vab Vbc Vca Van Vbn Vcn S1 S3 S5
0 0 0 0 0 0 0 0 0
0 -Vdc Vdc 0 0 Vdc 0 0 1
-Vdc Vdc 0 0 Vdc 0 0 1 0
-Vdc 0 Vdc 0 Vdc Vdc 0 1 1
Vdc 0 -Vdc Vdc 0 0 1 0 0
0 -Vdc Vdc Vdc 0 Vdc 1 0 1
0 Vdc -Vdc Vdc Vdc 0 1 1 0
0 0 0 Vdc Vdc Vdc 1 1 1
From table.3.1 we can see there are 6 active switching states (001, 010, 011, 100, 101, 110) and two
non-active switching states (000, 111). The switching states and reference voltage can be
transformed into switching vectors and space voltage vector in αβ frame by using Clarke
transformation. The resulting vector diagram is a hexagon in αβ frame shown in figure.3.11 below.
Figure 3.11 State space hexagon resulting from SVPWM
The idea of SVPWM is to approximate the reference voltage vector by applying time-averaged
adjacent switching vectors. The maximum line-to-line voltage output of the inverter commanded by
21 | P a g e
SVPWM is √
√ . SVPWM do not generate harmonics at both even and odd multiples of
fundamental frequency unlike SPWM.
By comparing SVPWM and SPWM, it is observed that SVPWM is more efficient and provide better
quality outputs. The SVPWM also display good compatibility with vector control. It is then concluded
that for this project, SVPWM will be used as the switching strategy for the power converters.
3.5 Grid filters Grid filters are used for eliminating the high frequency harmonics produced by the grid-tied inverter
[16]. Common filter types used for grid applications are L, LC and LCL filters [38]. The inductor blocks
the high frequency harmonics and the capacitor shorts them. For filter design, size and dimension
must be considered. The size of inductor increases with increasing applied frequency, and the size of
capacitor decreases with increasing applied frequency [38]. LCL filter is superior as far as size and
dimension are concerned [39]. However the effectiveness of a grid filter must also take into
consideration how well it attenuates current harmonics at high frequencies. A comparison between
L, LC and LCL filters based on their frequency response is done in this section in order to understand
the advantages and disadvantages of each type.
Neglecting inductor parasitic resistances, the transfer function of an L-type, LC-type and LCL-type
filter for a single phase is shown in equation (31-33) respectively:
(31)
(32)
(33)
L and C are filter inductance and capacitance respectively.
Using the transfer functions of each filter type, the frequency response for each filter was plotted on
a bode diagram using Matlab. The total filter inductance and capacitance (LC and LCL filters) are kept
the same for all three filters where and . Since the switching frequency of the
inverter would not be below the range of kHz, the bode plot has a range from kHz upwards.
Figure.3.12 below is the simulated frequency response for each filter type.
22 | P a g e
Figure 3.12 Frequency response of L, LC and LCL filters
Figure.3.12 shows that for the same filter inductance and capacitance, LCL filter has superior
attenuation characteristics at low and high frequencies compared to L and LC-type filters. This
means high frequency harmonics of the inverter output can be easily filtered out by the LCL filter.
However, since LCL filter is a third order system, this means there will be a resonant peak in the
transfer function [40]. This can be seen both from figure.3.11 and the transfer function of the LCL
filter. To damp the large gain at the resonant frequency a resistor can be added in series with the
filter capacitor, this is known as passive damping [24]. Figure.3.13 below shows the circuit of a
damped LCL-filter.
Figure 3.13 Extracted from [38] Series resistor damped LCL filter
From figure.3.13 the transfer function for a series resistor damped LCL filter was derived in [38] as:
(34)
Resonant frequency of an LCL filter is defined as [16]:
23 | P a g e
√
(35)
Figure.3.14 below shows the effect of a damping resistor, with various values, on the frequency
response of the LCL filter. The resistor values are percentages of the capacitor impedance at the
resonant frequency. The filter inductance values and capacitance values are the same as used for the
different filter frequency response analysis.
Figure 3.14 Series resistor Damped LCL filter with varying resistor values
From Figure.3.14 it can be seen that by adding a damping resistor in series with the filter capacitor,
the resonant peak is eliminated. The system is more damped with increasing value of the series
resistor. Due consideration must be given for choosing the resistor value as increasing resistance
means increasing power losses in the filter. In general a rule of thumb for choosing the resistor value
was discussed in [16] where:
(36)
Equation (36) is justified by figure.3.14, as for a damping resistance at thirty percent of the resonant
capacitance; the system shows superior magnitude response.
The design procedure for a LCL filter is derived from [24] which mainly constitute the calculations for
the filter component parameter to guarantee system stability. It is assumed that the current ripple is
caused primarily by the dominant harmonic at the switching frequency. The actual design procedure
is presented in the filter design section of Chapter 4.
24 | P a g e
Chapter 4 - Modelling The models of relevant system components with their governing mathematical equations are
presented in this chapter. These models are needed to provide the necessary information and
knowledge for the controller design. Furthermore, some of the models will be implemented in
Simulink for the machine side system. This is due to the reason that the PMSG model was built using
the standard Simulink library, blocks from the Simpowersystems library do not interface well with
the standard Simulink library. Hence components used for the machine-side simulation must be built
using the standard Simulink library based on mathematical equations. The model of the PMSG was
presented in Chapter 3, so it will not be included in this chapter.
4.1 Phase Locked Loop (PLL) The phase locked loop is an integral component for the grid-side system. It is the most often used
synchronization technique used to synchronize the voltage source converter output current to the
grid voltage [20]. Information about the utility voltage such as phase, amplitude and frequency can
be obtained by using the PLL for fast detection. For the UPF grid control method, the phase angle of
the grid voltage is vital information as it is used to transform the voltage source converter current
from abc frame to dq frame. PLL technique is implemented based on a feedback system, a
generalized PLL structure is shown in figure.4.1 below.
Figure 4.1 Extracted from [41] Generalized structure of PLL for grid applications
For the structure shown in figure.4.1, it can be seen that in order to implement PLL a pair of
orthogonal voltage vectors are required. For a three-phase system, these voltage vectors can be
easily acquired by transforming the grid abc voltage to its equivalents using the Clarke
transformation. Using a simple inverse tangent function the phase angle can be determined from
the components of the grid voltage. However, when the input voltage frequency is varied,
stationery error may occur in the detected angle. This can be compensated using a simple PI
controller with the reference for the phase angle set to 0. The output of the PI controller is the
frequency of the grid voltage. The voltage controlled oscillator usually is implemented as an
integrator in power system applications. The output of the VCO will be the grid voltage phase angle
and fed back to the abc to transformation. Using the above theory, a model of PLL was
developed in Simulink. The PI controller parameters and a Simulink schematic diagram of the model
for the PLL are shown in Appendix A figure.10.1.
4.2 Voltage source converter (VSC) The voltage source converter can be modelled as an average model using its gate signals. As
discussed in chapter 3, a voltage source converter using pulse-width-modulation is commanded in
such a way that the gate signals applied to the top switches determines the converter output
25 | P a g e
voltage. Consider the three-phase inverter shown in figure.3.10, the signals applied to switches S1,
S3 and S5 are da, db and dc respectively. These signals are binary variables of magnitude 1 or 0, this
means that three switches one per each leg of the inverter will be on at each switching instant. The
inverter output leg voltage with respect to the negative dc bus can be defined by equation (37) [20]:
(37)
Consider the inverter in figure.3.10 the output line voltages of the inverter have the expression:
(38)
The voltage between the inverter phase and the centre star point of the three-phase filter capacitors
is defined by equation (39) [20]:
(39)
Using equation (37 – 39), inverter phase voltages are derived in equation (40):
(
)
(
)
(
)
(40)
Since the converter used is a voltage source, current output on the AC side will be dependent on the
inverter voltage and the grid load configuration. The DC side current can be calculated as a function
of phase currents and switches configuration in equation (41) [20]:
(41)
Based on the above equations, a Simulink model for the voltage source converter was derived and
the schematic diagram is shown in Appendix C figure.10.5.
4.3 LCL filter The model of the LCL filter is needed for controller design, as discussed in the grid filter section from
chapter 3. The LCL filter can be modelled using per phase analysis. The single phase circuit diagram
of a LCL filter is presented in figure.4.2 below.
Figure 4.2 Extracted from [20] LCL filter circuit
26 | P a g e
From figure.4.2, the circuit equations in s-plane can be written as:
(
)
(42)
Equation set (42) can be modelled using block diagram shown in figure.4.3 below.
Figure 4.3 Extracted from [20] Single phase LCL model in s-plane
The transfer function was determined in equation (34), for convenience it is presented again below.
Note the parasitic resistance for the inverter and grid side inductors are neglected for independent
filter modeling, however, it must be considered when designing the controller. These resistances can
be lumped together with inverter and grid impedances as they are connected in series.
4.4 Filter design The following limitations must be considered for an LCL-filter design [24]:
1. Total inductance of the LCL-filter must be less than 0.1 per unit to limit the voltage drop
across the filter.
2. Capacitor value should be chosen to maintain power factor. 5% is typically applied.
3. Resonant frequency should be such that:
(43)
4. The grid-side and inverter-side inductances:
where relates the grid-side and inverter-side inductances in such a way that it
sets how much of the inverter current is attenuated by the filter to achieve the desirable
grid current at the switching frequency harmonic order . The governing
equation for the above relationship is shown in equation (44) below.
( ( )
( ))
| ( )|
(44)
Using the above limitations, the following procedure is implemented for the filter design with the
parameters of the system shown in Table.4.1:
27 | P a g e
Table 4.1 System Rated Parameters
Parameter Value
380V
5.5kW
7.86A
5kHz
50Hz
700V
Base values:
Maximum filter inductance:
This is in accordance with limitation 1.
Filter capacitance:
Applying limitation 2, 5% of system rating is applied to the filter capacitance to limit the
reactive power absorbed by the filter.
To choose appropriate values for the filter inductances, limitation 4 must be applied. is
first chosen to be . Equation (44) is then plotted using Matlab. The result is shown in
Figure.4.4 below to show the relationship between attenuation and .
Figure 4.4 Relationship between attenuation and r
28 | P a g e
From figure.4.4 The value of is chosen to be 1.2 so that the attenuation at switching
frequency is approximately 0.06. Hence the resulting value for
. Checking with which is
smaller than .
Resonant frequency and damping resistor:
After all the component values have been calculated, the resonant frequency can be
checked with equation (45):
√
(45)
The bode plot for the designed filter is plotted using Matlab and presented in Figure.4.5
below.
Figure 4.5 Bode plot of LCL filter
It can be seen that the resonant frequency is at 1598 Hz which corresponds to the calculated
value of 1597.85 Hz. The resonant frequency adheres to limitation 3. As discussed in chapter
3 a large resonant peak can be observed from figure.4.5, this will be eliminated by a passive
damping resistor connected in series with the filter capacitor.
Using the general rule for damping resistor selection, the resistance value is chosen to be
30% of the capacitor reactance at resonant frequency. That is:
.
The bode plot for the designed LCL filter after the addition of the damping resistor is shown
in figure.4.6 below.
29 | P a g e
Figure 4.6 Bode plot of LCL filter after damping
Table.4.2 below shows all the calculated parameters for the designed filter.
Table 4.2 Calculated filter parameters
Parameter Value
26.25 Ω
0.0836 mH
121.2606 µF
8.36 mH
6.063 µF
3 mH
1.2
3.6 mH
1597.85 Hz
5.476 Ω
0.1 Ω
0.12 Ω
4.5 Grid model The grid is modelled as three ideal sinusoidal voltage sources each displaced by 120 degrees from
each other. The source generates voltage at the fundamental frequency of the grid. The phasor
diagram of grid voltages is shown in figure.4.7 below.
30 | P a g e
Figure 4.7 Extracted from [20] Grid voltage phasors
The active and reactive power is:
(46)
√ (47)
4.6 DC link voltage The DC link circuit is represented as an ideal capacitor with series resistance representing the
internal resistance of the capacitor. The circuit diagram of the DC link is shown in figure.4.8 below.
Figure 4.8 Extracted from [41] DC link circuit of AC-DC-AC converter
The loop equation for the circuit presented in figure.4.8 above can be written as:
∫
(48)
31 | P a g e
Chapter 5 - Controller design The control system is designed based on the discussion of vector control in chapter 3 and the system
models presented in chapter 4. The grid-side and machine-side can be controlled independently
using the PWM back-to-back converter topology. Both machine-side and grid-side control scheme
consists of 3 loops with the outer loop for speed/voltage regulation and inner loops for current
control and these loops all use simple PI controllers due to its compatibility with dq frame variables.
This section utilizes the theory covered in the PI controller tuning technique section and
Matlab/Sisotool for PI controller parameter tuning. In order to simulate a system that is as real as
possible, discrete simulation should be implemented as real systems are limited by the sampling rate
of the transducer. The time delay caused by this discretization must be taken into account when
designing the controllers.
5.1 Machine-side controllers design The machine side control system consists of the speed outer loop and inner dq-axis current loops as
discussed in chapter 3. The governing equations for machine were presented in equations (7 – 13).
Looking at the voltage equations of the PMSG in equation (7) and (8), it can be observed that there is
inherent cross coupling. This complicates the design of the control as the system will behave like a
multiple-input-multiple-output system. Decoupling should be implemented at the output of the PI
controllers so as to cancel out the coupling terms in the PMSG model. The full controller structure is
illustrated in figure.5.1 below.
Figure 5.1 Adapted from [2] Machine-side full controller structure
The transfer function of the PI controllers used has the following form:
(49)
32 | P a g e
5.1.1 DQ-axis current controllers
Based on the analysis of different control techniques for field oriented control in chapter 3, the
maximum torque per ampere method is chosen as it minimizes the stator current hence has
superiority in terms of loss reduction in the machine. In order to design the controller, the loop of
current trajectory should be approximated by transfer functions for different components.
Figure.5.2 below is the q-axis current control loop.
Figure 5.2 Q-axis current control loop
Since the machine is decoupled by the control algorithm, d and q-axis current loops will have
identical responses. Using the maximum torque per ampere method the d-axis current is set to 0.
This means the electromagnetic torque produced by the machine is purely dependent on the q-axis
current. Hence only the q-axis current controller needs to be tuned. Based on the electrical part of
the PMSG model presented in chapter 3, the machine transfer function can be expressed as:
(50)
The transfer function for the machine can thus be expressed as:
and
(51)
The converter and sampling delay can be modelled as simple first order transfer functions with time
constants that represent their statistical average delay [4].
(52)
(53)
The closed loop transfer function of the current control loop is:
To simplify the transfer function, we know that the zero of the PI controller is used to cancel the
slowest pole of the transfer function, this means the time constant of the machine = . The
converter time constant and sampling time constant can be lumped together as a new time
constant .
33 | P a g e
The characteristic equation of after the above simplification is expressed below in equation
(54), comparing it to the modulus optimum equation for second order systems in equation (22) and
setting the damping ratio to be 0.707, the gain parameters of the PI controller can be calculated as
follows:
√
(54)
Using machine parameters for the simulation, switching frequency of 5 kHz and sampling frequency
of 10 kHz, the parameter for the PI controller was determined:
Using Matlab/Sisotool, the designed controller was simulated with the above designed controller
parameter. The system was discretized using the zero order hold method and simulated in z-domain.
The open-loop root locus and bode plot are shown below in figure.5.3 and figure.5.4.
Figure 5.3 Root locus plot for the current controller
34 | P a g e
Figure 5.4 Open loop bode plot for the current controller
From figure.5.3 it can be seen that the closed loop poles lie on the 0.707 damping trace. This
validates the designed controller and indicates that the system is stable. Figure.5.4 shows the
current loop has a gain margin of 17.2 and a phase margin of 63.5 thus further indicate the stability
of the loop. A step test is performed on the current loop; the result is shown in figure.5.5 below.
Figure 5.5 Step response of the current loop
Figure.5.5 shows that for a step test, the current loop system has a settling time of 1.2 ms and a
4.07% overshoot. This dynamic behavior is within acceptable range. However, it can be improved.
Using Matlab/Sisotool, the parameters of the PI controller was altered, the new values are:
35 | P a g e
The step response of the improved current loop is shown in figure.5.6 below.
Figure 5.6 Improved current loop step response
From figure.5.6, it can be seen no overshoot is present and the settling time was reduced to 1.1 ms.
5.1.2 Speed controller
The structure of the speed controller is presented in figure.5.7, which includes the mechanical part
of the PMSG and the current control loop.
Figure 5.7 Speed control loop for the PMSG
The transfer function for the PI controller and sampling delay is the same as presented in equation
(12) and (13). Base on the mechanical part of the PMSG model presented in chapter 3, the transfer
function of the machine and can be expressed as:
(55)
(56)
The closed loop transfer function of the current loop must be derived in order to simplify the speed
control loop. In [16], an easy way for deriving the current loop transfer function was discussed
36 | P a g e
where the author approximated it by a delay of three times the sampling time. Thus the
approximated transfer function for the current loop is:
(57)
To check the validity of the approximated current loop transfer function, the closed loop response of
the actual current loop and the approximated current loop was compared. Result from the
comparison is presented in figure.5.8 below.
Figure 5.8 Closed loop response comparison between actual current loop and approximated current loop
Figure.5.8 shows that the approximated response is very close to the actual current loop response,
even though the transfer function is much less complex.
The open loop transfer function for the speed loop is presented by equation (58) below.
(58)
The following approximations are valid near the vicinity of crossover frequency [4]:
From the above approximations can be simplified to:
(59)
Let
, the closed loop transfer function of the speed loop is derived as:
(60)
Comparing the denominator of to the symmetrical optimum transfer function presented in
equation (29). That is:
37 | P a g e
(
) (
)
From the above comparison, setting the damping ration as 0.707, the following equations are
derived for calculating the PI controller gain parameters:
(61)
(
) (62)
(
)
(63)
(64)
Using equation (61-64), the gain parameters for the speed PI controller are calculated and presented
below:
Using Matlab/Sisotool, the designed controller was simulated with the above designed controller
parameter. The system was discretized using the zero order hold method and simulated in z-domain.
The open-loop root locus and bode plot are shown below in figure.5.9 and figure.5.10.
Figure 5.9 Root locus plot for the speed controller
38 | P a g e
Figure 5.10 Bode plot for the speed control loop
From figure.5.9 it can be seen that the closed loop poles lie on the 0.707 damping trace. This
validates the designed controller and indicates that the system is stable. Figure.5.10 shows the
speed loop has a gain margin of 22.8 and a phase margin of 60.4 thus further indicate the stability of
the loop. A step test is performed on the speed loop; the result is shown in figure.5.11 below.
Figure 5.11 Closed loop step response of the designed speed control loop
Figure.5.11 shows that for a step test, the speed loop system has a settling time of 35 ms and a
10.03% overshoot. This dynamic behavior is within acceptable range. The parameter gains were
altered in Matlab/Sisotool for system response improvement; however it is realized that the system
is already at optimum condition hence the designed parameters were left as is.
39 | P a g e
5.2 Grid-side controllers design The grid-side control loops are similar to the machine-side control loops; the difference lies in that
the outer loop regulates the dc-link voltage which is an electrical quantity, hence it must react to
system disturbances faster than the machine-side speed loop. For the current loop, UPF is
implemented. The q-axis current is set to 0 to satisfy the UPF condition hence d-axis current controls
the current loop behaviour; this means d-axis current controller must be tuned. The inherent
coupling of the grid is decoupled by the control algorithm similar to the machine-side control.
Figure.5.12 below illustrates the structure of the grid-side control.
Figure 5.12 Adapted from [20] Grid-side controller structure
5.2.1 DQ-axis current controllers
The dq-axis current controller tuning is similar to that of the machine side, both current loops have
the same dynamics as q-axis current is set to 0. Hence the tuning will be made only for the d-axis
controller. Figure.5.13 below shows the grid-side current control loop.
Figure 5.13 Grid-side current loop
From figure.5.13, it can be seen that all the transfer functions can be presented by equation (52),
(53) and (49) with the addition of can be derived from the filter model presented in chapter
4. Due to the complex nature of the filter model, a method for simplifying the transfer function was
found in [16], the transfer function of the filter was approximated by ignoring the filter capacitance
for low frequencies (i.e. 50Hz) giving the new equation:
( )
(65)
40 | P a g e
Note and are the inverter-side and grid-side inductor parasitic resistance. As mentioned in the
filter design section from chapter 4, these resistances must be included in the control design as they
affect the system dynamic behavior. To validate this approximation, a sine wave was modulated as
the input for both the actual filter and approximated filter transfer function, the output was then
compared. The frequency of the input was set as 50 Hz then 1000 Hz. Figure.5.14, 5.15 and 5.16
shows the modulated sine wave, comparison of filter response at 50 Hz and 1000 Hz.
Figure 5.14 Modulated sine wave input for the filter
Figure 5.15 Comparison of filter response to an input at 50 Hz
41 | P a g e
Figure 5.16 Comparison of filter response to an input at 1000 Hz
From figure.5.15 and 5.16, it can be seen that the approximation for the LCL filter transfer function is
indeed valid for low frequency input.
Using the same tuning method for the machine-side current controller, adding the time constant of
the converter delay and the sampling delay i.e. , the following equations are used to
tune the grid-side current controller:
√
(66)
Using the set of equations (66) and the LCL filter parameter from table.4.2, the gain parameters are
listed below:
The designed controller gain was replaced by a new set of gains; this is the result of using the actual
LCL filter transfer function. The designed gain parameters were used for the actual LCL filter and
displayed a significant amount of oscillation. Thus the gain was altered to improve the system
dynamics. The new set of gain parameters are listed below:
42 | P a g e
Using Matlab/Sisotool, the designed controller was simulated with the above designed controller
parameter. The system was discretized using the zero order hold method and simulated in z-domain.
The open-loop root locus and bode plot are shown below in figure.5.17 and figure.5.18.
Figure 5.17 Root locus plot for the grid-side current control loop
Figure 5.18 Open loop bode plot for the grid-side current control loop
From figure.5.18, it shows that the current loop has a gain margin of 9,62 and a phase margin of 77.1
thus indicating the system is stable. A step test was done for the grid-side current loop, figure.5.19
below presents the result:
43 | P a g e
Figure 5.19 Step response of the designed grid-side current loop
Figure.5.19 shows that the step response of the grid-side current loop has a settling time of 2ms and
no overshoot. This displays good system response.
5.2.2 DC-link voltage controller
The structure of the voltage controller is presented in figure.5.20, which includes the transfer
function of the dc-link capacitor.
Figure 5.20 Grid-side voltage control loop
The transfer function for the current loop is again approximated using the same method for the
machine-side speed loop controller design. The transfer function for the capacitor can be derived
from the model of the capacitor presented in chapter 4 as:
(67)
The open loop transfer function for the voltage loop is presented by equation (68) below.
(68)
44 | P a g e
The following approximations are valid near the vicinity of crossover frequency [4]:
From the above approximations can be simplified to:
(69)
Let
, the closed loop transfer function of the speed loop is derived as:
(70)
Comparing the denominator of to the symmetrical optimum transfer function presented in
equation (29). That is:
(
) (
)
From the above comparison, setting the damping ration as 0.707, the following equations are
derived for calculating the PI controller gain parameters:
(71)
(
) (72)
(
)
(73)
(74)
Using equation (71-74), the gain parameters for the speed PI controller are calculated and presented
below:
Using Matlab/Sisotool, the designed controller was simulated with the above designed controller
parameter. The system was discretized using the zero order hold method and simulated in z-domain.
The open-loop root locus and bode plot are shown below in figure.5.21 and figure.5.22.
45 | P a g e
Figure 5.21 Root locus plot for the voltage controller
Figure 5.22 Bode plot for the voltage control loop
From figure.5.21 it can be seen that the closed loop poles lie on the 0.707 damping trace. This
validates the designed controller and indicates that the system is stable. Figure.5.22 shows the
voltage loop has a gain margin of 25 and a phase margin of 66.5 thus further indicate the stability of
the loop. A step test is performed on the voltage loop; the result is shown in figure.5.23 below.
46 | P a g e
Figure 5.23 Closed loop step response of the designed voltage control loop
Figure.5.23 shows that for a step test, the voltage loop system has a settling time of 150 ms and a
5.81% overshoot. This dynamic behavior is within acceptable range. The parameter gains were
altered in Matlab/Sisotool for system response improvement; however it is realized that the system
is already at optimum condition hence the designed parameters were left as is.
47 | P a g e
Chapter 6 - Simulation and analysis The modelled system is simulated using Matlab/Simulink. The results are analysed in this section for
observation on the effectiveness of the implemented control strategy as well as the switching
scheme. The models were verified first for their accuracy. Simulations for the machine and grid side
were performed separately first, then the complete system was connected and simulated as a
whole. Note the results presented for the independent machine and grid side are for current in the
positive direction for ease of presentation. However, the results presented for the complete system
simulation are for currents in their actual direction as it is important to show the back-to-back power
flow capability of the PWM converters. The sampling frequency for the simulation is set to 10000 Hz.
The switching scheme used is the SVPWM with the switching frequency set to 5000 Hz. The model
used for the SVPWM simulations was adapted from the SVPWM model done by Siva Malla. A
schematic diagram of the adapted model is shown in Appendix D figure.10.6.
6.1 Model verification For any system design and modelling, before conducting actual simulations the model needs to be
verified for good accuracy when results are obtained. The machine side model for this project is
especially evaluated before actual simulation, the reason being that in order to provide good
understanding of the system and its control mechanism, the model of the PMSG was decided to be
derived from its governing equations instead of using the standard model block in Simulink. The
model was developed and presented in chapter 3. Thorough verification was achieved by comparing
the load/input mechanical torque step response of the derived model to the actual Simulink model
using the same set of machine parameters (default Simulink machine parameters). The Simulink
system model used for this verification is shown in Appendix E figure.10.7. When the machine is
operating in generator mode, the currents are negative and hence the electromagnetic torque
output will be negative. Figure.6.1 to figure.6.4 below shows the machine response as a motor. The
load torque was stepped at 0.25 second, the whole simulation runs between 0.0 and 0.5 seconds.
Figure 6.1 Electromagnetic torque response comparison during motoring mode
48 | P a g e
Figure 6.2 Rotor angle comparison during motoring mode
Figure 6.3 Rotor speed comparison during motoring mode
49 | P a g e
Figure 6.4 dq-axis current comparison during motoring mode
From the above results it can be seen that although the responses of both model settle at identical
points, however the derived model displays much more oscillation at stepped point and during the
machine starting period. This is due to the fact that governor control is implemented internally for
the Simulink PMSM model. The oscillation in the derived model response can be eliminated by
implementing the vector control algorithm. Note the rotor angle for the derived model was
modulated for convenient data reading. The above figures shows the motoring operation of the
PMSM, in order to verify full effectiveness of the derived machine model, the same simulation was
performed again with the input mechanical torque being a negative step (-1 N.m). Figure.6.5 below
presents the verification results for the PMSM generating operation.
Figure 6.5 Electromagnetic torque response during generating mode
Figure.6.5 shows that the developed electromagnetic torque is negative, this is indeed correct since
power flow from the rotor to the stator hence current is in the negative direction (positive direction
chosen to be from stator to rotor). From the above results, the derived model can be concluded as
fit for simulation purposes.
50 | P a g e
6.2 Grid side simulations Grid side operations are mainly aimed to regulate the DC link voltage. As the load demand increase,
more current will be flowing in to the dc link. According to equation (48) used for the DC-link model
presented in chapter 4 that is:
∫
It can be seen that the machine side dc current and grid side dc current must remain constant in
order to keep the dc link voltage fixed. An increase in the supplied current will cause an increase in
the dc link voltage. The grid side control monitors the dc link voltage and increases the grid side
current by altering the d-axis current component hence the amount of real power delivered to the
grid. This section presents results obtained from independent simulations for the grid side so as to
demonstrate the concept discussed above.
The DC-link voltage is set at 700V, as discussed in [42] that for a PWM voltage source converter, the
DC-link voltage must be higher than the DC-link voltage produced by a diode rectifier under the
same operating conditions. The DC-link capacitor is chosen to be 1000 µF for good DC current ripple
rejection. The simulation for the grid side is decoupled from the machine side by supplying the DC
link with a constant DC current source. Step tests are performed separately first for the current and
voltage control loops to verify the controller gains calculated in section 5.2. A schematic diagram of
the independent grid-side simulation is shown in the Appendix F figure.10.8.
6.2.1 Current Step response of the grid side converter
For the current step response, the current source and the capacitor are replaced by a constant DC
voltage source so that the voltage control loop can be neglected. The d-axis current reference is
provided by a step input. The simulation is run from t = 0s to t = 0.5s. The reference current is first
stepped to 5 A at t = 0.15s, then stepped down to 3 A at t = 0.3s. Figure.6.6 and 6.7 below shows the
current step response of the grid side control loop during actual simulation.
Figure 6.6 dq-axis current response compared to references
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Figure 6.7 dq-axis current response zoomed in at t = 0.15s
Figure.6.6 shows that the d and q-axis currents follow the reference values closely; the noise
observed is caused by the converter switching operation. Figure.6.7 is a zoomed in version of
figure.6.6, as can be seen the settling time of the current loop step response is approximately 2.5ms
with slight overshoot. This complies closely to the results obtained from the grid-side controller
design section in chapter 5. The difference in overshoot and settling time can be explained as the
result of using approximated model transfer functions when the controllers were designed.
6.2.2 Voltage step response of the grid-side converter
For the voltage control loop, the constant DC voltage source is replaced by a capacitor (initial voltage
set at 700 V) and a controlled current source. The supply current and the reference voltage are
provided by step inputs. The simulation runs from t = 0s to t = 1s. In order to observe the voltage
step response, the supply current was kept at 0A. The reference voltage was stepped up from 800V
at t = 0.3s and then stepped down to 750V at t = 0.6s. Figure.6.8 below shows the voltage step
response for the grid-side converter during actual simulation.
Figure 6.8 DC voltage response compared to the reference voltage
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Figure.6.8 shows that the DC voltage follows the reference voltage closely; the settling time is
approximately 110ms with no overshoot. These results comply closely to the results obtained from
the grid-side voltage controller design section in chapter 5.
6.2.3 DC link control in relation with active/reactive power flow to the grid
The grid-side converter’s main purpose is to keep the DC link voltage constant as input power varies.
This is achieved due to the control of the d-axis component of the grid current. As the input power
to the DC link is increased or decreased, the d-axis current is increased or decreased by the
controller. Since UPF is implemented and hence q-axis current is kept at zero, the output power to
the grid is directly controlled by the d-axis current. For this project only balanced grid condition is
considered and no reactive power compensation is implemented, thus reactive power supplied to
the grid is kept at 0 throughout the simulation process. The input power is simulated using the signal
builder block in Simulink, the DC-link current input is provided by the division between input power
and DC-link voltage since:
The simulation was performed for the time period between t = 0s and t = 1s. The input power was
stepped at t = 0s, t = 0.3s and t = 0.6s. Figure.6.9 below shows the input power and calculated input
DC-link current.
Figure 6.9 DC-link input power and current
The simulation results of the grid behaviour for input power variation presented above are shown
below in figure.6.10 to 6.14.
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Figure 6.10 Comparison between grid active/reactive power and input DC link power
Figure.6.10 presents the grid active/reactive power response to varying DC link input power. The
grid powers are calculated using equations (45) and (46). It can be seen that the actual grid active
power tracks very well the reference input power. The reactive power is fixed at 0Var since the q-
axis current is forced to be 0. Figure.6.11 below shows the dq-axis currents behaviour as input power
is varied.
Figure 6.11 dq-axis current during input power variation
From figure.6.11 it is clear that the d-axis current is being varied as a function of error measured
between the reference DC-link voltage and actual DC-link voltage, as illustrated in figure.5.13 at t =
0.3s and again at t = 0.6s.In return the changing d-axis current counteracts the effect induced on the
DC-link voltage by the varying input DC-link current. The q-axis current is fixed at zero as expected.
The corresponding measured DC-link voltage variation is shown in figure.6.12 below.
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Figure 6.12 DC-link voltage response due to DC-link current variation
Figure.6.12 very clearly shows that as the DC-link current input was increased at t = 0s and t = 0.3s,
the DC-link voltage is trying also to increase. The voltage controller tracks the error and provides the
corresponding d-axis current reference in order to bring the DC-link voltage back down to its set
value. At t = 0.6s the input DC-link current is decreased, hence the DC link voltage shows a dip as it
tries to decrease with the decreasing input power. Figure.6.13 below shows the actual grid currents
and voltage behaviour for the varying power input to the grid.
Figure 6.13 Grid currents and voltage behaviour for varying grid input power
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Figure.6.13 shows how the d-axis current is used to control the grid current. Since q-axis current is
fixed at zero, the grid current varies as a function of d-axis current. It can be seen from figure.6.13
and 6.11 that the amplitude of the three-phase grid currents corresponds to the d-axis current
magnitude. It is also noted that the grid voltage do not change since the grid is modelled as a three-
phase balanced voltage supply. Note the grid voltage presented in figure.6.13 is the phase voltage.
In order to observe the effectiveness of the implemented UPF control, single phase voltage and
current of phase A is compared in figure.6.14 below.
Figure 6.14 Grid phase A voltage and current
Figure.6.14 shows the phase A grid voltage and current are in phase hence the UPF condition is
satisfied. It is also noticeable that the control implemented keeps the currents in phase with voltage
even when the input power to the grid is increased or decreased.
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6.3 Machine side simulations The machine side simulations involve presentation of results obtained by testing the FOC strategy.
The simulations carried out are similar to the grid-side simulations. However, extensive analysis was
performed on the speed response and DC-link voltage variation in relation to different applied shaft
torque. The simulation for the machine side is done independently without the grid side system. For
this project, a micro-turbine is connected to the generator. This means the mechanical torque input
from the turbine is dependent on the grid load demand. However, the model of the turbine is not
included in the scope of this project. The load demand is simulated using the signal builder block as
power steps. The input torque for the generator is derived by dividing the load power demand by
the operating speed of the generator. This section includes independent current and speed control
loop simulations, similar to the grid-side simulations, in order to validate the control system. The
machine parameter used for the simulations is listed in table 6.1 below. A schematic diagram of the
independent machine-side simulation is shown in the Appendix G figure.10.9.
Table 6.1 Machine parameters used for the simulation
Stator resistance 12.5 mΩ
Stator inductance 0.165 mH
Pole pairs 2
Inertia 0.011
Permanent magnet flux linkage 0.2388
Rated speed 20000 rpm
Rated voltage
6.3.1 Current step response of the machine-side converter
The current control of the machine consists of two loops for the rotor and quadrature axis
components of the stator current. With the outer speed loop disconnected, the q-axis current
reference is provided by stepped inputs and the d-axis current is force to 0 since maximum torque
per ampere control method is used and the machine type is surface mounted. The speed of the
machine was kept constant and the applied shaft torque was set to 0. Figure.6.15 and 6.16 below
shows the dq-axis current response. The simulation runs from t = 0s to t = 0.1s. The q-axis current
reference was stepped from 0A to -6A at t = 0.05s.
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Figure 6.15 dq-axis current step response
Figure 6.16 dq-axis current step response (Zoomed in)
Figure.6.15 shows that the d and q-axis current follows its reference current closely. There is a slight
dip in the d-axis current during the transient period of the q-axis current. This is due to the dip in
speed of the machine when applied shaft torque is varied. This idea will be elaborated in a later
section. Figure.6.16 is a zoomed in version of figure.6.15, as can be seen the settling time of the
current loop step response is approximately 1.2ms with slight overshoot. This complies closely to the
results obtained from the machine-side current controller design section in chapter 5.
6.3.2 Speed step response of the machine-side converter
For the speed control loop, the input reference value for the q-axis current loop is provided by the
outer speed loop. The reference value for the speed loop is provided by a step input. The output
speed of the machine is now fed back to the outer speed control loop and the torque is kept
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constant. Note the reference value for the speed loop is provided in electrical terms governed by the
equation:
This is due to the way the mathematical model of the machine was setup. Figure.6.17 below
presents the result obtained from the step test for the machine-side speed loop. The simulation runs
from t = 0s to t = 1s. The machine speed set-point was stepped at t = 0s to half rated speed i.e.
10000rpm then it was stepped at t = 0.5s to rated speed i.e. 20000rpm.
Figure 6.17 Machine-side speed loop step response
Figure 6.18 Machine-side speed loop step response (zoomed in)
Figure.6.17 shows the machine speed loop step response, the speed measurement was presented in
both electrical and mechanical form, as well as in revolutions per minute form. Observing the
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measurements, the machine model again shows good accuracy. The actual speed of the machine
tracks the reference speed very well. Figure.6.18 is a zoomed in version of figure.6.17, it shows step
response has a settling time of approximately 40ms and an overshoot approximately 15.3%. This
complies closely to the results obtained from the machine-side speed controller design section in
chapter 5.
6.3.3 Speed control in relation to applied shaft torque due to load demand variation
The main purpose of the machine-side converter is to keep the operating speed of the machine at a
constant set point regardless of the applied shaft torque. Since the PMSG will be connected to a
micro-turbine, the amount of power produced by the mechanical torque is directly related to the
grid load demand. Referring back to equation (13) that is:
(
)
If then the speed of the machine will increase. The difference between the
electromagnetic torque and the applied mechanical torque is known as the acceleration torque.
Note if the difference is negative then the machine will decelerate. The speed control is
implemented in conjunction with current control in such a way that if the applied mechanical torque
was increased, the q-axis current will increase accordingly governed by equation (7) that is:
Since maximum torque per amperes method is implemented, d-axis current is kept at 0. By
controlling the q-axis current, the electromagnetic torque will be increased or decreased to counter
the change in the applied mechanical torque hence keeping the speed constant. The friction and
windage losses of the machine were neglected in the model. Hence torque differences only occur
during transient periods of the q-axis current. The simulation for this section uses grid load power
demand and a speed set-point as inputs. The output is the speed of the machine and power
generated by the machine-induced electromagnetic torque. The simulations are first performed with
the machine running at rated speed, then the speed was stepped down to half rated speed and the
same load power requirement was applied. Figure.6.19 below shows the reference power demand
and required torque at rated speed.
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Figure 6.19 Required power and torque from the machine at rated speed
The input and output power of the machine is related to the torque by the following equation:
The required load power is divided by the reference speed of the machine to determine how much
torque must be applied. Using the above presented torque values as the input for the system at
rated speed, results obtained from the simulation for the machine at rated speed are presented in
Figure.6.20 to 6.26 below. The simulation runs from t = 0s to t = 3s with input power and torque
steps at t = 0s, t = 1s and t = 2s as shown in figure.6.20.
Figure 6.20 Torque response to the load demand variation at rated speed
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Figure 6.21 Rated machine speed response
Figure 6.22 dq-axis current response at rated speed
Figure.6.20, 6.21 and 6.22 illustrates the relationship between q-axis current and speed of the
machine during input torque variations. At t = 1s, input torque step causes the electromagnetic
torque produced to increase and eventually settle at the same value as the input torque. Since is
bigger than the machine decelerates causing the speed dip at t = 1s shown in figure.6.21. The
speed control loop calculates the error between the decreased speed and the reference speed
hence providing the reference value for the q-axis current. The q-axis current is increased in order to
increase so as to eliminate the deceleration caused by torque imbalance and hence bringing the
speed back to the reference value. At t = 2s, input torque was decreased causing a reversal effect
compared to the input step at t = 1s. The rotor axis current component remains at zero throughout
as expected since MTPA control was implemented. This means the stator current of the machine will
only be dependent on the q-axis current i.e. q-axis current value equal to the amplitude of the stator
current as shown in figure.6.23 below. The stator voltage stays constant with the generator speed
also shown in figure.6.23.
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Figure 6.23 Stator current and voltage response at rated speed
The frequency of the output stator voltage and currents are governed by the equation:
From figure.6.23, it can be seen that the frequency of the three-phase stator voltage and current is
666.67 Hz. This frequency can be obtained using the above equation as well. The frequency
validation shows that the derived mathematical model of the machine is fully capable of handling
high speed operations. Since the machine is running at rated speed thus 666.67 Hz is the rated
output frequency of the machine. Since the friction and windage losses of the machine are
neglected, the only losses should be due to the internal impedance of the machine; this is shown in
figure.6.24 below as the output power is compared to the input power.
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Figure 6.24 Output power response compared to the reference input power at rated speed
Note the turbine connected to the generator is not within the scope of this project, it is assumed
that the turbine has an instantaneous response to load variations. Using the ratio between the input
and output power shown in figure.6.24, an approximation for the efficiency of the designed
machine-side system at rated speed to be 95%.
The above simulations are then repeated for half rated machine speed. The same analysis will not be
presented again, only relevant information with respect to the effect of varying the machine speed
will be extracted and analysed. As speed of the machine was decreased, to generate the same
amount of power, the mechanical torque input required from the microturbine will be increased.
The new set of input torque with the same power demand is shown in figure.6.25 below.
Figure 6.25 Torque and power demand for half rated machine speed
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Figure.6.25 shows that the power input remains the same, however, the corresponding torque
demand has doubled as compared to the torque demand for the machine at rated speed. This
results in the stator current to increase and the stator voltage to decrease. The results are shown in
figure.6.26 below.
Figure 6.26 Stator current and voltage and half rated machine speed
From figure.6.26 it can be seen low speed operation of the PMSG is undesirable as the current
produced for the same amount of power output is much greater at lower machine speed. This
implies much more losses during machine operation.
6.3.4 DC-link voltage variation with respect to machine torque variation
As discussed in section 6.2 with the grid-side simulation, as current from the machine side varies due
to varying load demand, the dc link voltage will vary accordingly until the current from machine side
is balanced with the current flowing into the grid-side. This section demonstrates the DC-link voltage
variation from the machine-side perspective. The simulation was performed using a resistor
connected to the terminal of the DC-link to dissipate the power generated by the machine. This is for
the reason that during the simulation it was found that the capacitor will charge up infinitely due to
the constant current input from the rectifier. The resistor is modelled as a constant impedance load.
The simulation runs from t = 0s to t = 4s. The DC-link capacitor was assumed to be initially charged at
700V. At t = 1s, a resistor of 100Ω is connected to the terminals of the DC-link capacitor. Figure.6.27
below shows the shaft torque variation.
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Figure 6.27 Shaft torque variation
Figure.6.27 shows that the shaft torque of the machine was stepped from -6 N.m to -8 N.m at t = 1s,
then decreased to -5 N.m at t = 2s. An increase in the shaft torque will cause the DC-link current to
increase and a decrease in shaft torque will cause the DC-link current to decrease. This causes an
imbalance in the DC-link currents. As the resistor side current tries to balance the generator side
current, the DC-link voltage will either increase or decrease. The resulting DC-link voltage variations
as well as the DC-link currents are shown in figure.6.28 and 6.29 below.
Figure 6.28 DC-link voltage variation
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Figure 6.29 DC-link currents variation
Figure.6.28 and 6.29 shows that as the generator side current increases, the resistor side current
raises so as to keeping the DC-link current in equilibrium. During the transient period of the currents,
the DC-link voltage is increasing due to the capacitor charging. When the generator side current
became balanced with the resistor side current at t = 1.6s, DC-link voltage stopped increasing and
remained constant. When the currents started decreasing at t = 2s, the same principle applies.
However, the capacitor is now discharging hence the reduction in DC-link voltage. These variations in
the DC-link voltage is regulated by the grid-side control as shown in section 6.2.
6.4 Complete system simulation In this section, the machine-side and grid-side system are connected together and simulated to see
how effective the control strategy implemented work on the system as a whole. The main purpose
of the vector control is to regulate the machine speed and the DC-link voltage under varying load
conditions. Figure 6.30 to 6.35 below shows the complete system behaviour as the input torque to
the machine varies. The simulation runs from t = 0s to t = 4s. The torque applied to the machine is
varied at t = 0s, t = 1s and t = 2s as shown in figure.6.30 below. Note for this section, all results are
presented for currents in their actual direction, positive values means the current is flowing from
grid to the generator and vice versa. A Simulink schematic diagram for the complete system
simulation is presented in Appendix H figure.10.10.
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Figure 6.30 Applied torque to the machine for the complete system
As the input torque for the machine varies the current flowing into the DC-link increases as shown in
figure.6.31 below. The DC-link voltage will try to decrease at t = 0s and t = 1s and increase at t = 3s.
This voltage variation will be regulated by the grid-side voltage control loop as can be seen in
figure.6.32. Note the DC-link current is filtered for ease of presentation.
Figure 6.31 DC-link current for the complete system
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Figure 6.32 DC-link current for the complete system
From figure.6.32 it can be seen that the voltage is regulated at 700V by the grid-side voltage control.
The active and reactive power flow from the machine to the grid is shown in figure.6.33 below
where the power produced by the machine-side is compared to the power into the grid. The reactive
power is kept at 0 since UPF is implemented.
Figure 6.33 Machine and grid-side active and reactive power
From figure.6.33, by comparing the input machine-side power and the output grid-side power, the
efficiency for the complete system is determined to be approximately 95.6%. The losses are mainly
due to the switching of the converters as well as filter and grid impedances. One of the main
purposes of the AC to AC converter is to change the frequency of the generator output voltage and
currents to the grid fundamental frequency. Figure.6.34 and 6.35 below shows the frequency
transformation by comparing the machine output voltage and current waveforms to the resulting
grid voltage and current waveforms.
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Figure 6.34 Machine-side voltages and currents
Figure 6.35 Grid-side voltages and currents
Comparing the voltage and current waveforms from figure.6.34 and figure.6.35, it can be seen that
the machine-side waveform frequency is 666.67 HZ and the grid-side waveform frequency is 50 Hz
which is the grid fundamental frequency. Hence it can be concluded that the high frequency output
of the machine is effectively transformed to the fundamental frequency required for grid operations.
6.4.1 Back-to-Back Power flow
The chosen converter topology is a back-to-back PWM voltage source converter. As discussed in the literature review, this topology allows power to flow from grid side during machine start-up operation. Since the converter is a voltage source that means the reversal of the power flow is a result of current reversal. The back-to-back power flow operation is illustrated in this section as a comparison to the previous section where the power is flowing from generator to the grid. The same amount of torque was applied to the generator model; however, positive this time which means the machine is operating in motoring mode. Figure.6.36 and 6.37 shows the machine and grid-side voltage and current waveforms during the inverse operation of the complete system.
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Figure 6.36 Machine-side voltage and current during inverse operation
Figure 6.37 Grid-side voltage and current during inverse operation
By observing figure.6.36 and 6.37 then comparing them to figure.6.34 and 6.35, it can be seen that during machine generating mode, the currents are in anti-phase with the voltage indicating the power is flowing from the generator to the grid. During machine motoring mode, the power is flowing from the grid to the machine side since the current is in phase with the voltage as can be seen from figure.6.36 and 6.37. Figure.6.38 below shows the DC-link voltage is kept positive as mentioned earlier that the power flow reversal is dependent only on the current reversal.
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Figure 6.38 DC-link voltage during inverse operation
Comparing figure.6.38 to figure.6.32 it can be seen that the DC-link voltage dips and rises are opposite during machine generating and motoring mode. This is expected since the current is flowing in the opposite direction during both operating modes.
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6.5 Grid filter efficiency The main function of the grid filter is to filter out the high frequency harmonics of the grid-side
converter output current. A general rule for the efficiency of a grid filter is governed by the 5% THD
limit of grid currents [24]. For this project a LCL filter is used, the design of the filter was done in
chapter 4. Referring back to the bode plot of the designed filter in figure.4.6 It can be seen that the
filter has a -50 dB attenuation at approximately 3000 Hz. Since the switching frequency is 5000 Hz
based on SVPWM strategy, the designed filter should be able to attenuate the high frequency
harmonics in the grid-side converter output current. The FFT analysis tool of the powergui block in
Matlab/Simulink was used to obtain the harmonic analysis of the grid-side currents before and after
filtering. The simulation uses the same operating conditions from section 6.4, the FFT analysis is
done on the grid-side currents for the period between t = 0.5s and t = 0.9s (20 cycles with
fundamental frequency at 50 Hz). The results are shown and compared in figure.6.39 and 6.40
below.
Figure 6.39 FFT analysis of grid-side current before filtering
Figure 6.40 FFT analysis of grid-side current after filtering
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By comparing figure.6.40 and 6.39, it can be seen that the THD content of the grid-side current
before filtering is 30.27% and the THD content of the grid-side current after filtering is 1.70%. From
the FFT analysis it can be seen that harmonics at higher frequencies are almost completely
eliminated by the LCL filter, this is expected since these kind of filter are known to have superior high
frequency attenuation. The corresponding current waveforms are shown in figure.6.41 and 6.42
below.
Figure 6.41 Grid current before filtering
Figure 6.42 Grid current after filtering
From figure.6.41 and 6.42, it can be seen clearly that the current waveforms after filtering has much
less harmonics than the current waveforms before filtering. Since the grid current after filtering has
a THD of 1.70% which is within the 5% THD limit, it can be concluded that the designed filter is
effective for the system under analysis.
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Chapter 7 - Conclusions The goal of this project was to design a system that will effectively interface a high speed PMSG to
the grid by converting the high frequency output of the generator to the grid fundamental
frequency. Suitable control and switching strategy must be chosen based on the literature review
conducted on the possible converter topologies for such high speed application. Furthermore, a grid
filter must be chosen based on efficiency with respect to harmonic attenuation. A model of the
PMSG must be derived for implementing the chosen control strategy. The entire system must be
properly designed and implemented in simulation to verify the accuracy and effectiveness of the
designed system. From the analytical and simulated results obtained throughout this thesis certain
conclusions can be drawn. These are discussed in this section.
7.1 Converter topology chosen A literature review was conducted on the possible topologies of power converters that are suitable
for interfacing a high speed generator to the grid. Based on the research, it is decided that a back-to-
back PWM AC-DC-AC converter is most suitable. Using this topology, no external source is needed to
start the generator and the machine-side is effectively decoupled from the grid-side so independent
control can be implemented on both ends. It is by far the most well developed converter topology
for grid interface applications and hence offer a wider variety of control options.
7.2 Model of the PMSG derived The model of the PMSG is derived using the reference frame theory. By comparing the developed
PMSG model and the Matlab/Simulink PMSG model, it is concluded that the derived model is
suitable for simulation and analysis. However, differences in model responses can be observed. This
is due to the obvious reason that the Matlab model is much better developed with internal control
mechanism implemented.
7.3 Filter analysis and design An analysis on the possible filters may be used for grid application was conducted. Results were
obtained based on the frequency responses for different types of filters. It was concluded that LCL
filter has superior performance at higher frequency and the resonance problem can be eliminated by
passive damping techniques. The filter design was based on the method discussed in past literatures
and adheres to all the limitations. The efficiency of the filter was verified in simulation using the 5%
THD limit in grid-side current.
7.4 Control and switching strategy The control method and its complimenting switching strategy were chosen based on the topology of
the converter. The control algorithm was designed and tested in simulation.
7.4.1 Choosing the control method and switching strategy
The AC-DC-AC converter topology allows independent control on the machine and grid-side system.
The vector control method was chosen for its superiority in good system dynamic behaviors. For this
type of control either SPWM or SVPWM switching strategy may be implemented. However, from a
comparison between SPWM and SVPWM conducted in section.3.3 it is clear that SVPWM produce
output with less harmonic content and is 15% more efficient than SPWM. Thus SVPWM is chosen as
the switching strategy for the final system.
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7.4.2 Design and simulation of the system with control algorithm implemented
The Controllers are designed based on the models derived for the machine and grid-side systems.
Theoretical system responses with designed controllers were obtained using Matlab/Sisotool. These
controllers are first tested independently in simulation on the machine and grid-side system. System
response results from actual simulations were compared to the theoretical system responses and it
can be concluded that the designed controllers are suitable for application. Minor differences did
occur due to approximations used during the design phase. The machine-side and grid-side were
connected for the simulation of the complete system. Results show that the designed controller was
able to regulate the speed of the machine and the DC-link voltage. The high frequency output of the
generator was converted to the grid fundamental frequency.
7.5 Assumptions made The machine model was derived neglecting frictional and windage losses and will have more ideal
behavior than a real machine. However the purpose of this project is to analyze theoretically the
control system designed hence the model is applicable. The micro-turbine model is not within the
scope of this project, the input mechanical torque for the generator is assumed to have an instant
response to varying load demands. This is an unrealistic assumption as load variation always happen
earlier in time than the turbine response. However, this assumption has to be made due to the
absence of a micro-turbine model.
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Chapter 8 - Recommendations Based on the above conclusions, the following recommendations are made.
8.1 Improve machine model accuracy The machine model derived in this project does not represent realistic machine behaviors. To
improve the accuracy of the model, more sophisticated derivation is required. Aspects such as the
effect of temperature variation on the stator inductance, viscous damping and saturation effects of
the magnets should be considered. Furthermore the system could be implemented using a
difference PM machine, with interior mounted magnets, for better high speed operations.
8.2 Include micro-turbine model Due to the absence of micro-turbine model, the system designed has significant short coming in
terms of its ability to imitate a real life system. This project can be improved by including the micro-
turbine model to monitor grid load conditions. This will yield much more accurate dynamics at the
generator input.
8.3 Introduce realistic operating conditions The simulation results show the designed system is a valid one. However, the operating conditions
are rather ideal. In this project, it is assumed that the machine does not undergo saturation
conditions and the grid is perfectly balanced. No fault analysis was performed. By introducing more
realistic operation such as machine heating and grid unbalance, better analysis on the system can be
achieved.
8.4 Explore alternative converter topologies This project is done based on an AC-DC-AC converter that has two full-bridge two-level PWM
converters. Research into multi-level converters can yield interesting results. Indirect converter
topologies should also be explored for future work.
8.5 Explore alternative control strategies Sensorless control strategies such as the direct torque control for the machine and direct power
control for the grid should be considered. These methods could yield better results when the system
is actually implemented in real time as the sampling requirement on the transducers can be greatly
reduced. Comparison between difference embedded control techniques such as constant stator flux
control and constant torque angle control will provide better understanding for machine dynamics.
8.6 Improve filter design methods Using more sophisticated design methods to obtain filter component parameters should be
investigated for better grid-side system behaviors.
8.7 Implement the designed system The simulated system in this project can be implemented to validate the theoretical results.
Alteration for the system can be made based on experimental results for better system
performance.
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Chapter 9 - List of References
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system," IEEE Trans. Power Del., vol. vol. 20, no. no.3, pp. pg. 2182-2192, 2005.
[2] A. Pritescu, "Control of a saturated permanent magnet synchronous motor," Aalborg University,
Denmark, 2010.
[3] C. Zwyssig and J. Kolar, "Design of a 100 W, 500000 rpm permanent-magnet generator for
mesoscale gas turbines," in 40th Conf. Rec. IAS Annu. Meeting, Hong Kong, 2005.
[4] R. Krishnan, Electric motor drives: modeling, analysis, and control, Prentice Hall, 2011.
[5] A. A. Hinai and A. Feliachi, "Dynamic model of a microturbine used as a distributed generator,"
in 35th Southeastern Symp. Syst. Theor., 2002.
[6] O. Fethi, L. A. Dessaint and K. Al-Haddad, "Modeling and simulation of the electric part of a grid
connected microturbine," in Proc. IEEE Power Eng. Soc. Gen. Meeting, 2004.
[7] D. A. Khaburi and A. Nazempour, "Design and simulation of a PWM rectifier connected to a PM
generator of micro turbine unit," Scientia Iranica, vol. 19, no. 3, pp. 820-828, 2013.
[8] Z. Ye, T. C. Y. Wang, S. Gautam and R. Zhang, "Efficiency comparison for microturbine power
conditioning systems," in IEEE Power Electron. Specialist Conf., 2003.
[9] Kumar.A., ""Modeling and control of micro-trubine based distributed generation system,"
International Journal of Circuits and Signal Processing, vol. 3, no. 2, pp. 65-72, 2009.
[10] J. Itoh, A. Odaka and I. Sato, "High efficiency power conversion using a matrix converter," Fuji
Electric Review, Fuji, 2004.
[11] H. Polinder, N. H. M. Hofmeester, L. J. J. Offringa and W. Deleroi, "Cycloconverter for high speed
permanent magnet generator units," in Power electronics and Applications, Fifth European
Conference, Europe, 1993.
[12] C. Busca, A.-I. Stan, T. Stanciu and D. I. Stroe, "Control of permanent magnet synchronous
generator for large wind trubines," Industrial Electronics, vol. vol., no. no., pp. pg. 3871 - 3876,
2010.
[13] C. Busca, A. I. Stan, T. Stanciu and D. I. Stroe, "Control of Permanent Magnet Synchronous
Generator for large wind turbines," Industrial Electronics, vol. vol., no. no., pp. pg. 3871 - 3876,
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[14] T. Instruments, "Field Orientated Control of 3-phase AC-Motors," Texas Instruments Europe,
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Texas, 1998.
[15] Y. Zhao, W. Qiao and L. Qu, "A space-vector modulated sensorless direct-torque control for
direct-drive PMSG wind turbines," in Industry Applications Society Annual Meeting, Las Vegas,
2012.
[16] J. G. d. l. Bat, "Development of a System for Testing Grid-Connected Permanent Magnet Wind
Generators," Cape Town, 2011.
[17] A. Opritescu, "Control of a saturated permanent magnet synchronous motor," AALBORG
University, AALBORG, 2010.
[18] M. Moussa, A. Helal, Y. Gaber and H. Youssef, "Unity Power Factor control of permanent
magnet motor drive system," in Power System Conference, Middle-East, 2008.
[19] A. Consoli, G. Scarcella, G. Scelba, S. Sindoni and A. Testa, "Steady-State and Transient Analysis
of Maximum Torque per Ampere Control for IPMSMs," Industry Applications Society Annual
Meeting, vol. vol., no. no., pp. pp. 1, 5-9, 2008.
[20] G. A. Raducu, "Control of Grid Side inverter in a B2B Configuration for WT Applications," Master
Thesis, Aalborg University , Aalborg, 2008.
[21] R. Marouani and A. Mami, "Voltage Oriented Control Applied to a Grid Connected Photovoltaic
System with Maximum Power Point Tracking Technique," American Journal of Applied Sciences,
vol. vol.7, no. no.8, pp. pg.1168-1173, 2010.
[22] K. P. Rao, D. S. Sao and D. J. Subrahmanyam, "Development of a Grid Connected Inverter for
Solar PV Systems with Energy Capture Improvement Based on Current Control Strategy,"
International Journal of Scientific and Research Publications, vol. vol.3, no. no.4, p. pg., 2013.
[23] I. H. G. V. M. Surprenant, "Phase locked loop control of inverters in a microgrid," Proc. IEEE
EnergyConvers, vol. vol.9, no. no.4, pp. pp.667-672, 2011.
[24] F. Blaabjerg and S. H. M. Liserre, "Design and Control of an LCL-Filter_based Three-phase Active
Rectifier," IEEE Transactions On Industry Applications, vol. vol.41, no. no.5, p. pg., 2005.
[25] S. A. M., "Wavelet modulated DC-AC power inverters," Memorial University of Newfoundland,
2007.
[26] A. Tatu, P. Kapil, V. Patel and J. Patel, "Review of modulation schemes for loss analysis in
inverters," in Nirma University International Conference, Nirma, 2012.
[27] H. Hussin, A. Saparon, M. Muhamad and M. D. Risin, "Sinusoidal Pulse Width Modulation Design
and Implementation by Focusing on Reducing Harmonic Content," in Mathematical/Analytical
Modelling and Computer Simulation, Asia, 2010.
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[28] J. Holtz, "Pulse width Modulation - A Survey," IEEE Transactions On Industrial Electronics, vol.
vol. 39, no. no. 5, 2010.
[29] K. Michal and P. Krzysztof, "Analysis Of Pulse Width Modulation Techniques For AC/DC Line-Side
Converters," University of Technology Studies and Materials, 2006.
[30] M. A. Boost and P. D. Ziogas, "State-of-the-Art Carrier PWM techniques: A critiacal Evaluation,"
IEEE transactions on Industry Applications , vol. vol. 24, no. no. 2, pp. pp. 271-280, 1988.
[31] A. Devices, "Reference Frame Conversions," Analog Devices Inc, 2002.
[32] T. Instruments, "Digital Signal Processing Solution for Permanent Magnet Synchronous Motor,"
Texas Instruments Incorporated, Texas, 1997.
[33] Haoran, "Study of PWM Rectifier/Inverter for a High Speed Generator Power System," in Power
and Energy Engineering Conference (APPEEC), Asia-Pacific, 2010.
[34] M. Liserre, P. Rodriquez and R. Teodorescu, "Grid Converters for photovoltaic and Wind Power
systems," 2011.
[35] R.-E. Precup and S. Preitl, "An extension of tuning relations after symmetrical optimum method
for PI and PID controllers," Automatica, pp. pp. 1731-1736, 1999.
[36] M. Braae and M. Machaba, "Explicit Damping Factor Specification in Symmetrical Optimum
Tuning of PI Controllers," 03 09 2014. [Online]. Available:
http://www.nt.ntnu.no/users/skoge/prost/proceedings/afcon03/Papers/050.pdf. [Accessed 03
09 2014].
[37] Mohan, Undeland and Robbins, Power Electronics - Converters, Applications and Design, New
Jersey: JOHN WILEY & SONS, INC., 1989.
[38] D. Lee, "Design Methodology of an LCL filter for Grid Connected Inverter Applications," Thesis
project, UCT, Cape Town, 2011.
[39] X. M. Zha, Y. Zhou, S. Duan and F. Liu, "Design and Research on Parameter of LCL filter in Three-
Phase Grid-Connected Inverter," in Power Electronics and Motion Control Conference, 2009.
[40] F. Blaabjberg and S. H. M. Liserre, "Design and Control of an LCL-Filter based Three-phase Active
Rectifier," IEEE Transactions on Industry Applications, vol. vol. 41, no. no. 5, 2005.
[41] A. D. H. P. S. F. B. Florin Iov, "Wind Turbine Blockset in Matlab/Simulink," Aalborg University,
Denmark, 2004.
[42] J. Rodriguez, J. Dixon, J. Espinoza, J. Pontt and P. Lezana, "PWM regenerative rectifiers: state of
the art," Industrial Electronics, vol. 52, no. no.1, pp. 5 - 22, 2005.
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Chapter 10 – Appendices
10.1 Appendix A: PLL Model The model for the PLL implemented in Matlab/Simulink is presented in Figure.10.1 below.
Figure 10.1 PLL Matlab/Simulink Schematic diagram
The derivation for the PI controller parameters for the PLL is shown in this section. The transfer
function for the PLL consists of the PI controller and an integrator:
The closed loop transfer function of the PLL can be derived as:
The requirements for the PLL are 5% overshoot, settling time within 2% band and the damping ratio
is 0.7071. The restriction imposed on the natural frequency is thus
where
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10.2 Appendix B: PMSG model
Electrical part of the model
Figure 10.2 Electrical part of the PMSG model
Mechanical part of the model
Figure 10.3 Mechanical part of the PMSG model
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Complete PMSG model
Figure 10.4 Complete PMSG model
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10.3 Appendix C: VSC model The Simulink block for the VSC is shown in figure.10.5 below. The phase voltage gain with respect to
the command signals can be given by the following equation using a matrix gain:
[
]
[
] [
]
Figure 10.5 VSC simulink schematic
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10.4 Appendix D: Adapted Simulink model for SVPWM
Figure 10.6 Adapted simulink model for the SVPWM
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10.5 Appendix E: Simulink model used for PMSG model verification
Figure 10.7 PMSG verification system in Simulink
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10.6 Appendix F: Independent grid-side Simulink model with control
implemented
Figure 10.8 Independent grid-side simulink model
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10.7 Appendix G: Independent machine-side Simulink model with control
implemented
Figure 10.9 Independent machine-side simulation
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10.8 Appendix H: Simulink schematic for the complete system with full
control strategy implemented
Figure 10.10 Complete system simulation in simulink
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Chapter 11 – EBE Faculty: Assessment of
Ethics in Research Projects Any person planning to undertake research in the Faculty of Engineering and the Built Environment at the University of Cape Town is required to complete this form before collecting or analysing data. When completed it should be submitted to the supervisor (where applicable) and from there to the Head of Department. If any of the questions below have been answered YES, and the applicant is NOT a fourth year student, the Head should forward this form for approval by the Faculty EIR committee: submit to Ms Zulpha Geyer ([email protected]; Chem Eng Building, Ph 021 650 4791).Students must include a copy of the completed form with the final year project when it is submitted for examination.
Name of Principal Researcher/Student: Xiao Ming Hu Department: ELECTRICAL ENGINEERING
If a Student: YES Degree: BSc in Electrical Engineering Supervisor: Professor M.A. Khan
If a Research Contract indicate source of funding/sponsorship:
Research Project Title: Design of a Converter for Interfacing a High-Speed Generator to the Grid
Overview of ethics issues in your research project: Question 1: Is there a possibility that your research could cause harm to a third party (i.e. a person not involved in your project)?
YES NO
Question 2: Is your research making use of human subjects as sources of data? If your answer is YES, please complete Addendum 2.
YES NO
Question 3: Does your research involve the participation of or provision of services to communities? If your answer is YES, please complete Addendum 3.
YES NO
Question 4: If your research is sponsored, is there any potential for conflicts of interest? If your answer is YES, please complete Addendum 4.
YES NO
If you have answered YES to any of the above questions, please append a copy of your research proposal, as well as any interview schedules or questionnaires (Addendum 1) and please complete further addenda as appropriate.
I hereby undertake to carry out my research in such a way that there is no apparent legal objection to the nature or the method of research; and
the research will not compromise staff or students or the other responsibilities of the University;
the stated objective will be achieved, and the findings will have a high degree of validity;
limitations and alternative interpretations will be considered;
the findings could be subject to peer review and publicly available; and
I will comply with the conventions of copyright and avoid any practice that would constitute plagiarism. Signed by:
Full name and signature Date
Principal Researcher/Student:
Xiao Ming Hu
16 October 2014
This application is approved by:
Supervisor (if applicable): Professor M.A. Khan
16 October 2014
HOD (or delegated nominee): Final authority for all assessments with NO to all questions and for all undergraduate research. Janine Buxey
16 October 2014
Chair : Faculty EIR Committee For applicants other than undergraduate students who have answered YES to any of the above questions.