Control of Power Electronic Converters with Microgrid Applications
Description
Discover a systematic approach to design controllers for power electronic converters and circuits
In Control of Power Electronic Converters with Microgrid Applications, distinguished academics and authors Drs. Arindam Ghosh and Firuz Zare deliver a systematic exploration of design controllers for power electronic converters and circuits. The book offers readers the knowledge necessary to effectively design intelligent control mechanisms. It covers the theoretical requirements, like advanced control theories and the analysis and conditioning of AC signals as well as controller development and control.
The authors provide readers with discussions of custom power devices, as well as both DC and AC microgrids. They also discuss the harmonic issues that are crucial in this area, as well as harmonic standardization. The book addresses a widespread lack of understanding in the control philosophy that can lead to a stable operation of converters, with a focus on the application of power electronics to power distribution systems.
Readers will also benefit from the inclusion of:
* A thorough introduction to controller design for different power electronic converter configurations in microgrid systems (both AC and DC)
* A presentation of emerging technology in power distribution systems to integrate different renewable energy sources
* Chapters on DC-DC converters and DC microgrids, as well as DC-AC converter modulation techniques and custom power devices, predictive control, and AC microgrids
Perfect for manufacturers of power converters, microgrid developers and installers, as well as consultants who work in this area, Control of Power Electronic Converters with Microgrid Applications is also an indispensable reference for graduate students, senior undergraduate students, and researchers seeking a one-stop resource for the design of controllers for power electronic converters and circuits.
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Persons
Arindam Ghosh, PhD, is a Research Academic Professor at Curtin University, Perth, Australia. He obtained his PhD from the University of Calgary, Canada. He was with the Indian Institute of Technology Kanpur from 1985 to 2006 and a Research Capacity Building Professor at Queensland University of Technology, Brisbane, Australia from 2006 to 2013. He was a Fulbright Scholar in 2003. He is a Fellow of the Indian National Academy of Engineering: INAE (2005) and a Fellow of the Institute of Electrical and Electronics Engineers: IEEE (2006). He was conferred the IEEE PES Nari Hingorani Custom Power Award in 2019. He has published over 450 peer reviewed journal and conference articles and has authored 2 books.
Firuz Zare, PhD, is Head of the School of Electrical Engineering and Robotics, Queensland University of Technology, and an IEEE Fellow. He has over 20 years of experience in academia and industry and has published 250 peer-reviewed journal and conference papers.
Content
Author Biographies xv
Preface xvii
Acknowledgments xxi
1 Introduction 1
1.1 Introduction to Power Electronics 4
1.2 Power Converter Modes of Operation 7
1.3 Power Converter Topologies 9
1.4 Harmonics and Filters 10
1.5 Power Converter Operating Conditions, Modelling, and Control 12
1.6 Control of Power Electronic Systems 14
1.6.1 Open-loop Versus Closed-loop Control 14
1.6.2 Nonlinear Systems 16
1.6.3 Piecewise Linear Systems 17
1.7 Power Distribution Systems 18
1.8 Concluding Remarks 20
References 20
2 Analysis of AC Signals 23
2.1 Symmetrical Components 24
2.1.1 Voltage Unbalanced Factor (VUF) 25
2.1.2 Real and Reactive Power 26
2.2 Instantaneous Symmetrical Components 27
2.2.1 Estimating Symmetrical Components from Instantaneous Measurements 29
2.2.2 Instantaneous Real and Reactive Power 34
2.3 Harmonics 37
2.4 Clarke and Park Transforms 39
2.4.1 Clarke Transform 39
2.4.2 Park Transform 40
2.4.3 Real and Reactive Power 41
2.4.4 Analyzing a Three-phase Circuit 43
2.4.5 Relation Between Clarke and Park Transforms 45
2.5 Phase Locked Loop (PLL) 46
2.5.1 Three-phase PLL System 47
2.5.2 PLL for Unbalanced System 50
2.5.3 Frequency Estimation of Balanced Signal Using aß Components 52
2.6 Concluding Remarks 53
Problems 54
Notes and References 56
3 Review of SISO Control Systems 59
3.1 Transfer Function and Time Response 60
3.1.1 Steady State Error and DC Gain 60
3.1.2 System Damping and Stability 62
3.1.3 Shaping a Second-order Response 63
3.1.4 Step Response of First- and Higher-order Systems 65
3.2 Routh-Hurwitz's Stability Test 66
3.3 Root Locus 69
3.3.1 Number of Branches and Terminal Points 70
3.3.2 Real Axis Locus 71
3.3.3 Breakaway and Break-in Points 73
3.4 PID Control 76
3.4.1 PI Controller 77
3.4.2 PD Controller 78
3.4.3 Tuning of PID Controllers 81
3.5 Frequency Response Methods 83
3.5.1 Bode Plot 85
3.5.2 Nyquist (Polar) Plot 89
3.5.3 Nyquist Stability Criterion 91
3.6 Relative Stability 95
3.6.1 Phase and Gain Margins 95
3.6.2 Bandwidth 101
3.7 Compensator Design 104
3.7.1 Lead Compensator 104
3.7.2 Lag Compensator 108
3.7.3 Lead-lag Compensator 108
3.8 Discrete-time Control 110
3.8.1 Discrete-time Representation 110
3.8.2 The z-transform 111
3.8.3 Transformation from Continuous Time to Discrete Time 112
3.8.4 Mapping s-Plane into z-Plane 112
3.8.5 Difference Equation and Transfer Function 113
3.8.6 Digital PID Control 115
3.9 Concluding Remarks 115
Problems 116
Notes and References 120
4 Power Electronic Control Design Challenges 123
4.1 Analysis of Buck Converter 123
4.1.1 Designing a Buck Converter 126
4.1.2 The Need for a Controller 128
4.1.3 Dynamic State of a Power Converter 133
4.1.4 Averaging Method 133
4.1.5 Small Signal Model of Buck Converter 135
4.1.6 Transfer Function of Buck Converter 136
4.1.7 Control of Buck Converter 136
4.2 Transfer Function of Boost Converter 140
4.2.1 Control of Boost Converter 141
4.2.2 Two-loop Control of Boost Converter 144
4.2.3 Some Practical Issues 150
4.3 Concluding Remarks 151
Problems 151
Notes and References 152
5 State Space Analysis and Design 153
5.1 State Space Representation of Linear Systems 154
5.1.1 Continuous-time Systems 154
5.1.2 Discrete-time Systems 155
5.2 Solution of State Equation of a Continuous-time System 156
5.2.1 State Transition Matrix 156
5.2.2 Properties of State Transition Matrix 158
5.2.3 State Transition Equation 159
5.3 Solution of State Equation of a Discrete-time System 160
5.3.1 State Transition Matrix 161
5.3.2 Computation of State Transition Matrix 161
5.3.3 Discretization of a Continuous-time System 162
5.4 Relation Between State Space Form and Transfer Function 164
5.4.1 Continuous-time System 164
5.4.2 Discrete-time System 166
5.5 Eigenvalues and Eigenvectors 167
5.5.1 Eigenvalues 167
5.5.2 Eigenvectors 168
5.6 Diagonalization of a Matrix Using Similarity Transform 170
5.6.1 Matrix with Distinct Eigenvalues 170
5.6.2 Matrix with Repeated Eigenvalues 173
5.7 Controllability of LTI Systems 174
5.7.1 Implication of Cayley-Hamilton Theorem 176
5.7.2 Controllability Test Condition 176
5.8 Observability of LTI Systems 178
5.9 Pole Placement Through State Feedback 180
5.9.1 Pole Placement with Integral Action 183
5.9.2 Linear Quadratic Regulator (LQR) 185
5.9.3 Discrete-time State Feedback with Integral Control 187
5.10 Observer Design (Full Order) 187
5.10.1 Separation Principle 188
5.11 Control of DC-DC Converter 190
5.11.1 Steady State Calculation 192
5.11.2 Linearized Model of a Boost Converter 195
5.11.3 State Feedback Control of a Boost Converter 196
5.12 Concluding Remarks 200
Problems 201
Notes and References 204
6 Discrete-time Control 207
6.1 Minimum Variance (MV) Prediction and Control 208
6.1.1 Discrete-time Models for SISO Systems 208
6.1.2 MV Prediction 209
6.1.3 MV Control Law 212
6.1.4 One-step-ahead Control 214
6.2 Pole Placement Controller 218
6.2.1 Pole Shift Control 222
6.3 Generalized Predictive Control (GPC) 225
6.3.1 Simplified GPC Computation 233
6.4 Adaptive Control 234
6.5 Least-squares Estimation 235
6.5.1 Matrix Inversion Lemma 237
6.5.2 Recursive Least-squares (RLS) Identification 238
6.5.3 Bias and Consistency 242
6.6 Self-tuning Controller 244
6.6.1 MV Self-tuning Control 244
6.6.2 Pole Shift Self-tuning Control 248
6.6.3 Self-tuning Control of Boost Converter 249
6.7 Concluding Remarks 252
Problems 253
Notes and References 254
7 DC-AC Converter Modulation Techniques 257
7.1 Single-phase Bridge Converter 258
7.1.1 Hysteresis Current Control 259
7.1.2 Bipolar Sinusoidal Pulse Width Modulation (SPWM) 263
7.1.3 Unipolar Sinusoidal Pulse Width Modulation 265
7.2 SPWM of Three-phase Bridge Converter 267
7.3 Space Vector Modulation (SVM) 271
7.3.1 Calculation of Space Vectors 272
7.3.2 Common Mode Voltage 273
7.3.3 Timing Calculations 274
7.3.4 An Alternate Method for Timing Calculations 277
7.3.5 Sequencing of Space Vectors 279
7.4 SPWM with Third Harmonic Injection 282
7.5 Multilevel Converters 285
7.5.1 Diode-clamped Multilevel Converter 290
7.5.2 Switching States of Diode-clamped Multilevel Converters 291
7.5.3 Flying Capacitor Multilevel Converter 295
7.5.4 Cascaded Multilevel Converter 302
7.5.5 Modular Multilevel Converter (MMC) 302
7.5.6 PWM of Multilevel Converters 303
7.6 Concluding Remarks 306
Problems 307
Notes and References 307
8 Control of DC-AC Converters 311
8.1 Filter Structure and Design 311
8.1.1 Filter Design 313
8.1.2 Filter with Passive Damping 315
8.2 State Feedback Based PWM Voltage Control 315
8.2.1 HPF-based Control Design 318
8.2.2 Observer-based Current Estimation 321
8.3 State Feedback Based SVPWM Voltage Control 323
8.4 Sliding Mode Control 324
8.4.1 Sliding Mode Voltage Control 326
8.5 State Feedback Current Control 330
8.6 Output Feedback Current Control 333
8.7 Concluding Remarks 336
Problems 337
Notes and References 338
9 VSC Applications in Custom Power 341
9.1 DSTATCOM in Voltage Control Mode 342
9.1.1 Discrete-time PWM State Feedback Control 346
9.1.2 Discrete-time Output Feedback PWM Control 348
9.1.3 Voltage Control Using Four-leg Converter 351
9.1.4 The Effect of System Frequency 353
9.1.5 Power Factor Correction 357
9.2 Load Compensation 360
9.2.1 Classical Load Compensation Technique 360
9.2.2 Load Compensation Using VSC 363
9.3 Other Custom Power Devices 367
9.4 Concluding Remarks 370
Problems 370
Notes and References 373
10 Microgrids 377
10.1 Operating Modes of a Converter 380
10.2 Grid Forming Converters 381
10.2.1 PI Control in dq-domain 382
10.2.2 State Feedback Control in dq-domain 385
10.3 Grid Feeding Converters 389
10.4 Grid Supporting Converters for Islanded Operation of Microgrids 392
10.4.1 Active and Reactive Over a Feeder 393
10.4.2 Inductive Grid 394
10.4.3 Resistive Grid 398
10.4.4 Consideration of Line Impedances 400
10.4.5 Virtual Impedance 402
10.4.6 Inclusion of Nondispatchable Sources 405
10.4.7 Angle Droop Control 406
10.5 Grid-connected Operation of Microgrid 411
10.6 DC Microgrids 415
10.6.1 P-V Droop Control 417
10.6.2 The Effect of Line Resistances 419
10.6.3 I-V Droop Control 421
10.6.4 DCMG Operation with DC-DC Converters 423
10.7 Integrated AC-DC System 424
10.7.1 Dual Active Bridge (DAB) 425
10.7.2 AC Utility Connected DCMG 429
10.8 Control Hierarchies of Microgrids 430
10.8.1 Primary Control 430
10.8.2 Secondary Control 432
10.8.3 Tertiary Control 433
10.9 Smart Distribution Networks: Networked Microgrids 434
10.9.1 Interconnection of Networked Microgrids 435
10.10 Microgrids in Cluster 439
10.10.1 The Concept of Power Exchange Highway (PEH) 442
10.10.2 Operation of DC Power Exchange Highway (DC-PEH) 444
10.10.3 Overload Detection and Surplus Power Calculation 445
10.10.4 Operation of DC-PEH 447
10.10.5 Dynamic Droop Gain Selection 448
10.11 Concluding Remarks 456
Problems 457
Notes and References 460
11 Harmonics in Electrical and Electronic Systems 465
11.1 Harmonics and Interharmonics 465
11.1.1 High-frequency Harmonics (2-150 kHz) 467
11.1.2 EMI in the Frequency Range of 150 kHz-30 MHz 468
11.1.3 Common Mode and Differential Mode Harmonics and Noises 469
11.1.4 Stiff and Weak Grids 470
11.2 Power Quality Factors and Definitions 471
11.2.1 Harmonic Distortion 471
11.2.2 Power and Displacement Factors 473
11.3 Harmonics Generated by Power Electronics in Power Systems 474
11.3.1 Harmonic Analysis at a Load Side (a Three-phase Inverter) 477
11.3.2 Harmonic Analysis at a Grid Side (a Three-phase Rectifier) 479
11.3.3 Harmonic Analysis at Grid Side (Single-phase Rectifier with and without PF Correction System) 484
11.3.4 Harmonic Analysis at Grid Side (AFE) 488
11.4 Power Quality Regulations and Standards 491
11.4.1 IEEE Standards 491
11.4.2 IEEE 519 491
11.4.3 IEEE 1547 494
11.4.4 IEEE 1662-2008 494
11.4.5 IEEE 1826-2012 495
11.4.6 IEEE 1709-2010 496
11.4.7 IEC Standards 497
11.5 Concluding Remarks 499
Notes and References 499
Index 501
Preface
Power converter applications in power systems have a long history. One of the first installations of high-voltage direct current (HVDC) transmission systems was on the Swedish island of Gotland in 1954. Mercury arc valves were used in the project. These were replaced by thyristor valves in 1967. Since then, other thyristor-based devices like the static var compensator (SVC), the thyristor-controlled series compensator (TCSC), etc., started finding applications in power transmission systems. However, with the advance of insulated-gate bipolar transistor (IGBT) technology, voltage source converters (VSCs) have started gaining prominence in power system applications. Currently, several VSC-based devices have been used in power transmission applications, such as in VSC-HVDC, flexible alternating current transmission systems (FACTS) devices, etc. At the same time, VSC applications in power distribution systems have been gaining prominence in custom power technologies and in microgrids.
With increased concerns about climate change, there has been an increased application of power electronic converters in power systems and an increase in the use of solar photovoltaic (PV) or wind power generation. Since these renewable generators are intermittent in nature, energy storage devices (predominantly battery energy storages) are being used for both storing energy and smoothing power fluctuations. Since VSCs generate harmonics, they are equipped with output passive filters. These filters can cause resonance with the rest of the system. Therefore, the control of power electronic devices has gained prominence in recent times. A very large number of publications have appeared in different IEEE Transactions about converter controls and their usages.
The concept of a microgrid has gained much attention in recent times. Microgrids are small power systems that have distributed generators (s), battery storage units, and customer loads located in close proximity. They can either be connected to the utility grids or be operated independently in an autonomous mode. They can provide fuel diversity and can increase the reliability and resilience of power delivery systems. Microgrids have been installed in communities, university campuses, hospitals, manufacturing sites, as well as in military installations. Moreover, remote area microgrids have the potential of providing reliable power to locations that are far away from power lines. Even though small or medium-sized diesel or gas-fired generators can be used in a microgrid, power-converter-interfaced generators are most prevalent as they interconnect renewable generators and battery storages. Therefore, power converter control is a very critical issue for microgrid applications as well.
The aim of this book is twofold: to review the control theories used for smart power converter control and to review the applications of these control concepts in power electronic converters used in power distribution systems. A voltage source converter can have several different control aspects that depend on its application. However, the basic principles are somewhat common. Therefore, a systematic approach has been taken for the application-specific converter control design in the book.
Three chapters in the book cover control theory. Most of the materials that are presented in these chapters can be used for a senior level undergraduate course or a junior level graduate course. There are several worked examples and design tips that can be used in MATLAB®, a product of MathWorks. The advantage of using MATLAB® is that complex control algorithms can easily be tested and verified using this software. In this book, MATLAB® has also been used for power converter controller design, while the design concepts have been verified through the Manitoba HVDC Research Center's EMTDC/PSCAD simulation package.
The book is organized in 11 chapters. Chapter 1 introduces the book. This chapter presents a basic introduction to power electronic components and power converter modes of operation and topologies. The need for harmonic filtering is also discussed briefly. Since most of the power converters can be modeled as piece-wise linear circuits, they need be linearized for feedback control design. This is also discussed in this chapter.
The methods of analysis of AC signals are presented in Chapter 2. Topics such as symmetrical components (phasor and instantaneous), Clarke and Park transforms, and the principle and use of phase locked loop (PLL) are covered in this chapter.
Chapter 3 provides an in-depth review of the classical control for single-input, single-output (SISO) systems. Since most classical control analysis and design approaches are similar for both continuous-time and discrete-time systems, more focus has been given to continuous-time systems in the book. Topics such as Routh-Hurwitz's criterion, root locus, frequency response methods, Nyquist stability criterion, relative stability, compensator design, and the PID controller and its tuning are covered along with several numerical examples. At the end of the chapter, discrete-time representation and z-transform are discussed.
Power converter control design in classical domain is discussed in Chapter 4. Specifically, DC-DC converters, such as buck and boost converters, are analyzed in detail. The process of deriving models of these converters using averaging methods and then designing classical controllers using these linearized models are explained. It also shows that a simple output voltage control is not sufficient for a boost converter since it has a right-half s-plane zero. A two-loop control design is also presented.
State space analysis and control design in both continuous- and discrete-time domains are presented in Chapter 5. Different topics such as the representation of a SISO system in state space domain, solutions of state equations, eigenvalues, and eigenvectors are covered in this chapter. Also, modal analysis using diagonalization, controllability, and observability are discussed. A state feedback control design using pole placement and a linear quadratic regulator is explained. The process of eliminating any steady state error using an integral control action is also described. At the end of the chapter, the process of deriving a DC-DC boost converter model using state space averaging as well as designing a controller that has a much superior performance are demonstrated.
Chapter 6 discusses control system design in the discrete-time domain, where prediction-based controllers are explained. Topics that are covered in this chapter include minimum variance prediction and control, pole placement in the polynomial domain, generalized predictive control, and self-tuning adaptive control that combines recursive parameter estimation with control design. A numerical example of the self-tuning control of a boost converter is also presented.
The open-loop control of DC-AC converters is covered in Chapter 7, where hysteretic current control and sinusoidal pulse with modulation (SPWM) for both bipolar and unipolar modulations are discussed. The concept of space vectors and space vector pulse width modulation (SVPWM) are also presented in this chapter. It also discusses how the performance of SPWM can be improved through a third harmonic injection. Different multilevel converters - such as diode-clamped, flying capacitor, cascaded, and modular - are also discussed in this chapter, along with the SPWM methods that can be used in multilevel converter output voltage modulation.
Chapter 8 presents several techniques of closed-loop control of DC-AC converters, and discusses both voltage and current controllers. To eliminate the harmonics generated by voltage source converters, they are equipped by output passive LC or LCL filters. First, a typical filter design principle is discussed. This is followed by a discussion of the state feedback based PWM and SVPWM voltage control of VSCs and sliding mode voltage control. Current control, using both state feedback and output feedback, is also discussed.
Power conditioning devices that are used for power quality improvements in power distribution networks use DC-AC converters that need to be controlled in some specific manner to achieve their goals. Such devices are discussed in Chapter 9, where, in particular, the structure and operating principles of a distribution static compensator (DSTATCOM) are presented. The chapter demonstrates that this device can be used for both voltage control, where a distribution bus voltage can be controlled against the load harmonics and unbalance, and for current control for load compensation. The associated converter control method is also presented.
Chapter 10 discusses microgrids. Both DC and AC microgrids are considered. The primary control applications in these microgrids are in the form of droop controllers, which are covered in detail in this chapter. Examples of different converter control principles that can be used for renewable energy integration are included in this chapter as well as the evolving smart power distribution systems that may contain several microgrids. Some of the possible connection and operating principles of microgrid networks are...
