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.

• Author Biographies xvPreface xviiAcknowledgments xxi1 Introduction 11.1 Introduction to Power Electronics 41.2 Power Converter Modes of Operation 71.3 Power Converter Topologies 91.4 Harmonics and Filters 101.5 Power Converter Operating Conditions, Modelling, and Control 121.6 Control of Power Electronic Systems 141.6.1 Open-loop Versus Closed-loop Control 141.6.2 Nonlinear Systems 161.6.3 Piecewise Linear Systems 171.7 Power Distribution Systems 181.8 Concluding Remarks 20References 202 Analysis of AC Signals 232.1 Symmetrical Components 242.1.1 Voltage Unbalanced Factor (VUF) 252.1.2 Real and Reactive Power 262.2 Instantaneous Symmetrical Components 272.2.1 Estimating Symmetrical Components from Instantaneous Measurements 292.2.2 Instantaneous Real and Reactive Power 342.3 Harmonics 372.4 Clarke and Park Transforms 392.4.1 Clarke Transform 392.4.2 Park Transform 402.4.3 Real and Reactive Power 412.4.4 Analyzing a Three-phase Circuit 432.4.5 Relation Between Clarke and Park Transforms 452.5 Phase Locked Loop (PLL) 462.5.1 Three-phase PLL System 472.5.2 PLL for Unbalanced System 502.5.3 Frequency Estimation of Balanced Signal Using αβ Components 522.6 Concluding Remarks 53Problems 54Notes and References 563 Review of SISO Control Systems 593.1 Transfer Function and Time Response 603.1.1 Steady State Error and DC Gain 603.1.2 System Damping and Stability 623.1.3 Shaping a Second-order Response 633.1.4 Step Response of First- and Higher-order Systems 653.2 Routh–Hurwitz’s Stability Test 663.3 Root Locus 693.3.1 Number of Branches and Terminal Points 703.3.2 Real Axis Locus 713.3.3 Breakaway and Break-in Points 733.4 PID Control 763.4.1 PI Controller 773.4.2 PD Controller 783.4.3 Tuning of PID Controllers 813.5 Frequency Response Methods 833.5.1 Bode Plot 853.5.2 Nyquist (Polar) Plot 893.5.3 Nyquist Stability Criterion 913.6 Relative Stability 953.6.1 Phase and Gain Margins 953.6.2 Bandwidth 1013.7 Compensator Design 1043.7.1 Lead Compensator 1043.7.2 Lag Compensator 1083.7.3 Lead–lag Compensator 1083.8 Discrete-time Control 1103.8.1 Discrete-time Representation 1103.8.2 The z-transform 1113.8.3 Transformation from Continuous Time to Discrete Time 1123.8.4 Mapping s-Plane into z-Plane 1123.8.5 Difference Equation and Transfer Function 1133.8.6 Digital PID Control 1153.9 Concluding Remarks 115Problems 116Notes and References 1204 Power Electronic Control Design Challenges 1234.1 Analysis of Buck Converter 1234.1.1 Designing a Buck Converter 1264.1.2 The Need for a Controller 1284.1.3 Dynamic State of a Power Converter 1334.1.4 Averaging Method 1334.1.5 Small Signal Model of Buck Converter 1354.1.6 Transfer Function of Buck Converter 1364.1.7 Control of Buck Converter 1364.2 Transfer Function of Boost Converter 1404.2.1 Control of Boost Converter 1414.2.2 Two-loop Control of Boost Converter 1444.2.3 Some Practical Issues 1504.3 Concluding Remarks 151Problems 151Notes and References 1525 State Space Analysis and Design 1535.1 State Space Representation of Linear Systems 1545.1.1 Continuous-time Systems 1545.1.2 Discrete-time Systems 1555.2 Solution of State Equation of a Continuous-time System 1565.2.1 State Transition Matrix 1565.2.2 Properties of State Transition Matrix 1585.2.3 State Transition Equation 1595.3 Solution of State Equation of a Discrete-time System 1605.3.1 State Transition Matrix 1615.3.2 Computation of State Transition Matrix 1615.3.3 Discretization of a Continuous-time System 1625.4 Relation Between State Space Form and Transfer Function 1645.4.1 Continuous-time System 1645.4.2 Discrete-time System 1665.5 Eigenvalues and Eigenvectors 1675.5.1 Eigenvalues 1675.5.2 Eigenvectors 1685.6 Diagonalization of a Matrix Using Similarity Transform 1705.6.1 Matrix with Distinct Eigenvalues 1705.6.2 Matrix with Repeated Eigenvalues 1735.7 Controllability of LTI Systems 1745.7.1 Implication of Cayley–Hamilton Theorem 1765.7.2 Controllability Test Condition 1765.8 Observability of LTI Systems 1785.9 Pole Placement Through State Feedback 1805.9.1 Pole Placement with Integral Action 1835.9.2 Linear Quadratic Regulator (LQR) 1855.9.3 Discrete-time State Feedback with Integral Control 1875.10 Observer Design (Full Order) 1875.10.1 Separation Principle 1885.11 Control of DC-DC Converter 1905.11.1 Steady State Calculation 1925.11.2 Linearized Model of a Boost Converter 1955.11.3 State Feedback Control of a Boost Converter 1965.12 Concluding Remarks 200Problems 201Notes and References 2046 Discrete-time Control 2076.1 Minimum Variance (MV) Prediction and Control 2086.1.1 Discrete-time Models for SISO Systems 2086.1.2 MV Prediction 2096.1.3 MV Control Law 2126.1.4 One-step-ahead Control 2146.2 Pole Placement Controller 2186.2.1 Pole Shift Control 2226.3 Generalized Predictive Control (GPC) 2256.3.1 Simplified GPC Computation 2336.4 Adaptive Control 2346.5 Least-squares Estimation 2356.5.1 Matrix Inversion Lemma 2376.5.2 Recursive Least-squares (RLS) Identification 2386.5.3 Bias and Consistency 2426.6 Self-tuning Controller 2446.6.1 MV Self-tuning Control 2446.6.2 Pole Shift Self-tuning Control 2486.6.3 Self-tuning Control of Boost Converter 2496.7 Concluding Remarks 252Problems 253Notes and References 2547 DC-AC Converter Modulation Techniques 2577.1 Single-phase Bridge Converter 2587.1.1 Hysteresis Current Control 2597.1.2 Bipolar Sinusoidal Pulse Width Modulation (SPWM) 2637.1.3 Unipolar Sinusoidal Pulse Width Modulation 2657.2 SPWM of Three-phase Bridge Converter 2677.3 Space Vector Modulation (SVM) 2717.3.1 Calculation of Space Vectors 2727.3.2 Common Mode Voltage 2737.3.3 Timing Calculations 2747.3.4 An Alternate Method for Timing Calculations 2777.3.5 Sequencing of Space Vectors 2797.4 SPWM with Third Harmonic Injection 2827.5 Multilevel Converters 2857.5.1 Diode-clamped Multilevel Converter 2907.5.2 Switching States of Diode-clamped Multilevel Converters 2917.5.3 Flying Capacitor Multilevel Converter 2957.5.4 Cascaded Multilevel Converter 3027.5.5 Modular Multilevel Converter (MMC) 3027.5.6 PWM of Multilevel Converters 3037.6 Concluding Remarks 306Problems 307Notes and References 3078 Control of DC-AC Converters 3118.1 Filter Structure and Design 3118.1.1 Filter Design 3138.1.2 Filter with Passive Damping 3158.2 State Feedback Based PWM Voltage Control 3158.2.1 HPF-based Control Design 3188.2.2 Observer-based Current Estimation 3218.3 State Feedback Based SVPWM Voltage Control 3238.4 Sliding Mode Control 3248.4.1 Sliding Mode Voltage Control 3268.5 State Feedback Current Control 3308.6 Output Feedback Current Control 3338.7 Concluding Remarks 336Problems 337Notes and References 3389 VSC Applications in Custom Power 3419.1 DSTATCOM in Voltage Control Mode 3429.1.1 Discrete-time PWM State Feedback Control 3469.1.2 Discrete-time Output Feedback PWM Control 3489.1.3 Voltage Control Using Four-leg Converter 3519.1.4 The Effect of System Frequency 3539.1.5 Power Factor Correction 3579.2 Load Compensation 3609.2.1 Classical Load Compensation Technique 3609.2.2 Load Compensation Using VSC 3639.3 Other Custom Power Devices 3679.4 Concluding Remarks 370Problems 370Notes and References 37310 Microgrids 37710.1 Operating Modes of a Converter 38010.2 Grid Forming Converters 38110.2.1 PI Control in dq-domain 38210.2.2 State Feedback Control in dq-domain 38510.3 Grid Feeding Converters 38910.4 Grid Supporting Converters for Islanded Operation of Microgrids 39210.4.1 Active and Reactive Over a Feeder 39310.4.2 Inductive Grid 39410.4.3 Resistive Grid 39810.4.4 Consideration of Line Impedances 40010.4.5 Virtual Impedance 40210.4.6 Inclusion of Nondispatchable Sources 40510.4.7 Angle Droop Control 40610.5 Grid-connected Operation of Microgrid 41110.6 DC Microgrids 41510.6.1 P-V Droop Control 41710.6.2 The Effect of Line Resistances 41910.6.3 I-V Droop Control 42110.6.4 DCMG Operation with DC-DC Converters 42310.7 Integrated AC-DC System 42410.7.1 Dual Active Bridge (DAB) 42510.7.2 AC Utility Connected DCMG 42910.8 Control Hierarchies of Microgrids 43010.8.1 Primary Control 43010.8.2 Secondary Control 43210.8.3 Tertiary Control 43310.9 Smart Distribution Networks: Networked Microgrids 43410.9.1 Interconnection of Networked Microgrids 43510.10 Microgrids in Cluster 43910.10.1 The Concept of Power Exchange Highway (PEH) 44210.10.2 Operation of DC Power Exchange Highway (DC-PEH) 44410.10.3 Overload Detection and Surplus Power Calculation 44510.10.4 Operation of DC-PEH 44710.10.5 Dynamic Droop Gain Selection 44810.11 Concluding Remarks 456Problems 457Notes and References 46011 Harmonics in Electrical and Electronic Systems 46511.1 Harmonics and Interharmonics 46511.1.1 High-frequency Harmonics (2–150 kHz) 46711.1.2 EMI in the Frequency Range of 150 kHz–30 MHz 46811.1.3 Common Mode and Differential Mode Harmonics and Noises 46911.1.4 Stiff and Weak Grids 47011.2 Power Quality Factors and Definitions 47111.2.1 Harmonic Distortion 47111.2.2 Power and Displacement Factors 47311.3 Harmonics Generated by Power Electronics in Power Systems 47411.3.1 Harmonic Analysis at a Load Side (a Three-phase Inverter) 47711.3.2 Harmonic Analysis at a Grid Side (a Three-phase Rectifier) 47911.3.3 Harmonic Analysis at Grid Side (Single-phase Rectifier with and without PF Correction System) 48411.3.4 Harmonic Analysis at Grid Side (AFE) 48811.4 Power Quality Regulations and Standards 49111.4.1 IEEE Standards 49111.4.2 IEEE 519 49111.4.3 IEEE 1547 49411.4.4 IEEE 1662-2008 49411.4.5 IEEE 1826-2012 49511.4.6 IEEE 1709-2010 49611.4.7 IEC Standards 49711.5 Concluding Remarks 499Notes and References 499Index 501

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.

• Author Biographies xvPreface xviiAcknowledgments xxi1 Introduction 11.1 Introduction to Power Electronics 41.2 Power Converter Modes of Operation 71.3 Power Converter Topologies 91.4 Harmonics and Filters 101.5 Power Converter Operating Conditions, Modelling, and Control 121.6 Control of Power Electronic Systems 141.6.1 Open-loop Versus Closed-loop Control 141.6.2 Nonlinear Systems 161.6.3 Piecewise Linear Systems 171.7 Power Distribution Systems 181.8 Concluding Remarks 20References 202 Analysis of AC Signals 232.1 Symmetrical Components 242.1.1 Voltage Unbalanced Factor (VUF) 252.1.2 Real and Reactive Power 262.2 Instantaneous Symmetrical Components 272.2.1 Estimating Symmetrical Components from Instantaneous Measurements 292.2.2 Instantaneous Real and Reactive Power 342.3 Harmonics 372.4 Clarke and Park Transforms 392.4.1 Clarke Transform 392.4.2 Park Transform 402.4.3 Real and Reactive Power 412.4.4 Analyzing a Three-phase Circuit 432.4.5 Relation Between Clarke and Park Transforms 452.5 Phase Locked Loop (PLL) 462.5.1 Three-phase PLL System 472.5.2 PLL for Unbalanced System 502.5.3 Frequency Estimation of Balanced Signal Using αβ Components 522.6 Concluding Remarks 53Problems 54Notes and References 563 Review of SISO Control Systems 593.1 Transfer Function and Time Response 603.1.1 Steady State Error and DC Gain 603.1.2 System Damping and Stability 623.1.3 Shaping a Second-order Response 633.1.4 Step Response of First- and Higher-order Systems 653.2 Routh–Hurwitz’s Stability Test 663.3 Root Locus 693.3.1 Number of Branches and Terminal Points 703.3.2 Real Axis Locus 713.3.3 Breakaway and Break-in Points 733.4 PID Control 763.4.1 PI Controller 773.4.2 PD Controller 783.4.3 Tuning of PID Controllers 813.5 Frequency Response Methods 833.5.1 Bode Plot 853.5.2 Nyquist (Polar) Plot 893.5.3 Nyquist Stability Criterion 913.6 Relative Stability 953.6.1 Phase and Gain Margins 953.6.2 Bandwidth 1013.7 Compensator Design 1043.7.1 Lead Compensator 1043.7.2 Lag Compensator 1083.7.3 Lead–lag Compensator 1083.8 Discrete-time Control 1103.8.1 Discrete-time Representation 1103.8.2 The z-transform 1113.8.3 Transformation from Continuous Time to Discrete Time 1123.8.4 Mapping s-Plane into z-Plane 1123.8.5 Difference Equation and Transfer Function 1133.8.6 Digital PID Control 1153.9 Concluding Remarks 115Problems 116Notes and References 1204 Power Electronic Control Design Challenges 1234.1 Analysis of Buck Converter 1234.1.1 Designing a Buck Converter 1264.1.2 The Need for a Controller 1284.1.3 Dynamic State of a Power Converter 1334.1.4 Averaging Method 1334.1.5 Small Signal Model of Buck Converter 1354.1.6 Transfer Function of Buck Converter 1364.1.7 Control of Buck Converter 1364.2 Transfer Function of Boost Converter 1404.2.1 Control of Boost Converter 1414.2.2 Two-loop Control of Boost Converter 1444.2.3 Some Practical Issues 1504.3 Concluding Remarks 151Problems 151Notes and References 1525 State Space Analysis and Design 1535.1 State Space Representation of Linear Systems 1545.1.1 Continuous-time Systems 1545.1.2 Discrete-time Systems 1555.2 Solution of State Equation of a Continuous-time System 1565.2.1 State Transition Matrix 1565.2.2 Properties of State Transition Matrix 1585.2.3 State Transition Equation 1595.3 Solution of State Equation of a Discrete-time System 1605.3.1 State Transition Matrix 1615.3.2 Computation of State Transition Matrix 1615.3.3 Discretization of a Continuous-time System 1625.4 Relation Between State Space Form and Transfer Function 1645.4.1 Continuous-time System 1645.4.2 Discrete-time System 1665.5 Eigenvalues and Eigenvectors 1675.5.1 Eigenvalues 1675.5.2 Eigenvectors 1685.6 Diagonalization of a Matrix Using Similarity Transform 1705.6.1 Matrix with Distinct Eigenvalues 1705.6.2 Matrix with Repeated Eigenvalues 1735.7 Controllability of LTI Systems 1745.7.1 Implication of Cayley–Hamilton Theorem 1765.7.2 Controllability Test Condition 1765.8 Observability of LTI Systems 1785.9 Pole Placement Through State Feedback 1805.9.1 Pole Placement with Integral Action 1835.9.2 Linear Quadratic Regulator (LQR) 1855.9.3 Discrete-time State Feedback with Integral Control 1875.10 Observer Design (Full Order) 1875.10.1 Separation Principle 1885.11 Control of DC-DC Converter 1905.11.1 Steady State Calculation 1925.11.2 Linearized Model of a Boost Converter 1955.11.3 State Feedback Control of a Boost Converter 1965.12 Concluding Remarks 200Problems 201Notes and References 2046 Discrete-time Control 2076.1 Minimum Variance (MV) Prediction and Control 2086.1.1 Discrete-time Models for SISO Systems 2086.1.2 MV Prediction 2096.1.3 MV Control Law 2126.1.4 One-step-ahead Control 2146.2 Pole Placement Controller 2186.2.1 Pole Shift Control 2226.3 Generalized Predictive Control (GPC) 2256.3.1 Simplified GPC Computation 2336.4 Adaptive Control 2346.5 Least-squares Estimation 2356.5.1 Matrix Inversion Lemma 2376.5.2 Recursive Least-squares (RLS) Identification 2386.5.3 Bias and Consistency 2426.6 Self-tuning Controller 2446.6.1 MV Self-tuning Control 2446.6.2 Pole Shift Self-tuning Control 2486.6.3 Self-tuning Control of Boost Converter 2496.7 Concluding Remarks 252Problems 253Notes and References 2547 DC-AC Converter Modulation Techniques 2577.1 Single-phase Bridge Converter 2587.1.1 Hysteresis Current Control 2597.1.2 Bipolar Sinusoidal Pulse Width Modulation (SPWM) 2637.1.3 Unipolar Sinusoidal Pulse Width Modulation 2657.2 SPWM of Three-phase Bridge Converter 2677.3 Space Vector Modulation (SVM) 2717.3.1 Calculation of Space Vectors 2727.3.2 Common Mode Voltage 2737.3.3 Timing Calculations 2747.3.4 An Alternate Method for Timing Calculations 2777.3.5 Sequencing of Space Vectors 2797.4 SPWM with Third Harmonic Injection 2827.5 Multilevel Converters 2857.5.1 Diode-clamped Multilevel Converter 2907.5.2 Switching States of Diode-clamped Multilevel Converters 2917.5.3 Flying Capacitor Multilevel Converter 2957.5.4 Cascaded Multilevel Converter 3027.5.5 Modular Multilevel Converter (MMC) 3027.5.6 PWM of Multilevel Converters 3037.6 Concluding Remarks 306Problems 307Notes and References 3078 Control of DC-AC Converters 3118.1 Filter Structure and Design 3118.1.1 Filter Design 3138.1.2 Filter with Passive Damping 3158.2 State Feedback Based PWM Voltage Control 3158.2.1 HPF-based Control Design 3188.2.2 Observer-based Current Estimation 3218.3 State Feedback Based SVPWM Voltage Control 3238.4 Sliding Mode Control 3248.4.1 Sliding Mode Voltage Control 3268.5 State Feedback Current Control 3308.6 Output Feedback Current Control 3338.7 Concluding Remarks 336Problems 337Notes and References 3389 VSC Applications in Custom Power 3419.1 DSTATCOM in Voltage Control Mode 3429.1.1 Discrete-time PWM State Feedback Control 3469.1.2 Discrete-time Output Feedback PWM Control 3489.1.3 Voltage Control Using Four-leg Converter 3519.1.4 The Effect of System Frequency 3539.1.5 Power Factor Correction 3579.2 Load Compensation 3609.2.1 Classical Load Compensation Technique 3609.2.2 Load Compensation Using VSC 3639.3 Other Custom Power Devices 3679.4 Concluding Remarks 370Problems 370Notes and References 37310 Microgrids 37710.1 Operating Modes of a Converter 38010.2 Grid Forming Converters 38110.2.1 PI Control in dq-domain 38210.2.2 State Feedback Control in dq-domain 38510.3 Grid Feeding Converters 38910.4 Grid Supporting Converters for Islanded Operation of Microgrids 39210.4.1 Active and Reactive Over a Feeder 39310.4.2 Inductive Grid 39410.4.3 Resistive Grid 39810.4.4 Consideration of Line Impedances 40010.4.5 Virtual Impedance 40210.4.6 Inclusion of Nondispatchable Sources 40510.4.7 Angle Droop Control 40610.5 Grid-connected Operation of Microgrid 41110.6 DC Microgrids 41510.6.1 P-V Droop Control 41710.6.2 The Effect of Line Resistances 41910.6.3 I-V Droop Control 42110.6.4 DCMG Operation with DC-DC Converters 42310.7 Integrated AC-DC System 42410.7.1 Dual Active Bridge (DAB) 42510.7.2 AC Utility Connected DCMG 42910.8 Control Hierarchies of Microgrids 43010.8.1 Primary Control 43010.8.2 Secondary Control 43210.8.3 Tertiary Control 43310.9 Smart Distribution Networks: Networked Microgrids 43410.9.1 Interconnection of Networked Microgrids 43510.10 Microgrids in Cluster 43910.10.1 The Concept of Power Exchange Highway (PEH) 44210.10.2 Operation of DC Power Exchange Highway (DC-PEH) 44410.10.3 Overload Detection and Surplus Power Calculation 44510.10.4 Operation of DC-PEH 44710.10.5 Dynamic Droop Gain Selection 44810.11 Concluding Remarks 456Problems 457Notes and References 46011 Harmonics in Electrical and Electronic Systems 46511.1 Harmonics and Interharmonics 46511.1.1 High-frequency Harmonics (2–150 kHz) 46711.1.2 EMI in the Frequency Range of 150 kHz–30 MHz 46811.1.3 Common Mode and Differential Mode Harmonics and Noises 46911.1.4 Stiff and Weak Grids 47011.2 Power Quality Factors and Definitions 47111.2.1 Harmonic Distortion 47111.2.2 Power and Displacement Factors 47311.3 Harmonics Generated by Power Electronics in Power Systems 47411.3.1 Harmonic Analysis at a Load Side (a Three-phase Inverter) 47711.3.2 Harmonic Analysis at a Grid Side (a Three-phase Rectifier) 47911.3.3 Harmonic Analysis at Grid Side (Single-phase Rectifier with and without PF Correction System) 48411.3.4 Harmonic Analysis at Grid Side (AFE) 48811.4 Power Quality Regulations and Standards 49111.4.1 IEEE Standards 49111.4.2 IEEE 519 49111.4.3 IEEE 1547 49411.4.4 IEEE 1662-2008 49411.4.5 IEEE 1826-2012 49511.4.6 IEEE 1709-2010 49611.4.7 IEC Standards 49711.5 Concluding Remarks 499Notes and References 499Index 501

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.

• Author Biographies xvPreface xviiAcknowledgments xxi1 Introduction 11.1 Introduction to Power Electronics 41.2 Power Converter Modes of Operation 71.3 Power Converter Topologies 91.4 Harmonics and Filters 101.5 Power Converter Operating Conditions, Modelling, and Control 121.6 Control of Power Electronic Systems 141.6.1 Open-loop Versus Closed-loop Control 141.6.2 Nonlinear Systems 161.6.3 Piecewise Linear Systems 171.7 Power Distribution Systems 181.8 Concluding Remarks 20References 202 Analysis of AC Signals 232.1 Symmetrical Components 242.1.1 Voltage Unbalanced Factor (VUF) 252.1.2 Real and Reactive Power 262.2 Instantaneous Symmetrical Components 272.2.1 Estimating Symmetrical Components from Instantaneous Measurements 292.2.2 Instantaneous Real and Reactive Power 342.3 Harmonics 372.4 Clarke and Park Transforms 392.4.1 Clarke Transform 392.4.2 Park Transform 402.4.3 Real and Reactive Power 412.4.4 Analyzing a Three-phase Circuit 432.4.5 Relation Between Clarke and Park Transforms 452.5 Phase Locked Loop (PLL) 462.5.1 Three-phase PLL System 472.5.2 PLL for Unbalanced System 502.5.3 Frequency Estimation of Balanced Signal Using αβ Components 522.6 Concluding Remarks 53Problems 54Notes and References 563 Review of SISO Control Systems 593.1 Transfer Function and Time Response 603.1.1 Steady State Error and DC Gain 603.1.2 System Damping and Stability 623.1.3 Shaping a Second-order Response 633.1.4 Step Response of First- and Higher-order Systems 653.2 Routh–Hurwitz’s Stability Test 663.3 Root Locus 693.3.1 Number of Branches and Terminal Points 703.3.2 Real Axis Locus 713.3.3 Breakaway and Break-in Points 733.4 PID Control 763.4.1 PI Controller 773.4.2 PD Controller 783.4.3 Tuning of PID Controllers 813.5 Frequency Response Methods 833.5.1 Bode Plot 853.5.2 Nyquist (Polar) Plot 893.5.3 Nyquist Stability Criterion 913.6 Relative Stability 953.6.1 Phase and Gain Margins 953.6.2 Bandwidth 1013.7 Compensator Design 1043.7.1 Lead Compensator 1043.7.2 Lag Compensator 1083.7.3 Lead–lag Compensator 1083.8 Discrete-time Control 1103.8.1 Discrete-time Representation 1103.8.2 The z-transform 1113.8.3 Transformation from Continuous Time to Discrete Time 1123.8.4 Mapping s-Plane into z-Plane 1123.8.5 Difference Equation and Transfer Function 1133.8.6 Digital PID Control 1153.9 Concluding Remarks 115Problems 116Notes and References 1204 Power Electronic Control Design Challenges 1234.1 Analysis of Buck Converter 1234.1.1 Designing a Buck Converter 1264.1.2 The Need for a Controller 1284.1.3 Dynamic State of a Power Converter 1334.1.4 Averaging Method 1334.1.5 Small Signal Model of Buck Converter 1354.1.6 Transfer Function of Buck Converter 1364.1.7 Control of Buck Converter 1364.2 Transfer Function of Boost Converter 1404.2.1 Control of Boost Converter 1414.2.2 Two-loop Control of Boost Converter 1444.2.3 Some Practical Issues 1504.3 Concluding Remarks 151Problems 151Notes and References 1525 State Space Analysis and Design 1535.1 State Space Representation of Linear Systems 1545.1.1 Continuous-time Systems 1545.1.2 Discrete-time Systems 1555.2 Solution of State Equation of a Continuous-time System 1565.2.1 State Transition Matrix 1565.2.2 Properties of State Transition Matrix 1585.2.3 State Transition Equation 1595.3 Solution of State Equation of a Discrete-time System 1605.3.1 State Transition Matrix 1615.3.2 Computation of State Transition Matrix 1615.3.3 Discretization of a Continuous-time System 1625.4 Relation Between State Space Form and Transfer Function 1645.4.1 Continuous-time System 1645.4.2 Discrete-time System 1665.5 Eigenvalues and Eigenvectors 1675.5.1 Eigenvalues 1675.5.2 Eigenvectors 1685.6 Diagonalization of a Matrix Using Similarity Transform 1705.6.1 Matrix with Distinct Eigenvalues 1705.6.2 Matrix with Repeated Eigenvalues 1735.7 Controllability of LTI Systems 1745.7.1 Implication of Cayley–Hamilton Theorem 1765.7.2 Controllability Test Condition 1765.8 Observability of LTI Systems 1785.9 Pole Placement Through State Feedback 1805.9.1 Pole Placement with Integral Action 1835.9.2 Linear Quadratic Regulator (LQR) 1855.9.3 Discrete-time State Feedback with Integral Control 1875.10 Observer Design (Full Order) 1875.10.1 Separation Principle 1885.11 Control of DC-DC Converter 1905.11.1 Steady State Calculation 1925.11.2 Linearized Model of a Boost Converter 1955.11.3 State Feedback Control of a Boost Converter 1965.12 Concluding Remarks 200Problems 201Notes and References 2046 Discrete-time Control 2076.1 Minimum Variance (MV) Prediction and Control 2086.1.1 Discrete-time Models for SISO Systems 2086.1.2 MV Prediction 2096.1.3 MV Control Law 2126.1.4 One-step-ahead Control 2146.2 Pole Placement Controller 2186.2.1 Pole Shift Control 2226.3 Generalized Predictive Control (GPC) 2256.3.1 Simplified GPC Computation 2336.4 Adaptive Control 2346.5 Least-squares Estimation 2356.5.1 Matrix Inversion Lemma 2376.5.2 Recursive Least-squares (RLS) Identification 2386.5.3 Bias and Consistency 2426.6 Self-tuning Controller 2446.6.1 MV Self-tuning Control 2446.6.2 Pole Shift Self-tuning Control 2486.6.3 Self-tuning Control of Boost Converter 2496.7 Concluding Remarks 252Problems 253Notes and References 2547 DC-AC Converter Modulation Techniques 2577.1 Single-phase Bridge Converter 2587.1.1 Hysteresis Current Control 2597.1.2 Bipolar Sinusoidal Pulse Width Modulation (SPWM) 2637.1.3 Unipolar Sinusoidal Pulse Width Modulation 2657.2 SPWM of Three-phase Bridge Converter 2677.3 Space Vector Modulation (SVM) 2717.3.1 Calculation of Space Vectors 2727.3.2 Common Mode Voltage 2737.3.3 Timing Calculations 2747.3.4 An Alternate Method for Timing Calculations 2777.3.5 Sequencing of Space Vectors 2797.4 SPWM with Third Harmonic Injection 2827.5 Multilevel Converters 2857.5.1 Diode-clamped Multilevel Converter 2907.5.2 Switching States of Diode-clamped Multilevel Converters 2917.5.3 Flying Capacitor Multilevel Converter 2957.5.4 Cascaded Multilevel Converter 3027.5.5 Modular Multilevel Converter (MMC) 3027.5.6 PWM of Multilevel Converters 3037.6 Concluding Remarks 306Problems 307Notes and References 3078 Control of DC-AC Converters 3118.1 Filter Structure and Design 3118.1.1 Filter Design 3138.1.2 Filter with Passive Damping 3158.2 State Feedback Based PWM Voltage Control 3158.2.1 HPF-based Control Design 3188.2.2 Observer-based Current Estimation 3218.3 State Feedback Based SVPWM Voltage Control 3238.4 Sliding Mode Control 3248.4.1 Sliding Mode Voltage Control 3268.5 State Feedback Current Control 3308.6 Output Feedback Current Control 3338.7 Concluding Remarks 336Problems 337Notes and References 3389 VSC Applications in Custom Power 3419.1 DSTATCOM in Voltage Control Mode 3429.1.1 Discrete-time PWM State Feedback Control 3469.1.2 Discrete-time Output Feedback PWM Control 3489.1.3 Voltage Control Using Four-leg Converter 3519.1.4 The Effect of System Frequency 3539.1.5 Power Factor Correction 3579.2 Load Compensation 3609.2.1 Classical Load Compensation Technique 3609.2.2 Load Compensation Using VSC 3639.3 Other Custom Power Devices 3679.4 Concluding Remarks 370Problems 370Notes and References 37310 Microgrids 37710.1 Operating Modes of a Converter 38010.2 Grid Forming Converters 38110.2.1 PI Control in dq-domain 38210.2.2 State Feedback Control in dq-domain 38510.3 Grid Feeding Converters 38910.4 Grid Supporting Converters for Islanded Operation of Microgrids 39210.4.1 Active and Reactive Over a Feeder 39310.4.2 Inductive Grid 39410.4.3 Resistive Grid 39810.4.4 Consideration of Line Impedances 40010.4.5 Virtual Impedance 40210.4.6 Inclusion of Nondispatchable Sources 40510.4.7 Angle Droop Control 40610.5 Grid-connected Operation of Microgrid 41110.6 DC Microgrids 41510.6.1 P-V Droop Control 41710.6.2 The Effect of Line Resistances 41910.6.3 I-V Droop Control 42110.6.4 DCMG Operation with DC-DC Converters 42310.7 Integrated AC-DC System 42410.7.1 Dual Active Bridge (DAB) 42510.7.2 AC Utility Connected DCMG 42910.8 Control Hierarchies of Microgrids 43010.8.1 Primary Control 43010.8.2 Secondary Control 43210.8.3 Tertiary Control 43310.9 Smart Distribution Networks: Networked Microgrids 43410.9.1 Interconnection of Networked Microgrids 43510.10 Microgrids in Cluster 43910.10.1 The Concept of Power Exchange Highway (PEH) 44210.10.2 Operation of DC Power Exchange Highway (DC-PEH) 44410.10.3 Overload Detection and Surplus Power Calculation 44510.10.4 Operation of DC-PEH 44710.10.5 Dynamic Droop Gain Selection 44810.11 Concluding Remarks 456Problems 457Notes and References 46011 Harmonics in Electrical and Electronic Systems 46511.1 Harmonics and Interharmonics 46511.1.1 High-frequency Harmonics (2–150 kHz) 46711.1.2 EMI in the Frequency Range of 150 kHz–30 MHz 46811.1.3 Common Mode and Differential Mode Harmonics and Noises 46911.1.4 Stiff and Weak Grids 47011.2 Power Quality Factors and Definitions 47111.2.1 Harmonic Distortion 47111.2.2 Power and Displacement Factors 47311.3 Harmonics Generated by Power Electronics in Power Systems 47411.3.1 Harmonic Analysis at a Load Side (a Three-phase Inverter) 47711.3.2 Harmonic Analysis at a Grid Side (a Three-phase Rectifier) 47911.3.3 Harmonic Analysis at Grid Side (Single-phase Rectifier with and without PF Correction System) 48411.3.4 Harmonic Analysis at Grid Side (AFE) 48811.4 Power Quality Regulations and Standards 49111.4.1 IEEE Standards 49111.4.2 IEEE 519 49111.4.3 IEEE 1547 49411.4.4 IEEE 1662-2008 49411.4.5 IEEE 1826-2012 49511.4.6 IEEE 1709-2010 49611.4.7 IEC Standards 49711.5 Concluding Remarks 499Notes and References 499Index 501