Advanced Control of Power Converters

About the Authors xiii List of Abbreviations xvii Preface xix Acknowledgment xxi About the Companion Website xxiii 1 Introduction 1 1.1 General Remarks 1 1.2 Basic Closed-Loop Control for Power Converters 3 1.3 Mathematical Modeling of Power Converters 4 1.4 Basic Control Objectives 6 1.4.1 Closed-Loop Stability 6 1.4.2 Settling Time 10 1.4.3 Steady-State Error 11 1.4.4 Robustness to Parameter Variations and Disturbances 12 1.5 Performance Evaluation 12 1.5.1 Simulation-Based Method 12 1.5.2 Experimental Method 13 1.6 Contents of the Book 13 References 15 2 Introduction to Advanced Control Methods 17 2.1 Classical Control Methods for Power Converters 17 2.2 Sliding Mode Control 18 2.3 Lyapunov Function-Based Control 22 2.3.1 Lyapunov’s Linearization Method 23 2.3.2 Lyapunov’s Direct Method 24 2.4 Model Predictive Control 27 2.4.1 Functional Principle 27 2.4.2 Basic Concept 28 2.4.3 Cost Function 29 References 30 3 Design of Sliding Mode Control for Power Converters 33 3.1 Introduction 33 3.2 Sliding Mode Control of DC–DC Buck and Cuk Converters 33 3.3 Sliding Mode Control Design Procedure 44 3.3.1 Selection of Sliding Surface Function 44 3.3.2 Control Input Design 46 3.4 Chattering Mitigation Techniques 48 3.4.1 Hysteresis Function Technique 48 3.4.2 Boundary Layer Technique 49 3.4.3 State Observer Technique 50 3.5 Modulation Techniques 51 3.5.1 Hysteresis Modulation Technique 51 3.5.2 Sinusoidal Pulse Width Modulation Technique 52 3.5.3 Space Vector Modulation Technique 53 3.6 Other Types of Sliding Mode Control 54 3.6.1 Terminal Sliding Mode Control 54 3.6.2 Second-Order Sliding Mode Control 54 References 55 4 Design of Lyapunov Function-Based Control for Power Converters 59 4.1 Introduction 59 4.2 Lyapunov-Function-Based Control Design Using Direct Method 59 4.3 Lyapunov Function-Based Control of DC–DC Buck Converter 62 4.4 Lyapunov Function-Based Control of DC–DC Boost Converter 67 References 71 5 Design of Model Predictive Control 73 5.1 Introduction 73 5.2 Predictive Control Methods 73 5.3 FCS Model Predictive Control 75 5.3.1 Design Procedure 76 5.3.2 Tutorial 1: Implementation of FCS-MPC for Three-Phase VSI 80 5.4 CCS Model Predictive Control 86 5.4.1 Incremental Models 86 5.4.2 Predictive Model 88 5.4.3 Cost Function in CCSMPC 92 5.4.4 Cost Function Minimization 93 5.4.5 Receding Control Horizon Principle 96 5.4.6 Closed-Loop of an MPC System 97 5.4.7 Discrete Linear Quadratic Regulators 97 5.4.8 Formulation of the Constraints in MPC 99 5.4.9 Optimization with Equality Constraints 103 5.4.10 Optimization with Inequality Constraints 105 5.4.11 MPC for Multi-Input Multi-Output Systems 108 5.4.12 Tutorial 2: MPC Design For a Grid-Connected VSI in dq Frame 109 5.5 Design and Implementation Issues 112 5.5.1 Cost Function Selection 112 5.5.1.1 Examples for Primary Control Objectives 113 5.5.1.2 Examples for Secondary Control Objectives 114 5.5.2 Weighting Factor Design 114 5.5.2.1 Empirical Selection Method 115 5.5.2.2 Equal-Weighted Cost-Function-Based Selection Method 116 5.5.2.3 Lookup Table-Based Selection Method 117 References 118 6 MATLAB/Simulink Tutorial on Physical Modeling and Experimental Setup 121 6.1 Introduction 121 6.2 Building Simulation Model for Power Converters 121 6.2.1 Building Simulation Model for Single-Phase Grid-Connected Inverter Based on Sliding Mode Control 122 6.2.2 Building Simulation Model for Three-Phase Rectifier Based on Lyapunov-Function-Based Control 126 6.2.3 Building Simulation Model for Quasi-Z Source Three-Phase Four-Leg Inverter Based on Model Predictive Control 131 6.2.4 Building Simulation Model for Distributed Generations in Islanded AC Microgrid 137 6.3 Building Real-Time Model for a Single-Phase T-Type Rectifier 142 6.4 Building Rapid Control Prototyping for a Single-Phase T-Type Rectifier 154 6.4.1 Components in the Experimental Testbed 155 6.4.1.1 Grid Simulator 155 6.4.1.2 A Single-Phase T-Type Rectifier Prototype 156 6.4.1.3 Measurement Board 157 6.4.1.4 Programmable Load 158 6.4.1.5 Controller 158 6.4.2 Building Control Structure on OP- 5707 158 References 162 7 Sliding Mode Control of Various Power Converters 163 7.1 Introduction 163 7.2 Single-Phase Grid-Connected Inverter with LCL Filter 163 7.2.1 Mathematical Modeling of Grid-Connected Inverter with LCL Filter 164 7.2.2 Sliding Mode Control 165 7.2.3 PWM Signal Generation Using Hysteresis Modulation 168 7.2.3.1 Single-Band Hysteresis Function 168 7.2.3.2 Double-Band Hysteresis Function 168 7.2.4 Switching Frequency Computation 170 7.2.4.1 Switching Frequency Computation with Single-Band Hysteresis Modulation 170 7.2.4.2 Switching Frequency Computation with Double-Band Hysteresis Modulation 171 7.2.5 Selection of Control Gains 172 7.2.6 Simulation Study 174 7.2.7 Experimental Study 177 7.3 Three-Phase Grid-Connected Inverter with LCL Filter 180 7.3.1 Physical Model Equations for a Three-Phase Grid-Connected VSI with an LCL Filter 181 7.3.2 Control System 182 7.3.2.1 Reduced State-Space Model of the Converter 183 7.3.2.2 Model Discretization and KF Adaptive Equation 187 7.3.2.3 Sliding Surfaces with Active Damping Capability 188 7.3.3 Stability Analysis 189 7.3.3.1 Discrete-Time Equivalent Control Deduction 189 7.3.3.2 Closed-Loop System Equations 191 7.3.3.3 Test of Robustness Against Parameters Uncertainties 192 7.3.4 Experimental Study 192 7.3.4.1 Test of Robustness Against Grid Inductance Variations 192 7.3.4.2 Test of Stability in Case of Grid Harmonics Near the Resonance Frequency 196 7.3.4.3 Test of the VSI Against Sudden Changes in the Reference Current 196 7.3.4.4 Test of the VSI Under Distorted Grid 198 7.3.4.5 Test of the VSI Under Voltage Sags 198 7.3.5 Computational Load and Performances of the Control Algorithm 199 7.4 Three-Phase AC–DC Rectifier 200 7.4.1 Nonlinear Model of the Unity Power Factor Rectifier 200 7.4.2 Problem Formulation 202 7.4.3 Axis-Decoupling Based on an Estimator 203 7.4.4 Control System 205 7.4.4.1 Kalman Filter 206 7.4.4.2 Practical Considerations: Election of Q and R Matrices 208 7.4.4.3 Practical Considerations: Computational Burden Reduction 208 7.4.5 Sliding Mode Control 209 7.4.5.1 Inner Control Loop 209 7.4.5.2 Outer Control Loop 210 7.4.6 Hysteresis Band Generator with Switching Decision Algorithm 212 7.4.7 Experimental Study 215 7.5 Three-Phase Transformerless Dynamic Voltage Restorer 224 7.5.1 Mathematical Modeling of Transformerless Dynamic Voltage Restorer 224 7.5.2 Design of Sliding Mode Control for TDVR 225 7.5.3 Time-Varying Switching Frequency with Single-Band Hysteresis 227 7.5.4 Constant Switching Frequency with Boundary Layer 229 7.5.5 Simulation Study 231 7.5.6 Experimental Study 233 7.6 Three-Phase Shunt Active Power Filter 240 7.6.1 Nonlinear Model of the SAPF 240 7.6.2 Problem Formulation 242 7.6.3 Control System 243 7.6.3.1 State Model of the Converter 243 7.6.3.2 Kalman Filter 245 7.6.3.3 Sliding Mode Control 246 7.6.3.4 Hysteresis Band Generator with SDA 247 7.6.4 Experimental Study 248 7.6.4.1 Response of the SAPF to Load Variations 249 7.6.4.2 SAPF Performances Under a Distorted Grid 253 7.6.4.3 SAPF Performances Under Grid Voltage Sags 254 7.6.4.4 Spectrum of the Control Signal 254 References 257 8 Design of Lyapunov Function-Based Control of Various Power Converters 261 8.1 Introduction 261 8.2 Single-Phase Grid-Connected Inverter with LCL Filter 261 8.2.1 Mathematical Modeling and Controller Design 261 8.2.2 Controller Modification with Capacitor Voltage Feedback 264 8.2.3 Inverter-Side Current Reference Generation Using Proportional- Resonant Controller 264 8.2.4 Grid Current Transfer Function 266 8.2.5 Harmonic Attenuation and Harmonic Impedance 267 8.2.6 Results 270 8.3 Single-Phase Quasi-Z-Source Grid-Connected Inverter with LCL Filter 277 8.3.1 Quasi-Z-Source Network Modeling 277 8.3.2 Grid-Connected Inverter Modeling 280 8.3.3 Control of Quasi-Z-Source Network 281 8.3.4 Control of Grid-Connected Inverter 281 8.3.5 Reference Generation Using Cascaded PR Control 282 8.3.6 Results 283 8.4 Single-Phase Uninterruptible Power Supply Inverter 287 8.4.1 Mathematical Modeling of Uninterruptible Power Supply Inverter 287 8.4.2 Controller Design 288 8.4.3 Criteria for Selecting Control Parameters 290 8.4.4 Results 292 8.5 Three-Phase Voltage-Source AC–DC Rectifier 298 8.5.1 Mathematical Modeling of Rectifier 298 8.5.2 Controller Design 301 8.5.3 Results 304 References 307 9 Model Predictive Control of Various Converters 309 9.1 CCS MPC Method for a Three-Phase Grid-Connected VSI 309 9.1.1 Model Predictive Control Design 310 9.1.1.1 VSI Incremental Model with an Embedded Integrator 310 9.1.1.2 Predictive Model of the Converter 311 9.1.1.3 Cost Function Minimization 312 9.1.1.4 Inclusion of Constraints 313 9.1.2 MATLAB ® /Simulink ® Implementation 315 9.1.3 Simulation Studies 322 9.2 Model Predictive Control Method for Single-Phase Three-Level Shunt Active Filter 325 9.2.1 Modeling of Shunt Active Filter (SAPF) 325 9.2.2 The Energy-Function-Based MPC 328 9.2.2.1 Design of Energy-Function-Based MPC 328 9.2.2.2 Discrete-Time Model 331 9.2.3 Experimental Studies 332 9.2.3.1 Steady-State and Dynamic Response Tests 333 9.2.3.2 Comparison with Classical MPC Method 337 9.3 Model Predictive Control of Quasi-Z Source Three-Phase Four-Leg Inverter 341 9.3.1 qZS Four-Leg Inverter Model 341 9.3.2 MPC Algorithm 345 9.3.2.1 Determination of References 345 9.3.2.2 Discrete-Time Models of the System 346 9.3.2.3 Cost Function Optimization 347 9.3.2.4 Control Algorithm 347 9.3.3 Simulation Results 349 9.4 Weighting Factorless Model Predictive Control for DC–DC SEPIC Converters 352 9.4.1 Principle of Control Strategy 352 9.4.1.1 Conventional Model Predictive Current Control 355 9.4.1.2 Cost Function Analysis of Conventional MPC 356 9.4.1.3 Cost Function Design of Presented MPC in [11] 358 9.4.1.4 Output Voltage Control 361 9.4.2 Experimental Results 362 9.4.2.1 Switching Frequency Control Test 362 9.4.2.2 Dynamic Response Test Under Input Voltage Variation 363 9.4.2.3 Dynamic Response Test Under Load Change 366 9.4.2.4 Influence of Parameter Mismatch 367 9.5 Model Predictive Droop Control of Distributed Generation Inverters in Islanded AC Microgrid 370 9.5.1 Conventional Droop Control 370 9.5.2 Control Technique 373 9.5.2.1 Reference Voltage Generation Through Droop Control 373 9.5.2.2 Model Predictive Control 374 9.5.3 Simulation Results 376 9.6 FCS-MPC for a Three-Phase Shunt Active Power Filter 378 9.6.1 System Modeling 381 9.6.2 Control Technique 383 9.6.3 FCS-MPC with Reduced States 384 9.6.3.1 Vector Selection Based on Vector Operation 384 9.6.3.2 Cost Function Minimization Procedure 387 9.6.3.3 Kalman Filter 387 9.6.4 Experimental Results 389 9.7 FCS-MPC for a Single-Phase T-Type Rectifier 395 9.7.1 Modeling of Single-Phase T-Type Rectifier 395 9.7.2 Model Predictive Control 397 9.7.2.1 Sensorless Grid Voltage Estimation 397 9.7.2.2 Reference Current Generation 400 9.7.2.3 MPC for the T-Type Rectifier 400 9.7.2.4 MPC for the Power Decoupling Circuit 402 9.7.3 Experimental Studies 404 9.7.3.1 Steady-State Analysis 404 9.7.3.2 Robustness Analysis 404 9.8 Predictive Torque Control of Brushless Doubly Fed Induction Generator Fed by a Matrix Converter 408 9.8.1 Overview of the System Model 411 9.8.1.1 Topology Overview 411 9.8.1.2 Mathematical Model of the CDFIG 412 9.8.1.3 Mathematical Model of the Matrix Converter 414 9.8.2 Predictive Torque Control of CDFIG 415 9.8.2.1 Outer Loop 416 9.8.2.2 Internal Model of the Controller 416 9.8.2.3 Cost Function Minimization 418 9.8.3 Simulation Results 418 9.9 An Enhanced Finite Control Set Model Predictive Control Method with Self-Balancing Capacitor Voltages for Three-Level T-Type Rectifiers 420 9.9.1 Overview of the System Model 422 9.9.2 Problem Definition 424 9.9.3 Derivation of Lyapunov-Energy Function 425 9.9.4 Discrete-Time Model 428 9.9.5 Experimental Studies 429 References 431 Index 435