Table of Contents
Preface xiii
About the Authors xv
Part One Introduction 1
1 Introduction 3
1.1 Introduction 3
1.2 Implementation of Current-Fed Converters 6
1.3 Dynamic Modeling of Power Electronic Converters 7
1.4 Linear Equivalent Circuits 8
1.5 Impedance-Based Stability Assessment 12
1.6 Time Domain-Based Dynamic Analysis 14
1.7 Renewable Energy System Principles 17
1.8 Content Review 19
References 20
2 Dynamic Analysis and Control Design Preliminaries 27
2.1 Introduction 27
2.2 Generalized Dynamic Representations – DC–DC 27
2.2.1 Introduction 27
2.2.2 Generalized Dynamic Representations 29
2.2.3 Generalized Closed-Loop Dynamics 30
2.2.4 Generalized Cascaded Control Schemes 33
2.2.5 Generalized Source and Load Interactions 38
2.2.6 Generalized Impedance-Based Stability Assessment 40
2.3 Generalized Dynamic Representations: DC–AC, AC–DC, and AC–AC 42
2.3.1 Introduction 42
2.3.2 Generalized Dynamic Representations 44
2.3.3 Generalized Closed-Loop Dynamics 48
2.3.4 Generalized Cascaded Control Schemes 50
2.3.5 Generalized Source and Load Interactions 54
2.3.6 Generalized Impedance-Based Stability Assessment 56
2.4 Small-Signal Modeling 57
2.4.1 Introduction 57
2.4.2 Average Modeling and Linearization 60
2.4.3 Modeling Coupled-Inductor Converters 64
2.4.4 Modeling in Synchronous Reference Frame 66
2.5 Control Design Preliminaries 77
2.5.1 Introduction 77
2.5.2 Transfer Functions 77
2.5.3 Stability 84
2.5.4 Transient Performance 95
2.5.5 Feedback-Loop Design Constraints 100
2.5.6 Controller Implementations 103
2.5.7 Optocoupler Isolation 108
2.5.8 Application of Digital Control 109
2.6 Resonant LC-Type Circuits 110
2.6.1 Introduction 110
2.6.2 Single-Section LC Filter 112
2.6.3 LCL Filter 113
2.6.4 CLCL Filter 115
References 117
Part Two Voltage-Fed DC–DC Converters 123
3 Dynamic Modeling of Direct-on-Time Control 125
3.1 Introduction 125
3.2 Direct-on-Time Control 127
3.3 Generalized Modeling Technique 129
3.3.1 Buck Converter 131
3.3.2 Boost Converter 134
3.3.3 Buck–Boost Converter 136
3.3.4 Superbuck Converter 140
3.4 Fixed-Frequency Operation in CCM 142
3.4.1 Buck Converter 143
3.4.2 Boost Converter 146
3.4.3 Buck–Boost Converter 149
3.4.4 Superbuck Converter 153
3.4.5 Coupled-Inductor Superbuck Converter 157
3.5 Fixed-Frequency Operation in DCM 163
3.5.1 Buck Converter 164
3.5.2 Boost Converter 167
3.5.3 Buck–Boost Converter 170
3.6 Source and Load Interactions 173
3.6.1 Source Interactions 173
3.6.2 Input Voltage Feedforward 174
3.6.3 Load Interactions 176
3.6.4 Output-Current Feedforward 177
3.7 Impedance-Based Stability Issues 179
3.8 Dynamic Review 181
References 186
4 Dynamic Modeling of Current-Mode Control 189
4.1 Introduction 189
4.2 Peak Current Mode Control 190
4.2.1 PCM Control Principles 190
4.2.2 Development of Duty-Ratio Constraints in CCM 192
4.2.3 Development of Duty-Ratio Constraints in DCM 195
4.2.4 Origin and Consequences of Mode Limits in CCM and DCM 196
4.2.5 Duty-Ratio Constraints in CCM 201
4.2.5.1 Buck Converter 201
4.2.5.2 Boost Converter 201
4.2.5.3 Buck–Boost Converter 202
4.2.5.4 Superbuck Converter 204
4.2.5.5 Coupled-Inductor Superbuck Converter 205
4.2.6 Duty-Ratio Constraints in DCM 205
4.2.6.1 Buck Converter 205
4.2.6.2 Boost Converter 206
4.2.6.3 Buck–Boost Converter 206
4.2.7 General PCM Transfer Functions in CCM 207
4.2.8 PCM State Spaces and Transfer Functions in CCM 209
4.2.8.1 Buck Converter 209
4.2.8.2 Boost Converter 211
4.2.8.3 Buck–Boost Converter 213
4.2.8.4 Superbuck Converter 215
4.2.8.5 Coupled-Inductor Superbuck Converter 219
4.2.9 PCM State Spaces in DCM 222
4.2.9.1 Buck Converter 222
4.2.9.2 Boost Converter 222
4.2.9.3 Buck–Boost Converter 223
4.3 Average Current-Mode Control 224
4.3.1 Introduction 224
4.3.2 ACM Control Principle 225
4.3.3 Modeling with Full Ripple Inductor Current Feedback 226
4.4 Variable-Frequency Control 230
4.4.1 Introduction 230
4.4.2 Self-Oscillation Modeling – DOT and PCM Control 231
4.5 Source and Load Interactions 239
4.5.1 Output Current Feedforward 240
4.6 Impedance-Based Stability Issues 243
4.7 Dynamic Review 244
4.8 Critical Discussions on PCM Models and Their Validation 249
4.8.1 Ridley’s Models 249
4.8.2 The Book PCM Model in CCM 252
4.8.3 Evaluation of PCM-Controlled Buck in CCM 253
4.8.4 Evaluation of PCM-Controlled Boost in CCM 258
4.8.5 Concluding Remarks 259
References 260
5 Dynamic Modeling of Current-Output Converters 265
5.1 Introduction 265
5.2 Dynamic Modeling 267
5.3 Source and Load Interactions 269
5.3.1 Source Interactions 269
5.3.2 Load Interactions 270
5.4 Impedance-Based Stability Issues 271
5.5 Dynamic Review 272
References 275
6 Control Design Issues in Voltage-Fed DC–DC Converters 277
6.1 Introduction 277
6.2 Developing Switching and Average Models 279
6.2.1 Switching Models 279
6.2.2 Averaged Models 287
6.3 Factors Affecting Transient Response 291
6.3.1 Output Voltage Undershoot 292
6.3.2 Settling Time 294
6.4 Remote Sensing 304
6.4.1 Introduction 304
6.4.2 Remote Sensing Dynamic Effect Analysis Method 304
6.4.3 Remote Sensing Impedance Block Examples 306
6.4.4 Experimental Evidence 307
6.5 Simple Control Design Method 310
6.5.1 DDR-Controlled Buck Converter 312
6.5.2 PCM-Controlled Buck Converter 315
6.5.3 DDR-Controlled Boost Converter 321
6.5.4 PCM-Controlled Boost Converter 325
6.6 PCM-Controlled Superbuck Converter: Experimental Examples 330
6.6.1 Introduction 330
6.6.2 Discrete-Inductor Superbuck 331
6.6.3 Coupled-Inductor Superbuck 332
6.7 Concluding Remarks 334
References 334
Part Three Current-Fed Converters 339
7 Introduction to Current-Fed Converters 341
7.1 Introduction 341
7.2 Duality Transformation Basics 341
7.3 Duality-Transformed Converters 345
7.4 Input Capacitor-Based Converters 351
References 352
8 Dynamic Modeling of DDR-Controlled CF Converters 355
8.1 Introduction 355
8.2 Dynamic Models 356
8.2.1 Duality Transformed Converters 358
8.2.1.1 Buck Converter 358
8.2.1.2 Boost Converter 365
8.2.1.3 Noninverting Buck–Boost Converter 368
8.2.1.4 CF Superbuck Converter 372
8.2.2 Input Capacitor-Based Converters 376
8.2.2.1 Buck Power-Stage Converter 377
8.2.2.2 Boost Power-Stage Converter 383
8.2.2.3 Noninverting Buck–Boost Power-Stage Converter 387
8.3 Source and Load Interactions 390
8.3.1 CF-CO Converters 390
8.3.1.1 Source Interactions 390
8.3.1.2 Load Interactions 391
8.3.2 CF-VO Converters 392
8.3.2.1 Source Interactions 392
8.3.2.2 Load Interactions 393
8.4 Impedance-Based Stability Assessment 394
8.5 Output-Voltage Feedforward 394
8.6 Dynamic Review 397
References 400
9 Dynamic Modeling of PCM/PVM-Controlled CF Converters 403
9.1 Introduction 403
9.2 Duty-Ratio Constraints and Dynamic Models under PCM Control 404
9.2.1 Buck Power-Stage Converter 405
9.2.2 Boost Power-Stage Converter 410
9.3 Duty-Ratio Constraints and Dynamic Models under PVM Control 413
9.3.1 CF Buck Converter 414
9.3.2 CF Superbuck Converter 418
9.4 Concluding Remarks 420
References 420
10 Introduction to Photovoltaic Generator 423
10.1 Introduction 423
10.2 Solar Cell Properties 424
10.3 PV Generator 429
10.4 MPP Tracking Methods 432
10.5 MPP Tracking Design Issues 436
10.5.1 Introduction 436
10.5.2 General Dynamics of PV Power 437
10.5.3 PV Interfacing Converter Operating at Open Loop 439
10.5.4 PV Interfacing Converter Operating at Closed Loop 447
10.5.4.1 Reduced-Order Models: Intuitive Model Reduction 452
10.5.4.2 Reduced-Order Models: Control-Engineering-Based Method 454
10.5.4.3 Reduced-Order Model Verification 455
10.6 Concluding Remarks 461
References 461
11 Photovoltaic Generator Interfacing Issues 465
11.1 Introduction 465
11.2 Centralized PV System Architecture 465
11.3 Distributed PV System Architectures 465
11.4 PV Generator-Induced Effects on Interfacing-Converter Dynamics 470
11.4.1 Introduction 470
11.4.2 PV Generator Effects on Converter Dynamics 474
11.4.2.1 Buck Power-Stage Converter 476
11.4.2.2 Boost Power-Stage Converter 477
11.4.2.3 CF Superbuck Converter 480
11.5 Stability Issues in PV Generator Interfacing 482
11.5.1 Buck Power-Stage Converter 483
11.5.2 CF Superbuck Converter 485
11.5.3 Concluding Remarks 488
11.6 Control Design Issues 488
References 488
Part Four Three-Phase Grid-Connected Converters 491
12 Dynamic Modeling of Three-Phase Inverters 493
12.1 Introduction 493
12.2 Dynamic Model of Voltage-Fed Inverter 494
12.2.1 Average Model of Voltage-Fed Inverter 494
12.2.2 Linearized State-Space and Open-Loop Dynamics 499
12.2.3 Control Block Diagrams of Voltage-Fed Inverter 503
12.2.4 Verification of Open-Loop Model 503
12.3 Dynamic Model of Current-Fed Inverter 507
12.3.1 Average Model of Current-Fed Inverter 507
12.3.2 Linearized Model and Open-Loop Dynamics 510
12.3.3 Control Block Diagrams of Current-Fed Inverter 512
12.3.4 Verification of Open-Loop Model 512
12.4 Source-Affected Dynamics of Current-Fed Inverter 515
12.4.1 Source Effect: Photovoltaic Generator 517
12.4.2 Source Effect: Experimental Validation 520
12.5 Dynamic Model of Current-Fed Inverter with LCL-Filter 524
12.5.1 Average Model of Current-Fed Inverter with LCL-Filter 525
12.5.2 Linearized State-Space and Open-Loop Dynamics 527
12.6 Summary 528
Appendix 12.A 528
References 530
13 Control Design of Grid-Connected Three-Phase Inverters 533
13.1 Introduction 533
13.2 Synchronous Reference Frame Phase-Locked-Loop 533
13.2.1 Linearized Model of SRF-PLL 536
13.2.2 Control Design of SRF-PLL 538
13.2.3 Damping Ratio and Undamped Natural Frequency 541
13.2.4 Control Design Example and Experimental Verification 541
13.2.5 The Effect of Unbalanced Grid Voltages 544
13.3 AC Current Control 547
13.3.1 Current Control in the dq-Domain 548
13.3.2 Current Control in Voltage-Fed Inverters 548
13.4 Decoupling Gains 559
13.5 Grid Voltage Feedforward 562
13.6 Cascaded Control Scheme in Current-Fed Inverters 563
13.6.1 Control Block Diagrams 564
13.6.2 Control Design of Cascaded Loops 566
13.6.3 Instability Caused by RHP-Pole 570
13.6.4 Stability Assessment Using the Nyquist Stability Criterion 574
13.6.5 Design Example: Three-Phase Photovoltaic Inverter 574
13.7 Case Study: Instability Due to RHP-Pole 581
13.8 Summary 583
References 583
14 Reduced-Order Closed-Loop Modeling of Inverters 587
14.1 Introduction 587
14.2 Reduced-Order Model of Voltage-Fed Inverter 587
14.2.1 Closed-Loop Model with AC Current Control 588
14.2.2 Closed-Loop Model with SRF-PLL 591
14.2.3 Closed-Loop Input Admittance 595
14.2.4 Output Impedance with Grid Voltage Feedforward 596
14.2.5 Impedance Characteristics of Voltage-Fed Inverters 602
14.3 Reduced-Order Model of Current-Fed Inverter with L-Type Filter 602
14.3.1 Closed-Loop Model with Cascaded Control Scheme 602
14.3.2 Effect of Input Voltage Control Bandwidth 605
14.3.3 Effect of AC Current Control Bandwidth 606
14.3.4 Experimental Verification: Measured Impedance d-Component 608
14.3.5 Effect of SRF-PLL 609
14.3.6 Effect of Grid Voltage Feedforward on Impedance d-Component 610
14.3.7 Effect of Grid Voltage Feedforward on Impedance q-Component 615
14.4 Closed-Loop Model of Current-Fed Inverter with LC-Type Filter 619
14.4.1 Experimental Verification of Impedance Model 625
14.4.2 Impedance Characteristics of Inverter with LC-Filter and Feedforward 630
14.5 Summary 630
References 630
15 Multivariable Closed-Loop Modeling of Inverters 633
15.1 Introduction 633
15.2 Full-Order Model of Current-Fed Inverter with L-Type Filter 633
15.2.1 Verification of Dynamic Model 643
15.3 Experimental Verification of Admittance Model 646
15.4 Full-Order Model of Current-Fed Inverter with LCL-Type Filter 648
15.4.1 Verification of Closed-Loop Model 653
15.4.2 Measured Output Impedance of PV Inverter 656
15.5 Summary 659
References 660
16 Impedance-Based Stability Assessment 663
16.1 Introduction 663
16.2 Modeling of Three-Phase Load Impedance in the dq-Domain 664
16.3 Impedance-Based Stability Criterion 667
16.4 Case Studies 669
16.4.1 Instability Due to High-Bandwidth PLL in Weak Grid 669
16.4.2 Instability Due to Control Delay in Feedforward Path 674
16.5 Summary 678
References 678
17 Dynamic Modeling of Three-Phase Active Rectifiers 681
17.1 Introduction 681
17.2 Open-Loop Dynamics 681
17.3 Verification of Open-Loop Model 688
17.4 Experimental Results 691
17.5 Summary 695
References 695
Index 697
