Control and Filter Design of Single-Phase Grid-Connected Converters

A state-of-the-art discussion of modern grid inverters

In Control and Filter Design of Single-Phase Grid-Connected Converters, a team of distinguished researchers deliver a robust and authoritative treatment of critical distributed power generation technologies, grid-connected inverter designs, and renewable energy utilization. The book includes detailed explanations of the system structure of distributed generation (DG)-grid interface converters and the methods of controlling DG-grid interface voltage source converters (VSCs) with high-order filters.

The authors also explore the challenges and obstacles associated with modern power electronic grid-connected inverter control technology and introduce some designed systems that meet these challenges, such as the grid impedance canceller.

Readers will discover demonstrations of basic principles, guidelines, examples, and design and simulation programs for grid-connected inverters based on LCL/LLCL technology. They will also find:

• A thorough introduction to the architectures of DG-grid interfacing converters, including the challenges of controlling DG-grid interfacing VSCs with high-order filters
• Comprehensive explorations of the control structure and modulation techniques of single-phase grid-tied inverters
• Practical discussions of an LLCL power filter for single-phase grid-tied inverters
• Fulsome treatments of design methods of passive damping for LCL/LLCL-filtered grid-tied inverters

Perfect for researchers, postgraduate students, and senior level undergraduate students of electrical engineering, Control and Filter Design of Single-Phase Grid-Connected Converters will also benefit research & development engineers involved with the design and manufacture of power electronic inverters.

Weimin Wu is a Professor in the Department of Electrical Engineering at the Shanghai Maritime University in China.

Frede Blaabjerg is a Professor in the Department of Energy at Aalborg University in Denmark.

Henry Chung is Chair Professor of Electrical Engineering at City University in Hong Kong, China.

Yuanbin He is Associate Professor in the School of Automation at Hangzhou Dianzi University in China.

Min Huang is a Lecturer in the Department of Electrical Engineering at the Shanghai Maritime University in China.

Author Biography xiii

Preface xvii

Part I Background 1

1 Introduction 3

1.1 Architecture of DG Grid-Connected Converter 3

1.1.1 Power Conversion Stage 5

1.1.1.1 Switching Network 5

1.1.1.2 Output Filter 6

1.1.2 Control Stage 7

1.2 Challenges for Controlling DG Grid-Connected VSCs with High-Order Power Filter 8

1.2.1 Intrinsic Challenges 8

1.2.1.1 Filter Parametric Sensitivities 9

1.2.1.2 Digital Delay 10

1.2.2 Extrinsic Challenges 10

1.2.2.1 Grid Impedance Variation 10

1.2.2.2 Disturbances at the PCC 10

1.3 Methods for Controlling DG Grid-Connected VSCs with High-Order Power Filter 12

1.3.1 Methodologies to Assess the Stability of DG Grid-Connected VSCs 12

1.3.1.1 Eigenvalue-Based Analysis 12

1.3.1.2 Impedance-Based Stability Analysis 12

1.3.1.3 Application Issue Related to Impedance-Based Stability Analysis 13

1.3.2 Methods to Mitigate Filter Resonance 14

1.3.2.1 Online Grid Impedance Estimation 14

1.3.2.2 Inherent Damping 15

1.3.2.3 Passive Damping 15

1.3.2.4 Active Damping 17

1.3.2.5 Hybrid Damping 19

1.3.3 Harmonic distortion Mitigation Methods 20

1.4 Supplementary Note 21

References 22

2 Control Structure and Modulation Techniques of Single-Phase Grid-Connected Inverter 29

2.1 Control Structure of Single-Phase Grid-Connected Inverter 29

2.1.1 Natural Frame Control 30

2.1.2 Synchronous Reference Frame Control 32

2.1.3 Grid Synchronization Methods 33

2.1.3.1 Zero-Crossing Method 33

2.1.3.2 Filtering of Grid Voltages 34

2.1.3.3 PLL Technique 34

2.2 Modulation Methods 35

2.2.1 Unipolar Modulation Method 35

2.2.1.1 Continuous Unipolar Modulation 36

2.2.1.2 Discontinuous Unipolar Modulation 36

2.2.2 Bipolar Modulation Method 39

2.3 Summary 40

References 41

Part II LCL/LLCL Power Filter 43

3 An LLCL Power Filter for Single-Phase Grid-Connected Inverter 45

3.1 Introduction 45

3.2 Principle of Traditional LCL Filter and Proposed LLCL Filter 46

3.3 Parametric Design of LCL and LLCL Filters 49

3.3.1 Constraints and Procedure of Power Filter Design 49

3.3.2 Saving Analysis on the Grid-Side Inductance 53

3.3.3 Specific Design Consideration for a Simple Passive Damping Strategy 53

3.4 Design Examples for LCL and LLCL filters 54

3.5 Experimental Results 56

3.5.1 Experimental Results 57

3.5.2 Analysis and Discussion 58

3.6 Summary 59

References 59

4 Modeling and Suppressing Conducted Electromagnetic Interference Noise for LCL/LLCL-Filtered Single-Phase Transformerless Grid-Connected Inverter 61

4.1 Introduction 61

4.2 Conducted EMI Noise Analysis 62

4.2.1 CM and DM Voltage Noises 62

4.2.2 Spectrum of DM and CM Voltage Noise for GCI Using DUPWM 64

4.2.3 Spectrum of DM Voltage Noise for GCI Using BPWM 67

4.3 Modified LLCL Filter to Fully Suppress the Conducted EMI Noise for GCI Using DUPWM 68

4.3.1 Modified Solution for LLCL Filter 68

4.3.2 Improved Parameter Design of LLCL filter 72

4.3.3 Constraints on Harmonics of the Grid-Injected Current and EMI Noise Within 150 kHz to 1 MHz 72

4.3.3.1 Constraints on Leakage Current 73

4.3.4 Experimental Verification 74

4.3.4.1 Power Spectrum of the Grid-Injected Current 75

4.3.4.2 Measured Conducted EMI Noise 75

4.3.5 Negative Dc-rail Voltage with Respect to the Earth V Dc_n and Leakage Current 78

4.4 Novel DM EMI Suppressor for LLCL-Filtered GCI without CM Noise Issue 79

4.4.1 Proposed DM EMI Suppressor 79

4.4.2 Experimental Verification 83

4.5 Summary 85

4.5.1 For Single-Phase Transformerless GCI Using DUPWM 85

4.5.2 For Single-Phase Transformerless GCI Using BPWM or a System Without cm EMI Noise Issue 85

References 86

Part III Passive Damping 89

5 Design of Passive Damper for LCL/LLCL-Filtered Grid-Connected Inverter 91

5.1 Introduction 91

5.2 Design Method for Passive Damping 92

5.2.1 Passive Damping Scheme of LCL Filter 92

5.2.2 Passive Damping Scheme of LLCL Filter 95

5.2.3 Design Example 97

5.3 Analysis of Power Loss Caused by the Filter 98

5.3.1 Passive Damping Power Loss 98

5.3.2 Power Losses in Inductors 100

5.4 Experimental Results 101

5.5 Summary 110

References 113

6 Composite Passive Damping Scheme for LLCL-Filtered Grid-Connected Inverter 115

6.1 Introduction 115

6.2 Upper and Lower Limits of the PR + HC Controller Gain 116

6.2.1 LLCL Filter-Based Grid-Connected Inverter Configuration 116

6.2.2 Lower Limit of the PR + HC Controller Gain 117

6.2.3 Upper Limit of the PR + HC Controller Gain 118

6.3 E-Q-Factor-Based Passive Damping Design 119

6.3.1 Principle of the Equivalent Q-Factor Method 119

6.3.2 E-Q-Factor-Based RC Parallel Damping Design 121

6.3.3 E-Q-Factor-Based RL Series Damping Design 124

6.4 New Composite Passive Damping Scheme for the LLCL Filter 126

6.4.1 Composite Passive Damping Scheme 126

6.4.2 Design Example 127

6.4.3 Analysis of Achieved Damping 129

6.5 Experimental Verification 134

6.6 Summary 136

References 138

Part IV Robust Control Design 139

7 Robust Hybrid Damper Design for LCL/LLCL-Filtered Grid-Connected Inverter 141

7.1 Introduction 141

7.2 Control Bandwidth Analysis of the Grid-Current Feedback Method 142

7.2.1 LCL/LLCL-Filtered Grid-Connected Inverter System 142

7.2.2 Maximum Achieved Bandwidth of the Control Method 143

7.3 Proposed Single-Loop Control with High Bandwidth 145

7.3.1 Mathematical Model of the Proposed Single-Loop Control with Hybrid Damper 145

7.3.2 System-Characteristics-Based Single-Loop Control Design Methodology 148

Step 1: Design of the RC Parallel Damper 148

Step 2: Design of the Proportionality Coefficient K p of the PR + HC Regulator 148

Step 3: Determination of the Critical Grid Inductance 149

Step 4: Determination of the Critical Frequency Region for Case 1 and the Critical Frequency (f 0 of Case 1 and f L0 of Case 2) 151

Step 5: Design of the Digital Notch Filter 152

Step 6: Checking the Phase Margin of the Entire System 153

7.4 Design Example 155

7.4.1 System Design 155

7.4.2 System Parameter Robustness Analysis 156

7.5 Experimental Verification 156

7.6 Summary 160

References 161

8 Robust Impedance-Based Design of LLCL-Filtered Grid-Connected Inverter against the Wide Variation of Grid Reactance 163

8.1 Introduction 163

8.2 Modeling of the LLCL-Type Grid-Connected Inverter 164

8.2.1 System Description 164

8.2.2 Norton Equivalent Model 165

8.3 Stability Analysis Considering Grid-Reactance Variation 166

8.3.1 Non-Passive Regions of Inverter Output Admittance 166

8.3.2 Possible Instability Under the Wide Variation of Grid Reactance 167

8.4 Proposed Measures and Design Procedure Under the Grid-Reactance Variation Condition 168

8.4.1 Proposed Measures Against Grid-Reactance Variation 168

8.4.2 Design Procedure 170

Step 1- Calculate the Minimum Grid Inductance L g_min 170

Step 2- Design L 1 ,C total , and L 2 171

Step 3- Design the Bypass Filtering Branch 172

Step 4- Design the Minimum Grid Capacitance C g_min 172

Step 5- Design the Proportional Gain K P of the PR+HC Regulator 172

Step 6- Select C EMI ,C d , and R d 173

Step 7- Check F I < F D 2 175

8.5 Design Example 177

8.6 Simulation and Experimental Verification 179

8.6.1 Simulation 179

8.6.2 Experiments 182

8.6.2.1 Experimental Results 183

8.6.2.2 Analysis and Discussion 185

8.7 Summary 187

References 187

Part V Active Damping 191

9 Active Damping of LLCL-Filter Resonance Based on LC-Trap Voltage or Current Feedback 193

9.1 Introduction 193

9.2 Control of LLCL-Filtered Grid Converter 194

9.2.1 Description and General Control 194

9.2.2 Block Diagrams of Different Active Dampers 196

9.2.3 Effects of Delay G d (s) 197

9.3 Circuit Equivalences of LLCL Active Dampers 199

9.3.1 General Virtual Impedance Model 199

9.3.2 LC-Trap Voltage Feedback 200

9.3.3 LC-Trap Current Feedback 204

9.4 Z-Domain Root-Locus Analysis 206

9.4.1 Z-Domain Transfer Functions 206

9.4.2 Root-Locus Analyses with Different Active Dampers 207

9.4.3 Comparison 209

9.5 Experimental Verification 209

9.6 Summary 212

References 213

10 Enhancement of System Stability Using Active Cancelation to Eliminate the Effect of Grid Impedance on System Stability and Injected Power Quality of Grid-Connected Inverter 217

10.1 Introduction 217

10.2 Principle of the Grid Impedance Cancelator 218

10.3 Modeling with the Grid Impedance Cancelator 221

10.3.1 System Configuration with the Grid Impedance Cancelator 221

10.3.2 AC Voltage Regulation 222

10.3.3 Active Damping Function 222

10.3.4 dc Capacitor Voltage Control 226

10.4 Modeling of the Grid Impedance Cancelator 226

10.5 Experimental Verification 231

10.6 Summary 239

References 239

Index 241

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.