Control and Filter Design of Single-Phase Grid-Connected Converters
Description
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.
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Persons
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 of 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.
Content
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
1
Introduction
A paradigm shift from large power plants to small distributed generation (DG) systems located at the point of consumption is an emerging trend in the field of electricity. In recent years, DG systems have been powered by photovoltaic (PV) cells, wind turbines, wave generators, fuel cells, small hydro-powered, and gas-powered combined heat and power stations [1-5]. As reported by the Global Renewable Energy Policy Multi-Stakeholder Network REN21, solar PV cells and wind are currently the mainstream options in the power sector with an increasing number of countries generating more than 20% of their electricity. As shown in Figure 1.1, the installed renewable power capacity increased beyond 200 GW in 2019 (mostly with solar PV cells), which is the largest increase ever. During the same year, 57% of renewable power capacity additions were using solar PV cells (direct current) followed by wind power (approximately 60 GW for 30%) and hydropower (approximately 16 GW for 8%). The remaining 5% of additions were from bio-power, geothermal power, and concentrating solar thermal power. For the fifth year in a row, net additions of renewable power generation capacity clearly outpaced the net installations of fossil fuel and nuclear power capacity combined as shown in Figure 1.2. Globally, 32 countries had at least 10 GW of renewable power capacity in 2019; a decade earlier, it was only 19 countries. In most countries, producing electricity from wind and solar PV cells is cost-effective than generating electricity from new coal-fired power plants.
1.1 Architecture of DG Grid-Connected Converter
Regardless of the type of renewable energy source, a DG grid-connected converter is essential for converting the energy produced by the source to the grid [2, 3]. Considering their high degree of modularity, scalability, adaptability, maintainability, and autonomic behavior, DG grid-connected converters have been widely employed in many commercial, industrial, and domestic applications.
Figure 1.1 Estimated renewable share of total final energy consumption, 2018.
Source:[1]/REN21.
Figure 1.2 Renewable and non-renewable shares of net annual additions in power generation capacity, 2009-2019.
Source:[1]/REN21.
The basic structure of a modern DG grid-connected converter is similar to that of power electronics systems. It consists of a power conversion stage (PCS) and a controller. Its architecture is shown in Figure 1.3. The controller includes basic functions, specific functions, and ancillary functions [4]. The basic functions are necessary to ensure normal operation of the system and specific functions are used to meet the industrial requirements. The ancillary functions are optional depending on specific applications such as microgrid applications [5]. The basic functions of the controller are typically composed of grid synchronization or phase-locked loop (PLL), DC-link voltage regulation, and output current regulation.
Figure 1.3 Architecture of DG grid-connected converter.
1.1.1 Power Conversion Stage
The PCS of DG grid-connected converter consists of a switching network and an output filter as shown in Figure 1.3. The switching network converts incoming DC power into high-frequency AC power. The output filter allows the line-frequency component to pass and attenuate, thus switching harmonics to the grid to meet statutory requirements, such as IEEE519-2014 [6] and IEC61727-2004 [7].
1.1.1.1 Switching Network
Based on input source types, the switching network of DG grid-connected converters can be classified into two basic types as shown in Figure 1.4 [8]. Figure 1.4a, b depict a two-level bridge for the current source converter and voltage source converter (VSC), respectively. The number n varies with the system configuration.
Figure 1.4 Configurations of switching networks. (a) Current source converter; (b) voltage source converter.
Considering that a VSC with bidirectional power feature plays a major role in distributed renewable generation systems, switching networks with n = 1, 2, and 3 for single- and three-phase voltage-source inverters (VSIs) are extensively studied.
1.1.1.2 Output Filter
The power grid is an infinite bus bar; hence, the grid interfacing circuit at the point-of-common-coupling (PCC) must be inductive. The simplest form of output filter for VSI is an inductor (L). The lower limit of the filter inductance is determined by the harmonic requirement of the grid-injected current according to IEEE 519-1992, where the percentage relative to the nominal grid-side fundamental current is specified in Table 1.1. The harmonic currents at different harmonic frequencies can be calculated from the ratio of corresponding harmonic voltage amplitudes to the filter impedance characteristics. The first-order L-type filter has a simple structure and is easy to install; however, it has relatively poor attenuation of switching harmonics, resulting in a very large size.
Thus, as shown in Figure 1.5, the industry prefers to use higher-order filters, such as a third-order inductor-capacitor-inductor (LCL) filter or a third-order LCL filter with a parallel notch circuit (LLCL filter) [9] to achieve better switching harmonic attenuation with small reactive elements.
Table 1.1 Maximum permitted harmonic current distortion in percentage of current Ig according to IEEE 519-1992.
Individual harmonic order h h<11 11=h<17 17=h<23 23=h<35 35<h THD Percentage (%) 4.0 2.0 1.5 0.6 0.3 5.0Figure 1.5 Filter configurations.
1.1.2 Control Stage
Depending on their operation, DG grid-connected converters can be classified into grid-feeding, grid-supporting, and grid-forming power converters [10, 11].
The grid-forming converters can be represented as an ideal AC voltage source with a low-output impedance by setting the voltage amplitude E* and frequency ?* of the local grid using a proper control loop as illustrated in Figure 1.6a.
Correspondingly, grid-feeding power converters are designed to deliver power to an energized grid. They can be represented as an ideal current source connected to the grid in parallel with high impedance. The simplified scheme of the grid-feeding power converter is depicted in Figure 1.6b where P* and Q* represent the active and reactive powers to be delivered, respectively. In this application, it is important to note that the current source should be perfectly synchronized with the AC voltage at the connection point to accurately regulate the active and reactive power exchanged with the grid. Currently, the grid-feeding power converter is still the mainstream of grid-connected converters, and it is also the focus of the following study.
Figure 1.6 Simplified representation of grid-connected power converters. (a) Grid-forming; (b) grid-feeding.
1.2 Challenges for Controlling DG Grid-Connected VSCs with High-Order Power Filter
Modern DG grid-connected VSC must remain stable for different grid conditions, especially when higher-order output filters such as LCL or LLCL filters are used to minimize the size of reactive components. Additionally, they are necessary to address many intrinsic and extrinsic challenges in current regulation, such as oscillation due to filter resonance, filter parametric sensitivities, digital delay, uncertainty of the grid condition, and disturbances at the PCC.
1.2.1 Intrinsic Challenges
- Filter resonance
To reduce the size and weight of the filter, the most commonly applied solution is to use a high-order LCL or LLCL filter instead of a first-order L filter. However, the presence of multiple reactive elements, such as inductive and capacitive components, results in resonant frequencies. Thus, the output resonates when the inverter with LCL or LLCL filter is subject to disturbances [9]. In particular, filter resonance results in system instability [12, 13].
Depending on the output current detection positions as shown in Figure 1.7a, there are two methods for regulating the output current of the system: (i) by directly controlling the grid current or (ii) by controlling the converter-side current. The transfer function characteristics in the frequency domain are plotted in Figure 1.7b where the resonant poles are formed by the parallel converter grid-side inductors and...
