{"product_id":"control-and-filter-design-of-single-phase-grid-connected-converters-isbn-9781119886549","title":"Control and Filter Design of Single-Phase Grid-Connected Converters","description":"Control and Filter Design of \u003cb\u003eSingle-Phase Grid-Connected Converters\u003c\/b\u003e \u003cp\u003e\u003cb\u003eA state-of-the-art discussion of modern grid inverters\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eIn \u003ci\u003eControl and Filter Design of Single-Phase Grid-Connected Converters\u003c\/i\u003e, 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. \u003c\/p\u003e\u003cp\u003eThe 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. \u003c\/p\u003e\u003cp\u003eReaders 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: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e A thorough introduction to the architectures of DG-grid interfacing converters, including the challenges of controlling DG-grid interfacing VSCs with high-order filters\u003c\/li\u003e \u003cli\u003e Comprehensive explorations of the control structure and modulation techniques of single-phase grid-tied inverters\u003c\/li\u003e \u003cli\u003e Practical discussions of an LLCL power filter for single-phase grid-tied inverters\u003c\/li\u003e \u003cli\u003e Fulsome treatments of design methods of passive damping for LCL\/LLCL-filtered grid-tied inverters\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003ePerfect for researchers, postgraduate students, and senior level undergraduate students of electrical engineering, \u003ci\u003eControl and Filter Design of Single-Phase Grid-Connected Converters \u003c\/i\u003ewill also benefit research \u0026amp; development engineers involved with the design and manufacture of power electronic inverters. \u003c\/p\u003e\u003cp\u003eAuthor Biography xiii\u003c\/p\u003e \u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Background 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Architecture of DG Grid-Connected Converter 3\u003c\/p\u003e \u003cp\u003e1.1.1 Power Conversion Stage 5\u003c\/p\u003e \u003cp\u003e1.1.1.1 Switching Network 5\u003c\/p\u003e \u003cp\u003e1.1.1.2 Output Filter 6\u003c\/p\u003e \u003cp\u003e1.1.2 Control Stage 7\u003c\/p\u003e \u003cp\u003e1.2 Challenges for Controlling DG Grid-Connected VSCs with High-Order Power Filter 8\u003c\/p\u003e \u003cp\u003e1.2.1 Intrinsic Challenges 8\u003c\/p\u003e \u003cp\u003e1.2.1.1 Filter Parametric Sensitivities 9\u003c\/p\u003e \u003cp\u003e1.2.1.2 Digital Delay 10\u003c\/p\u003e \u003cp\u003e1.2.2 Extrinsic Challenges 10\u003c\/p\u003e \u003cp\u003e1.2.2.1 Grid Impedance Variation 10\u003c\/p\u003e \u003cp\u003e1.2.2.2 Disturbances at the PCC 10\u003c\/p\u003e \u003cp\u003e1.3 Methods for Controlling DG Grid-Connected VSCs with High-Order Power Filter 12\u003c\/p\u003e \u003cp\u003e1.3.1 Methodologies to Assess the Stability of DG Grid-Connected VSCs 12\u003c\/p\u003e \u003cp\u003e1.3.1.1 Eigenvalue-Based Analysis 12\u003c\/p\u003e \u003cp\u003e1.3.1.2 Impedance-Based Stability Analysis 12\u003c\/p\u003e \u003cp\u003e1.3.1.3 Application Issue Related to Impedance-Based Stability Analysis 13\u003c\/p\u003e \u003cp\u003e1.3.2 Methods to Mitigate Filter Resonance 14\u003c\/p\u003e \u003cp\u003e1.3.2.1 Online Grid Impedance Estimation 14\u003c\/p\u003e \u003cp\u003e1.3.2.2 Inherent Damping 15\u003c\/p\u003e \u003cp\u003e1.3.2.3 Passive Damping 15\u003c\/p\u003e \u003cp\u003e1.3.2.4 Active Damping 17\u003c\/p\u003e \u003cp\u003e1.3.2.5 Hybrid Damping 19\u003c\/p\u003e \u003cp\u003e1.3.3 Harmonic distortion Mitigation Methods 20\u003c\/p\u003e \u003cp\u003e1.4 Supplementary Note 21\u003c\/p\u003e \u003cp\u003eReferences 22\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Control Structure and Modulation Techniques of Single-Phase Grid-Connected Inverter 29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Control Structure of Single-Phase Grid-Connected Inverter 29\u003c\/p\u003e \u003cp\u003e2.1.1 Natural Frame Control 30\u003c\/p\u003e \u003cp\u003e2.1.2 Synchronous Reference Frame Control 32\u003c\/p\u003e \u003cp\u003e2.1.3 Grid Synchronization Methods 33\u003c\/p\u003e \u003cp\u003e2.1.3.1 Zero-Crossing Method 33\u003c\/p\u003e \u003cp\u003e2.1.3.2 Filtering of Grid Voltages 34\u003c\/p\u003e \u003cp\u003e2.1.3.3 PLL Technique 34\u003c\/p\u003e \u003cp\u003e2.2 Modulation Methods 35\u003c\/p\u003e \u003cp\u003e2.2.1 Unipolar Modulation Method 35\u003c\/p\u003e \u003cp\u003e2.2.1.1 Continuous Unipolar Modulation 36\u003c\/p\u003e \u003cp\u003e2.2.1.2 Discontinuous Unipolar Modulation 36\u003c\/p\u003e \u003cp\u003e2.2.2 Bipolar Modulation Method 39\u003c\/p\u003e \u003cp\u003e2.3 Summary 40\u003c\/p\u003e \u003cp\u003eReferences 41\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II LCL\/LLCL Power Filter 43\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 An LLCL Power Filter for Single-Phase Grid-Connected Inverter 45\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 45\u003c\/p\u003e \u003cp\u003e3.2 Principle of Traditional LCL Filter and Proposed LLCL Filter 46\u003c\/p\u003e \u003cp\u003e3.3 Parametric Design of LCL and LLCL Filters 49\u003c\/p\u003e \u003cp\u003e3.3.1 Constraints and Procedure of Power Filter Design 49\u003c\/p\u003e \u003cp\u003e3.3.2 Saving Analysis on the Grid-Side Inductance 53\u003c\/p\u003e \u003cp\u003e3.3.3 Specific Design Consideration for a Simple Passive Damping Strategy 53\u003c\/p\u003e \u003cp\u003e3.4 Design Examples for LCL and LLCL filters 54\u003c\/p\u003e \u003cp\u003e3.5 Experimental Results 56\u003c\/p\u003e \u003cp\u003e3.5.1 Experimental Results 57\u003c\/p\u003e \u003cp\u003e3.5.2 Analysis and Discussion 58\u003c\/p\u003e \u003cp\u003e3.6 Summary 59\u003c\/p\u003e \u003cp\u003eReferences 59\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Modeling and Suppressing Conducted Electromagnetic Interference Noise for LCL\/LLCL-Filtered Single-Phase Transformerless Grid-Connected Inverter 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 61\u003c\/p\u003e \u003cp\u003e4.2 Conducted EMI Noise Analysis 62\u003c\/p\u003e \u003cp\u003e4.2.1 CM and DM Voltage Noises 62\u003c\/p\u003e \u003cp\u003e4.2.2 Spectrum of DM and CM Voltage Noise for GCI Using DUPWM 64\u003c\/p\u003e \u003cp\u003e4.2.3 Spectrum of DM Voltage Noise for GCI Using BPWM 67\u003c\/p\u003e \u003cp\u003e4.3 Modified LLCL Filter to Fully Suppress the Conducted EMI Noise for GCI Using DUPWM 68\u003c\/p\u003e \u003cp\u003e4.3.1 Modified Solution for LLCL Filter 68\u003c\/p\u003e \u003cp\u003e4.3.2 Improved Parameter Design of LLCL filter 72\u003c\/p\u003e \u003cp\u003e4.3.3 Constraints on Harmonics of the Grid-Injected Current and EMI Noise Within 150 kHz to 1 MHz 72\u003c\/p\u003e \u003cp\u003e4.3.3.1 Constraints on Leakage Current 73\u003c\/p\u003e \u003cp\u003e4.3.4 Experimental Verification 74\u003c\/p\u003e \u003cp\u003e4.3.4.1 Power Spectrum of the Grid-Injected Current 75\u003c\/p\u003e \u003cp\u003e4.3.4.2 Measured Conducted EMI Noise 75\u003c\/p\u003e \u003cp\u003e4.3.5 Negative Dc-rail Voltage with Respect to the Earth V Dc_n and Leakage Current 78\u003c\/p\u003e \u003cp\u003e4.4 Novel DM EMI Suppressor for LLCL-Filtered GCI without CM Noise Issue 79\u003c\/p\u003e \u003cp\u003e4.4.1 Proposed DM EMI Suppressor 79\u003c\/p\u003e \u003cp\u003e4.4.2 Experimental Verification 83\u003c\/p\u003e \u003cp\u003e4.5 Summary 85\u003c\/p\u003e \u003cp\u003e4.5.1 For Single-Phase Transformerless GCI Using DUPWM 85\u003c\/p\u003e \u003cp\u003e4.5.2 For Single-Phase Transformerless GCI Using BPWM or a System Without cm EMI Noise Issue 85\u003c\/p\u003e \u003cp\u003eReferences 86\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Passive Damping 89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Design of Passive Damper for LCL\/LLCL-Filtered Grid-Connected Inverter 91\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 91\u003c\/p\u003e \u003cp\u003e5.2 Design Method for Passive Damping 92\u003c\/p\u003e \u003cp\u003e5.2.1 Passive Damping Scheme of LCL Filter 92\u003c\/p\u003e \u003cp\u003e5.2.2 Passive Damping Scheme of LLCL Filter 95\u003c\/p\u003e \u003cp\u003e5.2.3 Design Example 97\u003c\/p\u003e \u003cp\u003e5.3 Analysis of Power Loss Caused by the Filter 98\u003c\/p\u003e \u003cp\u003e5.3.1 Passive Damping Power Loss 98\u003c\/p\u003e \u003cp\u003e5.3.2 Power Losses in Inductors 100\u003c\/p\u003e \u003cp\u003e5.4 Experimental Results 101\u003c\/p\u003e \u003cp\u003e5.5 Summary 110\u003c\/p\u003e \u003cp\u003eReferences 113\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Composite Passive Damping Scheme for LLCL-Filtered Grid-Connected Inverter 115\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 115\u003c\/p\u003e \u003cp\u003e6.2 Upper and Lower Limits of the PR + HC Controller Gain 116\u003c\/p\u003e \u003cp\u003e6.2.1 LLCL Filter-Based Grid-Connected Inverter Configuration 116\u003c\/p\u003e \u003cp\u003e6.2.2 Lower Limit of the PR + HC Controller Gain 117\u003c\/p\u003e \u003cp\u003e6.2.3 Upper Limit of the PR + HC Controller Gain 118\u003c\/p\u003e \u003cp\u003e6.3 E-Q-Factor-Based Passive Damping Design 119\u003c\/p\u003e \u003cp\u003e6.3.1 Principle of the Equivalent Q-Factor Method 119\u003c\/p\u003e \u003cp\u003e6.3.2 E-Q-Factor-Based RC Parallel Damping Design 121\u003c\/p\u003e \u003cp\u003e6.3.3 E-Q-Factor-Based RL Series Damping Design 124\u003c\/p\u003e \u003cp\u003e6.4 New Composite Passive Damping Scheme for the LLCL Filter 126\u003c\/p\u003e \u003cp\u003e6.4.1 Composite Passive Damping Scheme 126\u003c\/p\u003e \u003cp\u003e6.4.2 Design Example 127\u003c\/p\u003e \u003cp\u003e6.4.3 Analysis of Achieved Damping 129\u003c\/p\u003e \u003cp\u003e6.5 Experimental Verification 134\u003c\/p\u003e \u003cp\u003e6.6 Summary 136\u003c\/p\u003e \u003cp\u003eReferences 138\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Robust Control Design 139\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Robust Hybrid Damper Design for LCL\/LLCL-Filtered Grid-Connected Inverter 141\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 141\u003c\/p\u003e \u003cp\u003e7.2 Control Bandwidth Analysis of the Grid-Current Feedback Method 142\u003c\/p\u003e \u003cp\u003e7.2.1 LCL\/LLCL-Filtered Grid-Connected Inverter System 142\u003c\/p\u003e \u003cp\u003e7.2.2 Maximum Achieved Bandwidth of the Control Method 143\u003c\/p\u003e \u003cp\u003e7.3 Proposed Single-Loop Control with High Bandwidth 145\u003c\/p\u003e \u003cp\u003e7.3.1 Mathematical Model of the Proposed Single-Loop Control with Hybrid Damper 145\u003c\/p\u003e \u003cp\u003e7.3.2 System-Characteristics-Based Single-Loop Control Design Methodology 148\u003c\/p\u003e \u003cp\u003eStep 1: Design of the RC Parallel Damper 148\u003c\/p\u003e \u003cp\u003eStep 2: Design of the Proportionality Coefficient K p of the PR + HC Regulator 148\u003c\/p\u003e \u003cp\u003eStep 3: Determination of the Critical Grid Inductance 149\u003c\/p\u003e \u003cp\u003eStep 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\u003c\/p\u003e \u003cp\u003eStep 5: Design of the Digital Notch Filter 152\u003c\/p\u003e \u003cp\u003eStep 6: Checking the Phase Margin of the Entire System 153\u003c\/p\u003e \u003cp\u003e7.4 Design Example 155\u003c\/p\u003e \u003cp\u003e7.4.1 System Design 155\u003c\/p\u003e \u003cp\u003e7.4.2 System Parameter Robustness Analysis 156\u003c\/p\u003e \u003cp\u003e7.5 Experimental Verification 156\u003c\/p\u003e \u003cp\u003e7.6 Summary 160\u003c\/p\u003e \u003cp\u003eReferences 161\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Robust Impedance-Based Design of LLCL-Filtered Grid-Connected Inverter against the Wide Variation of Grid Reactance 163\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 163\u003c\/p\u003e \u003cp\u003e8.2 Modeling of the LLCL-Type Grid-Connected Inverter 164\u003c\/p\u003e \u003cp\u003e8.2.1 System Description 164\u003c\/p\u003e \u003cp\u003e8.2.2 Norton Equivalent Model 165\u003c\/p\u003e \u003cp\u003e8.3 Stability Analysis Considering Grid-Reactance Variation 166\u003c\/p\u003e \u003cp\u003e8.3.1 Non-Passive Regions of Inverter Output Admittance 166\u003c\/p\u003e \u003cp\u003e8.3.2 Possible Instability Under the Wide Variation of Grid Reactance 167\u003c\/p\u003e \u003cp\u003e8.4 Proposed Measures and Design Procedure Under the Grid-Reactance Variation Condition 168\u003c\/p\u003e \u003cp\u003e8.4.1 Proposed Measures Against Grid-Reactance Variation 168\u003c\/p\u003e \u003cp\u003e8.4.2 Design Procedure 170\u003c\/p\u003e \u003cp\u003eStep 1- Calculate the Minimum Grid Inductance L g_min 170\u003c\/p\u003e \u003cp\u003eStep 2- Design L 1 ,C total , and L 2 171\u003c\/p\u003e \u003cp\u003eStep 3- Design the Bypass Filtering Branch 172\u003c\/p\u003e \u003cp\u003eStep 4- Design the Minimum Grid Capacitance C g_min 172\u003c\/p\u003e \u003cp\u003eStep 5- Design the Proportional Gain K P of the PR+HC Regulator 172\u003c\/p\u003e \u003cp\u003eStep 6- Select C EMI ,C d , and R d 173\u003c\/p\u003e \u003cp\u003eStep 7- Check F I \u0026lt; F D 2 175\u003c\/p\u003e \u003cp\u003e8.5 Design Example 177\u003c\/p\u003e \u003cp\u003e8.6 Simulation and Experimental Verification 179\u003c\/p\u003e \u003cp\u003e8.6.1 Simulation 179\u003c\/p\u003e \u003cp\u003e8.6.2 Experiments 182\u003c\/p\u003e \u003cp\u003e8.6.2.1 Experimental Results 183\u003c\/p\u003e \u003cp\u003e8.6.2.2 Analysis and Discussion 185\u003c\/p\u003e \u003cp\u003e8.7 Summary 187\u003c\/p\u003e \u003cp\u003eReferences 187\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V Active Damping 191\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Active Damping of LLCL-Filter Resonance Based on LC-Trap Voltage or Current Feedback 193\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 193\u003c\/p\u003e \u003cp\u003e9.2 Control of LLCL-Filtered Grid Converter 194\u003c\/p\u003e \u003cp\u003e9.2.1 Description and General Control 194\u003c\/p\u003e \u003cp\u003e9.2.2 Block Diagrams of Different Active Dampers 196\u003c\/p\u003e \u003cp\u003e9.2.3 Effects of Delay G d (s) 197\u003c\/p\u003e \u003cp\u003e9.3 Circuit Equivalences of LLCL Active Dampers 199\u003c\/p\u003e \u003cp\u003e9.3.1 General Virtual Impedance Model 199\u003c\/p\u003e \u003cp\u003e9.3.2 LC-Trap Voltage Feedback 200\u003c\/p\u003e \u003cp\u003e9.3.3 LC-Trap Current Feedback 204\u003c\/p\u003e \u003cp\u003e9.4 Z-Domain Root-Locus Analysis 206\u003c\/p\u003e \u003cp\u003e9.4.1 Z-Domain Transfer Functions 206\u003c\/p\u003e \u003cp\u003e9.4.2 Root-Locus Analyses with Different Active Dampers 207\u003c\/p\u003e \u003cp\u003e9.4.3 Comparison 209\u003c\/p\u003e \u003cp\u003e9.5 Experimental Verification 209\u003c\/p\u003e \u003cp\u003e9.6 Summary 212\u003c\/p\u003e \u003cp\u003eReferences 213\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 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\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 217\u003c\/p\u003e \u003cp\u003e10.2 Principle of the Grid Impedance Cancelator 218\u003c\/p\u003e \u003cp\u003e10.3 Modeling with the Grid Impedance Cancelator 221\u003c\/p\u003e \u003cp\u003e10.3.1 System Configuration with the Grid Impedance Cancelator 221\u003c\/p\u003e \u003cp\u003e10.3.2 AC Voltage Regulation 222\u003c\/p\u003e \u003cp\u003e10.3.3 Active Damping Function 222\u003c\/p\u003e \u003cp\u003e10.3.4 dc Capacitor Voltage Control 226\u003c\/p\u003e \u003cp\u003e10.4 Modeling of the Grid Impedance Cancelator 226\u003c\/p\u003e \u003cp\u003e10.5 Experimental Verification 231\u003c\/p\u003e \u003cp\u003e10.6 Summary 239\u003c\/p\u003e \u003cp\u003eReferences 239\u003c\/p\u003e \u003cp\u003eIndex 241\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eWeimin Wu\u003c\/b\u003e is a Professor in the Department of Electrical Engineering at the Shanghai Maritime University in China. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrede Blaabjerg\u003c\/b\u003e is a Professor in the Department of Energy at Aalborg University in Denmark. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eHenry Chung\u003c\/b\u003e is Chair Professor of Electrical Engineering at City University of Hong Kong, China. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eYuanbin He\u003c\/b\u003e is Associate Professor in the School of Automation at Hangzhou Dianzi University in China. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eMin Huang\u003c\/b\u003e is a Lecturer in the Department of Electrical Engineering at the Shanghai Maritime University in China.    \u003c\/p\u003e\u003cp\u003e\u003cb\u003eA state-of-the-art discussion of modern grid inverters\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eIn \u003ci\u003eControl and Filter Design of Single-Phase Grid-Connected Converters\u003c\/i\u003e, 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. \u003c\/p\u003e\u003cp\u003eThe 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. \u003c\/p\u003e\u003cp\u003eReaders 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: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e A thorough introduction to the architectures of DG-grid interfacing converters, including the challenges of controlling DG-grid interfacing VSCs with high-order filters\u003c\/li\u003e \u003cli\u003e Comprehensive explorations of the control structure and modulation techniques of single-phase grid-tied inverters\u003c\/li\u003e \u003cli\u003e Practical discussions of an LLCL power filter for single-phase grid-tied inverters\u003c\/li\u003e \u003cli\u003e Fulsome treatments of design methods of passive damping for LCL\/LLCL-filtered grid-tied inverters\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003ePerfect for researchers, postgraduate students, and senior level undergraduate students of electrical engineering, \u003ci\u003eControl and Filter Design of Single-Phase Grid-Connected Converters \u003c\/i\u003ewill also benefit research \u0026amp; development engineers involved with the design and manufacture of power electronic inverters.\u003c\/p\u003e","brand":"Wiley-IEEE Press","offers":[{"title":"Default Title","offer_id":47988986806501,"sku":"NP9781119886549","price":150.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119886549.jpg?v=1761782326","url":"https:\/\/k12savings.com\/products\/control-and-filter-design-of-single-phase-grid-connected-converters-isbn-9781119886549","provider":"K12savings","version":"1.0","type":"link"}