LCL

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LCL-type grid-connected inverter, being a conversion interface between the ... three-phase inverters, and presents the design methods of LCL filters for both.
CPSS Power Electronics Series Series editors Wei Chen, Fuzhou University, Fuzhou, Fujian, China Yongzheng Chen, Liaoning University of Technology, Jinzhou, Liaoning, China Xiangning He, Zhejiang University, Hangzhou, Zhejiang, China Yongdong Li, Tsinghua University, Beijing, China Jingjun Liu, Xi’an Jiaotong University, Xi’an, Shaanxi, China An Luo, Hunan University, Changsha, Hunan, China Xikui Ma, Xi’an Jiaotong University, Xi’an, Shaanxi, China Xinbo Ruan, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China Kuang Shen, Zhejiang University, Hangzhou, Zhejiang, China Dianguo Xu, Harbin Institute of Technology, Harbin, Heilongjiang, China Jianping Xu, Xinan Jiaotong University, Chengdu, Sichuan, China Mark Dehong Xu, Zhejiang University, Hangzhou, Zhejiang, China Xiaoming Zha, Wuhan University, Wuhan, Hubei, China Bo Zhang, South China University of Technology, Guangzhou, Guangdong, China Lei Zhang, China Power Supply Society, Tianjin, China Xin Zhang, Hefei University of Technology, Hefei, Anhui, China Zhengming Zhao, Tsinghua University, Beijing, China Qionglin Zheng, Beijing Jiaotong University, Beijing, China Luowei Zhou, Chongqing University, Chongqing, China

This series comprises advanced textbooks, research monographs, professional books, and reference works covering different aspects of power electronics, such as Variable Frequency Power Supply, DC Power Supply, Magnetic Technology, New Energy Power Conversion, Electromagnetic Compatibility as well as Wireless Power Transfer Technology and Equipment. The series features leading Chinese scholars and researchers and publishes authored books as well as edited compilations. It aims to provide critical reviews of important subjects in the field, publish new discoveries and significant progress that has been made in development of applications and the advancement of principles, theories and designs, and report cutting-edge research and relevant technologies. The CPSS Power Electronics series has an editorial board with members from the China Power Supply Society and a consulting editor from Springer. Readership: Research scientists in universities, research institutions and the industry, graduate students, and senior undergraduates.

More information about this series at http://www.springer.com/series/15422

Xinbo Ruan Xuehua Wang Donghua Pan Dongsheng Yang Weiwei Li Chenlei Bao •





Control Techniques for LCL-Type Grid-Connected Inverters

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Dongsheng Yang Nanjing University of Aeronautics and Astronautics Nanjing, Jiangsu China

Xinbo Ruan College of Automation Engineering Nanjing University of Aeronautics and Astronautics Nanjing, Jiangsu China

Weiwei Li Huazhong University of Science and Technology Wuhan, Hubei China

Xuehua Wang Huazhong University of Science and Technology Wuhan, Hubei China

Chenlei Bao Huazhong University of Science and Technology Wuhan, Hubei China

Donghua Pan Huazhong University of Science and Technology Wuhan, Hubei China

ISSN 2520-8853 CPSS Power Electronics Series ISBN 978-981-10-4276-8 DOI 10.1007/978-981-10-4277-5

ISSN 2520-8861

(electronic)

ISBN 978-981-10-4277-5

(eBook)

Jointly published with Science Press, Beijing, China ISBN: 978-7-03-043810-2 Science Press, Beijing The printed edition is not for sale in China Mainland. Customers from China Mainland please order the print book from Science Press Library of Congress Control Number: 2017936335 © Springer Nature Singapore Pte Ltd. and Science Press 2018 This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

Renewable energy-based distributed power generation systems (RE-DPGS) represent promising solutions to mitigate energy crisis and environmental pollution. The LCL-type grid-connected inverter, being a conversion interface between the renewable energy power generation units and the power grid, has been widely used to convert dc power to high-quality ac power and feed it into the grid, and it plays an important role in maintaining safe, stable, and high-quality operation of RE-DPGS. This book aims to present the control techniques for the LCL-type grid-connected inverter to improve the system stability, control performance, and suppression of grid current harmonics. The detailed theoretical analysis with design examples and experimental validations are included. This book contains twelve chapters. Chapter 1 gives a brief review of the key techniques for the LCL-type grid-connected inverter, including the design and magnetic integration of the LCL filter, design of the controller parameters, the control delay effects in digital control and the methods of reducing the control delays, suppression of the grid current distortion caused by the grid voltage harmonics, and the grid impedance effects on the system stability and the methods to improve the system stability. Chapter 2 introduces the modulation strategies for the single-phase and three-phase inverters, and presents the design methods of LCL filters for both single-phase and three-phase inverters. Chapter 3 presents magnetic integration methods for LCL filters, aiming to reduce volume and weight. In Chap. 4, the resonance hazard of LCL filters is analyzed, and six basic passive-damping solutions are discussed in terms of their effects on the characteristics of LCL filters. It is pointed out that adding a resistor in parallel with the filter capacitor can effectively damp the resonance peak and does not affect the frequency response of the LCL filter, but it results in high power loss. The

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active-damping solutions, equivalent to a virtual resistor in parallel with the filter capacitor, are derived, and the capacitor-current-feedback active-damping is found superior for its simple implementation and effectiveness. Chapter 5 presents a step-by-step parameter design method for the LCL-type grid- connected inverter with capacitor-current-feedback active-damping, including the capacitor current feedback coefficient and current regulator parameters. In Chaps. 6 and 7, methods based on full feedforward of the grid voltage are proposed for single-phase and three-phase grid-connected inverters with capacitor-current-feedback active-damping. The feedforward function consists of a proportional, a derivative, and a second-derivative component. The proposed full feedforward scheme does not only reduce the steady-state error of the grid current effectively, but also suppresses the grid current distortion arising from the harmonics in the grid voltage. In Chap. 8, the mechanism of the control delay in digital control systems is discussed, and the influence of the digital control delay on the system stability and control performance are analyzed in detail. Then, the range of the LCL filter resonance frequency that would lead to instability is identified and hence should be avoided. Then, the system stability evaluation method is presented by checking the phase margin and the gain margin at one-sixth of sampling frequency (fs/6) and the resonance frequency of the LCL filter. In Chap. 9, a real-time sampling method is presented to reduce the computational delay, and it is not restricted by the modulation scheme and can be applied to the single-phase and three-phase grid-connected inverters. Furthermore, a real-time computational method with dual sampling modes is given to completely eliminate the computation delay, and it is suitable for the single-phase grid-connected inverter since it is based on the unipolar SPWM. With the two computation delay reduction methods, the steady-state and dynamic performances of the LCL-type gridconnected inverter can be improved, and high robustness against the grid-impedance variation is obtained. In Chaps. 10 and 11, the virtual series–parallel impedance shaping method and weighted-feedforward scheme of grid voltages are proposed, respectively. The purpose is to improve the harmonic rejection capability and the stability robustness of the LCL-type grid-connected inverter when connected into a weak grid. In Chap. 12, the complex-vector-filter method (CVFM) is adopted to derive various prefilters in the synchronous reference frame phase-locked loops (SRF-PLLs), and some insights into the relationships among different prefilters are drawn. A brief comparison is presented to highlight the features of each prefilter. Moreover, a generalized second-order complex-vector filter (GSO-CVF) with faster dynamic response and a third-order complex-vector filter (TO-CVF) with higher harmonic attenuation are proposed with the help of the CVFM, which are useful to improve the dynamic performance and the harmonic attenuation ability of the PLL for the grid-connected inverter.

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This book is essential and valuable reference for the graduate students and academics majoring in power electronics and renewable energy generation system and the engineers being engaged in developing grid-connected inverters for photovoltaic system and wind turbine generation system. Senior undergraduate students majoring in electrical engineering and automation engineering would also find this book useful. Nanjing, China Wuhan, China Wuhan, China Nanjing, China Wuhan, China Wuhan, China

Xinbo Ruan Xuehua Wang Donghua Pan Dongsheng Yang Weiwei Li Chenlei Bao

Acknowledgements

This research monograph summarizes the research work on the control techniques for LCL-type grid-connected inverters since the key project of National Natural Science Foundation of China, titled “Research on Energy Conversion, Control, and Grid-Connection Operation of Renewable Energy Based Distributed Power Generation Systems”, was funded in 2008. We wish to thank the members of the key project of National Natural Science Foundation of China: Prof. Chengxiong Mao, Prof. Buhan Zhang, Prof. Yi Luo, Prof. Kai Zhang, Prof. Xudong Zou, and Prof. Yu Zhang from Huazhong University of Science and Technology (HUST), Wuhan, China, and Prof. Weiyang Wu, Prof. Chunjiang Zhang, Prof. Xiaofeng Sun, and Prof. Xiaoqiang Guo from Yanshan University, Qinhuangdao, China, for their outstanding contribution to this key project. We also wish to express my sincere appreciation and gratitude to Prof. Yuan Pan, Prof. Shijie Cheng, Prof. Xianzhong Duan, Prof. Jian Chen, Prof. Yong Kang, Prof. KexunYu, Prof. Shanxu Duan, Prof. Hua Lin, Ms. Taomin Zou, and Ms. Yi Li in the School of Electrical and Electronic Engineering, HUST, for their great support during the application and research of this key project. We are grateful to Prof. Lijian Ding, Director of the Fifth Engineering Section, Engineering and Materials Department, National Natural Science Foundation of China, and Prof. Weiming Ma from Naval University of Engineering, Wuhan, China, for their great support and kind encouragement. We also wish to thank Prof. Chengshan Wang from Tianjin University, Tianjin, China, and Prof. An Luo from Hunan University, Changsha, China, for inviting me to participate in the project of National Basic Research Program of China (973 Program), titled “Research on the Fundamentals of Distributed Power Generation and Supply Systems”. Special thanks are due to Prof. Chi. K. Tse from Hong Kong Polytechnic University for his suggestions in the writing of this book, which have led to improvements in clarity and readability. The work in this book was supported by the National Natural Science Foundation of China under Award 50837003, the National Basic Research Program

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of China (973 Program) under Award 2009CB219706, and Jiangsu Province 333 Program for Excellent Talents under Award BRA2012141. I would like to express my sincere thanks to these supports. It has been a great pleasure to work with the colleagues of Springer, Science Press, China, and China Power Supply Society (CPSS). The support and help from Mr. Wayne Hu (the project editor) are greatly appreciated. January 2017

Contents

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Design of LCL Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 PWM for Single-Phase Full-Bridge Grid-Connected Inverter . . 2.1.1 Bipolar SPWM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Unipolar SPWM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 PWM for Three-Phase Grid-Connected Inverter . . . . . . . . . . . . . 2.2.1 SPWM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Harmonic Injection SPWM Control . . . . . . . . . . . . . . . . 2.3 LCL Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Design of the Inverter-Side Inductor . . . . . . . . . . . . . . . 2.3.2 Filter Capacitor Design . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Grid-Side Inductor Design . . . . . . . . . . . . . . . . . . . . . . . 2.4 Design Examples for LCL Filter . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Single-Phase LCL Filter . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Energy Situation and Environmental Issues . . . . . . . . . . . . 1.2 Renewable Energy-Based Distributed Power Generation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Key Issues of LCL-Type Grid-Connected Inverters . . . . . . 1.3.1 Design and Magnetic Integration of LCL Filter . . . 1.3.2 Resonance Damping Methods of LCL Filter . . . . . 1.3.3 Controller Design of Grid-Connected Inverters . . . 1.3.4 Effects of Control Delay and the Compensation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.5 Suppression of Grid Current Distortion Caused by Grid Voltage Harmonics . . . . . . . . . . . . . . . . . . 1.3.6 Grid-Impedance Effects on System Stability and the Improvement Methods . . . . . . . . . . . . . . . 1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2.4.2 Three-Phase LCL Filter . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Magnetic Integration of LCL Filters . . . . . . . . . . . . . . . . . . . . . 3.1 Magnetic Integration of LCL Filters . . . . . . . . . . . . . . . . . . 3.1.1 Magnetic Integration of Single-Phase LCL Filter . . 3.1.2 Magnetic Integration of Three-Phase LCL Filter . . 3.2 Coupling Effect on Attenuating Ability of LCL Filter . . . . . 3.2.1 Magnetic Circuit of Integrated Inductors . . . . . . . . 3.2.2 Characteristics of LCL Filter with Coupled Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Design Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Magnetics Design for Single-Phase LCL Filter . . . 3.3.2 Magnetics Design for Three-Phase LCL Filter . . . . 3.4 Experimental Verification . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Experimental Results for Single-Phase LCL Filter . 3.4.2 Experimental Results for Three-Phase LCL Filter . 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Resonance Damping Methods of LCL Filter . . . . . . . . . . 4.1 Resonance Hazard of LCL Filter . . . . . . . . . . . . . . . . 4.2 Passive-Damping Solutions . . . . . . . . . . . . . . . . . . . . 4.2.1 Basic Passive Damping . . . . . . . . . . . . . . . . 4.2.2 Improved Passive Damping . . . . . . . . . . . . . 4.3 Active-Damping Solutions . . . . . . . . . . . . . . . . . . . . 4.3.1 State-Variable-Feedback Active Damping . . 4.3.2 Notch-Filter-Based Active Damping . . . . . . 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Controller Design for LCL-Type Grid-Connected Inverter with Capacitor-Current-Feedback Active-Damping . . . . . . . . . . . . . 5.1 Modeling LCL-Type Grid-Connected Inverter . . . . . . . . . . . . . . 5.2 Frequency Responses of Capacitor-Current-Feedback Active-Damping and PI Regulator . . . . . . . . . . . . . . . . . . . . . . . 5.3 Constraints for Controller Parameters . . . . . . . . . . . . . . . . . . . . . 5.3.1 Requirement of Steady-State Error . . . . . . . . . . . . . . . . 5.3.2 Controller Parameters Constrained by Steady-State Error and Stability Margin . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Pulse-Width Modulation (PWM) Constraint . . . . . . . . . 5.4 Design Procedure for Capacitor-Current-Feedback Coefficient and PI Regulator Parameters . . . . . . . . . . . . . . . . . . . 5.5 Extension of the Proposed Design Method . . . . . . . . . . . . . . . . .

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5.5.1

Controller Design Based on PI Regulator with Grid Voltage Feedforward Scheme . . . 5.5.2 Controller Design Based on PR Regulator. . 5.6 Design Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Design Results with PI Regulator . . . . . . . . 5.6.2 Design Results with PR Regulator. . . . . . . . 5.7 Experimental Verification . . . . . . . . . . . . . . . . . . . . . 5.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

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Full-Feedforward of Grid Voltage for Single-Phase LCL-Type Grid-Connected Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Effects of the Grid Voltage on the Grid Current . . . . . . . . . . . . . 6.3 Full-Feedforward Scheme for Single-Phase LCL-Type Grid-Connected Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Derivation of Full-Feedforward Function of Grid Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Discussion of the Three Feedforward Components . . . . 6.3.3 Discussion of Full-Feedforward Scheme with Main Circuit Parameters Variations . . . . . . . . . . . . . . . . . . . . 6.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Full-Feedforward Scheme of Grid Voltages for Three-Phase LCL-Type Grid-Connected Inverters . . . . . . . . . . . . . . . . . . . . . 7.1 Modeling the Three-Phase LCL-Type Grid-Connected Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Model in the Stationary a–b Frame . . . . . . . . . . . . 7.1.2 Model in the Synchronous d–q Frame . . . . . . . . . . 7.2 Derivation of the Full-Feedforward Scheme of Grid Voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Full-Feedforward Scheme in the Stationary a–b Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Full-Feedforward Scheme in the Synchronous d–q Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Full-Feedforward Scheme in the Hybrid Frame . . . 7.3 Discussion of the Full-Feedforward Functions . . . . . . . . . . 7.3.1 Discussion of the Effect of Three Components in the Full-Feedforward Function . . . . . . . . . . . . . 7.3.2 Harmonic Attenuation Affected by LCL Filter Parameter Mismatches . . . . . . . . . . . . . . . . . . . . . .

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7.3.3

Comparison Between the Feedforward Functions for the L-Type and the LCL-Type Three-Phase Grid-Connected Inverter . . . . . . . . . . . . . . . . . . . . 7.4 Experimental Verification . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Description of the Prototype . . . . . . . . . . . . . . . . . 7.4.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

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Design Considerations of Digitally Controlled LCL-Type Grid-Connected Inverter with Capacitor-Current-Feedback Active-Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Control Delay in Digital Control System . . . . . . . . . . . . . . . . . . 8.3 Effect of Control Delay on Loop Gain and Capacitor-Current-Feedback Active-Damping . . . . . . . . . . . . . . . 8.3.1 Equivalent Impedance of Capacitor-Current-Feedback Active-Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Discrete-Time Expression of the Loop Gain . . . . . . . . . 8.3.3 RHP Poles of the System Loop Gain . . . . . . . . . . . . . . 8.4 Stability Constraint Conditions for Digitally Controlled System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Nyquist Stability Criterion . . . . . . . . . . . . . . . . . . . . . . . 8.4.2 System Stability Constraint Conditions . . . . . . . . . . . . . 8.5 Design Considerations of the Controller Parameters of Digitally Controlled LCL-Type Grid-Connected Inverter . . . . . . 8.5.1 Forbidden Region of the LCL Filter Resonance Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5.2 Constraints of the Controller Parameters . . . . . . . . . . . . 8.5.3 Design of LCL Filter, PR Regulator and Capacitor-Current-Feedback Coefficient . . . . . . . . . . . . . 8.6 Design of Current Regulator for Digitally Controlled LCL-Type Grid-Connected Inverter Without Damping . . . . . . . . 8.6.1 Stability Necessary Constraint for Digitally Controlled LCL-Type Grid-Connected Inverter Without Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6.2 Design of Grid Current Regulator and Analysis of System Performance . . . . . . . . . . . . . . . . . . . . . . . . . 8.7 Design Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7.1 Design Example with Capacitor-Current-Feedback Active-Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7.2 Design Example Without Damping . . . . . . . . . . . . . . . . 8.8 Experimental Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.8.1 Experimental Validation for the Case with Capacitor-Current-Feedback Active-Damping . . . .

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8.8.2 Experimental Validation Without Damping . . . . . . Comparison of System Performance with Three Control Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Reduction of Computation Delay for Improving Stability and Control Performance of LCL-Type Grid-Connected Inverters . . . . . 9.1 Effects of Computation and PWM Delays . . . . . . . . . . . . . . . . . 9.1.1 Modeling the Digitally Controlled LCL-Type Grid-Connected Inverter . . . . . . . . . . . . . . . . . . . . . . . . 9.1.2 Improvement of Damping Performance with Reduced Computation Delay . . . . . . . . . . . . . . . . . 9.1.3 Improvement of Control Performance with Reduced Computation Delay . . . . . . . . . . . . . . . . . 9.2 Real-Time Sampling Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Sampling-Induced Aliasing of the Capacitor Current . . . 9.2.2 Design Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.3 Experimental Verification . . . . . . . . . . . . . . . . . . . . . . . 9.3 Real-Time Computation Method with Dual Sampling Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Derivation of the Real-Time Computation Method . . . . 9.3.2 Design Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.3 Experimental Verification . . . . . . . . . . . . . . . . . . . . . . . 9.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 Impedance Shaping of LCL-Type Grid-Connected Inverter to Improve Its Adaptability to Weak Grid . . . . . . . . . . . . . . . . 10.1 Derivation of Impedance-Based Stability Criterion for Grid-Connected Inverter . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Output Impedance Model of Grid-Connected Inverter . . . . 10.3 Relationship Between Output Impedance and Control Performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Output Impedance Shaping Method . . . . . . . . . . . . . . . . . . 10.4.1 Parallel Impedance Shaping Method . . . . . . . . . . . 10.4.2 Series–Parallel Impedance Shaping Method. . . . . . 10.4.3 Discussion of the Series–Parallel Impedance Shaping Method . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Experimental Verification . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.1 Prototype Design . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 10.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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11 Weighted-Feedforward Scheme of Grid Voltages for the Three-Phase LCL-Type Grid-Connected Inverters Under Weak Grid Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Impedance-Based Stability Criterion . . . . . . . . . . . . . . . . . . 11.2 Stability Analysis Under Weak Grid Condition . . . . . . . . . 11.2.1 Derivation of Output Impedance of Grid-Connected Inverter . . . . . . . . . . . . . . . . . . . . 11.2.2 Stability of Grid-Connected Inverter Under Weak Grid Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Characteristics of the Inverter Output Impedance . . . . . . . . 11.3.1 Characteristics of the Inverter Output Impedance Without Feedforward Scheme . . . . . . . . . . . . . . . . 11.3.2 Inverter Output Impedance Affected by the Full-Feedforward Scheme . . . . . . . . . . . . . . . . . . . 11.4 Weighted-Feedforward Scheme of Grid Voltages . . . . . . . . 11.4.1 The Proposed Weighted-Feedforward Scheme of Grid Voltages . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.2 Realization of the Weighted-Feedforward Scheme of Grid Voltages . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.3 Tuning of the Weighted Coefficients . . . . . . . . . . . 11.5 Experimental Verification . . . . . . . . . . . . . . . . . . . . . . . . . . 11.5.1 Stability Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.5.2 Harmonic Suppression Test . . . . . . . . . . . . . . . . . . 11.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Prefilter-Based Synchronous Reference Frame Phase-Locked Loop Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Operation Principle of SRF-PLL . . . . . . . . . . . . . . . . . . . . . 12.3 Prefilter-Based SRF-PLL . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3.1 Complex-Vector-Filter Method (CVFM) . . . . . . . . 12.3.2 Derivation of the Prefilters with the CVFM. . . . . . 12.4 Generalized Second-Order Complex-Vector Filter . . . . . . . 12.5 Third-Order Complex-Vector Filter. . . . . . . . . . . . . . . . . . . 12.6 Simulation and Experimental Verification . . . . . . . . . . . . . . 12.6.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . 12.6.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 12.6.3 Brief Comparison . . . . . . . . . . . . . . . . . . . . . . . . . 12.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

About the Authors

Xinbo Ruan was born in Hubei Province, China, in 1970. He received the B.S. and Ph.D. degrees in electrical engineering from Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 1991 and 1996, respectively. In 1996, he joined the Faculty of Electrical Engineering Teaching and Research Division, NUAA, where he became a professor in the College of Automation Engineering in 2002 and has been engaged in teaching and research in the field of power electronics. From August to October 2007, he was a research fellow in the Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong, China. From March 2008 to August 2011, he was also with the School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, China. He is a guest professor at Beijing Jiaotong University, Beijing, China, Hefei University of Technology, Hefei, China, and Wuhan University, Wuhan, China. He is the author or co-author of seven books and more than 300 technical papers published in journals and conferences. His main research interests include soft-switching dc–dc converters, soft-switching inverters, power factor correction converters, modeling the converters, power electronics system integration, and renewable energy generation system. Dr. Ruan was a recipient of the Delta Scholarship by the Delta Environment and Education Fund in 2003 and was a recipient of the Special Appointed Professor of the Chang Jiang Scholars Program by the Ministry of Education, China, in 2007. From 2005 to 2013, he served as vice president of the China Power Supply Society. From 2014 to 2016, he served as vice chair of the Technical Committee on Renewable Energy Systems within the IEEE Industrial Electronics Society. Currently, He is an associate editor for the IEEE Transactions on Industrial Electronics, IEEE Transactions on Power Electronics, IEEE Transactions on Circuits and System II, and the IEEE Journal of Emerging and Selected Topics on Power Electronics. He was elevated to IEEE fellow in 2015. Xuehua Wang was born in Hubei Province, China, in 1978. He received the B.S. degree in electrical engineering from Nanjing University of Technology, Nanjing, China, in 2001, and the M.S. and Ph.D. degrees in electrical engineering from

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About the Authors

Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2004 and 2008, respectively. From October 2008 to March 2011, he was a postdoctoral fellow at Huazhong University of Science and Technology (HUST), Wuhan, China. Since April 2011, he joined the School of Electrical and Electronic Engineering, HUST, and he is currently an associate professor. His main research interests include multilevel inverter and renewable energy generation system. Donghua Pan was born in Hubei Province, China, in 1987. He received the B.S. and Ph.D. degrees in electrical and electronic engineering from Huazhong University of Science and Technology, Wuhan, China, in 2010 and 2015, respectively. He is currently a research engineer with Suzhou Inovance Technology Co., Ltd., Suzhou, China. His research interests include magnetic integration technique and renewable energy generation system. Dongsheng Yang was born in Jiangsu, China, in 1984. He received the B.S., M.S., and Ph.D. degrees, all in electrical engineering from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2008, 2011, and 2016, respectively. He is currently a postdoctoral fellow at Aalborg University, Denmark. His main research interests include grid-connected inverter control and renewable energy generation systems. Weiwei Li was born in Henan Province, China, in 1987. He received the B.S. and Ph.D. degrees in electrical engineering from Huazhong University of Science and Technology, Wuhan, China, in 2009 and 2014, respectively. He is currently a research assistant in SEPRI of China Southern Power Grid Co., Ltd, Guangzhou, China. His research interests include HVDC power transmission, dc distribution, and renewable energy generation systems. Chenlei Bao was born in Zhejiang Province, China, in 1987. He received the B.S. degree in electrical engineering and automation from Harbin Institute of Technology, Harbin, China, in 2010, and the M.S. degree in electrical engineering from Huazhong University of Science and Technology, Wuhan, China, in 2013. In April 2013, he joined the Shanghai Marine Equipment Research Institute, Shanghai, China. His current research interests include digital control technique and renewable energy generation system.

Abbreviations

ANF ASM CVF CVFM DPGS DSC DSP E-PLL FNC FPC GSO-CVF LF LPF MAF NF PCC PD PF PI PLL PO PR PSF PU PWM Q-PLL RE-DPGS RHP RMS R/P

Adaptive notch filter Averaged switch model Complex vector filter Complex-vector-filter method Distributed power generation system Delayed signal cancellation Digital signal processor Enhanced phase-locked loop Fundamental negative-sequence components Fundamental positive-sequence components Generalized second-order complex-vector filter Loop filter Low-pass filter Moving average filter Notch filter Point of common coupling Phase detector Power factor Proportional integral Phase-locked loop Percentage overshoot Proportional resonant Positive-sequence filter Per unit Pulse-width modulation Quadrature phase-locked loop Renewable energy-based distributed power generation system Right half plane Root-mean-square Reserves to production

xix

xx

SGT SO SO-CVF SOF SOGI SPWM SRF-PLL THD TO TO-CVF VCO VSI ZC-PLL ZOH

Abbreviations

Sliding Goertzel transform Symmetrical optimum Second-order complex-vector filter Second-order scalar filter Second-order generalized integrator Sinusoidal pulse-width modulation Synchronous reference frame PLL Total harmonic distortion Technical optimum Third-order complex-vector filter Voltage-controlled oscillator Voltage source inverter Zero-crossing PLL Zero-order hold