Accurate Stability Analysis of Three-Phase Converter System Connected to Weak Grid under Coordinate System Transformation

Abstract

This paper studies the simplified impedance criterion of the three-phase converter system in different coordinate systems. In addition, the influence of small signal stability of converter units under the weak grid is discussed in three-phase converter systems. Firstly, a small signal model of a three-phase grid-connected converter system is established based on the voltage and current double closed-loop control strategy in dq real coordinate system and the dynamic characteristics of SRF-PLL (Synchronous Reference Frame Phase-Locked Loop). Then, based on the coordinate transformation, the admittance models in the dq real coordinate system and the fb complex coordinate system are derived. Through the analysis of the admittance Bode diagram, the amplitude-frequency characteristics of the three-phase converter system have conjugate symmetry in the real coordinate system and diagonal conjugate symmetry in the complex coordinate system. Therefore, the three-phase symmetrical system can be stabilized only by drawing the Nyquist curve of the open-loop transfer function GH_f or GHb. The three-phase asymmetric system can also be stabilized by drawing the Nyquist curve of the modified open-loop transfer function GH_fM or GH_bM. Finally, the simulation results show that the converter system loses stability when the transmission line impedance L_g = 0.6 pu. In this case, the three current decoupling terms will cause the system to lose stability, but the relative stability of the current reference value is the best, and the phase angle margin is −6.8°. Also, without considering the phase-locked loop dynamics, the system is in a steady state, otherwise, the system loses stability, and the system output current has a 39 Hz oscillation, which is consistent with the theoretical analysis results.

Keywords:

• small signal stability
• power converters
• doubly fed induction generator
• integration of renewable energy sources
• SRF-PLL
• admittance model
• fb complex coordinate system
• coordinates transformation
• weak grid

ACKNOWLEDGMENTS

This work was partly supported by the National Natural Science Foundation of China (NSFC) under grant No. 51977026, the Science and Technology Program of Sichuan Province under grant No. 2021YFG0255, and the Sichuan Provincial Postdoctoral Science Foundation under grant No. 246861.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Jiaqing Fu

Jiaqing Fu received the B.Sc. degree in electrical engineering and automation from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2021, where he is currently pursuing the M.Sc. degree in electrical engineering. His main research interests include stability analysis of inverters and modeling of renewable-energy generation systems.

Yang Han

Yang Han (S’08-M’10-SM’17) received the Ph.D. degree in Electrical Engineering from Shanghai Jiaotong University (SJTU), Shanghai, China, in 2010. In 2010, he joined the University of Electronic Science and Technology of China (UESTC), Chengdu, China, where he has been an Associate Professor in 2013, and Full professor in 2021. From March 2014 to March 2015, he was a Visiting Scholar with the Department of Energy Technology, Aalborg University, Aalborg, Denmark. He is currently with the School of Mechanical and Electrical Engineering, UESTC. His research interests include the ac/dc microgrids, active distribution networks, power quality, grid-connected converters for renewable energy systems, active power filters, multilevel converters, and static synchronous compensators (STATCOMs). Dr. Han has received several national and provincial projects, and more than 30 industrial projects in the area of power electronics, smart grid, microgrid, and power quality analysis and compensation. He holds more than 40 issued and pending patents. Dr. Han was listed as “World’s Top 2% Scientist” by Stanford University in 2023, and the recipient of the Young Scientist Award in CPESE 2021, the Provincial Science and Technology Award in 2020 and 2022, Science and Technology Award from Sichuan Electric Power Company in 2019, Academic Talent Award by UESTC, in 2017, Baekhyun Award by the Korean Institute of Power Electronics, in 2016. He has published a book “Modeling and Control of Power Electronic Converters for Microgrid Applications”, ISBN: 978-3-030-74512-7, Springer. He served as an Associate Editor of Journal of Power Electronics and IEEE ACCESS (2019-2020).

Amr S. Zalhaf

Amr S. Zalhaf was born in Tanta, Egypt, in 1988. He received the B.Sc. and M.Sc. degrees in electrical engineering from Tanta University, Tanta, Egypt, in 2010 and 2014, respectively, and the Ph.D. degree in Energy resources engineering from Egypt-Japan University of Science and Technology (E-JUST), Alexandria, Egypt, in 2019. Since 2010, he has been with the Faculty of Engineering, Tanta University, Egypt, where he became an Assistant Professor since 2019. He was a visiting scholar with the Department of Electrical and Electronic Engineering, School of Engineering, Tokyo Institute of Technology, Tokyo, Japan in 2018. Currently, he is a Postdoctoral fellow at the School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China (UESTC), Chengdu, China. He is also an active reviewer for many international journals and conferences. His research interests include Lightning Protection, Wind Energy, PV systems, Smart Grids, Internet of Things (IoT), Load Side Management, Power System Stability, HVDC transmission, and Power Quality. He was awarded a research project by the Sichuan Provincial Postdoctoral Science Foundation under grant No. 246861 in 2022.

Songling Zhang

Songling Zhang received the B.Sc. degree in electrical engineering and automation from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2019, where he is currently pursuing the M.Sc. degree in electrical engineering. His main research interests include stability analysis of inverters.

Ping Yang

Ping Yang received the B.S. degree in mechanical engineering from Shanghai Jiao Tong University (SJTU), Shanghai, China, in 1984, and the M.S. degree in mechanical engineering from Sichuan University, in 1987.,He was visiting Victory University, Australia, from July 2004 to August 2004, and a Visiting Scholar with the S. M. Wu Manufacturing Research Center, University of Michigan, Ann Arbor, USA, from August 2009 to February 2010, and was visiting the University of California at Irvine, Irvine, USA, from October 2012 to November 2012. He is currently a Full Professor with the School of Mechatronics Engineering, University of Electronic Science and Technology of China (UESTC), Chengdu, China. He is also the Dean of the School of Mechanical and Electrical Engineering, UESTC. He has authored more than 60 articles in various journals and international conferences, and several books on mechatronics and instrumentation. He received several provincial awards for his contribution in teaching and academic research. His research includes mechatronics engineering, electrical engineering and automation, computer-aided control and instrumentation, smart mechatronics, and detection and automation of mechanical equipment.

Congling Wang

Congling Wang received the B.Sc. degree from the Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1991, and the M.Sc. degree from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 1996. Since 1996, he has been a Faculty Member with the School of Mechatronics Engineering. He is currently an Associate Professor with UESTC. His research interests include mechatronics engineering, electrical engineering, and automation.

Ilhami Colak

Ilhami Colak received his diploma in electrical engineering from Gazi University, Turkey, in 1985. Then, he did his M.Sc. degree at Gazi University in 1991. After that, he received his MPhil. degree from Birmingham University in England in 1991. He received his Ph.D. degree from Aston University in England in 1994. He became an Assistant Professor, an Associate Professor, and a full Professor in 1995, 1999, and 2005, respectively. He also spent around 3 years at the European Commission Research Centre (JRC) as an expert in the field of smart grids in the Netherlands. He is currently holding the positions of vice-rector and dean of the Engineering and Architecture, Faculty of Nisantasi University, Turkey. He can be contacted at email: [email protected]

Mohamed M. F. Darwish

Mohamed M. F. Darwish (Senior Member, IEEE) was born in Cairo, Egypt. He received the B.Sc., M.Sc., and Ph.D. degrees in Electrical Engineering from the Faculty of Engineering at Shoubra, Benha University, Cairo, in May 2011, June 2014, and January 2018, respectively. From 2016 to 2017, he joined as a Ph.D. student with the Department of Electrical Engineering and Automation (EEA), Aalto University, Finland, and Prof. M. Lehtonen’s Group. He is currently working as an Associate Professor with the Department of Electrical Engineering, Faculty of Engineering at Shoubra, Benha University. He was also a Postdoctoral Researcher with the Department of EEA, School of Electrical Engineering, Aalto University. He has co-authored several international IEEE journals and conferences. His research interests include fault diagnosis, high voltage, cable insulation, nano-fluids, renewables, distributed generation, optimization, applied machine learning, the IoT, Industry 4.0, and control systems. He received the Best Ph.D. thesis prize that serves industrial life and society all over the Benha University Staff for the academic year (2018–2019). Since 2021, he has been a Topic Editor in Catalysts journal, also becomes a Guest Editor for several special issues in international journals. Furthermore, in 2022, he got also the Prestigious Benha University Encouragement Award in the field of Engineering Sciences and Technologies for the academic year (2021–2022) for his scientific contributions as a distinguished scholar younger than 40 years. Further, in 2022, he has been nominated as a Young Editorial Board Member of Applied Energy Journal. Besides, being a Subject Editor and Associate Editor in IET Generation, Transmission & Distribution, and Frontiers in Energy Research Journals. In addition, Editor of the Electric Power Components and Systems Journal. Finally, in 2023, he has been promoted to Associate Editor in High Voltage Journal. Recently, he has been listed among the world’s top 2% scientists by Stanford University and Elsevier–2023.