Islanded Microgrid System Modeling Based on Kuramoto Coupled Oscillator Theory

doi:10.11930/j.issn.1004-9649.202404032

Abstract

Abstract:

To further explore the implicit collective dynamics within the synchronization phenomenon of various complex systems, the Kuramoto model is introduced to describe the evolution of globally sinusoidal coupled phase oscillator systems with natural frequency distributions. This paper proposes a Kuramoto modeling method for island microgrid systems from the perspective of oscillator synchronization, clarifying the transient characteristics of frequency synchronization among different units in the microgrid. Firstly, a deep analysis is conducted to explore the similarities between the operational characteristics of each unit in the microgrid and the dynamic characteristics of Kuramoto oscillators, and a Kuramoto model is established based on the differences in operational characteristics. Then, the dynamic equations of Kuramoto oscillators classified by inertia are derived according to their inertial properties, and a first- and second-order mixed inhomogeneous Kuramoto model is constructed to represent the entire system. Finally, a 3-machine 5-node microgrid system is built on the Simulink simulation platform to verify the applicability of the Kuramoto synchronization theory in microgrid modeling. The similarity between the frequency synchronization of the Kuramoto model and the transient-to-steady-state process of the microgrid is revealed, laying a theoretical foundation for quantitative analysis of transient stability and the construction of transient energy functions.

Key words: islanded microgrid, coupled oscillators, transient stability, synchronization, kuramoto model

LI Cheng, ZHANG Haiyu, SONG Huihui, QU Yanbin, ZHANG Xin, LI Yingying. Islanded Microgrid System Modeling Based on Kuramoto Coupled Oscillator Theory[J]. Electric Power, 2025, 58(11): 193-204.

Add to citation manager EndNote|Ris|BibTeX

URL: https://www.electricpower.com.cn/EN/10.11930/j.issn.1004-9649.202404032

https://www.electricpower.com.cn/EN/Y2025/V58/I11/193

Figures/Tables 22

References 35

1	丁坤, 陈博洋, 秦建茹, 等. 大规模新能源集群接入弱电网的消纳能力评估方法[J]. 电力建设, 2023, 44 (11): 86- 94.
	DING Kun, CHEN Boyang, QIN Jianru, et al. Evaluation method of consumption ability of new large scale energy clusters connected to weak grids[J]. Electric Power Construction, 2023, 44 (11): 86- 94.
2	林其友, 蒋文良, 李媛媛, 等. 基于母线电压分层的直流微网系统协调控制[J]. 中国电力, 2022, 55 (2): 166- 171,180.
	LIN Qiyou, JIANG Wenliang, LI Yuanyuan, et al. Coordinated control of DC microgrid system based on bus voltage stratification[J]. Electric Power, 2022, 55 (2): 166- 171,180.
3	ROSSO R, WANG X F, LISERRE M, et al. Grid-forming converters: control approaches, grid-synchronization, and future trends—a review[J]. IEEE Open Journal of Industry Applications, 2021, 2, 93- 109.
4	KURAMOTO Y. Self-entrainment of a population of coupled non-linear oscillators[J]. Proceedings of the International Symposium on Mathematical Problems in Theoretical Physics, 1975, 39, 420- 422.
5	林伟廷, 曹娟. 基于Kuramoto的常规导弹作战体系同步效能评估[J]. 指挥控制与仿真, 2018, 40 (1): 75- 79.
	LIN Weiting, CAO Juan. Effectiveness evaluation for synchronous characteristics of convetional missile combat system based on kuramoto model[J]. Command Control & Simulation, 2018, 40 (1): 75- 79.
6	DÖRFLER F, CHERTKOV M, BULLO F. Synchronization in complex oscillator networks and smart grids[J]. Proceedings of the National Academy of Sciences of the United States of America, 2013, 110 (6): 2005- 2010.
7	FILATRELLA G, NIELSEN A H, PEDERSEN N F. Analysis of a power grid using a Kuramoto-like model[J]. The European Physical Journal B, 2008, 61 (4): 485- 491.
8	万千, 夏成军, 管霖, 等. 含高渗透率分布式电源的独立微网的稳定性研究综述[J]. 电网技术, 2019, 43 (2): 598- 612.
	WAN Qian, XIA Chengjun, GUAN Lin, et al. Review on stability of isolated microgrid with highly penetrated distributed generations[J]. Power System Technology, 2019, 43 (2): 598- 612.
9	朱蜀, 刘开培, 秦亮, 等. 电力电子化电力系统暂态稳定性分析综述[J]. 中国电机工程学报, 2017, 37 (14): 3947- 3962.
	ZHU Shu, LIU Kaipei, QIN Liang, et al. Analysis of transient stability of power electronics dominated power system: an overview[J]. Proceedings of the CSEE, 2017, 37 (14): 3947- 3962.
10	周艳真, 查显煜, 兰健, 等. 基于数据增强和深度残差网络的电力系统暂态稳定预测[J]. 中国电力, 2020, 53 (1): 22- 31.
	ZHOU Yanzhen, ZHA Xianyu, LAN Jian, et al. Transient stability prediction of power systems based on deep residual network and data augmentation[J]. Electric Power, 2020, 53 (1): 22- 31.
11	黎萌. 电力系统暂态稳定时域仿真终止判据的研究[D]. 杭州: 浙江大学, 2015.
	LI Meng. Research on termination algorithm of time-domain simulation for power system transient stability[D]. Hangzhou: Zhejiang University, 2015.
12	KUNDUR P. 电力系统稳定与控制[M]. 《电力系统稳定与控制》翻译组, 译. 北京: 中国电力出版社, 2002.
	KUNDUR P. Power system stability and control[M]. "Power System Stability and Control"translation group, Translated. Beijing: China Electric Power Press, 2002.
13	DÖRFLER F, BULLO F. Transient stability analysis in power networks and synchronization of non-uniform Kuramoto oscillators[J]. Journal of Nanjing Institute of Meteorology, 2009.
14	DE PERSIS C, MONSHIZADEH N. Bregman storage functions for microgrid control[J]. IEEE Transactions on Automatic Control, 2018, 63 (1): 53- 68.
15	ZHU L J, HILL D J. Stability analysis of power systems: a network synchronization perspective[J]. SIAM Journal on Control and Optimization, 2018, 56 (3): 1640- 1664.
16	SCHMIETENDORF K, PEINKE J, KAMPS O. The impact of turbulent renewable energy production on power grid stability and quality[J]. The European Physical Journal B, 2017, 90 (11): 222.
17	DÖRFLER F, BULLO F. On the critical coupling for kuramoto oscillators[J]. SIAM Journal on Applied Dynamical Systems, 2011, 10 (3): 1070- 1099.
18	DORFLER F, BULLO F. Kron reduction of graphs with applications to electrical networks[J]. IEEE Transactions on Circuits and Systems I: Regular Papers, 2013, 60 (1): 150- 163.
19	DORFLER F, BULLO F. Synchronization of power networks: network reduction and effective resistance[J]. IFAC Proceedings Volumes, 2010, 43 (19): 197- 202.
20	DÖRFLER F, BULLO F. Spectral analysis of synchronization in a lossless structure-preserving power network model[C]//2010 First IEEE International Conference on Smart Grid Communications. Gaithersburg, MD, USA. IEEE, 2010: 179–184.
21	DÖRFLER F, BULLO F. Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators[C]//Proceedings of the 2010 American Control Conference. Baltimore, MD, USA. IEEE, 2010: 930–937.
22	DÖRFLER F, BULLO F. Topological equivalence of a structure-preserving power network model and a non-uniform Kuramoto model of coupled oscillators[C]//2011 50th IEEE Conference on Decision and Control and European Control Conference. Orlando, FL, USA. IEEE, 2011: 7099–7104.
23	DÖRFLER F, BULLO F. Synchronization in complex networks of phase oscillators: a survey[J]. Automatica, 2014, 50 (6): 1539- 1564.
24	杨柳. 基于二阶非均匀Kuramoto模型的电力系统暂态稳定分析[D]. 哈尔滨: 哈尔滨工业大学, 2015.
	YANG Liu. Power system transient stability analysis via second-order non-uniform kuramoto model[D]. Harbin: Harbin Institute of Technology, 2015.
25	SONAM K, WAGH S R, SINGH N M. Synchronized operating point stability of multimachine power system using holomorphic embedding in kuramoto framework[C]//2019 North American Power Symposium (NAPS). Wichita, KS, USA. IEEE, 2019: 1–6.
26	张谦. 基于改进Gronwall不等式的电力系统暂态稳定研究[D]. 杭州: 浙江大学, 2022.
	ZHANG Qian. Stability based on improved Gronwall inequality[D]. Hangzhou: Zhejiang University, 2022.
27	WU L, POTA H R, PETERSEN I R. Synchronization conditions for a multirate kuramoto network with an arbitrary topology and nonidentical oscillators[J]. IEEE Transactions on Cybernetics, 2019, 49 (6): 2242- 2254.
28	CHOI Y P, LI Z C. Synchronization of nonuniform Kuramoto oscillators for power grids with general connectivity and dampings[J]. Nonlinearity, 2019, 32 (2): 559- 583.
29	邹焱. 基于Kuramoto模型的电力系统暂态稳定性分析与提升方法[D]. 杭州: 浙江大学, 2023.
30	郑志刚, 李晓文, 张廷宪. 同步现象: Kuramoto模型及其他[C]//2007年全国复杂系统研究论坛. 北京: 2007年全国复杂系统研究论坛论文汇编, 2005: 379–394.
	ZHENG Zhigang, LI Xiaowen, ZHANG Tingxian. Synchronization phenomenon: Kuramoto model and others[C]//2007 National Forum on complex Systems Research. Beijing, China: Papers Compilation of the National Forum on complex Systems Research 2007, 2005: 379–394.
31	薛小平. 关于2类群体运动模型的综述: Cucker-Smale模型与Kuramoto模型[J]. 四川师范大学学报(自然科学版), 2017, 40 (6): 711- 721.
	XUE Xiaoping. A survey on two types of multi-agent models: the Cucker-Smale model and the Kuramoto model[J]. Journal of Sichuan Normal University (Natural Science), 2017, 40 (6): 711- 721.
32	CONROY J F, WATSON R. Frequency response capability of full converter wind turbine generators in comparison to conventional generation[J]. IEEE Transactions on Power Systems, 2008, 23 (2): 649- 656.
33	毋炳鑫, 谢卫华, 叶红恩. 交直流混合微电网直流母线电压稳定控制技术[J]. 中国电力, 2017, 50 (1): 62- 66.
	WU Bingxin, XIE Weihua, YE Hongen. Study on DC bus voltage deviation control autonomy in hybrid AC/DC micro-grid[J]. Electric Power, 2017, 50 (1): 62- 66.
34	李佳蔚, 张冠宇. 大规模分布式新能源接入对省级电网稳定性影响[J]. 中国电力, 2024, 57 (6): 174- 180.
	LI Jiawei, ZHANG Guanyu. Impact of large scale distributed new energy access on provincial power grid stability[J]. Electric Power, 2024, 57 (6): 174- 180.
35	孙佳航, 王小华, 黄景光, 等. 基于MPC-VSG的孤岛微电网频率和电压动态稳定控制策略[J]. 中国电力, 2023, 56 (6): 51- 60, 81.
	SUN Jiahang, WANG Xiaohua, HUANG Jingguang, et al. MPC-VSG based control strategy for dynamic stability of frequency and voltage in islanded microgrid[J]. Electric Power, 2023, 56 (6): 51- 60, 81.

有无惯性	发电单元	负荷单元	馈线单元	储能单元
有	小型柴油发电机；双轴结构的微型燃气轮机	电机型负荷	—	—
无	变速风力发电；光伏发电；单轴结构的微型燃气轮机	频率型负荷；恒功率型负荷；恒导纳型负荷	内部馈线 PCC开关	飞轮储能；蓄电池储能；超级电容；燃料电池

有无惯性	发电单元	负荷单元	馈线单元	储能单元
有	小型柴油发电机；双轴结构的微型燃气轮机	电机型负荷	—	—
无	变速风力发电；光伏发电；单轴结构的微型燃气轮机	频率型负荷；恒功率型负荷；恒导纳型负荷	内部馈线 PCC开关	飞轮储能；蓄电池储能；超级电容；燃料电池

典型无惯性单元		模型
微网PCC开关节点		微网并网模式： $0=P_{i}-\displaystyle\sum_{i=1}^{N} E_{i} E_{j}\left\|Y_{ij}\right\| \sin (\theta_{i}-\theta_{j}+\varphi_{ij}) $ 恒功率DER单元
微网PCC开关节点		微网孤岛模式： $ 0=\displaystyle\sum_{i=1}^{N} E_{i} E_{j}\left\|Y_{ij}\right\| \sin (\theta_{i}-\theta_{j}+\varphi_{ij}) $ 馈线单元
恒功率型负荷模型		$0=-P_{{\rm L}, i}-\displaystyle\sum_{j=1}^{N} E_{i} E_{j}\left\|Y_{ij}\right\| \sin (\theta_{i}-\theta_{j}+\varphi_{ij}) $
恒电纳型负荷模型		Kron化简

典型无惯性单元		模型
微网PCC开关节点		微网并网模式： $0=P_{i}-\displaystyle\sum_{i=1}^{N} E_{i} E_{j}\left\|Y_{ij}\right\| \sin (\theta_{i}-\theta_{j}+\varphi_{ij}) $ 恒功率DER单元
微网PCC开关节点		微网孤岛模式： $ 0=\displaystyle\sum_{i=1}^{N} E_{i} E_{j}\left\|Y_{ij}\right\| \sin (\theta_{i}-\theta_{j}+\varphi_{ij}) $ 馈线单元
恒功率型负荷模型		$0=-P_{{\rm L}, i}-\displaystyle\sum_{j=1}^{N} E_{i} E_{j}\left\|Y_{ij}\right\| \sin (\theta_{i}-\theta_{j}+\varphi_{ij}) $
恒电纳型负荷模型		Kron化简

节点	节点特性	M_i（×10⁴）	D_i（×10⁵）	P_M,i（×10⁴）	E_i
2	风力发电单元	0	0.56	1	310
3	柴油发电机	0.61	0.83	2	310
4	储能单元	0	1.60	3	310
5	综合负荷单元	1.51	0.60	–6	310