Dissipative energy flow-based port characteristic analysis of modular multilevel converter under sub-synchronous oscillation

doi:10.3785/j.issn.1008-973X.2025.09.017

Journal of ZheJiang University (Engineering Science)

2025, Vol. 59

Issue (9): 1931-1941 DOI: 10.3785/j.issn.1008-973X.2025.09.017

Dissipative energy flow-based port characteristic analysis of modular multilevel converter under sub-synchronous oscillation

Yuan WANG1(

),Ye LI1,Xianglong LIU1,Guojing DONG1,Yating CHEN1,Yuchen ZHANG1,Junjie CHEN1,Xiaoting MA1,Xingxi YANG2,Ji XIANG2,*(

)

1. Inner Mongolia Power Economic and Technological Research Institute, Hohhot 010010, China
2. College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China

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Abstract

A risk of sub-synchronous oscillation (SSO) exists when a modular multilevel converter (MMC) is interconnected with weak grids or wind turbines. Conventional time-domain or frequency-domain methods are inadequate for analyzing such SSO risks due to the complex topology of MMC. Thus, a dissipative energy flow-based method was proposed to investigate the impact of MMCs on system SSO. The dynamic response of the MMC terminal under SSO conditions was analyzed with consideration of the phase-locked loop and outer loops of MMC control system. An expression for the average slope of MMC terminal dissipative energy flow was derived, reflecting the source/sink characteristics of the MMC terminal and quantifying the additional damping level provided to the system. A time-domain simulation model was established in Simulink for an interconnected system comprising an MMC, a doubly-fed induction generator, and an infinite bus. Simulation results validated the correctness of the derived expression, demonstrated the influence of MMC parameters on dissipative energy flow, and revealed the relationship between MMC terminal dissipative energy flow and system stability.

Key words： modular multilevel converter (MMC) constant power control sub-synchronous oscillation dissipative energy flow source/sink characteristic

Received: 16 April 2024 Published: 25 August 2025

CLC:

TM 711

Fund: 国家重点研发计划资助项目(2021YFB2400700)；内蒙古电力集团科技项目(2023-3-3).

Corresponding Authors: Ji XIANG E-mail: 1270290575@qq.com;jxiang@zju.edu.cn

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	Yuan WANG
	Ye LI
	Xianglong LIU
	Guojing DONG
	Yating CHEN
	Yuchen ZHANG
	Junjie CHEN
	Xiaoting MA
	Xingxi YANG
	Ji XIANG

Cite this article:

Yuan WANG,Ye LI,Xianglong LIU,Guojing DONG,Yating CHEN,Yuchen ZHANG,Junjie CHEN,Xiaoting MA,Xingxi YANG,Ji XIANG. Dissipative energy flow-based port characteristic analysis of modular multilevel converter under sub-synchronous oscillation. Journal of ZheJiang University (Engineering Science), 2025, 59(9): 1931-1941.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.09.017 OR https://www.zjujournals.com/eng/Y2025/V59/I9/1931

基于耗散能流的次同步振荡下模块化多电平换流器端口特性分析

模块化多电平换流器(MMC)拓扑结构复杂，难以利用传统时域或频域方法分析，且MMC与弱电网、风机互联时存在次同步振荡（SSO）风险. 为此，基于耗散能流研究次同步振荡时 MMC 与系统之间的暂态能量交互特性，从而评定MMC对系统次同步振荡的影响. 考虑锁相环以及MMC控制环外环作用，研究次同步振荡下MMC端口响应. 构建MMC端口耗散能流平均斜率的表达式，该表达式能够反映MMC端口的振荡能量源/汇特性及其为系统提供的附加阻尼水平. 基于Simulink建立MMC-双馈风机-无穷大节点互联系统的时域仿真模型，通过时域仿真结果验证了耗散能流表达式的正确性，且揭示了MMC各参数对耗散能流的影响，反映了MMC端口耗散能流与系统稳定性的联系.

关键词： 模块化多电平换流器(MMC), 定功率控制, 次同步振荡, 耗散能流, 源汇特性

Fig.1 MMC topology (connected to an equivalent power grid)

Fig.2 Diagram of MMC inner current feedback loop

Fig.3 Model of SRF-PLL

Fig.4 Small-signal equivalent model of SRF-PLL

Fig.5 Diagram of MMC constant power control

Fig.6 MMC-DFIG-infinite bus interconnected system

Tab.1 Simulation system parameters

Fig.7 Waveform and frequency spectrum of PCC voltage

Fig.8 Waveforms and frequency spectrums of dq-axis voltage and current of MMC and PLL frequency output

Fig.9 Active power output of DFIG when SSO converges

Fig.10 Measured and calculated values of

${\overline {\dot W} _{\text{D}}}$

when SSO converges

Fig.11 Active power output of DFIG when SSO diverges

Fig.12 Measured and calculated values of

${\overline {\dot W} _{\text{D}}}$

when SSO diverges

Fig.13 Simulation results under different power outer loop parameters

Fig.14 Simulation results under different PLL parameters

Fig.15 Simulation results under different MMC active power references

Fig.16 Simplified MMC constant power control loop

Fig.17 Curves of

${\overline {\dot W} _{\text{D}}}$

under different constant-power loop bandwidths

Fig.18 Curves of

${\overline {\dot W} _{\text{D}}}$

under different PLL bandwidths


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[1]	ZHAO Wen jian, YANG Kun, CHEN Guo zhu. DC voltage control method of modular multilevel converter[J]. Journal of ZheJiang University (Engineering Science), 2015, 49(9): 1749-1754.

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