Abstract：Modular multilevel converters (MMCs) are one of the most promising solutions for integrating renewable energy sources from remote areas into the AC grid. However, the high impedance of long-distance transmission lines causes challenges to the stability of grid-connected MMC systems under a weak grid. Although the interaction of two-level voltage source converters with weak grids and their stability issues have been intensively studied recently, these results are not applicable to grid-connected MMC systems because of the internal dynamic characteristics of MMC. In addition, there are significant coupling effects between these internal dynamics and the AC-side and DC-side output variables. Therefore, the stability of grid-connected MMC systems under a weak grid, especially the ambiguity of the system interaction mechanism and the small-signal stability, still needs further in-depth research. This paper proposes a small-signal transfer function model to describe the interaction between grid impedance, phase-locked loop (PLL), fundamental frequency current control (FFCC), and circulating current suppression control. The instability mechanism of grid-connected MMC systems caused by the coupling effect of grid impedance and PLL under a weak grid is revealed. First, for the circuit topology and average value model of the grid-connected MMC system, this paper uses the vector representation method of common- and differential-mode signals to construct the basic circuit equations. Then, through coordinate transformation, a linearizable time-varying model of MMC in a synchronous rotating dq coordinate system is established, and the small-signal transfer function model of the grid-connected MMC system is derived. It is found that under the weak grid, the coupling effect between grid impedance and PLL is the key factor affecting the stability of grid-connected MMC systems, and its mechanism is mainly analyzed through the system equivalent loop gain. Then, this paper proposes an analysis method combined with the transfer function zero-pole analysis and the frequency domain characteristics. The results show that the coupling effect of grid impedance and PLL introduces a right half-plane pole in the system equivalent loop gain, thereby destroying the system stability. This potential instability problem can be alleviated by increasing the gain of FFCC. A loop compensation scheme is designed to eliminate the coupling effect between grid impedance and PLL and solve the right half-plane pole problem, thereby improving the stability of grid-connected MMC systems. The following conclusions can be drawn. (1) Under a weak grid, the coupling effect of grid impedance and PLL introduces right half-plane poles in equivalent loop gain, which is the main reason for the instability of the grid-connected MMC system. (2) Increasing the gain of FFC can alleviate the instability caused by the coupling effect of grid impedance and PLL. An effective loop compensation scheme must be designed to eliminate this potential instability problem. (3) The stability analysis method combining the zero-pole analysis of equivalent loop gain with the frequency domain characteristics can effectively solve the subsystem’s stability problem and overcome the limitations of the traditional impedance stability analysis method.
吴向阳, 何梨梨, 李杨, 帅智康. 弱电网下电网阻抗与PLL耦合效应对并网MMC系统稳定性的影响分析[J]. 电工技术学报, 2025, 40(4): 1236-1253.
Wu Xiangyang, He Lili, Li Yang, Shuai Zhikang. Analysis of the Influence of Grid Impedance and PLL Coupling Effect on the Stability of Grid-Connected MMC Systems under Weak Grid. Transactions of China Electrotechnical Society, 2025, 40(4): 1236-1253.
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2025, Vol. 40 
