Abstract：The modular multilevel converter (MMC), characterized by its modularity, superior waveform quality, and scalability, has emerged as a pivotal topology in flexible high-voltage direct current (HVDC) transmission systems. However, its large-scale deployment on offshore platforms and in urban grid interconnections is hindered by excessive volume and weight, primarily due to cascaded submodules (SMs). Hybrid MMC topologies that integrate device series connection and SM cascading have emerged as promising solutions for enhancing power density. Nevertheless, the energy balance challenge caused by segmented sinusoidal waveforms and current-path switching in such topologies severely limits their engineering viability. Traditional energy-balancing approaches, including arm voltage control and harmonic current injection, have significant drawbacks: limited voltage regulation ranges, increased hardware complexity, and reduced efficiency. This study focuses on the arm-multiplexing MMC (AM-MMC), a lightweight topology with relatively good performance, to address these limitations through circulating-current-optimized energy-balancing control. Firstly, a high-dimensional dynamic model based on arm equivalent modulation (AEM) strategy is established to express the time-varying coupling effects inherent to AM-MMC’s multiplexed arm operation. The model elucidates the mechanism of circulating current generation through precise analysis of submodule capacitor voltage components, the nonlinear characteristics of dynamic switching functions, and multi-frequency harmonic voltage-current interactions. Secondly, the energy balance and the quantitative characterization of circulating current involvement in energy balance processes are analyzed. With retaining the second-harmonic component of the circulating current for simplified control, a fundamental characteristic of the AM-MMC is identified. That is, the minimum required amplitude of the second-harmonic circulating current maintains a constant proportion with the DC-side current when the modulation ratio is held constant. Then, a methodology is established to determine this proportionality coefficient across different modulation ratios. Finally, a control strategy for circulating current optimization is proposed. Given the complexity of calculating proportionality coefficients, an offline coefficient configuration is adopted to ensure the dynamic performance of the proposed strategy. However, due to the linearization and averaging approximations in the mathematical modeling process, the theoretically derived coefficients inevitably contain certain inaccuracies. To further improve control precision, an online optimization section is introduced. This section integrates the submodule capacitor’s voltage feedback with a PI controller to optimize real-time coefficients, and a PIR controller regulates the circulating current. A cross-scale verification platform is developed, including an 85 MV·A/±35 kV simulation system and a 3.2 kV·A/±150 V hardware prototype. The following conclusions can be drawn. (1) The proposed strategy achieves optimal coordination between energy balance and circulating current suppression, while addressing the limitations of additional hardware requirements and voltage regulation constraints. (2) By the dominant harmonic component regulation with offline-predetermined coefficients and online optimization, this approach ensures dynamic stability and a wide voltage regulation range with minimal trade-offs in scenarios like offshore wind farm integration, where a lightweight topology is required. Thus, an economically viable and efficient engineering solution can be offered. (3) Beyond specific implementations, the developed methodology establishes a universal framework for lightweight topologies. As an inherent characteristic of MMCs, the circulating current enables facile control without additional hardware requirements for energy balance control.
张振, 王毅, 刘伯文, 杨顺, 高玉华. 基于环流优化的桥臂复用型模块化多电平换流器能量平衡策略研究[J]. 电工技术学报, 2026, 41(8): 2697-2717.
Zhang Zhen, Wang Yi, Liu Bowen, Yang Shun, Gao Yuhua. Research on Energy Balance Strategy of Arm Multiplexing Modular Multilevel Converter Based on Circulating Current Optimization. Transactions of China Electrotechnical Society, 2026, 41(8): 2697-2717.
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2026, Vol. 41 
