基于Floquet理论的模块化多电平换流器小信号稳定性分析

为更好地描述模块化多电平换流器(Modular Multilevel Converter, MMC)中高次谐波动态的相互作用，基于线性时间周期(Linear Time-Periodic, LTP)系统理论对MMC进行建模，并基于Floquet理论进行MMC系统的小信号稳定性分析。首先通过MMC的桥臂平均值模型建立系统的非线性时间周期系统模型，然后围绕周期轨道将该模型线性化得到MMC的LTP模型，最后通过针对LTP系统的Floquet理论分析MMC的小信号稳定性。分析结果表明：LTP模型可以准确描述MMC的小信号动态响应特性；Floquet分析可以精确刻画MMC参数构成的稳定边界。此外，所提模型和稳定性分析结果通过了基于MMC聚合模型的电磁暂态仿真和验证。

Small-signal stability analysis of modular multilevel converters based on Floquet theory

In order to better describe the dynamic interaction of high-order harmonics in Modular Multilevel Converters (MMCs), this paper models the MMCs based on Linear Time-Periodic (LTP) system theory, and performs a small-signal stability analysis of MMCs based on Floquet theory. First, the nonlinear time-periodic system model is established based on the bridge arm average model of the MMC, and then the model is linearized around the periodic orbit to obtain the LTP model of the MMC. Finally, the small-signal stability of the MMC is analyzed by the Floquet theory for the LTP system. The results show that the LTP model can accurately describe the small-signal dynamic response characteristics of the MMC; Floquet analysis can accurately portray the stability boundary composed of the MMC parameters. In addition, the model and stability analysis results are verified by electromagnetic transient simulation based on the MMC aggregation model. This work is supported by the National Key Research and Development Program of China (No. 2017YFB0903705).