重访基于类Nyquist阻抗的变流器型交流系统判据
Revisiting Nyquist-Like Impedance-Based Criteria for Converter-Based AC Systems
AI总结：
本文明确了变流器型交流系统小信号稳定性分析中两类类Nyquist阻抗判据的特性，针对特征值判据的歧义提出基于对数导数的模态识别判据，并通过PSCAD仿真验证了理论分析。
摘要：
多种基于类Nyquist阻抗的判据被用于变流器型交流系统的小信号稳定性分析。通常认为基于行列式的判据可判定系统整体稳定性，而基于特征值的判据能更深入揭示失稳机理。本文从状态空间得到的阻抗矩阵的零极点计算入手，结合Smith-McMillan形对上述认知予以明确，随后基于阻抗分析的常见假设——即各子系统互联前可稳定运行，阐明了基于行列式的判据的绝对可靠性。然而，当Nyquist图中出现围绕原点的逆时针包围时，基于特征值的判据确实存在歧义。为此，本文提出一种基于对数导数的判据，可利用环路阻抗的频率响应直接识别系统模态，该判据以传递函数矩阵的Schur补为坚实理论基础。通过并网两电平电压源变流器的PSCAD仿真验证了理论分析的正确性。
英文摘要：
Multiple types of Nyquist-like impedance-based criteria are utilized for the small-signal stability analysis of converter-based AC systems. It is usually considered that the determinant-based criterion can determine the overall stability of a system while the eigenvalue-based criterion can give more insights into the mechanism of the instability. This paper specifies such understandings starting with the zero-pole calculation of impedance matrices obtained by state-spaces with the Smith-McMillan form, then clarifying the absolute reliability of determinant-based criterion with the common assumption for impedance-based analysis that each subsystem can stably operate before the interconnection. However, ambiguities do exist for the eigenvalue-based criterion when an anticlockwise encirclement around the origin is observed in the Nyquist plot. To this end, a logarithmic derivative-based criterion to directly identify the system modes using the frequency responses of loop impedances is proposed, which owns a solid theoretical basis of the Schur complement of transfer function matrices. The theoretical analysis is validated using a PSCAD simulation of a grid-connected two-level voltage source converter.
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