The synchronous d-q based small-signal stability using the eigenvalue analysis and impedance methods is widely employed to assess system stability. Generally, the harmonics are ignored in the stability analysis, and such assumption may lead to inaccuracies in the stability predictions, particularly, in harmonic-polluted ac grids. Typically, the harmonic state-space method (HSS) facilitates stability studies of linear time-periodic systems, which considers the impact of harmonics. The use of the d-q dynamic phasor state space and impedance methods offer significant advantages over the HSS counterpart, as they reduce system order, suitable for studying control systems, retain coupling between harmonics, and simplify the stability study under unbalanced conditions. This study extends dynamic phasor modelling for studying stability of modern power systems that include power converters. It is shown that the proposed methods reproduce the typical response of STATCOM at the fundamental frequency, as well as, in the presence of significant low-order harmonics, using both eigenvalues and impedance analysis. Quantitative validations of the proposed extended models against synchronous dq small-signal models confirm their validity.

中文翻译：

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STATCOM连接到电网以进行稳定性分析的广义dq-动态相量建模

使用特征值分析和阻抗方法的基于同步dq的小信号稳定性被广泛用于评估系统稳定性。通常，在稳定性分析中会忽略谐波，而这种假设可能会导致稳定性预测不准确，尤其是在谐波污染的交流电网中。通常，谐波状态空间方法（HSS）有助于线性时间周期系统的稳定性研究，该系统考虑了谐波的影响。dq动态相量状态空间和阻抗方法的使用提供了优于HSS对应方法的显着优势，因为它们减少了系统阶数，适合于研究控制系统，保留了谐波之间的耦合，并简化了不平衡条件下的稳定性研究。这项研究扩展了动态相量建模，以研究包括电源转换器的现代电力系统的稳定性。结果表明，所提出的方法使用特征值和阻抗分析，都能在基频以及存在大量低阶谐波的情况下，重现STATCOM的典型响应。对同步dq小信号模型提出的扩展模型的定量验证证实了它们的有效性。