In this paper, we investigate the stability properties of inverter-based microgrids by establishing the possible presence of the so-called critical clusters - groups of inverters with their control settings being close to the stability boundary. For this, we consider the spectrum of the weighted admittance matrix of the network and show that its distinct eigenvalues correspond to inverter clusters, whose structure can be revealed by the corresponding eigenvector. We show that the maximum eigenvalue of the weighted admittance matrix corresponds to the cluster, closest to stability boundary. We also establish, that there exists a boundary on the value of this eigenvalue, that corresponds to the stability of the overall system. Thus, we make it possible to certify the stability of the system and find the groups of inverters in which control settings are closest to the stability boundary.

中文翻译：

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基于逆变器的微电网中关键集群的识别

在本文中，我们通过建立所谓的临界集群（其控制设置接近稳定边界的逆变器组）的可能存在来研究基于逆变器的微电网的稳定性特性。为此，我们考虑了网络的加权导纳矩阵的频谱，并表明其不同的特征值对应于逆变器簇，其结构可以通过相应的特征向量来揭示。我们表明加权导纳矩阵的最大特征值对应于最接近稳定边界的集群。我们还确定，该特征值的值存在一个边界，对应于整个系统的稳定性。因此，