This paper presents a mathematical analysis of how wind generation impacts the coherency property of power systems. Coherency arises from time-scale separation in the dynamics of synchronous generators, where generator states inside a coherent area synchronize over a fast time-scale due to stronger coupling, while the areas themselves synchronize over a slower time-scale due to weaker coupling. This time-scale separation is reflected in the form of a spectral separation in the weighted Laplacian matrix describing the swing dynamics of the generators. However, when wind farms with doubly-fed induction generators (DFIG) are integrated in the system then this Laplacian matrix changes based on both the level of wind penetration and the location of the wind farms. The modified Laplacian changes the effective slow eigenspace of the generators. Depending on penetration level, this change may result in changing the identities of the coherent areas. We develop a theoretical framework to quantify this modification, and validate our results with numerical simulations of the IEEE 68-bus system with one and multiple wind farms. We compare our model based results on clustering with results using measurement-based principal component analysis to substantiate our derivations.

中文翻译：

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风穿透对电力系统慢相干影响的建模和量化

本文对风力发电如何影响电力系统的相干特性进行了数学分析。相干性源于同步发电机动力学中的时间尺度分离，其中相干区域内的发电机状态由于耦合较强而在快速时间尺度上同步，而区域本身由于耦合较弱而在较慢时间尺度上同步。这种时间尺度分离以描述发电机摆动动态的加权拉普拉斯矩阵中的频谱分离的形式反映出来。然而，当具有双馈感应发电机 (DFIG) 的风电场集成到系统中时，该拉普拉斯矩阵会根据风渗透水平和风电场位置发生变化。修正的拉普拉斯算子改变了生成器的有效慢特征空间。根据渗透级别，这种变化可能会导致相关区域的身份发生变化。我们开发了一个理论框架来量化这种修改，并通过具有一个和多个风电场的 IEEE 68 总线系统的数值模拟来验证我们的结果。我们将基于模型的聚类结果与使用基于测量的主成分分析的结果进行比较，以证实我们的推导。