Modeling and Quantifying the Impact of Wind Penetration on Slow Coherency of Power Systems

This paper presents a mathematical analysis of how wind generation impacts the slow coherency property of power systems. Slow 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 into 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 the penetration level, this change may result in changing the identities of the coherent areas. We develop a theoretical framework to quantify this modification, and propose an equivalent Laplacian matrix to compute the modified coherent areas. Results are validated using the IEEE 68-bus test system with one and multiple wind farms. The model-based slow coherency results are compared with measurement-based principal component analysis to substantiate our derivations.