  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.
