Novel results on slow coherency in consensus and power networks

Abstract — We revisit the classic slow coherency and area aggregation approach to model reduction in power networks. The slow coherency approach is based on identifying sparsely and densely connected areas of a network, within which all generators swing coherently. A time-scale separation and singular perturbation analysis then results in a reduced low-order system, where coherent areas are collapsed into aggregate variables. Here, we study the application of slow coherency and area aggregation to first-order consensus systems and second-order power system swing dynamics. We unify different theoretic approaches and ideas found throughout the literature, we relax some technical assumptions, and we extend existing results. In particular, we provide a complete analysis of the second-order swing dynamics – without restrictive assumptions on the system damping. Moreover, we identify the reduced aggregate models as generalized first or second-order Laplacian flows with multiple time constants, aggregate damping and inertia matrices, and possibly adverse interactions. I