Novel results on slow coherency in consensus and power networks

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.