A networked reduced model for electrical networks with constant power loads

We consider structure preserving power networks with proper algebraic constraints resulting from constant power loads. Both for the linear and the nonlinear model of the network, we propose explicit reduced order models which are expressed in terms of ordinary differential equations. The relative frequencies among all the buses in the original power grid are readily tractable in the proposed reduced models. For deriving these reduced models, we introduce the “projected pseudo incidence” matrix which yields a novel decomposition of the reduced Laplacian matrix. With the help of this new matrix, we are able to eliminate the proper algebraic constraints while preserving the crucial frequency information of the loads.