The Price of Synchrony: Evaluating the Resistive Losses in Synchronizing Power Networks

Abstract

This paper investigates the resistive power losses that are incurred in keeping a network of synchronous generators in a synchronous state. These losses arise due to the transient power-flow fluctuations that occur when the system is perturbed from a synchronous state by a small transient event or in the face of persistent stochastic disturbances. We call these losses the “price of synchrony,” as they reflect the real power-flow costs incurred in resynchronizing the system. In the case of small fluctuations at each generator node, we show how the total network's resistive losses can be quantified using an ${\cal H}_{2}$ norm of a linear system of coupled swing equations subject to distributed disturbances. This norm is shown to be a function of transmission-line and generator properties, to scale unboundedly with network size, and to be weakly dependent on the network topology. This conclusion differentiates the price of synchrony from typical power systems stability notions, which show highly connected networks to be more coherent and, thus, easier to synchronize. In particular, the price of synchrony is more dependent on a network's size than its topology. We discuss possible implications of these results in terms of the design of future power grids, which are expected to have highly distributed generation resources leading to larger networks with the potential for greater transient losses.