Signal-Anticipating in Local Voltage Control in Distribution Systems

Zhiyuan Liu, Seungil You, Xinyang Zhou, Guohui Ding, Lijun Chen

Published 2018-11-23Version 1

We consider the signal-anticipating behavior in local Volt/VAR control for distribution systems. We define a voltage control game and show that the signal-anticipating voltage control is the best response algorithm of the voltage control game. We show that the voltage control game has a unique Nash equilibrium, characterize it as the optimum of a global optimization problem, and establish its asymptotic global stability. We then introduce the notion of the price of signal-anticipating (PoSA) to characterize the impact of the signal-anticipating in local voltage control, and use the gap in cost between the network equilibrium in the signal-taking voltage control and the Nash equilibrium in the signal-anticipating voltage control as the metric for PoSA. We characterize analytically and numerically how the PoSA scales with the size, topology, and heterogeneity of the power network for a few network settings. Our results show that the PoSA is upper bounded by a constant and the average PoSA per node will go to zero as the size of the network becomes large. This is desirable as it means that the PoSA will not be arbitrarily large, no matter what the size of the network is, and no mechanism is needed to mitigate the signal-anticipating behavior.