Signal-anticipating in local voltage control in distribution systems

In this paper, we consider the signal-anticipating behavior in local volt/var control in 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 further 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 how the PoSA scales with the size, topology, and heterogeneity of the power network for a few special cases. We find that the stronger the coupling between different buses is, the larger the PoSA is; the linear network gives the largest PoSA among all possible topologies, but as the size of the network increases, the PoSA will saturate.