Local voltage control in distribution systems: An incremental control algorithm
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 signalanticipating (PoSA) to characterize the impact of the signalanticipating 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.