Equilibrium and dynamics of local voltage control in distribution systems

We consider a class of local volt/var control schemes where the control decision on the reactive power at a bus depends only on the local bus voltage. These local algorithms form a feedback dynamical system and collectively determine the bus voltages of a power network. We show that the dynamical system has a unique equilibrium by interpreting the dynamics as a distributed algorithm for solving a certain convex optimization problem whose unique optimal point is the system equilibrium. Moreover, the objective function serves as a Lyapunov function implying global asymptotic stability of the equilibrium. The optimization based model does not only provide a way to characterize the equilibrium, but also suggests a principled way to engineer the control. We apply the results to study the parameter setting for the inverter-based volt/var control in the proposed IEEE 1547.8 standard.