Optimal Distributed Control of Reactive Power Via the Alternating Direction Method of Multipliers

We formulate the control of reactive power generation by photovoltaic inverters in a power distribution circuit as a constrained optimization that aims to minimize power losses subject to finite inverter capacity and upper and lower voltage limits at all nodes in the circuit. When voltage variations along the circuit are small and losses of both real and reactive powers are small compared with the respective flows, the resulting optimization problem is convex. Moreover, the cost function is separable enabling a distributed online implementation with node-local computations using only local measurements augmented with limited information from the neighboring nodes communicated over cyber channels. Such an approach lies between the fully centralized and local policy approaches previously considered. We explore protocols based on the dual-ascent method and on the alternating direction method of multipliers (ADMMs), and find that the ADMM protocol performs significantly better.