  We formulate the control of reactive power generation by photovoltaic
inverters in a power distribution circuit as a constrained optimization that
aims to minimize reactive 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 to the respective flows, the resulting optimization
problem is convex. Moreover, the cost function is separable enabling a
distributed, on-line 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 (ADMM) and find that the ADMM protocol performs
significantly better.

Optimization and Control;Systems and Control