Stochastic loss minimization for power distribution networks

Distribution systems will be critically challenged by reverse power flows and voltage fluctuations due to the integration of distributed renewable generation, demand response, and electric vehicles. Yet the same transformative changes coupled with advances in microelectronics offer new opportunities for reactive power management in distribution grids. In this context and considering the increasing time-variability of distributed generation and demand, a scheme for stochastic loss minimization is developed here. Given uncertain active power injections, a stochastic reactive control algorithm is devised. Leveraging the recent convex relaxation of optimal power flow problems, it is shown that the subgradient of the power losses can be obtained as the Lagrange multiplier of the related second-order cone program (SOCP). Numerical tests on a 47-bus test feeder with high photovoltaic penetration corroborates the power efficiency and voltage profile advantage of the novel stochastic method over its deterministic alternative.