Decentralized Stochastic Programming for Real and Reactive Power Management in Distribution Systems

The stochastic nature of solar renewable power poses challenges in distribution networks with high-penetration photovoltaic (PV) generation in terms of achieving thermal loss minimization, voltage regulation, and customer satisfaction. This paper introduces a stochastic optimization model for real and reactive power management in such distribution systems with high level of residential-scale PV penetration. Decision variables include demand response schedules of programmable loads, as well as reactive power consumption or generation by the PV inverters in a fashion adaptive to the uncertain real power generated by the PV units. A decentralized algorithm based on the alternating direction method of multipliers (ADMM) is developed. The algorithm features closed-form updates per node, and requires communication only between neighboring nodes. The performance of the algorithm is evaluated on a typical rural distribution circuit using computer simulations. The proposed method is demonstrated to have superior voltage regulation in comparison to local reactive power control alternatives.