Voltage regulation in electricity distribution networks using the conditional value-at-risk

Voltage regulation in distribution networks featuring high penetration of distributed photovoltaic (PV) generation is particularly challenging due to the stochastic nature of solar energy. To ensure that voltage levels remain within safety margins, this paper introduces a real and reactive power optimization model that penalizes the conditional value-at-risk of the voltage deviation from its nominal value. This risk-averse approach guarantees that node voltages across the network remain close to their nominal value with a specified probability. Decision variables are the real power consumption of controllable loads and reactive power consumption or generation from PV inverters. Adopting a scenario-based model for the uncertain solar power, the overall problem amounts to a convex quadratic program. Numerical tests for typical residential distribution networks exhibit the effectiveness of the model in achieving voltage regulation as compared to alternative risk-neutral approaches.