On Static and Adaptive Policies for Chance-Constrained Voltage Regulation

Electricity distribution networks are envisioned to host an increasing number of photovoltaic (PV) generators. PV units are equipped with inverters that can inject or absorb reactive power, a capability that can be crucial for supporting safe nodal voltages. Inverter set points are designed as solutions of optimal power flow formulations with specifications on the probability that nodal voltages remain within safe bounds. This paper compares various designs for chance-constrained voltage regulation. Due to their inherent nonconvexity, chance constraints are replaced by the conditional-value-at-risk, which offers a conservative convex approximation. The focus is on designs that yield static reactive power control policies or policies that can control the reactive power in a fashion adaptive to the uncertain renewable energy production and load consumption.