Regulating Voltage Magnitude and Phase Imbalance using DERs via Volt/VAR Control Rules

Fluctuations of active power injections by rooftop photovoltaics (PVs) and distributed energy resources (DERs) challenge voltage regulation in distribution grids. Reactive power support by DERs following Volt/VAR (VVR) rules driven by local data has been advocated as an effective fast-response mechanism to regulate voltage. Customizing the parameters of VVR rules is a non-trivial task for grid operators as VVR rules give rise to nonlinear dynamics and should operate under diverse and uncertain loading conditions. Existing works typically resort to linearized models of presumably balanced grids, and design VVR rules to regulate voltage magnitudes alone. Under the practical setting of single-phase DERs operating over unbalanced feeders modeled according to the exact AC power flow equations, injecting reactive power to regulate voltage could aggravate voltage phase imbalance issues. This work optimally designs VVR rules to regulate voltage and reduce voltage unbalance factors (VUF) in multiphase distribution grids. To avoid mixed-integer programs, we formulate a stochastic optimization program and surrogate chance constraints by smooth approximations. The program is solved via an iterative primal-dual algorithm, for which gradients are computed via implicit differentiation at grid equilibrium states. Numerical tests corroborate that if properly designed, VVR rules can regulate voltage magnitudes and phase imbalance alike.