Deep Learning for Optimal Volt/VAR Control using Distributed Energy Resources

Given their intermittency, distributed energy resources (DERs) have been commissioned with regulating voltages at fast timescales. Although the IEEE 1547 standard specifies the shape of Volt/VAR control rules, it is not clear how to optimally customize them per DER. Optimal rule design (ORD) is a challenging problem as Volt/VAR rules introduce nonlinear dynamics, require bilinear optimization models, and lurk trade-offs between stability and steady-state performance. To tackle ORD, we develop a deep neural network (DNN) that serves as a digital twin of Volt/VAR dynamics. The DNN takes grid conditions as inputs, uses rule parameters as weights, and computes equilibrium voltages as outputs. Thanks to this genuine design, ORD is reformulated as a deep learning task using grid scenarios as training data and aiming at driving the predicted variables being the equilibrium voltages close to unity. The learning task is solved by modifying efficient deep-learning routines to enforce constraints on rule parameters. In the course of DNN-based ORD, we also review and expand on stability conditions and convergence rates for Volt/VAR rules on single-/multi-phase feeders. To benchmark the optimality and runtime of DNN-based ORD, we also devise a novel mixed-integer nonlinear program formulation. Numerical tests showcase the merits of DNN-based ORD.