Stochasticity agnostic solution to the AC optimal power flow by recursive bound tightening with top‐down heuristically inducted binary decision trees

Abstract

The efficient solution of the AC optimal power flow (OPF) for all cases and electrical grids is not guaranteed. Heuristics, approximations and relaxations have been proposed aplenty, each with pros and cons. This work proposes to solve the AC OPF with binary decision trees (BDTs). The solution starts with the full feasible set of an AC OPF instance, and, iteratively, BDTs tighten the constraints/bounds of that set, to improve the occurring feasible set by the median of the objective function of the preceding set. The medians of the objective function of the progressively tightened feasible sets will converge to the global optimum of the AC OPF. Recent proofs for the estimate performance of top-down BDT learning heuristics ensure convergence of the method to the global optimum, provided the feasible set is adequately sampled for the BDT training. The recursive implementation of the method and the inductive nature of BDTs may also yield dispatches at multiple optimality levels for the same AC OPF instance, to account for stochastic resources. The performance of the proposed AC OPF solution is assessed over multiple cases by NICTA and the IEEE PES task force on benchmarks for validation of emerging power system algorithms.