Empirical Investigation of Non-Convexities in Optimal Power Flow Problems

TL;DR

This paper empirically investigates the non-convexities in optimal power flow problems, characterizing their difficulty and proposing test cases to benchmark solution algorithms.

Contribution

It provides an empirical analysis of non-convexities in small OPF problems and introduces medium-sized test cases to challenge various algorithms.

Findings

Some OPF problems have nearly convex feasible spaces.

Non-convexities can significantly affect solution difficulty.

New test cases help benchmark algorithm performance.

Abstract

Optimal power flow (OPF) is a central problem in the operation of electric power systems. An OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering limits. These constraints can yield non-convex feasible spaces that result in significant computational challenges. Despite these non-convexities, local solution algorithms actually find the global optima of some practical OPF problems. This suggests that OPF problems have a range of difficulty: some problems appear to have convex or "nearly convex" feasible spaces in terms of the voltage magnitudes and power injections, while other problems can exhibit significant non-convexities. Understanding this range of problem difficulty is helpful for creating new test cases for algorithmic benchmarking purposes. Leveraging recently developed computational tools for exploring OPF feasible spaces, this paper first describes an empirical study that aims to characterize non-convexities for small OPF problems. This paper then proposes and analyzes several medium-size test cases that challenge a variety of solution algorithms.