Computing the Feasible Spaces of Optimal Power Flow Problems

TL;DR

This paper introduces an algorithm that accurately computes the entire feasible solution space of small optimal power flow problems by combining discretization, polynomial homotopy continuation, and convex relaxation techniques.

Contribution

It presents a novel method for provably determining the feasible spaces of OPF problems using discretization, NPHC, and relaxation-based pruning, improving understanding of solution regions.

Findings

Successfully computed feasible spaces for two small test cases.

Demonstrated the effectiveness of bound tightening and grid pruning.

Provided a new approach for analyzing OPF solution spaces.

Abstract

The solution to an optimal power flow (OPF) problem provides a minimum cost operating point for an electric power system. The performance of OPF solution techniques strongly depends on the problem's feasible space. This paper presents an algorithm for provably computing the entire feasible spaces of small OPF problems to within a specified discretization tolerance. Specifically, the feasible space is computed by discretizing certain of the OPF problem's inequality constraints to obtain a set of power flow equations. All solutions to the power flow equations at each discretization point are obtained using the Numerical Polynomial Homotopy Continuation (NPHC) algorithm. To improve computational tractability, "bound tightening" and "grid pruning" algorithms use convex relaxations to eliminate the consideration of discretization points for which the power flow equations are provably infeasible. The proposed algorithm is used to generate the feasible spaces of two small test cases.