Solving the power flow equations: a monotone operator approach

TL;DR

This paper introduces a novel method using monotone operator theory to reliably solve power flow equations, especially under conditions where traditional methods struggle due to poor initial guesses, by computing a domain guaranteeing solution existence.

Contribution

The paper proposes an offline optimization approach to compute a monotonicity domain for power flow equations, enabling efficient and certifiable solution finding without relying on initial guesses.

Findings

The method can compute a monotonicity domain that includes all relevant solutions.

The approach is validated on IEEE test cases showing practical tractability.

It provides a certifiable solution existence guarantee.

Abstract

The AC power flow equations underlie all operational aspects of power systems. They are solved routinely in operational practice using the Newton-Raphson method and its variants. These methods work well given a good initial "guess" for the solution, which is always available in normal system operations. However, with the increase in levels of intermittent generation, the assumption of a good initial guess always being available is no longer valid. In this paper, we solve this problem using the theory of monotone operators. We show that it is possible to compute (using an offline optimization) a "monotonicity domain" in the space of voltage phasors. Given this domain, there is a simple efficient algorithm that will either find a solution in the domain, or provably certify that no solutions exist in it. We validate the approach on several IEEE test cases and demonstrate that the offline optimization can be performed tractably and the computed "monotonicity domain" includes all practically relevant power flow solutions.