Convergence Analysis of Fixed Point Chance Constrained Optimal Power Flow Problems

TL;DR

This paper analyzes the convergence conditions of a fixed point iteration method used in chance constrained optimal power flow problems, supported by numerical experiments on large IEEE networks.

Contribution

It provides the first detailed convergence analysis for the fixed point approach in chance constrained optimal power flow, enhancing understanding of its reliability.

Findings

Convergence conditions depend on specific problem parameters.

Numerical experiments validate theoretical convergence criteria.

Large IEEE network simulations demonstrate practical applicability.

Abstract

For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach is not necessarily guaranteed. This article analyses the convergence conditions for this fixed point approach, and reports numerical experiments including for large IEEE networks.