An Iterative Approach to Improving Solution Quality for AC Optimal Power Flow Problems

TL;DR

This paper introduces an iterative method that enhances AC optimal power flow solutions by leveraging dual variables and partial Lagrangian optimization, effectively escaping local solutions to reach global optima in standard network tests.

Contribution

The paper presents a novel iterative approach combining existing solvers with partial Lagrangian optimization to improve solution quality for ACOPF problems.

Findings

Algorithm can escape local solutions within a few iterations.

Effective on standard IEEE networks.

Achieves global optimal solutions.

Abstract

The existence of multiple solutions to AC optimal power flow (ACOPF) problems has been noted for decades. Existing solvers are generally successful in finding local solutions, which satisfy first and second order optimality conditions, but may not be globally optimal. In this paper, we propose a simple iterative approach to improve the quality of solutions to ACOPF problems. First, we call an existing solver for the ACOPF problem. From the solution and the associated dual variables, we form a partial Lagrangian. Then we optimize this partial Lagrangian and use its solution as a warm start to call the solver again for the ACOPF problem. By repeating this process, we can iteratively improve the solution quality, moving from local solutions to global ones. We show the effectiveness of our algorithm on standard IEEE networks. The simulation results show that our algorithm can escape from local solutions to achieve global optimums within a few iterations.