A Coordinate-Descent Algorithm for Tracking Solutions in Time-Varying Optimal Power Flows

TL;DR

This paper introduces a coordinate-descent algorithm designed to efficiently track solutions of time-varying polynomial optimization problems, specifically applied to power system optimal power flow relaxations, with theoretical bounds on accuracy and computational effort.

Contribution

It presents a novel coordinate-descent method for real-time tracking of solutions in dynamic power system optimization problems, with theoretical performance guarantees.

Findings

Bound the difference between approximate and true optimal costs over time.

Establish bounds on the number of iterations needed for desired accuracy.

Demonstrate effectiveness on AC optimal power flow relaxations.

Abstract

Consider a polynomial optimisation problem, whose instances vary continuously over time. We propose to use a coordinate-descent algorithm for solving such time-varying optimisation problems. In particular, we focus on relaxations of transmission-constrained problems in power systems. On the example of the alternating-current optimal power flows (ACOPF), we bound the difference between the current approximate optimal cost generated by our algorithm and the optimal cost for a relaxation using the most recent data from above by a function of the properties of the instance and the rate of change to the instance over time. We also bound the number of floating-point operations that need to be performed between two updates in order to guarantee the error is bounded from above by a given constant.