Optimal Power Flow Pursuit in the Alternating Current Model

TL;DR

This paper addresses the challenge of solving time-varying AC optimal power flow problems by proposing approaches that provide bounds on optimality gaps and computational effort, improving real-time power system optimization.

Contribution

It introduces methods for handling polynomial optimization in dynamic power systems, including bounds on optimality gaps and computational complexity for ACOPFs.

Findings

Provides an upper bound on the optimal cost difference over time.

Establishes bounds on the number of floating-point operations needed.

Demonstrates the approach on ACOPF problems.

Abstract

Transmission-constrained problems in power systems can be cast as polynomial optimization problems whose coefficients vary over time. We consider the complications therein and suggest several approaches. On the example of the alternating-current optimal power flows (ACOPFs), we illustrate one of the approaches in detail. For the time-varying ACOPF, we provide an upper bound for the difference between the optimal cost for a relaxation using the most recent data and the current approximate optimal cost generated by our algorithm. This bound is a function of the properties of the instance and the rate of change of the coefficients over time. Moreover, we also bound the number of floating-point operations to perform between two subsequent updates to ensure a bounded error.