Mathematical Programming formulations for the Alternating Current Optimal Power Flow problem

TL;DR

This paper surveys various mathematical programming formulations and relaxations for the complex, nonconvex AC optimal power flow problem, which is crucial for efficient and reliable electrical grid operation.

Contribution

It systematically derives and compares different formulation variants and relaxations for the AC optimal power flow problem, highlighting their mathematical properties.

Findings

Different formulations offer trade-offs between accuracy and computational complexity

Relaxations can provide bounds and insights into the original nonconvex problem

The survey clarifies the landscape of mathematical approaches for AC optimal power flow

Abstract

Power flow refers to the injection of power on the lines of an electrical grid, so that all the injections at the nodes form a consistent flow within the network. Optimality, in this setting, is usually intended as the minimization of the cost of generating power. Current can either be direct or alternating: while the former yields approximate linear programming formulations, the latter yields formulations of a much more interesting sort: namely, nonconvex nonlinear programs in complex numbers. In this technical survey, we derive formulation variants and relaxations of the alternating current optimal power flow problem.