Computational and numerical analysis of AC optimal power flow formulations on large-scale power grids

We report that alternating current optimal power flow (AC-OPF) is a fundamental tool in electric utilities to determine optimal operation of the various resources. Typically, the AC-OPF problem uses power balance formulation containing voltages and power equations. Yet, there is no comprehensive comparison of the different AC-OPF formulations, especially for large-scale networks. This paper presents a detailed comparative evaluation of different formulations of the AC-OPF problem on networks ranging from 9-bus to 25,000 buses. Three different formulations: 1) power balance with polar voltages, 2) power balance with Cartesian voltages, and 3) current balance with Cartesian voltages are discussed in detail by comparing their characteristics, and numerical and computational performance.