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

•An in-depth comparison of the AC-OPF model for three formulations: power balance polar, power balance Cartesian and current balance Cartesian presenting their characteristic differences.•Comparison of structural differences in terms of number of variables, constraints and non-zeros in Jacobian and hessian matrix.•Numerical and computational performance evaluation for the AC-OPF formulations on nine different test cases including large-scale synthetic U.S. networks. 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. We compare the performance of the three methods in terms of computational speed, number of iterations, and number of non-zeros in Jacobian and Hessian matrix. The numerical results show that power balance polar formulation had the best performance on small number of bus system but on a large-scale test grid current balance cartesian outperformed the other two formulations.