Ill-conditioned Optimal Power Flow solutions and performance of non-linear programming solvers

In this paper, the performance of the most popular non-linear programming solvers (e.g. IPOPT, KNITRO, LOQO, MINOS and SNOPT) is evaluated for applications in power systems and treatment of ill-conditioned systems related to optimal power flow (OPF) solutions. Regarding the applications, the maximum loading point problem modeled as an optimization problem is used as an OPF example. Also, it is used to describe the ill-conditioned OPF solutions, the sensitivity matrices obtained in the OPF process, and conditions related to linear independence (LI) loss singularity analysis. Simulations using a simple two-bus and IEEE test systems are carried out to evaluate the performance of solvers for solving LI loss singularity cases, which were obtained upon the original data systems. Some of the Lagrange multipliers corresponding to the constraints tend to infinity when the LI condition is violated, which implies that the OPF solution is ill-conditioned. In this case, the number of iterations increases (convergence problems) significantly for all solvers, and some solvers presented oscillatory process.