Step size optimization based interior point algorithm: Applications and treatment of ill-conditioning in optimal power flow solutions

In this work a step size optimization based nonlinear interior point (IP) algorithm is proposed 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 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 singularity analysis. Simulations using a simple test system are carried out to evaluate its performance for solving ill-conditioned systems in comparison to conventional IP methods. The proposed method provides a better convergence path towards well-conditioned optimal solution; it also presents more information (step size, Lagrange multipliers, eigenvalue analysis) in case the optimal point is singular or infeasible, which is classified as ill-conditioned optimal solution.