Analysis of the precision of a second-order conic model to solve the optimal power dispatch problem in electric power systems

This paper presents in-depth comparative analyses of nonlinear nonconvex programming (NLNCP) and secondorder conic programming (SOCP) models to solve the optimal power flow problem in electric power systems. For comparative purposes, two objective functions are considered 1) minimization of the active power generation costs; and 2) minimization of the active power losses in the transmission branches. The robustness and precision of the NLNCP and SOCP models are analyzed and discussed considering the feasibility of the active and reactive power balance constraints and the values of the objective functions. The obtained operational points are verified through the solution of the AC power flow problem using the Newton-Raphson method. For both models, numerical experiments show consistent active power dispatch, however, limit violations in the reactive power generation limits are observed in the solutions obtained by the SOCP model. To address this issue, two variations in the formulation of the SOCP model are proposed 1) considering a penalty factor in the generation of reactive energy; and 2) considering a minimum resistance in branches of the power system that have resistance equal to zero. The solution of these modified SOCP models can eliminate or significantly reduce reactive power dispatch limit violations