Evaluation of convex optimization models for minimizing losses in distribution systems

Abstract

This paper proposes the evaluation of convex models for short-term energy dispatch, optimizing the location of generators and minimizing losses in distribution networks. For this purpose, convex models are used in a 12-hour period with an hourly variation of the demand, using the IEEE system of 15 radial type nodes. Due to the nodal injection active and reactive power equations, the problem becomes non-convex and requires more computational resources to find local optimal solutions. To address the nonlinearity problem. The Wirtinger calculus and the second-order conic approximation are analyzed. The first model solves in 8.12 seconds with voltage errors of 0.63% and angle of 1.40%, and the second model in 17.8 seconds with errors of 0.61% and 1.38%, respectively. The optimal  location of the generating units are nodes 7, 8 and 10. The objective function value for each model is 0.00731149 p.u. for the nonlinear model, 0.00734619 p.u, for the Wirtinger model 0.00744715 p.u, and for the second order conic approximation model (SOC), with a base of 100 kVA.