Development of a Convex Programming Model for Optimal Power Flow Problems

Mauro Viegas da Silva, Mahdi Porakbari-Kasmaei, J. Roberto Sanches Mantovani

Published 2018-10-18Version 1

The optimal power flow (OPF) is an optimization model dedicated to the development of computational tools used for the planning and operation of electric power systems (EPS). In this work, based on the polar formulation, an extended convex model is presented. To do so, the sinusoidal and cosinusoidal terms are the toughest part of the convexification process, since such types of functions oscillate between concave and convex. These functions are not initially convex, but there is a possibility of finding a convex underestimator (CU) for them. To obtain this CU, the Taylor series presents a good, however nonconvex, approximation for such trigonometric functions. Although the model remains nonconvex, these terms can be recast to the corresponding equivalent convex terms. The obtained convex model of the OPF is tested and analyzed using the IEEE 14-, 30-, 54-, and 118-bus test systems.