  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.
