Development of a Convex Programming Model for Optimal Power Flow Problems

TL;DR

This paper introduces an extended convex programming model for optimal power flow problems, utilizing convex underestimators for trigonometric functions to improve computational efficiency in power system planning.

Contribution

It presents a novel convexification approach for OPF using Taylor series-based convex underestimators for sinusoidal terms, enhancing existing models.

Findings

Model tested on IEEE test systems

Convex model shows promising accuracy

Potential for improved computational efficiency

Abstract

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.