Fundamental Review of the OPF Problem: Challenges, Solutions, and State-of-the-Art Algorithms

Abstract

Optimal power flow (OPF) is critical for maintaining the secure and economic operation of power systems. In this paper, a fundamental analysis of the OPF problem is provided. As a common nonlinear programming (NLP) problem for mathematicians, the reason why the OPF problem is challenging for power engineers is analyzed. It is shown that the nonlinearity of power flow equations is the main factor that makes the OPF problem hard to solve. Ideas for handling the power flow equations are summarized. Existing OPF methods are further divided into three categories based on how the power flow equations are handled: OPF methods with the strict alternate current (AC) network model, OPF methods based on convex relaxation, and OPF methods with linearized network models. A comprehensive review of the state-of-the-art OPF algorithms in each category is presented. The features, advantages, and disadvantages of different categories are analyzed. Additionally, the prevalent industrial practices related to OPF calculations are presented. Extensions of the OPF problem, including security-constrained OPF (SCOPF), OPF with discrete variables, and OPF with uncertainties, are discussed.