AC Optimal Power Flow in Power Systems With Renewable Energy Integration: A Review of Formulations and Case Studies

The primary goal of a power system is to provide consumers with reliable access to power at the most economical cost. Under the declining costs of renewable energy sources, the increasing cost of natural gas, and growing emissions control policies, investment in variable renewable energy (VRE) sources including wind and solar is accelerating. As a fundamental optimization tool in the operation and planning of electric power systems, the optimal power flow (OPF) is critical for setting the optimal state of control variables by minimizing desired objective while satisfying all related constraints. However, a comprehensive review of the generic OPF framework that includes all categories of objectives, control variables, and constraints will provide a valuable background to many of the integration studies that are necessary to facilitate the transition of energy systems. A comprehensive OPF framework is essential for researchers to identify the most critical challenges to their applications to develop new solution methods to improve computational efficiency and to take advantage of the increasing computing power to reduce the number of approximations in OPF models. In this work, we aim to provide a comprehensive survey and a generic OPF formulation, along with a detailed explanation of the major formulations for conventional OPF objective functions, control variables, and network constraints, in particular those related to the handling of VREs. This article also highlights the modeling and challenges in the distribution system, and potential formulations to incorporate with the significant variability and intermittency of VRE sources. In addition to a discussion of various formulations and foci for the OPF problem, we compare the implications of these decisions on a small case study to highlight differences.