History of Optimal Power Flow and Formulations

The purpose of this paper is to present a literature review of the AC Optimal Power Flow (ACOPF) problem and propose areas where the ACOPF could be improved. The ACOPF is at the heart of Independent System Operator (ISO) power markets, and is solved in some form every year for system planning, every day for day‐ahead markets, every hour, and even every 5 minutes. It was first formulated in 1962, and formulations have changed little over the years. With advances in computing power and solution algorithms, we can model more of the constraints and remove unnecessary limits and approximations that were previously required to find a solution in reasonable time. One example is nonlinear voltage magnitude constraints that are modeled as linear thermal proxy constraints. In this paper, we refer to the full ACOPF as an ACOPF that simultaneously optimizes real and reactive power. Today, 50 years after the problem was formulated, we still do not have a fast, robust solution technique for the full ACOPF. Finding a good solution technique for the full ACOPF could potentially save tens of billions of dollars annually. Based on our literature review, we find that the ACOPF research community lacks a common understanding of the problem, its formulation, and objective functions. However, we do not claim that this literature review is a complete review—our intent was simply to capture the major formulations of the ACOPF. Instead, in this paper, we seek to clearly present the ACOPF problem through clear formulations of the problem and its parameters. This paper defines and discusses the polar power‐voltage, rectangular power‐voltage, and rectangular current‐voltage formulations of the ACOPF. Additionally, it discusses the different types of constraints and objective functions. This paper lays the groundwork for further research on the convex approximation of the ACOPF solution space, a survey of solution techniques, and computational performance of different formulations. Disclaimer: The views presented are the personal views of the authors and not the Federal Energy Regulatory Commission or any of its Commissioners. History of Optimal Power Flow and Formulations • December 2012 Page 3 Table of