Optimal Power Flow: A Review of State-of-the-Art Techniques and Future Perspectives

The Optimal Power Flow (OPF) problem has become increasingly pivotal in the planning and operation of modern power systems. With the expansion of the grid scale, the advent of smart grid technologies, and the unpredictable nature of renewable energy sources (RESs), interest in OPF has surged. These challenges with new energy storage have introduced a heightened level of uncertainty into the power system's operation as well as planning. Because of this, OPF is seen as an important tool for achieving different goals, such as optimizing the distribution of resources, making electrical networks more efficient, and so on. However, the OPF problem is inherently difficult to solve because of its non-linear characteristics. Different constraints and limitations intrinsic to real power system grids further accentuate this complexity. Moreover, modern power systems have incorporated new constraints, which make the OPF problem more complex in terms of mathematical formulation and solution. This paper offers a comprehensive and foundational review of OPF, covering the main concept, mathematical formulation, OPF types, comprehensive OPF optimization problem concepts, and the various methods developed to solve it. Additionally, it explores the evolution of these methods from conventional approaches to advanced and recent techniques, including mathematical methods and artificial intelligence methods, which include metaheuristic (search-based) and machine learning algorithms (data-driven). The paper also discusses various types of convex relaxation methods in depth. Ultimately, the paper highlights key gaps, challenges, and opportunities for future research.