A review on symbolic regression in power systems: Methods, applications, and future directions

As power systems evolve with the increasing integration of renewable energy sources and smart grid technologies, there is a growing demand for flexible and scalable modeling approaches capable of capturing the complex dynamics of modern grids. This review focuses on symbolic regression, a powerful methodology for deriving parsimonious and interpretable mathematical models directly from data. Symbolic regression is particularly valuable for power systems due to its ability to uncover governing equations without prior structural assumptions, enabling transparent and data-driven insights into nonlinear system behavior. The paper presents a comprehensive overview of symbolic regression methods, including sparse identification of nonlinear dynamics, automatic regression for governing equations, and deep symbolic regression, highlighting their applications in power systems. Through comparative case studies of the single machine infinite bus system, grid-following, and grid-forming inverters, we analyze the strengths, limitations, and suitability of each symbolic regression method in modeling nonlinear power system dynamics. Additionally, we identify critical research gaps and discuss future directions for leveraging symbolic regression in the optimization, control, and operation of modern power grids. This review aims to provide a valuable resource for researchers and engineers seeking innovative, data-driven solutions for modeling in the context of evolving power system infrastructure. • The term symbolic regression in power systems has been well-established. • A detailed explanation of various methods that provide parsimonious mathematical expressions from synthetic or real data is presented. • All applications that have been explored in this domain are covered. • A comparative study involving three different case studies including single machine infinite bus system, grid-following and grid-forming inverter is discussed. • For the first time, the automatic regression for governing equations (ARGOS) method is applied to power system case studies. • A thorough critical analysis of symbolic regression methods, including their advantages, disadvantages, research gaps, and potential applications for future directions is provided.