A Review on Symbolic Regression in Power Systems: Methods, Applications, and Future Directions

TL;DR

The paper surveys symbolic regression approaches—SINDy, ARGOS, and deep SR—for data-driven modeling of nonlinear power-system dynamics, emphasizing their mechanisms, strengths, and limitations. Through comparative case studies on SMIB, grid-following, and grid-forming inverter dynamics, it shows SINDy delivering the best transient accuracy and computational efficiency, ARGOS offering robust performance with uncertainty quantification, and deep SR delivering flexible, interpretable models at higher computational cost. It also highlights data-quality challenges, real-world validation gaps, and deployment hurdles in large-scale grids, proposing targeted research directions to enhance robustness, scalability, and practicality. The work aims to guide researchers and engineers toward effective, interpretable data-driven modeling for modern power grids while identifying key gaps to accelerate real-world adoption.

Abstract

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. 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 inverter, 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.

Figures (7)

• Figure 1: Diagram representing the workflow for model identification using symbolic regression methods, from collecting real or synthetic data to identifying the system in terms of mathematical expressions.
• Figure 2: One-line diagram of a single-machine infinite bus system with parameters in p.u.: R=0.05, X=0.3, $\overline{V_1}$=1.05, $\overline{V_2}$=1.0, P=0.8, $X'_d$=0.2 9308946.
• Figure 3: Performance comparison of SR methods applying to the generated dataset for single machine infinite bus system.
• Figure 4: Performance comparison of SR methods applied to the generated dataset for a grid-following inverter, focusing on the current in the d-axis ($i_d$).
• Figure 5: Performance comparison of SR methods applied to the generated dataset for a grid-following inverter, focusing on the current in the q-axis ($i_q$).