Reinforcement Learning Based Symbolic Regression for Load Modeling

TL;DR

The paper addresses the challenge of deriving accurate, interpretable dynamic load relationships in power systems with increasing variability. It introduces an Actor-Critic symbolic regression framework that builds a fixed-depth, trainable expression tree where the Actor selects operators and the Critic optimizes coefficients, guided by a risk-seeking policy gradient. A candidate-pool mechanism and gradient-based fine-tuning enable efficient search and robust generalization, achieving lower RMSE than baselines such as ANN, ZIP, and Polynomial Regression across bus and line fault scenarios. This approach provides a scalable, interpretable alternative for dynamic load modeling, with practical implications for stability analysis and system planning.

Abstract

With the increasing penetration of renewable energy sources, growing demand variability, and evolving grid control strategies, accurate and efficient load modeling has become a critical yet challenging task. Traditional methods, such as fixed-form parametric models and data-driven approaches, often struggle to balance accuracy, computational efficiency, and interpretability. This paper introduces a novel symbolic regression algorithm based on the Actor-Critic reinforcement learning framework, specifically tailored for dynamic load modeling. The algorithm employs a trainable expression tree with controlled depth and a predefined set of operators to generate compact and interpretable mathematical expressions. The Actor network probabilistically selects operators for the symbolic expression, while the Critic evaluates the resulting expression tree through a loss function. To further enhance performance, a candidate pool mechanism is implemented to store high-performing expressions, which are subsequently fine-tuned using gradient descent. By focusing on simplicity and precision, the proposed method significantly reduces computational complexity while preserving interpretability. Experimental results validate its superior performance compared to existing benchmarks, which offers a robust and scalable solution for dynamic load modeling and system analysis in modern power systems.

Figures (4)

• Figure 1: Overview of the proposed actor-critic symbolic regression algorithm.
• Figure 2: Computational rule of a binary tree.
• Figure 3: Performance evaluation of the proposed symbolic regression algorithm under bus fault scenario.
• Figure 4: Performance evaluation of the proposed symbolic regression algorithm under line fault scenario.