A Physics-Guided Symbolic Regression Framework for Multi-Resolution Dynamic Equivalent Modeling of Power Systems

The transition toward renewable-dominated power systems introduces significant complexity and nonlinearity, rendering traditional mechanism-based modeling computationally prohibitive for real-time security assessment. While data-driven approaches offer computational efficiency, they fundamentally lack physical interpretability and often exhibit generalization failures under rare, large-signal disturbances due to the absence of intrinsic physical constraints. To bridge this gap, this paper proposes a Physics-Guided Symbolic Regression (PGSR) framework for constructing interpretable and robust dynamic equivalent models. The methodology embeds domain knowledge via topological masks and dimensional consistency rules to restrict the evolutionary search space to physically admissible manifolds. A multi-resolution extraction strategy based on the Pareto frontier is developed to autonomously identify both linear small-signal models and nonlinear large-signal formulations adaptable to varying analytical requirements. Furthermore, a post hoc verification stage based on Lyapunov stability theory ensures the dynamic validity and energy dissipation properties of the generated equations. A case study on the WSCC 9-bus system demonstrates that the proposed method accurately recovers the underlying Taylor-series structure of swing equations and significantly outperforms four data-driven baselines—including polynomial, kernel, and neural network models—in out-of-distribution generalization, achieving 12–42× lower trajectory error under unseen large perturbations.