Linear Power System Modeling and Analysis Across Wide Operating Ranges: A Hierarchical Neural State-Space Equation Approach

Developing a unified small-signal model for modern, large-scale power systems that remains accurate across a wide range of operating ranges presents a formidable challenge. Traditional methods, spanning mechanistic modeling, modal identification, and deep learning, have yet to fully overcome persistent limitations in accuracy, universal applicability, and interpretability. In this paper, a novel hierarchical neural state-space equation approach is proposed to overcome these obstacles, achieving strong representation, high interpretability, and superior adaptability to both system scale and varying operating points. Specifically, we first introduce neural state-space equations integrated with virtual state observers to accurately characterize the dynamics of power system devices, even in the presence of unmeasurable states. Subsequently, a hierarchical architecture is designed to handle the modeling complexity across a wide range of operating conditions, flexibly decoupling device and grid models to effectively mitigate the curse of dimensionality. Finally, a set of spatiotemporal data transformations and a multi-stage training strategy with a multi-objective loss function is employed to enhance the models efficiency and generalization. Numerical results on the two-machine three-bus system and the Guangdong Power Grid verify the superior performance of the proposed method, presenting it as a powerful new tool for small-signal stability analysis.