Application of the Hankel-Norm Optimal Reduction Algorithm in Order Reduction of High-Order Linear Power Systems

This study focuses on addressing the computational challenges posed by high-order linear power system models, specifically targeting the New England system model, which is characterized by 66 state variables. The primary objective is to reduce the model's order while retaining its essential dynamic characteristics. To achieve this objective, the Hankel-norm Optimal Reduction (HOR) algorithm is employed, involving the resolution of Lyapunov equations to compute controllability and observability Gramians, extraction of singular value matrices, and execution of structural transformations to determine the optimal reduced order. Evaluation through impulse response and Bode analyses indicates that reduced-order models of orders 10, 11, and 12 closely approximate the original system's behavior. Notably, the 12th-order model demonstrates superior accuracy, exhibiting norm errors of approximately 2.03×10⁻⁴, 1.39×10⁻⁴, and 1.73×10⁻⁴ for the 10th, 11th, and 12th orders, respectively. These findings suggest that the HOR algorithm effectively simplifies the model's complexity while ensuring robust control performance and precise dynamic analysis. The results of this study have significant implications for real-time simulation and the integration of reduced-order models with adaptive control and data-driven optimization strategies in modern power grids.