Application of Stochastically Balanced Model Reduction to Simplify LTI Models of Air Core Transformers

This study investigates the effectiveness of the Stochastically Balanced Model Reduction (SBMR) method for reducing the order of complex Linear Time-Invariant (LTI) systems, aiming to strike an optimal balance between model fidelity and computational complexity. To address this challenge, an SBMR procedure was developed by solving the Lyapunov and Riccati equations to determine the controllability and observability Gramian matrices. Subsequently, Singular Value Decomposition (SVD) was employed to extract Hankel singular values and construct projection matrices, thereby establishing a reduced-order state-space model. The experimental results obtained from a 10th-order air core transformer model reveal that the 5th-order reduced model exhibits an almost perfect match with the original system in terms of impulse response, magnitude, and phase across the entire frequency range, achieving an H∞ error of 5.795817×10⁻³. In contrast, although the 4th-order model preserves the system characteristics in certain time and frequency intervals, it demonstrates significant deviations (H∞ = 3.348487×10⁻²) in other regions. Overall, the findings confirm the feasibility and effectiveness of SBMR in simplifying LTI systems while retaining essential dynamic properties, paving the way for its potential application in modern control systems with lower computational costs.