A Model Order Reduction Method for Small-Signal Stability Analysis in Power Systems

Small-signal stability analysis focuses on evaluating the ability of the power system to maintain synchronous operation and return to steady state under small disturbances. To address the escalating computational complexity and storage requirements caused by exponential growth in system dimensionality, this paper proposes a structure-preserving low-rank balanced truncation method via ε-embedding procedure and Hermite polynomials for small-signal stability analysis of power systems. This method employs Hermite polynomials for low-rank approximation of the controllability and observability Gramians to avoid solving two large-scale Lyapunov equations to compute the Gramians, significantly reducing the computational complexity. This approach reduces system dimensionality from thousands to tens of dimensions while preserving dominant dynamic characteristics and capturing the response of the system to small disturbances. The efficiency of the proposed algorithm is demonstrated through a numerical example, with the reduced-order model preserving the important properties of the original high-order model, including time and frequency domain responses as well as eigenvalues.