Modeling and Analysis of Electromagnetic Oscillations in Power Networks: A Matrix Pencil Approach

Power networks, while transmitting electromagnetic energy, also serve as channels for the propagation of both free and forced oscillations. To effectively understand and control these oscillations, it is crucial to model and analyze the dynamics of power networks, identifying potential oscillation risks. In this paper, we develop a matrix pencil-based dynamical model for general passive power networks, focusing on free and forced oscillation analysis. We discuss the underlying principles, model assumptions, and model formulation in detail. Specifically, the matrix pencil models for lumped-parameter transformers, distributed-parameter transmission lines, and the entire power network with arbitrary topology are comprehensively analyzed. The relationships between the dynamic model, the excitation source, network resonance, and the frequency-domain equivalent impedance are explored. Based on this model, an eigen-analysis method is developed to calculate critical modes, associated eigen-structures, and impedance. Comparative numerical results from the eigen-analysis method, analytical solutions, and EMT simulations are presented to validate the proposed approach.