Efficient Resonance Mode Analysis-Based Methodology for Resonance Studies in Multi-Terminal Transmission Grids

Resonances in transmission grids can increase harmonic voltages and currents in the presence of nonlinear loads and cause dynamic instabilities. Although frequency scan analysis is commonly used to assess resonances, resonance mode analysis (RMA) provides a more detailed understanding of resonances and is more useful for harmonic power quality and stability studies. However, RMA is a time-consuming task that involves eigenpair decomposition of the impedance matrix over a frequency range. To reduce computational effort, rapid RMA (r_RMA) based on the power iteration method, or faster RMA (f_RMA), are proposed, but these approaches can suffer from convergence issues due to the matrix spectrum. To amend this, the paper contributes a Lanczos method-based RMA (L_RMA) that applies the non-Hermitian Lanczos method to obtain the dominant eigenvalue of the impedance matrix. The accuracies, computational times and convergence rates of the four RMA-based approaches (RMA, r_RMA, f_RMA and L_RMA) are compared in ten IEEE and seven synthetic test power systems. It is verified that r_RMA and f_RMA are the best choices for small transmission grids, while L_RMA offers significant time-saving benefits in large multi-terminal transmission grids with sparse admittance matrices. Overall, the study offers an RMA-based methodology for resonance studies validated by MATLAB/Simulink simulation.