A Faster Resonance Mode Analysis Approach Based on a Modified Shifted-Inverse Power Iteration Method

Resonance mode analysis (RMA) is a promising approach for harmonic power quality and stability studies because it enables the characterization of resonances. However, RMA requires the determination of the eigenpair decomposition of the nodal admittance matrix over the frequency scan, which is a high time-consuming task. Alternative RMA based on the power iteration (PI) method reduces this computational effort. The PI method is an efficient time-saving tool because it calculates only the dominant eigenvalue of the inverted nodal admittance matrix, but convergence of the method is seriously compromised by the matrix spectrum. To remedy this, the article contributes a faster RMA approach based on a modified shifted-inverse power iteration (MSIPI) method, which reduces the computational time of the above RMA approaches without loss of accuracy in the characterization of resonance frequencies and modal impedances. The MSIPI method applies a linear shift to the nodal admittance matrix, followed by an inverse transformation to the shifted matrix to conduct the iterative method towards the smallest modulus eigenvalue over the frequency scan with a fast convergence. The proposed approach is checked for performance in ten IEEE and three synthetic test power systems. MATLAB/Simulink simulations are compared with the proposed approach.