Sequential computation of the complete eigensystem for the study zone in small signal stability analysis of large power systems

A efficient method is reported for the calculation of the complete set of eigenvalues and eigenvectors associated with the state variables in a specified study zone of a large power system, linearized for the purpose of small-signal stability studies. The computation is performed in two stages. Stage 1 starts with a set of first guesses for the eigenvalues, and reduces the full system model to the size of the nucleus for which a QR algorithm gives all eigenvalues and eigenvectors. These are the starting values for stage 2, which uses augmented system state equations to refine the eigenpairs, by means of the inverse power method, Newton´s method and deflection techniques. A computer implementation called STEPS (Sequential Two-stage Eigenanalysis for Power Systems) is based on the described procedures. Illustrative results are given for a 117-bus test system with 30 machines