Tracing of critical eigenvalues for power system analysis via continuation of invariant subspaces and projected Arnoldi method

The continuation of invariant subspaces algorithm combined with projected Arnoldi method is presented to trace the critical (rightmost or least damping ratio) eigenvalues for the power system stability analysis. A predictor-corrector method is applied to calculate the critical eigenvalues trajectories as power system parameters change. The method can handle eigenvalues with any multiplicity during the trace processes. The subspace dimension inflation and deflation is applied to deal with eigenvalue overlap. And the subspace update is proposed by an efficient projected Arnoldi method which can utilize known information from the traced eigenvalues and subspaces.