An efficient method called the Krylov-Schur method for computing critical eigenvalues of large-scale power systems is proposed. The Krylov-Schur method is equivalent to implicitly restarted Arnoldi (IRA) method mathematically but offers two advantages. First

the numerical instability of the IRA algorithm is avoided. Second

it is easier to lock converged eigenvalues

by which subsequent computation can be carried out on subspaces with lower dimensions in less operations. By using Cayley transformation

the critical eigenvalues are mapped onto extreme eigenvalues for calculation by Krylov-Schur method. The sparsity of augmented state matrix is used to improve the efficiency of the algorithm. The proposed method has been tested on systems with orders of 2 940 and 5 727. The results show that Krylov-Schur method is highly efficient and reliable.