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A new methodology for the calculation of critical eigenvalues in the small signal stability analysis of large power systems is presented in this paper. The Jacobi-Davidson method, which is a very recent subspace iteration method, is suggested to compute the rightmost eigenvalues. The method is attractive as a new powerful technique for solving a variety of large sparse eigenproblems. The method combined Davidson's idea of taking a different subspace with Jacobi's idea of restricting the search of an update to the subspace orthogonal to current eigenvector approximation. An exact solution of the correction equation leads to quadratic convergence for the selected Ritz values. Based on the iterative construction of a partial Schur form and the effective restart, the algorithms are suitable for the efficient computation of a large number of eigenvalues and clustering eigenvalues. The proposed method is applied to a practical 46-machine system, and the results of the experiment are described.