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The real variant of the Jacobi-Davidson QR (RJDQR) method is a novel and efficient subspace iteration method to find a selected subset eigenvalues of a real unsymmetric matrix and is favourable to eigenanalysis for the power system small signal stability. In this study, the RJDQR method in conjunction with a flexible selection strategy of critical eigenvalue detection criteria for the small signal stability analysis is presented. Compared with the original Jacobi-Davidson QR (JDQR) method, the RJDQR method keeps the search subspace real and constructs a partial real Schur form iteratively to improve the overall performance. These strategies significantly accelerate iteration convergence and completely avoid repeated computation of the detected eigenvalues. Numerical examples demonstrate the efficiency of the RJDQR method adopting the proposed selection strategy in pursuing eigenanalysis tasks of 89- and 120-machine systems. The results show that it is capable of effectively finding critical eigenvalues in large power systems.