The synchronizing torque matrices for a multimachine power system are analyzed. Two representations are used: the classical and a detailed one. It is shown that steady-state instability can be identified by checking the signs of the roots of the synchronizing matrix. This method has the advantage of the applicability to any representation classical or detailed. It also does not have the disadvantage of the identification of instability by the sign of the determinant of the Jacobian suggested in the Russian literature. The idea is checked using two systems: one with five machines and the other with ten.
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