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On-line identification of eigenvalues by use of superconducting magnetic energy storage (SMES) has been proposed. In case of the methods by use of sinusoidal power changes, imaginary parts of eigenvalues were measured in any power systems. However, real parts of them were measured only in one-machine infinite bus system. This paper describes a new method by use of sinusoidal power changes for identification of real parts of eigenvalues in multi-machine power system. Simulations in order to examine the method by use of an analogue type power system simulator are also described.