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This paper describes a method for analyzing the direct stability of a multi-machine system that consists of three machines and one resistive superconductive fault current limiter (SFCL). The resistive SFCL, which affects the transient stability of a multi-machine power system, must be taken into account. In order to evaluate the transient stability in the power system, a direct stability analysis that has rapid prediction stability is used. Although the equal-area criterion method is useful in determining the stability as a transient stability evaluation method, the method is only applicable to a one-machine system connected to an infinite bus or to a two-machine system. Therefore, the transient energy function (TEF) should be constructed. Using the TEF, the effect of the SFCL in the multi-machine system can be identified by increasing the critical clearing time.