This research has developed a procedure in which the transient energy margin, for a multimachine power system obtained by the transient energy function method, is related to the apparent impedance of a line protected by the out-of-step relay;In this procedure, only the multimachine system parameters are used, and the conventional intermediate step of forming a two-machine equivalent is eliminated;Two types of energy-based criteria are derived to relate the apparent impedance to the transient energy margin obtained: (i) with the original multimachine system, and (ii) with the inertial equivalents of two groups of machines separated by the line protected by the out-of-step relay;An approximation of the post-disturbance trajectory is developed for the rotor angle positions between the instance of disturbance removal and the controlling u.e.p. Two such approximations are investigated: (i) a linear trajectory, and (ii) the Fourier series approximation. The energy-based criteria are then applied along this approximated trajectory. A technique for generating the swing impedance locus is also presented;The method is tested for a loss of generation distrubance on a 23-generator, 211-bus equivalent of the Florida Power & Light Company network. The results obtained are compared with time simulation results.