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The transient-energy method is a newly developed means of checking and quantitatively evaluating the transient stability of a system of three, or possibly more synchronous machines. Each machine is represented by a constant-magnitude voltage behind a fixed reactance (usually the transient reactance) and all losses and nonsynchronous loads are assumed to be constant throughout the transient. The method is developed in this paper specifically for the 3-machine problem and is demonstrated in two examples. The potential energy required to displace the machine rotors from the relative positions which they would occupy in steady-state after-transient operation is the basic function utilized; it may be expressed as a scalar potential function of two rotor-difference angles. Two critical (zero-slope) points of the potential energy function are located graphically; those points are 1. The minimum, which is the locus of steady-state after-transient operation. 2. The minimax, the rotor-difference-angle combination at which stability may be lost with the smallest amount of transient energy. The potential energy of (2) with respect to (1) is computed and compared with the initial transient energy, calculated with respect to condition 1. If the allowable transient energy (former) exceeds the actual transient energy (latter), the system is stable.
Philip C. Magnusson (Wed,) studied this question.