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This paper considers the use of a discrete supplementary control for transient stability enhancement of multimachine power systems. The principle advantage of the method presented in this paper is that off-line compuations are used. This permits the application of the supplementary control of a ``multimachine'' power system. The designation ``multimachine'' is used in this context to denote systems of up to three machines; for practical systems containing more than three machines, appropriate model order reduction is suggested. Supplementary controls differ from primary controls in that they are only used during disturbances rather than continuously. Attention is focused on the insertion of braking resistors and a specially designed dynamic programming algorithm is described for optimal resistor switching. The switching strategy is computed off-line so that the online computational requirements are minimal. The contribution of this paper is in the area of multimachine control and, in particular, a power system emergency state control. Topics concerning control models, optimization criteria and characteristics of discrete supplementary controls have been addressed. Control strategies are evaluated through digital and analog simulation involving a ten machine test system. A systematic approach to the optimization of multi-stage decision processes, called dynamic programming, was introduced by Bellman in the 1950' s [1-2]. Dynamic programming principles provide a perspective for examining optimization problems which lead to iterative functional equations. These equations are efficiently solved by using a digital computer and employing a dynamic programming computational procedure described by Larson .