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Analysis of the stability of power systems following a transient disturbance involves the study of a large set of nonlinear differential equations. A new approach to the quantitative study of the transient stability of large power systems is presented, using the second method of Liapunov. A region of asymptotic stability for the postfault system is obtained through Liapunov theorems. If the initial conditions of the postfault system at the time of switching to restore normal operation lie within this region, the system will be stable. The extreme value of the time at which the conditions of the system are at the boundary of the region of asymptotic stability gives the critical switching time. A general description of a digital computer program and the results of its application to a 4-machine system are given.