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The critical clearing time (CCT) often determines the maximum power output of a critical generator (CG) in a multi-machine network if transient stability is to be maintained under fault conditions. Using a time domain simulation method the CG can be identified and its maximum power limit (MPL) established. This paper proposes a novel method of using a neural network to predict the MPL of the CG. Both weighted and weightless neural networks are used and compared using Sobol sequences (Sob) to select the training patterns. The methods are tested on a 4 machine, 11 bus and a 10 machine, 39 bus New England system under variation of loading, fault location and network structures. It is shown that the permissible MPL of the CG can be established to within 5% of those obtained by time simulation.