Power system black-outs caused by a transient instability initiated by some severe disburbance must be avoided. The societal costs of such black-outs are very high. Present methods for assessing transient instabilities are generally based on global off-line methodologies. A serious technological need exists for developing a methodology for transient stability assessment (TSA), dealing with reduced parameter and observation sets such that on-line implementation becomes feasible. The value of such methodology rests in the subsequent development of: (i) new protection and control hardware for system components, and (ii) for the augmentation of stability boundaries by the active control of network elements installed for this purpose. The research is intended to impact on this need for an on-line TSA methodology. Power systems which are presently limiting transmission levels due to potential transient instabilities, could thereupon more fully utilize installed transmission capacity towards thermal rather than transient stability limits. The need for additional transmission construction on such systems may then be less critical because, in effect, more useful capacity would be available with lines presently in service.