Dynamic stability monitoring techniques based on the stability boundary

Two alternative methods are presented for monitoring system transient stability, that is, stability of a state that results upon clearing a particular disturbance from a system. Both methods utilize the results of earlier work to define the stability boundary through its components, the stable manifolds of N-1 order equilibria. Both determine the position of the initial state on either side of the stability boundary. To reduce the computational burden, both take advantage of dynamic clustering techniques and selection of candidate or critical unstable equilibria, that is, equilibria where the stable manifold is near the initial state. Both use expansion techniques for the computation. Nevertheless, the approaches are quite different, with one method using coordinate imbedding, and the other using linear transformation of distances. Thus there are major tradeoffs in carrying out the monitoring by either method, although both promise highly efficient and practical computations