Efficient computation of the stability boundary for a machine connected to a quasi-infinite busbar

We seek to determine the transient stability of a synchronous machine connected to a quasi-infinite busbar. We compute the boundaries of the transient basins of boundedness (TBB) by a judicious application of the inverse Poincare map to the boundary of the region of bounded solutions. This approach does not require the stringent assumptions often required by the Lyapunov methods used in power engineering, such as first-swing stability, and lossless power transmission and undamped machine dynamics. For a given level of resolution represented by an N × N grid of initial conditions (initial states), the new algorithm, referred to as the Boundary Mapping (BM) algorithm, is expected to be N times faster than the brute-force integration of the swing equation. Often, N is about few hundreds, and hence, the new algorithm is expected to be faster by two orders of magnitude for the same level of resolution. Moreover, the BM algorithm can compute the boundary exactly if needed.