A test for the existence of solutions in ill-conditioned power systems

A complete analytical study of the invariant manifolds for the Newton-Raphson solution of the power flow equations is presented. Based on these results, a new test is developed to reduce the computational effort of finding the solutions to ill-conditioned power systems. A detailed study of some well-known test systems clearly indicates that the new method is at least 50% more efficient than the conventional Newton-Raphson method in finding a pair of close solutions in ill-conditioned power systems