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

Abstract

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 computation 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 percent more efficient than the conventional Newton-Raphson in finding a pair of close solutions in ill-conditioned power systems.

A Sufficient Condition for Power Flow Insolvability With Applications to Voltage Stability Margins

“…Other work on sufficient conditions for power flow solvability includes [7], which focuses on the decoupled (active powervoltage angle, reactive power-voltage magnitude) power flow model. Reference [8] describes a modified Newton-Raphson iteration tailored to the type of ill-conditioning that can appear in power systems problems. While convergence to a solution may be judged a constructive sufficient condition to demonstrate solvability, such approaches do not escape the fundamental limitations of a locally convergent iteration.…”