See Also
Matrix A in the linear equation Ax = b is ill-conditioned if small changes in the entries of the vector b radically change the solution vector x. Ill-conditioned matrices are particularly troublesome in iterative solvers such as AC power flow algorithm implementations. One iteration of the AC power flow solves the linear equations J Δx = Δy where J is the Jacobian matrix, Δx is the vector of voltage magnitude and angle differences and Δy is the vector of real and reactive power mismatches.
A power flow Jacobian can become ill-conditioned if the system branches present reactances that differ in orders of magnitude, such as very short lines or zero impedance branches. Because the reactance of switching devices is negligible compared to that of transmission lines and transformers, modeling but a short number of switching devices in the Jacobian is prohibitive. The lower the value of the reactance, the more ill-conditioned the Jacobian will become. On the other hand, if the assumed reactance value is not too low, the solution would be inaccurate resulting in larger bus voltage angles. In Simulator switching devices that are present in Full-Topology Models are handled by Integrated Topology Processing, producing an exact and robust numerical solution.