In steady-state voltage stability analysis, as load increases toward a maximum, conventional Newton-Raphson power flow Jacobian matrix becomes increasingly ill-conditioned so power flow fails to converge before reaching maximum loading. A method to directly eliminate this singularity reformulates the power flow problem by introducing an AQ bus with specified bus angle and reactive power consumption of a load bus. For steady-state voltage stability analysis, the angle separation between the swing bus and AQ bus can be varied to control power transfer to the load, rather than specifying the load power itself. For an AQ bus, the power flow formulation is only made up of a reactive power equation, thus reducing the size of the Jacobian matrix by one. This reduced Jacobian matrix is nonsingular at the critical voltage point, eliminating a major difficulty in voltage stability analysis for power system operations.
STATEMENT OF GOVERNMENT INTEREST
 The invention described herein may be manufactured and used by or for the Government for governmental purposes without the payment of any royalty thereon and was supported in part by the DOE/CERTS award 7040520 and in part by the Engineering Research Center Program of the National Science Foundation and the Department of Energy under NSF Award Number EEC-1041877 and the CURENT Industry Partnership Program.