Approximation of nose curves with conic sections

Abstract:
The power flow equation and the corresponding PV-curve also called nose curve play an important role in steadystate voltage stability. A traditional method to solve the power flow equation and to construct the nose curve is the Newton-Raphson-method. But the method has some stability issue at the critical point. The importance of the steady-state voltage stability limit and the bad condition at the critical point of the Newton-method make it necessary to search for other solutions. Therefore this paper presents a method to solve easy two bus systems with quadrics and conic sections. This method gives an exact and explicit solution for the nose curve in two bus situations. Additionally, there are no stability and condition problems at the critical point. A way to find steady-state voltage stability limits is also shown and discussed.