Fast computational methods for locating fold points for the power flow equations

Voltage collapse in a power system can occur following a progressive decline in voltage magnitude at the system buses and, mathematically, this phenomenon is associated with a fold bifurcation point occurring in the nonlinear algebraic equations used to model the power system. In this paper, we first discuss some of the methods used to speed up the process of detecting a fold bifurcation, focussing on designing test function methods to predict a performance index. We then discuss some iterative methods that can be used to improve the Newton iterations. In particular, we present new and efficient preconditioners of the two-level type for the Jacobian matrix. Numerical results are given using standard IEEE test bus systems.