Risk estimation of the distance to voltage instability using a second order approximation of the saddle-node bifurcation surface

Prevention of voltage instability in electric power systems is an important objective that the system operators have to meet. Under certain circumstances the operating point of the power system may start drifting towards the set of voltage unstable operating points. If no preventive measures are taken, after some time, the operating point may eventually become voltage unstable. It will thus be preferable to have a measure of the risk of voltage collapse in future loading states. This paper presents a novel method for estimation of the probability distribution of the load-space distance to the point where voltage instability induced by saddle-node bifurcation occurs. Another result of the method is an estimate of the probability distribution of the time to voltage instability for a power system with uncertain future loading scenarios. The method uses a second order approximation of the saddle-node bifurcation surface. The proposed method can be used in power system security assessments.