Fast method to determine an area of vulnerability for stochastic prediction of voltage sags

A fast method determines the areas of vulnerability for sensitive loads in a mesh network. The area of vulnerability for a sensitive load is essential for the estimation of the expected number of voltage sags from the utility system. In general, an area of vulnerability is determined by performing a short-circuit analysis at many different points on lines and buses. Such a method is inefficient for identifying the area of vulnerability in a large mesh network. Two equations of the voltage-sag magnitudes and phase-angle jumps due to faults along a line are derived by using the impedance matrix building algorithm. By using the derived equation of voltage-sag magnitude, the area of vulnerability can be determined without performing short-circuit analysis. A fast and efficient numerical method to identify the area of vulnerability is also described. The method developed was used to determine the areas of vulnerability for three sensitive loads in the IEEE 30-bus test system.