Computation of the Minimum Voltage Stability Margin Considering Loading Uncertainties and Contingency Analysis

This paper presents a hybrid method to calculate the minimum Voltage Stability Margin (VSM) for voltage security assessment of electric power systems, considering uncertainties in the Load Growth Direction (LGD). First, a sampling algorithm was developed (based on the Cross-Entropy method, which samples by importance) in order to obtain a set of critical growth directions that violate the predefined limits for the VSM. After that, the Differential Evolution method was applied to develop an algorithm that constructs a stratified sample set, starting from the previous set of critical directions as its initial population. The combination of both algorithms is capable of identifying the minimum voltage stability margin considering the most critical LGD associated to a particular base case of the system, which is the main contribution of this paper. Furthermore, the algorithms were extended to perform contingency analysis, in such a way that they can deal with the conditions that actually pose the highest threats to voltage stability in electric power systems. The method was tested and validated on a reduced Brazilian south-southeast system model composed of 107 buses.