Probabilistic assessment of static voltage stability in distribution systems considering wind generation using catastrophe theory

With increasing penetration of distributed generations, the importance of the voltage stability assessment of distribution networks has been increased. Considering this situation, a probabilistic model is proposed to evaluate the voltage stability of distribution network integrating wind turbine (WT) units. With this intention, a probabilistic voltage stability index (PVSI) of a radial distribution system with wind power generation is presented. This index investigates the probabilistic risk of voltage collapse for all the buses of system considering uncertainty of WTs. Therefore, the most sensitive bus to the voltage collapse can be identified. The problem model is based on the catastrophe theory that can find the bifurcation point of system. Three-point estimation method is employed to calculate the statistical moments of voltage and PVSI of nodes. Moreover, to estimate the cumulative distribution function of output random variables, the Cornish-Fisher series are used. The performance of the probabilistic index is tested on the IEEE 69-bus radial distribution system where different load models are considered. The results demonstrate that the PVSI can accurately predict the voltage instability condition of the system.