Probabilistic voltage stability assessment of distribution networks with wind generation using combined cumulants and maximum entropy method

From the voltage stability viewpoint, a proper probabilistic analysis of the active distribution networks is essential for distribution system operator to identify and rank the weak buses of system. This paper introduces a probabilistic voltage stability index (VSI) to study the local stability of radial distribution networks including wind generation uncertainty. This index can identify the most sensitive bus to the voltage collapse. The proposed model combines the cumulants with the maximum entropy technique based on a backward/forward sweep technique. The suggested method evaluates not only the voltage magnitude, but also the voltage stability condition of each node in a probabilistic manner. Furthermore, the uncertainties of distributed generation and load demand are taken into account by this index. The proposed methodology is applied to IEEE 33-bus and 69-bus distribution test systems, and the results are interpreted. Four scenarios are studied to assess the impacts of substation voltage changes and different probability density functions of load on the distribution functions of voltage and VSI. Moreover, the effects of voltage dependent load model on the probabilistic VSI are studied. The results of different case studies have demonstrated that the proposed approach is fast and accurate.