Probabilistic evaluation for static voltage stability for unbalanced three-phase distribution system

To investigate the impact of the randomness of renewable energy generation on distributed network, the authors propose a non-linear three-phase maximum loadability model. Considering uncertainty such as wind power generation and load forecasting deviation, a probabilistic evaluation of static voltage stability for distributed network is presented based on cumulants method. Correlations between adjacent wind farms are also considered. Maximal load increment models of three-phase balanced/unbalanced power system are solved by improved self-adaptive particle swarm optimisation algorithm. Two approximation expansions named Cornish-Fisher expansion and Gram-Charlier expansion are employed to obtain probability distribution of random variables. Relation of probabilistic performances including means and variances between balanced system and unbalanced system could be obtained. 25-bus/33-bus unbalanced system and 33-bus balanced system are studied as examples to validate effectiveness of their proposed method, and results based on cumulants method are compared with Monte Carlo simulations.