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

Abstract

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.