Uncertain power flow calculation and global sensitivity analysis considering parametric probability-boxes

Probabilistic power flow is one of the fundamental tools for assessing the impacts of uncertainties on the operating states of power systems. However, this analysis requires sufficient historical data to obtain precise probability distributions of input variables, which may not be met in practical engineering problems. In this paper, input variables with insufficient data are represented by parametric probability boxes (p-boxes), i.e., probability distributions with imprecise parameters. In order to facilitate the uncertain power flow calculation with p-boxes, a polynomial chaos expansion-based method is developed. Moreover, the interval-valued Borgonovo index is proposed for global sensitivity analysis and to identify the input variables that have critical impacts on systems. The simulations in IEEE 14-bus and 118-bus systems verify the accuracy and efficiency of the proposed method by comparing it with the conventional double-loop sampling method.