Basis-adaptive sparse polynomial chaos expansion for probabilistic power flow

This paper introduces the basis-adaptive sparse polynomial chaos (BASPC) expansion to perform the probabilistic power flow (PPF) analysis in power systems. The proposed method takes advantage of three state-of-the-art uncertainty quantification methodologies reasonably: the hyperbolic scheme to truncate the infinite polynomial chaos (PC) series; the least angle regression (LARS) technique to select the optimal degree of each univariate PC series; and the Copula to deal with nonlinear correlations among random input variables. Consequently, the proposed method brings appealing features to PPF, including the ability to handle the large-scale uncertainty sources; to tackle the nonlinear correlation among the random inputs; to analytically calculate representative statistics of the desired outputs; and to dramatically alleviate the computational burden as of traditional methods. The accuracy and efficiency of the proposed method are verified through either quantitative indicators or graphical results of PPF on both the IEEE European Low Voltage Test Feeder and the IEEE 123 Node Test Feeder, in presence of more than one hundred correlated uncertain input variables.