The Cumulant Tensor Framework for the Probabilistic Power Flow

This paper upgrades the univariate cumulant based approach to solve the probabilistic power flow (PPF) by considering higher-order joint and univariate cumulants in the tensor form. The historical data of wind farms and loads are used to derive their statistical characteristics in the tensor form. The DC formulation of the power flow equations coupled with the principle of maximum entropy are employed to reconstruct the distribution functions of the branch power flow. The robustness of the proposed method is verified comparing with the empirical distribution obtained by the Monte Carlo simulation. The comparison with the traditional method of the univariate cumulants combined with the covariance matrix demonstrated that joint cumulants of order higher than two cannot be neglected when there is a high degree of dependence between random variables or their marginal distributions are far from normal.