Fast Cumulant Method for Probabilistic Power Flow Considering the Nonlinear Relationship of Wind Power Generation

Currently, the increasing wind power penetration, with consequent randomness and variability, presents great challenges to power system planning and operation. Probabilistic power flow (PPF) has been developed to calculate the power flow under uncertain circumstances. However, the current wind power models are subject to specific probability distributions, limiting their accuracies in wider applications. Additionally, the cumulant method (CM)-based PPF, if nonlinear relationship is considered in, would face an impractically high computational complexity. To address these problems in modeling and cumulant calculation, this article proposes a novel generalized density/distribution fitting method (GDFM) combining with the Copula function to establish a joint probability model for wind power generation. A special impulse- mixed probability density (IMPD) integration method is also introduced to derive the input cumulants from the model. Finally, a fast cumulant method (FCM) is proposed to reduce the computational burden of output cumulant calculation while retaining a high accuracy in a nonlinear context. Case study on the IEEE-118 test system validates the effectiveness of the proposed methods, and a real application to a provincial power grid in China provides some useful power flow risk information for decision making. The whole FCM-based PPF scheme can be helpful for future power flow examination in power system planning and operation.