Probabilistic Load Flow Calculation for Grid-connected Wind Power Systems based on the Rosenblatt Inverse Transform and Improved Maximum Entropy Expansion

This paper proposes an improved probabilistic load flow (PLF) calculation for wind power grid connection systems (WPGCS) based on the cumlant method (CM), Rosenblatt inverse transformation (RIT) and an improved maximum entropy expansion (IMEE). The proposed method is designed to accurately capture the effects of wind power uncertainty and correlation, thereby establishing a comprehensive framework for probabilistic load flow analysis. First,the adaptive reflectance kernel density estimation (ARKDE) is introduced to construct the probabilistic model of wind speed, explicitly accounting for its bounded characteristics and improving the accuracy of dependence modeling using Copula function. Second, the RIT is applied to accurately transform wind speed correlation samples, satisfying the prerequisites of the CM. As a key step, the Gaussian function is incorporated into the maximum entropy model to expand distributions of output state variables, thereby elucidating how the configuration of input random variables such as wind speed distribution influences the resulting distributions of output state variables. Additionally, the constraints of the maximum entropy model are converted from integral to algebraic forms, which enhances computational efficiency. Finally, the proposed method is validated on the IEEE-30 system integrated with integrated wind farms. The results demonstrate the effectiveness and accuracy of the method