Probabilistic power flow method based on monotonic consistency interpolation and enhanced sample permutation

As a crucial method for analyzing the randomness of renewable energy generation and the uncertainty of power flows, the probabilistic power flow (PPF) calculation provides reliable foundations for power flow optimization and security domain analysis for scenarios with high penetration of renewable energy. This paper proposes an improved PPF method, which addresses the common issues of low accuracy and limited applicability in the traditional PPF method. First, considering the random variables are typically represented as multiple discrete points in real world, the proposed PPF method utilizes a monotonic consistency-based piecewise cubic Hermite interpolating polynomial (MCBP) method to fit the discrete points of random variables, thereby obtaining the cumulative distribution function with well-behaved mathematical performance for random variables and enhancing the scalability of the proposed method. Second, to improve the accuracy of the PPF calculation, a novel correlation analysis method named enhanced sample permutation (ESP) is proposed to reduce the correlation analysis errors that are generally overlooked by the existing PPF algorithms. Finally, the performance of the proposed method and error metrics are evaluated using multiple case studies, showing its advantages in accuracy and computational efficiency with the low sample size.