Nataf-KernelDensity-Spline-based point estimate method for handling wind power correlation in probabilistic load flow

Abstract

Modern power systems integrated with renewable energies (REs) contain many uncertainties. The proposed method introduces a novel approach to address the challenges associated with wind power generation uncertainty in probabilistic load flow (PLF) studies. Unlike conventional methods that use wind speed as an input, the paper advocates for utilizing wind generator output power (WGOP) as an input to the point estimate method (PEM) in solving PLF. The uniqueness lies in recognizing the distinct behavior of wind power uncertainty, where not all random samples of wind speed contribute to actual wind power production. The paper suggests a Nataf-KernelDensity-Spline-based PEM, combining the Nataf transformation, Kernel density estimation (KDE), and cubic spline interpolation. This innovative integration effectively manages wind power correlation within the analytical framework. By incorporating spline interpolation and kernel density estimation into the traditional PEM, the proposed method significantly enhances accuracy. To validate the effectiveness of the proposed approach, the method is applied to IEEE-9 and IEEE-57 bus test systems, considering uncertainties related to load, wind power generation (WPG), solar power generation (SPG), and conventional generator (CoG) outages. Comparative analysis with Monte Carlo simulation (MCS) results demonstrates that the proposed method outperforms the conventional PEM in terms of accuracy. Overall, the paper contributes a pioneering solution that not only highlights the importance of using WGOP as an input in PLF but also introduces a sophisticated method that surpasses traditional approaches, improving accuracy in power system studies involving renewable energy integration. The accuracy of the proposed method is validated by comparing its results with those obtained through Monte Carlo simulation (MCS), where the proposed method yields more accurate results than the conventional PEM.