Power System Uncertainty Modeling Based on Gaussian Process

Abstract

In order to solve the problem of low accuracy of parameter estimation in expectation maximization algorithm, a modeling method based on Gaussian component number reduction is proposed. Taking the nonparametric kernel density estimation results as the base Gaussian mixture model, the Gaussian mixture model with any number of Gaussian components can be established by reducing the number of Gaussian components by using the density-preserving hierarchical expectation maximization algorithm, which overcomes the problem that the expectation maximization algorithm has low parameter estimation accuracy when there are many Gaussian components. In order to reduce the burden of modeling calculation under large samples, a hierarchical modeling method based on time scale is proposed. In order to solve the problem of Gaussian component number combination explosion of independent random variables, a hierarchical modeling method of “combination-reduction” is proposed. The proposed method is tested by using measured multidimensional wind speed data and load data with complex distribution characteristics. The experimental results show that the Pearson and Spearman correlation coefficients of GMM constructed based on this method are very close to the sample data. The absolute value of Pearson correlation coefficient error is 0.03739, and the root mean square value of error is 0.02388. The absolute value of Spearman correlation coefficient error is 0.11693, and the root mean square error is 0.05797. Conclusion: The accuracy of the proposed method is significantly better than that of Gaussian mixture model and Copula function method based on expectation maximization algorithm.