Parameter Estimation of a Gaussian Mixture Model for Wind Power Forecast Error by Riemann L-BFGS Optimization

With the increasing penetration of wind power into the electricity grid, wind power forecast error analysis plays an important role in operations scheduling. To better describe the characteristics of power forecast error, a probability density function should be established. Compared with the Kernel density estimation method, this paper adopts the Gaussian mixture model (GMM), which is flexible enough to capture different error distribution characteristics, such as bias, heavy tail, multi-peak, and so on. In addition, for GMM parameter estimation, when dealing with a large number of multi-dimensional data sets or unbalanced overlapping mixtures, the expectation maximization (EM) algorithm shows a slower convergence speed and requires a high number of iterations. In this paper, a new L-BFGS optimization method, based on the Riemannian manifold, is used for GMM parameter estimation. Based on actual wind power forecast error data, the suitability of the model and the new optimization algorithm was verified in large, multi-dimensional data sets. The new optimization algorithm has fewer iterations than the EM algorithm, with an improved convergence speed.