A generative hidden Markov model of the clear-sky index

Abstract

Clear-sky index (CSI) generative models are of paramount importance in, e.g., studying the integration of solar power in the electricity grid. Several models have recently been proposed with methodologies that are related to hidden Markov models (HMMs). In this paper, we formally employ HMMs, with Gaussian distributions, to generate CSI time-series. The authors propose two different methodologies. The first is a completely data-driven approach, where an HMM with Gaussian observation distributions is proposed. In the second, the means of these Gaussian observation distributions were predefined based on the fraction of time of bright sunshine from the site. Finally, the authors also propose a novel method to improve the autocorrelation function (ACF) of HMMs in general. The two methods were tested on two datasets representing two different climate regions. The performance of the two methodologies varied between the two datasets and among the compared performance metrics. Moreover, both the proposed methods underperformed in reproducing the ACF as compared to state-of-the-art models. However, the method proposed to improve the ACF was able to reduce the mean absolute error (MAE) of the ACF by up to 19%. In summary, the proposed models were able to achieve a Kolmogorov-Smirnov test score as low as 0.042 and MAE of the ACF as low as 0.012. These results are comparable with the state-of-the-art models. Moreover, the proposed models were fast to train. HMMs are shown to be viable CSI generative models. The code for the model and the simulations performed in this paper can be found in the GitHub repository: HMM-CSI-generativeModel.