Day-Ahead Hierarchical Probabilistic Load Forecasting with Linear Quantile Regression and Empirical Copulas

In the smart grid era, high granular data play an important role in providing an enormous amount of information for industry and commerce, both temporally and spatially. With massive data, a hierarchical structure can be constructed, containing load series at diverse levels. With the fluctuation and uncertainty of power supply and demand increasing rapidly, hierarchical probabilistic load forecasting is necessary for a hierarchy formed by power system network, which can provide comprehensive information on electricity consumption at different levels. System operators or power market participants can make coherent decisions based on coherent forecasting. The challenge for hierarchical probabilistic load forecasting is how to produce probabilistically coherent forecasts. In order to simplify the prediction procedure and improve the prediction accuracy, an effective approach that could generate probabilistically coherent forecasts for a hierarchy is introduced in this paper. The proposed methodology has three major achievements: 1) a naive multiple linear regression model is proposed for bottom-level series; 2) a novel approach of combining quantile regression and empirical copulas is proposed to estimate the joint distribution of random variables; 3) to improve the prediction accuracy, a weighted correction method based on constrained quantile regression is introduced to adjust predictive distributions at the bottom level. In case of studies, the effectiveness of our proposed method is verified by using two public datasets. Compared with four benchmarks, evaluation results show that the proposed approach makes better performance.