Nonparametric probabilistic load forecasting based on quantile combination in electrical power systems

Yaoyao He, Chaojin Cao, Shuo Wang, Hong Fu

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Probabilistic load forecasting (PLF) aims to predict the future uncertainties of loads to reduce the potential risks in power system planning and operation. In the increasingly complex power market environment, exploring advanced approaches to obtain more accurate PLF is still a significant topic. Optimizing individual forecasting method is no longer the only direction to improve the accuracy of load forecasting in recent years. Researchers started to focus on combination methods because of their better accuracy in most cases than a single model. There are existing combination methods designed for parametric environment, where some results are based on the certain assumption (e.g., Gaussian distribution assumption of single prediction). Combining probabilistic forecasts in nonparametric environment is rarely investigated, because modeling the combination problem without assuming distributions of parameters is hard. This paper proposes a novel combined model for probabilistic forecasting tailored to nonparametric environments, which combines multiple quantile-based models by minimizing the overall loss function composed of continuous ranked probability score (CRPS) under kernel density estimation (KDE). We define a multilayer Gaussian mixture distribution, which is an extended form of Gaussian mixture distribution that can simulate any distribution type in nonparametric environment. Based on the multilayer Gaussian mixture distribution, the combined model is further formulated into a quadratic programming problem with linear restrictions that can be solved efficiently. Case studies are performed using benchmark and competition datasets from the United States and China. The results show that our proposed method outperforms the best individual model and other existing combination methods. In summary, this paper constructs a complete theoretical framework of nonparametric probabilistic combination forecasting and proves its effectiveness in practical application.
Original languageEnglish
Article number119507
Number of pages14
JournalApplied Energy
Early online date1 Jul 2022
Publication statusPublished - 15 Sept 2022


  • Combination of quantile forecasts
  • Continuous ranked probability score
  • Kernel density estimation
  • Probabilistic load forecasting


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