Appendix for Nonparametric Multivariate Probability Density Forecast in Smart Grids With Deep Learning

TL;DR

This paper introduces a nonparametric deep learning-based multivariate density forecasting model for smart grids that captures distributions and correlations without prior assumptions, demonstrating superior performance in various scenarios.

Contribution

It presents a novel neural network approach for joint density forecasting that does not rely on predefined distributional assumptions, enhancing accuracy and flexibility.

Findings

Outperforms existing models in accuracy and correlation capturing

Effective in short-term wind speed and power forecasting

Accurately predicts electricity load with reliable intervals

Abstract

This paper proposes a nonparametric multivariate density forecast model based on deep learning. It not only offers the whole marginal distribution of each random variable in forecasting targets, but also reveals the future correlation between them. Differing from existing multivariate density forecast models, the proposed method requires no a priori hypotheses on the forecasted joint probability distribution of forecasting targets. In addition, based on the universal approximation capability of neural networks, the real joint cumulative distribution functions of forecasting targets are well-approximated by a special positive-weighted deep neural network in the proposed method. Numerical tests from different scenarios were implemented under a comprehensive verification framework for evaluation, including the very short-term forecast of the wind speed, wind power, and the day-ahead forecast of the aggregated electricity load. Testing results corroborate the superiority of the proposed method over current multivariate density forecast models considering the accordance with reality, prediction interval width, and correlations between different random variables.