This work proposes a quantile regression neural network based on a novel constrained weighted quantile loss (CWQLoss) and its application to probabilistic short and medium-term electric-load forecasting of special interest for smart grids operations. The method allows any point forecast neural network based on a multivariate multi-output regression model to be expanded to become a quantile regression model. CWQLoss extends the pinball loss to more than one quantile by creating a weighted average for all predictions in the forecast window and across all quantiles. The pinball loss for each quantile is evaluated separately. The proposed method imposes additional constraints on the quantile values and their associated weights. It is shown that these restrictions are important to have a stable and efficient model. Quantile weights are learned end-to-end by gradient descent along with the network weights. The proposed model achieves two objectives: (a) produce probabilistic (quantile and interval) forecasts with an associated probability for the predicted target values. (b) generate point forecasts by adopting the forecast for the median (0.5 quantiles). We provide specific metrics for point and probabilistic forecasts to evaluate the results considering both objectives. A comprehensive comparison is performed between a selection of classic and advanced forecasting models with the proposed quantile forecasting model. We consider different scenarios for the duration of the forecast window (1 h, 1-day, 1-week, and 1-month), with the proposed model achieving the best results in almost all scenarios. Additionally, we show that the proposed method obtains the best results when an additive ensemble neural network is used as the base model. The experimental results are drawn from real loads of a medium-sized city in Spain.
Keywords: deep learning; deep learning additive ensemble model; machine learning; quantile forecasting; short and medium-term electric-load forecasting.