Combining Probabilistic Load Forecasts

We often find simple averaging as a plausible solution for combining point forecasts. Combining probabilistic forecasts is not that trivial. The literature of combining probabilistic load forecasts is rather limited. Previously, we developed a Quantile Regression Averaging (QRA) method to generate probabilistic load forecasts by combining point forecasts. This work is a follow up, where we combine probabilistic load forecasts to generate a more accurate probabilistic forecast. The method we proposed here is a Constrained Quantile Regression Averaging (CQRA) method, where the parameters of a quantile regression model are non-negative and sum up to 1. We applied the method to loads at both high voltage level and household level, showing better results than the benchmarks.

Among my papers published so far, this one has the shortest title.

Citation
Yi Wang, Ning Zhang, Yushi Tan, Tao Hong, Daniel Kirschen, and Chongqing Kang, "Combining probabilistic load forecasts," IEEE Transactions on Smart Grid, in press, available online. (arXiv; IEEE Xplore).

Combining Probabilistic Load Forecasts

Yi Wang, Ning Zhang, Yushi Tan, Tao Hong, Daniel Kirschen, and Chongqing Kang

Abstract

Probabilistic load forecasts provide comprehensive information about future load uncertainties. In recent years, many methodologies and techniques have been proposed for probabilistic load forecasting. Forecast combination, a widely recognized best practice in point forecasting literature, has never been formally adopted to combine probabilistic load forecasts. This paper proposes a constrained quantile regression averaging (CQRA) method to create an improved ensemble from several individual probabilistic forecasts. We formulate the CQRA parameter estimation problem as a linear program with the objective of minimizing the pinball loss and the constraints that the parameters are nonnegative and summing up to one. We demonstrate the effectiveness of the proposed method using two publicly available datasets, the ISO New England data and Irish smart meter data. Comparing with the best individual probabilistic forecast, the ensemble can reduce the pinball score by 4.39% on average. The proposed ensemble also demonstrates superior performance over nine other benchmark ensembles.