Implementation of two statistical methods for Ensemble Prediction Systems in the management of electrical systems

Abstract

This paper presents a study of two statistical post-processing methods implemented on forecasts of Meteo-France temperatures provided by the ensemble prediction system (EPS) The results are useful in the management of electricity consumption at EDF France. Those methods are the Best-Member Method (BMM) proposed by Fortin (2006), and the Bayesian Model Averaging method (BMA) proposed by Raftery (2004). The idea behind the BMM is to design for each lead time in the data set the best forecast among all k forecasts provided by the temperature prediction system, to construct an error pattern using only the errors made by those "best members" and to then "dress" all the members of the initial prediction system with this error pattern. The BMA method is a statistical method which combines predictive distributions from different sources. The BMA predictive probability density function (PDF) of the quantity of interest is a weighted average of PDFs centered on the bias-corrected forecasts, where the weights are equal to posterior probabilities of the models generating the forecasts and reflect the accuracy (skill) of the models over the training period. The resulting forecasts implemented on our data set are compared with one another and compared to the initial forecasts, using scores which measure the accuracy and/or the spread of the EPS: the Mean Absolute Error (MAE), the Root Mean Square Error (RMSE), the Ignorance Score, the Continuous Rank Probability Score (CRPS), the Talagrand Diagram, the Bias and the Mean. The purpose is to improve the probability density function of the forecasts, preserving at the same time the quality of the mean forecasts. The presentation is accessible to readers with an intermediate level of statistics.