Forecasting Intra Day Load Curves Using Sparse Functional Regression
- 1.7k Downloads
In this paper we provide a prediction method, the prediction box, based on a sparse learning process elaborated on very high dimensional information, which will be able to include new – potentially high dimensional – influential variables and adapt to different contexts of prediction. We elaborate and test this method in the setting of predicting the national French intra day load curve, over a period of time of 7 years on a large data basis including daily French electrical consumptions as well as many meteorological inputs, calendar statements and functional dictionaries. The prediction box incorporates a huge contextual information coming from the past, organizes it in a manageable way through the construction of a smart encyclopedia of scenarios, provides experts elaborating strategies of prediction by comparing the day at hand to referring scenarios extracted from the encyclopedia, and then harmonizes the different experts. More precisely, the prediction box is built using successive learning procedures: elaboration of a data base of historical scenarios organized on a high dimensional and functional learning of the intra day load curves, construction of expert forecasters using a retrieval information task among the scenarios, final aggregation of the experts. The results on the national French intra day load curves strongly show the benefits of using a sparse functional model to forecast the electricity consumption. They also appear to meet quite well with the business knowledge of consumption forecasters and even shed new lights on the domain.
KeywordsOrdinary Little Square Cloud Cover Meteorological Variable Load Curve Sparse Approximation
The authors thank RTE for the financial support through two industrial contracts, LPMA for hosting our researches, and Karine Tribouley for taking part of an earlier elaboration of this project.
- 1.Antoniadis, A., Brossat, X., Cugliari, J., & Poggi, J. M. (2010). Clustering functional data using wavelets. In Proceedings of the 19th international conference on computational statistics, COMPSTAT, Paris, 697–704.Google Scholar
- 4.Catoni, O. (2004). Statistical learning theory and stochastic optimization, volume 1851 of Lecture notes in mathematics. Berlin: Springer.Google Scholar
- 5.Chakhchoukh, Y., Panciatici, P., & Bondon, P. (2009). Robust estimation of SARIMA models: Application to short-term load forecasting. In IEEE workshop on statistical signal processing, CardiffGoogle Scholar
- 7.Dalalyan, A. S., & Tsybakov, A. B. (2008). Aggregation by exponentiel weighting, sharp oracle inequalities and sparsity. In COLT, Helsinki (pp. 97–111).Google Scholar
- 12.Kerkyacharian, G., Mougeot, M., Picard, D., & Tribouley, K. (2009). Learning out of leaders. In Multiscale, nonlinear and adaptive approximation (Lecture notes in computer science). Berlin: Springer.Google Scholar
- 13.Lefieux, V. (2007). Modèles semi-paramétriques appliqués à la prévision des séries temporelles: cas de la consommation d’ électricité.Google Scholar
- 14.Marin, F. J., Garcia-Lagos, F., & Sandoval, F. (2002). Global model for short term load forecasting using artificial neural networks. IEE Proceedings – Generation, Transmission, and Distribution, 149, 121–125.Google Scholar
- 17.Mougeot, M., Picard, D., Tribouley, K., Lefieux, V., & Maillard-Teyssier, L. (2013). Sparse approximation and fit of intraday load curves in a high dimentional framework. Advanced in Adaptive Data Analysis, 5. http://www.worldscientific.com/doi/pdf/10.1142/S1793536913500167.
- 19.Poggi, J. M. (1994). Prévision non paramétrique de la consommation d’électricité. Revue de Statistique Appliquée, 42, 83–98.Google Scholar
- 23.Tsybakov, A. B. (2003). Optimal rates of aggregation. In COLT, Washington, DC (pp. 303–313).Google Scholar