Analysis and statistical modeling of electrical consumption data.

Summary In October 2014, the French Environment and Energy Management Agency (ADEME) in cooperation with the company ENEDIS (formerly ERDF for Électricité Réseau Distribution France) started a research project called "smart-grid SOLidarity-ENergy-iNovation" (SOLENN) with the objectives of studying the control of electricity consumption by supporting households and securing the electricity supply among others. This thesis is part of the above-mentioned objectives. The SOLENN project is piloted by the ADEME and took place in the town of Lorient. The aim of the project is to implement a pedagogy to make households aware of energy saving. In this context, we discuss a method for estimating extreme quantiles and rare event probabilities for non-parametric functional data which is the subject of an R package. We then propose an extension of the famous Cox proportional hazards model and allow the estimation of rare event probabilities and extreme quantiles. Finally, we give the application of some statistical models developed in this paper on electricity consumption data and which proved to be useful for the SOLENN project. A first application is in connection with the shaving program led by ENEDIS in order to secure the operation of the electrical network. A second application is the implementation of the linear model to study the effect of several individual visits on the electricity consumption.