Simulation of household electricity consumption by using functional data analysis

Obtaining patterns for electricity consumption in a particular household is a key issue to simulate and dimension the electricity supply needed in an isolated house. The electricity consumption profile (load curve) of a user is a function that indicates the electrical consumption in a dwelling over a period of time, usually one day. When this function is considered as a datum and several days are observed, a sample of functions is obtained. Functional Data Analysis (FDA) provides procedures and techniques to analyze this kind of data. Specifically, functional linear regression is used to estimate the average daily consumption of electricity for a given household type. Classification of households is carried out by using characteristics of the dwellings and their inhabitants. Nevertheless, the electricity consumption is very variable among different households, even those belonging to the same type. Inhabitant behavior strongly influences energy consumption patterns and is an important factor that accounts for a major share of the observed variability in the household consumption. The error term of the regression model captures this specific variability. In this paper we propose a method for its modeling based on a functional principal component analysis, which captures the homoscedasticity and main variability patterns, followed by fitting a sinusoidal function series to the error remainder. This statistical modeling facilitates the simulation of new individual load curves for any household, depending on the profile of the dwelling and its inhabitants. We illustrate this methodology with a real data set of household consumptions.