Modelling residential electricity consumption
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Abstract. Our work is devoted to the problem of modeling residential electricity consumption based on time series formed by sequential values of metering devices related to smart-grid technologies. Residential consumption is an important component of the overall energy system. The study of this component is of particular importance in our time of epidemics, the spread of remote types of work, and increased dependence on Internet technologies. Mathematical models for the nature of consumption that allow us to identify patterns, to identify similarities in such patterns would be extremely useful for the tasks of short-term forecasting and demand prediction, and for ensuring the stability of the functioning of the energy supply system as a whole. We note that there is a special need for models that use only data from smart-grid devices, without involving other types of data, such as the number of inhabitants, income, area of the dwelling, and others, for remote monitoring based on current data. In the works [1] and [2], the coefficient of similarity and the coefficient of auto-similarity were first introduced to describe the nature of consumption, identify possible patterns and measure the stability of these patterns, to determine cases when such patterns do not exist. The cited works on real data demonstrate the effectiveness of these coefficients for monitoring consumption, and the results obtained are an achievement in the field of energy. At the same time, these works do not contain the study of these computational structures from the point of view of applied mathematics, since this is beyond the scope of energy science. This work is devoted to filling this gap. In our work, some properties of the coefficient of similarity and the coefficient of auto-similarity associated with the use of the correlation approach have been established, and the recognition ability of the coefficients for fixed data has been studied, compared with the Szekely’s coefficient of the distance correlation) ([3] and [4]). The testing of this technology has been performed on data obtained by the project [5].
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