the coefficient of similarity, the coefficient of auto-similarity, modelling, residential electricity consumption, statistical analysis, correlation, smart-grid, classification.

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].

1. Mamchych T., Wallin F. (2014) Looking for patterns in residential electricity consumption. Energy Procedia 61, pp. 1768–1771. Doi:10.1016/j.egypro.2014.12.208.  

2. Mamchych T., Wallin F. (2015) Stability of patterns in residential electricity consumption. Energy Procedia 75, pp. 2738–2744. Doi:10.1016/j.egypro.2015.07.494. 

3. Székely, Gábor J., Rizzo, Maria L., Bakirov, Nail K. (December 2007). “Measuring and testing dependence by correlation of distances”. The Annals of Statistics. 35 (6): 2769–2794. Doi:10.1214/009053607000000505. 

4. Szekely G. J. and Rizzo M. L. (2017) The Energy of Data, The Annual Review of Statistics and Its Applications. Extended Review, 4:447-479. Doi:10.1146/annurev-statistics-060116-054026.  

6. Zimmermann J. P. (2009). End-use metering campaign in 400 households in Sweden. Assessment of the potential electricity savings. Enertech.  

7. Available at: https://ec.europa.eu/eurostat/statistics-explained/index.php?title=Energy_consumption_in_ households. 

8. Mingyue Guo, Youngsik Choi, So-Min Cheong, Zheng O’Neill (2025) Current and future residential electricity demand using large-scale smart meter data in a changing climate. Sustainable Cities and Society, 130 (15), 106623. 

9. Mavlonov J., Ruzimov S., Tonoli A., Amati N., Mukhitdinov A. (2023) Sensitivity Analysis of Electric Energy Consumption in Battery Electric Vehicles with Different Electric Motors. World Electr. Veh. J. 14, 36. Doi.org/10.3390/wevj14020036.  

10. Matsui K., Yamagata Y., Kawakubo Sh. (2019) Real-time sensing in residential area using IoT technology for finding usage patterns to suggest action plan to conserve energy. Energy Procedia 158, pp. 6438–6445. Doi:10.1016/j.egypro.2019.01.171.  

11. Williams B., Hooper R. J., Gnoth D. and Chase J. G. (2025) Residential Electricity Demand Modelling: Validation of a Behavioural Agent-Based Approach. Energies, 18 (6), 1314. Doi.org/10.3390/en18061314.  

12. Pak W., Kim I., Choi J. (2021) Proposal of the energy consumption analysis process for the residential houses using big data analytics technique. Journal of Computational Design and Engineering, 8 (6), pp. 1591–1604. Doi.org/10.1093/jcde/qwab063.  

13. Softah W., Tafakori L., Song H. (2025) Analyzing and predicting residential electricity consumption using smart meter data: A copula-based approach. Energy and Buildings, 332 (1), 115432 Doi.org/10.1016/j.enbuild.2025.115432.  

14. Hosseini B. (2025) Forecasting household monthly electricity consumption using the similar pattern algorithm. Academia Green Energy, 2. Doi.org/10.20935/AcadEnergy7500.  

15. Scheidt F., Medinová H., Ludwig N., Richter B., Staudt Ph., Weinhardt Ch. Data analytics in the electricity sector –A quantitative and qualitative literature review. Energy and AI 1 (2020) 100009. Available at: https://doi.org/10.1016/j.egyai.2020.100009. 

1. Mamchych T., Wallin F. (2014) Looking for patterns in residential electricity consumption. Energy Procedia 61, pp. 1768–1771. Doi:10.1016/j.egypro.2014.12.208.  

2. Mamchych T., Wallin F. (2015) Stability of patterns in residential electricity consumption. Energy Procedia 75, pp. 2738–2744. Doi:10.1016/j.egypro.2015.07.494. 

3. Székely, Gábor J., Rizzo, Maria L., Bakirov, Nail K. (December 2007). “Measuring and testing dependence by correlation of distances”. The Annals of Statistics. 35 (6): 2769–2794. Doi:10.1214/009053607000000505. 

4. Szekely G. J. and Rizzo M. L. (2017) The Energy of Data, The Annual Review of Statistics and Its Applications. Extended Review, 4:447-479. Doi:10.1146/annurev-statistics-060116-054026.  

6. Zimmermann J. P. (2009). End-use metering campaign in 400 households in Sweden. Assessment of the potential electricity savings. Enertech.  

7. Available at: https://ec.europa.eu/eurostat/statistics-explained/index.php?title=Energy_consumption_in_ households. 

8. Mingyue Guo, Youngsik Choi, So-Min Cheong, Zheng O’Neill (2025) Current and future residential electricity demand using large-scale smart meter data in a changing climate. Sustainable Cities and Society, 130 (15), 106623. 

9. Mavlonov J., Ruzimov S., Tonoli A., Amati N., Mukhitdinov A. (2023) Sensitivity Analysis of Electric Energy Consumption in Battery Electric Vehicles with Different Electric Motors. World Electr. Veh. J. 14, 36. Doi.org/10.3390/wevj14020036.  

10. Matsui K., Yamagata Y., Kawakubo Sh. (2019) Real-time sensing in residential area using IoT technology for finding usage patterns to suggest action plan to conserve energy. Energy Procedia 158, pp. 6438–6445. Doi:10.1016/j.egypro.2019.01.171.  

11. Williams B., Hooper R. J., Gnoth D. and Chase J. G. (2025) Residential Electricity Demand Modelling: Validation of a Behavioural Agent-Based Approach. Energies, 18 (6), 1314. Doi.org/10.3390/en18061314.  

12. Pak W., Kim I., Choi J. (2021) Proposal of the energy consumption analysis process for the residential houses using big data analytics technique. Journal of Computational Design and Engineering, 8 (6), pp. 1591–1604. Doi.org/10.1093/jcde/qwab063.  

13. Softah W., Tafakori L., Song H. (2025) Analyzing and predicting residential electricity consumption using smart meter data: A copula-based approach. Energy and Buildings, 332 (1), 115432 Doi.org/10.1016/j.enbuild.2025.115432.  

14. Hosseini B. (2025) Forecasting household monthly electricity consumption using the similar pattern algorithm. Academia Green Energy, 2. Doi.org/10.20935/AcadEnergy7500.  

15. Scheidt F., Medinová H., Ludwig N., Richter B., Staudt Ph., Weinhardt Ch. Data analytics in the electricity sector –A quantitative and qualitative literature review. Energy and AI 1 (2020) 100009. Available at: https://doi.org/10.1016/j.egyai.2020.100009.