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Benford’s Law in Electric Distribution Network

Author

Listed:
  • Jaroslav Petráš

    (Department of Electric Power Engineering, Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice-Sever, Slovakia)

  • Marek Pavlík

    (Department of Electric Power Engineering, Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice-Sever, Slovakia)

  • Ján Zbojovský

    (Department of Electric Power Engineering, Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice-Sever, Slovakia)

  • Ardian Hyseni

    (Department of Electric Power Engineering, Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice-Sever, Slovakia)

  • Jozef Dudiak

    (Východoslovenská distribučná, a.s., Mlynská 31, 042 91 Košice, Slovakia)

Abstract

Benford’s law can be used as a method to detect non-natural changes in data sets with certain properties; in our case, the dataset was collected from electricity metering devices. In this paper, we present a theoretical background behind this law. We applied Benford’s law first digit probability distribution test for electricity metering data sets acquired from smart electricity meters, i.e., the natural data of electricity consumption acquired during a specific time interval. We present the results of Benford’s law distribution for an original measured dataset with no artificial intervention and a set of results for different kinds of affected datasets created by simulated artificial intervention. Comparing these two dataset types with each other and with the theoretical probability distribution provided us the proof that with this kind of data, Benford’s law can be applied and that it can extract the dataset’s artificial manipulation markers. As presented in the results part of the article, non-affected datasets mostly have a deviation from BL theoretical probability values below 10%, rarely between 10% and 20%. On the other side, simulated affected datasets show deviations mostly above 20%, often approximately 70%, but rarely lower than 20%, and this only in the case of affecting a small part of the original dataset (10%), which represents only a small magnitude of intervention.

Suggested Citation

  • Jaroslav Petráš & Marek Pavlík & Ján Zbojovský & Ardian Hyseni & Jozef Dudiak, 2023. "Benford’s Law in Electric Distribution Network," Mathematics, MDPI, vol. 11(18), pages 1-27, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3863-:d:1236723
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    References listed on IDEAS

    as
    1. Pietronero, L. & Tosatti, E. & Tosatti, V. & Vespignani, A., 2001. "Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 297-304.
    2. Yan, Xiaoyong & Yang, Seong-Gyu & Kim, Beom Jun & Minnhagen, Petter, 2018. "Benford’s law and first letter of words," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 305-315.
    3. Huang, Yasheng & Niu, Zhiyong & Yang, Clair, 2020. "Testing firm-level data quality in China against Benford’s Law," Economics Letters, Elsevier, vol. 192(C).
    4. Steven J. Miller, 2015. "Benford's Law: Theory and Applications," Economics Books, Princeton University Press, edition 1, number 10527.
    5. Ricardo Sartori Cella & Ercilio Zanolla, 2018. "Benford’s Law and transparency: an analysis of municipal expenditure," Brazilian Business Review, Fucape Business School, vol. 15(4), pages 331-347, July.
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    Cited by:

    1. Marek Pavlík & Matej Bereš & Ardian Hyseni & Jaroslav Petráš, 2024. "Statistical Analysis of Electricity Prices in Germany Using Benford’s Law," Energies, MDPI, vol. 17(18), pages 1-20, September.

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