Analysis of the Percolation Model of the Electric Distribution Stations Network

Authors

  • Yuri P. Virchenko Belgorod State Shukhov’s Technological University
  • Vladislav E. Parkhomenko Belgorod State Shukhov’s Technological University

DOI:

https://doi.org/10.52575/2687-0959-2026-58-1-88-95

Keywords:

Bernoulli’s Random Field, Probability of Uptime, External Cluster Board, Cluster Expansion, Pair Percolation Function

Abstract

A mathematical model is being developed to calculate the reliability of a network of electrical substations connected to a fixed central distribution station. Each kth substation in the network is a finite graph Γ vertex in the model. It is characterizes by the probability pk of its uptime. Aggregate of all these characteristics defines a nonuniform Bernoulli random field with the probability distibution {pk ; k = 1 ÷ N}. In the framework of the model the uptime of the concrete kth substation in the network is understood as the presence of its percolation connection with a central distribution station. A formula is derived for assessing the reliability of each of the network’s substations, and a numerical calculation algorithm is proposed for this characteristic.

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Author Biographies

Yuri P. Virchenko, Belgorod State Shukhov’s Technological University

Doctor of Physical and Mathematical Sciences, Professor of the Department of Software, Belgorod State Shukhov’s Technological University,
Belgorod, Russia
E-mail: virch@bsuedu.ru
ORCID: 0000-0002-5413-6179

Vladislav E. Parkhomenko, Belgorod State Shukhov’s Technological University

Graduate Student of the Department of Software, Belgorod State Shukhov’s Technological University,
Belgorod, Russia
ORCID: 0009-0000-8608-8119

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Published

2026-03-30

How to Cite

Virchenko, Y. P., & Parkhomenko, V. E. (2026). Analysis of the Percolation Model of the Electric Distribution Stations Network. Applied Mathematics & Physics, 58(1), 88-95. https://doi.org/10.52575/2687-0959-2026-58-1-88-95

Issue

Vol. 58 No. 1 (2026)

Section

Physics. Mathematical modeling

Copyright (c) 2026 Applied Mathematics & Physics

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