Method of integro-differential equations for interpreting the results of vertical electrical sounding of the soil
DOI:
https://doi.org/10.20998/2074-272X.2021.5.09Keywords:
electrical substation, grounding arrangements, vertical electrical sounding, Schlumberger method, method of integro-differential equationsAbstract
The paper is devoted to the problem of determining the geoelectric structure of the soil within the procedure of testing the grounding arrangements of existing power plants and substations to the required depth in conditions of dense development. To solve the problem, it was proposed to use the Schlumbergers method , which has a greater sounding depth compared to the Wenner electrode array. The purpose of the work is to develop a mathematical model for interpreting the results of soil sounding by the Schlumberger method in the form of a four-layer geoelectric structure. Methodology. To construct a mathematical model, it is proposed to use the solution of a particular problem about the field of a point current source, which, like the observation point, is located in the first layer of a four-layer soil. Based on this expressions, a system of linear algebraic equations of the 7-th order with respect to the unknown coefficients ai and bi was compiled. On the basis of its analytical solution, an expression for the potential of the electric field was obtained for conducting VES (the point current source and the observation point are located only on the soil surface). Results. Comparison of the results of soil sounding by the Schlumberger installation and the interpretation of its results for the same points shows a sufficient degree of approximation: the maximum relative error does not exceed 9.7 % (for the second point), and the average relative error is 3.6 %. Originality. Based on the obtained expression, a test version of the program was implemented in Visual Basic for Applications to interpret the results of VES by the Schlumberger method. To check the obtained expressions, the interpretation of the VES results was carried out on the territory of a 150 kV substation of one of the mining and processing plants in the city of Kriviy Rih. Practical significance. The developed mathematical model will make it possible to increase the sounding depth, and, consequently, the accuracy of determining the standardized parameters of the grounding arrangements of power stations and substations.
References
IEEE Std 80-2013. Guide for Safety in AC Substation Grounding. New York, IEEE, 2013. 206 p. doi: https://doi.org/10.1109/IEEESTD.2015.7109078.
IEEE Std 81-2012. Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials of a Grounding System. New York, IEEE, 2012. 86 p. doi: https://doi.org/10.1109/IEEESTD.2012.6392181.
Kolesnikov V.P. Osnovy interpretatsii elektricheskikh zondirovanii [The base of interpretation of electrical soundings]. Moscow, Scientific World Publ., 2007. 248 p. (Rus).
Koliushko D.G., Rudenko S.S., Koliushko G.M. Analysis of electrophysical characteristics of grounds in the vicinity electrical substation of Ukraine. Electrical Engineering & Electromechanics, 2015, no. 3, pp. 67-72. (Rus). doi: https://doi.org/10.20998/2074-272x.2015.3.10.
Koliushko D.G., Rudenko S.S. Interpretation the results of the vertical electrical sounding as the geoelectrical half space with four layer. Bulletin of NTU «KhPІ», 2015, no. 12 (1121), pp. 324-329. (Rus).
Koliushko D.G., Rudenko S.S., Asmolova L.V., Tkachova T.I. Determination of the soil sounding depth for the earthing resistance calculation of substations 35 kV. Electrical Engineering & Electromechanics, 2020, no. 1, pp. 52-55. doi: https://doi.org/10.20998/2074-272x.2020.1.08.
Lagace P.J., Fortin J., Crainic E.D. Interpretation of resistivity sounding measurements in N-layer soil using electrostatic images. IEEE Transactions on Power Delivery, 1996, vol. 11, no. 3, pp. 1349-1354. doi: https://doi.org/10.1109/61.517490.
Colominas I., Navarrina F., Casteleiro M. Analysis of transferred Earth potentials in grounding systems: a BEM numerical approach. IEEE Transactions on Power Delivery, 2005, vol. 20, no. 1, pp. 339-345. doi: https://doi.org/10.1109/TPWRD.2004.835035.
Arnautovski-Toseva V., Grcev L. Image and exact models of a vertical wire penetrating a two-layered earth. IEEE Transactions on Electromagnetic Compatibility, 2011, vol. 53, no. 4, pp. 968-976. doi: https://doi.org/10.1109/TEMC.2011.2149533.
Arnautovski-Toseva V., Grcev L. On the image model of a buried horizontal wire. IEEE Transactions on Electromagnetic Compatibility, 2016, vol. 58, no. 1, pp. 278-286. doi: https://doi.org/10.1109/TEMC.2015.2506608.
Burgsdorf V.V., Yakobs A.I. Zazemlyayushchie ustroystva elektroustanovok [Grounding arrangement of electrical installations]. Moscow, Energoatomizdat Publ., 1987. 400 p. (Rus).
Rencher A.C., Christensen W.F. Methods of multivariate analysis, Third Edition. John Wiley & Sons, Inc., 2012. 768 p. doi: https://doi.org/10.1002/9781118391686.
O. Rezinkin, M. Rezinkina, A. Danyluk, R. Tomashevskyi, Formation of high-voltage pulses with nanosecond fronts in low-impedance loads. IEEE 2nd Ukraine Conference on Electrical and Computer Engineering (UKRCON), 2019, pp. 464-467 doi: https://doi.org/10.1109/UKRCON.2019.8880015.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 D. G. Koliushko, S. S. Rudenko, A. N. Saliba
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
