<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">ipolytech</journal-id><journal-title-group><journal-title xml:lang="ru">iPolytech Journal</journal-title><trans-title-group xml:lang="en"><trans-title>iPolytech Journal</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2782-4004</issn><issn pub-type="epub">2782-6341</issn><publisher><publisher-name>Irkutsk National Research Technical University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21285/1814-3520-2023-3-552-564</article-id><article-id custom-type="edn" pub-id-type="custom">PGNVMM</article-id><article-id custom-type="elpub" pub-id-type="custom">ipolytech-736</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ЭНЕРГЕТИКА</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>POWER ENGINEERING</subject></subj-group></article-categories><title-group><article-title>Моделирование электромагнитных влияний многопроводных тяговых сетей на трубопроводы</article-title><trans-title-group xml:lang="en"><trans-title>Modeling of electromagnetic influences of multi-wire traction networks for pipelines</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0484-2857</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Суслов</surname><given-names>К. В</given-names></name><name name-style="western" xml:lang="en"><surname>Suslov</surname><given-names>K. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Суслов Константин Витальевич, д.т.н., профессор, профессор кафедры электроснабжения и электротехники, Иркутский национальный исследовательский технический университет; профессор кафедры гидроэнергетики и возобновляемых источников энергии, Национальный исследовательский университет «Московский энергетический институт»</p><p>664074, г. Иркутск, ул. Лермонтова, 83</p><p>111250, г. Москва, ул. Красноказарменная, д. 14, стр. 1</p></bio><bio xml:lang="en"><p>Konstantin V. Suslov, Dr. Sci. (Eng.), Professor, Professor of the Department of Power Supply and Electrical Engineering, School of Power Engineering, Irkutsk National Research Technical University; Professor of the Department of Hydropower Engineering and Renewable Energy, National Research University “Moscow Power Engineering Institute”</p><p>83 Lermontov St., Irkutsk 664074</p><p>14, Krasnokazarmennaya St., Moscow 111250</p></bio><email xlink:type="simple">dr.souslov@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-6543-1790</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Крюков</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kryukov</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Крюков Андрей Васильевич, д.т.н., профессор, профессор кафедры электроснабжения и электротехники, Иркутский национальный исследовательский технический университет; профессор кафедры электроэнергетики транспорта, Иркутский государственный университет путей сообщения</p><p>664074, г. Иркутск, ул. Лермонтова, 83</p><p>664074, г. Иркутск, ул. Чернышевского, 15</p></bio><bio xml:lang="en"><p>Andrey V. Kryukov, Dr. Sci. (Eng.), Professor, Professor of the Department of Power Supply and Electrical Engineering, Irkutsk National Research Technical University; Professor of the Department of Electric Power Engineering of Transport, Irkutsk State Transport University</p><p>83, Lermontov St., Irkutsk 664074</p><p>15, Chernyshevsky St., Irkutsk 664074</p></bio><email xlink:type="simple">and_kryukov@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5183-3040</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Илюшин</surname><given-names>П. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Ilyushin</surname><given-names>P. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Илюшин Павел Владимирович, д.т.н., руководитель</p><p>117186, г. Москва, ул. Нагорная, д. 31, корп. 2</p></bio><bio xml:lang="en"><p>Pavel V. Ilyushin, Dr. Sci. (Eng.), Head of the Center</p><p>31, Nagornaya St., Moscow 117186</p></bio><email xlink:type="simple">ilyushin.pv@mail.ru</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7712-9537</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Черепанов</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Cherepanov</surname><given-names>A. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Черепанов Александр Валерьевич, к.т.н., доцент, доцент кафедры электроэнергетики транспорта</p><p>664074, г. Иркутск, ул. Чернышевского, 15</p></bio><bio xml:lang="en"><p>Aleksandr V. Cherepanov, Cand. Sci. (Eng.), Associate Professor, Associate Professor of the Department of Electric Power Engineering of Transport</p><p>15, Chernyshevsky St., Irkutsk 664074</p></bio><email xlink:type="simple">smart_grid@mail.ru</email><xref ref-type="aff" rid="aff-4"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3272-5738</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Крюков</surname><given-names>А. Е.</given-names></name><name name-style="western" xml:lang="en"><surname>Kryukov</surname><given-names>A. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Крюков Александр Егорович, аспирант</p><p>664074, г. Иркутск, ул. Лермонтова, 83</p></bio><bio xml:lang="en"><p>Aleksandr E. Kryukov, Postgraduate Student</p><p>83, Lermontov St., Irkutsk 664074</p></bio><email xlink:type="simple">appleforevor@mail.ru</email><xref ref-type="aff" rid="aff-5"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Иркутский национальный исследовательский технический университет; Национальный исследовательский университет «Московский энергетический институт»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Irkutsk National Research Technical University; National Research University “Moscow Power Engineering Institute”</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Иркутский национальный исследовательский технический университет; Иркутский государственный университет путей сообщения</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Irkutsk National Research Technical University; Irkutsk State Transport University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Центр интеллектуальных электроэнергетических систем и распределенной энергетики Института энергетических исследований РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Center for Intelligent Electric Power Systems and Distributed Energy of the Energy Research Institute RAS</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-4"><aff xml:lang="ru"><institution>Иркутский государственный университет путей сообщения</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Irkutsk State Transport University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-5"><aff xml:lang="ru"><institution>Иркутский национальный исследовательский технический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Irkutsk National Research Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2023</year></pub-date><pub-date pub-type="epub"><day>03</day><month>10</month><year>2023</year></pub-date><volume>27</volume><issue>3</issue><fpage>552</fpage><lpage>564</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Суслов К.В., Крюков А.В., Илюшин П.В., Черепанов А.В., Крюков А.Е., 2023</copyright-statement><copyright-year>2023</copyright-year><copyright-holder xml:lang="ru">Суслов К.В., Крюков А.В., Илюшин П.В., Черепанов А.В., Крюков А.Е.</copyright-holder><copyright-holder xml:lang="en">Suslov K.V., Kryukov A.V., Ilyushin P.V., Cherepanov A.V., Kryukov A.E.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://ipolytech.elpub.ru/jour/article/view/736">https://ipolytech.elpub.ru/jour/article/view/736</self-uri><abstract><p>Цель  – исследовать  силы  резания на  единичном  зерне  при воздействии  его  на  обрабатываемый материал. Аналитическое исследование проведено на модели единичного абразивного зерна в виде стержня с закругленной по радиусу вершиной, действующего на обрабатываемый материал. Для расчета интенсивности деформации пластически оттесняемого материала заготовки под действием единичного зерна использован метод линий скольжения (метод  характеристик).  В  результате  проведенных  аналитических  исследований  – пластического деформирования материала, оттеснения заторможенной зоны и трения ее о поверхность зерна при движении вверх в виде стружки, трения зерна о пластически деформированный материал, а также воздействия динамической составляющей пластического деформирования – разработаны математические модели по всем перечисленным факторам. Доказана значимость динамической составляющей в общем балансе сил, связанных с пластическим деформированием, путем определения отношения динамического напряжения на линии разрыва к пределу текучести на сдвиг. На примере расчета данной зависимости для материалов Д16Т и 30ХГСА установлено, что целесообразно учитывать динамическую составляющую силы резания при скорости соударения единичного зерна с обрабатываемой поверхностью свыше 50 м/с. Приведены графики зависимости относительной силы на зерне от относительной глубины внедрения зерна. Предложенная методика расчета сил резания на единичном зерне позволяет рассчитывать суммарную силу взаимодействия единичного зерна с обрабатываемым материалом. Для перехода к заданным способу обработки и обрабатываемому материалу необходимо определить количество зерен, участвующих в контакте, продолжительность контакта, скорость резания. Имея эти данные, можно рассчитывать производительность процесса и показатели качества обработанной поверхности.</p></abstract><trans-abstract xml:lang="en"><p>In this work, digital models for determining the electromagnetic inﬂuences of multi-wire traction networks on pipelines are developed. When developing models, an approach based on multiphase behaviour simulation of electric power systems was used. This approach adequately addresses all the inﬂuencing factors, which include modules and phases  of  currents  ﬂowing  through  the  overhead  contact  wire  suspension,  6–10–25  kV  power  transmission  lines  laid on the supports of the overhead line, and lines of rails. In addition, it is possible to take into account similar parameters for stresses at the nodal points of a multi-wire system. Among the key factors are the railway clearance when laying pipes parallel to the railway track, railway clearance trajectory in the presence of non-parallel sections, and the electrical characteristics of the soil along the clearance route. The research results demonstrated that a 25 kV electromagnetically unbalanced traction network exerts signiﬁcant inﬂuence on a pipeline running in parallel. It was shown that the maximum induced voltages at speciﬁc points along the pipe fall within the range of 300–700 V, which signiﬁcantly exceeds the permissible level of 60 V. It was revealed that currents exceeding 20 A ﬂowing through the pipe can have an adverse effect on anticorrosive protection devices. To mitigate electromagnetic impacts on the pipeline, the following measures are recommended: reducing the length of pipeline and railway clearance sections, increasing the gap between the traction network and the pipe, and installing an additional grounding source. The pipe can be connected to the supplementary grounding source through ﬁlters tuned to a frequency of 50 Hz, which involve capacitor units to prevent malfunctions during the operation of pipeline protection devices. Thus, the developed digital models allow the induced voltages generated by multi-wire traction networks and the currents ﬂowing through the pipes to be adequately determined. These models offer an informed choice of measures that ensure the safety of pipeline maintenance.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>электроэнергетические системы</kwd><kwd>тяговые сети 25 кв</kwd><kwd>электромагнитные влияния на трубопроводы</kwd></kwd-group><kwd-group xml:lang="en"><kwd>electric power systems</kwd><kwd>25 kV traction networks</kwd><kwd>electromagnetic influences on pipelines</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследования выполнены в рамках государственного задания «Проведение прикладных научных исследований» по теме «Разработка методов, алгоритмов и программного обеспечения для моделирования режимов систем тягового электроснабжения железных дорог постоянного тока и электромагнитных полей на тяговых подстанциях железных дорог переменного тока».</funding-statement><funding-statement xml:lang="en">The research was carried out as a part of the state task "Implementation of applied scientific research" on the topic "Development of methods, algorithms and software for modeling the modes of traction power supply systems for DC railways and electromagnetic fields at traction substations for AC railways".</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Котельников А.В., Косарев А.Б. Электромагнитное влияние тяговых сетей переменного тока на металлические коммуникации // Электричество. 1992. № 9. С. 26–34.</mixed-citation><mixed-citation xml:lang="en">Kotel'nikov A.V., Kosarev A.B. Electromagnetic inﬂuence of AC traction networks on metal communications. Elektrichestvo. 1992;9:26-34. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Technische Richtlinien-71 (TRL-71). EMR-Technic Kathodischer Korrosionsschutz fur Erdgasfernleitungen. P. 80.</mixed-citation><mixed-citation xml:lang="en">Technische Richtlinien-71 (TRL-71). EMR-Technic Kathodischer Korrosionsschutz fur Erdgasfernleitungen. P. 80.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Шамшетдинов К.Л. Особенности электрометрического контроля противокоррозионной защиты подземных трубопроводов в условиях влияния высоковольтных линий электропередач // Трубопроводный транспорт: теория и практика. 2008. № 1. С. 58–60.</mixed-citation><mixed-citation xml:lang="en">Shamshetdinov K.L. Features of electrometric control of underground pipeline corrosion protection under the inﬂuence of high-voltage power lines. Truboprovodnyj transport: teoriya i praktika. 2008;1:58-60. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Ратнер М.П. Индуктивное влияние электрифицированных железных дорог на электрические сети и трубопроводы. М.: Транспорт, 1966. 164 с.</mixed-citation><mixed-citation xml:lang="en">Ratner M.P. Inductive inﬂuence of electriﬁed railways on electrical networks and pipelines. Moscow: Transport; 1966, 164p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Коннова Е.И., Косарев А.Б. Расчет электромагнитного влияния сетей переменного тока на металлические коммуникации // Вестник ВНИИЖТ. № 2. 1990. С. 17–19.</mixed-citation><mixed-citation xml:lang="en">Konnova E.I., Kosarev A.B. Calculation of the electromagnetic inﬂuence of alternating current networks on metal communications. Vestnik Nauchno-issledovatel'skogo instituta zheleznodorozhnogo transporta = Russian Railway Science Journal. 1990;2:17-19. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Charalambous C.A., Demetriou A., Lazari A.L., Nikolaidis A.I. Effects of electromagnetic interference on underground pipelines caused by the operation of high voltage ac traction systems: the impact of harmonics // IEEE Transactions on Power Delivery. 2018. Vol. 33. Iss. 6. Р. 2664–2672. https://doi.org/10.1109/TPWRD.2018.2803080.</mixed-citation><mixed-citation xml:lang="en">Charalambous C.A., Demetriou A., Lazari A.L., Nikolaidis A.I. Effects of electromagnetic interference on underground pipelines caused by the operation of high voltage AC traction systems: the impact of harmonics. In: IEEE Transactions on Power Delivery. 2018;33(6):2664-2672. https://doi.org/10.1109/TPWRD.2018.2803080.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Czumbil L., Micu D., Munteanu C., Stet D., Tomoioaga B. Optimal design of the pipeline right-of-way nearby high voltage transmission lines using genetic algorithms // 50th International Universities Power Engineering Conference. 2015. https://doi.org/10.1109/UPEC.2015.7339841.</mixed-citation><mixed-citation xml:lang="en">Czumbil L., Micu D., Munteanu C., Stet D., Tomoioaga B. Optimal design of the pipeline right-of-way nearby high voltage transmission lines using genetic algorithms. In: 50th International Universities Power En-gineering Conference. 2015. https://doi.org/10.1109/UPEC.2015.7339841.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Gupta A., Thomas M.J. Coupling of high voltage AC power lines ﬁelds to metallic pipelines // 9th International Conference on Electro Magnetic Interference and Compatibility (Bangalore, 23–24 February 2006). Bangalore, 2016.</mixed-citation><mixed-citation xml:lang="en">Gupta A., Thomas M.J. Coupling of high voltage AC power lines ﬁelds to metallic pipelines. In: 9th International Conference on Electro Magnetic Interference and Compatibility. 23–24 February 2006, Bangalore.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Shahri A.S., Nair N.-K.C. Overhead shielding wire and induced potential on pipeline located close to high voltage transmission // Australasian Universities Power Engineering Conference. 2016. https://doi.org/10.1109/AUPEC.2016.7749379.</mixed-citation><mixed-citation xml:lang="en">Shahri A.S., Nair N.-K.C. Overhead shielding wire and induced potential on pipeline located close to high voltage transmission. In: Australasian Universities Power Engineering Conference. 2016. https://doi.org/10.1109/AUPEC.2016.7749379.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Alshahr A.S. Assessment of induced potential on metallic pipeline located nearby to EHV AC OHTL // IEEE 2nd International Conference on Signal, Control and Communication. 2021. https://doi.org/10.1109/SCC53769.2021.9768375.</mixed-citation><mixed-citation xml:lang="en">Alshahr A.S. Assessment  of  induced  potential  on  metallic  pipeline  located  nearby  to  EHV AC  OHTL.  In:  IEEE  2nd International Conference on Signal, Control and Communication. 2021. https://doi.org/10.1109/SCC53769.2021.9768375.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Janda Z., Nohác̆ K. Analysis of the inductive effects of overhead lines to close pipelines // Proceedings of the 2014 15th International Scientiﬁc Conference on Electric Power Engineering. 2014. https://doi.org/10.1109/EPE.2014.6839430.</mixed-citation><mixed-citation xml:lang="en">Janda Z., Nohác̆ K. Analysis of the inductive effects of overhead lines to close pipelines. In:  Proceedings of the 2014 15th International Scientiﬁc Conference on Electric Power Engineering. 2014.  https://doi.org/10.1109/EPE.2014.6839430.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Mu Wenzhe, Zhao Zhibin, Zhu Yongmei, Lei Xiaozhou. A rapid modeling for analysis the effect of transmission line to oil and gas pipeline // Asia-Paciﬁc International Symposium on Electromagnetic Compatibility. 2016. Vol. 1. https://doi.org/10.1109/APEMC.2016.7522916.</mixed-citation><mixed-citation xml:lang="en">Mu Wenzhe, Zhao Zhibin, Zhu Yongmei, Lei Xiaozhou. A rapid modeling for analysis the effect of trans-mission line to oil and gas pipeline. In: Asia-Paciﬁc International Symposium on Electromagnetic Compatibility. 2016. Vol. 1.  https://doi.org/10.1109/APEMC.2016.7522916.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Chai Chia Soon, Kadir M.Z.A.A., Izadi M., Jasni J, Gomes C. The effect of electromagnetic ﬁelds due to hv line on the parallel pipeline // IEEE International Conference on Power and Energy. 2014. https://doi.org/10.1109/PECON.2014.7062407.</mixed-citation><mixed-citation xml:lang="en">Chai Chia Soon, Kadir M.Z.A.A., Izadi M., Jasni J, Gomes C. The effect of electromagnetic ﬁelds due to hv line on the parallel pipeline. In:  IEEE International Conference on Power and Energy. 2014. https://doi.org/10.1109/PECON.2014.7062407.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Sawma E., Zeitoun B., Harmouche N., Georges S., Hamad M., Slaoui F.H. Electromagnetic induction in pipelines due to overhead high voltage power lines // International Conference on Power System Technology. 2010. https://doi.org/10.1109/POWERCON.2010.5666086.</mixed-citation><mixed-citation xml:lang="en">Sawma E., Zeitoun B., Harmouche N., Georges S., Hamad M., Slaoui F.H. Electromagnetic induction in pipelines due to overhead high voltage power lines. In: International Conference on Power System Technology. 2010. https://doi.org/10.1109/POWERCON.2010.5666086.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Junyang Li Xun. Interference on buried pipeline with insulating ﬂange near high voltage transmission line // 2nd IEEE Advanced Information Management,Communicates,Electronic and Automation Control Conference. 2018. https://doi.org/10.1109/IMCEC.2018.8469489.</mixed-citation><mixed-citation xml:lang="en">Junyang Li Xun. Interference on buried pipeline with insulating ﬂange near high voltage transmission line. In:  2nd IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference. 2018. https://doi.org/10.1109/IMCEC.2018.8469489.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Shwehdi M.H., Alaqil M.A., Mohamed S.R. EMF Analysis for a 380kV transmission OHL in the vicinity of buried pipelines // IEEE Access. 2020. Vol. 8. Р. 3710–3717. https://doi.org/10.1109/ACCESS.2019.2961109.</mixed-citation><mixed-citation xml:lang="en">Shwehdi M.H., Alaqil M.A., Mohamed S.R. EMF Analysis for a 380kV transmission OHL in the vicinity of buried pipelines. In: IEEE Access. 2020;8:3710-3717. https://doi.org/10.1109/ACCESS.2019.2961109.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Shahri A.S.A., Nair N.-K.C. AC potential on pipelines nearby EHV power lines due to low frequency induction // Australasian Universities Power Engineering Conference (Wollongong, 27–30 September 2015). Wollongong: IEEE, 2015. https://doi.org/10.1109/AUPEC.2015.7324828.</mixed-citation><mixed-citation xml:lang="en">Shahri A.S.A.,  Nair  N.-K.C. AC  potential  on  pipelines  nearby  EHV  power  lines  due  to  low  frequency  induction.  In: Australasian Universities Power Engineering Conference. 27–30 September 2015, Wollongong. Wollongong: IEEE; 2015. https://doi.org/10.1109/AUPEC.2015.7324828.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Dawalibi F., Pinho A. Computerized analysis of power systems and pipelines proximity effects // IEEE Transactions on Power Delivery. 1986. Vol. 1. Iss. 2. P. 40–48. https://doi.org/10.1109/TPWRD.1986.4307932.</mixed-citation><mixed-citation xml:lang="en">Dawalibi F., Pinho A. Computerized analysis of power systems and pipelines proximity effects. In:  IEEE Transactions on Power Delivery. 1986;1(2):40-48. https://doi.org/10.1109/TPWRD.1986.4307932.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Haifeng Sun, Pei Wang, Haojing Chang, Xiancang Ai, Tianlong E., Bonian Su, et al. Study on electromagnetic inﬂuence of 750 kV AC transmission lines on multiple buried pipelines // Asia-Paciﬁc International Symposium on Electromagnetic Compatibility. 2016. https://doi.org/10.1109/APEMC.2016.7522725.</mixed-citation><mixed-citation xml:lang="en">Haifeng Sun, Pei Wang, Haojing Chang, Xiancang Ai, Tianlong E., Bonian Su, et al. Study on electro-magnetic inﬂuence of 750 kV AC transmission lines on multiple buried pipelines. In: Asia-Paciﬁc International Symposium on Electromagnetic Compatibility. 2016. https://doi.org/10.1109/APEMC.2016.7522725.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Liu Xing-Ting, Wang Wei, Yu Hua. Analysis of mutual electromagnetic inﬂuence between transmission line and buried pipeline // 4th International Conference on Information Science and Control Engineering. 2017. https://doi.org/10.1109/ICISCE.2017.293.</mixed-citation><mixed-citation xml:lang="en">Liu Xing-Ting, Wang Wei, Yu Hua. Analysis of mutual electromagnetic inﬂuence between transmission line and buried pipeline. In: 4th International Conference on Information Science and Control Engineering. 2017. https://doi.org/10.1109/ ICISCE.2017.293.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Alshahri A.S., Dinh Minh Thi Nguyet, Nair N.K.C. Induced voltage on pipeline located close to high voltage lines due to electromagnetic induction // Australasian Universities Power Engineering Conference. 2014. https://doi.org/10.1109/AUPEC.2014.6966589.</mixed-citation><mixed-citation xml:lang="en">Alshahri A.S., Dinh Minh Thi Nguyet, Nair N.K.C. Induced voltage on pipeline located close to high voltage lines due to  electromagnetic  induction.  In:  Australasian  Universities  Power  Engineering  Conference.  2014.  https://doi.org/10.1109/AUPEC.2014.6966589.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Lu Duo, Liu Chenlong, Qi Lei, Yuan Hui. Mitigation of electromagnetic inﬂuence on the buried metal pipeline near overhead AC transmission line // Sixth International Conference on Electromagnetic Field Problems and Applications. 2012. https://doi.org/10.1109/ICEF.2012.6310384.</mixed-citation><mixed-citation xml:lang="en">Lu  Duo,  Liu  Chenlong,  Qi  Lei, Yuan  Hui.  Mitigation  of  electromagnetic  inﬂuence  on  the  buried  metal  pipe-line  near overhead AC transmission line. In: Sixth International Conference on Electromagnetic Field Problems and Applications. 2012. https://doi.org/10.1109/ICEF.2012.6310384.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Adamek M., Vostracky Z. Interference from transmission lines to buried pipelines // 16th International Scientiﬁc Conference on Electric Power Engineering. 2015.</mixed-citation><mixed-citation xml:lang="en">Adamek  M.,  Vostracky  Z.  Interference  from  transmission  lines  to  buried  pipelines.  In:  16th  International  Scientiﬁc Conference on Electric Power Engineering. 2015.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Закарюкин В.П., Крюков А.В. Сложнонесимметричные режимы электрических систем. Иркутск: Иркутский ун-т, 2005. 273 с.</mixed-citation><mixed-citation xml:lang="en">Zakaryukin V.P., Kryukov A.V. Complex unbalanced modes of electrical systems. Irkutsk: Irkutsk State University; 2005, 273 p. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Zakaryukin V.P., Kryukov A.V. Determination of the induced voltages when nonparallel power lines are adjacent to one another // Power Technology and Engineering. 2015. Vol. 49. Iss. 4. P. 304–309. https://doi.org/10.1007/s10749-015-0620-4.</mixed-citation><mixed-citation xml:lang="en">Zakaryukin V.P., Kryukov A.V. Determination of the induced voltages when nonparallel power lines are adjacent to one another. Power Technology and Engineering. 2015;49(4):304-309.  https://doi.org/10.1007/s10749-015-0620-4.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Carson I.R. Wave propagation in overhead wires with ground return // Bell Systems Technical Journal. 1926. Vol. 5. Iss. 4. P. 539–554. https://doi.org/10.1002/j.1538-7305.1926.tb00122.x.</mixed-citation><mixed-citation xml:lang="en">Carson I.R. Wave propagation in overhead wires with ground return. Bell Systems Technical Journal. 1926;5(4):539-554. https://doi.org/10.1002/j.1538-7305.1926.tb00122.x.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Василянский А.М., Мамошин Р.Р., Якимов Г.Б. Совершенствование системы тягового электроснабжения железных дорог, электрифицированных на переменном токе 27,5 кВ, 50 Гц // Железные дороги мира. 2002. № 8. С. 40–46.</mixed-citation><mixed-citation xml:lang="en">Vasilyanskij A.M., Mamoshin R.R., Yakimov G.B. Improvement of the traction power supply system for 27.5 kV, 50 Hz alternating current railways. Zheleznye dorogi mira. 2002;8:40-46. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Закарюкин В.П., Крюков А.В. Определение собственных и взаимных сопротивлений в многопроводных системах, содержащих подземные провода // Современные технологии. Системный анализ. Моделирование. 2021. № 1. С. 184–191. https://doi.org/10.26731/1813-9108.2021.1(69).184-191.</mixed-citation><mixed-citation xml:lang="en">Zakaryukin V.P., Kryukov A.V. Determination of self-impedances and mutual impedances in multi-wire systems containing underground wires. Sovremennye tehnologii.  Sistemnyj analiz.  Modelirovanie = Modern technologies. System analysis. Modeling. 2021;1:184-191. (In Russ.). https://doi.org/10.26731/1813-9108.2021.1(69).184-191.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
