<!DOCTYPE article
PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.4 20190208//EN"
       "JATS-journalpublishing1.dtd">
<article 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" article-type="research-article" dtd-version="1.4" xml:lang="en">
 <front>
  <journal-meta>
   <journal-id journal-id-type="publisher-id">Solnechno-Zemnaya Fizika</journal-id>
   <journal-title-group>
    <journal-title xml:lang="en">Solnechno-Zemnaya Fizika</journal-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Солнечно-земная физика</trans-title>
    </trans-title-group>
   </journal-title-group>
   <issn publication-format="online">2712-9640</issn>
  </journal-meta>
  <article-meta>
   <article-id pub-id-type="publisher-id">113886</article-id>
   <article-id pub-id-type="doi">10.12737/szf-121202613</article-id>
   <article-id pub-id-type="edn">kxegkn</article-id>
   <article-categories>
    <subj-group subj-group-type="toc-heading" xml:lang="ru">
     <subject>Результаты  исследований</subject>
    </subj-group>
    <subj-group subj-group-type="toc-heading" xml:lang="en">
     <subject>Results of current research</subject>
    </subj-group>
    <subj-group>
     <subject>Результаты  исследований</subject>
    </subj-group>
   </article-categories>
   <title-group>
    <article-title xml:lang="en">Probabilistic assessment of geomagnetically induced current levels based on auroral localization and structure data</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Вероятностная оценка уровня геоиндуцированных токов по данным о локализации и структуре полярных сияний</trans-title>
    </trans-title-group>
   </title-group>
   <contrib-group content-type="authors">
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Воробьев</surname>
       <given-names>Андрей Владимирович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Vorobev</surname>
       <given-names>Andrey Vladimirovich</given-names>
      </name>
     </name-alternatives>
     <email>geomagnet@list.ru</email>
     <xref ref-type="aff" rid="aff-1"/>
     <xref ref-type="aff" rid="aff-2"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-6476-9471</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Соловьёв</surname>
       <given-names>Анатолий Александрович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Soloviev</surname>
       <given-names>Anatoly Aleksandrovich</given-names>
      </name>
     </name-alternatives>
     <email>rjes@wdcb.ru</email>
     <bio xml:lang="ru">
      <p>доктор физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>doctor of physical and mathematical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-3"/>
     <xref ref-type="aff" rid="aff-4"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Воробьева</surname>
       <given-names>Гульнара Равильевна</given-names>
      </name>
      <name xml:lang="en">
       <surname>Vorobeva</surname>
       <given-names>Gulnara Ravilevna</given-names>
      </name>
     </name-alternatives>
     <email>gulnara.vorobeva@gmail.com</email>
     <xref ref-type="aff" rid="aff-5"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Лапин</surname>
       <given-names>Александр Николаевич</given-names>
      </name>
      <name xml:lang="en">
       <surname>Lapin</surname>
       <given-names>Aleksandr Nikolaevich</given-names>
      </name>
     </name-alternatives>
     <email>meccos160@yandex.ru</email>
     <xref ref-type="aff" rid="aff-6"/>
    </contrib>
   </contrib-group>
   <aff-alternatives id="aff-1">
    <aff>
     <institution xml:lang="ru">Геофизический центр РАН</institution>
     <city>Москва</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Geophysical Center RAS</institution>
     <city>Moscow</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">Уфимский университет науки и технологий</institution>
     <city>Уфа</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Ufa University of Science and Technology</institution>
     <city>Ufa</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-3">
    <aff>
     <institution xml:lang="ru">Геофизический центр РАН</institution>
     <city>Москва</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Geophysical Center RAS</institution>
     <city>Moscow</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-4">
    <aff>
     <institution xml:lang="ru">Институт физики Земли им. О.Ю. Шмидта РАН</institution>
     <city>Москва</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Schmidt Institute of Physics of the Earth, RAS</institution>
     <city>Moscow</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-5">
    <aff>
     <institution xml:lang="ru">Уфимский университет науки и технологий</institution>
     <city>Уфа</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Ufa University of Science and Technology</institution>
     <city>Ufa</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-6">
    <aff>
     <institution xml:lang="ru">Уфимский университет науки и технологий</institution>
     <city>Уфа</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Ufa University of Science and Technology</institution>
     <city>Ufa</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <pub-date publication-format="print" date-type="pub" iso-8601-date="2026-03-25T13:15:14+03:00">
    <day>25</day>
    <month>03</month>
    <year>2026</year>
   </pub-date>
   <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-03-25T13:15:14+03:00">
    <day>25</day>
    <month>03</month>
    <year>2026</year>
   </pub-date>
   <volume>12</volume>
   <issue>1</issue>
   <fpage>125</fpage>
   <lpage>133</lpage>
   <history>
    <date date-type="received" iso-8601-date="2025-05-05T00:00:00+03:00">
     <day>05</day>
     <month>05</month>
     <year>2025</year>
    </date>
    <date date-type="accepted" iso-8601-date="2025-07-14T00:00:00+03:00">
     <day>14</day>
     <month>07</month>
     <year>2025</year>
    </date>
   </history>
   <self-uri xlink:href="https://naukaru.ru/en/nauka/article/113886/view">https://naukaru.ru/en/nauka/article/113886/view</self-uri>
   <abstract xml:lang="ru">
    <p>Разработка вероятностных и статистических моделей для оперативной оценки техносферных рисков, возникающих вследствие воздействия космической погоды на высокоширотные энергосистемы, является актуальной задачей с выраженным прикладным характером. Наибольшую практическую значимость такие модели имеют в полярных и субполярных регионах, недостаточно обеспеченных надежными источниками геомагнитных данных.&#13;
В работе предлагается оригинальный способ безаппаратной (без использования специализированного оборудования) оценки уровня геоиндуцированных токов (ГИТ) в энергосистемах Арктической зоны РФ, заключающийся в интерпретации визуально-различимых признаков полярных сияний как естественных индикаторов состояния космической погоды. На примере рассмотренного региона в целом и подстанции 330 кВ «Выходной» магистральной электрической сети «Северный транзит» в частности показана устойчивая статистическая взаимосвязь между областью наблюдения сияний, их структурой и уровнем ГИТ в высокоширотных энергосистемах. Установлено, что в периоды наблюдения дискретных сияний c вероятностью свыше 7.5 % уровень ГИТ превышает 10 А, в то время как при сияниях диффузного типа вероятность достижения такого значения составляет всего 0.31 %.&#13;
В условиях отсутствия или дефицита данных аппаратных измерений полученные модели возможно использовать для оценки вероятности возникновения экстремальных ГИТ в заполярных энергораспределительных системах и сетях, опираясь лишь на естественные индикаторы, наблюдаемые невооруженным глазом. Практическое применение представленных моделей может способствовать повышению эффективности решений, принимаемых в условиях низкой осведомленности в соответствующей предметной области</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>Development of new probabilistic and statistical models for operational assessment of technospheric risks caused by space weather impacts on high-latitude power systems is a relevant research task with significant practical applications. Such models are of the greatest practical importance in polar and subpolar regions with insufficient availability of reliable and accurate geomagnetic data sources.&#13;
This paper presents an original approach to hardware-free (without specialized equipment) assessment of geomagnetically induced current (GIC) levels in power systems of the Russian Arctic zone by interpreting visually observable auroral features as natural indicators of space weather conditions. Using the case study of the 330 kV Vykhodnoy substation in the Severny Transit main power grid, a stable statistical relationship is demonstrated between the auroral observation area, auroral structure, and GIC levels in high-latitude power systems. It is established that during periods of discrete auroras the probability of GIC exceeding 10 A is over 7.5 %, whereas for diffuse auroras this probability is only 0.31 %.&#13;
In the absence or scarcity of instrumental measurement data, the developed models can be employed to estimate the likelihood of extreme GIC in Arctic power distribution systems and grids, relying solely on visual natural indicators. The practical application of the proposed models in certain scenarios may improve decision-making efficiency in situations with low situational awareness in the relevant field</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>геомагнитные вариации</kwd>
    <kwd>космическая погода</kwd>
    <kwd>высокоширотные энергосистемы</kwd>
    <kwd>статистические модели</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>geomagnetic variations</kwd>
    <kwd>space weather</kwd>
    <kwd>high-latitude power grids</kwd>
    <kwd>statistical models</kwd>
   </kwd-group>
   <funding-group>
    <funding-statement xml:lang="ru">Исследование выполнено при поддержке Российского научного фонда (проект № 21-77-30010-П)</funding-statement>
    <funding-statement xml:lang="en">The work was financially supported by the Russian Science Foundation (Project No. 21-77-30010-P)</funding-statement>
   </funding-group>
  </article-meta>
 </front>
 <body>
  <p></p>
 </body>
 <back>
  <ref-list>
   <ref id="B1">
    <label>1.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Вахнина В.В., Черненко А.Н., Кузнецов В.А. Влияние геоиндуцированных токов на насыщение магнитной системы силовых трансформаторов. Вектор науки Тольяттинского государственного университета. 2012, № 3(21), с. 65–69.</mixed-citation>
     <mixed-citation xml:lang="en">Barannik M.B., Danilin A.N., Kat’kalov Yu.V., Kolobov V.V., Sakharov Ya.A., Selivanov V.N. A system for recording geomagnetically induced currents in neutrals of power autotransformers. Instruments and Experimental Techniques. 2012, vol. 55, no. 1, pp. 110–115. DOI: 10.1134/S0020441211060121.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B2">
    <label>2.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Воробьев А.В., Пилипенко В.А. Подход к восстановлению геомагнитных данных на базе концепции цифровых двойников. Солнечно-земная физика. 2021, т. 7, № 2, с. 53–62. DOI: 10.12737/szf-72202105 / Vorobev A.V., Pilipenko V.A. Geomagnetic data recovery approach based on the concept of digital twins. Sol.-Terr. Phys. 2021, vol. 7, iss. 2, pp. 48–56. DOI: 10.12737/stp-72202105.</mixed-citation>
     <mixed-citation xml:lang="en">Danilov G.A., Denchik Yu.M., Ivanov M.N., Sitnikov G.V. Povyshenie kachestva funktsionirovaniya linii elek-troperedachi [Improving the Quality of Operation of Power Transmission Lines]. Moscow; Berlin, 2015, 558 p. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B3">
    <label>3.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Воробьев В.Г., Сахаров Я.А., Ягодкина О.И. и др. Геоиндуцированные токи и их связь с положением западной электроструи и границами авроральных высыпаний. Труды Кольского научного центра РАН. 2018, т. 5, вып. 4, с. 16–28.</mixed-citation>
     <mixed-citation xml:lang="en">Dimitrova D.S., Kaishev V.K., Tan S. Computing the Kolmogorov-Smirnov distribution when the underlying CDF is purely discrete, mixed, or continuous. Journal of Statistical Software. 2020, vol. 95, iss. 10, pp. 1–42. DOI: 10.18637/jss.v095.i10.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B4">
    <label>4.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Воробьев А.В., Пилипенко В.А., Сахаров Я.А., Селиванов В.Н. Статистические взаимосвязи вариаций геомагнитного поля, аврорального электроджета и геоиндуцированных токов. Солнечно-земная физика. 2019, т. 5, № 1, с. 48–58. DOI: 10.12737/szf-51201905 / Vorobev A.V., Pilipenko V.A., Sakharov Ya.A., Selivanov V.N. Statistical relationships between variations of the geomagnetic field, auroral electrojet, and geomagnetically induced currents. Sol.-Terr. Phys. 2019, vol. 5, iss. 1, pp. 35–42. DOI: 10.12737/stp-51201905.</mixed-citation>
     <mixed-citation xml:lang="en">Dobbins R.W., Schriiver K. Electrical Claims and Space Weather. Measuring the Visible Effects of an Invisible Force June 2015. URL: https://centerforsecuritypolicy.org/wp-content/uploads/2022/06/Appendix-F-2015Zurich-ElectricalClaimsandSpaceWeather.pdf (accessed May 3, 2025).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B5">
    <label>5.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Воробьев А.В., Соловьев А.А., Пилипенко В.А., Воробьева Г.Р. Интерактивная компьютерная модель для прогноза и анализа полярных сияний. Солнечно-земная физика. 2022, т. 8, № 2, с. 93–100. DOI: 10.12737/szf-82202213 / Vorobev A.V., Soloviev A.A., Pilipenko V.A., Vorobeva G.R. Interactive computer model for aurora forecast and analysis. Sol.-Terr. Phys. 2022, vol. 7, iss. 2, pp. 84–90. DOI: 10.12737/stp-82202213.</mixed-citation>
     <mixed-citation xml:lang="en">Eckhard L., Werner A.S., Markus A. Log-normal Distributions across the Sciences: Keys and Clues: On the charms of statistics, and how mechanical models resembling gambling machines offer a link to a handy way to characterize log-normal distributions, which can provide deeper insight into variability and probability — normal or log-normal: That is the question. BioScience. 2001, vol. 51, no. 5, pp. 341–352. DOI: 10.1641/0006-3568(2001)051[0341:LNDATS]2.0.CO;2.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B6">
    <label>6.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Воробьев А.В., Соловьев А.А., Пилипенко В.А. и др. Локальная диагностика наличия полярных сияний на основе интеллектуального анализа геомагнитных данных. Солнечно-земная физика. 2023, т. 9, №. 2, c. 26–34. DOI: 10.12737/szf-92202303 / Vorobev A.V., Soloviev A.A., Pilipenko V.A., et al. Local diagnostics of aurora presence based on intelligent analysis of geomagnetic data. Sol.-Terr. Phys. 2023, vol. 9, iss. 2, pp. 22–30. DOI: 10.12737/stp-92202303.</mixed-citation>
     <mixed-citation xml:lang="en">Eroshenko E.A., Belov A.V., Boteler D., et al.  Effects of strong geomagnetic storms on Northern railways in Russia. Adv. Space Res. 2010, vol. 46, iss. 9, pp. 1102–1110. DOI: 10.1016/j.asr.2010.05.017.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B7">
    <label>7.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Воробьев А.В., Лапин А.Н., Соловьев А.А., Воробьева Г.Р. Подход к интерпретации естественных индикаторов состояния космической погоды для оценки эффектов ее воздействия на высокоширотные энергосистемы. Физика Земли. 2024, № 4, с. 100–110. DOI: 10.31857/S0002333724040071.</mixed-citation>
     <mixed-citation xml:lang="en">Gvishiani A.D., Lukyanova R.Yu. Assessment of the influence of geomagnetic disturbances on the trajectory of directional drilling of deep wells in the Arctic region. The Fundamental Basis of Innovative Technologies in the Oil and Gas Industry. Proc. All-Russian Scientific Conference dedicated to the 30th anniversary of the Institute of Oil and Gas Geophysics of the Russian Academy of Sciences. 2017, p. 46. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B8">
    <label>8.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Гвишиани А.Д., Лукьянова Р.Ю. Оценка влияния геомагнитных возмущений на траекторию наклонно-направленного бурения глубоких скважин в Арктическом регионе. Фундаментальный базис инновационных технологий нефтяной и газовой промышленности. Материалы Всероссийской научной конференции, посвященной 30-летию ИПНГ РАН. 2017, с. 46.</mixed-citation>
     <mixed-citation xml:lang="en">Gvozdarev A.Yu., Sivokon V.P., Khomutov S.Yu. Estimation of the magnitude of geomagnetically induced currents in the Central energy district of the Kamchatka Krai energy system. Vestnik KRAUNTS. Fiz.-mat. nauki [Bulletin of KRAUNC. Phys.-math. sci.]. 2024, vol. 49, no. 4, pp. 185–202. DOI: 10.26117/2079-6641-2024-49-4-185-202. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B9">
    <label>9.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Гвоздарев А.Ю., Сивоконь В. П., Хомутов С.Ю. Оценка величины геомагнитно-индуцированных токов в Центральном энергорайоне энергосистемы Камчатского края. Вестник КРАУНЦ. Физ.-мат. науки. 2024, т. 49, № 4, с. 185–202. DOI: 10.26117/2079-6641-2024-49-4-185-202.</mixed-citation>
     <mixed-citation xml:lang="en">Kanonidi H.D., Oraevsky V.N., Belov A.V., et al. Failures in the operation of railway automation during geomagnetic storms. Problems of forecasting emergency situations. Sollection of Materials from a Scientific and Practical Conference. 2002, pp. 41–42. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B10">
    <label>10.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Данилов Г.А., Денчик Ю.М., Иванов М.Н., Ситников Г.В. Повышение качества функционирования линий электропередачи. М.; Берлин: Директ-Медиа, 2015. 558 c.</mixed-citation>
     <mixed-citation xml:lang="en">Kataoka R., Ngwira C. Extreme geomagnetically induced currents. Prog. in Earth and Planet. Sci. 2016, no. 3, p. 23.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B11">
    <label>11.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Зеленый Л.М., Петрукович А.А. Арктика. Космическая погода. Природа. 2015, № 9, с. 31–39.</mixed-citation>
     <mixed-citation xml:lang="en">Marshall R.A., Smith E.A., Francis M.J., Waters C.L., Sciffer M.D. A preliminary risk assessment of the Australian region power network to space weather. Space Weather. 2011, vol. 9, S10004. DOI: 10.1029/2011SW000685.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B12">
    <label>12.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Канониди Х.Д., Ораевский В.Н., Белов А.В. и др. Сбои в работе железнодорожной автоматики во время геомагнитных бурь. Проблемы прогнозирования чрезвычайных ситуаций: сборник материалов научно-практической конференции. 2002, с. 41–42.</mixed-citation>
     <mixed-citation xml:lang="en">Pilipenko A.V. Space weather impact on ground-based technological systems. Sol.-Terr. Phys. 2021, vol. 7, iss. 3, pp. 68–104. DOI: 10.12737/stp-73202106.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B13">
    <label>13.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Пилипенко В.А. Воздействие космической погоды на наземные технологические системы. Солнечно-земная физика. 2021, т. 7, № 3, с. 72–110. DOI: 10.12737/szf-73202106 / Pilipenko A.V. Space weather impact on ground-based technological systems. Sol.-Terr. Phys. 2021, vol. 7, iss. 3, pp. 68–104. DOI: 10.12737/stp-73202106.</mixed-citation>
     <mixed-citation xml:lang="en">Pilipenko V.A., Chernikov A.A., Soloviev A.A., et al.  The influence of space weather on the reliability of transport systems at high latitudes. Russ. J. Earth Sci. 2023, vol. 23, ES2008. DOI: 10.2205/2023ES000824. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B14">
    <label>14.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Пилипенко В.А., Черников А.А., Соловьев А.А. и др. Влияние космической погоды на надежность функционирования транспортных систем на высоких широтах. Russian Journal of Earth Sciences. 2023, т. 23, ES2008. DOI: 10.2205/2023ES000824.</mixed-citation>
     <mixed-citation xml:lang="en">Pilipenko V.A., Kozyreva O.V., Belakhovsky V.B., et al.  What should we know to predict geomagnetically induced currents in power transmission lines. Russ. J. Earth Sci.  2024, vol. 24, ES6006. DOI: 10.2205/2024es000954.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B15">
    <label>15.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Птицына Н.Г., Тясто М.И., Касинский В.В., Ляхов Н.Н. Влияние космической погоды на технические системы: сбои железнодорожной аппаратуры во время геомагнитных бурь. Солнечно-земная физика. 2008, вып. 12(125), т. 2, с. 360.</mixed-citation>
     <mixed-citation xml:lang="en">Pirjola R., Pulkkinen A., Viljanen A. Studies of space weather effects on the Finnish natural gas pipeline and on the Finnish high-voltage power system. Adv. Space Res. 2003, vol. 31, iss. 4, pp. 795–805. DOI: 10.1016/S0273-1177(02)00781-0.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B16">
    <label>16.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Пуляев В.И., Усачев Ю.В. Магнитная буря — причина отключения ВЛ 330 кВ. Энергетик. 2002, № 7, с. 18–20.</mixed-citation>
     <mixed-citation xml:lang="en">Ptitsyna N.G., Tyasto M.I., Kasinsky V.V., Lyakhov N.N. Impact of space weather on technical systems: Failures of railway equipment during geomagnetic storms. Solnechno-zemnaya fizika [Sol.-Terr. Phys]. 2008, iss. 12(125), vol. 2, p. 360. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B17">
    <label>17.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Селиванов В.Н., Аксенович Т.В., Билин В.А. и др. База данных геоиндуцированных токов в магистральной электрической сети «Северный транзит». Солнечно-земная физика. 2023, т. 9, № 3, с. 100–110. DOI: 10.12737/szf-93202311 / Selivanov V.N., Aksenovich T.V., Bilin V.A., et al. Database of geomagnetically induced currents in the main transmission line “Northern Transit”. Sol.-Terr. Phys. 2023, vol. 9, iss. 3, pp. 93–101. DOI: 10.12737/stp-93202311.</mixed-citation>
     <mixed-citation xml:lang="en">Pulyayev V.I., Usachev Yu.V. Magnetic storm — the reason for the shutdown of the 330 kV power transmission line. Energetik [Power Engineer]. 2002, no. 7, p. 18. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B18">
    <label>18.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Соколова О.Н., Сахаров Я.А., Грицутенко С.С., Коровкин Н.В. Алгоритм анализа устойчивости энергосистем к геомагнитным бурям. Известия РАН. Энергетика. 2019, с. 33–52. DOI: 10.1134/S0002331019050145.</mixed-citation>
     <mixed-citation xml:lang="en">Radasky W., Emin Z., Adams R, van Baelen J. CIGRE TB 780: Understanding of geomagnetic storm environment for high voltage power grids. Technical report. 2019.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B19">
    <label>19.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Ягова Н.В., Розенберг И.Н., Гвишиани А.Д. и др. Исследование влияния геомагнитной активности на функционирование систем железнодорожной автоматики в Арктической зоне России. Арктика: экология и экономика. 2023, т. 13, № 3, с. 341–352. DOI: 10.25283/2223-4594-2023-3-341-352.</mixed-citation>
     <mixed-citation xml:lang="en">Scott D.W. On optimal and data-based histograms. Biometrika. 1979, vol. 66, pp. 605–610. DOI: 10.1093/biomet/66.3.605.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B20">
    <label>20.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Ягодкина О.И., Воробьев В.Г., Шекунова Е.С. Наблюдения полярных сияний над Кольским полуостровом. Труды Кольского научного центра РАН. 2019, т. 10, № 8-5, с. 43–55. DOI: 10.25702/KSC.2307-5252.2019.10.8.</mixed-citation>
     <mixed-citation xml:lang="en">Selivanov V.N., Aksenovich T.V., Bilin V.A., Kolobov V.V., Sakharov Ya.A. Database of geomagnetically induced currents in the main transmission line “Northern Transit”. Sol.-Terr. Phys. 2023, vol. 9, iss. 3, pp. 93–101. DOI: 10.12737/stp-93202311.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B21">
    <label>21.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Barannik M.B., Danilin A.N., Kat’kalov Yu.V., et al. A system for recording geomagnetically induced currents in neutrals of power autotransformers. Instruments and Experimental Techniques. 2012, vol. 55, no. 1, pp. 110–115. DOI: 10.1134/S0020441211060121.</mixed-citation>
     <mixed-citation xml:lang="en">Sigernes F., Holmen S.E., Biles D., Chen X., Dyrland M. Auroral all-sky camera calibration. Geosci. Instrum. Method. Data Syst. 2014, vol. 3, pp. 241–245. DOI: 10.5194/gi-3-241-2014.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B22">
    <label>22.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Dimitrova D.S., Kaishev V.K., Tan S. Computing the Kolmogorov–Smirnov distribution when the underlying CDF is purely discrete, mixed, or continuous. Journal of Statistical Software. 2020, vol. 95, iss. 10, pp. 1–42. DOI: 10.18637/jss.v095.i10.</mixed-citation>
     <mixed-citation xml:lang="en">Sokolova O.N., Sakharov Ya.A., Gritsutenko S.S., Korovkin N.V. Algorithm for analyzing the stability of power systems to geomagnetic storms. Izvestiya RAN. Energetika [Proc. Russian Academy of Sciences. Power Engineering]. 2019, no. 5, pp. 33–52. DOI: 10.1134/S0002331019050145. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B23">
    <label>23.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Dobbins R.W., Schriiver K. Electrical Claims and Space Weather. Measuring the Visible Effects of an Invisible Force June 2015. URL: https://centerforsecuritypolicy.org/wp-content/uploads/2022/06/Appendix-F-2015Zurich-ElectricalClaimsandSpaceWeather.pdf (дата обращения   3 мая 2025 г.).</mixed-citation>
     <mixed-citation xml:lang="en">Soloviev A.A., Sidorov R.V., Oshchenko A.A., Zaitcev A.N. On the need for accurate monitoring of the geomagnetic field during directional drilling in the Russian Arctic. Izvestiya, Physics of the Solid Earth. 2022, vol. 58, pp. 420–434. DOI: 10.1134/S1069351322020124.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B24">
    <label>24.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Eckhard L., Werner A.S., Markus A. Log-normal distributions across the sciences: keys and clues: on the charms of statistics, and how mechanical models resembling gambling machines offer a link to a handy way to characterize log-normal distributions, which can provide deeper insight into variability and probability — normal or log-normal: That is the question. BioScience. 2001, vol. 51, no. 5, pp. 341–352. DOI: 10.1641/0006-3568(2001)051[0341:LNDATS]2.0.CO;2.</mixed-citation>
     <mixed-citation xml:lang="en">Tanskanen E.I. A comprehensive high-throughput analysis of substorms observed by IMAGE magnetometer network: Years 1993–2003 examined. J. Geophys. Res. 2009, vol. 114, A05204. DOI: 10.1029/2008JA013682.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B25">
    <label>25.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Eroshenko E.A., Belov A.V., Boteler D., et al. Effects of strong geomagnetic storms on Northern railways in Russia. Adv. Space Res. 2010, vol. 46, iss. 9, pp. 1102–1110. DOI: 10.1016/j.asr.2010.05.017.</mixed-citation>
     <mixed-citation xml:lang="en">Vakhnina V.V., Chernenko A.N., Kuznetsov V.A. Influence of geo-induced currents on the saturation of the magnetic system of power transformers. Vektor nauki Tol'yattinskogo gosudarstvennogo universiteta [Vector of Science of Togliatti State University]. 2012, no. 3(21), pp. 65–69. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B26">
    <label>26.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Kataoka R., Ngwira C. Extreme geomagnetically induced currents. Prog. in Earth and Planet. Sci. 2016, no. 3, p. 23.</mixed-citation>
     <mixed-citation xml:lang="en">Vorobev A.V., Pilipenko V.A. Geomagnetic data recovery approach based on the concept of digital twins. Sol.-Terr. Phys. 2021, vol. 7, iss. 2, pp. 48–56. DOI: 10.12737/stp-72202105.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B27">
    <label>27.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Marshall R.A., Smith E.A., Francis M.J., et al. A preliminary risk assessment of the Australian region power network to space weather. Space Weather. 2011, vol. 9, S10004. DOI: 10.1029/2011SW000685.</mixed-citation>
     <mixed-citation xml:lang="en">Vorobev A.V., Pilipenko V.A., Sakharov Ya.A., Selivanov V.N. Statistical relationships between variations of the geomagnetic field, auroral electrojet, and geomagnetically induced currents. Sol.-Terr. Phys. 2019, vol. 5, iss. 1, pp. 35–42. DOI: 10.12737/stp-51201905.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B28">
    <label>28.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Pilipenko V.A., Kozyreva O.V., Belakhovsky V.B., et al. What should we know to predict geomagnetically induced currents in power transmission lines. Russian Journal of Earth Sciences. 2024, vol. 24, ES6006. DOI: 10.2205/2024es000954.</mixed-citation>
     <mixed-citation xml:lang="en">Vorobev A., Soloviev A., Pilipenko V., et al.  An approach to diagnostics of geomagnetically induced currents based on ground magnetometers data. App. Sci. 2022a, vol. 12, 1522. DOI: 10.3390/app12031522.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B29">
    <label>29.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Pirjola R., Pulkkinen A., Viljanen A. Studies of space weather effects on the Finnish natural gas pipeline and on the Finnish high-voltage power system. Adv. Space Res. 2003, vol. 31, iss. 4, pp. 795–805. DOI: 10.1016/S0273-1177(02)00781-0.</mixed-citation>
     <mixed-citation xml:lang="en">Vorobev A.V., Soloviev A.A., Pilipenko V.A., Vorobeva G.R. Interactive computer model for aurora forecast and analysis. Sol.-Terr. Phys. 2022b, vol. 7, iss. 2, pp. 84–90. DOI: 10.12737/stp-82202213.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B30">
    <label>30.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Radasky W., Emin Z., Adams R, van Baelen J. CIGRE TB 780: Understanding of geomagnetic storm environment for high voltage power grids. Technical report. 2019.</mixed-citation>
     <mixed-citation xml:lang="en">Vorobev A.V., Soloviev A.A., Pilipenko V.A., et al.  Local diagnostics of aurora presence based on intelligent analysis of geomagnetic data. Sol.-Terr. Phys. 2023, vol. 9, iss. 2, pp. 22–30. DOI: 10.12737/stp-92202303.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B31">
    <label>31.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Scott D.W. On optimal and data-based histograms. Biometrika. 1979, vol. 66, pp. 605–610. DOI: 10.1093/biomet/66.3.605.</mixed-citation>
     <mixed-citation xml:lang="en">Vorobev A.V., Lapin A.N., Soloviev A.A., Vorobeva G.R. An approach to interpreting space weather natural indicators to evaluate the impact of space weather on high-latitude power systems. Izvestiya, Physics of the Solid Earth. 2024, vol. 60, pp. 604–611. DOI: 10.1134/S106935132470054X.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B32">
    <label>32.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Sigernes F., Holmen S.E., Biles D., et al. Auroral all-sky camera calibration. Geosci. Instrum. Method. Data Syst. 2014, no. 3, pp. 241–245. DOI: 10.5194/gi-3-241-2014.</mixed-citation>
     <mixed-citation xml:lang="en">Vorobyov V.G., Sakharov Ya.A., Yagodkina O.I., et al. Geoinduced currents and their relationship with the position of the western electrojet and the boundaries of auroral precipitation. Proc. Kola Science Center of the Russian Academy of Sciences. 2018, vol. 5, no. 4, pp. 16–28. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B33">
    <label>33.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Soloviev A.A., Sidorov R.V., Oshchenko A.A., Zaitcev A.N. On the need for accurate monitoring of the geomagnetic field during directional drilling in the Russian Arctic. Izvestiya, Physics of the Solid Earth. 2022, vol. 58, pp. 420–434. DOI: 10.1134/S1069351322020124.</mixed-citation>
     <mixed-citation xml:lang="en">Wintoft P., Wik M., Viljanen A. Solar wind driven empirical forecast models of the time derivative of the ground magnetic field. J. Space Weather Space Climate. 2015, vol. 5, A7. DOI: 10.1051/swsc/2015008.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B34">
    <label>34.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Tanskanen E.I. A comprehensive high-throughput analysis of substorms observed by IMAGE magnetometer network: Years 1993–2003 examined. J. Geophys. Res. 2009, vol. 114, A05204. DOI: 10.1029/2008JA013682.</mixed-citation>
     <mixed-citation xml:lang="en">Yagodkina O.I., Vorobyov V.G., Shekunova E.S. Observations of polar lights over the Kola Peninsula.  Proc. Kola Science Center of the Russian Academy of Sciences. 2019, vol. 10, no. 8-5, pp. 43–55. DOI: 10.25702/KSC.2307-5252.2019.10.8. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B35">
    <label>35.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Vorobev A., Soloviev A., Pilipenko V., et al. An approach to diagnostics of geomagnetically induced currents based on ground magnetometers data. App. Sci. 2022, vol. 12, 1522. DOI: 10.3390/app12031522.</mixed-citation>
     <mixed-citation xml:lang="en">Yagova N.V., Rosenberg I.N., Gvishiani A.D., et al.  tudy of the influence of geomagnetic activity on the functioning of railway automation systems in the Arctic zone of Russia. Arktika: ekologiya i ekonomika [Arctic: Ecology and Economics]. 2023, vol. 13, no. 3, pp. 341–352. DOI: 10.25283/2223-4594-2023-3-341-352. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B36">
    <label>36.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Wintoft P., Wik M., Viljanen A. Solar wind driven empirical forecast models of the time derivative of the ground magnetic field. J. Space Weather Space Climate. 2015, vol. 5, A7. DOI: 10.1051/swsc/2015008.</mixed-citation>
     <mixed-citation xml:lang="en">Zeleny L.M., Petrukovich A.A. Arctic. Space weather. Priroda [Nature]. 2015, no. 9, pp. 31–39. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B37">
    <label>37.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">URL: https://aurora-forecast.ru (дата обращения 3 мая 2025 г.).</mixed-citation>
     <mixed-citation xml:lang="en">URL: https://aurora-forecast.ru (accessed May 3, 2025).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B38">
    <label>38.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">URL: http://pgia.ru/lang/ru/archive_pgi (дата обращения 3 мая 2025 г.).</mixed-citation>
     <mixed-citation xml:lang="en">URL: http://pgia.ru/lang/ru/archive_pgi (accessed May 3, 2025).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B39">
    <label>39.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">URL: http://gic.en51.ru (дата обращения 3 мая 2025 г.).</mixed-citation>
     <mixed-citation xml:lang="en">URL: http://gic.en51.ru (accessed May 3, 2025).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B40">
    <label>40.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">URL: http://aurora.pgia.ru:8071/?p=2 (дата обращения 3 мая 2025 г.).</mixed-citation>
     <mixed-citation xml:lang="en">URL: http://aurora.pgia.ru:8071/?p=2 (accessed May 3, 2025).</mixed-citation>
    </citation-alternatives>
   </ref>
  </ref-list>
 </back>
</article>
