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<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">10.21285/1814-3520-2026-1-34-56</article-id><article-id custom-type="edn" pub-id-type="custom">VEFOVA</article-id><article-id custom-type="elpub" pub-id-type="custom">ipolytech-1031</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>Частотный пуск синхронной машины по арктангенциальному закону</article-title><trans-title-group xml:lang="en"><trans-title>Frequency-controlled start of a synchronous machine based on an arctangent law</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0003-3111-0165</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Блинников</surname><given-names>М. Е.</given-names></name><name name-style="western" xml:lang="en"><surname>Blinnikov</surname><given-names>M. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Блинников Михаил Евгеньевич, аспирант</p><p>660074, г. Красноярск, ул. Академика Киренского, 26</p></bio><bio xml:lang="en"><p>Mikhail E. Blinnikov, Postgraduate Student</p><p>26 Kirensky St., Krasnoyarsk, 660074</p></bio><email xlink:type="simple">mikhail1997blinnikov@mail.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/0000-0002-8676-3177</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Пантелеев</surname><given-names>В. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Panteleev</surname><given-names>V. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Пантелеев Василий Иванович, доктор технических наук, профессор, заведующий кафедрой электроэнергетики</p><p>660074, г. Красноярск, ул. Академика Киренского, 26</p></bio><bio xml:lang="en"><p>Vasiliy I. Panteleev, Dr. Sci. (Eng.), Professor, Head of the Electric Power Engineering Department</p><p>26 Kirensky St., Krasnoyarsk, 660074</p></bio><email xlink:type="simple">pvi0808@rambler.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Сибирский федеральный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Siberian Federal University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>29</day><month>03</month><year>2026</year></pub-date><volume>30</volume><issue>1</issue><fpage>47</fpage><lpage>56</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Блинников М.Е., Пантелеев В.И., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Блинников М.Е., Пантелеев В.И.</copyright-holder><copyright-holder xml:lang="en">Blinnikov M.E., Panteleev V.I.</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/1031">https://ipolytech.elpub.ru/jour/article/view/1031</self-uri><abstract><p>Цель – формирование закона и представление методики расчета параметров арктангенциального частотного пуска синхронной машины с маховичным накопителем энергии. Объектом исследования является электротехнический комплекс с маховичным накопителем энергии в составе трансформаторной подстанции непромышленных потребителей. Данный комплекс состоит из маховичного накопителя, синхронной машины, преобразователя частоты и системы управления. Анализ протекающих при пуске процессов выполнен в относительных единицах в dq-координатах. Для описания начального этапа пуска изменение частоты и напряжения представлены линейной, изменение электромагнитного момента синусоидальной, а изменение угла нагрузки квадратичной зависимостью от времени. Для проверки результатов проведено имитационное моделирование в среде SimInTech на основании системы дифференциальных уравнений Парка–Горева для синхронной машины. Представлено краткое описание и предложена методика расчета параметров закона частотного пуска c изменением частоты по арктангенциальной зависимости для синхронной машины с маховичным накопителем энергии. Эту зависимость можно характеризировать параметром σ, определяющим максимум ускорения, и продолжительностью пуска Tп. Показано, что ускорение ротора и потребляемый ток достигают наибольших значений к середине продолжительности пускового режима. Сравнение результатов расчета параметров частотного пуска для синхронной машины с маховичным накопителем и имитационного моделирования показало наибольшее отклонение параметров до 13%. Предложенный закон управления частотного пуска и методика расчета его параметров для синхронной машины с маховичным накопителем энергии позволяют обеспечить регулируемый пуск с заданным пиковым значением пускового тока и расчетной продолжительностью пуска. Результаты работы могут способствовать стандартизации и распространению маховичных накопителей энергии на действующих и вновь вводимых объектах.</p></abstract><trans-abstract xml:lang="en"><p>This study presents a control law and the methodology for calculating the parameters of a frequency-controlled start using an arctangent-based approach for a synchronous machine equipped with a flywheel energy storage system. The electrical engineering system incorporating a flywheel energy storage unit within a transformer substation serving non-industrial consumers was examined. This system consists of a flywheel energy storage unit, a synchronous machine, a frequency converter, and a control system. The startup processes were analyzed in perunit values using dq coordinates. The initial startup stage was described using a linear function for frequency and voltage, a sinusoidal function for electromagnetic torque, and a quadratic time dependence for load angle. The results were validated by simulation modeling in the SimInTech environment, which is based on the Park–Gorev system of differential equations for a synchronous machine. A methodology is proposed for calculating the parameters of a frequency-controlled start law with arctangent frequency variation for a synchronous machine with a flywheel energy storage system. The proposed law is defined by a parameter s that determines the maximum acceleration and start duration Ts. The results show that rotor acceleration and current consumption reach their maximum values near the midpoint of the startup interval. A comparison between the calculated frequency-start parameters for the synchronous machine with flywheel energy storage and the simulation results revealed a maximum parameter deviation of up to 13%. The proposed frequency-start control law and the associated methodology for calculating its parameters enable a controlled start with a specified peak starting current and a predetermined start duration. These results support the standardization and wider adoption of flywheel energy storage systems in both existing and newly commissioned facilities.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>маховичный накопитель энергии</kwd><kwd>обратимый преобразователь энергии</kwd><kwd>частотный пуск</kwd><kwd>арктангенциальный закон управления</kwd><kwd>синхронная машина</kwd><kwd>втягивание в синхронизм</kwd><kwd>распределенная энергетика</kwd></kwd-group><kwd-group xml:lang="en"><kwd>flywheel energy storage</kwd><kwd>reversible energy converter</kwd><kwd>underfrequency relay</kwd><kwd>arctangent varying frequency law</kwd><kwd>synchronous machine</kwd><kwd>pulling into synchronism</kwd><kwd>distributed power generation</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Добрего К.B. К вопросу создания гибридных систем накопления электроэнергии // Энергетика. 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