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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">probener</journal-id><journal-title-group><journal-title xml:lang="ru">Известия высших учебных заведений. ПРОБЛЕМЫ ЭНЕРГЕТИКИ</journal-title><trans-title-group xml:lang="en"><trans-title>Power engineering: research, equipment, technology</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1998-9903</issn><issn pub-type="epub">2658-5456</issn><publisher><publisher-name>Kazan State Power Engineering  University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.30724/1998-9903-2021-23-5-13-23</article-id><article-id custom-type="elpub" pub-id-type="custom">probener-1980</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>Использование многомодельной прогнозной оценки состояния систем электроснабжения для обнаружения кибер-атак</article-title><trans-title-group xml:lang="en"><trans-title>The usage of power system multi-model forecasting aided state estimation for cyber attack detection</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Лукичева</surname><given-names>И. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Lukicheva</surname><given-names>I. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Лукичева Ирина Александровна – стажер-исследователь Сколковского института науки и технологий центра Энергетических наук и технологий</p><p>г. Нижний Новгород</p></bio><bio xml:lang="en"><p>Irina A. Lukicheva</p><p>Nizhny Novgorod</p></bio><email xlink:type="simple">lukicheva.ir@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Куликов</surname><given-names>А. Л.</given-names></name><name name-style="western" xml:lang="en"><surname>Kulikov</surname><given-names>A. L.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Куликов Александр Леонидович – д-р техн. наук, профессор кафедры «Электроэнергетика, электроснабжение и силовая электроника»</p><p>г. Нижний Новгород</p></bio><bio xml:lang="en"><p>Alexander L. Kulikov</p><p>Nizhny Novgorod</p></bio><email xlink:type="simple">inventor61@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Нижегородский государственный технический университет им. Р.Е. Алексеева</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Nizhny Novgorod State Technical University R.E. Alekseeva</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2021</year></pub-date><pub-date pub-type="epub"><day>09</day><month>01</month><year>2022</year></pub-date><volume>23</volume><issue>5</issue><fpage>13</fpage><lpage>23</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Лукичева И.А., Куликов А.Л., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Лукичева И.А., Куликов А.Л.</copyright-holder><copyright-holder xml:lang="en">Lukicheva I.A., Kulikov A.L.</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://www.energyret.ru/jour/article/view/1980">https://www.energyret.ru/jour/article/view/1980</self-uri><abstract><sec><title>ЦЕЛЬ</title><p>ЦЕЛЬ. Интеллектуальные электрические сети предполагают широкое использование информационной инфраструктуры. Такая совокупная киберфизическая система может подвергаться воздействию кибератак. Одним из способов противодействия кибератакам является оценка состояния, позволяющая уточнять показания установленных в сети измерителей параметров электрической сети, а также использовать избыточность измерений для фильтрации поврежденных данных. В частности, при подмене реального измерения фальшивым или сбое в функционировании каналов связи возможно обнаружение ложных данных и их восстановление. Однако существует класс кибератак с вводом неверных данных, направленный на искажение результатов оценки состояния. Целью исследования было разработать алгоритм оценки состояния, сохраняющий высокую точность в условиях кибер-атак.</p></sec><sec><title>МЕТОДЫ</title><p>МЕТОДЫ. Авторами предлагается метод прогнозируемой оценки состояния, основанный на многомодельном дискретном следящем оценивании параметра фильтром Калмана. Многомодельная оценка определяется как взвешенная сумма одномодельных оценок, полученных с использованием различных переходных моделей. Обнаружение кибератаки реализуется с помощью инновационного анализа и анализа невязки измерения и оценки. Анализ работы предложенного алгоритма производился с помощью имитационного моделирования на примере 30-ти узловой схемы IEEE в программном комплексе MatLab.</p></sec><sec><title>РЕЗУЛЬТАТЫ</title><p>РЕЗУЛЬТАТЫ. В статье описана кибер-атака с вводом неверных данных и ее специфика воздействия на оценку состояния. Разработан алгоритм многомодельной прогнозируемой оценки состояния, позволяющий обнаруживать кибер-атаку и восстанавливать искаженные данные. Выполнено моделирование работы алгоритма и доказана его эффективность.</p></sec><sec><title>ЗАКЛЮЧЕНИЕ</title><p>ЗАКЛЮЧЕНИЕ. Результаты показали точность обнаружения кибератаки 100% в случае больших внесенных искажений параметров. Использование многомодельной прогнозируемой оценки состояния является эффективным методом защиты от воздействия кибер-атак на энергосистему.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>THE PURPOSE</title><p>THE PURPOSE. Smart electrical grids involve extensive use of information infrastructure. Such an aggregate cyber-physical system can be subject to cyber attacks. One of the ways to counter cyberattacks is state estimation. State Estimation is used to identify the present power system operating state and eliminating metering errors and corrupted data. In particular, when a real measurement is replaced by a false one by a malefactor or a failure in the functioning of communication channels occurs, it is possible to detect false data and restore them. However, there is a class of cyberattacks, so-called False Data Injection Attack, aimed at distorting the results of the state estimation. The aim of the research was to develop a state estimation algorithm, which is able to work in the presence of cyber-attack with high accuracy.</p></sec><sec><title>METHODS</title><p>METHODS. The authors propose a Multi-Model Forecasting-Aided State Estimation method based on multi-model discrete tracking parameter estimation by the Kalman filter. The multimodal state estimator consisted of three single state estimators, which produced single estimates using different forecasting models. In this paper only linear forecasting models were considered, such as autoregression model, vector autoregression model and Holt’s exponen tial smoothing. When we obtained the multi-model estimate as the weighted sum of the single-model estimates. Cyberattack detection was implemented through innovative and residual analysis. The analysis of the proposed algorithm performance was carried out by simulation modeling using the example of a IEEE 30-bus system in Matlab.</p></sec><sec><title>RESULTS</title><p>RESULTS. The paper describes an false data injection cyber attack and its specific impact on power system state estimation. A Multi - Model Forecasting-Aided State Estimation algorithm has been developed, which allows detecting cyber attacks and recovering corrupted data. Simulation of the algorithm has been carried out and its efficiency has been proved.</p></sec><sec><title>CONCLUSION</title><p>CONCLUSION. The results showed the cyber attack detection rate of 100%. The Multi-Model Forecasting-Aided State Estimation is an protective measure against the impact of cyber attacks on power system.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>авторегрессия</kwd><kwd>векторная авторегрессия</kwd><kwd>кибератака</kwd><kwd>оценка состояния</kwd><kwd>фильтрация Калмана</kwd><kwd>экспоненциальное сглаживание Хольта</kwd><kwd>электроэнергетическая система</kwd></kwd-group><kwd-group xml:lang="en"><kwd>autoregression</kwd><kwd>cyberattack</kwd><kwd>electric power system</kwd><kwd>Holt exponential smoothing</kwd><kwd>Kalman filtering</kwd><kwd>state estimation</kwd><kwd>vector autoregression</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">Колосок И.Н., Гурина Л.А. 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