2411-3336 2541-9404 Записки Горного института Journal of Mining Institute Санкт-Петербургский горный университет императрицы Екатерины ΙΙ Empress Catherine II Saint Petersburg Mining University 10.31897/PMI.2022.33 CJGQKP pmi-14928 https://pmi.spmi.ru/pmi/article/view/14928 Энергетика Energy industry Application of the cybernetic approach to price-dependent demand response for underground mining enterprise electricity consumption Использование кибернетического подхода к ценозависимому управлению спросом на потребляемую подземным горно-добывающим предприятием электроэнергию Nikolaev Aleksandr V. Николаев А. В. Nikolaev Aleksandr V. nikolaev0811@mail.ru 0000-0002-4601-5780 Пермский национальный исследовательский политехнический университет (Пермь, Россия) Perm National Research Polytechnic University (Perm, Russia) Vöth Stefan Фёт Ш. Vöth Stefan stefan.voeth@thga.de 0000-0002-0705-973X Высшая школа технических наук Георга Агриколы (Бохум, Германия) George Agricola Graduate School of Technical Sciences (Bochum, Germany) Kychkin Aleksei V. Кычкин А. В. Kychkin Aleksei V. avkychkin@hse.ru 0000-0003-0626-5803 Национальный исследовательский университет «Высшая школа экономики», филиал в г. Пермь (Пермь, Россия) National Research University Higher School of Economics, Branch in Perm (Perm, Russia) 13 07 2022 2023 261 403 414 12 05 2021 11 05 2022 19 07 2023 © 2022 А. В. Николаев, Ш. Фёт, А. В. Кычкин © 2022 Aleksandr V. Nikolaev, Stefan Vöth, Aleksei V. Kychkin 2022 А. В. Николаев, Ш. Фёт, А. В. Кычкин Aleksandr V. Nikolaev, Stefan Vöth, Aleksei V. Kychkin Эта статья доступна по лицензии Creative Commons Attribution 4.0 International (CC BY 4.0) This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0) https://pmi.spmi.ru/pmi/article/view/14928

В статье рассматривается кибернетическая модель ценозависимого управления спросом на электроэнергию (Demand Response, DR), потребляемую подземным горно-добывающим предприятием (ПГДП), в частности главной вентиляторной установкой (ГВУ). Предложены схема модели управления энергопотреблением ГВУ в режиме DR и имплементации кибернетического подхода к DR на базе платформы Интернета вещей. Описаны основные функциональные требования и алгоритм работы платформы, показано взаимодействие платформы с симулятором цифровой модели ПГДП, на которой будут заранее имитироваться процессы, связанные с осуществлением технологического процесса проветривания и управления спросом на электроэнергию. Приведены результаты моделирования снижения нагрузки на ГВУ горно-добывающего предприятия на сутки вперед. Представленное решение позволяет заблаговременно определять требуемые затраты электроэнергии на работу ГВУ, управлять ее работой в энергосберегающем режиме, учитывать прогнозируемые изменения в плановом (например, при спуске-подъеме рабочих по вентиляционному стволу) и внеплановом (например, при изменении параметров наружного воздуха) режимах. Результаты исследования могут быть использованы для снижения себестоимости добычи полезного ископаемого ПГДП без ущерба для безопасности технологических процессов, как за счет реализации энергосберегающих технических, технологических или иных мероприятий, так и при участии предприятий в рынке DR. Предложенная модель дает ПГДП гарантированное получение финансовой компенсации за счет обоснованного изменения профиля энергопотребления ГВУ в часы высокого спроса на электроэнергию, устанавливаемые системным оператором Единой энергетической системы.

The article considers a cybernetic model for the price-dependent demand response (DR) consumed by an underground mining enterprise (UGME), in particular, the main fan unit (MFU). A scheme of the model for managing the energy consumption of a MFU in the DR mode and the implementation of the cybernetic approach to the DR based on the IoT platform are proposed. The main functional requirements and the algorithm of the platform operation are described, the interaction of the platform with the UGME digital model simulator, on which the processes associated with the implementation of the technological process of ventilation and electricity demand response will be simulated in advance, is shown. The results of modeling the reduction in the load on the MFU of a mining enterprise for the day ahead are given. The presented solution makes it possible to determine in advance the necessary power consumption for the operation of the main power supply unit, manage its operation in an energy-saving mode and take into account the predicted changes in the planned one (e.g., when men hoisting along an air shaft) and unscheduled (e.g., when changing outdoor air parameters) modes. The results of the study can be used to reduce the cost of UGME without compromising the safety of technological processes, both through the implementation of energy-saving technical, technological or other measures, and with the participation of enterprises in the DR market. The proposed model ensures a guaranteed receipt of financial compensation for the UGME due to a reasonable change in the power consumption profile of the MFU during the hours of high demand for electricity, set by the system operator of the Unified Energy System.

 Ключевые слова управление спросом на электроэнергию кибернетический подход системная архитектура платформа Интернета вещей подземное горнодобывающее предприятие краткосрочное прогнозирование нагрузки цифровой двойник Keywords demand response cybernetic approach system architecture Internet of Things platform underground mining enterprise short-term load forecasting digital twin Исследование выполнено при финансовой поддержке правительства Пермского края в рамках проекта Международной исследовательской группы «Разработка цифровой модели прогнозирования и ценозависимого управления спросом на электроэнергию, потребляемую подземными горнодобывающими предприятиями», 2020 г. (соглашение № С-26/506 от 09.03.2021) The study was carried out with the financial support of the Government of the Perm Territory within the framework of the International Research Group “Development of a digital model for forecasting and price-dependent demand response for electricity consumed by the underground mining enterprises” project, 2020 (agreement N С26/506 dated 09.03.2021) Николаев А.В. Способ проветривания уклонных блоков нефтешахт, повышающий энергоэффективность подземной добычи нефти // Нефтяное хозяйство. 2016. № 11. C. 133-136. Nikolaev A.V. The method for ventilating the slope blocks of oil mines enhancing the energy efficiency of the underground oil production. Neftyanoe khozyaistvo. 2016. N 11, p. 133-136 (in Russian). Vilhena Costa de L., Silva da J.M. Cost-saving electrical energy consumption in underground ventilation by the use of ventilation on demand // Mining Technology. 2020. Vol. 129. Iss. 1. P. 1-8. DOI: 10.1080/25726668.2019.1651581 Vilhena Costa de L., Silva da J.M. Cost-saving electrical energy consumption in underground ventilation by the use of ventilation on demand. Mining Technology. 2020. Vol. 129. Iss. 1, p. 1-8. DOI: 10.1080/25726668.2019.1651581 Wallace K., Prosser B., Stinnette J.D. The practice of mine ventilation engineering // International Journal of Mining Science and Technology. 2015. Vol. 25. Iss. 2. P. 165-169. DOI: 10.1016/j.ijmst.2015.02.001 Wallace K., Prosser B., Stinnette J.D. The practice of mine ventilation engineering. International Journal of Mining Science and Technology. 2015. Vol. 25. Iss. 2, p. 165-169. DOI: 10.1016/j.ijmst.2015.02.001 Каменских А.А. Разработка методов контроля и снижения поверхностных утечек воздуха на рудниках: Автореф. дис. ... канд. техн. наук. Пермь: Горный институт Уральского отделения РАН, 2011. 20 с. Kamenskikh A.A. Development of methods to control and reduce surface air leakage in mines: Avtoref. dis. ... kand. tekhn. nauk. Perm: Gornyi institut Uralskogo otdeleniya RAN, 2011, p. 20 (in Russian). Николаев А.В., Алыменко Н.И., Садыков Р.И. Расчет величины поверхностных утечек воздуха на калийных рудниках // Вестник Пермского национального исследовательского политехнического университета. Геология. Нефтегазовое и горное дело. 2012. № 5. С. 115-121. Nikolaev A.V., Alymenko N.I., Sadykov R.I. Calculation of surface air leaks at potash mine. Bulletin of Perm University. Geology. 2012. N 5, p. 115-121 (in Russian). Головатый И.И., Круглов Ю.В., Левин Л.Ю. Шахтная вентиляторная установка с системой автоматического управления для рециркуляционного проветривания калийных рудников // Горный журнал. 2010. № 8. С. 78-80. Golovatyi I.I., Kruglov Yu.V., Levin L.Yu. Mine fan installation with automatic control system for recirculation ventilation of potash mines. Gornyi Zhurnal. 2010. N 8, p. 78-80 (in Russian). Круглов Ю.В., Левин Л.Ю., Зайцев А.В. Моделирование переходных процессов в вентиляционных сетях подземных рудников // Физико-технические проблемы разработки полезных ископаемых. 2011. № 5. С. 101-109. Kruglov Yu.V., Levin L.Yu., Zaitsev A.V. Сalculation method for the unsteady air supply in mine ventilation networks. Journal of Mining Science. 2011. Vol. 47. N 5, p. 651-659 (in Russian). Зайцев А.В. Научные основы расчета и управления тепловым режимом подземных рудников: Автореф. дис. … д-ра техн. наук. Пермь: Пермский национальный исследовательский политехнический университет, 2019. 44 с. Zaitsev A.V. Scientific basis for calculating and managing the thermal regime of underground mines: Avtoref. dis. … d-ra tekhn. nauk. Perm: Permskii natsionalnyi issledovatel'skii politekhnicheskii universitet 2019, p. 44 (in Russian). Gendler S.G., Kovshov S.V. Estimation and reduction of mining-induced damage of the environment and work area air in mining and processing of mineral stuff for the building industry // Eurasian mining. 2016. № 1. С. 45-49. DOI: 10.17580/em.2016.01.08 Gendler S.G., Kovshov S.V. Estimation and reduction of mining-induced damage of the environment and work area air in mining and processing of mineral stuff for the building industry. Eurasian mining. 2016. N 1, p. 45-49. DOI: 10.17580/em.2016.01.08 Николаев А.В. Энергоэффективное кондиционирование шахтного воздуха в неглубоких рудниках // Горный журнал. 2017. № 3. С. 71-74. DOI: 10.17580/gzh.2017.03.13 Nikolaev A.V. Energy-efficient air conditioning in shallow mines. Gornyi Zhurnal. 2017. Vol. 3, p. 71-74 (in Russian). DOI: 10.17580/gzh.2017.03.13 Кудж С.А., Цветков В.Я. Сетецентрическое управление и кибер-физические системы // Образовательные ресурсы и технологии. 2017. № 2(19). С. 86-92. DOI: 10.21777/2500-2112-2017-2-86-92 Kudzh S.A., Tsvetkov V.Ya. Network-centric control and cyber-physical systems. Educational resources and technology. 2017, p. 86-92 (in Russian). DOI: 10.21777/2500-2112-2017-2-86-92 Piette M., Sezgen O., Watson D. et al. Development and evaluation of fully automated demand response in large facilities // Lawrence Berkeley National Laboratory, 2004. Piette, M., Sezgen, O., Watson, D. et al. Development and evaluation of fully automated demand response in large facilities. Lawrence Berkeley National Laboratory, 2004. Sezgen O., Goldman C.A., Krishnarao P. Option value of electricity demand response // Energy. 2007. Vol. 32. Iss. 2. P. 108-119. DOI: 10.1016/j.energy.2006.03.024 Sezgen O., Goldman C.A., Krishnarao P. Option value of electricity demand response. Energy. 2007. Vol. 32. Iss. 2, p. 108-119. DOI: 10.1016/j.energy.2006.03.024 Valero S., Ortiz M., Senabre C. et al. Methods for customer and demand response policies selection in new electricity markets // IET Generation, Transmission & Distribution. 2007. Vol. 1. Iss. 1. P. 104-110. DOI: 10.1049/iet-gtd:20060183 Valero S., Ortiz M., Senabre C. et al. Methods for customer and demand response policies selection in new electricity markets. IET Generation, Transmission & Distribution. 2007. Vol. 1. Iss. 1, p. 104-110. DOI: 10.1049/iet-gtd:20060183 Chasparis G.C., Pichler M., Spreitzhofer J., Esterl T. A cooperative demand-response framework for day-ahead optimization in battery pools // Energy Informatics. 2019. Vol. 2. P. 1-17. DOI: 10.1186/s42162-019-0087-x Chasparis G.C., Pichler M., Spreitzhofer J., Esterl T. A cooperative demand-response framework for day-ahead optimization in battery pools. Energy Informatics. 2019. Vol. 2, p. 1-17. DOI: 10.1186/s42162-019-0087-x Soares L.J., Medeiros M.C. Modeling and forecasting short-term electricity load: A comparison of methods with an application to Brazilian data // International Journal of Forecasting. 2008. Vol. 24. Iss. 4. Р. 630-644. DOI: 10.1016/j.ijforecast.2008.08.003 Soares L.J., Medeiros M.C. Modeling and forecasting short-term electricity load: A comparison of methods with an application to Brazilian data. International Journal of Forecasting. 2008. Vol. 24. Iss. 4, p. 630-644. DOI: 10.1016/j.ijforecast.2008.08.003 Xu Y., Li N., Low S.H. Demand Response With Capacity Constrained Supply Function Bidding // IEEE Transactions on Power Systems. 2016. Vol. 31. № 2. P. 1377-1394. DOI: 10.1109/TPWRS.2015.2421932 Xu Y., Li N., Low S.H. Demand Response With Capacity Constrained Supply Function Bidding. IEEE Transactions on Power Systems. 2016. Vol. 31. N 2, p. 1377-1394. DOI: 10.1109/TPWRS.2015.2421932 Boikov A., Payor V., Savelev R., Kolesnikov A. Synthetic Data Generation for Steel Defect Detection and Classification Using Deep Learning. Symmetry. 2021. Vol. 13. Iss. 7. № 1176. DOI: 10.3390/sym13071176 Boikov A., Payor V., Savelev R., Kolesnikov A. Synthetic Data Generation for Steel Defect Detection and Classification Using Deep Learning. Symmetry. 2021. Vol. 13. Iss. 7. N 1176. DOI: 10.3390/sym13071176 Zhukovskiy Y.L., Kovalchuk M.S., Batueva D.E., Senchilo N.D. Development of an Algorithm for Regulating the Load Schedule of Educational Institutions Based on the Forecast of Electric Consumption within the Framework of Application of the Demand Response // Sustainability. 2021. Vol. 13 (24). № 13801. DOI: 10.3390/su132413801 Zhukovskiy Y.L., Kovalchuk M.S., Batueva D.E., Senchilo N.D. Development of an Algorithm for Regulating the Load Schedule of Educational Institutions Based on the Forecast of Electric Consumption within the Framework of Application of the Demand Response. Sustainability. 2021. Vol. 13 (24). N 13801. DOI: 10.3390/su132413801 Shabalov M.Yu., Zhukovskiy Yu.L., Buldysko A.D. et al. The influence of technological changes in energy efficiency on the infrastructure deterioration in the energy sector // Energy Reports. 2021. Vol. 7. P. 2664-2680. DOI: 10.1016/j.egyr.2021.05.001 Shabalov M.Yu, Zhukovskiy Yu.L., Buldysko A.D. et al. The influence of technological changes in energy efficiency on the infrastructure deterioration in the energy sector. Energy Reports. 2021. Vol. 7, p. 2664-2680. DOI: 10.1016/j.egyr.2021.05.001 Savard C., Iakovleva E., Ivanchenko D., Rassõlkin A. Accessible battery model with aging dependency // Energies. 2021. Vol. 14. Iss. 12. № 3493. DOI: 10.3390/en14123493 Savard C., Iakovleva E., Ivanchenko D., Rassõlkin A. Accessible battery model with aging dependency. Energies. 2021. Vol. 14. Iss. 12. N 3493. DOI: 10.3390/en14123493 Senchilo N.D., Ustinov D.A. Method for determining the optimal capacity of energy storage systems with a long-term forecast of power consumption // Energies. 2021. Vol. 14. Iss. 21. № 7098. DOI: 10.3390/en14217098 Senchilo N.D., Ustinov D.A. Method for determining the optimal capacity of energy storage systems with a long-term forecast of power consumption. Energies. 2021. Vol. 14. Iss. 21. N 7098. DOI: 10.3390/en14217098 Dicks F., Clausen E. Ventilation on Demand // Mining Report. 2017. Vol. 153. № 4. P. 334-341. Dicks F., Clausen E. Ventilation on Demand. Mining Report. 2017. Vol. 153. N 4, p. 334-341. Nikolaev A.V., Alymenko N.I., Kamenskikh A.A. et al. Factors defining value and direction of thermal pressure between the mine shafts and impact of the general mine natural draught on ventilation process of underground mining companies // IOP Conference. Series: Earth and Environmental Science. 2017. Vol. 87. № 052020. P. 561-566. DOI: 10.2991/aime-17.2017.91 Nikolaev A.V., Alymenko N.I., Kamenskikh A.A. et al. Factors defining value and direction of thermal pressure between the mine shafts and impact of the general mine natural draught on ventilation process of underground mining companies. IOP Conference. Series: Earth and Environmental Science. 2017. Vol. 87. N 052020, p. 561-566. DOI: 10.2991/aime-17.2017.91 Rogers D.P., Tsirkunov V.V. Weather and Climate Resilience: Effective Preparedness through National Meteorological and Hydrological Services // World Bank Publications. Washington, DC: Directions in Development – Environment and Sustainable Development, 2013. 152 p. Rogers D.P., Tsirkunov V.V. Weather and Climate Resilience: Effective Preparedness through National Meteorological and Hydrological Services. World Bank Publications. Washington, DC: Directions in Development – Environment and Sustainable Development, 2013, p. 152. Kychkin A., Nikolaev A. IoT-based Mine Ventilation Control System Architecture with Digital Twin // 2020 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM). 2020. № 9111995. 5 p. DOI: 10.1109/ICIEAM48468.2020.9111995 Kychkin A., Nikolaev A. IoT-based Mine Ventilation Control System Architecture with Digital Twin. 2020 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM). 2020. N 9111995, p. 5. DOI: 10.1109/ICIEAM48468.2020.9111995 Бедрицкий А.И., Коршунов А.А., Хандожко Л.А., Шаймарданов М.З. Гидрометеорологическая безопасность и устойчивое развитие России // Право и безопасность. 2007. № 1-2 (22-23). С. 7-13. Bedritskii A.I., Korshunov A.A., Khandozhko L.A., Shaimardanov M.Z. Hydrometeorological safety and sustainable development of Russia. Pravo i bezopasnost. 2007. N 1-2 (22-23), p. 7-13 (in Russian). Nikolaev A., Alymenko N., Kamenskih A., Nikolaev V. The results of air treatment process modeling at the location of the air curtain in the air suppliers and ventilation shafts // E3S Web of Conferences. 2017. Vol. 15. № 02004. 7 p. DOI: 10.1051/e3sconf/20171502004 Nikolaev A., Alymenko N., Kamenskih A., Nikolaev V. The results of air treatment process modeling at the location of the air curtain in the air suppliers and ventilation shafts. E3S Web of Conferences. 2017. Vol. 15. N 02004, p. 7. DOI: 10.1051/e3sconf/20171502004 Andersen F.M., Jensen S.G., Larsen H.V. et al. Analyses of Demand Response in Denmark. Denmark. Roskilde: Riso National Laboratory Information Service Department, 2006. 100 p. Andersen F.M., Jensen S.G., Larsen H.V. et al. Analyses of Demand Response in Denmark. Denmark. Roskilde: Riso National Laboratory Information Service Department, 2006, p. 100. Xu B., Zheng J., Wang Q. Analysis and Design of Real-Time Micro-Environment Parameter Monitoring System Based on Internet of Things // IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData). 15-18 December, 2016. Chengdu, China. 2016. P. 368-371. DOI: 10.1109/iThings-GreenCom-CPSCom-SmartData.2016.87 Xu B., Zheng J., Wang Q. Analysis and Design of Real-Time Micro-Environment Parameter Monitoring System Based on Internet of Things. IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData), 15-18 December 2016. Chengdu, China, 2016, p. 368-371. DOI: 10.1109/iThings-GreenCom-CPSCom-SmartData.2016.87 Gubbi J., Buyya R., Marusic S., Palaniswamia M. Internet of Things (IoT): A vision, architectural elements, and future directions // Future Generation Computer Systems. 2013. Vol. 29. Iss. 7. P. 1645-1660. DOI: 10.1016/j.future.2013.01.010 Gubbi J., Buyya R., Marusic S., Palaniswamia M. Internet of Things (IoT): A vision, architectural elements, and future directions. Future Generation Computer Systems. 2013. Vol. 29. Iss. 7, p. 1645-1660. DOI: 10.1016/j.future.2013.01.010 Kychkin A., Deryabin A.S., Neganova E., Markvirer V. IoT-Based Energy Management Assistant Architecture Design // 2019 IEEE 21st Conference on Business Informatics (CBI). IEEE Computer Society. 2019. Vol. 1. P. 522-530. DOI:10.1109/CBI.2019.00067 Kychkin A., Deryabin A.S., Neganova E., Markvirer V. IoT-Based Energy Management Assistant Architecture Design. 2019 IEEE 21st Conference on Business Informatics (CBI). IEEE Computer Society. 2019. Vol. 1, p. 522-530. DOI:10.1109/CBI.2019.00067 Mijić D., Varga E. Unified IoT Platform Architecture Platforms as Major IoT Building Blocks // International Conference on Computing and Network Communications (CoCoNet). 2018. P. 6-13. DOI: 10.1109/CoCoNet.2018.8476881 Mijić D., Varga E. Unified IoT Platform Architecture Platforms as Major IoT Building Blocks. International Conference on Computing and Network Communications (CoCoNet). 2018, p. 6-13. DOI: 10.1109/CoCoNet.2018.8476881 Lu Hou, Shaohang Zhao, Xiong Xiong et al. Internet of Things Cloud: Architecture and Implementation // IEEE Communications Magazine. 2016. Vol. 54. Iss.12. P. 32-39. DOI: 10.1109/MCOM.2016.1600398CM Lu Hou, Shaohang Zhao, Xiong Xiong et al. Internet of Things Cloud: Architecture and Implementation. IEEE Communications Magazine. 2016. Vol. 54. Iss.12, p. 32-39. DOI: 10.1109/MCOM.2016.1600398CM Kychkin A.V. Synthesizing a system for remote energy monitoring in manufacturing // Metallurgist. 2016. Vol. 59. № 9-10. P. 752-760. DOI: 10.1007/s11015-016-0170-5 Kychkin A.V. Synthesizing a system for remote energy monitoring in manufacturing. Metallurgist. 2016. Vol. 59. N 9-10, p. 752-760. DOI: 10.1007/s11015-016-0170-5 Lyakhomskiy A., Perfileva E., Kychkin A., Genrikh N. A software- hardware system of remote monitoring and analysis of the energy data // Russian Electrical Engineering. 2015. Vol. 86 (6). P. 314-319. DOI: 10.3103/S1068371215060103 Lyakhomskiy A., Perfileva E., Kychkin A., Genrikh N. A software- hardware system of remote monitoring and analysis of the energy data. Russian Electrical Engineering. 2015. Vol. 86 (6), p. 314-319. DOI: 10.3103/S1068371215060103 Faizrakhmanov R.A., Frank T., Kychkin A.V., Fedorov A.B. Sustainable energy consumption control using the MY-JEVIS energy management data system // Russian Electrical Engineering. 2011. Vol. 82 (11). P. 607-611. DOI: 10.3103/S1068371211110022 Faizrakhmanov R.A., Frank T., Kychkin A.V., Fedorov A.B. Sustainable energy consumption control using the MY-JEVIS energy management data system. Russian Electrical Engineering. 2011. Vol. 82 (11), p. 607-611. DOI: 10.3103/S1068371211110022 Vöth S., Vasilyeva M. Potential of Modelica for the creation of digital twins // Advances in raw material industries for sustainable development goals. London: Taylor & Francis Group, 2020. P. 386-389. DOI: 10.1201/9781003164395 Vöth S., Vasilyeva M. Potential of Modelica for the creation of digital twins. Advances in raw material industries for sustainable development goals. London: Taylor & Francis Group, 2020, p. 386-389. DOI: 10.1201/9781003164395 Vöth S., Bogdanov V., Pomazov D. Modeling of Efficiencies on Basis of Power Flow Directions using Modelica on the Example of Hoisting Systems // Project: Safety and Availability of Cranes. 2020. 6 p. Vöth S., Bogdanov V., Pomazov D. Modeling of Efficiencies on Basis of Power Flow Directions using Modelica on the Example of Hoisting Systems. Project: Safety and Availability of Cranes. 2020, p. 6.