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 MGAPVA pmi-16181 https://pmi.spmi.ru/pmi/article/view/16181 Энергетика Energy industry Increasing the energy efficiency of an autonomous power supply system of a drilling rig in case of voltage dips Повышение энергоэффективности автономной системы электроснабжения буровой установки при провалах напряжения Chervonchenko Sergei S. Червонченко С. С. Chervonchenko Sergei S. sergeychervonchenko@gmail.com 0009-0003-2839-9068 Санкт-Петербургский политехнический университет Петра Великого (Санкт-Петербург, Россия) Peter the Great St. Petersburg Polytechnic University (Saint Petersburg, Russia) Frolov Vladimir Ya. Фролов В. Я. Frolov Vladimir Ya. frolov.eed@gmail.com 0000-0002-1744-4375 Санкт-Петербургский политехнический университет Петра Великого (Санкт-Петербург, Россия) Peter the Great St. Petersburg Polytechnic University (Saint Petersburg, Russia) 19 07 2023 2023 261 470 478 12 03 2023 20 06 2023 19 07 2023 © 2023 С. С. Червонченко, В. Я. Фролов © 2023 Sergei S. Chervonchenko, Vladimir Ya. Frolov 2023 С. С. Червонченко, В. Я. Фролов Sergei S. Chervonchenko, Vladimir Ya. Frolov 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/16181

В статье рассматриваются аварийные режимы работы автономного электротехнического комплекса буровой установки. Раскрывается понятие провала напряжения и его влияние на технологический процесс промышленных предприятий. Представлено описание использующихся в электроснабжении промышленных предприятий способов и методов преодоления провалов напряжения и набросов нагрузки в автономных энергосистемах, из которых можно выделить ускоренный подъем ответственного оборудования для недопущения аварийных режимов, а также применение резервных накопителей, как правило аккумуляторных батарей. Разработан алгоритм взаимодействия аккумуляторной батареи и дизель-генераторной установки как резервных источников питания во время различных режимов работы электродвигателя с учетом набросов нагрузки, позволяющий успешно преодолеть провалы напряжения в системе как в переходном, так и в установившемся режимах. Предложен комбинированный метод устранения провала напряжения, особенностью которого является применение комбинированной структуры источников резервного питания в составе дизель-генераторной установки и аккумуляторной батареи, действующий на основании предложенного алгоритма взаимодействия в автономных электротехнических комплексах. Способ позволяет преодолеть резкие набросы нагрузки и провалы напряжения, вызванные дефицитом резервной мощности в электрической системе. Применение аккумуляторной батареи в качестве переходного элемента позволяет переключиться между основным и резервным источниками питания без остановки технологического и расширить порог перегрузки автономного электротехнического комплекса до 60 %. При использовании комбинированного метода повышается энергоэффективность автономного комплекса вследствие уменьшения количества аварийного отключения оборудования, прерываний технологического процесса и дополнительного расхода электроэнергии.

The article discusses the emergency modes of operation of an autonomous electrical complex of a drilling rig. The concept of voltage failure and its influence on the technological process of industrial enterprises is revealed. A description of the methods used in the power supply of industrial enterprises to overcome voltage dips and load surges in autonomous power systems is presented, from which it is possible to single out the accelerated lifting of critical equipment to prevent emergency conditions, as well as the use of backup storage, usually batteries. An algorithm has been developed for the interaction of the battery and the diesel generator set as backup power sources during various modes of operation of the electric motor, taking into account load surges, which allows successfully overcoming voltage dips in the system both in transient and in steady state. It is proposed to use a combined method to eliminate the voltage dip, a feature of which is the use of a combined structure of backup power sources as part of a diesel generator set and a battery, acting on the base of the proposed interaction algorithm in autonomous electrical complexes. The method makes it possible to overcome sudden load surges and voltage dips caused by a shortage of reserve power in the electrical system. The use of a rechargeable battery as a transitional element makes it possible to switch between the main and backup power sources without stopping the technological one and to expand the overload threshold of an autonomous electrical complex up to 60 %. The use of the combined method increases the energy efficiency of the autonomous complex due to a reduction in the number of emergency shutdowns of equipment, process interruptions and additional power consumption.

 Ключевые слова энергоэффективность провал напряжения генератор буровая установка резервное питание Keywords energy efficiency voltage dip generator drilling rig backup power Результаты исследования получены при финансовой поддержке Министерства науки и высшего образования Российской Федерации по проекту FSEG-2023-0012 The results of the study were obtained with the financial support of the Ministry of Science and Higher Education of the Russian Federation under the project FSEG-2023-0012 Georgilakis P.S., Hatziargyriou N.D. A review of power distribution planning in the modern power systems era: Models, methods and future research // Electric Power Systems Research. 2015. Vol. 121. P. 89-100. DOI: 10.1016/j.epsr.2014.12.010 Georgilakis P.S., Hatziargyriou N.D. A review of power distribution planning in the modern power systems era: Models, methods and future research. Electric Power Systems Research. 2015. Vol. 121, p. 89-100. DOI: 10.1016/j.epsr.2014.12.010 Tavares B., Soares F.J. An innovative approach for distribution network reinforcement planning: Using DER flexibility to minimize investment under uncertainty // Electric Power Systems Research. 2020. Vol. 183. № 106272. DOI: 10.1016/j.epsr.2020.106272 Tavares B., Soares F.J. An innovative approach for distribution network reinforcement planning: Using DER flexibility to minimize investment under uncertainty. Electric Power Systems Research. 2020. Vol. 183. N 106272. DOI: 10.1016/j.epsr.2020.106272 Gouin V., Alvarez-Hérault M.-C., Raison B. Innovative planning method for the construction of electrical distribution network master plans // Sustainable Energy, Grids and Networks. 2017. Vol. 10. P. 84-91. DOI: 10.1016/j.segan.2017.03.004 Gouin V., Alvarez-Hérault M.-C., Raison B. Innovative planning method for the construction of electrical distribution network master plans. Sustainable Energy, Grids and Networks. 2017. Vol. 10, p. 84-91. DOI: 10.1016/j.segan.2017.03.004 Yu Yang, Fan Jinfu, Wang Zhongjie et al. A dynamic ensemble method for residential short-term load forecasting // Alexandria Engineering Journal. 2023. Vol. 63. P. 75-88. DOI: 10.1016/j.aej.2022.07.050 Yu Yang, Fan Jinfu, Wang Zhongjie et al. A dynamic ensemble method for residential short-term load forecasting. Alexandria Engineering Journal. 2023. Vol. 63, p. 75-88. DOI: 10.1016/j.aej.2022.07.050 Bo Yang, Junting Wang, Yixuan Chen et al. Optimal sizing and placement of energy storage system in power grids: A state-of-the-art one-stop handbook // Journal of Energy Storage. 2020. Vol. 32. № 101814. DOI: 10.1016/j.est.2020.101814 Bo Yang, Junting Wang, Yixuan Chen et al. Optimal sizing and placement of energy storage system in power grids: A state-of-the-art one-stop handbook. Journal of Energy Storage. 2020. Vol. 32. N 101814. DOI: 10.1016/j.est.2020.101814 Санеев Б.Г., Иванова И.Ю., Тугузова Т.Ф. Развитие возобновляемой энергетики на востоке России в первой половине XXI века на фоне общероссийских тенденций // Энергетическая политика. 2016. Вып. 3. С. 66-73. Saneev B.G., Ivanova I.Yu., Tuguzova T.F. Development of renewable energy sector in the Russian east over the first half of the 21st century amidst national trends. Energy policy. 2016. Iss. 3, p. 66-73 (in Russian). Шпиганович А.Н., Шпиганович А.А., Богомолов И.И. Провалы напряжения в системах электроснабжения // Известия Тульского государственного университета. 2018. Вып. 12. С. 7-12. Shpiganovich A.N., Shpiganovitch A.A., Bogomolov I.I. Voltage sags in power systems. Izvestiya Tula State University. 2018. Iss. 12, p. 7-12 (in Russian). Ершов С.В., Пигалов М.С. Анализ средств и способов ограничения влияния провалов напряжения // Известия Тульского государственного университета. 2017. Вып. 12-1. С. 95-104. Ershov S.V., Pigalov M.S. Analysis of means and methods of limitation of influence voltage fails. Izvestiya Tula State University. 2017. Iss. 12-1, p. 95-104 (in Russian). Zarenia O., Salehpour M.J., Ghaedi R., Shafie-Khah M. Markov-Based Reliability Assessment for Distribution Systems Considering Failure Rates // IEEE Access. 2023. Vol. 11. P. 10018-10031. DOI: 10.1109/ACCESS.2023.3240778 Zarenia O., Salehpour M.J., Ghaedi R., Shafie-Khah M. Markov-Based Reliability Assessment for Distribution Systems Considering Failure Rates. IEEE Access. 2023. Vol. 11, p. 10018-10031. DOI: 10.1109/ACCESS.2023.3240778 Postigo Marcos F., Domingo C.M., San Román T.G. Improving distribution network resilience through automation, distributed energy resources, and undergrounding // International Journal of Electrical Power & Energy Systems. 2022. Vol. 141. № 108116. DOI: 10.1016/j.ijepes.2022.108116 Postigo Marcos F., Domingo C.M., San Román T.G. Improving distribution network resilience through automation, distributed energy resources, and undergrounding. International Journal of Electrical Power & Energy Systems. 2022. Vol. 141. N 108116. DOI: 10.1016/j.ijepes.2022.108116 Prathapaneni D.R., Detroja K.P. An integrated framework for optimal planning and operation schedule of microgrid under uncertainty // Sustainable Energy, Grids and Networks. 2019. Vol. 19. № 100232. DOI: 10.1016/j.segan.2019.100232 Prathapaneni D.R., Detroja K.P. An integrated framework for optimal planning and operation schedule of microgrid under uncertainty. Sustainable Energy, Grids and Networks. 2019. Vol. 19. N 100232. DOI: 10.1016/j.segan.2019.100232 Besselmann T.J., Cortinovis A., Van de Moortel S. et al. Increasing the Robustness of Large Electric Driven Compressor Systems During Voltage Dips // IEEE Transactions on Industry Applications. 2018. Vol. 54. Iss. 2. P. 1460-1468. DOI: 10.1109/TIA.2017.2781638 Besselmann T.J., Cortinovis A., Van de Moortel S. et al. Increasing the Robustness of Large Electric Driven Compressor Systems During Voltage Dips. IEEE Transactions on Industry Applications. 2018. Vol. 54. Iss. 2, p. 1460-1468. DOI: 10.1109/TIA.2017.2781638 Bagheri A., Bollen M.H.J., Gu I.Y.H. Improved characterization of multi-stage voltage dips based on the space phasor model // Electric Power Systems Research. 2018. Vol. 154. P. 319-328. DOI: 10.1016/j.epsr.2017.09.004 Bagheri A., Bollen M.H.J., Gu I.Y.H. Improved characterization of multi-stage voltage dips based on the space phasor model. Electric Power Systems Research. 2018. Vol. 154, p. 319-328. DOI: 10.1016/j.epsr.2017.09.004 Rastgou A., Moshtagh J., Bahramara S. Improved harmony search algorithm for electrical distribution network expansion planning in the presence of distributed generators // Energy. 2018. Vol. 151. P. 178-202. DOI: 10.1016/j.energy.2018.03.030 Rastgou A., Moshtagh J., Bahramara S. Improved harmony search algorithm for electrical distribution network expansion planning in the presence of distributed generators. Energy. 2018. Vol. 151, p. 178-202. DOI: 10.1016/j.energy.2018.03.030 Kandasamy M., Thangavel R.., Arumugam T. et al. Strategic incorporation of DSTATCOM and distributed generations in balanced and unbalanced radial power distribution networks considering time varying loads // Energy Reports. 2023. Vol. 9. P. 4345-4359. DOI: 10.1016/j.egyr.2023.03.076 Kandasamy M., Thangavel R., Arumugam T. et al. Strategic incorporation of DSTATCOM and distributed generations in balanced and unbalanced radial power distribution networks considering time varying loads. Energy Reports. 2023. Vol. 9, p. 4345-4359. DOI: 10.1016/j.egyr.2023.03.076 Zhukovskiy Yu.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. Iss. 24. № 13801. DOI: 10.3390/su132413801 Zhukovskiy Yu.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. Iss. 24. N 13801. DOI: 10.3390/su132413801 Червонченко С.С., Фролов В.Я. Анализ провала напряжения буровой установки, подключенной к локальной энергетической сети // VII Международная научно-практическая конференция «Инновации и перспективы развития горного машиностроения и электромеханики: IPDME-2020, 23-24 апреля 2020, Санкт-Петербург, Россия. СПб.: Санкт-Петербургский горный университет, 2020. С. 630-634. Chervonchenko S.S., Frolov V.Ya. Voltage dip analysis of a drilling rig connected to a local power grid. VII Mezhdunarodnaya nauchno-prakticheskaya konferentsiya “Innovatsii i perspektivy razvitiya gornogo mashinostroeniya i elektromekhaniki”: IPDME-2020, 23-24 aprelya 2020, Sankt-Peterburg, Rossiya. St. Pttersburg: Sankt-Peterburgskii gornyi universitet, 2020, p. 630-634 (in Russian). Gukovskiy Yu.L., Sychev Yu.A., Pelenev D.N. The Automatic Correction of Selective Action of Relay Protection System against Single Phase Earth Faults In Electrical Networks of Mining Enterprises // International Journal of Applied Engineering Research. 2017. Vol. 12. № 5. P. 833-838. Gukovskiy Yu.L., Sychev Yu.A., Pelenev D.N. The Automatic Correction of Selective Action of Relay Protection System against Single Phase Earth Faults In Electrical Networks of Mining Enterprises. International Journal of Applied Engineering Research. 2017. Vol. 12. N 5, p. 833-838. Belsky A.A., Glukhanich D.Y., Carrizosa M.J., Starshaia V.V. Analysis of specifications of solar photovoltaic panels // Renewable and Sustainable Energy Reviews. 2022. Vol. 159. № 112239. DOI: 10.1016/j.rser.2022.112239 Belsky A.A., Glukhanich D.Y., Carrizosa M.J., Starshaia V.V. Analysis of specifications of solar photovoltaic panels. Renewable and Sustainable Energy Reviews. 2022. Vol. 159. N 112239. DOI: 10.1016/j.rser.2022.112239 Barelli L., Bidini G., Pelosi D. et al. Comparative analysis of AC and DC bus configurations for flywheel-battery HESS integration in residential micro-grids // Energy. 2020. Vol. 204. № 117939. DOI: 10.1016/j.energy.2020.117939 Barelli L., Bidini G., Pelosi D. et al. Comparative analysis of AC and DC bus configurations for flywheel-battery HESS integration in residential micro-grids. Energy. 2020. Vol. 204. N 117939. DOI: 10.1016/j.energy.2020.117939 Шонин О.Б., Новожилов Н.Г., Крыльцов С.Б. Повышение устойчивости асинхронного электропривода с бездатчиковой скалярной системой управления при провалах напряжения сети // Известия Тульского государственного университета. 2016. Вып. 11-2. С. 507-519. Shonin O.B., Novozhilov N.G., Kryltcov S.B. Enhancing the stability of a sensorless V/F controlled VFD under voltage sags. Izvestiya Tula State University. 2016. Iss. 11-2, p. 507-519 (in Russian). Bardanov A.I., Solovev S.V., Alvarez R. et al. Upgrading the Power Capacity of a Three-Conductor MVAC Line by Converting to DC // Energies. 2022. Vol. 15. Iss. 3. № 1080. DOI: 10.3390/en15031080 Bardanov A.I., Solovev S.V., Alvarez R. et al. Upgrading the Power Capacity of a Three-Conductor MVAC Line by Converting to DC. Energies. 2022. Vol. 15. Iss. 3. N 1080. DOI: 10.3390/en15031080 Муньос-Гихоса Х.М., Крыльцов С.Б., Соловьев С.В. Применение активного выпрямителя в качестве компенсатора токов искажений в распределительных сетях 6-10 кВ // Записки Горного института. 2019. Т. 236. С. 229-238. DOI: 10.31897/PMI.2019.2.229 Munoz-Guijosa J.M., Kryltcov S.B., Solovev S.V. Application of an active rectifier used to mitigate currents distortion in 6-10 kV distribution grids. Journal of Mining Institute. 2019. Vol. 236, p. 229-238. DOI: 10.31897/PMI.2019.2.229 Iakovleva E.V., Guerra D.D. Improving the efficiency of the use of photovoltaic stations in the republic of Cuba // Journal of Physics: Conference Series. 2021. Vol. 1753. № 012056. DOI: 10.1088/1742-6596/1753/1/012056 Iakovleva E.V., Guerra D.D. Improving the efficiency of the use of photovoltaic stations in the republic of Cuba. Journal of Physics: Conference Series. 2021. Vol. 1753. N 012056. DOI: 10.1088/1742-6596/1753/1/012056 Васильков О.С., Батуева Д.Е., Хомяков К.А., Паляницин П.С. Выравнивание графика нагрузки предприятий за счет применения гибридных накопителей электроэнергии // Известия МГТУ «МАМИ». 2020. № 1 (43). С. 27-34. DOI: 10.31992/2074-0530-2020-43-1-27-34 Vasilkov O.S., Batueva D.E., Homyakov K.A., Palyanicin P.S. Aligning the load schedule of enterprises through the use of hybrid energy storage. Izvestiya MGTU “MAMI”. 2020. N 1 (43), p. 27-34 (in Russian). DOI: 10.31992/2074-0530-2020-43-1-27-34 Абрамович Б.Н. Система бесперебойного электроснабжения предприятий горной промышленности // Записки Горного института. 2018. Т. 229. С. 31-40. DOI: 10.25515/PMI.2018.1.31 Abramovich B.N. Uninterruptible Power Supply System for Mining Industry Enterprises. Journal of Mining Institute. 2018. Vol. 229, p. 31-40. DOI:10.25515/PMI.2018.1.31 Abramovich B., Sychev Yu.A., Pelenev D.N. Invariant protection of high-voltage electric motors of technological complexes at industrial enterprises at partial single-phase ground faults // IOP Conference Series: Materials Science and Engineering. 2018. Vol. 327. Iss. 5. № 052027. DOI: 10.1088/1757-899X/327/5/052027 Abramovich B., Sychev Yu.A., Pelenev D.N. Invariant protection of high-voltage electric motors of technological complexes at industrial enterprises at partial single-phase ground faults. IOP Conference Series: Materials Science and Engineering. 2018. Vol. 327. Iss. 5. N 052027. DOI: 10.1088/1757-899X/327/5/052027 Васильев Ю.Б., Шпенст В.А., Калашников О.В., Ульянов Г.Н. Обеспечение энергетической развязки электроприводов и сетей электроснабжения промышленных электротехнических комплексов // Записки Горного института. 2018. Т. 229. С. 41-49. DOI: 10.25515/PMI.2018.1.41 Vasilyev B.Yu., Shpenst V.A., Kalashnikov O.V., Ulyanov G.N. Providing Energy Decoupling of Electric Drive and Electric Grids for Industrial Electrical Installations. Journal of Mining Institute. 2018. Vol. 229, p. 41-49. DOI: 10.25515/PMI.2018.1.41 Forcan J., Forcan M. Optimal placement of remote-controlled switches in distribution networks considering load forecasting // Sustainable Energy, Grids and Networks. 2022. Vol. 30. № 100600. DOI: 10.1016/j.segan.2021.100600 Forcan J., Forcan M. Optimal placement of remote-controlled switches in distribution networks considering load forecasting. Sustainable Energy, Grids and Networks. 2022. Vol. 30. N 100600. DOI: 10.1016/j.segan.2021.100600 Ngom I., Mboup A.B., Thiaw L. et al. An Improved Control for DC-Link Fluctuation during Voltage Dip based on DFIG // 9th International Renewable Energy Congress (IREC), 20-22 March 2018, Hammamet, Tunisia. IEEE, 2018. P. 1-6. DOI: 10.1109/IREC.2018.8362458 Ngom I., Mboup A.B., Thiaw L. et al. An Improved Control for DC-Link Fluctuation during Voltage Dip based on DFIG. 9th International Renewable Energy Congress (IREC), 20-22 March 2018, Hammamet, Tunisia. IEEE, 2018, p. 1-6. DOI: 10.1109/IREC.2018.8362458 Pazouki E., Sozer Y., De Abreu-Garcia J.A. Fault Diagnosis and Fault-Tolerant Control Operation of Nonisolated DC-DC Converters // IEEE Transactions on Industry Applications. 2018. Vol. 54. Iss. 1. P. 310-320. DOI: 10.1109/TIA.2017.2751547 Pazouki E., Sozer Y., De Abreu-Garcia J.A. Fault Diagnosis and Fault-Tolerant Control Operation of Nonisolated DC-DC Converters. IEEE Transactions on Industry Applications. 2018. Vol. 54. Iss. 1. P. 310-320. DOI: 10.1109/TIA.2017.2751547 Zhukovskiy Y.L., Korolev N.A., Koteleva N.I. About increasing informativity of diagnostic system of asynchronous electric motor by extracting additional information from values of consumed current parameter // Journal of Physics: Conference Series. 2018. Vol. 1015. Iss. 3. № 032158. DOI: 10.1088/1742-6596/1015/3/032158 Zhukovskiy Y.L., Korolev N.A., Koteleva N.I. About increasing informativity of diagnostic system of asynchronous electric motor by extracting additional information from values of consumed current parameter. Journal of Physics: Conference Series. 2018. Vol. 1015. Iss. 3. N 032158. DOI: 10.1088/1742-6596/1015/3/032158 Malarev V.I., Kopteva A.V., Nogtev R.A. Electric Drive Simulation for Drilling Machine Spinner // IOP Conference Series: Earth and Environmental Science. 2018. Vol. 194. Iss. 5. № 052012. DOI: 10.1088/1755-1315/194/5/052012 Malarev V.I., Kopteva A.V., Nogtev R.A. Electric Drive Simulation for Drilling Machine Spinner. IOP Conference Series: Earth and Environmental Science. 2018. Vol. 194. Iss. 5. N 052012. DOI: 10.1088/1755-1315/194/5/052012 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 Шклярский Я.Э., Батуева Д.Е. Разработка алгоритма выбора режимов работы комплекса электроснабжения с ветродизельной электростанцией // Записки Горного института. 2022. Т. 253. С. 115-126. DOI: 10.31897/PMI.2022.7 Shklyarskiy Ya.E., Batueva D.E. Operation mode selection algorithm development of a wind-diesel power plant supply complex. Journal of Mining Institute. 2022. Vol. 253, p. 115-126. DOI: 10.31897/PMI.2022.7 Zhukovskiy Yu.L., Batueva D.E., Buldysko A.D. et al. Fossil Energy in the Framework of Sustainable Development: Analysis of Prospects and Development of Forecast Scenarios // Energies. 2021. Vol. 14. Iss. 17. № 5268. DOI: 10.3390/en14175268 Zhukovskiy Yu.L., Batueva D.E., Buldysko A.D. et al. Fossil Energy in the Framework of Sustainable Development: Analysis of Prospects and Development of Forecast Scenarios. Energies. 2021. Vol. 14. Iss. 17. N 5268. DOI: 10.3390/en14175268 Akbari K., Rahmani E., Abbasi A., Askari M.-R. Optimal placement of distributed generation in radial networks considering reliability and cost indices // Journal of Intelligent & Fuzzy Systems. 2016. Vol. 30. Iss. 2. P. 1077-1086. DOI: 10.3233/IFS-151883 Akbari K., Rahmani E., Abbasi A., Askari M.-R. Optimal placement of distributed generation in radial networks considering reliability and cost indices. Journal of Intelligent & Fuzzy Systems. 2016. Vol. 30. Iss. 2, p. 1077-1086. DOI: 10.3233/IFS-151883