DOI: https://doi.org/10.20998/2074-272X.2020.4.04

SIMPLIFIED MATHEMATICAL MODEL OF GROUP OF OVERHEAD POWER LINES MAGNETIC FIELD

B. I. Kuznetsov, T. B. Nikitina, I. V. Bovdui

Анотація


Цель. Разработан метод построения упрощенной математической модели магнитного поля группы воздушных линий электропередачи, позволяющий уменьшить количество проводников, которые учитываются в модели для снижения чувствительности модели к неопределенности параметров объекта управления. Методология. Метод основан на решении многокритериальной стохастической игры, в которой векторный выигрыш вычисляется на основании решений уравнений Максвелла в квазистационарном приближении. Решение игры находится на основе алгоритмов стохастической мультиагентной оптимизации мультироем частиц. Реализация метода осуществляется при определении количества, конфигурации, пространственного расположения и токов в проводниках на основе упрощенной математической модели магнитного поля группы воздушных линий электропередачи в заданной области пространства. Результаты. Приводятся результаты компьютерного моделирования и полевых экспериментальных исследований на примере группы из четырех воздушных линий электропередачи, содержащей 21проводник, где на основе разработанной упрощенной математической модели магнитного поля количество учитываемых в модели проводников уменьшено до 6, а погрешность моделирования при этом не превышает 4 %. Оригинальность. Впервые разработан метод построения упрощенной математической модели магнитного поля группы воздушных линий электропередачи на основе алгоритмов стохастической мультиагентной оптимизации мультироем частиц, позволяющий существенно упростить моделирование за счет уменьшения количества проводников, которые учитываются в модели для снижения чувствительности модели к неопределенности параметров объекта управления, и при этом ограничить погрешность моделирования на инженерном уровне 5-10 %. Практическая ценность. Приводятся практические рекомендации по обоснованному выбору минимального количества, конфигурации, пространственного расположения и токов в проводниках упрощенной математической модели магнитного поля, создаваемого группой воздушных линий электропередачи.

Ключові слова


воздушная линия электропередачи; магнитное поле; упрощенная математическая модель; компьютерное моделирование; полевые экспериментальные исследования

Повний текст:

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Посилання


Pravila ulashtuvannya electroustanovok [Electrical installation regulations]. Kharkiv, Fort Publ., 2017. 760 p. (Ukr).

Rozov V., Grinchenko V. Simulation and analysis of power frequency electromagnetic field in buildings closed to overhead lines. 2017 IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON). Kyiv, Ukraine, pp. 500-503. doi: 10.1109/UKRCON.2017.8100538.

Rozov V.Yu., Grinchenko V.S., Yerisov A.V., Dobrodeyev P.N. Efficient shielding of three-phase cable line magnetic field by passive loop under limited thermal effect on power cables. Electrical engineering & electromechanics, 2019, no.6, pp. 50-54. doi: 10.20998/2074-272X.2019.6.07.

Active Magnetic Shielding (Field Cancellation). Available at: http://www.emfservices.com/afcs.html (accessed 10 September 2012).

Rozov V.Yu., Reutskyi S.Yu., Pelevin D.Ye., Pyliugina O.Yu. The magnetic field of transmission lines and the methods of its mitigation to a safe level. Technical Electrodynamics, 2013, no. 2, pp. 3-9. (Rus).

Rozov V.Yu., Reutskyi S.Yu. Pyliugina O.Yu. The method of calculation of the magnetic field of three-phase power lines. Technical electrodynamics, 2014, no.5, pp. 11-13. (Rus).

Salceanu A., Paulet M., Alistar B.D., Asiminicesei O. Upon the contribution of image currents on the magnetic fields generated by overhead power lines. 2019 International Conference on Electromechanical and Energy Systems (SIELMEN). 2019. doi: 10.1109/sielmen.2019.8905880.

Bravo-Rodríguez J., Del-Pino-López J., Cruz-Romero P. A Survey on Optimization Techniques Applied to Magnetic Field Mitigation in Power Systems. Energies, 2019, vol.12, no.7, p. 1332. doi: 10.3390/en12071332.

Canova A., Giaccone L., Cirimele V. Active and passive shield for aerial power lines. 25th International Conference on Electricity Distribution Madrid, 3-6 June 2019. Paper no. 1096, pp. 1-5.

Sushchenko O.A., Tunik A.A. Robust optimization of the inertially stabilized platforms. 2012 2nd International Conference «Methods and Systems of Navigation and Motion Control» (MSNMC), Kiev, 2012, pp. 101-105. doi: 10.1109/msnmc.2012.6475102.

Sushchenko O.A. Robust control of angular motion of platform with payload based on H∞-synthesis. Journal of Automation and Information Sciences, 2016, vol. 48, no. 12, pp. 13-26. doi: 10.1615/jautomatinfscien.v48.i12.20.

Sushchenko O.A. Robust control of platforms with instrumentation. 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering (UKRCON), Lviv, Ukraine, 2019, pp. 518-521. doi: 10.1109/ukrcon.2019.8879969.

Zhiteckii L.S., Azarskov V.N., Solovchuk K.Y., Sushchenko O.A. Discrete-time robust steady-state control of nonlinear multivariable systems: a unified approach. IFAC Proceedings Volumes, 2014, vol. 47, no. 3, pp. 8140-8145. doi: 10.3182/20140824-6-za-1003.01985.

Zhiteckii L.S., Solovchuk K.Y. Robust adaptive pseudoinverse model-based control of an uncertain SIMO memoryless system with bounded disturbances. 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering (UKRCON), Lviv, Ukraine, 2019, pp. 621-627. doi: 10.1109/ukrcon.2019.8879824.

Chorna O., Chornyi O., Tytiuk V. Identification of changes in the parameters of induction motors during monitoring by measuring the induction of a magnetic field on the stator surface. 2019 IEEE International Conference on Modern Electrical and Energy Systems (MEES). Kremenchuk, 2019. doi: 10.1109/MEES.2019.8896554.

Chystiakov P., Chornyi O., Zhautikov B., Sivyakova G. Remote control of electromechanical systems based on computer simulators. 2017 International Conference on Modern Electrical and Energy Systems (MEES). Nov. 2017. doi: 10.1109/mees.2017.8248934.

Shenkman A., Sonkin N., Kamensky V. Active protection from electromagnetic field hazards of a high voltage power line. HAIT Journal of Science and Engineering. Series B: Applied Sciences and Engineering, Vol. 2, Issues 1-2, pp. 254-265.

Korol S., Buryan S., Pushkar M., Ostroverkhov M. Investigation the maximal values of flux and stator current of autonomous induction generator. 2017 IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON), May 2017. doi: 10.1109/ukrcon.2017.8100302.

Ostroverkhov M., Buryk M. Control of permanent magnet synchronous motor under conditions of parametric uncertainty. 2019 IEEE International Conference on Modern Electrical and Energy Systems (MEES), Sep. 2019. doi: 10.1109/mees.2019.8896635.

Ostroverkhov M., Pyzhov V., Korol S. Control of the electric drive under conditions of parametric uncertainty and coordinates' interrelation. 2017 International Conference on Modern Electrical and Energy Systems (MEES), Nov 2017. doi: 10.1109/mees.2017.8248953.

Panchenko V.V., Maslii A.S., Pomazan D.P., Buriakovskyi S.G. Determination of pulsation factors of the system of suppression of interfering harmonics of a semiconductor converter. Electrical engineering & electromechanics, 2018, no.4, pp. 24-28. doi: 10.20998/2074-272X.2018.4.04.

Buriakovskyi S.G., Maslii A.S., Panchenko V.V., Pomazan D.P., Denis I.V. The research of the operation modes of the diesel locomotive CHME3 on the imitation model. Electrical engineering & electromechanics, 2018, no.2, pp. 59-62. doi: 10.20998/2074-272X.2018.2.10.

Buriakovskyi S., Maslii A., Maslii A. Determining parameters of electric drive of a sleeper-type turnout based on electromagnet and linear inductor electric motor. Eastern-European Journal of Enterprise Technologies, 2016, vol.4, no.1(82), pp. 32-41. (Rus). doi: 10.15587/1729-4061.2016.75860.

Shchur I., Klymko V. Comparison of different types of electromechanical systems for creating of counter-rotating VAWT. 2017 IEEE First Ukraine Conf. on Electrical and Computer Engineering (UKRCON-2017), pp. 373-378. doi: 10.1109/ukrcon.2017.8100513.

Shchur I. Impact of nonsinusoidalness on efficiency of alternative electricity generation systems. 2010 International School on Nonsinusoidal Currents and Compensation, Lagow, 2010, pp. 218-223. doi: 10.1109/isncc.2010.5524483.

Zagirnyak M., Bisikalo O., Chorna O., Chornyi O. A model of the assessment of an induction motor condition and operation life, based on the measurement of the external magnetic field. 2018 IEEE 3rd International Conference on Intelligent Energy and Power Systems (IEPS). 2018. pp. 316-321. doi: 10.1109/ieps.2018.8559564.

Zagirnyak M., Chornyi O., Nykyforov V., Sakun O., Panchenko K. Experimental research of electromechanical and biological systems compatibility. Przegląd Elektrotechniczny, 2016, vol.1, no.1, pp. 130-133. doi: 10.15199/48.2016.01.31.

Zagirnyak M., Serhiienko S., Chornyi O. Innovative technologies in laboratory workshop for students of technical specialties. 2017 IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON), May 2017. doi: 10.1109/ukrcon.2017.8100446.

Ren Z., Pham M.-T., Koh C.S. Robust Global Optimization of Electromagnetic Devices With Uncertain Design Parameters: Comparison of the Worst Case Optimization Methods and Multiobjective Optimization Approach Using Gradient Index. IEEE Transactions on Magnetics, 2013, vol.49, no.2, pp. 851-859. doi: 10.1109/tmag.2012.2212713.

Galchenko V.Y., Yakimov A.N. A turmitobionic method for the solution of magnetic defectometry problems in structural-parametric optimization formulation. Russian Journal of Nondestructive Testing, 2014, vol.50, no.2, pp. 59-71. doi: 10.1134/s106183091402003x.

Gal’chenko V.Y., Yakimov A.N., Ostapushchenko D.L. Pareto-optimal parametric synthesis of axisymmetric magnetic systems with allowance for nonlinear properties of the ferromagnet. Technical Physics, 2012, vol.57, no.7, pp. 893-899. doi: 10.1134/s1063784212070110.

Ummels M. Stochastic Multiplayer Games Theory and Algorithms. Amsterdam University Press, 2010. 174 p.


Пристатейна бібліографія ГОСТ


  1. Pravila ulashtuvannya electroustanovok [Electrical installation regulations]. Kharkiv, Fort Publ., 2017. 760 p. (Ukr).
  2. Rozov V., Grinchenko V. Simulation and analysis of power frequency electromagnetic field in buildings closed to overhead lines. 2017 IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON). Kyiv, Ukraine, pp. 500-503. doi: 10.1109/UKRCON.2017.8100538.
  3. Rozov V.Yu., Grinchenko V.S., Yerisov A.V., Dobrodeyev P.N. Efficient shielding of three-phase cable line magnetic field by passive loop under limited thermal effect on power cables. Electrical engineering & electromechanics, 2019, no.6, pp. 50-54. doi: 10.20998/2074-272X.2019.6.07.
  4. Active Magnetic Shielding (Field Cancellation). Available at: http://www.emfservices.com/afcs.html (accessed 10 September 2012).
  5. Rozov V.Yu., Reutskyi S.Yu., Pelevin D.Ye., Pyliugina O.Yu. The magnetic field of transmission lines and the methods of its mitigation to a safe level. Technical Electrodynamics, 2013, no. 2, pp. 3-9. (Rus).
  6. Rozov V.Yu., Reutskyi S.Yu. Pyliugina O.Yu. The method of calculation of the magnetic field of three-phase power lines. Technical electrodynamics, 2014, no.5, pp. 11-13. (Rus).
  7. Salceanu A., Paulet M., Alistar B.D., Asiminicesei O. Upon the contribution of image currents on the magnetic fields generated by overhead power lines. 2019 International Conference on Electromechanical and Energy Systems (SIELMEN). 2019. doi: 10.1109/sielmen.2019.8905880.
  8. Bravo-Rodríguez J., Del-Pino-López J., Cruz-Romero P. A Survey on Optimization Techniques Applied to Magnetic Field Mitigation in Power Systems. Energies, 2019, vol.12, no.7, p. 1332. doi: 10.3390/en12071332.
  9. Canova A., Giaccone L., Cirimele V. Active and passive shield for aerial power lines. 25th International Conference on Electricity Distribution Madrid, 3-6 June 2019. Paper no. 1096, pp. 1-5.
  10. Sushchenko O.A., Tunik A.A. Robust optimization of the inertially stabilized platforms. 2012 2nd International Conference «Methods and Systems of Navigation and Motion Control» (MSNMC), Kiev, 2012, pp. 101-105. doi: 10.1109/msnmc.2012.6475102.
  11. Sushchenko O.A. Robust control of angular motion of platform with payload based on H∞-synthesis. Journal of Automation and Information Sciences, 2016, vol. 48, no. 12, pp. 13-26. doi: 10.1615/jautomatinfscien.v48.i12.20.
  12. Sushchenko O.A. Robust control of platforms with instrumentation. 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering (UKRCON), Lviv, Ukraine, 2019, pp. 518-521. doi: 10.1109/ukrcon.2019.8879969.
  13. Zhiteckii L.S., Azarskov V.N., Solovchuk K.Y., Sushchenko O.A. Discrete-time robust steady-state control of nonlinear multivariable systems: a unified approach. IFAC Proceedings Volumes, 2014, vol. 47, no. 3, pp. 8140-8145. doi: 10.3182/20140824-6-za-1003.01985.
  14. Zhiteckii L.S., Solovchuk K.Y. Robust adaptive pseudoinverse model-based control of an uncertain SIMO memoryless system with bounded disturbances. 2019 IEEE 2nd Ukraine Conference on Electrical and Computer Engineering (UKRCON), Lviv, Ukraine, 2019, pp. 621-627. doi: 10.1109/ukrcon.2019.8879824.
  15. Chorna O., Chornyi O., Tytiuk V. Identification of changes in the parameters of induction motors during monitoring by measuring the induction of a magnetic field on the stator surface. 2019 IEEE International Conference on Modern Electrical and Energy Systems (MEES). Kremenchuk, 2019. doi: 10.1109/MEES.2019.8896554.
  16. Chystiakov P., Chornyi O., Zhautikov B., Sivyakova G. Remote control of electromechanical systems based on computer simulators. 2017 International Conference on Modern Electrical and Energy Systems (MEES). Nov. 2017. doi: 10.1109/mees.2017.8248934.
  17. Shenkman A., Sonkin N., Kamensky V. Active protection from electromagnetic field hazards of a high voltage power line. HAIT Journal of Science and Engineering. Series B: Applied Sciences and Engineering, Vol. 2, Issues 1-2, pp. 254-265.
  18. Korol S., Buryan S., Pushkar M., Ostroverkhov M. Investigation the maximal values of flux and stator current of autonomous induction generator. 2017 IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON), May 2017. doi: 10.1109/ukrcon.2017.8100302.
  19. Ostroverkhov M., Buryk M. Control of permanent magnet synchronous motor under conditions of parametric uncertainty. 2019 IEEE International Conference on Modern Electrical and Energy Systems (MEES), Sep. 2019. doi: 10.1109/mees.2019.8896635.
  20. Ostroverkhov M., Pyzhov V., Korol S. Control of the electric drive under conditions of parametric uncertainty and coordinates' interrelation. 2017 International Conference on Modern Electrical and Energy Systems (MEES), Nov 2017. doi: 10.1109/mees.2017.8248953.
  21. Panchenko V.V., Maslii A.S., Pomazan D.P., Buriakovskyi S.G. Determination of pulsation factors of the system of suppression of interfering harmonics of a semiconductor converter. Electrical engineering & electromechanics, 2018, no.4, pp. 24-28. doi: 10.20998/2074-272X.2018.4.04.
  22. Buriakovskyi S.G., Maslii A.S., Panchenko V.V., Pomazan D.P., Denis I.V. The research of the operation modes of the diesel locomotive CHME3 on the imitation model. Electrical engineering & electromechanics, 2018, no.2, pp. 59-62. doi: 10.20998/2074-272X.2018.2.10.
  23. Buriakovskyi S., Maslii A., Maslii A. Determining parameters of electric drive of a sleeper-type turnout based on electromagnet and linear inductor electric motor. Eastern-European Journal of Enterprise Technologies, 2016, vol.4, no.1(82), pp. 32-41. (Rus). doi: 10.15587/1729-4061.2016.75860.
  24. Shchur I., Klymko V. Comparison of different types of electromechanical systems for creating of counter-rotating VAWT. 2017 IEEE First Ukraine Conf. on Electrical and Computer Engineering (UKRCON-2017), pp. 373-378. doi: 10.1109/ukrcon.2017.8100513.
  25. Shchur I. Impact of nonsinusoidalness on efficiency of alternative electricity generation systems. 2010 International School on Nonsinusoidal Currents and Compensation, Lagow, 2010, pp. 218-223. doi: 10.1109/isncc.2010.5524483.
  26. Zagirnyak M., Bisikalo O., Chorna O., Chornyi O. A model of the assessment of an induction motor condition and operation life, based on the measurement of the external magnetic field. 2018 IEEE 3rd International Conference on Intelligent Energy and Power Systems (IEPS). 2018. pp. 316-321. doi: 10.1109/ieps.2018.8559564.
  27. Zagirnyak M., Chornyi O., Nykyforov V., Sakun O., Panchenko K. Experimental research of electromechanical and biological systems compatibility. Przegląd Elektrotechniczny, 2016, vol.1, no.1, pp. 130-133. doi: 10.15199/48.2016.01.31.
  28. Zagirnyak M., Serhiienko S., Chornyi O. Innovative technologies in laboratory workshop for students of technical specialties. 2017 IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON), May 2017. doi: 10.1109/ukrcon.2017.8100446.
  29. Ren Z., Pham M.-T., Koh C.S. Robust Global Optimization of Electromagnetic Devices With Uncertain Design Parameters: Comparison of the Worst Case Optimization Methods and Multiobjective Optimization Approach Using Gradient Index. IEEE Transactions on Magnetics, 2013, vol.49, no.2, pp. 851-859. doi: 10.1109/tmag.2012.2212713.
  30. Galchenko V.Y., Yakimov A.N. A turmitobionic method for the solution of magnetic defectometry problems in structural-parametric optimization formulation. Russian Journal of Nondestructive Testing, 2014, vol.50, no.2, pp. 59-71. doi: 10.1134/s106183091402003x.
  31. Gal’chenko V.Y., Yakimov A.N., Ostapushchenko D.L. Pareto-optimal parametric synthesis of axisymmetric magnetic systems with allowance for nonlinear properties of the ferromagnet. Technical Physics, 2012, vol.57, no.7, pp. 893-899. doi: 10.1134/s1063784212070110.
  32. Ummels M. Stochastic Multiplayer Games Theory and Algorithms. Amsterdam University Press, 2010. 174 p.




Copyright (c) 2020 B. I. Kuznetsov, T. B. Nikitina, I. V. Bovdui


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