DOI: https://doi.org/10.20998/2074-272X.2019.4.03

HIGH VOLTAGE POWER LINES MAGNETIC FIELD SYSTEM OF ACTIVE SHIELDING WITH COMPENSATION COIL DIFFERENT SPATIAL ARRANGEMENT

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

Анотація


Цель. Синтез одноконтурной робастной системы активного экранирования магнитного поля, создаваемого группой высоковольтных линий электропередачи, с различным пространственным расположением экранирующей обмотки. Методология. Синтез 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. Исходными параметрами для синтеза системы активного экранирования являются расположение высоковольтных линий электропередачи по отношению к защищаемому пространству, геометрические размеры, количество проводов и рабочие токи линии электропередачи, а также размеры экранируемого пространства и нормативное значение индукции магнитного поля, которое должно быть достигнуто в результате экранирования. Целью синтеза системы активного экранирования является определение количества, конфигурации, пространственного расположения, схем электропитания и токов экранирующей обмоток, алгоритма работы системы управления, а также результирующего значения индукционного магнитного поля в точках экранируемого пространства. Результаты. Приводятся результаты трех вариантов синтеза одноконтурной робастной системы активного экранирования с различным пространственным расположением экранирующей обмотки для уменьшения магнитного поля, создаваемого группой высоковольтных линий электропередачи. Показана возможность существенного снижения уровня индукции исходного магнитного поля внутри экранируемого пространства и снижения чувствительности системы к неопределенности параметров системы. Оригинальность. Впервые проведены синтез, теоретические и экспериментальные исследования одноконтурной робастной системы активного экранирования магнитного поля, создаваемых группой высоковольтными линиями электропередач в области экранируемого пространства, с различным пространственным расположением экранирующей обмотки. Практическая ценность. Приводятся практические рекомендации по обоснованному выбору с точки зрения практической реализации пространственного расположения экранирующей обмотки одноконтурной робастной системы активного экранирования магнитного поля, создаваемого группой высоковольтных линий электропередач. 

Ключові слова


высоковольтные линии электропередачи; магнитное поле промышленной частоты; робастная система активного экранирования; многокритериальная стохастическая игра

Повний текст:

PDF ENG (English)

Посилання


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).

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

Ter Brake H.J.M., Huonker R., Rogalla H. New results in active noise compensation for magnetically shielded rooms. Measurement Science and Technology, 1993, Vol. 4, Issue 12, pp. 1370-1375. doi: 10.1088/0957-0233/4/12/010.

Celozzi S., Garzia F. Active shielding for power-frequency magnetic field reduction using genetic algorithms optimization. IEE Proceedings – Science, Measurement and Technology, 2004, Vol.151, no.1, pp. 2-7. doi: 10.1049/ip-smt:20040002.

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.

Beltran H., Fuster V., García M. Magnetic field reduction screening system for a magnetic field source used in industrial applications. 9 Congreso Hispano Luso de Ingeniería Eléctrica (9 CHLIE),Marbella (Málaga,Spain), 2005, pр. 84-99.

Rozov V.Yu., Grinchenko V.S., Pelevin D.Ye., Chunikhin K.V. Simulation of electromagnetic field in residential buildings located near overhead lines. Technical electrodynamics, 2016, no.3, pp. 6-8. (Rus).

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Celozzi S. Active compensation and partial shields for the power-frequency magnetic field reduction. IEEE International Symposium on Electromagnetic Compatibility. Minneapolis, USA, 2002, pp. 222-226. doi: 10.1109/isemc.2002.1032478.

Celozzi S., Garzia F. Magnetic field reduction by means of active shielding techniques. Environmental Health Risk II, 8 September, 2003, pp. 64-73. doi: 10.2495/ehr030091.

The World Health Organization. The International EMF Project. [Online]. Available at: http://www.who.int/peh-emf/project/en/. (accessed 17 February 2017).

Electrical installation regulations. 5th ed. The Ministry of Energy and Coal Mining ofUkraine, 2014. 277 p. (Ukr).

Cruz Romero P., Izquierdo Mitchell C., Burgos Payan, M. Optimal split-phase configurations. In Proceedings of the 2001 IEEE Porto Power Tech Proceedings (Cat. No.01EX502),Porto,Portugal, 10-13 September 2001, vol.3, p. 5.

Cruz Romero P., Izquierdo C., Burgos M., Ferrer L.F., Soto F., Llanos C., Pacheco J.D. Magnetic field mitigation in power lines with passive and active loops. In Proceedings of the CIGRE Session,Paris,France, 25-30 August 2002.

Barsali S., Giglioli R., Poli D. Active shielding of overhead line magnetic field: Design and applications. Electric Power Systems Research, 2014, vol.110, pp. 55-63. doi: 10.1016/j.epsr.2014.01.005.

DelPino Lopez J.C., Romero P.C. Influence of Different Types of Magnetic Shields on the Thermal Behavior and Ampacity of Underground Power Cables. IEEE Transactions on Power Delivery, 2011, vol.26, no.4, pp. 2659-2667. doi: 10.1109/tpwrd.2011.2158593.

Del Pino-Lopez J.C., Cruz-Romero P., Serrano-Iribarnegaray L. Impact of electromagnetic losses in closed two-component magnetic shields on the ampacity of underground power cables. Progress in electromagnetics research, 2013, vol.135, pp. 601-625. doi: 10.2528/pier12112303.

del-Pino-López J.C., Giaccone L., Canova A., Cruz-Romero P. Design of active loops for magnetic field mitigation in MV/LV substation surroundings. Electric Power Systems Research, 2015, vol.119, pp. 337-344. doi: 10.1016/j.epsr.2014.10.019.

del Pino Lopez J.C., Giaccone L., Canova A., Cruz Romero P. Ga-based active loop optimization for magnetic field mitigation of MV/LV substations. IEEE Latin America Transactions, 2014, vol.12, no.6, pp. 1055-1061. doi: 10.1109/tla.2014.6894000.

Canova A., Giaccone L. Real-time optimization of active loops for the magnetic field minimization. International Journal of Applied Electromagnetics and Mechanics, 2018, vol.56, pp. 97-106. doi: 10.3233/jae-172286.

Canova A., del-Pino-Lopez J.C., Giaccone L., Manca M. Active Shielding System for ELF Magnetic Fields. IEEE Transactions on Magnetics, 2015, vol.51, no.3, pp. 1-4. doi: 10.1109/tmag.2014.2354515.

Femia N., Petrone G., Spagnuolo G., Vitelli M. Optimization of Perturb and Observe Maximum Power Point Tracking Method. IEEE Transactions on Power Electronics, 2005, vol.20, no.4, pp. 963-973. doi: 10.1109/tpel.2005.850975.

Kuznetsov B.I., Turenko A.N., Nikitina T.B., Voloshko A.V., Kolomiets V.V. Method of synthesis of closed-loop systems of active shielding magnetic field of power transmission lines. Technical electrodynamics, 2016, no.4, pp. 8-10. (Rus).

Kuznetsov B.I., Nikitina T.B., Voloshko A.V., Bovdyj I.V., Vinichenko E.V., Kobilyanskiy B.B.. Synthesis of an active shielding system of the magnetic field of power lines based on multiobjective optimization. Electrical engineering & electromechanics, 2016, no.6, pp. 26-30. (Rus). doi: 10.20998/2074-272X.2016.6.05.

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.

Ranković A. Novel multi-objective optimization method of electric and magnetic field emissions from double-circuit overhead power line. International Transactions on Electrical Energy Systems, 2016, vol.27, no.2, p. e2243 doi: 10.1002/etep.2243.

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

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).

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., 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.

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.

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.

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.

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.

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.

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.

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.

Clerc M. Particle Swarm Optimization. London, ISTE Ltd., 2006. 244 p. doi: 10.1002/9780470612163.

Shoham Y., Leyton-Brown K. Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, 2009. 504 p.

Xiaohui Hu, Eberhart R.C., Yuhui Shi. Particle swarm with extended memory for multiobjective optimization. Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS’03 (Cat. No.03EX706). doi: 10.1109/sis.2003.1202267.

Michalewicz Z., Schoenauer M. Evolutionary Algorithms for Constrained Parameter Optimization Problems. Evolutionary Computation, 1996, vol.4, no.1, pp. 1-32. doi: 10.1162/evco.1996.4.1.1.

Parsopoulos K.E., Vrahatis, M.N. Particle Swarm Optimization Method for Constrained Optimization Problems. In Proceedings of the Euro-International Symposium on Computational Intelligence, 2002, pp. 174-181.

Pulido G.T., Coello C.A.C. A constraint-handling mechanism for particle swarm optimization. Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753). doi: 10.1109/cec.2004.1331060.

Ray T., Liew K.M. A Swarm Metaphor for Multiobjective Design Optimization. Engineering Optimization, 2002, vol.34, no.2, pp. 141-153. doi: 10.1080/03052150210915.

. Coello Coello C.A, Reyes-Sierra M. Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the-Art. International Journal of Computational Intelligence Research, 2006, vol.2, no.3, pp. 287-308. doi: 10.5019/j.ijcir.2006.68.

De Freitas Vaz A.I., Da G. Pinto Fernandes E.M. Optimization of nonlinear constrained particle swarm. Technological and Economic Development of Economy, 2006, vol.12, no.1, pp. 30-36. doi: 10.3846/13928619.2006.9637719.

Zilzter Eckart. Evolutionary algorithms for multiobjective optimizations: methods and applications. Ph. D. Thesis Swiss Federal Institute of Technology. Zurich, 1999. 114 p.

Xin-She Yang, Zhihua Cui, Renbin Xiao, Amir Hossein Gandomi, Mehmet Karamanoglu. Swarm Intelligence and Bio-Inspired Computation: Theory and Applications, Elsevier Inc., 2013. 450 p

Kuznetsov B.I., Nikitina T.B., Voloshko A.V., Bovdyj I.V., Vinichenko E.V., Kobilyanskiy B.B. Experimental research of magnetic field sensors spatial arrangement influence on efficiency of closed loop of active screening system of magnetic field of power line. Electrical engineering & electromechanics, 2017, no.1, pp. 16-20. doi: 10.20998/2074-272X.2017.1.03.


Пристатейна бібліографія ГОСТ


  1. 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).
  2. Active Magnetic Shielding (Field Cancellation). Available at: http://www.emfservices.com/afcs.html (accessed 10 September 2012).
  3. Ter Brake H.J.M., Huonker R., Rogalla H. New results in active noise compensation for magnetically shielded rooms. Measurement Science and Technology, 1993, Vol. 4, Issue 12, pp. 1370-1375. doi: 10.1088/0957-0233/4/12/010.
  4. Celozzi S., Garzia F. Active shielding for power-frequency magnetic field reduction using genetic algorithms optimization. IEE Proceedings – Science, Measurement and Technology, 2004, Vol.151, no.1, pp. 2-7. doi: 10.1049/ip-smt:20040002.
  5. 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.
  6. Beltran H., Fuster V., García M. Magnetic field reduction screening system for a magnetic field source used in industrial applications. 9 Congreso Hispano Luso de Ingeniería Eléctrica (9 CHLIE),Marbella (Málaga,Spain), 2005, pр. 84-99.
  7. Rozov V.Yu., Grinchenko V.S., Pelevin D.Ye., Chunikhin K.V. Simulation of electromagnetic field in residential buildings located near overhead lines. Technical electrodynamics, 2016, no.3, pp. 6-8. (Rus).
  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. Celozzi S. Active compensation and partial shields for the power-frequency magnetic field reduction. IEEE International Symposium on Electromagnetic Compatibility. Minneapolis, USA, 2002, pp. 222-226. doi: 10.1109/isemc.2002.1032478.
  10. Celozzi S., Garzia F. Magnetic field reduction by means of active shielding techniques. Environmental Health Risk II, 8 September, 2003, pp. 64-73. doi: 10.2495/ehr030091.
  11. The World Health Organization. The International EMF Project. [Online]. Available at: http://www.who.int/peh-emf/project/en/. (accessed 17 February 2017).
  12. Electrical installation regulations. 5th ed. The Ministry of Energy and Coal Mining ofUkraine, 2014. 277 p. (Ukr).
  13. Cruz Romero P., Izquierdo Mitchell C., Burgos Payan, M. Optimal split-phase configurations. In Proceedings of the 2001 IEEE Porto Power Tech Proceedings (Cat. No.01EX502),Porto,Portugal, 10-13 September 2001, vol.3, p. 5.
  14. Cruz Romero P., Izquierdo C., Burgos M., Ferrer L.F., Soto F., Llanos C., Pacheco J.D. Magnetic field mitigation in power lines with passive and active loops. In Proceedings of the CIGRE Session,Paris,France, 25-30 August 2002.
  15. Barsali S., Giglioli R., Poli D. Active shielding of overhead line magnetic field: Design and applications. Electric Power Systems Research, 2014, vol.110, pp. 55-63. doi: 10.1016/j.epsr.2014.01.005.
  16. DelPino Lopez J.C., Romero P.C. Influence of Different Types of Magnetic Shields on the Thermal Behavior and Ampacity of Underground Power Cables. IEEE Transactions on Power Delivery, 2011, vol.26, no.4, pp. 2659-2667. doi: 10.1109/tpwrd.2011.2158593.
  17. Del Pino-Lopez J.C., Cruz-Romero P., Serrano-Iribarnegaray L. Impact of electromagnetic losses in closed two-component magnetic shields on the ampacity of underground power cables. Progress in electromagnetics research, 2013, vol.135, pp. 601-625. doi: 10.2528/pier12112303.
  18. del-Pino-López J.C., Giaccone L., Canova A., Cruz-Romero P. Design of active loops for magnetic field mitigation in MV/LV substation surroundings. Electric Power Systems Research, 2015, vol.119, pp. 337-344. doi: 10.1016/j.epsr.2014.10.019.
  19. del Pino Lopez J.C., Giaccone L., Canova A., Cruz Romero P. Ga-based active loop optimization for magnetic field mitigation of MV/LV substations. IEEE Latin America Transactions, 2014, vol.12, no.6, pp. 1055-1061. doi: 10.1109/tla.2014.6894000.
  20. Canova A., Giaccone L. Real-time optimization of active loops for the magnetic field minimization. International Journal of Applied Electromagnetics and Mechanics, 2018, vol.56, pp. 97-106. doi: 10.3233/jae-172286.
  21. Canova A., del-Pino-Lopez J.C., Giaccone L., Manca M. Active Shielding System for ELF Magnetic Fields. IEEE Transactions on Magnetics, 2015, vol.51, no.3, pp. 1-4. doi: 10.1109/tmag.2014.2354515.
  22. Femia N., Petrone G., Spagnuolo G., Vitelli M. Optimization of Perturb and Observe Maximum Power Point Tracking Method. IEEE Transactions on Power Electronics, 2005, vol.20, no.4, pp. 963-973. doi: 10.1109/tpel.2005.850975.
  23. Kuznetsov B.I., Turenko A.N., Nikitina T.B., Voloshko A.V., Kolomiets V.V. Method of synthesis of closed-loop systems of active shielding magnetic field of power transmission lines. Technical electrodynamics, 2016, no.4, pp. 8-10. (Rus).
  24. Kuznetsov B.I., Nikitina T.B., Voloshko A.V., Bovdyj I.V., Vinichenko E.V., Kobilyanskiy B.B.. Synthesis of an active shielding system of the magnetic field of power lines based on multiobjective optimization. Electrical engineering & electromechanics, 2016, no.6, pp. 26-30. (Rus). doi: 10.20998/2074-272X.2016.6.05.
  25. 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.
  26. Ranković A. Novel multi-objective optimization method of electric and magnetic field emissions from double-circuit overhead power line. International Transactions on Electrical Energy Systems, 2016, vol.27, no.2, p. e2243 doi: 10.1002/etep.2243.
  27. Ummels M. Stochastic Multiplayer Games Theory and Algorithms. Amsterdam University Press, 2010. 174 p.
  28. 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).
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. 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.
  38. Clerc M. Particle Swarm Optimization. London, ISTE Ltd., 2006. 244 p. doi: 10.1002/9780470612163.
  39. Shoham Y., Leyton-Brown K. Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, 2009. 504 p.
  40. Xiaohui Hu, Eberhart R.C., Yuhui Shi. Particle swarm with extended memory for multiobjective optimization. Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS’03 (Cat. No.03EX706). doi: 10.1109/sis.2003.1202267.
  41. Michalewicz Z., Schoenauer M. Evolutionary Algorithms for Constrained Parameter Optimization Problems. Evolutionary Computation, 1996, vol.4, no.1, pp. 1-32. doi: 10.1162/evco.1996.4.1.1.
  42. Parsopoulos K.E., Vrahatis, M.N. Particle Swarm Optimization Method for Constrained Optimization Problems. In Proceedings of the Euro-International Symposium on Computational Intelligence, 2002, pp. 174-181.
  43. Pulido G.T., Coello C.A.C. A constraint-handling mechanism for particle swarm optimization. Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753). doi: 10.1109/cec.2004.1331060.
  44. Ray T., Liew K.M. A Swarm Metaphor for Multiobjective Design Optimization. Engineering Optimization, 2002, vol.34, no.2, pp. 141-153. doi: 10.1080/03052150210915.
  45. . Coello Coello C.A, Reyes-Sierra M. Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the-Art. International Journal of Computational Intelligence Research, 2006, vol.2, no.3, pp. 287-308. doi: 10.5019/j.ijcir.2006.68.
  46. De Freitas Vaz A.I., Da G. Pinto Fernandes E.M. Optimization of nonlinear constrained particle swarm. Technological and Economic Development of Economy, 2006, vol.12, no.1, pp. 30-36. doi: 10.3846/13928619.2006.9637719.
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