Features of field modeling of electromagnetic processes of trolley busbar
Keywords:busbar, electromagnetic field, 3D and 2D model, method, harmonics, frequency, verification
Purpose. Research and analysis trolley busbar’s parameters in condition of higher current harmonic actions, with taking into account the structural features of nonlinearity of magnetic and electrical properties of materials, proximity effects, surface and external surface effects.
Methodology. The researches were carried out using the electromagnetic field theory methods, the electrical circuit theory, mathematical physics, finite elements, interpolation, approximation and regression analysis.
Findings. The mathematical spatial model of electromagnetic processes in a steel trolley busbar in time statement of a problem of distribution of an electromagnetic field is developed. The dependences of the distribution of equipotential lines of the resulting z-component of the magnetic potential vector along the busbar, as well as the distribution of the resulting normal component of magnetic induction and magnetic field strength in the transverse (XY) cross section at non-sinusoidal current in busbar trolleys is obtained. Along the length of the busbar, in their cross section, the magnetic field tends to a plane-parallel shape it is proved. The error of the modulus of the vector magnetic potential along the length of the busbar does not exceed 0.9-1.2%. To reduce the dimension of the problem, computational resources and calculation time, a two-dimensional plane-parallel mathematical model in the frequency setting of the electromagnetic field distribution is proposed. To take into account the nonlinear magnetic properties of steel trolleys, to determine the effective magnetization curve for the nonlinear two-dimensional problem of the electromagnetic field of the busbar it is proposed. The verification results, according to the calculated voltage drop, confirm the high accuracy of the calculation and the reliability of the obtained results (error does not exceed 1.88% ÷ 2.06%) of the two-dimensional model in the frequency setting relative to the spatial model in the problem of time-dependent electrical -magnetic field is obtained.
Originality. A mathematical two-dimensional model of electromagnetic processes in the frequency formulation of the problem of electromagnetic field distribution in a trolley busbar is proposed, which takes into account design features, nonlinearity of magnetic and electrophysical properties of materials, proximity effects, surface and external surface effects, influence of harmonic current components power transmission, which allows with high accuracy and efficiency of numerical implementation to determine the parameters of the bus trolls for the corresponding values of the amplitudes and frequencies of the frequencies harmonics of the current.
Practical value. Verification of the calculated voltage drop confirms the high accuracy of the calculation and the reliability of the results (error does not exceed 1.88% ÷ 2.06%) of the two-dimensional model in the frequency reference relative to the spatial model in the problem of time-dependent electromagnetic field distribution is performed.
Yarymbash, D., Kotsur, M., Yarymbash, S., Kotsur, I. (2016). Osobennosti trekhmernogo modelirovaniya elektromagnitnykh polej asinkhronnogo dvigatelya. Elektrotekhnika ta elektroenergetika, 2, 43 – 50. DOI: http://dx.doi.org/10.15588/1607-6761-2016-2-5
Yarymbash, D., Kotsur, M., Subbotin, S., Oliinyk, A. (2017) New simulation approach of the electromagnetic fields in electrical ma-chines. IEEE: The International Conference on Information and Digital Technologies. Catalog Number CFP17CDT-USB. 452-457. DOI: 10.1109/DT.2017.8024332 (in English).
Yarymbash, D., Yarymbash, S., Kotsur, M., Divchuk, T. (2018). Analysis of inrush currents of the unloaded transformer using the circuit-field modelling methods. Eastern-European Journal of Enterprise Technologies, 3, 5 (93), 6-11. DOI: 10.15587/1729-4061.2018.134248 (in English).
Jiang, B., Wu, J., Povinelli, L. (1996). The origin of spurious solutions in computational elec-tromagnetics, Comput. Phys, 125, 104–123.
Yarymbash, D., Kotsur, M., Bezverkhnia, Yu., Kotsur I. (2018). Parameters determination of the trolley busbars by electromagnetic field simulation. IEEE 3rd International Conference on Intelligent Energy and Power Systems (IEPS), 76-79. DOI: 10.1109/IEPS.2018.8559576 (in Eng-lish).
Yarymbash, D., Kotsur, M., Yarymbash, S., Divchuk, T. (2018). Electromagnetic parame-ters determination of power transformers. IEEE 3rd International Conference on Intelli-gent Energy and Power Systems (IEPS), 70-75. DOI: 10.1109/IEPS.2018.8559573 (in Eng-lish).
Yarymbash, D., Kotsur, M., Yarymbash, S., Divchuk, T. (2019). Hysteresis and eddy cur-rents effects simulation in idling mode of the transformer. Problemele energeticii regionale, 39, 12-21. –DOI: 10.5281/zenodo.2650413. (in English).
Bessonov, L. (2003). Teoreticheskie osnovy el-ektrotekhniki. Elektromagnitnoe pole tokov, magnitnogo polya. Vysshaya shkola, 317 (in Russian).
Demirchan, K., Demirchan, V., Chechurin L. (1986). Mashinnye raschety elektromagnitnykh polej, Vysshaya shkola, 240. (in Russian)
Rosskopf, A., Bar, E., Joffe, C. (2014). Influence of linner skin- and proximity effects on conduction in litz wires. IEEE Trans. Power Electron., 29, 10, 5454–5461, DOI: 10.1109/TPEL.2013.2293847 (in Rus-sian).
Filippov, I. (1986) Teploobmen v elektricheskikh mashinakh: ucheb. pos. dlya vuzov. Energoatomizdat, 256. (in Russian)
Divchuk, T., Yarymbash, D., Yarymbash, S., Kylymnyk, I., Kotsur, M., Bezverkhnia, Y. (2018). Ytochyuyuchyy pidhid do vyznachenya funkcional´nykh zalezhnostey vidnosnykh magnitnykh pronyknostey ani-zotropnykh kholodnokatannykh staley (An adjusting approach to the determination of the permeability functional dependencies of aniso-tropic cold-rolled electrotechnical steels). Elec-trical Engineering And Power Engineering, 2, 6-15. doi:http://dx.doi.org/10.15588/1607-6761-2018-2-1 (in Ukrainian).
Landau, L. D. Lifshicz, E. M. Nauka (1988). Teoreticheskaya fizika. T. 2 Teoriya polya, 59. (in Russian)
Matveev, A. N. (1983). Elektrichestvo i magnetizm. Vysshaya shkola, 463. (in Rus-sian)
Yarymbash D., Kotsur M., Yarymbash S., Kylymnyk M. (2018). An error estimation of the current sensors of the automated control system of the technological process of graphitation. IEEE: 2018 IEEE 3rd Interna-tional Conference on Intelligent Energy and Power Systems (IEPS), 64-69. DOI: 10.1109/IEPS.2018.8559489 (in English).
Shuhong, Wang., Qingfu, Li, Jie Qiu, Shan Shi (2001). A new parametric finite element analy-sis software for electrical machine electromag-netic fields and its implementation. ICEMS'2001. Proceedings of the Fifth Interna-tional Conference on Electrical Machines and Systems (IEEE Cat. No.01EX501), 2, 1098-1101 doi: 10.1109/ICEMS.2001.971869.
Chernykh, I. V., (2002) Reshenie polevykh zadach s pomoshhyu programmy ELCUT 4.2 Izdatelstvo UGTI-UPI, 23. (in Russian)
Kotsur, M., Yarymbash, D., Kotsur, I., Yarym-bash, S. (2019). Improving efficiency in de-termining the inductance for the active part of an electric machine's armature by methods of field modeling. Eastern-European Journal of Enterprise Technologies, 6, 5 (102), 39-47. DOI: 10.15587/1729-4061.2019.185136 (in English).
Bida, V., Vaseczkij, Yu., Zakharchenko, S. (1990). K raschetu tokovedushhikh sistem, obrazovannykh konturami slozhnoj geometrii. Izvestiya VUZov. Elektromekhanika, 6, 19-21. (in Russian).
Vaseczkij, Yu., Kovbasenko, Yu. (1987). K raschetu magnitnogo polya prostranstvennykh konturov s tokom. Izvestiya VUZov. E`lektromekhanika, 5, 28–32. (in Russian).
Vaseczkij, Yu. M., (1989). Poverkhnostnyj effekt v massivnom provodnike, obrazuyushhem ploskij kontur. Tekhnicheskaya elektrodinamika, 12, 72–74. (in Russian).
Vaseczkij, Yu. M. (1987). Priblizhenny`j metod rascheta polya vnutri i v okrestnosti provodnika ploskogo kontura. Tekhnicheskaya e`lektrodinamika, 4, 5–7. (in Russian).
Kalantarov, P. L., Czejtlin, L. A. (1986). Raschet induktivnostej: spravochnaya kniga. Energoatomizdat, 488. (in Russian).
Czejtlin, L. A. (1950). Induktivnosti provodov i konturov. Gose`nergoizdat, 228. (in Russian).
МЭК (61000-3-12:2004) Electromagnetic compatibility (EMC) - Part 3-12: Limits - Lim-its for harmonic currents produced by equip-ment connected to public low-voltage systems with input current > 16 A and ≤ 75 A per phase IEC (61000-3-12: 2004) Sovmestimost´ tekhnichtskikh sredstv elektromagnitnaya. Ogranichenie garmonicheskikh sostsvlyaiushikh toka, sozdavaemykh tekhnicheskimi sredstvami potreblyaemymy tokom bolee 16A, no ne bolee 75A (v odnoy faze), podkluchaemykh k nizkovol´tnym sistemam electrosnabzheniya obshshego naznacheniya. Normy i metody ispytaniy. (Electromagnetic compatibility of technical means. Limit of harmonic current components created by technical means with a current consumption of more than 16 A, but not more than 75 A (in one phase), connected to low-voltage general-purpose power systems. Norms and methods of testing). (in Russian.).
Markov, B. L. (1984). Fizicheskoe modelirovanie v metallurgii. Metallurgiya, 119. (in Russian.).
Demirchan, K.S. (1974). Modelirovanie magnitnykh polej. E`nergiya, 288. (in Russian.).
Bul`, O.B. (2006). Metody rascheta magnitny`kh sistem elektricheskikh apparatov. Programma ANSYS Uchebnoe posobie dlya studentov vuzov. Akademiya, 288. (in Russian.).
Yarymbash, D., Kotsur, M., Yarymbash, S., Kylymnyk, I., Divchuk, T. (2020). Electro-magnetic Properties Determination of Electri-cal Steels [Electronic Resource]. IEEE: 15th In-ternational Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET), 185-189. DOI: 10.1109/TCSET49122.2020.235419 (in English).
Yarymbash, D., Kotsur, M., Yarymbash, S., Kotsur, I. (2016). Osobennosti trekhmernogo modelirovaniya elektromagnitnykh polej asinkhronnogo dvigatelya. Elektrotekhnika ta elektroenergetika, 2, 43–50. DOI: http://dx.doi.org/10.15588/1607-6761-2016-2-5 (in Russian).
Yarymbash, D., Yarymbash, S., Kotsur, I. Litvinov, D. (2018). Computer simulation of electromagnetic field with application the fre-quency adaptation method. Radio Electronics, Computer Science, Control, 1, 65-74. –DOI: https://doi.org/10.15588/1607-3274-2018-1-8 (in English).
Yarymbash, D., Kotsur, M., Bezverkhnia, Yu., Kotsur, I. (2018). Parameters Determination of the Trolley Busbars by Electromagnetic Field Simulation. IEEE: 2018 IEEE 3rd Internation-al Conference on Intelligent Energy and Power Systems (IEPS), 76-79. DOI: 10.1109/IEPS.2018.8559576 (in Eng-lish).
Kotsur, M., Yarymbash, D., Bezverkhnia, Yu., Kotsur, I. (2020). Determination of a busbar’s parameters by electromagnetic field simula-tion. IEEE Problems of Automated Electro-drive. Theory and Practice (PAEP), 1-4, doi: 10.1109/PAEP49887.2020.9240811. (in Eng-lish).
Paoli, G., Biro, G., Buchgraber, O. (1998). Complex representation in nonlinear time harmonic eddy current problems. Transactions on Magnetics, 34, 5, 2625 – 2628. (in English).
Koeppl, H., Paoli, G. (2002). Non-linear model-ing of a broadband SLIC for ADSL-Lite-over-POTS using harmonic analysis. IEEE Interna-tional Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353. II-II, doi: 10.1109/ISCAS.2002.1010942. (in English).
Junwei, Lu., Xiaojun, Zhao, Sotoshi, Yamada (2016). Harmonic balance methods used in computational electromagnetics. harmonic balance finite element method: applications in nonlinear electromagnetics and power systems. John Wiley & Sons Singapore Pte. Ltd, 304. (in English).
Junwei, Lu., Xiaojun, Zhao, Sotoshi, Yamada (2016). Nonlinear electromagnetic field and its harmonic problems in harmonic balance finite element method: applications in nonlinear electromagnetics and power systems. Wiley-IEEE Press, 1, 19-59. (in English).
Stockreiter, C. (2007). Тransfinite element method using the v-potential formulation with edge elements in the frequency domain. IEEE Transactions on Magnetics, 43, 4, 1349-1352. doi: 10.1109/TMAG.2006.891008. (in Eng-lish).
Paoli, G., Biro, O. (1997). Time harmonic eddy currents in non-linear media. «COMPEL» – The international journal for computation and mathematics in electrical and electronic engi-neering, 17, 5, 567-575. (in English).
Izmajlov, S. V. (1962). Kurs Elektrodinamiki: dlya fiziko-matematicheskikh fakultetov ped-agogicheskikh vuzov. Gos. Uchebn-pedagog. Izdatelstvovo ministerstva prosveshheniya RSFSR, 440. (in Russian).
Kotsur, M., Yarymbash, D., Kotsur, I., Yarym-bash, S. (2019). Improving efficiency in de-termining the inductance for the active part of an electric machine's armature by methods of field modeling [Electronic Resource]. Eastern-European Journal of Enterprise Technologies, 6, 5 (102), 39-47. DOI: 10.15587/1729-4061.2019.185136. (in English).
How to Cite
This work is licensed under a Creative Commons Attribution 4.0 International License.
Creative Commons Licensing Notifications in the Copyright Notices
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under aCreative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.