# MATHEMATICAL MODEL OF A QUICK-DRIVING ACTUATOR OF AN AUTOMATIC SWITCH WITH AN INSTANT-DYNAMIC AND BISTABLE MECHANISM

## Authors

• E. I. BAIDA National Technical University «Kharkiv Polytechnic Institute», Kharkiv, Ukraine
• O. G. VOLKOVA Zaporizhzhia National Technical University, Zaporizhzhia, Ukraine

## Keywords:

power circuit commutation, high-speed switch drive, induction-dynamic mechanism, bistable mechanism

## Abstract

Purpose. Development of a mathematical model of an induction-dynamic drive of a switch with two coils, working with a bistable mechanism, which ensures the fixation of the instant-dynamic mechanism (IDM) in trajectory extreme positions of the contact system.

Methodology. The solution of the problems posed in the work was carried out using methods for calculating the electromagnetic field, finite elements, theoretical mechanics, and solving differential equations.

Findings. The mathematical model of quick-driving actuator as part of instant dynamic and bistable mechanism was developed. It was based on electrical circuit’s electromagnetic equations and kinematic movements of the switching mechanism. Advantage of the given model is possibility of a breaker drive dynamic analysis basing on data of a contact pressure, pretravel and snatch gap. Initial data of the model formulation were outer circuit inductance, resistance of coils, which calculated on conductor cross-section and coils configuration. Initial conditions corresponded by Dirichlet conditions. Mathematical model equations system was calculated in cylindrical coordinate system. Problem was solved with the help ComsolMultiphysics system. Motion of the IDM movement part was modeled by deformation of a computational grid. Spring force and stress in a bistable mechanism construction were determined by initial data of a contact pressure, pretravel and snatch gap. Graphs by calculation data are shown, which allow to analyze of springing elements chose and make necessary adjustments on design stage and debugging construction. Operation parameters of mechanism work on IDM switch on and switch off stages were calculated. Value of movement, motion speed of armature breaker, currents of accelerating and retarding coils, summed electromagnetic and opposite force were figured.

Originality. The mathematical model of quick-driving actuator as part of instant-dynamic and bistable mechanism was developed. The model contains equations of electromagnetic field and motion equation. The mathematical model describes properly of physical process and can be used for development and research a design of quick-driving actuator.

Practical value. It follows from the calculations that with the help of variants of calculations it is possible to obtain the required drive parameters: a) short switching-on time which allows avoiding contact bounce during switching; b) high initial speed, hole short time (less than 1 ms) of contacts opening and reduce dynamic force on actuator elements and contact system.

## Author Biographies

### E. I. BAIDA, National Technical University «Kharkiv Polytechnic Institute», Kharkiv

Ph.D, Associate professor, Associate professor of the electrical apparatus department

### O. G. VOLKOVA, Zaporizhzhia National Technical University, Zaporizhzhia

Ph.D, Associate professor, Associate professor of the theoretical and general electrical engineering department

## References

[1] Evsin, D.V. (2009). Otkluhenie postojannogo toka vakuumnim kommutacionim apparatom s aksialnosimmetrihnim poperechnim magnitnim polem. Diss. kand. tech. nauk [Disconnection of direct current by a vacuum switching device with an axially symmetric transverse magnetic field. Cand. tech. sci. diss.]. Moskov, 142. [in Russian].

[2] Klymenko, B.V. (2012). Elektrychni aparaty. Elektromehanichna aparatura komutacii', keruvannja ta zahystu. Zagal'nyj kurs: navchal'nyj posibnyk. H: Tochka, 340.

[3] Klymenko, B. V., Grechko, A. M., Bugajchuk, V. M. (2017). Opytnyj obrazec dvuhpozicionnogo elektromagnitnogo privoda vakuumnogo vykljuchatelja srednego naprjazhenija [A pre-production model of two-position electromagnetic drive for an averagevoltage vacuum switch]. Electrical engineering&electromechanics, 5, 23-27. [in Russian].

[4] Alferov, D.F., Budovskiy, A.I., Evsin, D.V., Ivanov, V.P. Sidorov, V.A., Neugodnikov, I. P. (2008). Vakuumnyj vykljuchatel' postojannogo toka [Vacuum switch of a direct current]. Electro, 3, 25-28. [in Russian].

[5] Glinkowski, M., Greenwood A., Hill, J., Mauro, R., Varneckes, V. (1991) Capacitance switching with vacuum circuit-breakers. A comparative-evaluation. IEEE Trans. Power Deliv, 6, 1088–1095. [6] Barnes, M. (2018).Design and experimental tests on a superconducting hybrid DC circuit breaker. IEEE Transactions on Applied Superconductivity, 28 (3). DOI:10.1109/TASC.2018.2793226.

[7] Baida, E.I. (2013). Vlijanie gidravlicheskogo dempfera na dinamiku dvuhpozicionnogo poljarizovannogo aktuatora [Influence of the hydraulic damper on the dynamics of a two-position polarized actuator]. Electrical engineering & electromechanics, 5, 15-19. [in Russian]

[8] Bolux, V.F., Shukin, I.S. (2017). Issledovanie teplovyh processov v linejnom impul'snoindukcionnom elektrome-hanicheskom preobrazovateley ciklicheskogo tipa [Investigation of thermal processes in a linear pulse-induction electromechanical converter of the cyclic type]. Electrical engineering &electromechanics, 5, 14-22. [in Russian].

[9] Baida, E.I. (2012). Matematicheskie modeli podkljuchenija bistabil'nyh poljarizovannyh aktuatorov k istochnikam energii [Power connection mathemetical models of polarized bistable actuators to a source of electric power].Visnyk NTU "HPI", 49 (955), 3-8. [in Russian].

[10] Baida, E.I. (2013). Matematicheskaja model' rascheta dinamiki dvuhpozicionnyh jelektromagnitnyh aktuatorov vakuumnyh vykljuchatelej srednego naprjazhenija [Mathematical model of two-position electromagnetic actuator dynamics calculation for MV vacuum circuit-breaker]. Zhurnal nauchnyh publikacij aspirantov i doktorantov, 1 (79), 136 - 141. [in Russian].

[11] Baida, E.I. (2009). Matematicheskoe modelirovaniindukcionno-dinamicheskih sistem [Mathematical modeling of induction-dynamic systems]. Electrical engineering &electromechanics, 5, 13-16. [inRussian].

[12] Bissal, A. (2013). Licentiate thesis on the design of ultra-fast electromechanical. Stockholm, Sweden, 120.

[13] Divchuk, T., Yarymbash, D., Yarymbash, S., Kylymnyk, I., Kotsur, M., & Bezverkhnia, Y. (2018). Approach to determination of no load current of threephase power transformers with plane rods magnetic systems. Electrical Engineering And Power Engineering, 2, 56-66. DOI:http://dx.doi.org/10.15588/1607-6761-2017-2-6

[in Russian]

[14] Yarymbash, D., Kotsur, M., Yarymbash, S., Kotsur, I. (2016). Features of three-dimensional simulation of the electromagnetic fields of the asynchronous motors. Electrical Engineering And Power Engineering, 2, 43-50. DOI:http://dx.doi.org/10.15588/1607-6761-2016-2-5 [in Russian]

[15] Yarymbash, D., Kotsur, M., Yarymbash, S., & Kotsur, I. (2017). Features of parameter determination of the induction motor substitution circuit for short-circuit mode. Electrical Engineering And Power Engineering, 1, 24-30. DOI:http://dx.doi.org/10.15588/1607-6761-2017-1-4 [in Russian]

[16] Yarymbash, D., Yarymbash, S., Divchuk, T., & Kylymnik, I. (2016). Determination features of the power transformer short circuit parameters through field modeling. Electrical Engineering And Power Engineering, 1, 12-17. DOI: http://dx.doi.org/10.15588/1607-6761-2016-1-2 [in Russian]

[17] Kotsur, M., Kotsur, I., Andrienko, A., Andrienko, D. (2016). Opredelenie optimalnoy chastoty kommytacii ventiley preobrazovatelja po sheme chastotnotokovogo asinhronnogo-ventilnogo kaskada [Determination of the optimal switching frequency of the power switches of the frequency-current asynchronous-gate cascade converters]. Electrical Engineering And Power Engineering, 1, 5-11. DOI: http://dx.doi.org/10.15588/1607-6761-2016-1-1 [in Russian]

[18] Weijie Wen, Yulong Huang, Member, Mohmmad Al-Dweikat, Zu’an Zhang, Tiehan Cheng, Shutong Gao and Weidong Liu. (2015). Research on Operating Mechanism for Ultra-fast 40.5kV Vacuum Switches. IEEE Power &Energy Society, 2553 –2560. DOI: 10.1109/ TPWRD.2015.2409122

[18] Aleksandrov, G.N., Borisov, V.V., Ivanov, V.A. i dr. (1985). Teoriya elektricheskih apparatov. Uchebnikdla vuzov po specialnosti "Elektriheskie apparati". M. Vysshaya shkola, 312. [in Russian]

2018-05-31

## How to Cite

BAIDA, E. I., & VOLKOVA, O. G. (2018). MATHEMATICAL MODEL OF A QUICK-DRIVING ACTUATOR OF AN AUTOMATIC SWITCH WITH AN INSTANT-DYNAMIC AND BISTABLE MECHANISM. Electrical Engineering and Power Engineering, (1), 30–39. https://doi.org/10.15588/1607-6761-2018-1-4

Electrotechnics