MATHEMATICAL MODELING OF TRANSIENT ELECTROMAGNETIC PROCESSES IN THE BRIDGE SYSTEM OF TRANSFER OF A THREE-PHASE ACTION CURRENT ON THE BASIS OF VARIATION APPROACHES
DOI:
https://doi.org/10.31734/agroengineering2019.23.067Keywords:
mathematical model, transient processes, bridge current rectification system, variational approaches, Euler – Lagrangian equation, Hamilton – Ostrogradsky principleAbstract
The paper analyzes scientific publications, which confirm that today there is no unanimous theory of mathematical modeling of electrotechnical systems of rectification of alternating three-phase current. However, the study of transient electromagnetic processes is carried out, using ready-made computer programs, which are intended for not scientific, but engineering purposes. The research argues scientific and practical necessity of constructing of efficient and relatively simple models of electrotechnical systems of rectification of alternating three-phase current as the key elements of electric networks of direct current. The work emphasizes importance of development of a mathematical model of a three-phase bridge system of rectification of alternating current, which is performed according to the scheme of Larionov. According to the consolidated interdisciplinary (interdisciplinary) method of mathematical modeling, which is based on modifications of the Hamilton-Ostrogradsky integral variational principle, an equation of the electromagnetic state of the investigated electrotechnical system of straightening a three-phase alternating current is obtained. The mentioned mathematical model secures analysis of transient electromagnetic processes in the elements of the investigated electrotechnical system of straightening of the alternating three-phase current and their mutual influence in the physical processes under the load. Application of the variation approaches allows reproducing of physical processes in electrotechnical systems of alternating and direct currents with a high level of adequacy.
The article presents results of computer simulation of the start of the investigated electrotechnical system of rectification of alternating current in the steady state, which confirms the correctness and adequacy of the research, presented in the article. It is stated that, basing on the unified energy approach, development of interdisciplinary research methods supplies shaping of effective and adequate mathematical models of dynamic systems of various physical nature, which significantly expand the research capabilities of an eventual user.
References
Bessonov, L. A. (1973). Teoreticheskie osnovy elektrotehniki. Moskva: Vyissh. shk.
Bodnar, H. Y., & Shapovalov, O. V. (2008). Elektropryvid vodianoho nasosa protypozhezhnoho vodoprovodu z avtonomnym zhyvlenniam. Visnyk Natsionalnoho tekhnichnoho universytetu «KhPI». Problemy avtomatyzovanoho elektropryvodu. Teoriia i praktyka, 373 – 374.
Buslova, N. V., Vinoslavskii, V. N., Denisenko, G. N., & Perhach, V. S. (1986). Elektricheskie sistemyi i seti. Kiev: Vischa shk.
Vasidzu, K. (1987). Variatsionnyie metody v teorii uprugosti i plastichnosti. Moskva: Mir.
Vasyliv, K., Herman, A., & Dorosh, V. (2012). Matematychna model systemy elektrozhyvlennia na bazi ventylnoho peretvoriuvacha chastoty z lankoiu postiinoho strumu. Visnyk Lvivskoho natsionalnoho ahrarnoho universytetu: Ahroinzhenerni doslidzhennia, 16, 352 – 362.
Vasyliv, K. M. (2010). Metody i modeli analizu protsesiv avtonomnykh system elektrozhyvlennia na bazi asynkhro¬nizovanoho heneratora z bezkontaktnym kaskadnym modulovanym zbudzhuvachem. (Dys. … d-ra tekhn. nauk). Kyiv.
Venikov, V. A. (1972). Elektricheskie sistemy. Peredacha energii peremennym i postoiannyim tokom vysokogo napriazheniya. Moskva: Vyssh. shk.
Dizhur, D. P. (1985). Tsifrovoe modelirovanie elektroperedach postoiannogo toka. Peredacha energii postoyannym tokom, 51 – 63.
Levoniuk, V. R., Chaban, H. V. (2018). Doslidzhennia elektromekhanichnykh protsesiv u vymykachi nadvysokoi napruhy. Visnyk Lvivskoho natsionalnoho ahrarnoho universytetu: Ahroinzhenerni doslidzhennia, 22, 121 – 128.
Plahtyna, E. G. (1986). Matematicheskoe modelirovanie elektro-mashinno-ventilnyh sistem. Lvov: Vyscha shk.
Samotyi, V., & Dzelendziak, U. (2013). Matematychna model kaskadu «Odnofaznyi dvopivperiodnyi vypriamliach – motor postiinoho strumu z paralelnym zbudzhenniam». Visnyk Natsionalnoho universytetu “Lvivska politekhnika”. Elektroenerhetychni ta elektromekhanichni systemy, 753, 35 – 40.
Uaid, D., & Vudson, G. (1964). Elektromehanicheskoe preobrazovanie energii. Leningrad: Energiya.
Chaban, A. V., Levoniuk, V. R., Drobot, I. M., & Herman, A. F. (2016). Matematychne modeliuvannia perekhidnykh protsesiv u linii Lekhera v stani nerobochoho khodu. Elektrotekhnika i Elektromekhanika, 3, 30 – 35.
Chaban, A. V. (2015). Pryntsyp Hamiltona-Ostrohradskoho v elektro-mekhanichnykh systemakh. Lviv: Vyd-vo Tarasa Soroky.
Shimoni, K. (1964). Teoreticheskaia elektrotehnika. Moskva: Mir.
Czaban, A., Lis M., Sosnowski, J., & Lewoniuk, W. (2016). Model matematyczny dwuprzewej linii zasilania z wyko¬rzystaniem modyfikowanej zasady Hamiltona. Maszyny Elektryczne – Zeszyty Problemowe, 1 31 – 36.
Huo, X., & Lei, Y. (2010). A new method for calculating of transient electromagnetic responses of AC/DC power system with external electromagnetic pulse interference. Progress in Electromagnetics Research M, 245 – 260.
Jingfan, Z., Lin, X., Li, C., Du, Z., Zhao, Y., & Zhao, L. (2016). Hybrid simulation of AC-DC power system, based on the analytical method for computing transient response of HVDC. IEEE PES Asia-Pacific Power and Energy Engineering, 993 – 997.
Czaban, A., Lis, M., Chrzan, M., Szafraniec, A., & Levoniuk, V. (2018). Mathematical modelling of transient processes in power supply grid with distributed parameters. Przeglad elektrotechniczny, 1, 17 – 20.
Omid, B., Rajabi, A., Saeedi¬moghadam, M., & Isapour, K. (2015). Stability Improvement of AC System by Controllability of the HVDC. Inter-national Journal of Electrical and Computer Engineering, 3, 371 – 378.
