Improvement of the mathematical model of single­phase half­bridge inverter in state­variable form

Authors

DOI:

https://doi.org/10.15587/1729-4061.2018.139853

Keywords:

spurious capacitances, pulse-width modulation, matrix of the main sections, state variables, graph tree, topological equations.

Abstract

The mathematical model of the insulated-gate bipolar transistor in the IGBT module is improved due to the determination of analytical expressions for dynamic spurious capacitances of the device. The expressions are obtained by analytical differentiation of functions that approximate the dependence of the spurious capacitances of the transistor on the voltage between the collector and the emitter. The method of forming a mathematical model of the IGBT voltage inverter in the form of matrix differential equations of state in the Cauchy form and nonlinear equations is proposed. There are no restrictions on the number of transistors and the configuration of the circuit. The method is based on the matrix-topological method of electrical circuits analyzing. The application of this method is illustrated by the example of a single-phase half-bridge inverter with resistive load. The urgency of improving the mathematical model of the IGBT inverter is caused by the need to analyze the electrical safety of the state of the variable frequency circuit between the frequency converter and the motor. Existing models of frequency-controlled electric drives do not take into account a number of factors that significantly affect the accuracy of the simulation. Such factors include the dynamic nature of the IGBT spurious capacitances and the disconnection of one of the machine phases from the network during the dead time when switching adjacent power switches of the inverter. The obtained mathematical model differs from the well-known in advanced representation of separate elements by nonlinear differential equations and taking into account mutual influences. The proposed approach allows to investigate the high-frequency transient components of currents and voltages in electrical systems with semiconductor converters. This simplifies taking into account the recharging processes of the IGBT capacitances during a dead time when switching adjacent power switches in the model. The peculiarities of the IGBT inverter switching transients are revealed, in particular, the significant exceeding, more than twice, of the transistor current during opening the operating current at the end of the switching process.

Author Biographies

Sviatoslav Vasylets, National University of Water and Environmental Engineering Soborna str., 11, Rivne, Ukraine, 33028

Doctor of Technical Science, Associate Professor

Department of Automation, Electrical Engineering and Computer-Integrated Technologies

Kateryna Vasylets, National University of Water and Environmental Engineering Soborna str., 11, Rivne, Ukraine, 33028

Assistant

Department of Automation, Electrical Engineering and Computer-Integrated Technologies

References

  1. Ning, P., Meng, J., Wen, X. (2015). A Finite Differential Method based IGBT model in PSPICE. 2015 IEEE Applied Power Electronics Conference and Exposition (APEC). doi: https://doi.org/10.1109/apec.2015.7104482
  2. Zhang, F., Yang, X., Huang, L., Wang, K., Xu, G., Li, Y., Xie, R. (2017). A fixed topology Thévenin equivalent integral model for modular multilevel converters. International Transactions on Electrical Energy Systems, 28 (3), e2496. doi: https://doi.org/10.1002/etep.2496
  3. Chen, Y., Zhuo, F. (2016). Research on current sharing of paralleled IGBTs in different DC breaker circuit topologies. MATEC Web of Conferences, 63, 01010. doi: https://doi.org/10.1051/matecconf/20166301010
  4. Denz, P., Schmitt, T., Andres, M. (2014). Behavioral Modeling of Power Semiconductors in Modelica. Proceedings of the 10th International Modelica Conference, March 10-12, 2014, Lund, Sweden. doi: https://doi.org/10.3384/ecp14096343
  5. Grigorova, T. G., Asparuhova, K. K. (2014). Unified method for behavioral modeling of IGBT. Annual journal of electronics, 96–99. Available at: http://ecad.tu-sofia.bg/et/2014/ET2014/AJE_2014/096-C_Grigorova.pdf
  6. Ravi, R., Sunnivesh, S. (2017). Modeling and simulation of highly advanced multilevel inverter for speed control of induction motor. International journal of scientific & technology research, 6 (02), 232–236. Available at: http://www.ijstr.org/final-print/feb2017/Modeling-And-Simulation-Of-Highly-Advanced-Multilevel-Inverter-For-Speed-Control-Of-Induction-Motor.pdf
  7. Marković, N., Bjelić, S., Živanić, J., Milićević, V., Milićević, Z. (2016). Model of Transient Process Where Three-Phase Transducer Feeds Induction Motor Equivalent as a Variable Active-Inductive Load. Mathematical Problems in Engineering, 2016, 1–14. doi: https://doi.org/10.1155/2016/6740261
  8. Kovalev, E. B. (2012). Modelirovanie processa perekhoda asinhronnogo dvigatelya s trekhfaznogo rezhima raboty v odnofazniy. Vzryvozashchishchennoe elektrooborudovanie, 98–107. Available at: http://ea.donntu.edu.ua:8080/jspui/handle/123456789/15647
  9. Czapp, S. (2010). The effect of PWM frequency on the effectiveness of protection against electric shock using residual current devices. 2010 International School on Nonsinusoidal Currents and Compensation. doi: https://doi.org/10.1109/isncc.2010.5524515
  10. Hollander, H. (2013). Modeling of an IGBT and a gate unit: Degree project in Power Electronics. Stockholm: Royal Institute of Technology, 59. Available at: www.diva-portal.org/smash/get/diva2:636261/FULLTEXT01.pdf
  11. Syvokobylenko, V. F., Vasylets, S. V. (2017). Matematychne modeliuvannia perekhidnykh protsesiv v elektrotekhnichnykh kompleksakh shakhtnykh elektrychnykh merezh. Lutsk: Vezha-Druk, 272.
  12. StakPak IGBT Module 5SNA 2000K450300. Data Sheet, Doc. No. 5SYA 1431-01 10-2016 (2016). ABB Switzerland Ltd. Semiconductors, 9.

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Published

2018-07-31

How to Cite

Vasylets, S., & Vasylets, K. (2018). Improvement of the mathematical model of single­phase half­bridge inverter in state­variable form. Eastern-European Journal of Enterprise Technologies, 4(5 (94), 14–21. https://doi.org/10.15587/1729-4061.2018.139853

Issue

Vol. 4 No. 5 (94) (2018): Applied physics

Section

Applied physics

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Copyright (c) 2018 Sviatoslav Vasylets, Kateryna Vasylets

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