DOI: https://doi.org/10.15587/2312-8372.2019.154680

### The development of the mathematical model of a nonlinear electrical circuit with an independent controllable electromechanical energy converter

Mykola Ostroverkhov, Danylo Trinchuk

#### Abstract

The nonlinear electric circuit with an independent controllable electromechanical energy converter is the object of this research. Such circuit nowadays has large practical use in many vehicles. The developers of these vehicles conduct frequent research and calculations of these circuits during the design stage.

The one of the problems of such circuits is the complexity of its calculations. The circuit has a few nonlinear elements: an electric motor, a battery, and a supercapacitor. Numerical calculations of such circuit would be extremely complex and require huge computational power. As a result, a lot of existing models created for conducting research of such circuits are oversimplified, which leads to inaccuracy of energy calculations.

During this research the mathematical model of the circuit under consideration was created to be as simple as possible with the accuracy being acceptable for energy calculations. In order to achieve this, the existed models were examined: parameters, which have weak impact on electromagnetic processes, were neglected while momentary effect, such as the impulse form of energy transformation, and additional energy losses were taken under consideration. Thereafter the computer model of the nonlinear electric circuit with an independent controllable electromechanical energy converter was created to meet the accuracy requirements for energy calculations and to be reasonably complex at the same time.

The obtained model is more accurate for energy calculations than most of existing models due to the accounting of the impulse working modes of the electrical converter and electromagnetic losses of the electromechanical converter. Also due to the neglecting of some poser supply parameters that have slight effect on the energy losses this model is less complex then other accurate models of the circuit under consideration. Thus, the obtained model is optimal for the energy calculations of the nonlinear electric circuit with an independent controllable electromechanical converter.

#### Keywords

nonlinear electric circuit; Li-Ion battery; supercapacitor; induction motor

#### Full Text:

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#### References

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Biletskyi, O. O. (2016). Enerhetychni protsesy v kolakh zariadu superkondensatoriv zi zminnymy pochatkovymy napruhamy. Kyiv, 195.

Liu, S., Peng, J., Li, L., Gong, X., Lu, H. (2016). A MPC based energy management strategy for battery-supercapacitor combined energy storage system of HEV. 35th Chinese Control Conference, 8727‑8731. doi: http://doi.org/10.1109/chicc.2016.7554751

#### GOST Style Citations

Pankratov V. V. Vektornoe upravlenie asinkhronnym elektroprivodom. Novosibіrs'k, 1999. 66 p.

Stat'i o vektornom upravlenii. URL: http://xn----8sbecmada0aoptggbsmf4a0a.xn--p1ai/stati-o-vektornom-upravlenii.html

Shepherd C. M. Design of Primary and Secondary Cells // Journal of The Electrochemical Society. 1965. Vol. 112, Issue 7. P. 657–664. doi: http://doi.org/10.1149/1.2423659

Tang X. Li-ion battery parameter estimation for state of charge // American Control Conference (ACC). 2011. P. 941–946. doi: http://doi.org/10.1109/acc.2011.5990963

Wang C., Appleby A. J., Little F. E. Electrochemical impedance study of initial lithium ion intercalation into graphite powders // Electrochimica Acta. 2001. Vol. 46, Issue 12. P. 1793–1813. doi: http://doi.org/10.1016/s0013-4686(00)00782-9

Battery Management System: An Overview of Its Application in the Smart Grid and Electric Vehicles / Rahimi-Eichi H. et. al. // IEEE Industrial Electronics Magazine. 2013. Vol. 7, Issue 2. P. 4–16. doi: http://doi.org/10.1109/mie.2013.2250351

Lee J., Nam O., Cho B. H. Li-ion battery SOC estimation method based on the reduced order extended Kalman filtering // Journal of Power Sources. 2007. Vol. 174, Issue 1. P. 9–15. doi: http://doi.org/10.1016/j.jpowsour.2007.03.072

Matching the nanoporous carbon electrodes and organic electrolytes in double layer capacitors / Maletin Y. et. al. // Applied Physics A. 2005. Vol. 82, Issue 4. P. 653–657. doi: http://doi.org/10.1007/s00339-005-3416-9

Biletskyi O. O. Enerhetychni protsesy v kolakh zariadu superkondensatoriv zi zminnymy pochatkovymy napruhamy: PhD thesis. Kyiv, 2016. 195 p.

A MPC based energy management strategy for battery-supercapacitor combined energy storage system of HEV / Liu S. et. al. // 35th Chinese Control Conference. 2016. P. 8727‑8731. doi: http://doi.org/10.1109/chicc.2016.7554751

Copyright (c) 2019 Mykola Ostroverkhov, Danylo Trinchuk