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The National Academy of Sciences of Ukraine

The Institute of Electrodynamics

About Institute



T.V. Mysak
Institute of Electrodynamics of the National Academy of Sciences of Ukraine,
Peremohy, 56, Kyiv-57, 03680, Ukraine,
е-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it

The object of study is the sinusoidal voltage source that is composed of a PWM frequency converter with an output LC-filter and single-phase nonlinear output transformer. The mathematical description of nonlinear singularly perturbed system of differential equations for which the reduction has been performed. The nonlinearity is given to the form, which the synthesis control law using the method of Lyapunov functions will perform. The simulation results carried out within the limitations affecting the possibility of technical implementation of the resulting control law are presented. References 14, figures 6.
Key words: frequency converter, output LC-filter, one phase nonlinear transformer, singular perturbed system, Lyapunov functions method.

1. Antonovskaya O.G., Goriunov V.I. Selection of the parameters of a quadratic Lyapunov function when solving dynamic problems. Vestnik Nizhegorodskogo universiteta. 2014. No 3(1). P. 103–108. (Rus)
2. Baikov A.V.. Mathematical models of transformers when analyzing a power part of electric drives. Elektrotekhnika i elektroenergetika. 2013. No 5(102). P. 316–327. (Rus)
3. Volianskyi R., Poslaiko I., Sadovoi O. Determination of a desired characteristic polynomial for a generalized electromechanical optimal control system. Electric Power Engineering & Control Systems 2013 (EPECS-2013), 21–23 November 2013, Lviv, Ukraine. Р. 18–19. (Ukr)
4. Derzhavin O.M., Sidorova E.Yu. An approach to the study of a nonlinear nonautonomous singularly perturbed model of a dynamical system. Izvestiia Samarskogo nauchnogo tsentra Rossiiskoi akademii nauk. 2016. Volume 18, No 2(3). P. 888–890. (Rus)
5. Kalitin B.S. Stability of nonautonomous differential equations. Minsk, BGU, 2013. 264 p. (Rus)
6. Malkin I.G. Stability under constant disturbances. Prikladnaia matematika i mekhanika. 1944. Volume 8, No 3. P. 241–245. (Rus)
7. Misak T.V. Formation of a sinusoidal output voltage of a power supply unit with an output transformer in a sliding mode. Pratsi Instytutu elektrodynamiky NAN Ukrainy. 2016. No 43. P. 91–96. (Ukr)
8. Mykhalsky V.M. Means of improving the quality of electricity at the input and output of frequency and voltage converters with pulse-width modulation. Kyiv: Instytut elektrodynamiky NAN Ukrainy, 2013. 340 p. (Ukr)
9. Pentegov I.V., Krasnozhon A.V. Universal approximation of magnetization curves of electrical steels. Elektrotekhnika i Elektromekhanika. 2006. No 1. P. 66–70. (Rus)
10. Cold-rolled thin sheets. NLMK, Lipetsk. 2009. 42 p. (Rus)
11. Strygin V.V., Sobolev V.A., Gorlova E.Ya., Fridman E.Ya. Integral manifolds of singularly perturbed systems and some of their applications. Differentsialnie uravneniia. 1985. Volume XXI, No 10. P. 1723–1726. (Rus)
12. Ming-Shi Huang, Po-YiYeh, U-Ting Yeh, Meng-Gu Huang. Digital-Controlled Single-Phase Transformer-Based Inverter for Non-Linear Load Applications. IEEE Transactions On Industrial Informatics, Vol. 9, No. 2, May 2013. P. 1084–1093. DOI:
13. Naidu D.S., Sen S. Singular perturbation method for the transient analysis of a transformer. Electric Power Systems Research. 1982. Vol. 5, Iss. 4. Р. 307–313.
14. Ramesh R., A.John Dhanaseely, R.Malar. Design of Single phase inverter using PID controller For nonlinear load application. International Journal of Innovative Research in Technology & Science, Vol. 2. Iss. 5. September 30, 2014. P. 55–60.