Clean Power

Ukrainian (UA)English (United Kingdom)

The National Academy of Sciences of Ukraine


The Institute of Electrodynamics

About Institute

DOI: https://doi.org/10.15407/publishing2017.47.057

CONSTRUCTION OF OUTPUT VOLTAGE MODULATION FOR POWER SUPPLY WITH NON-LINEAR OUTPUT TRANSFORMER BY THE REDUCED ORDER MATHEMATICAL MODEL

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 frequency converter with an output LC-filter and a non-linear single-phase output transformer. A mathematical model of this source is constructed in the form of a nonlinear singularly perturbed system of differential equations. Conditions for the existence of an integral manifold in a system with a not - known -control in advance in general form are obtained. The possibility of decreasing the order of the mathematical model of this power source by means of an integral manifold in the form of a power series is shown. A synthesis of the control strategy is carried out by establishing a correspondence between the modulating function and the coefficients of the Lyapunov function. The results of modeling are presented. References 14, figures 2.
Key words: frequency converter, output LC-filter, nonlinear transformer, singularly-perturbed system, integral manifold, theorem of existence, reduction of order.


1. Voldek A.I. Electrical machines. Leningrad: Energiya, 1978. 832 p. (Rus)
2. Demidovych B.P. Lectures on the mathematical theory of sustainability. Moskva: Nauka, 1967. 472 p. (Rus)
3. Kanningkhem V. Introduction to the theory of nonlinear systems. Moskva, Leningrad: Gosenergoizdat, 1962. 456 p. (Rus)
4. Kryshchenko A.P., Kavinov A.V. Stabilization of affine systems. Differential equations. 2000. Volume 36, No 11. P. 1482–1487. (Rus) DOI: https://doi.org/10.1007/BF02757363
5. Lomov S.A. Introduction to the general theory of singular perturbations. Moskva: Nauka. Glavnaya redaktsiya fiz..mat. literatury, 1981. 400 p. (Rus)
6. Mysak T.V. Stabilization of the output voltage of a single-phase power supply with a non-linear output transformer. Pratsi Instytutu elektrodynamiky NAN Ukrainy. 2017. No 46. P. 60–70. (Ukr)
7. Mytropolskyi Yu.A., Lykova O.B. Integral manifolds in nonlinear mechanics. Moskva: Nauka. 1973. 512 p. (Rus)
8. Mykhalskyi V.M. Means of improving electricity quality at an input and output of the frequency and voltage converters with a pulse-width modulation. Kyiv: Instytut elektrodynamiky NAN Ukrainy, 2013. 340 p. (Ukr)
9. Naife A. Introduction to perturbation methods. Moskva: Mir, 1984. 534 p. (Rus)
10. Pankiv V.I., Tankevych E.M., Lutchin M.M. Approximation of the magnetization characteristics of current transformers. Pratsi Instytutu elektrodynamiky NAN Ukrainy. 2014. No 37. P. 82–90. (Ukr)
11. Pianykh B.E. Valve converters of electric energy parameters. Elektronika ta systemy upravlinnia. 2012. No 1(31). P. 28–30. (Ukr)
12. Strygin V.A., Sobolev V.V. Motions separation by the method of integral manifolds. Moskva: Nauka, 1988. 256 p. (Rus)
13. Yazdani A., Iravani R. Voltage-Sourced Converters In Power Systems. Modeling, Control and Applications. Published by John Wiley & Sons, Inc., Hoboken, New Jersey, 2010. 463 p.
14. Zhang L.J., Sun C.Q., Sun J.B. A Nonlinear Model for Marine High-voltage Transformer. Applied Mechanics and Materials, Vols. 602–605. 2014. P. 2572–2576.  DOI: https://doi.org/10.4028/www.scientific.net/AMM.602-605.2572