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The National Academy of Sciences of Ukraine

The Institute of Electrodynamics

About Institute



Yu.V. Rudenko*
Institute of electrodynamics of the National Academy of Sciences of Ukraine,
pr.Peremohy, 56, Kyiv, 03057, Ukraine,
e-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it

The application of state space averaging method using Lagrange theorems for calculating of semiconductor converters in a formalized matrix form is considered. Analytical expressions are obtained for calculating the average and pulsating components of variable states in two-interval processes in single-cycle converters. The matrix coefficients of model with averaged variables for buck converter in the continuous-current choke mode are determined for illustration. Advantages of considered method using Lagrange theorems are shown, which are characterized by at least of six times less computational complexity in comparison with traditional methods based on solving of differential equations (fitting method) and the possibility of pulsating components calculation in comparison with classical averaging methods. References 12, figures 2, tables 2.
Key words: methods for calculating and analyzing of semiconductor converters, averaging method in the state space, single-cycle semiconductor converters.

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4. Emadi A. Modeling and analysis of multiconverter DC power electronic systems using the generalized state-space averaging methods. IEEE Trans. Industrial Electronics. 2004. Vol.51, Issue 3. Pp. 661-668. (Eng) DOI:
5. Janke W. Averaged models of pulse-modulated DC-DC power converters. Technical University of Koszalin, Poland, Archives of Electrical Engineering, Vol. 61(4). 2012. Pp. 609-631. (Eng) DOI:
6. Rudenko Yu.V. Mode of averaging of pulse DC converter model. Tekhnichna Elektrodynamіka. 2017. No 3. Pp. 42-48. (Rus) DOI:
7. Rudenko Yu.V. Averaging of push-pull DC converter model. Tekhnichna Elektrodynamіka. 2018. No 1. Pp. 37-46. (Rus) DOI:
8. Maliar V.S. Theoretical laws of electrical engineering. Electric Circuits. L’viv: Vydavnytstvo Lvivs’koi politekhniky, 2012. 312 p. (Ukr)
9. Rudenko V.S., Zhuikov V.Ya., Suchik V.E. Graph-based analysis of process in semiconductor converters. Kyiv: Vydavnytstvo NTU Ukrainy KPI , 2010. 68 p. (Ukr)
10. Korn G., Korn T. Mathematical Handbook for Scientists and Engineers. Moskva: Nauka, 1984. 832 p. (Rus)
11. Rudenko Yu.V., Rudenko T.V. Averaging of model of the pulse converter with a second-degree circuit. Pratsi Instytutu elektrodynamiky Natsionalnoi Akademii Nauk Ukrainy. 2018. No 49. Pp. 88-97. (Rus) DOI:
12. Rudenko V.S., Zhuikov V.Ya., Korotyeyev I.Ye. Calculation of conversion technique systems. Kyiv: Tekhnika, 1980. 135 p. (Rus)

Received 18.05.2020