# Науковий вісник НГУ

## Interrelation of a clarke and fortescue transformation for the three-phase asymmetrical electrical network

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Authors:

O.V.Bialobrzheskyi, Cand. Sc. (Tech.), Assoc. Prof., Kremenchuk Mykhailo Ostrohradskyi National University, Kremenchuk, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

R.V.Vlasenko, Kremenchuk Mykhailo Ostrohradskyi National University, Kremenchuk, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract:

Purpose. Determination of the analytical interrelation of Clarke and Fortescue transformation for an asymmetric sinusoidal system of currents of a three-phase four-wire network.

Methodology. To find the way for the use of the direct, reverse and zero sequences as components of the power circulating in the intersection of the four-wire current line, a problem is set to determine the interrelation of Clarke (α-β-0) and Fortescue (1-2-0) transformations. An analysis of the order of calculation of the direct, reverse and zero sequences components is carried out for the general case and for every separate phase. Comparison of Clarke transformation for separate sequences is performed using Euler formulae in an exponential form. Analytical relations determining the components of the current and voltage of direct and reverse sequences in domain α-β-0 are obtained. The said relations are used as the basis for instantaneous power decomposition in the use of p-q theory. The performed numerical calculation of current and voltage components, as well as power according to p-q theory, confirms the obtained analytical results.

Findings. Interrelation of direct and reverse sequence conversion of voltages (currents) in domain 1-2-0 (Fortescue transformation) with voltages (currents) in domain α-β-0 (Clarke transformation) is analytically substantiated, which makes it possible to separate in the latter the components caused by the action of direct and reverse sequences.

Originality. Analytical determination of direct, reverse sequence components in domain α-βis proposed to use these components during calculation of instantaneous power according to p-q theory for four-wire lines.

Practical value. The obtained results present a part of the analysis of electric power components in electrical four-wire networks with asymmetric parameters of the mode and they can be developed for networks with non-sinusoidal voltages and currents.

References/Список літератури

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2. Zhemerov, G. G. and Iliina, O. V., 2007. Friese power theory and modern theory of power. Electrical engineering and Electromechanics, No. 8, pp. 63–65.

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7. Bialobrzheski, O. V. and Vlasenko, R. V., 2015. Interrelation of electric power parameters the mode a single-phase active filter with parameters of attaching stores. Naukovyi Visnyk Natsіonalnoho Hіrnychoho Unіversitetu, No. 4, pp. 79–84.

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9. Riyadi, S., 2014. Inverse Clarke Transformation based control method of a three-phase inverter for PV-Grid systems. Information Technology, Computer and Electrical Engineering (ICITACEE), No. 8, pp. 351–355.

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