Complex Fourier transform of currents or voltages of 3-phase system based on Clarke and extended Fortescue transform
Keywords:
Fourier transform, Fortescue transform, Clarke transform, 3-phase system of currents and voltages, harmonics, asymmetryAbstract
Fourier transform is a fundamental method of signal decomposition, including transients of currents and voltages. Spectra of 3-phase quantities are usual independent for all the phases. The drawback of this method is that it doesn’t explicitly show the kind of asymmetry of particular harmonics. Asymmetry is usually defined in practice with Fortescue transform, regarding only fundamental harmonics, thus asymmetry of remaining harmonics is neglected. The paper presents two methods of frequency representation of 3-phase system quantities, which provides complete and explicit information both about harmonic distortion and asymmetry. The methods utilize, respectively, Clarke, and Fortescue transformations. There is also shown the equivalency of both methods.References
Clarke, E., 1943, Circuit Analysis of A-C Power Systems, vol. I, Symmetrical and Related Components, John Wiley & Sons, New York.
[2] Fortescue, C.L., 1918, Method of Symmetrical Co-ordinates Applied to the Solution of Polyphase Networks, A.I.E.E. Transactions, vol. 37.
[3] Szabatin, J., 1982, Podstawy teorii sygnałów, Wydawnictwo Komunikacji i Łączności, Warszawa.
[4] Wojciechowski, D., 2010, Układ sterowania równoległym filtrem aktywnym ze sprzęgającym obwodem LCL, „Przegląd Elektrotechniczny”, R. 86, nr 2, s. 65–70.
Remove [1] Clarke, E., 1943, Circuit Analysis of A-C Power Systems, vol. I, Symmetrical and Related Components, John Wiley & Sons, New York.
[2] Fortescue, C.L., 1918, Method of Symmetrical Co-ordinates Applied to the Solution of Polyphase Networks, A.I.E.E. Transactions, vol. 37.
[3] Szabatin, J., 1982, Podstawy teorii sygnałów, Wydawnictwo Komunikacji i Łączności, Warszawa.
[4] Wojciechowski, D., 2010, Układ sterowania równoległym filtrem aktywnym ze sprzęgającym obwodem LCL, „Przegląd Elektrotechniczny”, R. 86, nr 2, s. 65–70.
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