CORRELATION EVALUATION OF THE FORTESCUE AND CLARKE TRANSFORMATIONS FOR UNSYMMETRICAL SYSTEM OF THE CURRENT VECTORS IN THE THREE-PHASE LINE

The paper considers one of the ways for improving power quality videlicet employment of the power active filtering-balancing devices capable of contemporaneous exercising compensation of the reactive power consumed from the mains, distortion power, and symmetrizing the phase currents with high precision and operating speed. In forming the current of the power active filtering-balancing device a few power theories gained ground, distinguishing among others the Frieze theory and the p–q theory. These presentations differ from the methods laid as theoretical grounds of the electric energy accounting systems.

The article presents an analysis in the compliant system of the effect of the current projections on the power components formation character. The authors formulate the advantages and defective features of the noted theories being applied in case of the power active filteringbalancing device operating with unsymmetrical parameters of the mains. The paper considers the vectors asymmetrical system presentation by means of the symmetrical components 1–2–0 (Fortescue transformation) and in via α–β–0 re-expression (Clarke transformation). For practical evaluation of the currents correlation in α–β–0 and 1–2–0 measuring systems, the authors stage and perform a series of experiments where oneand two-phase amplitude asymmetries, one-phase phasic dissymmetry as well as asymmetries with occurrence of higher harmonic components are realized. The currents effective values summary from the series of experiments being presented graphically as function of the unsymmetry current amplitude educe incongruity of the results. Visually however, a similarity of the form and the character is observed, which allows performing correlation coefficient estimation of the mean square values of the currents in α–β–0 and 1–2–0 systems. That allows making conclusion of a high degree of the obtained results correlation.

1. Burman, ?. P., Rozanov, Yu. K., Shakaryan, Yu. G. (2012). Managing Electric Energy Flows and Increasing Efficiency of the Electric Power Systems: educational aid. Moscow: Publishing house of MEI [Moscow Power Engineering Institute], 56–152 (in Russian).

2. Domnin, I. F., Zhemerov, G. G., Krylov, D. S., Sokol, E. I. (2004). Contemporary Theories of Power and their Application in the Conversion Systems of Power Electronics. Tekhn?chna elektrodinam?ka. Tem. vipusk "Problemi suchasno? elektrotekhn?ki" [Technical Electrdynamics. Special Issue. Power Electronics and Energy Efficiency], 1, 80–91 (in Russian).

3. State Standard 23875–88. Electrical Power Quality. Terms and Definitions. Moscow, Standards publishing, 1988. 15 p. (in Russian).

4. Fryze, S. (1931). Active, Reactive and Apparent Power in Circuits With Nonsinusoidal Voltage and Current. Przegl?d Elektrotechniczny [Electrical Review], 7, 193–203 ; 8, 225-234 (in Polish).

5. Fryze, S. (1932). Active, Reactive and Apparent Power in Circuits With Nonsinusoidal Voltage and Current. Przegl?d Elektrotechniczny [Electrical Review], 22, 673-676 (in Polish).

6. Akagi, H., Watanabe, E. H., Aredes, M. (2007). Instantaneous Power Theory and Applications to Power Conditioning. New Jersey, John Wiley&Sons, Inc. 389 p. Doi: 10.1002/0470118938

7. Gnilitskiy, V. V., Polishchuk, A. A. (2012). Assessment of Reactive Power and Load Compensation in Three-Wire Mains Based on Fryze Theory. Vostochno-Evropeiskii zhurnal peredovykh tekhnologii [Eastern-European Journal of Advanced Technologies], 1-8 (55), 38–41 (in Russian).

8. Chaplygin, ?. ?. (2006). Capacity Theory in Power Electronics: educational aid for students with major in Industrial Electronics. Moscow: MEI [Moscow Power Engineering Institute], 19–23 (in Russian).

9. Clarke, E. (1943). Circuit Analysis of A-C Power Systems. Vol. I. Symetricaland Related Components. New York, Wiley.

10. Byalobrzhyes’kiy, ?. V., Vlasenko, R. V. (2014). Analysis of Energy Processes in Three-Phase Power Active Filter with Application of Spectral Simulation. Elektrotekhn?ka ta elektroenergetika [Electrotecnics and Electroenergetics], 1, 12–18 (in Ukrainian).

11. Bollen, M., Gu, I. (2006). Signal Processing of Power Quality Disturbances. New York, Wiley Interscience. 861 p.

12. Sanjit, K. Mitra. (2000). Digital Signal Processing. A Computer-Based Approach. McGraw-Hill. 879 p.

13. Ribeiro, M. V., Szczupak, J., Iravani, M. R, Gu, I. Y. H., Dash, P. K., Mamishev, A. V. (2007). Emerging Signal Processing Techniques for Power Quality Applications. Eurasip Journal on Advances in Signal Processing, Vol. 2007, Article number 87425. Doi:10.1155/2007/87425.