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Progress In Electromagnetics Research B
ISSN: 1937-6472
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AN APPROACH TO THE MULTIVECTORIAL APPARENT POWER IN TERMS OF A GENERALIZED POYNTING MULTIVECTOR

By M. Castilla, J. C. Bravo, M. Ordonez, and J. C. Montano

Full Article PDF (269 KB)

Abstract:
The purpose of this paper is to explain an exact derivation of apparent power in n-sinusoidal operation founded on electromagnetic theory, until now unexplained by simple mathematical models. The aim is to explore a new tool for a rigorous mathematical and physical analysis of power equation from the Poynting Vector (PV) concept. A powerful mathematical structure is necessary and Geometric Algebra offers such a characteristic. In this sense, PV has been reformulated from a Multivectorial Euclidean Vector Space structure (CGn-R3) to obtain a Generalized Poynting Multivector (S). Consequently, from S, a suitable multivectorial form (P and D) of the Poynting Vector corresponds to each component of apparent power. In particular, this framework is essential for the clarification of the connection between a Complementary Poynting Multivector (D) and the power contribution due to cross-frequency products. A simple application example is presented as an illustration of the proposed power multivector analysis.

Citation:
M. Castilla, J. C. Bravo, M. Ordonez, and J. C. Montano, "An Approach to the Multivectorial Apparent Power in Terms of a Generalized Poynting Multivector," Progress In Electromagnetics Research B, Vol. 15, 401-422, 2009.
doi:10.2528/PIERB09042402

References:
1. Maxwell, J. C., "A dinamical theory of the electromagnetic field," Phil. Trans. of the Royal Society, Vol. 155, 459-512, London, 1865.
doi:10.1098/rstl.1865.0008

2. Steinmetz, C. P., Theory and Calculation of Alternating Current Phenomena, No. 15, 24, and 30, McGraw Publishing Company, New York, 1908.

3. Budeanu, C. I., "Puisances reactives et fictives," Instytut Romain de l'Energie, Bucharest, Romania, 1927.

4. Fryze, S., "Wirk-, blind-, und scheinleistung in elektrischen stromkreisen mit nicht-sinusoidalen verlauf von strom und spannung," Elekt. Z, Vol. 53, 596-599, 625-627, 700-702, 1932.

5. Sharon, D., "Reactive power definitions and power factor improvement in non-linear systems," Proc. IEE, Vol. 120, No. 6, June 1973.

6. Czarnecki, L. S., "Considerations on the reactive power in non-sinusoidal situations," IEEE Trans. on Instrument. and Meas., Vol. 36, No. 1, 399-404, 1985.
doi:10.1109/TIM.1985.4315358

7. Emanuel, A. E., "Power in nonsinusoidal situations, a review of definitions and physical meaning," IEEE Trans. on Power Delivery, Vol. 5, No. 3, 1377-1389, 1990.
doi:10.1109/61.57980

8. Sommariva, A. M., "Power analysis of one-port under periodic multi-sinusoidal linear operation," IEEE Trans. on Circuits and Systems --- Regular Papers, Vol. 53, No. 9, Sep. 2006.

9. Menti, A., T. Zacharias, and J. Milias-Argitis, "Geometric algebra: A powerful tool for representing power under nonsinusoidal conditions ," IEEE Trans. on Circuits and Systems I --- Regular Papers , Vol. 54, No. 3, Mar. 2007.

10. Slepian, J., "Energy flow in electrical systems --- the VI energy postulate ," AIEE Transactions, Vol. 61, 835-841, Dec. 1942.

11. Czarnecki, L. S., "Energy flow and power phenomena in electrical circuits: Illusions and reality," Electrical Engineering, Vol. 82, 119-126, Springer-Verlag, 2000.
doi:10.1007/s002020050002

12. Emanuel, A. E., "Poynting vector and the physical meaning of nonactive powers," IEEE Trans. on Instrument. and Meas., Vol. 54, No. 4, Aug. 2005.

13. Emanuel, A. E., "About the rejection of poynting vector in power systems analysis," Electrical Power Quality and Utilization, Vol. 13, No. 1, 43-49, 2007.

14. Cakareski, Z. and A. E. Emanuel, "On the physical meaning of non-active power in three-phase systems," IEEE Power Engineering Review, Vol. 19, No. 7, 46-47, Jul. 1999.
doi:10.1109/39.773787

15. Agunov, M. V. and A. V. Agunov, "On the power relationships in electrical circuits operating under nonsinusoidal conditions," Elektricesvo, No. 4, 53-56, 2005.

16. Sutherland, P. E., "On the definition of power in an electrical circuit," IEEE Trans. on Power Delivery, Vol. 22, No. 2, Apr. 2007.
doi:10.1109/TPWRD.2007.893194

17. Czarnecki, L. S., "Considerations on the concept of poynting vector contribution to power theory development," Sixth International Workshop on Power Definitions and Measurement under Nonsinusoidal Conditions , Milano, Italy, 2003.

18. Castilla, M., J. C. Bravo, M. Ordonez, and J. C. Montano, "Clifford theory: A geometrical interpretation of multivectorial apparent power," IEEE Trans. on Circuit and Systems I --- Regular Papers, Vol. 55, No. 10, Nov. 2008.

19. Castilla, M., J. C. Bravo, and M. Ordonez, "Geometric algebra: A multivectorial proof of tellegen's theorem in multiterminal networks," IET Circuits, Devices and Systems, Vol. 2, No. 4, Aug. 2008.

20. Hestenes, D., "Oersted medal lecture 2002: Reforming the mathematical language of physics," American Journal of Physics, Vol. 71, No. 2, 104-121, 2003.
doi:10.1119/1.1522700

21. Doers, L., C. Doran, and J. Lasenby, Applications of Geometrical Algebra in Computer Science and Engineering, Birkhauser, Boston, 2002.

22. Doran, Ch. and A. Lasenby, Geometric Algebra for Physicists, Cambridge University Press, 2005.

23. Demarest, K. R., Engineering Electromagnetics, Prentice Hall, 1988.


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