This paper deals with the current space-vector
decomposition in three-phase, three-wire systems on the basis of
some case studies. We propose four components of the current spacevector
in terms of DC and AC components of the instantaneous
active and reactive powers. The term of supplementary useless
current vector is also pointed out. The analysis shows that the current
decomposition which respects the definition of the instantaneous
apparent power vector is useful for compensation reasons only if the
supply voltages are sinusoidal. A modified definition of the
components of the current is proposed for the operation under
nonsinusoidal voltage conditions.
[1] S. Fryze, "Active, reactive and apparent power in circuits with
nonsinusoidal voltage and current," Przegl. Elektrotech, vol. 7, pp. 193-
203, 1931.
[2] M. Depenbrock, "Some remarks to active and fictitious power in
polyphase and single-phase systems," Europ. Trans. on Electrical
Power, vol. 3, pp. 15-19, 1993.
[3] H. Akagi, Y. Kanazawa, and A. Nabae, "Generalized theory of the
instantaneous reactive power in three-phase circuits," in Proc. Int.
Power Electronics Conf., Tokyo, Japan, pp. 1375-1386, 1983.
[4] H. Akagi and A. Nabae, "The p-q theory in three-phase systems under
non-sinusoidal conditions," Europ. Trans. on Electrical Power, vol. 3,
no. 1, pp. 27-31, 1993.
[5] M. Aredes and E. H. Watanabe, "New control algorithms for series and
shunt three-phase four-wire active power filters," IEEE Trans.Power
Delivery, vol. 10, no. 3, pp. 1649-1656, 1995.
[6] F. Z. Peng, G. W. Ott, and D. J. Adams, "Harmonic and reactive power
compensation based on the generalized instantaneous reactive power
theory for three-phase four-wire systems," IEEE Trans. On Power
Electronics, vol. 13, no. 6, pp. 1174-1181, 1998.
[7] M. Depenbrock, V. Staudt, and H. Wrede, "Concerning instantaneous
power compensation in three-phase systems by using p-q-r theory,"
IEEE Trans. on Power Electronics, vol. 19, no. 4, pp. 1151-1152, 2004.
[8] J. L. Willems, "A new interpretation of the Akagi-Nabae power
components for non-sinusoidal three-phase situations," IEEE
Transactions on Instrumentation and Measurement, vol. 41, no. 4, pp.
523-527, 1992.
[9] J. L. Willems, "Discussion of generalized theory of instantaneous
reactive quantity for multiphase power system," IEEE Transactions on
Power Delivery, vol. 21, no. 1, pp. 541 - 541, 2006.
[10] L. S. Czarnecki, "On some misinterpretations of the onstantaneous
reactive power p-q theory," IEEE Trans. on Power Electronics, vol. 19,
no. 3, pp. 828-836, 2004.
[11] L. S. Czarnecki, "Instantaneous reactive power p-q theory and power
properties of three-phase systems," IEEE Trans. on Power Delivery, vol.
21, no. 1, pp. 362-367, 2006.
[12] L. S. Czarnecki, "Orthogonal decomposition of the current in a
threephase nonlinear asymmetrical circuit with nonsinusoidal voltage,"
IEEE Trans. on Instrum. Meas., vol. IM-37, no. 1, pp. 30-34, 1988.
[13] L. S. Czarnecki, "Physical interpretation of the reactive power in terms
of the CPC power theory," Electrical Power Quality and Utilization
Journal, vol. XIII, no.1, pp. 89-95, 2007.
[14] F. de Leon and J. Cohen, "Discussion of "Instantaneous reactive power
- theory and power properties of three-phase systems"," IEEE Trans.
Power Delivery, vol. 23, no. 3, pp. 1693-1694, July 2008.
[15] L. S. Czarnecki, "Closure on "Instantaneous reactive power - theory and
power properties of three-phase systems"," IEEE Trans. Power Delivery,
vol. 23, no. 3, pp. 1695-1696, July 2008.
[1] S. Fryze, "Active, reactive and apparent power in circuits with
nonsinusoidal voltage and current," Przegl. Elektrotech, vol. 7, pp. 193-
203, 1931.
[2] M. Depenbrock, "Some remarks to active and fictitious power in
polyphase and single-phase systems," Europ. Trans. on Electrical
Power, vol. 3, pp. 15-19, 1993.
[3] H. Akagi, Y. Kanazawa, and A. Nabae, "Generalized theory of the
instantaneous reactive power in three-phase circuits," in Proc. Int.
Power Electronics Conf., Tokyo, Japan, pp. 1375-1386, 1983.
[4] H. Akagi and A. Nabae, "The p-q theory in three-phase systems under
non-sinusoidal conditions," Europ. Trans. on Electrical Power, vol. 3,
no. 1, pp. 27-31, 1993.
[5] M. Aredes and E. H. Watanabe, "New control algorithms for series and
shunt three-phase four-wire active power filters," IEEE Trans.Power
Delivery, vol. 10, no. 3, pp. 1649-1656, 1995.
[6] F. Z. Peng, G. W. Ott, and D. J. Adams, "Harmonic and reactive power
compensation based on the generalized instantaneous reactive power
theory for three-phase four-wire systems," IEEE Trans. On Power
Electronics, vol. 13, no. 6, pp. 1174-1181, 1998.
[7] M. Depenbrock, V. Staudt, and H. Wrede, "Concerning instantaneous
power compensation in three-phase systems by using p-q-r theory,"
IEEE Trans. on Power Electronics, vol. 19, no. 4, pp. 1151-1152, 2004.
[8] J. L. Willems, "A new interpretation of the Akagi-Nabae power
components for non-sinusoidal three-phase situations," IEEE
Transactions on Instrumentation and Measurement, vol. 41, no. 4, pp.
523-527, 1992.
[9] J. L. Willems, "Discussion of generalized theory of instantaneous
reactive quantity for multiphase power system," IEEE Transactions on
Power Delivery, vol. 21, no. 1, pp. 541 - 541, 2006.
[10] L. S. Czarnecki, "On some misinterpretations of the onstantaneous
reactive power p-q theory," IEEE Trans. on Power Electronics, vol. 19,
no. 3, pp. 828-836, 2004.
[11] L. S. Czarnecki, "Instantaneous reactive power p-q theory and power
properties of three-phase systems," IEEE Trans. on Power Delivery, vol.
21, no. 1, pp. 362-367, 2006.
[12] L. S. Czarnecki, "Orthogonal decomposition of the current in a
threephase nonlinear asymmetrical circuit with nonsinusoidal voltage,"
IEEE Trans. on Instrum. Meas., vol. IM-37, no. 1, pp. 30-34, 1988.
[13] L. S. Czarnecki, "Physical interpretation of the reactive power in terms
of the CPC power theory," Electrical Power Quality and Utilization
Journal, vol. XIII, no.1, pp. 89-95, 2007.
[14] F. de Leon and J. Cohen, "Discussion of "Instantaneous reactive power
- theory and power properties of three-phase systems"," IEEE Trans.
Power Delivery, vol. 23, no. 3, pp. 1693-1694, July 2008.
[15] L. S. Czarnecki, "Closure on "Instantaneous reactive power - theory and
power properties of three-phase systems"," IEEE Trans. Power Delivery,
vol. 23, no. 3, pp. 1695-1696, July 2008.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:55935", author = "Mihaela Popescu and Alexandru Bitoleanu and Mircea Dobriceanu", title = "Compensation–Based Current Decomposition", abstract = "This paper deals with the current space-vector
decomposition in three-phase, three-wire systems on the basis of
some case studies. We propose four components of the current spacevector
in terms of DC and AC components of the instantaneous
active and reactive powers. The term of supplementary useless
current vector is also pointed out. The analysis shows that the current
decomposition which respects the definition of the instantaneous
apparent power vector is useful for compensation reasons only if the
supply voltages are sinusoidal. A modified definition of the
components of the current is proposed for the operation under
nonsinusoidal voltage conditions.", keywords = "Active current, Active filtering, p–q theory, Reactive
current.", volume = "3", number = "1", pages = "17-6", }