Critical Evaluation Of Fbd, Pq And Cpt Current Decompositions For Four-wire Circuits

Fernando P. Marafão; Helmo K. M. Paredes; Luiz C. P. da Silva

doi:10.18618/REP.2009.4.277286

Authors

Fernando P. Marafão Campus de Sorocaba, Unesp – Univ Estadual Paulista Av. Três de Março, 511, Sorocaba, SP – Brazil – 18087-180
Helmo K. M. Paredes University of Campinas, School of Electrical and Computer Engineering Av. Albert Einstein, 400, Campinas, SP – Brazil – 13083-970
Luiz C. P. da Silva University of Campinas, School of Electrical and Computer Engineering Av. Albert Einstein, 400, Campinas, SP – Brazil – 13083-970

DOI:

https://doi.org/10.18618/REP.2009.4.277286

Keywords:

Current decomposition, FBD-theory, Harmonics, Homo-variables, Power theory, pq-theory, Unbalanced systems

Abstract

This paper investigates the major similarities and discrepancies of three important current decompositions proposed for the interpretation of unbalanced and/or non linear three-phase four-wire circuits. The considered approaches were the so-called FBD Theory, the pq-Theory and the CPT. Although the methods are based on different concepts, the results obtained under ideal conditions (sinusoidal and balanced signals) are very similar. The main differences appear in the presence of unbalanced and non linear load conditions. It will be demonstrated and discussed how the choice of the voltage referential and the return conductor impedance can influence in the resulting current components, as well as, the way of interpreting a power circuit with return conductor. Under linear unbalanced conditions, both FBD and pq-Theory suggest that the some current components contain a third-order harmonic. Besides, neither pq-Theory nor FBD method are able to provide accurate information for reactive current under unbalanced and distorted conditions, what seems to be done by means of the CPT.

Downloads

Download data is not yet available.

Author Biographies

Fernando P. Marafão, Campus de Sorocaba, Unesp – Univ Estadual Paulista Av. Três de Março, 511, Sorocaba, SP – Brazil – 18087-180

was born in José Bonifácio, Brazil in 1975. He received his B.S. degree (1998) in Electrical Engineering from Unesp – Univ Estadual Paulista, Brazil. In 2000 and 2004 he received, respectively, his Master and PhD degrees from University of Campinas, Brazil. His current interests are mainly concerned with different power definitions under multiphase nonlinear systems and its applications in power conditioning and revenue metering. He held in 2002, a visitor student position at the Department of Information Engineering of the University of Padova (Italy), working on digital control techniques for active power filters. In 2005 he joined the Group of Automation and Integrating Systems at Unesp, Sorocaba, Brazil, where he has been an Assistant Professor. Since 2007, he is also an external Professor of the Electrical Engineering Department of the Campus of Bauru (Unesp). Dr. Marafão is a member of the Brazilian Power Electronics Society (SOBRAEP), Brazilian Automatic Society (SBA) and IEEE.

Helmo K. M. Paredes, University of Campinas, School of Electrical and Computer Engineering Av. Albert Einstein, 400, Campinas, SP – Brazil – 13083-970

was born in Puno-Perú. He received his B.S. degree (2002) in Electrical Engineering from Arequipa National University (UNSA), Perú. In 2006 he received his Master degrees from University of Campinas (UNICAMP), Brazil. Currently, he is a PhD student at UNICAMP. His current interests are mainly concerned with power quality evaluation and power definitions under multiphase nonlinear systems. MSc. Paredes is a member of the Brazilian Power Electronics Society (SOBRAEP), and IEEE.

Luiz C. P. da Silva, University of Campinas, School of Electrical and Computer Engineering Av. Albert Einstein, 400, Campinas, SP – Brazil – 13083-970

was born in Brazil in 1972. He graduated in electrical engineering from the Federal University of Goiás, Brazil in 1995, and obtained MSc and PhD degrees in power systems engineering from the University of Campinas, Brazil, in 1997 and 2001 respectively. He worked as a visiting researcher at the University of Alberta, Canada, in 1999-2000, and as a guest professor at the Technical University of Denmark, in 2008. Since 2002 he is with the University of Campinas, Brazil, where he is an Associate Professor. His main areas of interest are power system stability and control and distributed generation.

References

C. I. Budeanu, "Puissances Reactives et Fictives" Instytut Romain de l'Energie, Pub. no. 2, Bucharest, Rumania, 1927.

N. L. Kuster and W. J. More, "On the Definition of Reactive Power under Non-Sinusoidal Condition", IEEE Trans. on Power Apparatus and Systems, vol.PAS-99, no. 5, pp. 1845-1854, Sept/Oct 1980. https://doi.org/10.1109/TPAS.1980.319833 DOI: https://doi.org/10.1109/TPAS.1980.319833

W. Shepherd, P. Zakikhani "Suggested Definition of Reactive Power for Non-sinusoidal Systems",Proc. Inst. Elec. Eng., vol. 119, pp. 1361-1362, Sept. 1972. https://doi.org/10.1049/piee.1972.0268 DOI: https://doi.org/10.1049/piee.1972.0268

L. S. Czarnecki, "Orthogonal Decomposition of the Currents in a 3-Phase Nonlinear Asymmetrical Circuit with a Nonsinusoidal Voltage Source", IEEE Trans. on Instrumentation and Measurements, vol. 37, no. 1, pp.30-34, March 1988. https://doi.org/10.1109/19.2658 DOI: https://doi.org/10.1109/19.2658

IEEE Trial-Use Standard Definitions for the Measurement of Electric Power Quantities under Sinusoidal, Non-sinusoidal, Balanced or Unbalanced Conditions, IEEE Standard 1459-2000, June, 2000. https://doi.org/10.1109/PESW.2002.985249 DOI: https://doi.org/10.1109/PESW.2002.985249

L.S. Czarnecki, "Currents' Physical Components (CPC) in Circuits with Non-sinusoidal Voltages and Currents. Part 1: Single-phase linear circuits", Electrical Power Quality and Utilization Journal, vol. XI, no. 2, pp. 3-14, 2005. https://doi.org/10.15199/48.2019.10.01

L.S. Czarnecki, "Currents Physical Components (CPC) in Circuits with Non-sinusoidal Voltages and Currents. Part 2: Three-phase three-wire linear circuits," Electrical Power Quality and Utilization Journal, vol. XII, no. 1, pp. 3-13, 2006. https://doi.org/10.15199/48.2019.10.01 DOI: https://doi.org/10.15199/48.2019.10.01

S. Fryze, "Wirk-, Blind- und Scheinleistung in Elektrischen Stromkreisen mit Nichtsinusförmigem Verlauf von Strom und Spannung", Elektrotechnische Zeitschrift, vol. 53, no. 25, pp. 596-599, 625-627, 700-702, 1933.

F. Buchholz, Das Begriffsystem Rechtleistung, Wirkleistung, totale Blindleistung, Selbstverlag München, 1950.

M. Depenbrock, "The FBD-Method, a Generally Applicable Tool For Analyzing Power Relations", IEEE Trans. on Power Systems, vol. 8, no. 2, 381-387, May 1993. https://doi.org/10.1109/59.260849 DOI: https://doi.org/10.1109/59.260849

M. Depenbrock, Quantities of a Multiterminal Circuit Determined on the Basis of Kirchhoff's Laws, ETEPEuropean Trans. on Electrical Power Engineering , vol. 8, no. 4, pp. 249- 257, 1998. https://doi.org/10.1002/etep.4450080405 DOI: https://doi.org/10.1002/etep.4450080405

H. Akagi, Y. Kanazawa, A. Nabae, "Generalized Theory of the Instantaneous Reactive Power in Three-Phase Circuits", in Proc. of International Power Electronics ConferenceJIEE-IPEC, pp. 1375-1386, 1983. https://doi.org/10.1002/eej.4391030409 DOI: https://doi.org/10.1002/eej.4391030409

H. Akagi, A. Nabae, The p-q Theory in Three-Phase Systems under Non-Sinusoidal Conditions", ETEP European Trans. on Electrical Power Engineering, vol. 3, no. 1, pp. 27-31, Jan./Feb. 1993. https://doi.org/10.1002/etep.4450030106 DOI: https://doi.org/10.1002/etep.4450030106

P. Tenti and P. Mattavelli, "A Time-Domain Approach to Power Term Definitions under Non-sinusoidal Conditions", in Proc. of Sixth International Workshop on Power Definitions and Measurements under Non-Sinusoidal Conditions, 2003. https://hdl.handle.net/11577/1372122

P. Tenti, E. Tedeschi, P. Mattavelli, "Optimization of Hybrid Filters for Distributed Harmonic and Reactive Compensation", in Proc. of IEEE International Conference on Power Electronics and Drive Systems PEDS, vol. 01, pp. 292-297, 2005. https://doi.org/10.1109/PEDS.2005.1619701 DOI: https://doi.org/10.1109/PEDS.2005.1619701

F. Peng, G. Ott, and D. Adams, "Harmonic and Reactive Power Compensation Based on the Generalized Instantaneous Reactive Power Theory for 3-phase 4-wire Systems", in Proc. of IEEE Power Electronics Specialists ConferencePESC, vol. 2, pp. 1089-1095, 1997. https://doi.org/10.1109/PESC.1997.616880 DOI: https://doi.org/10.1109/PESC.1997.616880

J. L. Willems, "Instantaneous Sinusoidal and Harmonic Active and Deactive Currents in Three-phase Power Systems", ETEP European Trans. on Electrical Power Engineering, vol. 4, no. 5, pp. 335-343. 1994. https://doi.org/10.1002/etep.4450040503 DOI: https://doi.org/10.1002/etep.4450040503

F. P. Marafão, Analysis and Control of Electrical Energy by means of Digital Processing Techniques. PhD Thesis. University of Campinas, Brazil, 2004. (in Portuguese).

E. Watanabe and M. Aredes, "Compensation of Non-periodic Currents Using the Instantaneous Reactive Power Theory", in Proc of Power Eng. Soc. Summer Meeting, vol. 2, pp. 994-999, 2000. https://doi.org/10.1109/PESS.2000.867509 DOI: https://doi.org/10.1109/PESS.2000.867509

M. K. Mishra, A. Joshi, and A. Ghosh, "Unified Shunt Compensator Algorithm Based on Generalized Instantaneous Reactive Power Theory," IEEE Trans. Gen, Trans, Distrib., vol. 148, no. 6, pp. 583-589, Nov. 2001. https://doi.org/10.1049/ip-gtd:20010567 DOI: https://doi.org/10.1049/ip-gtd:20010567

H. Kim, F. Blaabjerg, B. Bak-Jensen, and J. Choi, "Instantaneous Power Compensation in Three-phase Systems by Using p-q-r Theory", IEEE Trans. Power Electronics, vol. 17, no. 5, pp. 701-710, Sep. 2002. https://doi.org/10.1109/TPEL.2002.802185 DOI: https://doi.org/10.1109/TPEL.2002.802185

E. H. Watanabe, R. M. Stephan, and M. Aredes, "New Concept of Instantaneous Active and Reactive Powers in Electrical Systems with Generic Loads", IEEE Trans. Power Delivery vol. 8, no. 2, pp. 697-703, Apr. 1993. https://doi.org/10.1109/61.216877 DOI: https://doi.org/10.1109/61.216877

H. Kim, F. Blaabjerg, and B. Bak-Jensen, "Spectral Analysis of Instantaneous Powers in Single-phase and Three-phase Systems with use of p-q-r Theory". IEEE Transaction on Power Electronics vol. 17, no. 5, pp. 711-720, Sep. 2002. https://doi.org/10.1109/TPEL.2002.802188 DOI: https://doi.org/10.1109/TPEL.2002.802188

W. G. Morsi, and M. E. El-Hawary, "Defining Power Components in Nonsinusoidal Unbalanced Polyphase Systems: The Issues", IEEE Trans. Power Delivery, vol. 22, no. 4, pp. 2428-2438, October 2007. https://doi.org/10.1109/TPWRD.2007.905344 DOI: https://doi.org/10.1109/TPWRD.2007.905344

R. S. Herrera and P. Salmerón, "Instantaneous Reactive Power Theory: A Comparative Evaluation of Different Formulations", IEEE Trans. Power Delivery, vol. 22, no. 1, pp. 595-604, Jan. 2007. https://doi.org/10.1109/TPWRD.2006.881468 DOI: https://doi.org/10.1109/TPWRD.2006.881468

M. Malengret and C.T. Gaunt, "Decomposition of Currents in Three- and Four-Wire Systems", IEEE Trans. on Instrumentation and Measurement, vol. 57, no. 5, pp. 963-972, May 2008. https://doi.org/10.1109/TIM.2007.911705 DOI: https://doi.org/10.1109/TIM.2007.911705

J. L.Willems, "A New Interpretation of the Akagi-Nabae Power Components for Nonsinusoidal Three-phase Situations," IEEE Trans. on Instrumentation and Measurement, vol. 41, no. 4, pp. 523-527, Aug. 1992. https://doi.org/10.1109/19.155919 DOI: https://doi.org/10.1109/19.155919

M. Depenbrock, V. Staudt and H. Wrede, "Theoretical Investigation of Original and Modified Instantaneous Power Theory Applied to Four-Wire Systems". IEEE Trans. on Industrial Application, vol. 39, no. 4, pp. 1160-1168, July/Aug 2003. https://doi.org/10.1109/TIA.2003.814553 DOI: https://doi.org/10.1109/TIA.2003.814553

L. S. Czarnecki, "On Some Misinterpretations of the Instantaneous Reactive Power p-q Theory", IEEE Trans. Power Electronics vol. 19, no. 3, pp. 828-836, May. 2004. https://doi.org/10.1109/TPEL.2004.826500 DOI: https://doi.org/10.1109/TPEL.2004.826500

L. S. Czarnecki, "Instantaneous Reactive Power p-q Theory and Power Properties of Three-phase Systems," IEEE Trans. Power Delivery, vol. 21, no. 1, pp. 362-367, Jan. 2006. https://doi.org/10.1109/TPWRD.2005.852348 DOI: https://doi.org/10.1109/TPWRD.2005.852348

H. K. M. Paredes, F. P. Marafão, L. C. P. da Silva, "A Comparative Analysis of FBD, PQ and CPT Current Decompositions - Part I: Three-Phase Three-Wire Systems", in Proc. of IEEE PowerTech, 2009. https://doi.org/10.1109/PTC.2009.5282173 DOI: https://doi.org/10.1109/PTC.2009.5282173

F. P Marafão, S. M. Deckmann, and H. K. Morales P. "The influence of the Voltage Referential to Power Quality Evaluation", IEEE Latin America Magazine, vol. 6, no. 1, PP. 81-88, March 2008. (in Portuguese). https://doi.org/10.1109/TLA.2008.4461636 DOI: https://doi.org/10.1109/TLA.2008.4461636

E. Tedeschi and P. Tenti, "Cooperative Design and Control of Distributed Harmonic and Reactive Compensators", in Proc. of International School on Nonsinusoidal Currents and Compensation (ISNCC), pp. 1-6, June 2008. https://doi.org/10.1109/ISNCC.2008.4627482 DOI: https://doi.org/10.1109/ISNCC.2008.4627482

A. Blondel, "Measurement of Energy of Polyphase currents", in Proc. of International Electrical Congress, pp. 112-117, 1893.

A. E. Emanuel, "Reflections on the Effective Voltage Concept", in Proc. of International Workshop on Power Definitions and Measurements under Non-sinusoidal Conditions, 2003.

J. L. Willems and J. A. Ghijselen, "The Choice of the Voltage Reference and the Generalization of the Apparent Power", in Proc. of International Workshop on Power Definitions and Measurements under Non-sinusoidal Conditions, 2003.

J. L. Willems, J. A. Ghijselen and A. E. Emanuel, "The Apparent Power Concept and the IEEE Standard 1459-2000", IEEE Trans. Power Delivery,vol. 20, no. 2, pp. 876-884, Apr. 2005. https://doi.org/10.1109/TPWRD.2005.844267 DOI: https://doi.org/10.1109/TPWRD.2005.844267

J. Willems, "Critical Analysis of Different Current Decomposition and Compensation Schemes", in Proc.of International School on Nonsinusoidal Currents and Compensation ̧ (ISNCC), pp. 1-6, June 2008. https://doi.org/10.1109/ISNCC.2008.4627488 DOI: https://doi.org/10.1109/ISNCC.2008.4627488

E. Clarke, Circuit Analysis of A-C power systems, vol. I - Symmetrical and Related Components, New York: John Wiley and Sons, Inc, 1943.

T. H. Blakesley, "A New Electrical Theorem", in Proc. of the Physical Society of London, vol.13, pp. 65-67, 1894. https://doi.org/10.1088/1478-7814/13/1/307 DOI: https://doi.org/10.1088/1478-7814/13/1/307

V. Staudt, "Fryze - Buchholz - Depenbrock: A Time-Domain Power Theory", in Proc. of International School on Nonsinusoidal Currents and Compensation ̧ (ISNCC), pp. 1-6, June 2008. https://doi.org/10.1109/ISNCC.2008.4627481 DOI: https://doi.org/10.1109/ISNCC.2008.4627481