Ambiguity on the Definition of Power Quantities in Electrical System

##plugins.themes.academic_pro.article.sidebar##

Published Sep 30, 2009
Download
PDF
Statistic

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...
Volume 5, Issue 2, September 2009

##plugins.themes.academic_pro.article.main##

Sujatha Subhash
Central Power Research Institute, Bangalore
R. K. Hegde
Central Power Research Institute, Bangalore

Abstract

This paper aims at presenting a review of the definitions of power quantities in an electric system with distorted voltages and currents. This subject has been of interest for more than a century and over the years many definitions for reactive power and apparent power and compensation techniques have been developed. However none of these definitions characterize the distinguishing power quantities for all conditions of electrical circuit. A review of the ambiguities, confusion in the classical definition, power theories and difficulties in instrumentation, billing and compensation is presented in this paper.

##plugins.themes.academic_pro.article.details##

How to Cite
Subhash, S., & Hegde, R. K. (2009). Ambiguity on the Definition of Power Quantities in Electrical System. Power Research - A Journal of CPRI, 5(2), 87–103. Retrieved from https://node6473.myfcloud.com/~geosocin/CPRI/index.php/pr/article/view/699

References

  1. Steinnetz C P. Theory and Calculation of Alternating Current Phenomena, McGraw, New York, 1908.
  2. Budeanu C I. Puissances Reactives et Ficitives. Bucharest, Romania: Inst. Romain de I’Energie, 1927.
  3. Lyon W V. "Reactive power and unbalanced circuits," Electrical World, Vol. 75, No. 25, June 1920, pp. 1417-1420.
  4. Goodhue W M. Discussion to "Reactive power concepts in need of clarification," AIEE Transactions, Vol. 52, Sept. 1933, pp. 787.
  5. Fryze S. "Active, reactive and apparent power in circuits with non-sinusoidal voltage and current," (in Polish), Przegl. Elektrotech., No.7, pp. 193-203; ibid., No. 8, pp. 225-234, 1931; ibid., No. 22. 1932, pp. 673-676.
  6. (In German), Elektrorech. Z ., ibid., Vol. 53, pp. 596-599: Vol. 53, pp. 625-627; ibid., Vol. 53, 1932, pp. 700-702.
  7. Curtis L and Silsbee F B. Definition of power and related quantities, AIEE Trans. 54 (1935) 394-404.
  8. Lyon V. [Discussion to H. L. Curtis and F. B. Silsbee paper "Definitions of power and related quantities," AIEE Transactions, Vol. 54, No. 4, April 1935, pp. 394-404], Electrical Engineering, Oct. 1935, p. 1121.
  9. Mili´c M. "Integral representation of powers in periodic non-sinusoidal steady state and the concept of generalized powers," IEEE Trans. Educ., Aug. 1970 pp. 107-109.
  10. Kimbark E W. Direct Current Transmission, Vol. 1. New York: Wiley, 1971.
  11. Sharon I D. "Reactive power definition and power-factor improvement in non-linear systems," Proc. Inst. Elec. Eng., Vol. 120, No. 6, July 1973. pp. 704-706.
  12. Shepherd W and Zakikhani P. "Suggested definition of reactive power for nonsinusoidal systems," Proc. Inst. Elec. Eng., Vol. 119, No. 9, pp. 1361-1362, Sept. 1972, "DISCUSSION," ibid., Vol. 120, No. 7, pp. 796-798; "DISCUSSION," ibid., Vol. 121, No. 5, 1974, pp. 389-391.
  13. Guigi L, Otto R A and Putman T H. "Principles and application of static thyristor controlled shunt compensators," IEEE Trans. on Pow. Appl. and Syst., Vol. PAS-97, No. 5, Sept/Oct. 1978, pp. 1935-1945.
  14. Shepherd W and Z and P. "Energy flow and power factor in non-sinusoidal circuits" (Cambridge University Press, UK, 1979.
  15. Kusters N L and Moore M J M. "On the definition of reactive power under nonsinusoidal conditions", IEEE Trans. Power Appl. Syst., Vol. PAS-99, Sept. 1980, pp. 1845-1854.
  16. Page C H. "Reactive power in nonsinusoidal situations," IEEE Trans. Instrum. Meas., Vol. IM-29, Dec. 1980, pp. 420-423.
  17. Filipski P. "A new approach to reactive current and reactive power measurements in non-sinusoidal systems," IEEE Trans. Instrum. Meas., Vol. IM-29, Dec. 1980, pp. 423-426.
  18. CZARNECKI L S. "Minimization of distortion power of non- sinusoidal sources applied to linear loads", Proc. IEE, 1981, 128, (4).
  19. Miller T J E. "Reactive power control in electric systems," John Willey and Sons, 1982.
  20. Czamecki L S. "Additional discussion to reactive power under non-sinusoidal situations," IEEE Trans. Power App. Sysr., Vol. PAS-102, No 4, Apr. 1983, pp. 1023-1024.
  21. ibid., "Measurement principles of the reactive current rms value and the load susceptance for harmonic frequency meters for non-sinusoidal conditions," IEEE Trans. Instrum. Meas., No. 2, 1983, pp. 383-384.
  22. Stevens R H. "Power flow direction definitions for metering of bidirectional power," IEEE Transactions on Power Apparatus and Systems, Vol. 102, No. 9, Sept. 1983, pp. 3018-21.
  23. Akagi H, Kanazawa Y and Nabae A. "Generalized theory of the instantaneous reactive power in three-phase circuits", IPEC’83-Int. Power Electronics Conf., Tokyo, Japan, 1983, pp. 13751386.
  24. IEEE Power System Harmonics Working Group, Bibliography of Power System Harmonics, report, part I, IEEE Trans. Power Apparatus System, PAS-109, 9 (1984) pp. 2460-2462, part II, ibid.
  25. Akagi H, Kanazawa Y and Nabae A. "Instantaneous reactive power compensator comprising switching devices without energy storage components", IEEE Trans. Industry Applic., Vol. 20, May/June 1984, pp. 625-630.
  26. Czarnecki L S. "Considerations on reactive power in non-sinusoidal situation," IEEE Trans. Instrum. Meas., Vol. IM-34, Sept. 1985, pp. 399-404.
  27. Furuhashi T, Okuma S and Uchikawa Y. "A study on the theory of the instantaneous reactive power" IEEE Trans Ind Electronics, 1990, 37, pp. 86-90.
  28. Czamecki L S. "What is wrong with the Budeanu concept of reactive and distortion power and why it should be abandoned", IEEE Trans., 1987, IM-36, pp. 834-837.
  29. Gueth G, Enstedt P, Rey A and Menzies R W. "Individual phase control of a static compensator for load compensation and voltage balancing and regulation", IEEE Trans. Power Syst. 2 (4) (1987) pp. 898-904.
  30. Czarnecki L S. "Minimization of distortion power of non-sinusoidal situations," IEEE Trans. Instrum. Meas., Vol. 36, Mar. 1987, pp. 18-22.
  31. Mahmoud F W. "Effect of ADC quantization errors on some periodic signal measurements," IEEE Transactions on Instrumentation and Measurement, December 1987, Vol. 36, No. 4, pp. 983-989.
  32. Czarnecki L S. "Orthogonal decomposition of the currents in a 3phase non-linear asymmetrical Circuit with a non-sinusoidal voltages source" IEEE Trans. Instrum. Meas., Vol. 37, Mar. 1988, pp. 30-34.
  33. Czarnecki L S and Anna Lasicz. "Active, reactive and scattered current in circuits with non-periodic voltage of a Finite Energy" IEEE Trans. Instrum. Meas., Vol. 37, Sept. 1988, pp. 393-402.
  34. Slonim M A and Van WYK J D. "Power components in a system with sinusoidal and non-sinusoidal voltages and/or currents", Proc. IEE, 1988, 135, pp. 76-84.
  35. IEEE Standard Dictionary of Electrical and Electronics Terms ANSI:EKE std 100-1988, IEEE, New York, 1988.
  36. FILIPSKI P. "Power components in a system with sinusoidal and nonsinusoidal voltages and/or currents’, Proc. IEE, 1989, 136, (2).
  37. Czarnecki L S. "Comments on measurement and compensation of fictitious power under non-sinusoidal voltage and current conditions" IEEE Trans. Instrum. Meas., Vol. 39 No. 3, June 1989, pp. 839-841.
  38. Czamecki L S. "Reactive and unbalanced currents compensation in three-phase asymmetrical circuits under non-sinusoidal conditions," IEEE Trans. Instrum. Meas., Vol. 38, June 1989, pp. 754-759.
  39. Olejniczak K and Heydt G T. Basic mechanisms of generation and flow of harmonic signals in balanced and unbalanced three-phase power systems, IEEE Trans. Power Delivery 4 (4) (1989) pp. 2162-2168. [7]
  40. Lin C E, Chen T C and Huang C L. A real-time calculation method for optimal reactive power compensator, IEEE Trans. Power Syst. 4 (1989) pp. 643-652.
  41. Emanuel A and Czarnecki L S. "Power components in a system with sinusoidal and non-sinusoidal voltages and/or currents", Proc. IEE, 1990, 137, (3), pp. 134-136.
  42. Czarnecki L S and Tadeusz Swietlicki. "Powers in non-sinusoidal networks: their interpretation, analysis, and measurement" IEEE Trans. Instrum. Meas., Vol. 39, Apr. 1990, pp. 340-345.
  43. Slonim M A. "Distortion power in linear and non-linear systems", Int. J. Elect., 1990, 68, 9, pp. 769-778.
  44. Girgis, et al., "Measurement and characterization of harmonics and high frequency distortion for a large industrial load," IEEE Trans. Power Deliuery, Vol. PWRD-5, No. 1, Jan. 1990, pp. 427-434.
  45. Emanual E. "Power in non-sinusoidal situations. A review of definitions and physical meaning," IEEE Trans. Power Delivery 5 (3) (1990) pp. 1377-1389.
  46. Ferrero and Superti-Furga G. "A unified approach to un-balanced three-phase systems under non-sinusoidal conditions," Proc. of the 4th Int. Conf on Harmonics in Power Systems, Budapest, Hungary, 1990.
  47. Wyatt J L, Jr. and Ili´c M D. "Timedomain reactive power concepts for non-linear, non-sinusoidal or non-periodic networks," in IEEE Int. Symp. Circuits Syst., 1990, Vol. 1, pp. 387-390.
  48. Willems J L. "Power components in a system with sinusoidal and nonsinusoidal voltages and/or currents", Proc. IEE, 1990, 137, pp. 1361-1362.
  49. Czarnecki L S. "Comments on a new control philosophy for power electronics converters as ficticious power compensators", IEEE Trans. Power Electronics, Vol. 5, No 4, Oct. 1990, pp. 503-504.
  50. Czarnecki L S. "Scattered and reactive current, voltage and power in circuits with non-sinusoidal waveforms and their compensation", IEEE Trans. Instrum. Meas., Vol. 40, No 3, June 1991, pp. 563-567.
  51. Barnes R, Wong K T. "Unbalance and harmonic studies for the channel tunnel railway system", IEE Proc. B 138 (1991) pp. 41-50.
  52. Sun S Q and Kiyokawa H. "Decomposition of voltage, current and power", Proc. IEE, 1991, 138, (I), pp. 35-39.
  53. Sun S Q and Jiang C G. "Decomposition of Czarnecki‘s reactive current and reactive power", Proc. I E E , 1991, 138, (3), pp. 125-128.
  54. Gyarfas J, Rapant S. "Theory and practice of energy measurement of non-sinusoidal and asymmetrical currents and voltages," Europ. Trans. on Electr. Pow. Eng., ETEP, Vol. 1, No. 3, May/June 1991, pp. 159-164.
  55. Filipski P S. "Polyphase apparent power and power factor under distorted waveform conditions," IEEE Trans. on Power Deliv., PWRD-6, No. 3, 1991, pp. 1161-1165.
  56. Elharn B. Makram R B Haines, Girgis A A. "Effect of harmonic power distrortion in reactive power measurement", IEEE Transactions on Industry Applications, Vol. 28, No. 4, July/august 1992, pp. 782-787.
  57. Czarnecki L S. "Distortion power in systems with non-sinusoidal voltage", IEE Proc -B, Vol. 139, No. 3, MAY 1992, pp. 276-280.
  58. Czamecki L S, "Minimisation of unbalanced and reactive currents in three-phase aspetncal circuits with nonsinusoidal voltage," IEE Proc.-B, Vol. 139, No. 4, July 1992, pp. 347-354.
  59. Jacques L and Willems A. "New interpretation of the Akagi-Nabae power components for non-sinusoidal threephase situations", IEEE Trans. on Instr. Measur., Vol. 41, No. 4, August 1992, pp. 523-527.
  60. Donald R Zrudsky and Pichler J M. "Virtual instrument for instantaneous power measurements", IEEE Trans. on Instr. Measur., Vol. 41, No. 4, August 1992, pp. 528-534.
  61. Willems J L, "Current compensation in three-phase power systems," Eurp.Trans. on Electr. Power Eng., ETEP Vol. 3, No. 1, 1993, pp. 61-66.
  62. Emanuel A E. "On the definition of power factor and apparent power in unbalanced polyphase circuits with sinusoidal voltage and current," IEEE Trans. on Power Del., Vol. 8, No. 3, July 1993, pp. 84 1-847.
  63. Emanuel A E. "Apparent and reactive powers in three-phase systems: In search of a physical meaning and a better resolution," Eurp.Trans. on Electr. Power Eng., ETEP Vol. 3, No. 1, 1993, pp. 7-14.
  64. Akagi H and Nabae A. The p-q theory in three-phase systems under non-sinusoidal conditions, Europ. Trans. on Electrical Power, ETEP, Vol. 3, No. 1, January/ February 1993, pp. 27-31.
  65. Watanabe H, Stephan R M and Aredes M. "New concepts of instantaneous active and reactive powers in electrical systems with generic loads", IEEE Trans. Power Delivery 8 (2) (1993) pp. 697-703.
  66. Kazibwe W E and Sendaula M H. Electric power quality control techniques, Van Nostrand Reinhold, New York, 1993.
  67. Watanabe E H, Stephan R M and Aredes M. "New concepts of instantaneous active and reactive powers in electrical systems with generic loads", IEEE Trans. Power Delivery, Vol. 8, No. 2, April 1993, pp. 697-703.
  68. Ofori-Tenkorang J. "Power components in non-sinusoidal systems: Definitions and implications on power factor correction," MIT LEES Tech. Rep., TR94-001, Jan. 27, 1994.
  69. Wu C J, Liaw C M and Lee S Y. Microprocessor-based static reactive power compensators for unbalanced loads, Electr. Power Syst. Res. 31 (1994) pp. 51-55.
  70. Czarnecki L S and Hsu S M. "Thyristor controlled susceptances for balancing compensators operated under nonsinusoidal conditions", IEE Proc. Electr. Power Appl. 141 (1994) pp. 177-185.
  71. Depenbrock D A, Marshal and Van Wyk J D. "Formulating requirements for universally applicable power theory as control algorithm in power compensators". Europ. Trans. on Electrical Power, ETEP, Vol. 4, No. 6, Nov./Dec. 1994, pp. 445-456.
  72. Rossetto and Tenti P. "Evaluation of instantaneous power terms in multiphase systems: techniques and application to power-conditioning equipment", Europ. Trans. on Electrical Power, ETEP, Vol. 4, No. 6, Nov./Dec. 1994, pp. 469-475.
  73. Czamecki L S. "Power related phenomena in three-phase unbalanced systems", IEEE Transactions on Power Delivery, Vol. 10, No. 3, July 1995, pp. 1168-1176.
  74. Chang W N and Wu C J. "Developing static reactive power compensators in a power system simulator for power education", IEEE Trans. Power Syst. 10 (1995) pp. 1734-1741.
  75. Emanuel A E, "On the assessment of harmonic pollution," IEEE Transactions on Power Delivery, Vol. 10, No. 3, July 1995, pp. 1693-1698.
  76. Slonim M A and VanWyk J D. "Power components in a system with sinusoidal and non-sinusoidal voltages and or currents", IEEE Proc. 135 (2) (1995), pp. 76-84.
  77. LaWhite N. "Vector calculus of periodic nonsinusoidal signals for decomposition of power components in single and multiphase circuits," Master’s degree thesis, Dep. Elect. Eng., MIT, June 1995, pp. 16-17.
  78. Nedwick A F, Mistr Jr and Croasdale E B. "Reactive management a key to survival", IEEE Trans. Power Syst. 10 (1995) (1990s) pp. 1036-1042.
  79. Aredes and Watanabe E H. "New control algorithms for series and shunt threephase four-wire active power filters", IEEE Trans. Power Delivery, vol 10, no. 3, July 1995, pp. 1649-1656. the performance of harmonic power Analyzers.
  80. IEEE Working Group on Non-sinusoidal Situations, "Practical definitions for powers in systems with non-sinusoidal waveforms and unbalanced loads," IEEE Transactions on Power Delivery, Vol. 11, No. 1, Jan. 1996, pp.79-101.
  81. IEEE Working Group on Nonsinusoidal Situations, "A survey of North American electric utility concerns regarding non-sinusoidal waveforms," IEEE Transactions on Power Delivery, Vol. 11, No. 1, Jan. 1996, pp. 73-78.
  82. Swart P H, van Wyk J D and Case M J. "On the technique for localization of sources producing distortion in transmission networks," European Transactions on Electrical Powers (ETEP), Vol. 6, No. 5, Sept./Oct. 1996.
  83. Fang Z. Peng and Lai J S. "Generalised instantaneous reactive power theory for three-phase power systems" IEEE Trans Instrum Meas. 1996, 45, pp. 293-297.
  84. Akira Nabae and Toshikhiko Tanaka. "A new definition of Instantaneous activereactive current and power based on instantaneous space vectors on polar coordinates in three-phase circuits" IEEE Transactions on Power Delivery, Vol. 11, No. 1, July. 1996, pp. 1238-1243.
  85. Cristaldi L and Ferrero A. "Mathematical foundations of the instantaneous power concept: An algbraic approach", European Trans. on Electrical Power, ETEP, Vol. 6, No. 5, Sept./Oct. 1996, pp. 305-309.
  86. Salmeron and Montano J C. "Instantaneous power components in polyphase systems under non-sinusoidal conditions", IEE Proc. on Science, Measurement and Technology, Vol. 143, No. 2, Feb. 1996, pp. 239-297.
  87. D Sharon. "Power factor definition and power transfer quality in non-sinusoidal situations", IEEE Trans Instrum Meas., vol 45, No 3, June 1996, pp. 728-733.
  88. Niels LaWhite and Marija D. Ilic "Vector space decomposition of reactive power for periodic nonsinusoidal signals", IEEE Transactions on Circuits and Systems— I: Fundamental theory and applications, Vol. 44, No. 4, April 1997, pp. 338-346.
  89. Gyugyi L, Otto R A and Putman T H. "Principles and applications of static, thyristor-controlled shunt compensators", IEEE Trans. Power Appar. Syst. 97 (1978) pp. 1935-1945.
  90. Pretorius J H C, van Wyk J D and Swart P H. "An Evaluation of some alternative methods of power resolutions in a large industrial plant," Proceedings of the Eighths International Conference on Harmonics and Quality of Power (ICHQP- VIII), Athens, Vol. I, Oct. 1998, pp. 331-336.
  91. El-Sadek M Z. "Static Var compensation for phase balancing and power factor improvement of single phase train loads", Electr. Mach. Power Syst. 26 (1998) pp. 347-361.
  92. Lee S Y and Wu C J. "Combined compensation structure of a static Var compensator and an active filter for unbalanced three-phase distribution feeders with harmonic distortion", Electr. Power Syst. Res. 46 (1998) pp. 243-250.
  93. Driesen J, Van Th. Craenenbroek and Van Dommelen D. "The registration of harmonic power by analog and digital power meters," IEEE Trans. on Instrumentation and Measurement, Vol. 47, No. 1, Febr. 1998, pp. 195-198.
  94. Yoon W K and Devaney M J. "Power measurement using the wavelet Transform," IEEE Trans. on Instrumentation and Measurement, Vol. 47, No. 5, Oct. 1998, pp. 1205-1210.
  95. Fang Z. Peng OTT G W and Adams D J. "Harmonic and reactive power compensation based on the generalised instantaneous reactive power theory for three-phase four-wire systems", IEEE TransPower Electronics. 1998, 13, pp. 1174-1181.
  96. le Roux W and van Wyk J D. "Evaluation of residual network distortion during compensation according to the instantaneous power theory", European Trans. on Electrical Power, ETEP, Vol. 8, No. 5, Sept./Oct. 1998, pp. 337-344.
  97. Jose Cohen Francisco de Le6n Luis M. Herdndez "Physical time domain representation of powers in linear and non-linear electrical circuits" IEEE Transaction$ on Powcr Delivery, Vol 14, No 4, Octobcr 1999, pp. 1240-1249.
  98. Bhim Singh, Kamal Al-Haddad and Ambrish Chandra. "A review of active filters for power quality improvement", IEEE Transactions on Industrial Electronics, Vol. 46, No. 5, October 1999, pp. 960-971.
  99. Emanuel A E. "Apparent power definitions for three-phase systems," IEEE Transactions on Power Delivery, Vol. 14, No. 3, July 1999, pp. 767-72.
  100. Chen J H, Lee W J and Chen M S. "Using a static Var compensator to balance a distribution system", IEEE Trans. Ind. Appl. 35 (1999) pp. 298-304.
  101. Akagi H, Ogasawara S and Kim H. "The theory of instantaneous power in three-phase four-wire systems: A comprehensive approach," IEEE-IAS Annual Meeting 1999 Conference Record, Vol. 1, pp. 431-439.
  102. Gougler C A and Johnson J R. "Parallel active harmonic filters: Economical viable technology" IEEE Trans 1999.
  103. Nunez-Noriega C V and Karady G G. "Five step low frequency switching active filter for network harmonic compensation in substations", IEEE Trans on power Delivery Vol. 14, No. 4, Oct 1999, pp. 1298-1303.
  104. Huang S J and Wu J C. "A control algorithm for three-phase three-wired active power filters under nonideal mains voltages", IEEE Trans. on Power Electronics, Vol. 14, No. 4, July 1999, pp. 753-760.
  105. Morendaz-Eguilaz J M and Peracaula J. "Understanding AC power using the generalized instantaneous reactive power theory: Considerations for instrumentation of three-phase electronic converters," Proc. of the IEEE Int. Symp., Ind. Electr., ISIE. 99, Vol. 3, pp. 1273-1277.
  106. IEEE Std 1459-2000 IEEE "Trial-Use Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Non-sinusoidal, Balanced or Unbalanced Conditions".
  107. Shun-Li Lu a, Chin E. Lin b,*, ChingLien Huang. "Suggested power definition and measurement due to harmonic load", Electric Power Systems Research 53 (2000), pp. 73-81.
  108. Afonso J L. Couto C and Martins J S. "Active filters with control based on the p-q theory", IEEE Industrial Electronics Society Newsletter, vol. 47, nº3, Set. 2000, pp. 5-10.
  109. Ghosh A and Joshi A. "A new approach to load balancing and power factor correction in power distribution system", IEEE Trans. Power Delivery 2000, 15, pp. 417-422.
  110. Mishra M K, Ghosh A and Joshi A. "A new STATCOM topology to compensate loads containing AC and DC components", Proceedings of IEEE PES winter meeting, Singapore 2000.
  111. Watanabe E H and Aredes M. "Compensation of non-periodic currents using the instantaneous power theory," IEEE Power EngineeringSociety Summer Meeting, Seattle, Washington, July 1520, 2000, pp. 994-999.
  112. Toral S L, Quero J M and Franquelo L G. "Reactive power and energy measurement in the frequency domain using random pulse arithmetic", IEE froc.-Sci. Metis. Teclriiol., Vol. 148. No. 2, March 2001.
  113. Mishra M K, Joshi A and Ghosh A. "Unified shunt compensator algorithm based on generalized instantaneous reactive power theory", IEE Proc Gener. Transm. Distrib. Vol 148, no 0, Nov 2001 pp. 583-589.
  114. Afonso J L, Silva H R and Martins J S. "Active filters for power quality Improvement", IEEE Power Tech’ 2001, Porto, Portugal, Sep. 2001, pp. 10-13.
  115. Zambroni A C. et al,. "The effect of loading on reactive market power" IEEE 2001.
  116. San-Yi Lee a,*, Chi-Jui Wu b,1 and WeiNan Chang. "A compact control algorithm for reactive power compensation and load balancing with static Var compensator", Electric Power Systems Research 58 (2001), pp. 63-70.
  117. Lakshmikanth A and Medhat M. Morcos. "A power quality monitoring system: A case study in DSP-Based solutions for power electronics," IEEE Trans. on Instrumentation and Measurement, Vol. 50, No. 3, Jun. 2001, pp. 724-731.
  118. IEEE Std 1159-1995 (R2001) : IEEE recommended practice for monitoring electric power quality.
  119. Johan Driesen, Geert Deconinck, Jeroen Van Den Keybus, Bruno Bolsens, Karel De Brabandere, Koen Vanthournout, Ronnie Belmans and Leuven K U. "Development of a measurement system for power quantities in electrical energy distribution systems" IEEE 2002.
  120. Driesen J and Belmans R. "Wavelet-based power quantification approaches," accepted for presentation at IMTC 2002.
  121. E Moulien. "Measuring reactive power in energymeters", Metering Internal issue 1, 2002 pp. 52-54.
  122. Kim K, Blaabjerg F, Bak Jensen B and Choi J. "Instantaneous power compensation in three-phase system using p-q-r theory", IEEE Trans. on Power Electronics., Vol. 17, No. 5 Sept. 2002, pp. 701-710.
  123. Kim K, Blaabjerg F and Bak Jensen B. "Spectral analysis of instantaneous powers in single-phase and three-phase systems with use of p-q-r theory", IEEE Trans. on Power Electronics, Vol. 17, No. 5 Sept. 2002, pp. 711-720.
  124. Yan Xu, Leon M. Tolbert, Fang Z. Peng, John N. Chiasson and Jianqing Chen. "Compensation-based non-active power definition", IEEE Power Electronics letters, Vol. 1, No. 2, June 2003 pp. 45-50.
  125. Hanoch Lev-Ari and Aleksandar M. "Stankovic. Hilbert Space Techniques for Modeling and Compensation of Reactive Power in Energy Processing Systems", IEEE Transactions on Circuits and systems—i: Fundamental theory and applications, Vol. 50, No. 4, April 2003, pp. 540-556.
  126. Emílio F Couto, Júlio S Martins, João L. Afonso. "Simulation results of a shunt active power filter with control based on p-q theory", ICREPQ’03 International conference on renewable energies and power quality vigo, Espanha, 9-12 de April 2003, paper 394.
  127. João L Afonso, Sepúlveda Freitas M J and Júlio S Martins. "p-q theory power components calculations", ISIE’ 2003IEEE International Symposium on Industrial Electronics Rio de Janeiro, Brasil, 9-11 Junho de 2003, ISBN: 07803-7912-8.
  128. Leon M. Tolbert, Yan Xu, Jianqing Chen, Fang Z. Peng and John N. Chiasson. "Compensation of irregular currents with active filters".
  129. Leszek S. Czarnecki. "On some misinterpretations of the instantaneous reactive power p-q theory", Accepted for publication in IEEE Trans. on Power Electronics, 2003.
  130. IEEE Std 1159.3™-2003: IEEE Recommended Practice for the Transfer of Power Quality Data.
  131. N Kamel, AI_Tallaq and Feilat E A. "A new power definition in harmonic distorted power systems" CIGRE Session 2004, Paper C4-102.
  132. Harnaak Khalsa and Jingxin Zhang : "Performance of the IEEE standard definitions for the measurement of electrical power under nonsinusoidal conditions", Australasian Universities Power Engineering Conference (AUPEC 2004) 26-29 September 2004, Brisbane, Australia.
  133. Hanoch Lev-Ari and Aleksandar M. Stankovi´c. "Hilbert space techniques for reactive power compensation in polyphase systems with unequal line resistances", ICHQP Paper hqp056 IEEE 2004.
  134. JPV DU Toit, JHC Pretorius and Wa Cronje. "Non-linear load identification under non-sinusoidal conditions", L’Energia Elettrica - Volume 81 (2004) "Ricerche" pp. 111-115.
  135. Ghassemi F. "Should the theory of power be reviewed?" L’Energia Elettrica Volume 81 (2004) - "Ricerche" pp. 85-90.
  136. Jacques L. Willems and Jozef A. Ghijselen. "The relation between the generalized apparent power and the Voltage Reference" L’Energia Elettrica Vol. 81 (2004) - "Ricerche" pp. 37-45.
  137. Nicola Locci, Carlo Muscas and Sara Sulis. "Multi-point measurement techniques for harmonic pollution monitoring: a comparative analysis" L’Energia Elettrica - Volume 81 (2004) - "Ricerche" pp. 129-133.
  138. Thip Manmek, Colin Grantham and Toan Phung. "A new efficient algorithm for online measurement of power system quantities", The 30th Annual Conference of the IEEE Industrial Electronics Society, November 2-6, 2004, Busan, Korea pp. 1184-1189.
  139. Erhan Balci M and Hakan Hocaoglu M. "Comparison of power definitions for reactive power compensation in nonsinusoidal conditions" 11th International Conference on Harmonics and Quality of Power, 2004, pp. 519-524.
  140. Juraj Altus, Jan Michalk,Brainslav Dobrucky and L H Viet. "Single phase power active filter using instantaneous reactive power theory-theoretical and practical approach", Electric Power Quality and Utilisation Journal, Vol. 11, No 1, 2005, pp. 33-37.
  141. FERC Staff report: "Principles for efficient and reliable reactive power supply and consumption" - Feb. 4, 2005.
  142. Jovan È. Mikuloviael and Tomislav B. Šekara1. "Non-active power compensation in poly-phase systems under asymmetrical and non-sinusoidal conditions", Sixth International Symposium NIKOLA TESLA, October 18-20, 2006, Belgrade, SASA, Serbia.
  143. Leszek S. Czarnecki. "Could power properties of three-phase systems be described in terms of the pointing vector ?" IEEE Trans on Power Delivery Vol. 21, No. 1, Jan. 2006, pp. 339-344.
  144. Mario S F Brugnoni and Héctor L. Soibelzon. "Discrepancy in the reactive energy measurement in single phase systems", C I R E D 19th International Conference on Electricity Distribution Vienna, 21-24 May 2007, Paper No. 0745.
  145. Tolbert L M, Yan Xu, J Chen, Fang Z Peng and Chiasson J F. "Compensation of irregular currents with active filters".
  146. Luis Sainz, Joaquin Pedra and Manuel Caro. "Influence of the Steinmetz circuit capacitor failure on the Electric system harmonic response", IEEE Trans on Power Delivery Vol. 22, No. 2, April 2007, pp. 960-967.
  147. Yang Xiaoxian, Zheng Tao, Zhang Baohui, Ye Fengchun, Duan Jiandong and Shi Minghui "Research of impedance characteristics for medium-voltage power networks" IEEE Trans on Power Delivery Vol. 22, No. 2, April 2007, pp. 870-878.
  148. Jose Antenor Pomilio and Sigmar Maurer Deckmann. "Characterization and compensation of harmonics and reactive power of residential and commercial loads" IEEE Trans on Power Delivery Vol. 22, No. 2, April 2007, pp. 1049-1055.
  149. Peter Sutherland. "On the definition of power in an electrical system" IEEE Trans on Power Delivery Vol. 22, No. 2, April 2007, pp. 1100-1107.
  150. Reyes S Herrera and Patricio Salmeron. "Instantaneous reactive power theory - A comparative evaluation of different formulation", IEEE Trans on Power Delivery Vol. 22, No. 1, Jan. 2007, pp. 595-604.
  151. Horn A, Pittorino L A and Enslin J H R. "Evaluation of active power filter control algorithm under non-sinusoidal and unbalanced conditions", in Proc 7th Int Conf Harmonics and Quality Power. Oct. 16-18, 1996, pp. 217-224.
  152. Salmeron P and Montano J C. "Compensation in non-sinusoidal, unbalanced, three-phase, four wire systems with active power line are invited to offer their comments on the article. Please fill in the Reader’s Forum. conditioner", IEEE Trans Power Delivery Vol. 19, No. 4, Oct 2004, pp. 1968-1974.
  153. Emanuel A E. "Summary of IEEE Standard 1459:Definitions for the measurement of electric power quantities under sinusoidal, non-sinusoidal, balanced or unbalanced conditions", IEEE Trans Ind. Appl, Vol. 40, No. 3, May/Jun 2004. pp. 869-876.
  154. Willems J L, Ghijselen J A and Emanuel A E. "The apparent power concept and the IEEE standard 14592000", IEEE Trans Power Del Vol. 20, No 2, Apr 2005 pp. 876-884.
  155. ibid. "Addendum to the apparent power concept and the IEEE standard 14592000", IEEE Trans Power Del Vol. 20, No. 2, Apr 2005, pp. 885-886.
  156. Pigazo A and Victor M Moreno. "Accurate and computationally efficient implementation of the IEEE 1459-2000 Standard in three phase three wire power systems" IEEE Trans Power Del Vol. 22, No. 2, April 2007, pp. 752-757.