Historical overview

Phase angles of voltage phasors of power network buses have always been of special interest to power system engineers. It is well-known that active (real) power flow in a power line is very nearly proportional to the sine of the angle difference between voltages at the two terminals of the line. As many of the planning and operational considerations in a power network are directly concerned with the flow of real power, measuring angle differences across transmission has been of concern for many years. The earliest modern application involving direct measurement of phase angle differences was reported in three papers in early 1980s [1,2,3]. These systems used LORAN-C , GOES satellite transmissions, and the HBG radio transmissions (in Europe) in order to obtain synchronization of reference time at different locations in a power system. The next available positive-going zero-crossing of a phase voltage was used to estimate the local phase angle with respect to the...


Discrete Fourier Transform Inverse Fourier Transform Window Function Symmetrical Component Data Window 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Missout,G. and Girard, P., “Measurement of bus voltage angle between Montreal and Sept-Iles”, IEEE Transactions on PAS. Vol. 99, No. 2, March/April 1980, pp 536–539.CrossRefGoogle Scholar
  2. 2.
    Missout, G., Beland,J., and Bedard, G., “Dynamic measurement of the absolute voltage angle on long transmission Lines”, IEEE Transactions on PAS. Vol. 100, No. 11, November 1981, pp 4428–4434.CrossRefGoogle Scholar
  3. 3.
    Bonanomi,P., “Phase angle measurements with synchronized clocks — principles and applications”, IEEE Transactions on PAS. Vol. 100, No. 11, November 1981, pp 5036–5043.CrossRefGoogle Scholar
  4. 4.
    Phadke, A.G., Hlibka, T., and Ibrahim, M., “Fundamental basis for distance relaying with symmetrical components”, IEEE Transactions on PAS. Vol. 96, No. 2, March/April, 1977, pp 635–646.CrossRefGoogle Scholar
  5. 5.
    Phadke, A.G., Thorp, J.S, and Adamiak,M.G., “A new measurement technique for tracking voltage phasors, local system frequency, and rate of change of frequency”, IEEE Transactions on PAS. Vol. 102, No. 5, May 1983, pp 1025–1038.CrossRefGoogle Scholar
  6. 6.
    There is great wealth of information about the GPS system available in various technical publications. A highly readable account for the layman is available at the web-site There the interested reader will also find links to other source material.
  7. 7.
    “Macrodyne Model 1690 PMU Disturbance Recorder”, Macrodyne Inc. 4 Chelsea Place, Clifton Park, NY, 12065.Google Scholar
  8. 8.
    “IEEE Standard for Synchrophasors for Power Systems”, C37.118–2005, pp 56–57, IEEE 1344–1995. Sponsored by the Power System Relaying Committee of the Power Engineering Society, pp 56–57.Google Scholar
  9. 9.
    Papoulis, A., “The fourier integral and its applications”, McGraw-Hill, New York, 1962.MATHGoogle Scholar
  10. 10.
    Brigham, E.O., “The fast fourier transform”, Prentice Hall, Englewood Cliffs, 1974.Google Scholar
  11. 11.
    Phadke, A.G. and Thorp, J.S., “Computer relaying for power systems”, Research Studies Press, Reprinted August 1994.Google Scholar
  12. 12.
    Walker, J.S., “Fast fourier transforms”, Second Edition, CRC Press, 1996.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • A.G. Phadke
    • 1
  • J.S. Thorp
    • 1
  1. 1.Virginia Polytechnic Institute and State UniversityBlacksburgUSA

Personalised recommendations