Tutorial on Voltage Imbalance Assessment Requirements

The relative difference between the instrumentation input gains and phase could cause significant error in the assessment of power-system voltage unbalance.

The accuracy of the absolute voltage-level assessment is not so important as long as each input to the instrument shows exactly the same error. If the instrument causes a relative 0.07% deviation between two input-voltage magnitudes and 0.05° deviation in the argument, the display can give up to 0.065% unbalance added or subtracted to the actual voltage unbalance level of the power system. For example, if such a 0.07% magnitude and 0.05° deviation occurs between two voltage input circuits of the instrument, the value displayed can range between 0.935% and 1.065% when 1.000% voltage unbalance appears on the power system. The input-gain fluctuation and the sequence of the sampling circuit can cause that deviation and add the error.

Such good instrument input channel stability of less than 0.07% deviation in magnitude and 0.05° can also be affected during use and therefore the monitor should supply a tolerance test function.

The tolerance test is the difference between the highest and the lowest input voltage magnitudes and the highest phase angle recorded when all probes are connected to the same voltage for 10 min.

The window width and the equation used to assess fluctuating voltage of each phase can also affect both magnitude and angle of the measurement. To avoid such error, IEC 77A WG1/TF2(* ) defined specific window width of 12 cycles and applied Parseval’s theorem to attenuate the fluctuation effect.

The following recommendation gives the requirements which can be used to select the instrumentation if accurate voltage unbalance assessment is needed.

All harmonics should be filtered using an 8th-order filter or the FFT algorithm. Windows of 12 cycles for 60 Hz systems should be used for very rigorous assessment. The FFT results of such windows gives a picket fence Fc for every 5 Hz which should be used to optimise the assessment accuracy of the fundamental amplitude C1.

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There are several options to calculate the voltage unbalance factor uu depending on the accuracy needed. Options 1 to 3 gives the most rigourous assessment but Option 4 adds a 13% error in the uu assessed.

Option 1: Each phase-to-ground voltage is sampled and filtered, and the fundamental amplitude and phase angle are calculated to give the vectors , and . The instantaneous voltage unbalance factor (uu) is calculated as follows:

Option 2: Two phase-to-phase voltages are sampled and filtered to give the fundamental vectors , and . The instantaneous voltage unbalance factor (uu) is calculated as follows:

´ 100%

Option 3: Each phase-to-phase voltage is sampled and filtered, and the fundamental amplitude is calculated to give the moduli , and . The instantaneous voltage unbalance factor (uu) is calculated as follows:

´ 100%

Option 4: This option adds as much as 13% error to the voltage unbalance assessed. Each phase-to-phase voltage is sampled and filtered to give the fundamental amplitude, , and . The instantaneous voltage unbalance factor (uu) is calculated as follows:

The rms value of the phase-to-phase voltage should be avoided in assessing the voltage unbalance unless the voltage distortion factor is very low.

 

 

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References

  1. Roger Bergeron, "Voltage Unbalance on Dstribution Systems - Phase I", Canadian Electrical Association, Project No. 231 D 488, Montréal, Québec, January 1989.

  1. Westinghouse Electric Corporation. "Applied Protective Relaying", Silent Sentinels publication, Newark, New Jersey.

  1. Cumming, P.G. "Protection of Induction Motors Against Unbalance Voltage Operation", IEEE-PCI, September 1983, IEEE-PIT, June 1984 and IEEE-IAS October 1984.

  1. Roger Bergeron, "A Measurement Protocol for Power Quality Coordination", CIRED 1991, paper 2.17, April 1991.

  1. IEC 27-1 (1992).- Letter Symbols To Be Used in Electrical Technology. Part 1: General.

  1. IEC 146. Parts 1 to 6 .- Semiconductors Convertors.

  1.     IEC 375 (1972).- Conventions Concerning Electric and Magnetic Circuits.
  1. Roger Bergeron, "Power Quality Measurement Protocol, CEA Guide to Performing Power Quality Surveys," CEA report 220 D 711, Canadian Electrical Association 1 Westmount Square, Suite 1600 Montréal, Québec, Canada H3Z 2P9, 1996, 216 pp.