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Reactive Charging Current and Power Calculations
2

Reactive Charging Current and Power Calculations

Reactive Charging Current and Power Calculations

(OP)
Because of a discrepancy in some data, I attempted to verify some charging current/charging power calculations, and I am at a loss.  I have obtained the following formulas from an underground transmission systems reference book:

a.    X1 = X0 = [1/(2*pi*f*C)] * 10E+6   Ohms/1000 feet
b.    Ic = 2*pi*f*C * E0 * 10E-3             A/1000 feet
c.    kVAR = 2*pi*f*C * E0**2               kVA/1000 feet  

where:
   f = frequency in Hz
   C = cable capacitance in microfarads/1000 feet
   E0 = line to ground operating voltage in kV
   IC = charging current in A/1000 feet
   kVAR = reactive power per phase

The part I don’t understand is the units they claim--kVAR--for equation c.  If for example, one multiplies the current (Ic) in formula b by the Voltage to obtain the reactive charging power:
                           
                Voltage*Ic = Voltage*[2*pi*f*C*E0*10E-3]
  (E0*10E+3 volts)*Ic = (E0*10E+3 volts)*[2*pi*f*C*E0*10E-3]
                                = 2*pi*f*C*E0**2

The terms of the formula come out the same as those shown above in formula c.  But even though E0 is in kV, formula c is a result of the multiplication of the current (in amps) by the voltage (in volts).  I would therefore expect that the units would be in VAR, not kVAR.  [The result is the same using V**2/X instead of V*Ic.]  What am I missing?

Any guidance would be very much appreciated!

  - john

RE: Reactive Charging Current and Power Calculations

You aren't missing anything.  The results of formula c would be in var, not kvar, with the units given.

RE: Reactive Charging Current and Power Calculations

(OP)
[I saw the formula represented that way in more than one reference source, so I was reluctant to trust myself.  Thanks for the response.]

If I may, one follow-up question: The formulas for the reactive charging are defined for underground cables... are they applicable to overhead lines as well?  (Assuming that the capacitance is correctly calculated?)

Thx,

  - john

RE: Reactive Charging Current and Power Calculations

The same formula is applicable to overhead lines.

Michael Sidiropoulos

RE: Reactive Charging Current and Power Calculations

(OP)
Thank you both!

  - john

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