Reactive Charging Current and Power Calculations 2

[siberhusky]

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

 

[jghrist]

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

 

[siberhusky]

[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

 

[SidiropoulosM]

The same formula is applicable to overhead lines. Michael Sidiropoulos

 

[siberhusky]

Thank you both!

- john