Hi,
I am trying to figure out reactive power loss for a 965 ft 1/0 AWG
cable.
I have already calculated the power loss at .3397 kw.
total current=26.43
cable resistance=.000168
voltage=34.5 kv
power factor=.95
The formula for the kw is: ((26.43^2 x .000168) x3) X 965 =
339.74/1000 = .3397 kw
I have been trying to use the formula Q=(P*sin p.f) 1.73 to calculate
the KVAR loss, but I am not coming up with the right answer. The
answer should be about 8.19 KVAR.
Any idea?
Thanks,
Troy

Hi,
I am trying to figure out reactive power loss for a 965 ft 1/0 AWG
cable.
I have already calculated the power loss at .3397 kw.
total current=26.43
cable resistance=.000168
voltage=34.5 kv
power factor=.95
The formula for the kw is: ((26.43^2 x .000168) x3) X 965 =
339.74/1000 = .3397 kw
I have been trying to use the formula Q=(P*sin p.f) 1.73 to calculate
the KVAR loss, but I am not coming up with the right answer. The
answer should be about 18.19 KVAR.
Any idea?
Thanks,
Troy

No, the formula for Q at the load is Q=V*A*sqrt(1-pf^2)*1.73. To use 'sin'
you need to know the angle between current and voltage (which is
arccos(0.95) so another formula would be Q=P*sin(arccos(pf))*1.73). But
knowing that sin^2+cos^2=1 makes it possible to find the sin(angle) from the
pf directly as I showed.
But this will give you the reactive power of the *load*, not the amount of
reactive power (if any) in the *cable*. You can *not* use the real power
loss in the cable in the above formula.
To find the reactive power consumed in the cable, you need the cable's
reactance. A multi-conductor cable would have some capacitance as well as
inductance and resistance. But a cable this short, I doubt there is much
reactive losses anyway. Now, if it were a transmission line stretching a
few miles, that would be another story.
If you have precision instruments, an experimental method would be to
measure the power factor at the load end and then measure it again at the
supply end. With that and some math, you can figure out the difference in
reactive power through the cable.
The real power losses in such a cable are of interest because they cause
heating in the cable. The reactive 'losses' are probably of no consequence.
daestrom

Hi Daestrom,
Thanks for your help! Would it be the shunt capacitance reactance
that I need for the calculation? The data sheet I have shows 6691
ohms per kft

How many conductors are in the cable? What is the circular mil ohm dc
resistance of the conductor at 20 degrees C? What is the ambient
temperature?
If the cable is run as an individual conductor what is the
configuration and distances between it and other cables, and is this a
three phase sytem?
Is this a shielded conductor? Does it have a concentric neutral? Is
this cable in open air or in a duct?

Who is this, "Jacob Two Two's" cousin ?
Inconsequential...
I trust thou art not working for the mystical land of tomorrows Utility
Company.
The Mighty WontVolt

Yep. Then you have a 'transmission line' and you can look up formula for a
pi configuration for example (1/2 shunt cap, the series inductance, then the
other 1/2 shunt cap).
This type of 'four-terminal network' calculation is common for longer
transmission lines. In the olden days it was done with some simple
graphical methods, but nowadays a computer spreadsheet works just as good.
daestrom

6691ohms/kft doesn't appear to be a capacitive reactance figure. This
would imply that the total line capacitive reactance increases with
distance- it doesn't- the susceptance does. What is of more importance
at this length is the inductive reactance.
check your data.

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