On a balanced 3 phase given kw and V:
To find Current:
(kW x 1000) / (E x PF) = amps
I have a 208v, 50/60Hz, 9kW, 3 PH
kw=9
E=208
PF=???
I know PF = cos(theta)
or PF (3 PH) = Input Watts / (E x I x 1.732)
I am trying find the current??
I'm I doing something wrong? Because I thought PF has to be between 0
and 1.
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Power factor is a single phase relationship between phase voltage and phase
current . You are looking at line to line voltage for what appears to be a Y
system. There is an extra 30 degree shift between line voltage and line
current. For a balanced system it can be found from the KW/KVA ratio (your
last equation below which is the first expression re-ordered) as it would be
the same for each phase.
In this case the voltage is 208 line to line for a Y system(assumed because
of the voltage) and 120V line to neutral. The line current is
9000/(1.73*208*pf) =25/pf A and there is no information to find the pf.
Alternatively use 3000/120*pf =25*pf A (line and phase current the same for
a Y)and still no info for the power factor.
If you knew either the current or the pf then you could find the other but
otherwise you are stuck.
With the expressions that you give, you are stuck with an unknown angle
between phase voltage and phase current so you can't find the pf and without
the pf you can't find the current.
And, yes, pf is between 0 and 1. --
Don Kelly snipped-for-privacy@shawcross.ca
remove the X to answer

For motor, transformer, and other inductive laods assume a power
factor of about 0.7 to 0.8
For resistive loads assume a power factor of 1.0
Now you can find the amperes.
Power (in watts) = E x I x 1.732 x PF for three phase.

Power factor correction for a lagging power factor is seldom done in
for normal field installations, especially for small loads.
Transformers are usually rated in volt ameres because the power factor
is not know at time of manufacturer.

Transformers are rated in VA because that determines the maximum current
through the winding. The load watts don't matter to the transformer. In
other words, a one kVA transformer could deliver one kVA to a one kVAR
capacitor that draws zero watts, or to a heater that draws one kW. It is
fully loaded either way.
Ben Miller

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