Calculating three phase power

[raithrovers1]

How can I calculate the output power from a 3 phase UPS with unbalanced loads?
Load Voltage(Vrms)R-Y 409.8 Y-B 414.3 B-R 414.1
Load Voltage R-N 237.4 Y-N 238 B-N 239.7
Load Current(Arms) R 79 Y 27.7 B 41.3 N 68.4
Our engineer attached a Fluke scope meter to each phase voltage and current and then added them together. This came out at approximately 60kVA. But if you use P=V*I*1.73 for each phase and then sum these results this adds up to 105.6kVA.
Anyone help?

UPS engineer

http://www.calibrepower.co.uk

 

[waross]

Google "power factor"

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[rbulsara]

P=V*I*1.73 is for a "balanced" 3 phase power system, that is when I is equal in all three lines and V= V line to line.

For unbalanced system, calculate per phase values and add them up.

For each phase power, the formula is V*I where V is line to neutral or (Vll/1.732).

Rafiq Bulsara

http://www.srengineersct.com

 

[vandal06]

Notice that if you take your 105 kVA and divide by 1.73 you get the engineer's solution. That's a hint that you mis-applied an equation somewhere.

 

[ScottyUK]

Probably used the line voltage and not the phase-neutral voltage...?


----------------------------------

If we learn from our mistakes I'm getting a great education!

 

[rbulsara]

Even your engineer appears to have made a mistake in calcs.

Rafiq Bulsara

http://www.srengineersct.com

 

[PHovnanian]

Our engineer attached a Fluke scope meter to each phase voltage and current and then added them together. This came out at approximately 60kVA.

How was that connected and measured? Given your numbers, the only way I can get close to 60 kVA is by using the peak instead of RMS L-N voltages.

SUM( Vln * Il ) = 41.7 kVA

Vln = line-neutral voltages (Vr-n, etc.)
Il = line currents

Using the line to line voltages, the proper formula is

SUM( Vll * Il )/ 1.73 = 72.3/ 1.73 = 41.6 kVA

Vll = line to line voltage

which is close enough.

But if you use P=V*I*1.73 for each phase and then sum these results

But you don't. That will work for a balanced situation where V is Vll and V and I are the balanced line to line voltage, line current. But then you don't sum them.

 

[raithrovers1]

If I apply Rafiq's calcs I get 35.2kVA.
My post did not state clearly how my engineer took the readings. He attached a Fluke scopemeter to each phase and set the scope to kVA power and then added these results together.

UPS engineer

http://www.calibrepower.co.uk

 

[waross]

Note:
kW is power.
KVA is apparent power.
You are calculating apparent power, not true power. {rant off}
Yes, I get 35.2 KVA

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[raithrovers1]

Bill
Thanks but I realise that and will be applying 0.8pf for this UPS. Didn't want to confuse things any more!

UPS engineer

http://www.calibrepower.co.uk

 

[raithrovers1]

Things seem to make a bit more sense now. I think my engineer must have connected his scope phase to phase instead of phase to neutral. 1/1.73*60kVA = 34.7kVA which agrees with our sum of V*I for each phase.

UPS engineer

http://www.calibrepower.co.uk

 

[rbulsara]

There you go...!

Rafiq Bulsara

http://www.srengineersct.com

 

[pwrtran]

Blondel's theorem - in a system of N electrical conductors, N-1 electrical meter or wattmeter elements, when properly connected, will measure the electrical power or energy taken.

Your system is a 4-wire, so 3-element metering is adequate.

So, 35.2 kVA is the correct answer!