# Power Calculations in an Unbalanced 3 Phase Circuit

#### Houdini

Joined Dec 13, 2007
10
I have had some conflicting answers to how to measure and calculate the 3 phase power in an unbalanced circuit. Here is what I have.

480 Volt 3 Phase Supply that is supplying a machine. I have measured the current in all 3 legs and need to calculate the power ( eg: the power that will spin the electrical meter). If it was balanced and all the currents were the same,, I could use "1.73 X v X I"

I have read that you can use the 2 watt meter method (Measure the current and voltage on 2 of the phases and calculate the Power, then add them and that will be the Kw).

I1 = 2.9 Amps
I2 = 5.2 Amps
I3 = 3.9 Amps

What would be the way to calculate the power?

Thanks!!

#### recca02

Joined Apr 2, 2007
1,212
"1.73 X v X I"
that would have helped if those were the line current and line voltages.
if u measured current in each phase,just add all V*I for each phase to get apparent power i think that works for all balanced and unbalanced loads.
for active power add I^2R of all phases.

#### ruggierp

Joined Jun 22, 2018
1
If the load is balanced, the power is calculated as the [ 3x V(L-L)/3^0.5 x I ], which is 3^0.5 x 480Vac x I.
However since, the currents are not equal, there will be a phase shift between the line current and the line voltage, so the some of V(L-L)/3^0.5 x I for each line will give the VA of the system, but not the power.

To calculate the power from the values of the unbalanced line currents is a fairly elaborate calculation, beyond the scope of this answer.

Measuring the power using a three phase Watt meter, or using a 2-Watt or even a 3-Watt meter method would be advised.

#### WBahn

Joined Mar 31, 2012
29,829
Do you have access to a textbook on introductory circuit analysis? Most cover the two-wattmeter method in detail.

There are also lots of websites that go into it in various levels of detail. Here's just the first one I ran across.

https://circuitglobe.com/two-wattmeter-method-of-power-measurement.html

But it requires more than just measuring the amplitude of the currents. Wattmeters are sensitive to the power factor.