Line to Line or Line to Neutral voltage to calculate 3 phase power

I am confused as to whether or not I should use the line to line voltage on a 3 phase motor or the line to neutral voltage to calculate power? Would someone please be able to fill me in, and possibly offer an explanation as to why? I do believe there are explanations explaining how the L-L and L-N voltages are related, but I need to know which one is used to calculate power. Thank you.

• It depends on how the load is connected. Take the voltage that appears across the load, whether L-L or L-N. It may help to imagine a resistive heater first, understand that, then translate to a motor. – AaronD Mar 11 '15 at 18:41

You can use both voltages to calculate power, but it yields to a different expression. If $U_f$ is the line to neutral voltage and $i_L$ the current in one the lines, then:

$$P=3U_fi_L\cos \phi$$

Now because line to line voltage $U_L$ is related to $U_f$ by $U_L=\sqrt 3 U_f$, then after substituting in the previous expression we have:

$$P=\sqrt 3U_Li_L\cos \phi$$

S [VA] = Iline × Vline-line × √3.

Note S is 'apparent power', which has units of volt-amps. This is a different quantity to P, which has units of watts. S and P are related by the power factor.

• If you're going to give a mathematical answer, you need to define your terms. What is S[VA]? – Dave Tweed Mar 12 '15 at 13:09
• See above. Not much of an answer anyway; I had intended to add a diagram but didn't get time. – Li-aung Yip Mar 12 '15 at 13:11