# Is the current on a 3-phase AC motor (mostly) identical across all phases?

I would like to monitor long term current consumption changes over time (and derive power if I know the voltage) on a 3 phase cooling compressor for a walk-in fridge. I am not 100% sure right now, but lets assume its a 3-phase 3-wire system without separate neutral wire.

If I measure with a CT clamp close to the compressor (so definitely no other devices are connected to the phases between the clamp and the compressor), can I safely assume the current through the conductors is roughly identical? If I understand Blondels theorem correctly, you can use 2 current and voltage sensors, and

Total power = W1+W2


and

W1=i1(v1-v3)
W2=i2(v2-v3)


If I can assume that roughly i1=i2, and the RMS phase-to-phase voltages average out to be the same over time, then I would think I can just double the Irms and multiple by Vrms phase-to-phase, to get the total power consumption. Is that correct?

Does it matter for measuring if internally in the motor's connector box, the phases are connected in Wye or Delta configuration (as long as there is no separate neutral wire)? And in case of a 4-wire 3-phase system, I could then do the same but multiply it by 3?

• If you have or can get the nameplate data for the motor or for the fridge as a whole, you may be able to make a good estimate of the power used by the motor when it is running. Then you could determine the consumption changes over time by determining the run time. It seems likely that the run-time variation will be the major factor affecting consumption variation.
– user80875
Jul 13, 2021 at 12:44

Or is that not true?

It's not true unless you are prepared to make power calculations that don't account for power factor and suchlike.

can I safely assume the current through the conductors is roughly identical?

No you can't because each conductor current is shifted in phase to each other by close to 120° (for a balanced supply voltage and fairly balanced load): -

Picture from here. If you want to make huge compromises on power measurement accuracy then you can make the assumption of course.

If I understand Blondels theorem correctly, in that case the total current is then double the amount measured

There is nothing to suggest that you do understand that theorem correctly based on what you say. Blondel's theorem is basically that if your load has three wires then you need 3 minus 1 wattmeters to calculate power.

Does it matter for measuring if internally in the motor's connector box, the phases are connected in Wye or Delta configuration

The two wattmeter method for 3 wires connected wye or delta is perfectly accurate in both configurations.

• Thanks for the quick answer. I edited my question a little with my reasoning about Blondel's theorem, but that won't affect the power factor part of your answer I guess. But won't the power factor (averaging out over a day or week) affect the power consumption of all three phases equally over time? Or is that another inaccurate assumption compounding the I1=I2 question? To be clear, I am not talking about a quick power measurement manually for a minute, but more in constantly electronically monitoring it for weeks or months or more. Jul 13, 2021 at 9:04
• @DolfAndringa (1) No it won't (2) and (3) Yes it does but you can't determine PF with Vrms and Irms measurements; it needs to be more complex) (4) Irrelevant. Jul 13, 2021 at 10:00
• @DolfAndringa are we done here? Do you have any residual questions? If so please leave a comment else, select my answer as accepted. Jan 7 at 8:09