# Calculating single phase load from 3 phase power measurements

I need to record kW & kWh for individual phases on a circuit that has a 3 phase power meter that outputs the following data:

Total for all three phases:

• kW
• kWh
• kVA
• kVAr
• power factor
• Frequency (we can assume that this is universal across all phases)

For each phase, L1, L2, L3 the following readings are also available to me:

• Volts (L-N)
• Line Current (Amperage)

Considering that the load distributed unequally, I'm wondering whether there is a way to calculate individual load in kW, using the data that is available to me. It seems to me that it should be possible to use a ratio calculation to calculate how much of the total load belongs to each phase:

kWL1 = (kVAL1/kVAtot)*kWtot


Can someone confirm this hypothesis?

• Are you just reading the volts and amps, or are you reading them and storing their values? If you can store the values you could calculate everything from it numerically. You would need a sampling frequency of a kHz or more for it(meaning that you get the current and voltage values 1000 times per second). There are a few simple formulae which would do it for you if you have the data. Jan 8, 2015 at 11:08
• What Kurtovic seems to be saying is that you can calculate the missing per-phase power factors by measuring the instantaneous current and voltage peaks over time and thus determine the power factors.
– Fizz
Jan 8, 2015 at 13:05
• I can store the values, but unfortunately, I don't have a kHz resolution capability. V and A sampling is every 15 seconds. But thank you for a very good suggestion @Kurtovic Jan 11, 2015 at 4:41

I don't see any way to do this. You need the power factor of the individual phases and that's not available. The equation is incorrect.

$P_{actL1} = P_{appL1}\cdot\cos\varphi_1$

$P_{act,tot}/P_{app,tot}=$

$= (U\cdot I_{l1}\cdot \cos\varphi_1 + U\cdot I_{l2}\cdot \cos\varphi_2 + U\cdot I_{l3}\cdot \cos\varphi_3)/(I_{l1}\cdot U + I_{l2}\cdot U + I_{l3}\cdot U)$

$= ( I_{l1}\cdot \cos\varphi_1 + I_{l2}\cdot \cos\varphi_2 + I_{l3}\cdot \cos\varphi_3)/(I_{l1} + I_{l2} + I_{l3})$

and that is not equal to $\cos\varphi_1$.

• I think you have some typos on the last line. You probably mean = (Il1*PF1 + Il2*PF2 + Il3*PF3)/(Il1 + Il2 + Il3) but otherwise your proof seems correct. The way you wrote the last line, it implies Il1 = Il2 = Il3 and PF1 = PF2 = PF3, which of course only happens when the phases are perfectly balanced.
– Fizz
Jan 8, 2015 at 8:10
• Although this was the answer I was hoping not to receive, thank you for your time! Jan 11, 2015 at 4:45