# How does a power meter differentiate between three-phase and single-phase loads?

How does a three-phase power meter (for example the one used by my power company) know the difference between a single three-phase load and multiple single-phase loads?

For example: a three-phase heater at 4 kW (400 V * 10 A) vs three single phase heaters also totaling 10 A (230 V * 3.333333… A * 3 = 2.3 kW).

What am I missing here?

The difference is phase voltage vs line voltage.

Consider the following:

simulate this circuit – Schematic created using CircuitLab

In the 3P arrangement above, R, S, and T are "phases" with an RMS voltage of 230V separated (delay / phase difference) by 120 degrees each, N is the common (neutral). Above is a balanced system so the neutral current is zero.

For each phase, "phase voltage" is 230 Vrms. Each phase supplies a 100R load, therefore phase current for each is $$\I_R=I_S=I_T=230/100=2.3 \ \text{Arms}\$$, which makes ~530 Watts each and ~1.6 kW total.

4 kW (400 V * 10 A)

Now 400V here is the "line" voltage which is basically $$\\sqrt3\$$ times the phase voltage: $$\V_L=230 \ \sqrt3\approx 400 \text{V}\$$. This is the voltage across each phase i.e. R-S, R-T and S-T. So the phase voltage (i.e. R-N, S-N, and T-N) is 230V but the "line" voltage is 398V.

And 10A is the total RMS current of the network which is

$$I_{tot}=\sqrt{I_R^2+I_S^2+I_T^2}$$

where $$\I_{R,S,T}\$$ are "phase" currents. For a balanced network the phase currents will be equal so $$\I_{tot}=I_R \sqrt3\$$. And for the example circuit above, it's

$$I_{tot}=2.3\sqrt3\approx 4 \ \text{Arms}$$

Now if you multiply the "line" voltage with the total RMS current above, you'll get

$$P_T=V_L \ I_{tot}=1.6 \ \text{kW}$$

three single phase heaters also totaling 10 A (230 V * 3.333333… A * 3 = 2.3 kW)

The currents do not sum up to 10 A. The powers can be summed but the currents cannot because they are out of phase. All you can do is to take the square root of the sum of squares which I tried to show above.

• This is a brilliant answer, thank you. Commented Jan 26 at 10:14

How does a three-phase power meter (for example the one used by my power company) know the difference between a single three-phase load and multiple single-phase loads?

A properly designed power meter doesn't care whether the incoming supply is 3-phase or, whether there is a balanced 3-phase load on the output or, only a single phase load on the output. It won't even care (within reason) if the voltage supply is significantly non-sinusoidal either.

What am I missing here?

It calculates power delivered to the load from the supply irrespective of what I have mentioned above mentioned above.