Estimate energy usage from two-phase power measurements

Hello, I am currently using a EmonPi to monitor the current (and indirectly the power) of my house. I am storing in a dataset both phases (P_a and P_b) with a sampling rate of 30 seconds. Now, I would like to estimate the energy usage from the last month. How do I calculate that? First I thought that I should sum the power from phase A and the power from phase B and integrate both over the last month (Energy = integral of [P_a(t) + P_b(t)] * dt where dt = 30s = 0.00833h). However, my house has single-phase and two-phase loads. Is it okay to sum P_a and P_b in this case?

I am in Brazil. The voltage here is 127V and 220V.

That should give you the correct result, provided that you are measuring real power.

If you think about it, a resistive load connected between the two phases at 220 V will have the “wrong” voltage but that error will be exactly offset by the apparent poor power factor due to the 60° phase angle of the line-line current with respect to either line-neutral voltage.

Another way of looking at it is 3 wattmeters give you the correct answer whether the load is connected in star or in delta, even if it uses only two of the (normal in the UK) three phases.

Hello Robert, thank you for the answer! The UK model is similar to the
Brazilian then. We also use two phases and a neutral from a star
transformer. I wasn’t sure if I could just sum both

Not really. UK industrial and larger commercial premises will normally have all three phases, 240 V line-neutral and 415 V between lines. The neutral is earthed at the supply, and often at multiple points along the final distribution too. Very few domestic properties have a 3-phase supply, most are single phase 240 V - with a 60, 80 or 100 A fuse to protect the network from the consumer. That’s almost certainly why none of the OEM equipment is 3-phase.

I meant that the transformers from the distribution system are also star
based. But the houses usually have two phases and a neutral.

Yes, I knew that from the voltages you quoted.