Question: Our power meter has two "branches" - one for ground floor and one for upper floor, and on the bill we've got 2 readings, again one for each floor. Also from the street we've got 2 mains cables coming to the meter box. They may or may not be the same phase - how can I tell? This is in New Zealand, typically single-phase 240V power.

The reason is that we are considering solar panels and the single-phase inverters are much cheaper than the 3-phase ones. In fact I don't know if we can actually have a 3-phase inverter with an unbalanced power draw, and with the 3rd phase unused altogether.

The solar people looked at our meter box and they didn't know what to make of it. They suggested to only attach the PV to one of the branches but that kinda makes the investment less efficient as the other floor would get no benefit from the solar panels.

So my idea was to ask an electrician to change our setup to only use 1 mains cable for the whole house, disconnect the other one and then have a clean-cut single phase system where we can use the solar with a single-phase inverter. Does that make sense?

Answer: 
EU/NZ 3-phase distribution
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New Zealand uses European style power distribution. Power is distributed as high-voltage 3-phase "delta" (no neutral). At the neighborhood level, there is a transformer which steps this down to 3-phase "wye" (230V from phase to neutral; 400V phase to phase).

Any given house is given neutral and obviously 1 phase... but it may also get 2 or all 3 phases, depending on things like "is it in Germany?"

So when you say "2 phases" what you mean is "2 out of the 3 phases". And that is a perfectly reasonable configuration, especially for dual tenencies (2 meters).

The reason to do that is, it saves wire. Two services on the same phase need 2 separate neutrals. However on different phases, they can share the neutral. And due to the mathematics of 3-phase, no matter how the phases are loaded, neutral current will never exceed phase current. (Even if the 3rd phase is always 0 because it doesn't exist). So the neutral can be the same size as the live wires.

Balance is good
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The power company sorely needs all 3 phases to be balanced. It is inefficient and costly to run the generators with lopsided phase loading. For distribution transformers and wires, imbalanced load means wasting capacity, so larger wires are needed.

However, here's the thing about solar. If the sun is shining at your house, it's probably shining at your neighbor 3 doors down who also has solar. And 12 neighbors sharing your transformer also have solar. And 500 neighbors have solar who share your high voltage feeder. So the laws of large numbers kick in, evenly distributing all these "randomly phased" solar systems onto the high voltage feeders.

So you don't need to worry about it, because it will be lost in the averages. There's no reason to use a 3-phase solar inverter, since you might not even have the 3rd phase.
Get a multimeter set to AC voltage. Carefully measure the voltage between the two supply lives, trying not to electrocute yourself in the process.

On a 230V supply, two lives on the same phase will show no more than a few volts. Two lives on different phases will have around 400V between them. It's a bit less than twice the supply voltage.