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The power supply isn't needed, the emonTx is powered via the (USB to UART cable) FTDI programmer.

Thank you very much for the fast reply! 

That must sound stupid, but I got confused, should I use a 5V ac-ac power supply or a 9v ac-ac power supply?

The emonTx v2 needs to be "powered" by a 5v DC supply (when FTDI programmer or other 5v DC source isn't connected) and to "sense" the mains voltage it requires a 9v AC adapter, the 9v AC adapter is not mandatory as there are sketches and applications that do not "sense" voltage, but for the emonTx to function it must have 3.3v which it gets via the on-board voltage regulator that requires a 5v DC supply.

When you measure the mains voltage via the 9 V ac-ac adapter (I prefer 'measure'), you can get an accurate reading for the true power. If you don't have the ac-ac adapter, you tell it in software what your nominal mains voltage is, and hence you get only an estimate of 'apparent power' (i.e. the supposed voltage times current). Real Power and Apparent Power are the same for a resistive load but can be wildly different for other types of load - it's explained in Building Blocks.

Thanks again for the fast and helpful answers :-)

" If you don't have the ac-ac adapter, you tell it in software what your nominal mains voltage is"

Can you show me where in code a change this?

It's where the returned value from the call to the function calcIrms is multiplied by the constant 230 or 240, 230 being the nominal EU voltage and 240 the normal UK voltage.