Most euro/Schuko outlets do not require a third "pin" for earth/ground connection... this connection is made by some contacts on the walls of the socket. So, to get a good earth connection you need a plug with some flat metal strips on the side of the plug, like in this picture...

Does this look like a plug that would work in your country? This is what all the outlets in Germany were like. I am surprised to hear that Thomann would not ship with an appropriate power cord. Moog ships all Little Phatty to the EU with an appropriate Schuko plug, which has tabs for grounding.
If your outlet looks like this:

The metal spring contacts at top and bottom are the ground connection. No need for an extra pin on the plug.
Do your outlets look like the above?
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In any case, let's think about what could be the trouble and what you can do. First, if the power plug you have does not have the ground contacts (flat metal strips on the outside of the plug) then Thomann has replaced the power cord supplied by Moog with an inferior one... which seems unlikely.
Second, if you have the power plugged into a "bad" outlet, make sure it's really the outlet and not a problem with some other connection. Disconnect any/all audio cables from the LP but leave the power plugged in. Does the problem persist, or does it go away? I have encountered similar situations where the problem was actually a ground loop or voltage problem being caused by an effects pedal or mixer that was connected to the Little Phatty's audio output. This is important to test.
Once we are certain whether the problem is specific to the power plug or if it is to do with the audio connections, we can trouble-shoot further from there.
If it's a power problem, an uninterruptable power supply (UPS) or a power conditioner or line voltage regulator (like this?) might help.
You may wish to return this LP to Thomann if you can... I suspect you will get much better support in Denmark if you purchase from our official Danish distributor, High End Tentacles. Besides which, Ole is a super-nice, super-cool guy and could use your support.
Thanks,
Amos