Sorry if I don't use the right terminology, but I'm using the German version of the game.

What exactly does the "Consolidate Power"-Token (the one with the crown on it) with the star do?

Normaly the "Consolidate Power" Token gives me 1 Power token + 1 Power token per number of crowns in the area it is placed.

According to the German rules the "Consolidate Power" -token with the star lets me gather supplies in another area as well.

So, does that mean that if i own another area with one crown in it I get one additional Power token? Or do I get two additional power tokens as it would be if I had placed another "normal" "Consolidate Power"-token on this are?

Ok, after downloading and reading the English Rules, I think I got it now.

The "Consolidate Power"-token with the star does exactly the same thing as the normal "Consolidate Power"-token, exact that now I can use 3 tokens instead of two (if I am high enough on the Raven's track).

Is that correct?

That's correct.

I believe some use a houserule to allow the starred consolidate order to gain 1 extra power, but I've never done that.

Gaining power from three consolidate orders is a strong enough special for me.

Yeah, my friends used to want that rule until they found how quickly they max out their crowns what w/ expanding and generally trying to avoid having to fight