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This interesting article was just pointed out to me:

Japan space scientists make wireless energy breakthrough

This isn't actually the first time energy has been transmitted wirelessly over such distances.  In fact a demonstration in Hawaii beamed power 92 miles, though it was only 20 watts.  But this is the largest amount of power that has ever been beamed wirelessly (though the "electric kettle" comment doesn't make it sound like a lot, it's actually more than the peak power generation of the solar panels on my house).

This is relevant to space colonization for two reasons.  First, instead of having its own solar panels, a colony might well just have a (much smaller) receiving antenna, and buy power from a big power satellite nearby.  Second, building and maintaining those giant solar power satellites, which mainly sell their power to Earth, could provide an important source of income for a space economy.
Has anybody looked into Tesla's broadcast power for use in the habitat?
"True" Tesla wireless can be a fun topic. Tesla's name is sometimes synonymous with free energy and the like, and it can be difficult to get serious disussion about it. Still, if you take a decent look, he really really didn't think he was using traditional radio for his wireless system.

There are a few experiments I could point you to, but I've not been able to find anyone doing them properly.