Pretty much what the title says. The projector only works on power and I don't see any batteries but I'm not sure about the components of course, so is it safe to carry it in hand luggage or check in?
From a security screening perspective, I don't see any reason why you couldn't.
The TSA's What can I bring page says that in the US, projectors are allowed both in carry-on and checked bags. I expect the same to be true in other countries (you should check the rules for the departure and transit countries involved).
If you put it in your carry on, the main issue will be whether it fits, in terms of size and weight, in your carry-on allowance. Carry-on allowances vary a lot based on airline, type of flight, class, status, and more, so I'll let you check the rules which apply in your case.
If you put it in checked baggage, the same applies (though the allowances are much larger). You should also make sure it is well packed and protected so it doesn't get damaged. There's also a minor risk of theft.
In both cases, if you carry it across borders, there may be customs issues. This depends a lot on the country you travel to, the value of the projector, whether it is new or used (and possibly how long), your status in the destination country (visitor, resident...) and whether this is a temporary import (during a visit) or not. Without all those details it's difficult to tell you anything specific.