Go to Med Tek Research. Go into the lobby and open the door on the right hand side of the room. Found 4 Power Cores inside. Hell yeah...Power Armor here we go.......

Also if you start going off the beaten path and really start looking around the wooded areas, you will find random boxes and ammo boxes. I've found a ton of stuff today. I'm sitting on loads of ammo already and I've only completed a few missions.

So really look around the wooded areas......

I don't think the power cores are that rare. I've played 20 hours so far and I've got 13 now.

I have not played fallout in a while, but I just realized you had to equip any armor or weapons you give to the settlers. I at first thought all you had to do was just put it in their inventory. HAHHA ...And I found armor for the dog. Outstanding....

The more I play this, the more I want to tell Bethesda again...You did a great job on the console version.

Yeah there seems to be enough Cores not to ever worry about fuel.

I heard you can buy them from some merchants, have yet to see one in one's inventory, but I'm suspecting settlement merchants. I find a couple here and there...When I hit what looks to be a large town ruins, I go "Huh, which of these places has a generator I can yank the battery out of?"