To keep the power armor running, players will need to keep stocking up on fusion cores and while it is not that difficult to locate them in the game, you might still want to pick up them if you happen to be in the area.
After completing the third quest of the game, you will be given a key to access the Kellogg House. Once you are at the house, you will need to locate the desk, crouch down and press the red button. You should be able to pick up four fusion cores here.
More fusion cores can be found at the Castle although you will first need to eliminate the aquatic opponents first. If you happen to be at Ford Hagen, head to the western edge of the commonwealth and you will find more in the generator room.
You will also find some at the Weston Water Treatment plant.