How do I repair completely broken power armor if it is not already equipped to a suit of power armor?

Yes it is possible. The broken armor pieces have to be in your inventory, then you need to go to a power armor station (while not wearing the power armor) and go to craft mode (by pressing A on Xbox One, X on PS4, and E on PC)

Then you can see all the pieces you have in your inventory and you should be able to repair them by pressing Y / Triangle / T, no matter if they're completely or partially damaged.

Additionally to @WayneEra's answer:

When you let a companion wear Power Armor, it is possible that they'll automatically unequip broken pieces. When you see that, you'll need to trade with your companion to get the piece from their inventory into yours, so you can repair it.

Once the piece is repaired, you can give it back to your companion and they'll automatically add the repaired piece to their Power Armor frame, assuming they're still wearing it.