Traveling with portable power stations on an airplane is not an easy process. You might have to cross a few hurdles in order to carry them, based on where you live and the local airport rules. Most commercial airlines do not allow passengers to put any power supplies in their checked luggage. However, they do not enforce any limits or restrictions for the carry-on luggage that you can keep inside the cabin. However, you must be careful because there are some exceptions to the case.
Airport officials do not object to most portable power supply stations, but they might not let you keep a power supply which is too big and too heavy. Moreover, you might find it difficult for yourself to lug around bulky power stations. Even if you do manage to get them on the plane, you will not be able to fit them comfortably.