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To accumulate and reserve something for future use. The capacitor stores up potential energy in an electrical field that can be discharged very rapidly. We've been storing canned food and bottled water up ever since they made the announcement about the hurricane.
store something up
to build up and lay away a supply of something. The bears will store fat up for the long winter. They store up fat for the winter.
To accumulate and maintain a supply of something for future use: I recharged my phone battery to allow it to store up power for the long trip. Ants gather food all summer and store it up for the winter.