Power is simply the amount of energy being delivered per second. It is a rate. You can store energy, but you cannot store a rate.
You can always connect a bunch of batteries in series to get more voltage, and for any given current flow, more voltage means more power. So, with a million 1.5-volt batteries in series, you get deliver 1.5 million volts. For a current flow of only 0.1 amps, you are delivering 150,000 watts.
The real issue with batteries are
1. How much energy can they store for their weight?
2. How quickly can they be charged?
3. How long can they maintain a charge while sitting unused?
4. What is their total efficiency (energy delivered divided by energy spent charging)?
Lithium ion batteries have efficiencies of around 99%, the best of any battery type. Nanotechnology may allow for batteries to be charged much more quickly than before, solving a second problem.