We had one installed in our last place, in Washington state. Should never have bought the place, but that's another story. Lots of rain, yard sloped towards the house, lots of power outages, etc.
The battery that came with ours was a very large, 12-volt thing (like a car or truck battery), that was supposedly kept at full charge by being plugged into the AC wall outlet, using an in-line rectifier/transformer. We had lengthy power outages, and the longest lasted more than a day. Judging by the depth of water in the basement, the battery didn't keep the pump running very long (we weren't living there anymore, and the place was vacant). Best guess was about 4 or 5 hours, cycling on and off every 10 minutes or so, before the battery died.
Best to have a standby generator handy, to plug the sump pump (and a few other essential things) into.