You're on the right track of thinking ahead about what you should do and/or buy. The first thought that comes to mind is you should ask your Insurance Company for 'leads' on mfgrs. that make pumps w/backup units. Secondly, visit any Plumbing Supply House (in the YELLOW PAGES under PLUMBING - SUPPLIES) to see what they suggest. THEN, visit the Home Centers and look at what's on the shelf.
Unfortunately, 2 'factors' will drive your decision. 1) You will need more than a retro-fitted system. Either buy a system that's 'originally constructed' with AC/DC capabilities, or buy a SEPARATE battery-operated pump that's ONLY DC operated. Retrofitting a unit is not the best way to go. 2) You'll need to determine the best you can as to how MUCH water you're pumping in a worst-case scenario as well as how HIGH you're pumping it. Units are sold based on certain amounts of water flow through them.
Now, I have to ask - Where is all this water coming from??? Is the water re-entering the pit AFTER it's pumped out??? If so, you need to come up w/a better plan to divert the water AWAY from the foundation, and the pit. Are your gutters and downspouts dumping the water right at the base of the foundation? Here, too, you need to extend your downspouts and get the water AWAY from the foundation. Are you missing gutters, or do they leak, or does the water run over/under them? Bottom line here - Have them installed, replaced, or repaired. And lastly, is the landscaping around the foundation sloping the WRONG way? If so, fix the landscaping so that it's sloping AWAY from the foundation at least a distance of 3' from the foundation. Again, water will run back towards the foundation if the sloping is flat or improper.
95% of the causes of water in the basement is from all of the aforementioned sources. RARELY is it due to a 'rising or underground stream'. Drainage needs to be corrected or added (where it's wrong or missing.) The next time it rains, don your raincoat, boots, and an umbrella (watching out for lightening), and do a THOROUGH inspection of the landscape, gutters, and downspouts. Look UP and down; not just down. Watch where the water is going. If water is running off of a roof line that has no gutter or behind a gutter or OVER a gutter, or water is running out a downspout and back to the foundation, you have some work to do. It is all VERY inexpensive. If you still need that backup sump pump, you can do as I suggested. I don't own one but Home Depot sells one called the Basement Watchdog. It is an AC/DC unit. Again, read the specs to see if it will serve your purposes.