Sturdy is the word and cheap sweatshop crap don't cut it. Period.
Best panniers, IMO and IME, is Arkel. Period.
They're over-Designed, use quality material, are impeccably crafted and real-life tested in Quebec. Guaranteed for life. (except zippers)
http://www.arkel-od.com/
I've owned and used their LadyBug pannier/backpack for over eight years and still consider it the best accessory I've ever bought. (that and the Xtracycle)
A less expensive option would be something canvas from the surplus store. Get two of them. They can be customised, altered and repaired with a stitching awl and some rivets. You can even make them deluxe with the addition of fancy hook sets some manufacturers sell as replacement parts.
If you'd prefer something rigid there's the "Oyster Bucket" concept that can be adopted to most any size plastic container. Locking tool boxes are easy.
http://www.cobbworks.com/
In any case, if the panniers are only intended to carry batteries, look at front panniers. They're generally smaller and can be mounted on rear racks too. You'll probably want to upgrade the shockcord if the design incorporates it.
These canvas things were purchased ~1970. They've seen several self-supported bike tours as well as urban utility service carrying groceries, gardening stuff, carpentry and mechanics tools.

With the batteries inside it looks bad with a strap over each shoulder and a pack front and back but it would be the best way to carry it and leave your hands free. Having the batteries in the panniers means I don't have to carry a back pack to tote batteries if I'm leaving the bike unattended.
The batteries were originally carried in the Xtracycle's FreeLoaders but slid around, chafed the nylon and bumped against the FreeRadical's tubing members. The FreeLoaders are good at collecting water too. The old canvas panniers hadn't been used since I got the Xtracycle. Sometime after I'd gotten the batteries they jumped off the closet shelf as a solution that resolved those issues. As a bonus, the bike handles better with the weight carried slightly higher than it was.