This worked out great for our kitchen as an easy and inexpensive solution - the materials are cheap, and you don't need to dig around your walls to find an electrical connection. The LED strips put out a good amount of light and the batteries provide full power for several hours of continuous use. The strips are easily cut to fit any length of cabinet. I installed three sets in a weekend.
The idea of using 9V batteries and LED strips has a lot of potential uses...anywhere you want LED light but can't tie into a permanent electric source or would rather not deal with a transformer.
Step 1: Materials
12V LED ribbon lighting with adhesive back
These are sold as a continuous strip of lights on a reel. Every couple of inches has 3 LEDs and a board, you can cut them to length at marked spots between these repeating units. I bought mine on Amazon, they were ~$15 for 16 feet. I installed a double row of LEDs to increase the light output (4' of counter used 8' of lights). The color temperature of the ones I used is 3100 Kelvin - they are on the cool side - not like the older blue LEDs, but closer to fluorescent than incandescent.
9V (Actually 9.6V) rechargeable battery
The light strips are intended for 12V, but a 9V battery supplies sufficient current. Be aware that most recahrgeable 9V batteries are actually 7-8V, which may not be enough power. I used 9.6V versions which are a little more expensive, but still readily available online for ~$10.
Plenty of options at local electronics store.
Pretty simple, each has lead wires and connections for the battery terminals
2. Misc. soldering equipment and supplies (25W soldering iron, solder, wire, snips, helping hands, heat shrink tubing)
3. Installation hardware
All of this is specific to my existing cabinets.
Junction box extender
Plastic cover plate
9V Battery holder
Wood screws and washers
2"x1/4" PVC trim
My cabinets were rough on the bottom, I didn't think the lights would stick very well. I used this PVC product because I was confident the lights would adhere, and I could then attach it to the underside of the cabinet.
Step 2: Assemble Electronics
Working with the LED strips is pretty straightforward. A line is marked every 1.5" or so where they should be cut. This lets you fit the strips to your specific installation. I wanted two rows of lights under each cabinet, so I cut two strips, two small lengths of wire to conect them (long enough to make a 180 degree turn), and a longer wire to connect the lights to the switch and battery.
Solder LED Strips
To solder the LEDs, place a dollop of solder on each of the contacts on one end. Each reel comes with wire on both ends, so each reel has a couple pieces already set up for you. The connecting wires should be pre-tinned as well. Connect multiple strips together, positive to positive, by melting the drop of solder and attaching the wire end.
Solder switch and battery connector
The next step is to connect the switch to the battery holder and spare wire. The free ends of the connector and wire will be attached to the light strips.
Put it all together
Polarity matters for LEDs , so be sure to keep that in mind as you work. Its a good idea to test periodically so you know everything is going together properly. The last picture shows the whole assembly soldered together before I finished the shrink tubing. Note that the last end of the LED strip will be free.
Step 3: Install to Cabinets
This did take me a few tries to get right, I feel like there is a simpler solution but this one ended up working very well. It feels solid and looks clean.
Cut JB Mats
I used a hacksaw to cut one side off the JB extender. I then drilled two holes in the long side, and one in the short side that would rest against the cabinet overhang. I used a dremel to cut a circular hole in the cover plate.
Drill a hole in the bottom of the cabinet for the battery connector, and install a clip behind the jamb. The clip isn't necessary, but gives the battery a place to sit when it's all put together.
Install JB extender
When I was planning this out I didn't account for the coverplate being wider than the box extender; this was a problem because I expected to screw the sides of the box extender directly to the cabinet skirt. I ended up hot gluing a couple shims to each side of the extender so that the whole assembly would rest tight against the cabinets when attached. I predrilled into the cabinet skirt and attached the extender with wood screws - be very careful not to go all the way through! The third screw, in the short side of the extender, was necessary, without it the switch and cover plate would have too much movement.
Thread the light/switch assembly through the cover plate and plastic nut that comes with the switch. This has to be done before you attach the LED strips. Tighten the nut to hold the switch to the plate, push the battery connector through the hole in the bottom of the cabinet, and screw the cover plate to the battery extender.
Stick LED strip to PVC
Once the box assembly, switch, and lights have been tied to the cabinets it's time to stick the lights in place. If the underside of your cabinets is smooth then you might be able to stick the tape directly to them. Mine were rough, so first I stuck the light strips to a piece of PVC. Starting near the switch/box peel a few inches at a time and press firmly to the edge of the PVC. I worked all the way down one side, made the turn and came back. Leave extra room between the parallel strips to fasten to the underside of the cabinets.
The trim is held in place with a few wood screws and washers. Predrill the PVC for each screw. Holding the strip in place underneath the cabinet, predrill into the bottom face. Be very careful not to drill through the bottom of the cabinet, use a very small screw and more than one washer if necessary to keep the tip of the screw from poking through. The PVC and lights don't weigh much at all, so attach at a few spots and use the smallest screw that will hold to the cabinets.
It has been a few weeks, these are working well. We use the longest strip, ~4'-6" long most often, and the battery seems to last 5 days or so on a charge.