The Premise

Jonah's apartment complex has a garden, that is very popular into the evenings. It's currently lit by running an extension cord from one apartment out to the garden, but this is less than perfect. Jonah has an inkle to figure out if it can be cheaply lit by a small solar panel and a trickle-charged battery.

I'm thinking of using some 3 watt LED christmas lights, probably 6 strands to light the garden well enough to feel cozy. I don't have much experience with this stuff, but I've been reading around, and here's the math that I've come up with:

6 x (3 watts) = 18 watts with lights on

Let's say I want to leave the lights on for 4 hours.

18 watts x 4 hours = 72 watt hours of energy needed.

Ok, so how big a battery do I need for that sort of thing? Well, batteries are fairly complicated. Batteries are rated in amp-hours (number of amps times number of hours at that level).

Ok, so how many amps do I expect to draw with the lights on?

18 watts / 12 volts = 1.5 amps

Ok, so if I want to keep the lights on for 4 hours, I'll need 6 amp-hours of battery power. Great! Now I know how much battery I need. Now, what battery technology to use?

Picking a Battery Technology

I've checked out a few:

Best options:

• Gel or AGM "Deep Cycle" Lead Acid battery - smallest ones would be large enough for me. somewhat expensive. Some special disposal requirements, but not that harsh on the environment. Requires charge-management hardware.
• NiMH - available in the sizes I want, no memory effect, no special disposable requirements, pretty cheap. Solar charging would need to be evaluated. Requires charge-management hardware.

Other, worse options:

• NiCad - worse than NiMH in many ways: has memory effect, needs special disposal.
• Alkaline - only 10-15 recharge cycles! Ouch.
• Traditional lead-acid battery: needs quite a bit of maintenance, including electrolyte level checks every few months, and per-battery charge testing. Too much overhead.

Gel or AGM Deep Cycle Lead Acid Batteries

Lead-acid batteries have been around for a long long time. They are seemingly the only batteries used for marine and RV 12V power systems, and every solar system that I found relied on them. Lead-acid batteries used to require a significant investment in maintenance. They needed to be monitored regularly for electrolyte concentration (called specific gravity), as they evaporate some of the water in their fluids during charging. The newest generation of lead-acid batteries are being touted as "maintenance free", as they're fully sealed, and recover the vaporized water themselves. They still are pretty finicky about treatment, however.

Hm. Well, since most lead-acid batteries are rated over a 20 hr discharge, it would be nice to know how that corresponds to a 4-5 hour discharge. Faster discharge of a lead-acid battery causes it to output less energy. This is called the Peukert Effect, which is seemingly key to figuring out how much battery you need. The Peukert Number generally is in a range of 1.05 to 1.4, with 1.05 the best performing battery due to less internal resistance. This Page has more info, and here's a Peukert's number calculator.

Ok, so looking around on the web, I found a battery company called US Battery, which publishes specs on its batteries' performance as they're discharged at varying rates. This seems pretty useful to me.

Another note that I found about lead-acid batteries: you don't want to discharge even the "deep cycle" ones below about 50%, or you risk getting sulfurous crystal buildup on the electrodes, eroding the capacity.

Ok, so my application is fairly low power, so let's look at their smallest battery, the U1-HC. When discharged over 20 hours, it discharges 35 amp-hours of energy. That is an average current of 1.75 amps of the course of the discharge. Since I only need 1.5 amps, it seems like this battery, at least, would work. That sort of begs the question, how many lights could that battery power over a 4 hour average discharge? Well, we don't want to be taking our battery below 50% capacity, so let's take the specs for an 8 hour discharge, and we'll only use 4 of that. An 8 hour discharge gives me 30 amp-hours of energy, which gives an average current of 3.75 amps. That's enough to more than double my load! That's pretty exciting.

NiMH batteries

NiMH batteries are another exciting technology. They have no special disposal considerations, and many companies will even recycle them. They can be discharged 100s of times, have no memory effect, and are pretty cheap!

Form-factor: these guys come in the traditional AA, AAA, C & D cell batteries. The beefiest D-cell I saw in a quick survey was rated at 12 amp-hours! That's quite a battery! Ok, but seriously, all of those standard battery sizes are 1.2V per cell, meaning that I'd need to chain 10 of them together in series to make a 12V system to power my lights. When you put batteries in series, the voltages add, and the current averages, so I'd need 10 batteries each capable of more than 6 amp-hours of discharge. Seems like 10 D cell NiMH batteries with adequate capacity could be had for <$60, here, for example.

Uh oh! NiMH can't really be trickle-charged, according to this site and many others... Given that correct NiMH charging takes some serious hardware, and the telling lack of solar NiMH charge controllers, I'm going to abandon my NiMH search here, and turn back to the tried-and-true lead-acid battery.

basic lead-acid solar setup

According to http://www.solar4power.com/solar-power-basics.html:

For cheapness, I'm considering skipping the inverter part of this setup, and using 12V DC light strings of some kind. Those could get connected straight to the battery, with a switch (or better, a timer) to turn them on. Inverters also drain some of the efficiency of the system, so staying at 12V would be beneficial there, too.

Ok, so let's get some hardware!

• Here's a 18 amp-hour AGM lead-acid battery, which would give me adequate power over the 4 hour range. Bought for $22 (including shipping) on ebay.
• Here's a 12V charge controller with LVD. The LVD part stands for low voltage disconnect, which means that the charge controller monitors your battery state and will disconnect the lights from the battery if the battery gets dangerously low on charge. This has a degree of foolproofness that I think is nice. Rated at 6 amps * 12 V = 72W. Wiring code requires that solar charge controllers be rated for 25% above max wattage of the connected panels, so I can connect up to 60W of panels to this controller.

Solar Array Sizing

So, how many watts of solar do I really need? According to "Living On 12 Volts", a book I borrowed from Drew, "Charging a battery requires that you put 10-15% more Amp-hours in that you took out."

Let's go for the worst-case 15% loss in the charging process. That means that I need to put back 72W*1.15 = 82.8W of solar to charge back up the 72 W of power that my lights will consume. I have 5-6 hours of useful direct sunlight, so that's 14-16W of solar capacity to recharge my lights in 1 good day. If I'm willing to wait 2 days after a full discharge, I could half that.

--- a work in progress ---

comments from Soren

1. you can play with your amps and volts as much as you want by putting batteries or battery elements inline or in parallel
2. It's super-cool that you can buy 12v xmas lights, but my 120v lights were in series at ~2v/bulb so rewiring should be easy.
3. I have a couple strands of white LED xmas lights I got for $6 at Longs last season ... you're welcome to borrow/chop them. :)
4. PV Panels
5. rather than batteries, you might want to pump water uphill ... quick, what's 72 watt-hours in \"pound-feet\"? ... 10 tons of water across Jonah's 10-foot drop ... or is google wrong?
6. Stuart likes PVWatts for calculating how much solar you need. My (uninformed) rule of thumb has been that you get about 6 hours/day of optimal sunlight ... so if you want 72 Wh, you need 12W of solar. Unfortunately, PV Panels suggests a cost of roughly $120 ... :?
7. David B has completed and described a similar project.

--- notes for further explanation ---

DC conversion for 110V LED light strings

Froogle search for '12V light string'

a great article on the same premise. Glad to see that he's reached the same conclusions about many things. He's bought a battery for 15 hours of 13W burn, so my requirements are a bit smaller, thus the smaller battery.

(This is a work-in-progress, a blog of some sorts, I suppose)