Hurricane Sandy has motivated me to buy a generator, but I don’t want to add another gasoline engine to my “fleet.” Instead, I’d like to develop a small PV system to provide some backup energy.
Here’s what I was thinking: A 12-volt system with a 100 amp-hour battery should yield 1,200 watt-hours of energy, excluding inefficiencies. If I charge that battery with a 400-watt solar-electric array, it would take three hours of sunshine (under perfect conditions) to charge the battery. Is my math correct?
Dan Kostenbader • via email
Your basic math is sound. We just need to get some facts about solar-electric modules and batteries to get the full picture. Then we can fine-tune your calculations to make them realistic and useful.
Solar-electric modules are rated under specific conditions—we could call them “perfect” conditions. Technically, it’s 1,000 watts per square meter of sunlight at 77°F. However, reality is much different, since modules rarely receive the full amount of sunshine for long, and most modules operate at temperatures greater than 77°F most of the time, which reduces their output. (PV modules perform better at low temperatures.) It’s fairly common to apply a factor on calculations to accommodate for the difference between “perfect” and reality for an off-grid, battery-based system, and to account for other system inefficiencies. System designers usually choose an efficiency factor/rating between 0.6 and 0.7. (Batteryless grid-tied systems are more efficient.)
For your “hours of sunshine,” be careful. There’s a technical term—a peak sun-hour—that is a measure of solar energy (1,000 watts per square meter, for an hour). Sun-hours at various sites around the country have been measured; you can find tables that tell you how many peak sun-hours a location near you gets. To help understand the concept of peak sun-hours, you could imagine that from noon to 1 p.m. on a sunny day, an array might receive 1 peak sun-hour. In the morning, when the sun is rising and at an oblique angle to the array, it might take three or more hours of partial sun to equal 1 peak sun-hour. Peak sun-hours take into account the local weather, but not your site’s specific shading, which is another factor you’ll need to consider.
The other key modification to make to your math is based on battery needs. While it’s possible to discharge flooded lead-acid batteries as deeply as 80% once in a while (if they can be recharged quickly), it’s better to not discharge below 50%. A battery bank’s size is often calculated on a 50% discharge—this means you need twice as much total battery capacity as you want to use. Some designers are even more conservative, and some batteries have different characteristics that might affect the calculation.
The key factor that you didn’t mention is your load—how many watt-hours do you need in your solar-electric backup system, and for how many days? Most RE system designers typically start with this figure, designing the system around your electrical energy needs. Let’s take the numbers you did supply to make a more realistic formula (see table).
Battery sizing will be more complex because you’ll have to decide how many days without sun you want to provide for. And you will want some surplus generation—it’s better to have too much than too little—though the exact ratio between generating capacity and battery capacity could be debated among designers until the cows come home. It is also important to realize other equipment will be required to make the system work, such as a charge controller to regulate battery charging and an inverter if you want to power any AC loads with this system, along with the other required balance-of-system (BOS) components (i.e. disconnects, overcurrent protection, battery box, etc.).
Ian Woofenden • Home Power senior editor