# Sizing an Off-Grid Solar Power System

Some of the information in this post is broken down for those who may be reading this with little or no electrical knowledge. At some point, we all began at the beginning.

The mathematical equations used in the example below are the same regardless of how many watts you need to power. Simply insert your numbers into the same equations.

Note: w = watts, v = volts, a = amps, wh = watt hours, ah = Amp Hours

In order to build an efficient off-grid solar power system we first need to know how many watts of electricity we need to provide each day and for how long. The wattage of any given electronic device is usually found on the manufactures tag, if the watts are not listed on the device we can figure them if we know the voltage and amperage of the device.

Volts x Amps = Watts

In this example we need to supply 150w of electricity for 5 continuous hours each day.

What we need to know

• What size battery?
• How many watts of solar panel?
• How many amps for our solar charge controller?

Battery

The first equation we need to figure is how much battery power we’ll need to supply our 150w system for 5 hrs. For this we simply multiply our consumption (150w) by the hours of use (5 hrs).

150w x 5hr = 750wh

We need a battery that can supply 750wh for our load each day, but, this would be for continuous optimal weather conditions, so it’s important to figure for days of autonomy, or, days when the sun isn’t shining. A good estimate is 3 days of autonomy, or 3 days of backup power for days of reduced power from the solar array (solar panels). To figure this we multiply the watt hours by the 3 days.

750wh x 3 = 2250wh

2250wh is the total usable battery size for this system.

Understanding the difference in batteries

A 1000wh Lithium battery will deliver 1000wh.

However, the rule for a Lead Acid battery is 50% of discharge, this means we can only use half of the battery’s rated capacity. So, a lead acid battery rated for 1000wh is only good for 500wh.

Volts x Amps = Watts

12v x 100ah = 1200wh

A 12v 100ah lithium iron phosphate battery will deliver 1200wh, whereas the watt hour is cut in half with a lead acid battery.

1200wh x 2 = 2400wh

To fulfill our need of 2250wh (days of autonomy included) we need

2- 12v 100ah lithium iron phosphate batteries OR 4- 12v 100ah lead acid batteries

This will efficiently power a 150w system with 3 days of backup power.

Note: If you have 50ah batteries the quantity above will double.

If you live in a very sunny area you probably won’t need 3 days of backup power, in this case you could cut the battery requirements for this system in half. 1- 12v 100ah lithium battery or 2- 12v 100ah lead acid batteries.

Solar panels

To fully charge our 2400wh of battery power in one day we need to figure the size of our solar array.

On average in the U.S., we get 5 hours of straight sunshine per day, give or take considering your location. Knowing this makes the next equation very easy. We take our total watt hours of battery capacity and divide it by our hours of sunlight, in this case, 5.

2400wh divided by 5 hrs. of sun = 480w of solar array

It’s a good idea to up the wattage of the solar panels to ensure an efficient charge time. For this system I would go with a 600w solar array. Adding more solar panels will reduce battery charge time.

Solar Charge Controller

Now we have to figure what size Solar Charge Controller is needed to charge a 12v 2400wh battery with a 600w solar array.

To do this we take the size of our solar array, 600w, and divide it by the battery voltage. for this system we have either 2 lithium or 4 lead acid batteries wired in parallel, so, our voltage is still 12. This will give us the amps required for our solar charge controller to support our solar array at 12 volts.

Watts divided by volts = amps

600w divided by 12v = 50a

According to this we need a 50-amp solar charge controller to support this system, but, as with the solar array it’s best to make the solar charge control larger than necessary. I would go with a 60-amp solar charge controller for this system.

Summary

For this system to supply 150w of continuous power for 5 hrs. per day with 3 days of back-up power we will need

2- 12v 100ah lithium batteries OR 4- 12v 100ah lead acid batteries

600w solar array wired in parallel

60w solar charge controller

2500w Power Inverter (we have a 2400wh battery system so a 2500w inverter will work)

Important notes

On a sunny day this system will provide a lot of power, you could supply far more than 150w worth of electricity at any given time. For example, this would operate larger appliances for short periods of time for the reason that most all appliances operate at less than 2400w. However, if it’s cloudy we would have to reduce the load in order to reserve our 3 days of back-up power.

When designing a solar power system it’s best to over compensate with amp and watt ratings than to cut the system short. For example, we could use an 800w solar array with this system, we’d just have to get a 70a charge controller. 800w divided by 12v = 66.66a. The more wattage supplied by the solar array the faster the batteries will charge.