 # Solar Off-Grid System: Basic Calculation

In this installment of “Going Off-Grid with Solar” we are going to learn how to size our off-grid system’s PV array & battery bank size using a fictitious example to show how to calculate your own system.

This will not be too granular in detail to keep it very simple and easy to replicate for your own needs. Some simple calculations and you’re well on your way to determining just how much PV you will need as well as how much storage is going to be needed. So, let’s just dive in.

Rule of Thumb: PV array should be 120% of the daily load to sun-hour ratio, for the highest month ratio. The PV array DC kW rating should be no less than 40% of daily AC kW load in areas of Midwest and Southern U.S. around 30% for the Southwest U.S. and about 50% in the rest of U.S.

Example:

Average daily load – 3.2 kWh

Average daily sun-hours – 3.4 (Seattle, WA)

System size:

 Stored Battery energy (4 x daily usages) = 4 x 3.2 = 12.8 kWh Inverter KW (100% of instantaneous load 50% of daily requirement) = 1.6 kW PV array (no less than 50% of daily AC kWh load) = 1.6 kW Generator (2 x the inverter rating) = 3.2 kW

The very first thing that we want to evaluate are the loads that we wish to run off of our off-grid system. This can be a challenge because it is here that we discover just how much energy our appliances, lighting and our gadgets consume. It can be a tough pill to swallow that we have to be a little bit more energy conscious and maybe let go of some of our creature comforts in order to minimize the PV and battery requirement of our off-grid home.

With that in mind, let’s continue on with a made up off-grid system to learn how to calculate the weekly AC load. In this example, I want to include some lighting, a couple of ceiling fans, a fridge, TV, microwave, coffee pot and a toaster. These are my must have loads. I cannot live without my coffee pot!

I tally up the wattage that each of these loads draw:

 Lighting (CFL’s) = 98 Watts / 6 hours per day Ceiling Fans = 128 Watts / 8 hours per day TV = 125 Watts / 3 hours per day Microwave = 1,100 Watts / 6 minutes per day Coffee Pot = 700 Watts / 6 minutes per day (Keurig mini) Toaster = 1,1000 Watts / 6 minutes per day Total = 3,277 Watt-hours / day = 3,277 x 7 22,939 Watt-hours / week

At this point you want to multiply the wattage of each by the runtime and days per week that those appliances run. I determined that I use all of these every day and came up with a total of 22,939 Watt-hours per week. I want to add a little bit of padding to this to account for AC efficiency so I wanted to add an extra 25% to this number for a total of 28,673.75 Wh/week or 28.67kWh/week. (remember 120%).

Now that we know what the weekly AC load is going to be we can determine just how much PV is going to be needed to supply this off-grid system. The next step is to calculate the daily PV requirement. Now we know that we have 28,673.75 Wh/week. Divide this number by 7 days to get 4096.25 Wh/day or 4kWh/day.

28,673.75/7 = 4096.25

=> 4.096kWh/day

Then we can divide this value by the systems voltage. This could be 12, 24 or 48 volts. I’m going to use 48V as this systems voltage. So, I would need to divide 4,096.25 Wh/day by 48V to determine the daily Amp hour requirement of the system. This turns out to be 85.34Ah.

4096.25/48 = 85.34Ah/day

Knowing that our requirement is going to be 85.34Ah we divide this by the total average annual sun hours for the area. In this example, we consult a solar irradiance map to obtain the area’s sun hour value. Ours is going to be 3.4 hours (Seattle, WA). To get the array’s current requirement we divide 85.34Ah/3.4hrs.

#### PV (Solar) Sizing

Ah to A – 85.34/3.4 = 25.1A

The array must be 25.1A or greater.

The next step in calculating the PV array size is to select a module and find its ampere rating in the data sheet. I selected one with an ampere rating of 8.63 Isc and a voltage rating of 36.8 Voc. The next step in calculating our array size is to determine how many parallel modules will be required. Divide the array’s amperage requirement of 25.1 by the modules ampere rating. We come up with 3 modules or string in parallel.

# of String (modules) – 25.1/8.63 = 2.90 => 3.0

Next, we want to figure out how many series connected modules we will need. Divide the system voltage (48V) by the module’s voltage (36.8V). This will not be a whole number, but don’t fret just yet. We calculated that we need 1.43 series connected modules, rounding up to 2 modules per string in series. To calculate how many modules for the array we multiply the number in parallel by the number in series.

In our example will be using 6 modules (roughly 1.5kW system), total to complete the array, three parallel string with two modules in series.

#### Inverter Sizing

Inverter kW rating should be 100% of instantaneous load, if the instantaneous load is unknown, use 50% of daily load, which is our case 1600W or 1.6 kW.

#### Charge Controller Sizing

A charge controller rated at 30A connected to a battery bank operating at 54V (48V nominal) limits the charge controller capacity to 1620W.

• The PV array size is limited to the charge controller capacity
• e.g. A 1500watt PV array to this model charge controller would require 1ea. 30A charge controller
• 1500/1620 = .925 round up to ONE 30A charge controller

#### Battery Bank Sizing

Deep Cycling Lead Acid Batteries: These deep cycle batteries are designed to be deep cycled to 80% of their capacity without damage to the battery.

Repeated deep cycling will shorten the life of the battery. Leaving the battery in a discharged state will cause sulfates to grow in the positive plate and shorten the life of the battery (it is recommended to install generator in addition to PV for any off-grid system).

• It is best for battery to recover to full state of charge 100% SOC within 24 hours.
• It is common for batteries to vary between 1 to 4 days because of occasional cloudy and rainy weather; 40% to 80% DOD occurs during these periods.
• Manufacturers recommend a 20% average depth of discharge DOD.
• A range of 10% to 30% is acceptable
• 40% to 50% is acceptable if recovery is always made within 24 hours
• AGM (glass mate) batteries can be discharge up to 80% DOD.

Design Parameters:

• Average DOD and series-parallel connections
• Average daily load kWhs / DOD (30%) X load fraction (80%) = battery bank capacity kWhs
• The load fraction (% drawn from the battery during non-solar hours) is about 80%
• Battery banks should not have more than 3 parallel strings.
• Battery bank capacity (watts) / battery bank voltage = battery amp-hours
• Battery bank amp-hours / 2 = amp-hour for two parallel strings

Example:

• A 48V battery system using 12V, 350 amp-hr lead acid batteries
• # of batteries in series 48v/12 = 4 batteries
• Battery capacity (watts) = 48V X 350Ah = 16,800W or 16.8kW

We now know what our AC load requirement and subsequently what the PV array size will need to be, so we are now down to the last piece of the puzzle. To determine the size of your off-grid system’s battery bank you want to take the Daily amp hour requirement (85.34Ah/day) and multiply this by the total number of autonomous days that you want your system to have. Please note that the more autonomous days you want to have, the larger the battery bank is going to become. Batteries are the most expensive component of many off-grid projects.

For the area in this example I determined that I will need to have 4 days of autonomy, which is also rule of thumb. This would account for a few consecutive cloudy days and the system would still function without PV charging the battery bank. Our new daily amp hour requirement is now calculated to be 342Ah.

Autonomy Calculation = 4 days battery bank x 85.34Ah = 342Ah

I selected from a list of available batteries a 12V – 340Ah AGM battery. With this in mind, I can calculate the total number of batteries that will be required in this system. First, we need to decided how far down the battery will be drawn. Typically, you never want to exceed 50%. This can impact how long the life of the battery bank will be. I would urge to sway in the way of safety. In this system, I’m only going to draw them down to 30% capacity.

The calculation for this is to take the new total amp hour requirement of 342 and divide that by 30% and multiply by .80 (load fraction).

342/0.30X.80 = 912Ah

We come up with 912Ah of required capacity for the system. To find the number of parallel batteries we need to have we divide 912Ah by the capacity of the battery selected (340Ah). This calculation also does not come out to be a whole number. We round to the next whole number and come up with 4 parallel batteries.

912/340 = 3 battery strings in parallel

Now we want to know how many series connected batteries we will need. This is the easiest calculation by far. Take the system voltage (48V) and divide by the nominal battery voltage (12V) to come up with 4 series batteries for a total of 12 batteries for the entire system.

12Vx4 = 48V => 4 batteries in series = total of 12 batteries

#### Generator Sizing

Generator are required for stand-alone systems and should be sized for the full instantaneous load plus battery charging rate or 2x the inverter rating or 3.2kW generator.

Congrats! You have now calculated your first off-grid system. These are more granulated calculations that come later, but this will get you on the ground and running. With these basic calculation, you can easily adjust your system’s equipment by swapping out the batteries and modules to see which favor your system best.