Note: this page is a walk-through for sizing an imaginary system. See this article for the Big Picture.
Words of wisdom: “It is cheaper and easier to use less power than it is to make more power.” – highdesertranger
This article will show the math required to estimate the size of off-grid solar setup required to run specified loads. To get a system that meets our needs we will have to be thorough and honest with ourselves about:
This part is the least fun and the most important; we must account for every watt we intend to “spend” off-grid. Some people prefer pencil-and-paper, but doing the work on a spreadsheet (M$ Excel, freeware LibreOffice Calc, or free-to-use Google Docs) can make the work easier and more organized. You can also rapidly alter it to model new build ideas.
The goal is to come up with a daily target in watt-hours (Wh). There will be times we have to work in other units but Wh is the main thing.1) Watt-hours are calculated by multiplying the load's draw in watts by the hours it is expected to run. If we run a 4w device for 6 hours that is 24Wh (4W x 6h = 24Wh).
The power the device consumes will be printed on the device, the label, or the power adapter. If it's in watts we can use them directly. If it's listed in Amps (A) we will multiply the voltage (12vdc or 120vac, for example) times the Amps to get watts.
120vac x 2A = 240W.
12vdc x 2A = 24w.
Note: the loads below are silly. I am doing this on purpose so you will tabulate all your own loads and not on the example loads or resulting numbers.
We write down all our DC loads and the hours we expect to run them each day:
|12v coffee roaster||400||.25||100|
We will require 357Wh every day to run these items.
This starts out similar
|electric hot dog cooker||500||.25||125|
so 1,075Wh, it appears.
But running household appliances2) off solar3) will incur inverter losses. We will stipulate the inverter is 90% efficient. If you know the actual efficiency of your inverter use that instead. If the inverter does not publish an efficiency rating it might be as low as 80%.
To get the adjust number we divide the Wh by the inverter efficiency: 1,075Wh / 0.904) = 1,194Wh.
The devices above are presumed to draw their rated wattage while we use them: W x H = Wh.
Some devices, however, do not run all the time.5) Examples might be refrigerating devices6) that hold goods at 40F or something. If we had soda can vending machine rated at 60w but it only actually runs the compressor 1/3rd of the time7) it will be turned on 24hrs/day but only draw 480Wh 8) instead of 1,440Wh.
Our soda machine runs on 120vac so will incur inverter losses: 480Wh / .90 = 533Wh.
We will need 2,084Wh every day to run our intended loads.
You may find it useful to make day/night sections for both AC and DC. This will yield more accurate numbers if you run many of your loads in daylight instead of at night. It could save you from oversizing your battery bank.
Note that very big loads may require bigger banks to get the current throughput required. If you have a 120A load but the lithium is only rated to 100A discharge you will need ≥120Ah capacity regardless how small your actual Wh use is.
Most batteries do not charge 100% efficiently, so it may take more than 2,084Wh of solar harvest to get 2,084Wh that we can actually pull from the battery bank.
Finally we get to size something! We will divide the daily power requirement by the maximum depth of discharge preferable for each battery chemistry to get required battery capacity in Wh. Deep cycle batteries are traditionally rated in Ah (amp-hours), so we will divide Wh capacity by the battery chemistry's nominal voltage. See below.
Lead is typically discharged to 50% DoD as a good balance between performance and longevity.
2,084Wh / 0.50 DoD = 4,168Wh
4,168Wh / 12.0v nominal voltage = 347Ah of lead-chemistry required.
Also see the section on minimum charging current below.
Lithium is typically discharged to 80% DoD as a good balance between performance and longevity.
2,084Wh / 0.80 DoD = 2,605Wh
2,605Wh / 12.8v nominal voltage = 204Ah of lithium required.
Reminder: we need to harvest 2,316Wh every day to recharge our stipulated AGM bank.
Solar harvest directly affects how much panel we will need, but harvest will vary wildly depending on conditions, type of solar charge controller, time of year, location, even ambient temperatures and altitude.
The good news is that different locations get roughly predictable average amounts of sunlight during specified months, and scientists have tabulated this data. The data is expressed in terms of hours of Full Sun Equivalent and assumes flat-mounted panels. You can think of this as “hours of laboratory-perfect conditions”. The actual number of hours of sunlight in the day don't matter, nor do the average climatological conditions. 4 hours of FSE in Phoenix in summer might be 6.5 hours by the clock, while the same 4 hours of FSE in Anchorage might be 14 hours by the clock. No matter. The math works.
The actual hours of FSE will depend on where we are and month of the year. If we want the solar to Just Work10) we have to size it for the worst average yield we will experience. Let's consider these very different scenarios:
We can look up average FSE for these locations and times in charts like this.
We can work backward from FSE and required Wh to get our required panel: Wh required / hours of FSE / system efficiency11) = panel wattage required. Assuming an MPPT-equipped system:
PWM controllers are often sized thusly: rated panel wattage / 10 = charge controller rating in Amps.
Example: 400w / 10 = 40A PWM controller. They are inexpensive enough that a bit of oversize is no big deal.
MPPT controllers are more expensive so they often sized to the average solar harvest wattage rather than rated panel wattage. A rule of thumb might be rated panel wattage x system efficiency / nominal battery bank voltage.
Example: 423w15) x 0.85 / 12.0v lead battery = 29.96A controller, rounded to 30A.
Note: if your offgrid system will use lead-chemistry batteries and needs to last for years then read this section. If you are a weekend camper, use lithium, or only plan to keep the rig a couple years this section will not apply.
Lead-chemistry batteries have minimum and maximum charging current specifications. Going over the max is rarely a concern with solar-only charging but failure to meet minimums is a real issue.
Lead acid battteries typically require a minimum of C/10 charging current regularly to stay healthy. This would be 34.7A for a 347Ah AGM bank (347 / 10 = 34.7).16) Note that even our strong Montana numbers above only hit ~30A. We could:
Lithium batteries do not have a minimum charging current spec in the normal sense.
You may want to be sitting down for this.
The numbers above are for a single “day of autonomy”. In other words, we will fully charge the battery bank then get one day's use from it.
But what happens if we can't fully charge every day? Consider these situations:
In those cases we'd need to multiply the battery capacity and solar wattage by the days of autonomy we need. For two days of autonomy that 347Ah of AGM is now 694Ah, the 423w of panel in Montana in July just turned into 846W of panel, and the 30A MPPT is now 60A.
Holy crap, do people really do this?
In practice, there are factors that work in our favor.
Powering your off-grid life with solar is possible, but it does require a realistic assessment of your specfic needs and and understanding of how to meet them. You can often decrease panel requirements by augmenting with other charging sources or reducing your power consumption. Remember,
“It is cheaper and easier to use less power than it is to make more power.” – highdesertranger (R.I.P.)