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# Calculating an Off Grid System

Below calculations are based on internet advise and rules of thumb. We try to create a real life usable method to dimension a solar battery off grid system. We will check it against experts and until we do we can’t guarantee it is correct.

1. Power need

The calculations must start with how much power is needed. How much appliances need to run simultaneously drawing how much Watt for how long every day. Which loads are continuous and which are only part of the day.

How much Watt do appliances use?

Let’s say we have a mini-fridge that runs all day drawing 100 Watt. Then you have the use of lights at 50 Watt for four hours in the evening. Use of TV and laptop at combined 200 Watt for four hours as well. You also cook for 30 minutes using 1000 Watt cooling plate/microwave.

• Fridge =  100 Watt x 24 hours = 2.4 kWh
• Lights = 50 Watt x 8 hours = .4 kWh
• TV & Laptop = 200 Watt x 6 hours = 1.2 kWh
• Cooking = 1000 Watt x 0.7 hours = 0.7 kWh
• Total use if 4.7 kWh per 24 hours

Total you need to have stored 4.7 kWh ready to go. You also need to be able to loose 100 Watt every hour from when you stop charging and when you start charging again. Based on this load distribution we can determine the battery size.

2. Battery sizing

By putting the load in a spreadsheet and calculating the hourly use we can see that the ampere draw from the batteries peaks at six in the evening, when the lights are on, we have a fridge running and we cook. At that time we draw 54.16 Amperes at 12 volt. Because the normal current draw from a battery is about 10% of its size in Ah, we would need 540 Ah in batteries charged to 80% to do this comfortably. This 10% is caused by the fact batteries have lower actual capacities if the power draw is bigger. This is the so called Peukert law (named after a german scientist who discovered this). If you take 20 hours to discharge (5% amps) you get all of the charge, if you take 10 hours (like above at 10% amps) you get 78%, if you go faster this drops further to 40% if you discharge 1 one hour (100% amps).

This means we technically could design the system so the 54 amps are drawn from a battery that will just have the capacity to deliver it in one hour. If you do that 40% of capacity is available, so 40% = 54 Ah – > 100% = 135 Ah. But that assumes the battery is fully charged and you want to totally exhaust it. Batteries have to be oversized to take these and other effects into account. We could in theory choose two times the 135 Ah in size and be good, so 270 Ah, but the more we invest in battery capacity the longer the batteries last (a nicely commercial rule of thumb).

We also have a fridge that draws a constant 100 Watt. This is 8.3 amps, so trying to get a battery of 83 Ah would make sense. The battery however needs to be charged during the day which means it has be able to charge at a relatively high rate, a higher rate than the discharge rate. Charging has to be done at 10% of the Ah capacity of a (typical gel) battery, Lets say we take twice the 83 Ah we would need, then we have 166 Ah and can charge at 16.6 amps. But because of charging losses we need to do that for 14 hours! That is 10 for the battery and 40% more for charging losses. We don’t have 14 hours of sunlight, only about say 10 hours.  So in those 10 hours the max charging amps can not exceed 10% of the battery Ah, and the total charge must be at least 2.4 kWh (for 24 hours of fridge time) in the relevant season.

3. Panel sizing

The above shows there’s a complex interaction between battery capacity and solar panel size considering the max charging current and varying panel output. It would be nice if we could plot the panel output and charge state of the batteries over the course of 24 hours for different seasons. Add to that temperature effects on both solar panels and batteries. A way to simplify all of this is to take the max load on the batteries (54 amps) and take that as a battery capacity. Then size solar panels to charge it with max 54 amps (10% of battery capacity) and make sure the total 24 hour usage in kWh times 1.5 is delivered during daytime.

So the pack is sized for its peak use at 540 Ah. The panels must be sized to deliver the kWh times 1.5 at a minimum (so  in the lowest season). From the 24 hour spreadsheet we see the total kWh = 4.7 per 24 hours. 4.7 kWh times 1.5 is 7 kWh. Using a PV calculator we can size the system for the location to do that, deliver 7 kWh minimum. With a system of 1600 Wp we have more than 7 kWh delivered from march to september, the holiday season. This is for panels with an output of ~38 volt. This site gives you an idea how the output of panels varies. From the 1600 Wp size we can deduce that at its (theoretical) peak this means 1600 Watt output, divided by 38 is 42 amps (1200/38).

Solar system max amps = Wp /  Panel voltage

From the max 42 amps the panels deliver we can deduce we need at least 420 Ah in batteries. This is between the 135Ah and the 540Ah we got before. Sounds like we found a sweet spot here.

4. Charger selection

The solar charger must be able to handle the peak current of 42 amps. The more advanced the charger, the more you get out of your system and the longer the batteries will last.

5. Wiring

Wiring needs to be able to take the currents. 42 Amps is a lot of current, so wires need to be thick. Most people are used to high voltage AC that delivers power at lower currents (power is current times voltage). In a 12 Volt system the wires need to be thicker and as short as possible. For a list of wire diameters and ampere capacity look here.

So to recap our above system we have 420 Ah in batteries, 1600 Wp in solar panels and a solar charger that has a 40 amp output. Looking at a charger sizer calculator we can have 3 strings of 2 panels of 280 Wp totalling 1680 Wp. With a max 100 Volt / 50 Amp charger we have a viable configuration. But the 50 amps dictate a larger battery size. An available charger with lower amp output is 30 amps, which is to low. So we need to increase the battery pack to 500 Ah (or shop for other chargers). This configuration should be able to perform the set task.

We will look for a better way to estimate solar sizing as the above is not that satisfactory. Rule of thumb seems to be:

1. Peak amp usage x 10 -> min battery Ah
2. Total 24h kWh use x 1.5 for location dictates solar panel size
3. Charger chosen for max panel output in amps
4. String configuration (how panels are connected) adjusted to charger voltage needs

A good source of calculaors is Victron

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