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.
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.
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 3 hours = .15 kWh
- TV & Laptop = 200 Watt x 4 hours = .8 kWh
- Cooking = 1000 Watt x 0.5 hours = 0.5 kWh
Total you need to have stored 3.9 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).
3. Panel sizing
4. Charger selection
The energy in a 100 Ah 12 Volt battery is 100 x 12 = 1.200 Wh = 1.2 kWh
With the sometimes intermittend nature of dirty grid energy and the option to power one’s own electric vehicle the interest in electricity storage has grown. The use of electricity is usually overestimated, most people use about 10 kWh per day. Here we will explain how one calculates a solar storage system for this energy need.
The system needs to be able to deliver 10 kWh. The speed at which we want to use that 10kWh is also important, because a battery can only output so much current or its capacity will seem to go down. If you want to power a 1000 Wat heater for an hour (which with 10 kWh storage you could theoretically do for an hour), you draw 83 amps from the batteries. A rule of thumb is to not draw more than the Ah in amps. So if your battery is 40 Ah you can draw 40 Amps for an hour, so for a 1000 Wat heater you need 2,5 40 Ah batteries. Theoretically they will then run for an hour, but in reality we need to divide it by 2, so we get 5 40Ah batteries to safely deliver 1000 Watt for one hour. Take that 3 times and it seems we are fit for any normal usage. 15 40 Ah batteries, or 6 100 Ah batteries. Let’s assume that.
For charging we use solar panels. They need to charge the batteries to full capacity over de course of a day. This means that in the location the panels are mounted the sun must deliver the required energy to do that. We can pick a place in the South of France to make the calculation, let’s sat Cannes.
Battery capacity must be increased to ensure enough power output
First we need to calculate our required solar power, then we can see how many panels we need to reach that output (in kWh) in the chosen location. We have 600 Ah and as a rule of thumb we can charge them at a maximum of 10% in Amperes so that is 60 amps. At this rate it would take 10 hours to charge in an ideal world. Charging is inefficient however and the rule of thumb is it takes 40% more time. So not 10 but 14 hours. A day doesn’t have 14 hours so the battery pack must grow to ensure it can be charged with the daily output.
Battery pack size must also be increased to insure enough charging can take place in the time available.
If we double the pack size we have a 1200 Ah battery setup that can be charged to a full 600 Ah capacity in 7 hours. We’re talking 120 Amps max charging current now. A rule of thumb to dimension the panels is to take 1.5 times the load, so the batteries can charge even when the batteries are used. for 1500 Watt at 12 volt the need is for 15 12 volt 100 Wp panels. The total output of 15 100 Wp panels in Cannes is more than 5 kWh per day from april to october. The panels deliver plenty of power, and the batteries can top themselves up every day.
So this system has 12 100 Ah batteries and 15 100 Wp panels. We think it is has more capacity than we need. We are looking for a better estimate.
A commercial example
A website that sells solar battery systems seems to take a simple rule of thumb : It starts with the battery, so a 400 Ah one (2 times 200Ah), then it tries to secure the max charging current at about 10% of the 400 Ah, so about 40 amps. A bit less is produced by four 100 Wp 12 Volt panels (400/12 = 33 Amps) at maximum insolation. Lastlyth the charging controller is chosen to charge at 40 Amps. This then creates 4800 Wh of ‘autonomy’ whatever that means.
In our location the 400 Wp panels would generate max 2 kWh a day, which is 0.005 times more than the 400 Ah of the batteries. To turn this around, if you have 1500 Wp installed you generate 8 kWh at the peak of the summer, and charge 1600 Ah batteries. 1600 Ah batteries store 19.2 kWh so they would be charged halfway if there where no losses.
From 19.3 kWh in a fully charged battery you can use 9.6 kWh without problem. Then you need to recharge it and getting the last 20 percent of charge is the hardest. So you want to be between 40% and 80%
To be revised and continued..