Tesla car battery has about 6000 li-ion batteries. Each rated 3.7 V and 3500 mAh.
I asume ten 1m2 solar panel, each gives 150 W at 12 V (this gives about 12.5 A). For this problem, I put them in parallel, so together they give 1500 W, 12 V and 125 A.
The li-ion batteries will be in 3s, so they will behave like 2000 batteries in parallel, each 3s group will have 12 V (aprox.), and 3500 mAh capacity.
The total capacity of the battery group is 2000 cells x 3500 mAh = 7 ∗ 10^6 mAh = 7000 Ah.
The time the solar array needs to charge the batteries is: 7000 Ah / 125 A= 56h of good sunlight.
In a sunny location, lets say that you have 8h of good sunlight per day, so 56h / 8h/day = 7 days to charge the battery.
Have I missed something important? This is not homework, just curiosity. I think the solar panels are not really used in parallel because taking 125 A from them seems like a bad idea (very hot and melts everything). What else?
Best Answer
You're about right
I've checked your numbers and it looks like you have done the calculation correctly. 150W per square meter is pretty good, most panels will be a bit worse than that, even pointed at the noon sun. I expect an average of 150W for 8h a day is a bit optimistic too. Here in the UK the average is about 10% of the rated output, so it would take about 20 days, not 7. With sun tracking panels and a sunnier climate, you'd do better, but 7 days would be impressive.
You haven't considered efficiency losses either. Some energy will be lost in transmission from the panels to the car (either becasue of the huge current flowing, or in the converters mentioned below) and in charging the batteries. Probably only 10-15%, so not worth worrying about if you're just getting a general estimate.
You might also choose not to charge the batteries at 12V/125A. That would require some very thick, heavy cables - probably 8-10mm diameter copper. Instead it might be better to connect the solar panels to a converter and step up to 100-200V, ac or dc, and convert back at the car. Since the car has a built-in converter for 120Vac input, it would make sense to use that.