How much time needs a 1.5 kW solar panel to charge a car electric battery?

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?

• Something is wrong with your math markup. Aug 10, 2016 at 16:14
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• The only places with that much equivalent full sun are the polar regions and a very very very good day in eg Kabul - and, not then. See eg Phoenix Arizona 7.5 hours avg in June. Exceptional. NY, NY - 5.7 hours in June. Paris France - 5.1 hours in June. Sunny Glasgow, Scotland 4.6 hours in June. Kabul 7.4 June. Sep 10, 2016 at 14:26
• Annnnnd : Drum Roll :-) - Amundsen Scott - 9.6 hours in December Sep 10, 2016 at 14:46

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.

• I am looking for tables with solar panel output correlated with geographic latitude. Do you have any? Aug 10, 2016 at 17:10
• Afraid not. The 10% figure comes from the DECC in the UK, who are (were) a government body responsible for energy and climate change. Aug 10, 2016 at 17:19
• photovoltaic-software.com/pvgis.php Aug 10, 2016 at 19:28

A guy (cannot seem to be able to recover the nick) commented an answer, and then he deleted it. But it was interesting so I am putting it back:

Tesla car battery is rated about 75 kWh, so a 1.5 kW charging system will require 75 kWh / 1.5 kW = 50h

I dont know if this is right, but it seems very accurate.

• It's a very similar calculation to the one you have done. 12V * 2000 chains * 3500mAh = 84kWh. So instead of working that out from the number of batteries he looked it up on Tesla's website. Actual Tesla's have between 60 and 90kWh, so both his number and yours fit in that range. Aug 10, 2016 at 17:26
• Seems correct since Tesla wants people to use their cars as daily drivers. The idea is that people should be able to plug-in at home and the charging panel can deliver somewhere around 10kW to the battery for an overnight charge. Aug 10, 2016 at 17:28