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Free current from sun at supercharging stations

Well I didn`t do the math, because I don`t have the numbers.

Elon promised free charge from a supercharger for every Tesla Owner.
From an economic point of view this makes sense, if the current is all from the sun.
The sun panels on the supercharging stations.
There are 100 panels on the roof of the supercharging stations. Is this enought to produce
all of the current for 4-5 cars to load all the time?

In 1-2 years there will be more Teslas on the road, so the supercharger stations will be very busy.
Is it possible to create all the current for the cars with just 100 panels on the roof?

It is 4 am here, so this is a back of the envelope calc (mostly done in my head) with assumptions mentioned and are best gusses from memory and lack of calculator. So there most likely will be some issues that need correcting.
From the picture it appears that the 6 car solar array is about 25x60 feet. That is about 150 sq m. A good solar array might be able to produce 20% efficiency. The sun at the equater is I believe just over 1kW per sq m. So the array could produce 150x0.2x1.0=30kw per hour. Assuming that the arrays are located in the US andnthe average sun strength is about 80% of the equator then you get about 24 kw/ hour of daylight. Again assume that we get 10 hours of useful power per day x7 days per week you will get 1680 kw of generated power per week.
On average say that a MS user tops up with about a half a P85 battery charge equalling 40 kw. This would allow 42 cars to top up per week.
Elon mentioned just recently that most users draw at the weekends. So lets say that 2 people per weekday top up and the rest are at the weekend. This leaves 42-(2x5)/2=16 people could be serviced each weekend day. If half of these come within a two hour period that is 8 people will need service per hour. A 6 car station could serve probably upto 12 charges per hour (if everyone is considerate). So this gives about a 50% cushion which to me sound about right.
On the demand side of the equation, lets say that there 200 stations in operation by the end of 2015 and by then there are 66,000 Teslas on the road. Further that only 5% of all the miles driven by them needs Supercharger usage and that the average milage per car is 12000 miles per year. The consumption is .35 kw per mile on average. Then 12000*.05*.35*66000cars/200stations/52 weeks in a year/40kw per charge=33 cars a week need to be serviced. This is considerably less than the 42 cars per week that could be serviced and just as Elon Musk said would be a net energy producer for the grid.

That was an overall energy balance calc. Was assuming that grid connection where extra could be drawn from the grid during high demand times at the weekend and later repaid when demand is lower during the week. The solar array would not be able to direct feed the cars so some trading with the grid or local battery storage would be necessary.

I think they were just about forced to put solar on the roof, considering. What the heck, it all adds up and the more square feet the better.

It is my understanding that Solar City will be installing way more than just the charge station covers. They do not need to be colocated. Just on the grid with sufficient numbers to produce a net gain. I recall Elon saying the arrays will produce enough for a net gain and a positive cash flow. This was months ago. I love the idea of solar powered cars.

carlgo;
Car roofs are so small and badly situated for efficiency that you get a small trickle charge at high cost. Just a gesture, and a silly one at that.

lph;
Gov't stats show 5% of trips are long distance, but 30% of total miles. For some, their daily commutes are long enough to qualify!

@lph - Unless I missed it in your discussion, it appears you are assuming peak power production through the entire 10 hours of useful sunlight, when in fact it is a bell curve with peak production occurring only at solar noon on cloudless days. Since I took delivery of my ModS 85, I have Supercharged three times, all weekdays, and received in excess of 60kWhs each time. I salute TM's clean energy goals, but until they release real data, I will remain skeptical of their claims that the solar arrays are producing more than the growing number of ModS owners are using.

If they aren't Solarcity just builds more until they are. That's how it works.

Numbers are averages so one indivual may well do much more than 5%. However, I seem to remember it said that Tesla was thinking that on average people will go beyond the max range of the car only about 2% of the time, so I thought I was being conservative. A 200 mile trip is a long way for most and superchargers dont figure in the calc. untlil you do more than that in a day, assuming that you are able to charge during the night at home or at a hotel.
Anyway, the point of the exercise was to show that it could be a net generator of electricity as Elon Musk says (I believe).