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Extant Vehicles, Supercharger Numbers, and Distribution

Discussion in 'Charging Standards and Infrastructure' started by AudubonB, Aug 7, 2014.

  1. AudubonB

    AudubonB Mild-mannered Moderator Lord Vetinari*

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    This is, as the case with most of my posts, only half-a-post. To be completed by someone else, if so interested.


    Looking at Tesla's announced production rates, it appears that by the end of next year there will be on the roads a total of some 120,000 Model Ss, and by year-end 2016 perhaps double that in Model S & Model X combined.

    How does that compare to the perceived number of Supercharger bays, both now and expected at the end of the respective years, and of the continental distribution both of vehicles and SpC bays? Is Supercharger dissemination going to be keeping up with the number of vehicles on the road, in North America, in Europe, and in China/Asia?
     
  2. emupilot

    emupilot Member

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    Alot of superchargers providing connectivity along sparsely traveled routes probably will have spare capacity for some time, but there are many (like in California) which are often full. I don't think Tesla will be able to keep up by themselves when they are producing hundreds of thousands of cars per year. Hopefully the economic incentives will shift so that locations will do the legwork themselves and just get reimbursement from Tesla for the cost.
     
  3. Benz

    Benz Active Member

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    As more and more Tesla EV's will be delivered, simultaneously both the number of Supercharger stations and also the number of stalls at each Supercharger station will increase accordingly. So, investments in the expansion of the Supercharger network will increase as time goes by (certainly in the current and the next decade).
     
  4. Cottonwood

    Cottonwood Roadster#433, Model S#S37

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    It's a pretty simple calculation to calculate roughly how many stalls have to be built per car produced. This is in addition to those needed for geographical coverage. Let's make some assumptions. Feel free to modify them as you see fit.

    1. PTS = Percent of Tesla Charging on Superchargers. Assume 5%.
    2. AM = Average Miles driven per year by Teslas. I assume 12,000 miles per year.
    3. BDF = Busy Day Factor. The ratio of use on busy days vs average days. AKA, the Mother's Day factor for phone lines. Assume 2x.
    4. ACR = Average Charge Rate while using a Supercharger. Assume 200 mph.
    5. EQE = Erlang Queueing Efficiency to avoid queues at Superchargers. For a 10 Stall Supercharger it is 51%. Let's take that for big city, lots of Teslas, calculations.
    6. EBH = Equivalent Busy Hours of Supercharger use per day. If all the use per day were at the busy hour rate, then this times the busy hour rate would give you the charging per day. Assume 5.
    The number of Supercharger miles charged per busy day per car is AM/365*PTS*BDF. That is the Average Miles per year divided my 365 days per year times the percentage of miles that are Supercharger miles times the Busy Day Factor.

    A single stall at a supercharger can provide so many miles per day with minimal queues. That is ACR*EBH*EQE or the Average Charge Rate times the Equivalent Busy Hours per day time the Erlang Queueing Efficiency.

    The number of Teslas that can be supported by each stall is then the Miles per Day per Stall divided by the average Supercharger Miles per day per car or

    ACR*EBH*EQE/(AM/365*PTS*BDF)
    = 200 mph per Stall * 5 hours * 51% / (12,000 miles per year per Tesla / 365 days per year * 5% * 2
    = 155 Teslas per Stall​

    We assumed 10 Stall Superchargers, so that means that Tesla needs to build about one 10-Stall Supercharger per 1,550 Teslas. Because they are now making about 600 Teslas a day, then that means another Supercharger every 2.5 days now or about two per week. Counting world wide, they have been doing a little better than that. This does not seem to be a problem to me. Of course, as the production rate of cars goes up, so will the installation rate of Superchargers.

    My assumptions are WAGs (Wild Ass Guesses), but probably within reason, and better than SWAGs (Stupid Wild Ass Guesses). Tesla has all the monitoring tools needed to track actual usage, Superchargers nearing capacity, etc. It should be pretty easy for them to stay ahead of this. It's not rocket science. Telecommunications engineers have been doing these calculations and monitoring to stay ahead of demand and avoid the dreaded busy signal for over a century. With a little care and planning, Tesla should do fine.

    I also like the Green/Yellow/Red signaling that has been suggested. If this coding could be put on the car's map for Superchargers, that would be great. Green means no waiting, Yellow means some power sharing and Supercharger approaching capacity, and Red means queues happening regularly. This would allow drivers to plan stops, especially when, with greater Supercharger density, there are multiple choices of where to charge.
     
  5. AudubonB

    AudubonB Mild-mannered Moderator Lord Vetinari*

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    That's a good first stab at accounting for the variables, Cotton. As you wrote, I am pretty sure we know that TM has the mileage data, complete charging data and, well, they'd better have the production data! I see that you put in the 600/d production rate....that's one number we know is going to change significantly, which, ceteris paribus, means your bottom-line # of 2 new SpCs per week will have to increase as well.
     
  6. ecarfan

    ecarfan Well-Known Member

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    Cottonwood, excellent post. I only take issue with this:

    PTS = Percent of Tesla Charging on Superchargers. Assume 5%

    I think that is high, and suspect it is on average much less than 1% of all Teslas at any given moment are at a Supercharger. Or perhaps I do not properly understand what you mean by that parameter.
     
  7. Cottonwood

    Cottonwood Roadster#433, Model S#S37

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    Good question and I probably should have stated it better.

    PTS = Percent of Tesla Charging on Superchargers. Assume 5%

    A better definition is the percent of miles per year that each Tesla draws from a Supercharger. I am assuming that most miles are local and drawn from the home or work charger. Supercharger miles are mostly used on trips. Of course places like Hong Kong, New York, and London with many apartment/condo owners who need Supercharging on a more regular basis may distort this.

    My personal numbers are probably close to 15%, but many of my miles are from long distance drives.

    PTS is a pretty strong driver and linear with Superchargers needed. For example changing PTS from 5% to 10% means 4 Superchargers a week at today's production rate instead of 2 Superchargers a week.

    Another term to think about is EBH (Equivalent Busy Hours). I chose 5 because that is the approximate number used in the telephony world that I come from, and interestingly, is the number you use for solar PV production; on average over the year you get 5 hours of peak sun per day for fixed panels.

    If people charge more evenly over the day, then this term goes up and you need fewer Superchargers. For example changing EBH from 5 hours to 10 hours, it cuts in half the number of Superchargers needed.
     
  8. ecarfan

    ecarfan Well-Known Member

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    "A better definition is the percent of miles per year that each Tesla draws from a Supercharger. "

    Thanks, that makes sense to me. My guess is that percentage would be somewhere between 3 and 6 percent for an average of all Model S vehicles. Of course some cars might be much higher than 6, but I bet some cars are well below 3. Some cars never supercharge, perhaps because they are located more than 200 miles from the nearest SC, and that will certainly change over the next few years. And if Tesla goes ahead with Elon's stated intention to place SCs in some cities, that average percentage could increase.
     
  9. miimura

    miimura Active Member

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    After recent press releases regarding SuperCharger milestones for power delivery and Model S total miles driven, I calculated 8.12% of all Model S miles driven were powered by SuperChargers. That would include the comparatively small number of miles that were covered before SuperChargers were widely available. I can't find the reference now, but I posted it as a comment on one of the green car sites, probably InsideEVs.

    Edit: Found it.
     
  10. emupilot

    emupilot Member

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    At the 8% PTS cited by miimura, that would mean 32 superchargers per week in a few years when production will be 10 times what it is now - yikes!

    If the entire US fleet were converted to supercharger compatible vehicles, how would the number of supercharger stations compare with the number of gas stations we have now? Would the ratio of superchargers to gas stations be PTS x charging time / gas station filling time? Then we'd need about half as many supercharger stations as we have gas stations.
     
  11. RichardL

    RichardL Member

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    Don't think its 600 being built a DAY - its 600/wk, moving towards 1000/wk, then 2000/wk at end 2015.

    So by that it would be a Supercharger every 2 weeks or so...not quite so bad
     
  12. Cottonwood

    Cottonwood Roadster#433, Model S#S37

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    My oops... You are so correct. 600 per week is about 30,000 per year, about the current production rate. The current daily rate is about 120 per day.

    That means the the current Supercharger install rate is more than needed for capacity, and is mostly going in for coverage.

    Let's do the calculations again. Thanks for comments and corrections. Major changes in italics.

    1. PTS = Percent of Tesla miles recharged on Superchargers. Assume 10%. There was a Tesla report that showed a little over 8%. Assume more Supercharging in future.
    2. AM = Average Miles driven per year by Teslas. Assume 12,000 miles per year.
    3. BDF = Busy Day Factor. The ratio of use on busy days vs average days. AKA, the Mother's Day factor for phone lines. Assume 2x.
    4. ACR = Average Charge Rate while using a Supercharger. Assume 200 mph.
    5. EQE = Erlang Queueing Efficiency to avoid queues at Superchargers. For a 10 Stall Supercharger it is 51%. Let's take that for big city, lots of Teslas, calculations.
    6. EBH = Equivalent Busy Hours of Supercharger use per day. If all the use per day were at the busy hour rate, then this times the busy hour rate would give you the charging per day. Assume 8 hours. This was 5, but Tesla charging, especially on busy travel days is a little more spread out over the day.
    The number of Supercharger miles charged per busy day per car is AM/365*PTS*BDF. That is the Average Miles per year divided my 365 days per year times the percentage of miles that are Supercharger miles times the Busy Day Factor.

    A single stall at a supercharger can provide so many miles per day with minimal queues. That is ACR*EBH*EQE or the Average Charge Rate times the Equivalent Busy Hours per day time the Erlang Queueing Efficiency.

    The number of Teslas that can be supported by each stall is then the Miles per Day per Stall divided by the average Supercharger Miles per day per car or

    ACR*EBH*EQE/(AM/365*PTS*BDF)
    = 200 mph per Stall * 8 hours * 51% / (12,000 miles per year per Tesla / 365 days per year * 10% * 2
    = 124 Teslas per Stall​

    We assumed 10 Stall Superchargers, so that means that Tesla needs to build about one 10-Stall Supercharger per 1,240 Teslas. Because they are now making about 600 Teslas per week, then that means another Supercharger every 2 weeks now or about two per month for capacity. Counting world wide, they have been doing much better than that. Right now the install rate of Superchargers is dominated by getting coverage. As we have seen, there are some problem places like Hawthorne and Barstow, but Tesla is adding capacity to existing Superchargers and building more Superchargers in those locations.

    Of course, as the production rate of cars goes up, so will the installation rate of Superchargers. If the Tesla production rate goes up a factor of 10, then a new Supercharger will have to come on-line at the rate of about 5 Superchargers per week for capacity. That is not too much more than the current install rate for coverage. Once again, I don't see much of a problem; Tesla just needs to stay ahead of the game in their planning.

    I'm a retired engineer. Maybe they should hire me as a consultant... :biggrin:
     

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