TMC is an independent, primarily volunteer organization that relies on ad revenue to cover its operating costs. Please consider whitelisting TMC on your ad blocker or making a Paypal contribution here: paypal.me/SupportTMC

How to calculate cost of a single charge?

Discussion in 'Model S: Battery & Charging' started by Dreamin, Oct 17, 2013.

  1. Dreamin

    Dreamin Member

    Joined:
    Aug 7, 2013
    Messages:
    165
    Location:
    SoCal
    #1 Dreamin, Oct 17, 2013
    Last edited: Oct 17, 2013
    Would like to generally understand the math/formula to calculate this. Essentially, what are the formula's behind the charging applet on the Tesla website.

    Specifically, I'm trying to determine if it's cheaper to charge at home or work

    Home
    236V
    40A
    29mi/hr
    $0.16 / kWh

    Work
    204V
    30A
    19mi/hr
    $1.00 / hour
     
  2. ChadS

    ChadS Petroleum is for sissies

    Joined:
    Jul 16, 2009
    Messages:
    2,401
    There are varying amounts of overhead at different rates; but by and large for a specific charge you are paying for a certain number of kWh. You said it's $0.16/kWh at home.

    At work, 204V * 30A = 6.12kW. In an hour, by definition, you would get 6.12kWh. An hour of charging costs you $1, so that works out to...$0.16/kWh.

    Same price at work and at home. Might as well charge at home where you can charge at night, putting less stress on the grid and less likely to block others that might want to use the charger, or have to depend on a work charger that is probably less reliable than your home setup (if it charges by the hour, it's probably a networked charger and as Plug In America's surveys have shown, a non-trivial percentage of the time they aren't working. This has improved, but home is still probably more reliable).
     
  3. miimura

    miimura Active Member

    Joined:
    Aug 21, 2013
    Messages:
    1,251
    Location:
    Los Altos, CA
    Home: 100 miles / 29mi/hr = 3.45 hr
    236V*40A = 9.44kW
    $0.16/kWh * 9.44kW * 3.45hr = $5.21

    Work: 100 miles / 19mi/hr = 5.26hr * $1/hr = $5.26

    Basically, no difference.
     
  4. Dreamin

    Dreamin Member

    Joined:
    Aug 7, 2013
    Messages:
    165
    Location:
    SoCal
    What about UMC charger losses? This is accounted for at work (in the $1.00), but not at home. Would this make home charging 10-20% more expensive than work?
     
  5. ChadS

    ChadS Petroleum is for sissies

    Joined:
    Jul 16, 2009
    Messages:
    2,401
    The charger is in the car (see pic below for a rough diagram; the diagram only labels the rectifier, but that's a key part of the charger), so losses will be the same at both places.

    At home you use a UMC and at work you use an EVSE; both do the same simple job: protect you by not activating the 240V lines until the plug is in the car. They are really just safer outlets. They don't covert AC to DC, and I don't think they do any voltage regulation or anything like that. They may have some sort of GFI on them. Losses should be small, but more importantly similar between the two places.

    acdc tesla.jpg
     
  6. miimura

    miimura Active Member

    Joined:
    Aug 21, 2013
    Messages:
    1,251
    Location:
    Los Altos, CA
    The way I calculated the cost, the charging losses are rolled into your estimate of the mi/hr charge rate. The circuit will deliver 9.44kW from the wall. How much energy actually goes into the battery and what that means for range added is part of the estimate of miles/hr charging. If you're wrong about that, then of course, my cost is wrong too.
     
  7. Dreamin

    Dreamin Member

    Joined:
    Aug 7, 2013
    Messages:
    165
    Location:
    SoCal
    ChadS, thank you for the diagram and the earlier explanation. Your math makes perfect sense.

    Many threads discuss total charging losses and conclude it's 10-20%. I.e. Actual energy (from the wall) usage vs Tesla figures

    I understand the charging circuit is the entire red oval below. But I assume that the dash/app is showing the energy "consumed" by the car, not the energy supplied by the grid. The energy supplied by the grid is 10-20% higher due to losses in the entire charging circuit.

    The difference is: at home I'm paying for the energy supplied by the grid; at work, as i'm paying for the energy consumed by the car. I'm paying for the energy losses at home, but not at work.

    Am I thinking about this correctly?

    Charge.jpg
     
  8. EarlyAdopter

    EarlyAdopter Active Member

    Joined:
    Jun 24, 2012
    Messages:
    2,499
    Location:
    Redmond, WA
    The car app reports the current being supplied to the input section of the car's AC to DC converter, aka "the charger." The charging losses happen downstream from there, some in the actual AC to DC conversion itself and some at the battery. This is approximately 15% and will be the same with both of your power sources.

    The reason you're seeing different voltages reported at home vs work is that residential supply from the grid is single phase 240V while industrial/commercial supply is three phase 208V .
     
  9. Dreamin

    Dreamin Member

    Joined:
    Aug 7, 2013
    Messages:
    165
    Location:
    SoCal
    Thank you. Makes perfect sense now.
     
  10. brianman

    brianman Burrito Founder

    Joined:
    Nov 10, 2011
    Messages:
    15,487
    I thought we knew from Tom's Roadster analysis that loss varies across amperage. I would assume something similar for Model S.
     
  11. ChadS

    ChadS Petroleum is for sissies

    Joined:
    Jul 16, 2009
    Messages:
    2,401
    You are correct that in Tom's study, there was some efficiency loss at lower charge levels. But that was mostly at 120V, or at very low 240V amperages like 16A. From 24A to 70A the numbers weren't identical, but went up and down a bit (48A and 70A were both worse than 40A, for example) and all were within about 5% which I don't consider significant given his measuring method. And of course the battery size, chemistry, rectifier, battery conditioning, etc are all different in the Model S so who knows how much of that applies anyway.
     
  12. brianman

    brianman Burrito Founder

    Joined:
    Nov 10, 2011
    Messages:
    15,487
    Understood. Thanks.
     

Share This Page