How to calculate cost of a single charge?

[Dreamin]

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

 

[ChadS]

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).

 

[miimura]

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.

 

[Dreamin]

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?

 

[ChadS]

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.

 

[miimura]

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?

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.

 

[Dreamin]

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.

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?

 

[EarlyAdopter]

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 .

 

[Dreamin]

Thank you. Makes perfect sense now.

 

[brianman]

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.

I thought we knew from Tom's Roadster analysis that loss varies across amperage. I would assume something similar for Model S.

 

[ChadS]

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.

 

[brianman]

From 24A to 70A the numbers weren't identical, but went up and down a bit ... and all were within about 5% which I don't consider significant given his measuring method.

Understood. Thanks.