Charging math?

Charging math?

I can't figure this out for the life of me so let me know if I'm wrong. I've tried a public charging station that was receiving 200 volts at 32 amps. Was getting 18 to 19 miles an hour charge.

I'm now using a wall charger at a free location and getting 230 volts at 32 amps and showing 24 miles per hour. When doing the math, that's 7.5 kw and hour, which happens to be 10 percent of the battery. So 31 miles per hour. Add in some loss there, and I should at least be at 28 plus.

The other charger at 200 volts should be roughly 6.5kw an hour or 8.5 percent of the battery. That's 26 miles. Per hour before any loss. Even with loss, id guess 23 or 24 would be reasonable, not 18 or 19.

Is my math way off?

Jlomb436 | 2018年8月22日

A thought. Is the added range number based on watts per mile? So if you have higher wattage usage it's taking that into account?

Jlomb436 | 2018年8月22日

Well, in doing some quick math, 24 over 30 is 80 percent. If 230 is the avg watts per mile for the spa rated range, I'm rocking 279 lifetime. That's about 82 percent. So that math somewhat lines up.

teslarama | 2018年8月22日

Are you sure you are getting consistently 230V and 32A?
May be Tesla is using your past 30 mile watts/mile to calculate the miles added?
For example...lets say you are consuming 275 watt/mile..then 7500/275=27.27

Jlomb436 | 2018年8月22日

I'm thinking that too, using my previous watts per mile to calculate. Screen showing a constant 229/230 volts at 32 amps. It's an official tesla wall charger.

djharrington | 2018年8月22日

at what point in the charge cycle are you seeing your lower numbers? The mi/h charge rate is the average rate for the charging session. If you plugged in and looked at that number after just a couple minutes of charging, it will be lower due to the ramp-up period bringing the average down. | 2018年8月22日

A rated mile for the RWD Model 3 long range corresponds to 234 watt hours per the EPA and 252 watt hours per Tesla ((EPA measured range for full 78.2 kWh charge to be 334 miles and Tesla advertises 310)
Using the Tesla number, you should get an initial charge rate of about 25 mph for 200 volts, 32 amps.
The wall charger should be providing 30 miles per hour initially.

Not all the energy is going into charging the batteries. Some of the energy is lost to heating of the battery cells while charging. If the battery management turns on the cooling system for the batteries, this consumes added energy. Not sure how much but not nothing.

gm_xeon | 2018年8月22日

I'm no mathematician or battery expert, but I'll give some possible explanations.

First question: Why is voltage times amps not equal to the actual watt hours of battery charged in one hour?

To accurately answer that, we'd probably need to know where those amps are actually being measured. My guess is the amps are measured at a point before going into the battery, as such it can't really be directly converted to the charge rate of battery kilowatts per hour. The state of charge of the battery as well as charge rate can add considerable impedance through parasitic reactions; unless the amps are being computed taking into account the internal resistance and reactance of the battery as it increases in state of charge and while using a different charge rate, that could account for loss of charge efficiency as compared to just voltage times current. The miles per hour are certainly taking into account the real charge rate of the battery, probably because it's estimated by an increase in voltage of the battery pack, but I'd say the amps are suspect so the whole picture's not quite available. This I'd say explains why you cannot simply multiply voltage by current and get an accurate rate of charge in watts.

Second question: Why does the charge efficiency differ between the two different charge measurements?

Taking your figures, we can calculate the approximate effective watts per mile per hour going into the pack, and figure out approximately how much the charge rates differ in efficiency.

200V * 32A = 6.4 kWh = 18.5 miles per hour = 6.4 kWh / 18.5 miles per hour = 345.95 input watts per mile per hour

230V * 32A = 7.36 kWh = 24 miles per hour = 7.36 kWh / 24 miles per hour = 306.67 input watts per mile per hour

The lower rate of charge appears to be approximately 12% more efficient in terms of energy actually going into the battery. Since the screen only shows whole amps and whole miles per hour, the figures are a bit imprecise, but between whole numbers, the battery's increased impedance with state of charge and the higher rate of charge, a 12% reduction in charge efficiency between the two charge rates can in majority be explained.

Third question: Is the displayed range based on my driving efficiency? Does that affect the displayed charge rate in miles per hour?

No, it's based on the EPA test cycle rating.

This can be confirmed by being very economical during one battery discharge (slow acceleration, lower average speed, no climate control), then in a second battery discharge be much less economical (aggressive acceleration, maintain a higher average speed, use climate control). You will see that if afterwards you charge from the same state of charge, the miles per hour during charge and estimated range when done will be identical.

@djharrington that has some merit, he should definitely wait for the charge rate to settle before taking measurements. But I think it's an average that only covers a short amount of time relative to the current time. During a supercharging session the charge rate drops steadily from approximately 50% state of charge onwards. If it were an average for the whole session the displayed rate of charge would initially be very inaccurate after 50% and while it decreases the rate of charge because the first 50% of the charge session was at a fixed, high rate of charge and would have far too much weight in the formula. Additionally, superchargers can have reduced charge rate when many cars are charging at the same time, and this is reflected quickly on the screen in such a situation. I'd guess the displayed charge rate is likely 1 minute average at most.

Jlomb436 | 2018年8月22日

Hey everyone.

Yes, I didn't take those figures 30 seconds into charging. I waited about 5 minutes and then when I returned 90 minutes later it was at 230 volts and 32 amps. Showed 24 mph.

And I appreciate the effort that you put in GM, but if everyone else is getting 30, I'm just a tad confused. I get there are tons of variables, but it still doesn't make sense. Maybe I'll try this after more than 3 charges and see what it comes out to be.

Rutrow 3 | 2018年8月22日

I wonder when/if NIST (National Institute or Standards and Technology) will weigh (pun?) in on this question. They're the ones who certify whether the petrol pumps delivering your volume of fuel are giving you what you pay for. I'm no E.I., but it seems, from reading this forum, that there is a considerable discrepancy between what the cars think they get vs what the chargers are sending/charging you. At high currents there seems to be quite a bit of loss in the delivery cables, or the energy used by the car for climate control, battery cooling/heating, and lights and entertainment during charging may account for some of the difference between what your battery gets and what customers have to pay. It doesn't feel right that the customer should have to pay for the resistance loss depending on which charger they have to use if it's further from the control panel at the power source. Just like my home electrical service, the Super Chargers should meter the power from the "nozzle" and have the "friction loss" to the "pump" be included in the unit price for everyone equally.

Sorry about all the "scare quotes" but I'm trying to analogize this to gasoline delivery. | 2018年8月23日

@gm: nice thoughts but you are correct that you are not a mathematician but that's OK because your heart is in the right place. Volts times amperes = watts ( power ) not kilowatt hours (energy)

@Rutrow: nice pun. There is always waste in the transfer of energy. Gasoline evaporates as it leaves the pump to some extent but the pump doesn't know this. It just know how much passed through the metering mechanics.

Same with electricity. You pay for what you draw through the meter no matter how inefficiently you use it. The meter has no way of knowing this. Energy is lost heating up the wires to the car. Energy is lost in heat generated when charging the batteries. Energy is lost to control computers that monitor the battery pack and the car. Energy is lost in the rectifier circuitry that converts the AC current to DC to charge the battery pack. Energy is routed to charge the 12 volt battery. A good design minimizes these losses of energy but can't eliminate them.

Rocky_H | 2018年8月23日

@Jlomb436, Well, here’s the first thing. You are not going to get consistent or informative charging speed numbers from looking at the “miles per hour” number, because it’s not an instantaneous reading. It’s just a weird thing Tesla did, that the volts and amps and kilowatts are true instantaneous readings at the moment you’re looking at it, but the “miles per hour” number is an average value over the whole time of the charging session.

So what happens, and this is probably happening in the case of these two stations you’re comparing, is that as the current slowly ramps up, the miles per hour number is reading artificially low on one of them. It can take the current a minute or two to get up to its full rate, so if you’re looking at the number in the first 30 seconds or so, you probably aren’t getting an accurate number there. Check on it in 10 minutes or so, when they have both had a chance to steady out, and I think you’ll see the numbers that would make more sense.

@Jlomb436 & @teslrama, And no, the miles per hour value isn’t based on your driving efficiency. It’s based on a consumption constant for that model of car.

Jlomb436 | 2018年8月23日

@ Rocky, Thanks Rocky. That's where I'm confused though. I think I mentioned that while I did check it after 5 minutes and saw the average to be 24, I checked it when I returned 90 minutes later and still showing 24. So I have to assume I received an average of 24 mph. I can't imagine it needs a larger sample size than that.

So if I'm getting 7.3kw an hour, than in theory I should be getting 29-30 mph before any loss if the battery pack is 75.5kw. I believe 75.5 is accurate? Worst case, 28-29 seems reasonable at 230v @ 32 amps. Does anyone have first hand numbers they could provide when using their mobile connector? I'll try a third location and see what comes about. Still waiting for an electrician on my 14-50 NEMA.

djharrington | 2018年8月23日

You don’t need to know the pack capacity. You know your power (230V x 32A = 7.36kW). An hour of that would be 7.36kWh consumed. If there were no losses, that would be equate to ~31mph (7.36kWh/.238kWh/mi) added. The rates range is based on a factor that is model specific, as Rocky mentions. For the RWD, it is right around 235-240Wh/mi (put in a range because people argue over it, but that range is only a +/- 1% range).

As a point of reference, I always charged my RWD 3 (sold now) at 245V at 40A and the displayed session charge rate would always asymptote to 39mph. Yours is definitely lower. Your voltage is low, but that shouldn’t make a huge different in the charger efficiency.

If you’re not charging where the battery needs significant conditioning (hot or cold) while charging, your numbers do seem a little low. You’re missing about 1kW of power that I’d expect to be there (your number should be closer to 29mph, but you’re getting 24mph). That’s in the right range for some heating or cooling, but only you know your charging environment. I always charge in a climate controlled garage, and I really never have much fan action when charging.

Rocky_H | 2018年8月23日

Yeah, the pack capacity is irrelevant. You can use a simple ratio to approximate what some charging speeds should be from a known point, as it scales with the power.
On Tesla's site, they show 240V 32A, which is 7.7kW is 30 miles per hour.
With the 200V, that's 6.4kW and should be 24.93 miles per hour.
With the 230V, that's 7.36kW and should be 28.68 miles per hour.

The numbers you were seeing were 19 and 24, so yes, they are both showing a little low, but they seem close and reasonable. It seems there may be something else drawing some energy while it was charging, or the slow ramp up of the current at the beginning is still bringing the average down a bit several minutes later.

ramoska | 2018年8月23日

On Tesla's site, they show 240V 32A, which is 7.7kW is 30 miles per hour.

Does this mean if my Elec Comp charges me 1.5 cents a kW.... then I am only paying 11.55 cents an hour to charge my car?

Rocky_H | 2018年8月23日

@ramoska, Yes, that is correct. Your units seem a little funky, though. kW is a power level, and your electric company charges you by amounts of energy, not power. So they charge 1.5 cents per kWh (kilowatt hour). At a charging rate of 7.7kW, then yes, in one hour, it will consume 7.7 kWh of energy. So you would multiply your rate per kWh by 7.7 kWh used, for 11.55 cents of energy each hour.

You have a crazy low off-peak rate, though, if they only charge 1.5 cents per kWh.

Jlomb436 | 2018年8月23日


I am parking in the sun when charging, and it was about 75 out. I haven't had the car long enough to know when the cooling or heating for the pack kicks in.

I can try charging at night when it's about 60 out to see if I get different results. Personally, I don't think the "ramp" is a factor at all. When I plug it in, within 30 seconds I'm at the max voltage and amperage. Maybe even less. I get in my car and it's there. And with charging 90+ minutes, that's got to be a less than 1% difference in adjusting the average.

I'll keep charging and see if anything changes. Can anyone shed some light on when the cooling and heating is activated for the battery pack relative to the ambient temperature? I did drive about 4 miles from being parked to the location of the charger, so maybe that increased battery temps?

Jlomb436 | 2018年8月23日

@ ramoska,

I'm incredibly jealous of your off peak hours. Mine are 12 and 13 cents depending on summer/winter. That means you can "fill" your car up for just about a $1! That means your model 3 fuel costs are 47x cheaper than my gasoline bill :)

djharrington | 2018年8月23日

Driving 4 miles isn’t going to heat things up much (unless you are driving like a NASCAR). You said “location of the charger”. Does this mean you’re charging somewhere that you’re sitting in the car while charging?

Rocky_H | 2018年8月23日

@djharrington, +1
Yeah, that's kind of what I was referring to when I said there maybe some other energy usage. If the air conditioner is running while you're charging, that is diverting some of the incoming energy, and it will show as a slower rate of the battery charging.

djharrington | 2018年8月23日

Yes, I’ve never paid attention to how that’s reported because I only sit in the car when supercharging, and that’s such a dynamic process anyway. Just did it in the S. Took a few minutes for the average rate to come up to 29mph. Turned AC on full and got that average down to 24mph within a few minutes.

Jlomb436 | 2018年8月23日

@everyone. No, I wasn't inside the vehicle using additional energy. I should have mentioned that. I did go eat or walk around. Today was another example of where I went and grabbed lunched over a 45 minute period, got back and showed 24mph. I didn't race over that 4 miles either, normal 70 mph on the freeway.

Like I said, maybe I'll try another location tonight and leave it for an hour and see if the cooler ambient temp is a factor. I won't have my 240 in my garage for a little bit so I can't tell if it's the stations I'm using somehow or my vehicle.

Jlomb436 | 2018年8月24日

Sorry for the multiple responses folks.

I just tried charging last night on a different charger (3rd different one) and I was receiving 200 volts at 30 amps, 6.0KW an hour. I charged for 90 minutes and once I got back to the car, it showed 20 mph.

Tesla's website shows 7.7KW at 30 mph, which equals 256 watts a mile. 6000 watts / 256 = 23.43. Maybe there is a rounding error in there somewhere, but still seems slow. Even if I round up to 21, there is a 10% loss there somewhere.

Does anyone have some real world similar numbers they could share? My car was ambient temp and I drove it .5 miles from my house to charge and it was 70 degrees out. Thanks everyone.

billlake2000 | 2018年8月25日

sum ting wong. make service appt

johnse | 2018年8月25日

It is good that you are trying to understand all the ins and outs involved here. Unfortunately, there are a lot of variables.

I think you are paying too much attention to how you have driven the car with respect to the temperature of the battery. Without access to the service mode displays, we simply don’t know what the battery temp is, nor do we know what the optimum charging temp is.

What we do know is that some amount of the energy is invariably turned to heat in the charging of the battery. The car will use its AC system to cool the battery if it gets too hot (and it will need to cool proportionately more when charging at a higher rate). The car will also preheat the battery in very cold circumstances.

So it doesn’t matter if you are using AC to cool the cabin, though as @djharrington showed, that can slow charging a fair amount. The car will use AC to cool the battery.

In short, I doubt there is anything wrong with your car.

bryan.whitton | 2018年8月26日

Just out of curiosity, where are you that you have 230 Vac? Standard household voltage with split phase is 240 L1 - L2 and accordingly, 120 L1-N L2-N. 230 Vac hasn't been used is decades in most of the USA.
This is interesting to me because i work in the PV industry as a Product manager for an inverter company. I don't see real 230 but very rarely.

Rocky_H | 2018年8月27日

@bryan.whitton, Quote: "Just out of curiosity, where are you that you have 230 Vac?"

It's probably just voltage drop. People see 200 and 199V from supposedly 208V nominal circuits all the time when a building runs wire 175 feet out to a charging station in their parking lot. So it would not be surprising to me at all to see a building that has 238 or 239V to start with have it down to 230V at the far end of the circuit at the charging station, especially under load, which will drag it down by another volt or two.

afcop2 | 2018年8月27日


diegoPasadena | 2018年8月27日

I scanned the whole thread and hope I didn't miss this being mentioned, but did you try to compare the actual range increase after an hour/two, i.e. if you plugged it in with 30 miles remaining and it said it was charging at 24 m/h, did it display 54 miles of range after an hour?
I've never done this with a keen eye on the actual miles, but in rough terms, I have a place I go once a week, where I can plug in at a public charger. I usually get about 24 m/h, and it has been working out to roughly 70-75 miles added in the three hours I usually spend there. Normally, I get there with close to 200 miles of range left, and the charge rate doesn't seem to be affected by the state of the battery as much as when supercharging.

rjriker | 2018年8月27日

I use different math. I have 110 volts at home and get 4 miles of battery charge per hour. I used the Tesla Super Charger and got 5.3 miles per minute, or it would have been 318 per hour. If I calculated my information correctly, (my first attempt to document my charge) I only charged for 40 minutes and got 214 miles, and I did not share my charger during that time, and I started with only 38 miles left (plenty of room for more charge). In Oregon it is only costing me 4.6 cents per mile at home and since I do not daily commute it is easy to give it all the time it needs to get up to the 290 mark.

Jlomb436 | 2018年8月28日

Hey folks.

I appreciate the info here. It sounds like the ultimate test would be to charge the car after it's been sitting awhile with reasonable ambient temps to get a good indication of what it's maximum charge is. I do feel my circumstances are very average, with 70's ambient temps and mild driving.

Unfortunately, it may be a bit before I get 240 in my garage to perform that test. Our area had about 1000 homes destroyed due to fires so I will likely have to install 240 myself as every electrician I call mentions they are busy and not accepting work.

It was showing 229/230 volts. This was at a county building.

DaninChi | 2018年8月28日

Jlomb, answering your request for comps:
I’m charging my LR RWD model 3 right now at a public charger, getting 30A at 200V, reporting 23 mph. It’s 93 deg F in this parking garage. When the AC kicked on while I sat down, mph dropped to 21.
At home I have a 7.2 kW EVSE in a detached garage that reliably results in 28 mph charging.

M3BlueGeorgia | 2018年8月28日

I use a 14-30 "dryer" plug to charge at home, which allows 240V at 24A continuous, and I see 22mph when I charge the car overnight, which is pretty much spot-on expected. This plug is on a dedicated circuit.

Suggest you try charging either on a 10-30, 14-30 or 14-50 plug, where the latter provides 32A continuous. That would eliminate the variances introduced by the third-party charge stations and therefore you can figure out if its an issue with the car, or you just need to understand better how these third-party charge stations provide power.

finman100 | 2018年8月28日

uhg. So looking forward to NOT needing third-party charging (current Leafer, waiting for base Model 3). Tesla has this nailed for a lot of travel using Superchargers. Sure it is very nice to have destination/public charging when you know you are going to be parked doing something else for 2 hours or more, but...

For me, the hassle of finding non-Tesla public charging is REALLY why EVs (short-rangers, etc) are not catching on. These stations are either slowed with limited power, ICED, broken, EVed (EV plugged in, NOT charging), not available because there's only one space, or inconveniently located, or really expensive (50 cents a kWh is NOT competitive).

7 strikes and you're out in 2 1/3 successive innings. (trying a modified baseball reference, sorry)

Go Elon!

ramoska | 2020年4月7日

Super Off-Peak kWh........................................................................................................1.4164¢ per kWh Figured I would bring this back since we have more owners... Make sure you check with your Power Company!! I have Georgia Power and this is what I pay to charge my Model 3... Basically not even a dollar to fill up the tank if I charge from 11pm to 7am 365 days of the year. | 2020年4月7日

@ramoska - That's a crazy low price! Our PG&E cost is almost 10 times that for Super-Off peak. Makes roof solar a no-brainer here. Those that charge off the grid is still cheaper than $2 gas (which is $3 gas here in CA) for a comparable ICE car.

andy.connor.e | 2020年4月7日

Even my rate in NY which doesnt have peak rates is 8x higher than that price.

Tronguy | 2020年4月7日

And then, there's the maniacs with solar power on the roof and net metering. We pay $4.95 a month for connectivity to the grid; we get paid wholesale if, over a year's time, we generate more than we use, and pay retail if the running surplus goes negative in any month. Wholesale they-pay-us is around $0.015/kW-hr; retail we-pay-them is $0.12/kW-hr.
We haven't paid them in twelve years and the surplus they-pay-us covers the $4.95/month. And that includes the last year-and-a-half with the Tesla. As far as fuel goes, we drive around here for free. Beat that, if you will :).
(And that doesn't include the SRECs. We get one of those per MW-hr that the system generates, and that's 10 or 12 a year, depending upon sunlight. On the marketplace for such things in NJ we get around $210 per SREC.)

Tronguy | 2020年4月7日

And, in case anyone asks: Yep, we paid off the cost of the whole system a few years back. Besides the state subsidy (no longer offered) and federal 30% tax refund (still there) that came in at the time of installation, the SRECs and not paying for electricity paid for the rest a few years back. We'll be getting the SRECs for three more years.