Model 3 Range Constant Check

[dhrivnak]

As most of us know, the range meter takes the usable kWh in the battery and divides it by a constant to display the range remaining. That constant was the EPA value when I bought the car, and today I attempted to check whether the constant had changed.

Method: the general idea is to take a drive and divide kWh consumed by distance as displayed by the range meter. In order to reduce rounding errors I started and ended the test just as the range meter dropped a digit, and for kWh I reset a trip meter at the start of the test and then calculated the kWh as measured distance traveled * the Wh/mile displayed. Since the trip meter has one sig digit and my test was measured at 15.5 miles, the inaccuracy is ~ +/- 1/300 in both the distance and Wh/mile numbers. All told, ~ 1%

Results:

• Range dropped 22 miles
• 15.5 miles and 316 Wh/mile per the trip meter

The calculated constant is (15.5*316)/22 = 222.6 Wh/mile

If I recall correctly EPA is 227 Wh/mile for my Model 3 LR. Presuming my memory is correct, this is good evidence that the constant is unchanged.

Note the EPA number is measured at the wall so it includes all charging losses.

 

[AlanSubie4Life]

Note the EPA number is measured at the wall so it includes all charging losses.

Yes. I'm not sure where that 227Wh/rmi number came from (EPA is 26kWh/100 miles for LR RWD).

Anyway, germane to that, for the 90 miles of range pictures posted above, you can do the basic calculation using the empirical formula derived elsewhere here:

kW (battery) = 0.94*(kW(wall) - 250W)

And can just multiply both sides by hours to get kWh.

Using above data, which was from a Chargepoint, solving for kWh from the wall:

kWh (wall) = kWh (batt) / 0.94 + 0.25kWh = 23.65kWh

(Actual value according to Chargepoint was 23.53kWh, so formula is pretty close.)

So that's (for an AWD P) 23.53kWh for 90 miles, which works out to 26kWh/100 miles. Which doesn't quite work out, but then each mile of range in the car may be a little less than the EPA miles. But the actual value should be 29kWh/100 miles, which is a pretty big difference. Not sure exactly what the discrepancy there is - maybe a different charging method, or maybe charging overhead has been reduced a bit over time - but anyway, that's off-topic.

AWD constants: Charging: 245Wh/rmi, Discharging: 230-234Wh/rmi, line on consumption graph is at 250Wh/rmi.

 

[FactsBot]

Yes. I'm not sure where that 227Wh/rmi number came from (EPA is 26kWh/100 miles for LR RWD).

EPA number isn't useful.

They run the range test with all accessories off. Then get an average range of the UDDSu, UDDSv and HWY cycles. And derate this range by 0.7 to count for additional electric consumers and weather.

Since 0.7 derating factor is just an arbitrary number, 26kWh/100miles is an arbitrary number as well.

EPA measured the following range for the cycles for the LR RWD: 465, 495 and 455 and generated an average with some weighting. This was 477 miles.
477*0.7 = 334 miles. Tesla decided to use 310 miles first to match the AWD version. Later on they modified it to 325 miles.

227, which is 74.5kWh/325 miles = 229.2Wh/miles to be exact.. Some people use 74kWh, hence the 227.


One more thing, EPA doesn't use brand new cars if I'm correct. Document shows odometer was at 6k miles.

 

[AlanSubie4Life]

227, which is 74.5kWh/325 miles = 229.2Wh/miles to be exact.. Some people use 74kWh, hence the 227.

EPA number isn't useful.

Sure, it isn’t a “meaningful” mile as far as an actual distance that can be traveled, but the EPA number is still just a number that divides the energy in the battery into that many equally sized chunks of energy (as suggested by your first formula, though that formula should use the recharge event energy, not the energy in the battery).

So if you take the 89kWh from the recharge event (I think that is what it was In the document...maybe it was 87kWh...don’t have document in front of me right now):

89kWh/310 rated miles = 28.7kWh/100mi

This is very close to the AWD 29kWh/100mi (rounded) rating.

And I was just pointing out that my recharge event today seemed to be a bit more efficient than that, when referenced to the number of chunks of energy (90) that I added to the battery - and I am not sure why there was such a large discrepancy. It’s off by about 10%. Part of this may be due to the charging method used (perhaps more efficient than what was used in the EPA test but 6kW seems unlikely to be better...), and the rest could be due to actual reduction in total battery capacity - perhaps my full recharge event (to 304 rated miles) would only be something like 89kWh*304/310*0.9 = 78.5kWh, which if it is not due to charging efficiency improvements, would suggest that my battery simply has lost 10% capacity (not the 2% suggested by the rated miles reduction).

But no idea - I’d need to go back and review charging data from last year (I can) to compare - an event on 12/18/18 when the car was a month old shows 33.78 kWh from ChargePoint to add 126.5 rated miles, according to Stats. That is 26.7 kWh/100 miles (which is 2.7% higher than 26kWh/100mi...which is interesting that it is different). Still not 29kWh/100mi though. Not sure how accurate the ChargePoint meters are (there is no charge for using them).

Part of the difference may be due to the reserve buffer, of course. That is energy below zero rated miles which would have to be replenished in the recharge event - if it was used. But people keep experiencing this energy as not being available (car dies pretty soon after getting to 0, or even before - though it may be due to people demanding too many kW at that charge level). So if that (buffer energy not available) is the case, that energy would not have been available in the EPA test, unless the final depleting cycle is done at a very low steady discharge rate (it might be). So not sure the buffer can explain the discrepancy either.

 

[AdamVIP]

Dont listen to the range number after you charge. I always use percentage and have it set to an 80 percent charge for "full". The car routinely fills to 81%-83%. Others likely do that too. Unless you are going to 100% the number may not represent the percentage you think it does after charge.

 

[TimothyHW3]

As most of us know, the range meter takes the usable kWh in the battery and divides it by a constant to display the range remaining. That constant was the EPA value when I bought the car, and today I attempted to check whether the constant had changed.


If I recall correctly EPA is 227 Wh/mile for my Model 3 LR. Presuming my memory is correct, this is good evidence that the constant is unchanged.

Slight correction - it uses the FULL, not usable, divided by the consumption constant.

Usable = full minus 3.5kWh buffer (or 3.3 after about 20-30,000 miles as it slides down with degradation).

However the 100% is 100% from the usable. This is where there is a 4% difference.

You don't need to memorize the constant - just go to the energy graph and match the straight line with your avg. dotted line, it will display the constant in numbers.

Here is a video where I explain the difference.

 

[MarcG]

Slight correction - it uses the FULL, not usable, divided by the consumption constant.

Usable = full minus 3.5kWh buffer (or 3.3 after about 20-30,000 miles as it slides down with degradation).

However the 100% is 100% from the usable. This is where there is a 4% difference.

You don't need to memorize the constant - just go to the energy graph and match the straight line with your avg. dotted line, it will display the constant in numbers.

Here is a video where I explain the difference.

Thanks for the details and the video. My rated consumption constant appears to be 250 Wh/mi based on the energy consumption screen. Did this change recently for the performance AWD model?

 

[AlanSubie4Life]

Thanks for the details and the video. My rated consumption constant appears to be 250 Wh/mi based on the energy consumption screen. Did this change recently for the performance AWD model?

For 2018/2019 AWD & P, the constant is 245Wh/rmi and the line is at 250Wh/mi.

 

[MarcG]

For 2018/2019 AWD & P, the constant is 245Wh/rmi and the line is at 250Wh/mi.

Interesting, why would the line be at a different value than the constant?

 

[AlanSubie4Life]

Interesting, why would the line be at a different value than the constant?

No idea, really. May be that the kWh in the car read lower (larger kWh) than real kWh? Anyway, 250Wh/mi*310mi = 77.5kWh which is really close to the actual energy measured in Tesla's dyno test that they did when they were coming up with their number for the EPA rating. And it's really close to the energy contained in the battery when the car is brand new (it relatively quickly degrades to below 76kWh).

But it's generally the case that each rated mile as you add it is ~245Wh, each rated mile as you consume it is 234Wh (230Wh on the trip meter), except for when the car is new, when the consumed numbers are a couple % higher (it appears).

 

[MajorTom]

New poster, been lurking for a while now. Appreciate the technical answers and calculations.

I have a 2020 M3 Stealth P on 19s...Oct build, almost 7k miles. I can confirm that sometime in the last 2 months the rated wh/mi that appears on energy screen changed. It used to be around 250ish and now is 264. I also believe that with the new EPA numbers it has changed rated mileage & energy screen line move around if you change wheel size. Thought you would find useful.

 

[AlanSubie4Life]

New poster, been lurking for a while now. Appreciate the technical answers and calculations.

I have a 2020 M3 Stealth P on 19s...Oct build, almost 7k miles. I can confirm that sometime in the last 2 months the rated wh/mi that appears on energy screen changed. It used to be around 250ish and now is 264. I also believe that with the new EPA numbers it has changed rated mileage & energy screen line move around if you change wheel size. Thought you would find useful.

Thanks for the very clear picture showing the rated line is closer to 264 than 265Wh/mi.
We were aware of this change but it is the first picture I have seen of this specific line.

This means the charging constant is about 259Wh/rmi19. (That is what is used to perform the calculations on this screen and to calculate kWh added from rated miles added during a charging session.)

What is your rated range extrapolated to 100%? About 300 rated miles? Has it been steady?

If you have the opportunity it would be interesting to do a measurement of the discharge constant at this point of time on a new vehicle. That involves taking a warmed battery, then doing a long drive, and then dividing the energy used (distance * Wh/mi) by the rated miles used. Really requires more than 100 rated miles to be used in one continuous drive to be accurate. So it is kind of a pain.

On a degraded battery (though it is possible they are not hiding any degradation now - I have seen reports that 77.6kWh seems to be available for 2020 vehicles...), I would expect the discharge constant to be 247Wh/rmi19. And the trip meter constant might work out to closer to 243Wh/rmi19.

 

[MajorTom]

Can you explain the charging constant being used vs the rated range for energy consumption calcs? I don’t understand that piece.

regarding rated range projection - we’ve done a lot of road tripping without going much below 20%...so my 100% is off. That being said I charged to 100% this am and it showed 291 - however it said it had 30 min charging left and was pulling 4kW still...so that tells me the top end calcs are off. I unfortunately had to leave before it finished to see exactly where it is.

my rated miles * 264 puts me somewhere around 77kW but that’s without finishing the charge. Energy screen projected miles * consumption puts its about 1.5kW lower for what that’s worth.

 

[MarcG]

If you have the opportunity it would be interesting to do a measurement of the discharge constant at this point of time on a new vehicle. That involves taking a warmed battery, then doing a long drive, and then dividing the energy used (distance * Wh/mi) by the rated miles used. Really requires more than 100 rated miles to be used in one continuous drive to be accurate. So it is kind of a pain.

I'm not @MajorTom but I followed your advice on these calculations and ran the numbers for all the 100+ RM continuous highway drives I've logged since my car was new, and my average constant is 229.0 Wh/mi. I was expecting a higher constant that that given my car is an early-2019 M3P+.

Here's my data if you're interested -- "RM used" and "Wh/mi" are per what the car reported, and "kWh used" and "Constant" are calculated per your formulas:

RM Used Wh/mi  kWh Used  Constant
252      345     58.1      230.7
106      576     24.2      228.8
174      361     40.1      230.7
170      333     39.1      230.2
299      327     69.0      230.8
212      350     49.4      232.9
147      277     34.0      231.6
115      323     26.0      226.4
151      309     34.3      227.1
130      335     30.0      230.9
144      290     33.1      229.6
103      374     23.9      231.7
249      278     57.1      229.2
126      325     29.1      230.6
173      306     39.5      228.5
124      376     28.5      229.5
221      348     50.3      227.5
129      287     29.3      227.4
151      332     34.2      226.5
263      328     60.3      229.2
221      436     50.1      226.9
133      338     30.3      228.0
136      346     31.2      229.5
135      273     31.3      232.2
247      308     57.0      230.9
101      311     22.9      226.3
171      320     37.1      217.1
212      416     45.2      213.3
256      320     59.2      231.1
143      372     33.2      232.0
146      249     33.8      231.4
180      294     41.8      232.1
111      315     25.5      229.6
185      266     42.8      231.3
153      310     35.5      232.0

 

[AlanSubie4Life]

I'm not @MajorTom but I followed your advice on these calculations and ran the numbers for all the 100+ RM continuous highway drives I've logged since my car was new, and my average constant is 229.0 Wh/mi. I was expecting a higher constant that that given my car is an early-2019 M3P+.

Here's my data if you're interested -- "RM used" and "Wh/mi" are per what the car reported, and "kWh used" and "Constant" are calculated per your formulas:

RM Used Wh/mi  kWh Used  Constant
252      345     58.1      230.7
106      576     24.2      228.8
174      361     40.1      230.7
170      333     39.1      230.2
299      327     69.0      230.8
212      350     49.4      232.9
147      277     34.0      231.6
115      323     26.0      226.4
151      309     34.3      227.1
130      335     30.0      230.9
144      290     33.1      229.6
103      374     23.9      231.7
249      278     57.1      229.2
126      325     29.1      230.6
173      306     39.5      228.5
124      376     28.5      229.5
221      348     50.3      227.5
129      287     29.3      227.4
151      332     34.2      226.5
263      328     60.3      229.2
221      436     50.1      226.9
133      338     30.3      228.0
136      346     31.2      229.5
135      273     31.3      232.2
247      308     57.0      230.9
101      311     22.9      226.3
171      320     37.1      217.1
212      416     45.2      213.3
256      320     59.2      231.1
143      372     33.2      232.0
146      249     33.8      231.4
180      294     41.8      232.1
111      315     25.5      229.6
185      266     42.8      231.3
153      310     35.5      232.0

Thanks. Around 230Wh/mi is exactly what I would expect for a 2019 AWD of any form. That’s what I get with my 2018 3P. I am not sure what to make of the lower numbers. I would expect very heavy consumption to drive down the “constant” somewhat - but not to 213Wh/rmi. Could be vampire losses but if these drives were continuous...

Higher values are associated with a warming pack where rated miles reappear as you drive. (You don’t have significant instances of this apparently.)

If there were no heat losses, this value would be ~234Wh/mi. That is because your entire usable energy is 245Wh/mi * max rated miles, but that includes the buffer below 0 rated miles. That buffer is 4.5% of the pack energy. So each rated mile contains 245Wh*(1-bufferEnergy/maxPackEnergy) = 245*(1-0.045) = 234Wh.

 

[AlanSubie4Life]

Can you explain the charging constant being used vs the rated range for energy consumption calcs? I don’t understand that piece.

Honestly, I do not understand the positioning of the line. It does appear to be close to the correct value for a brand new car. But I generally have not found that it aligns with any readable quantity very well.

100% this am and it showed 291 - however it said it had 30 min charging left and was pulling 4kW still...so that tells me the top end calcs are off. I unfortunately had to leave before it finished to see exactly where it is.

That is odd. Seems pretty low for a 19” wheel selection. How many miles on the car? Is it a few months old already? Was the value higher right after the software update that changed the constant?

my rated miles * 264 puts me somewhere around 77kW but that’s without finishing the charge. Energy screen projected miles * consumption puts its about 1.5kW lower for what that’s worth.

Using max rated miles * rated line value I do not know what to do with. It may be correct for a brand new car as I said...
You can use the energy screen projected miles * recent efficiency, divided by the SoC % (with care to wait for a change in SoC % to get the extra decimal of precision), to tell you what your capacity would be if you read it back from the CAN. That ~75.5kWh would project out to ~291 rated miles (19”), which is what you see I guess.

 

[MarcG]

I would expect very heavy consumption to drive down the “constant” somewhat - but not to 213Wh/rmi. Could be vampire losses but if these drives were continuous...

Correct, all these drives were continuous on the freeway with no stopping at all. I always reset the trip meter after I get up to a constant speed and engage AP, and snap a photo of the trip meter showing all zeros and the rated miles at that moment. Then when I’m close to exiting the freeway, before even slowing down, I snap another picture showing the rated miles at that moment and all the info of the trip meter I had reset, such as miles driven and Wh/min consumption. The kWh value is a bit useless as it doesn’t show any decimal values, but I can derive it by multiplying miles driven by consumption (divided by 1000).

Higher values are associated with a warming pack where rated miles reappear as you drive. (You don’t have significant instances of this apparently.)

There actually are some pack warming instances in my data, as I was navigating to a supercharger in cold conditions (last few rows) and it showed the preconditioning message on the screen. Doesn’t that consumption get taken into account in the trip meter values though, therefore affecting all the value that I am taking into consideration when calculating the constant? I would assume total RM used and Wh/mi consumption would be updated when the pack is being warmed, since it consumes more energy, similarly to when cabin heat or AC are turned on.

 

[AlanSubie4Life]

Correct, all these drives were continuous on the freeway with no stopping at all. I always reset the trip meter after I get up to a constant speed and engage AP, and snap a photo of the trip meter showing all zeros and the rated miles at that moment. Then when I’m close to exiting the freeway, before even slowing down, I snap another picture showing the rated miles at that moment and all the info of the trip meter I had reset, such as miles driven and Wh/min consumption.

I wonder whether some of these deviations on the low side were correlated with reductions in your 100% rated range? They could correspond to instances where the BMS over-estimated energy available - and then it would adjust after the fact on the next charge, presumably. Not sure it's worth focusing on these instances, though, except out of curiosity, as they are simply outliers for whatever reason.

There actually are some pack warming instances in my data, as I was navigating to a supercharger in cold conditions (last few rows) and it showed the preconditioning message on the screen. Doesn’t that consumption get taken into account in the trip meter values though, therefore affecting all the value that I am taking into consideration when calculating the constant?

I'm talking about very cold packs where you actually have a significant reduction in rated miles (not typical California/San Francisco temps - though it is possible in SF). The preconditioning is different - it will take place even if your pack is relatively warm - it likes to make it HOT for supercharging. I would expect that energy should be counted. But, in the case where you're missing 10 miles on the display initially, due to cold, as your pack warms, you'll get those back, and if you're just looking at rated miles used, it will be substantially less than what you would expect. That would make the "constant" higher than expected (and the calculation would not be valid).

I did some more careful looking at the constants this morning...I always say 245Wh/rmi (charge), 234Wh/rmi (discharge) / ~230Wh/rmi (trip meter)....but it looks possible/likely that the 245Wh/rmi and 234Wh/rmi numbers are slightly lower. (As in, 244.5Wh/rmi (152Wh/rkm), and 233.5Wh/rmi.) It's hard to get enough precision (without API access - with API access it is easy). But these are also relatively unimportant details, obviously.

 

[MarcG]

I'm talking about very cold packs where you actually have a significant reduction in rated miles (not typical California/San Francisco temps - though it is possible in SF). The preconditioning is different - it will take place even if your pack is relatively warm - it likes to make it HOT for supercharging. I would expect that energy should be counted. But, in the case where you're missing 10 miles on the display initially, due to cold, as your pack warms, you'll get those back, and if you're just looking at rated miles used, it will be substantially less than what you would expect. That would make the "constant" higher than expected (and the calculation would not be valid).

I looked at weather, ambient temperature, and usage of AC/heater on these long trips, but do not see a correlation - maybe you can?

Constant ºC  ºF    AC/Heater    Weather
230.7    21  70    21ºC/70ºF    Sunny
228.8    22  72    21ºC/70ºF    Sunny
230.7    21  70    20ºC/68ºF    Cloudy
230.2    24  75    21ºC/70ºF    Sunny
230.8    28  82    21ºC/70ºF    Sunny
232.9    36  97    21ºC/70ºF    Sunny
231.6    29  84    21ºC/70ºF    Sunny
226.4    34  93    21ºC/70ºF    Sunny
227.1    30  86    21ºC/70ºF    Sunny
230.9    19  66    21ºC/70ºF    Dark/clear
229.6    28  82    21ºC/70ºF    Sunny
231.7    27  81    21ºC/70ºF    Sunny
229.2    24  75    21ºC/70ºF    Sunny
230.6    29  84    21ºC/70ºF    Sunny
228.5    20  68    21ºC/70ºF    Sunny
229.5    14  57    21ºC/70ºF    Sunny
227.5    15  59    21ºC/70ºF    Sunny
227.4    33  91    21ºC/70ºF    Sunny
226.5    19  66    None         Clear sunset
229.2     9  48    None         Clear sunrise
226.9    17  63    21ºC/70ºF    Sunny
228.0    18  64    21ºC/70ºF    Sunny
229.5    20  68    21ºC/70ºF    Sunny
232.2    15  59    None         Dark/clear
230.9    12  54    SeatHeat1    Dark/clear
226.3    21  70    21ºC/70ºF    Sunny
217.1     9  48    None         Drizzle
213.3     7  45    Defrost      Rain
231.1     5  41    Defrost      Sunny
232.0     6  43    None         Sunny
231.4     2  36    None         Cloudy
232.1     0  32    21ºC/70ºF    Snow
229.6     1  34    21ºC/70ºF    Snow
231.3     7  45    None         Rain
232.0    10  50    None         Drizzle

 

[AlanSubie4Life]

but do not see a correlation - maybe you can?

I'm only looking at the 217 & 213 values - all the rest are close enough given the precision we have available (clearly 230Wh/rmi is a good rule of thumb for the trip meter). For those 217Wh/rmi and 213Wh/rmi values, if you correlate them with your extrapolated range at 100%, do they correlate with a reduction of rated range after they occurred? They were very large discharges so I would expect that they would have been more accurate, but they weren't. Did you go to a very low SoC or was there anything else unusual about them?

I'm not entirely surprised by deviations like this, though I haven't seen them myself (but I have not done nearly as much tracking as you). In the end the BMS is just estimating the energy (very accurately in general!), and sometimes it might get it wrong.