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Method to calculate/extrapolate battery capacity from trip consumption

darth_vad3r

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May 6, 2019
1,574
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Canada
Someone on a battery usage thread got me thinking to look at this method a bit closer for myself.


TL;DR if you have a long enough trip with data points at the start/end, you can use the trip meter info to back-calculate what the car's drop in displayed % or km range equals in actual energy with a more precise "kWh" figure than "5 kWh" (e.g. 4.91 kWh). Using this number you can see how many kWh the car thinks "100%" is.


For a trip from point A to B (with no "park" time at all so vampire drain of any sort is not an issue), if you take the distance (d) in km (or mi) and the consumption (c) in Wh/km (or Wh/mi) you can calculate a more precise amount of energy used (e) than what is displayed by the trip meters. e.g.
d = 34.1 km
c = 144 Wh/km
e = d * c = 4,910.4 Wh = 4.91 kWh (vs displayed on trip meter as just "5 kWh")​

I was angling at trying to use this more precise consumption info to extrapolate the capacity the car thinks it has ... but unfortunately the lack of sig figs in the reported % SoC 'estimates' and the fact you have to subtract two of them to get % used for a trip makes for a pretty wide range there :(

e.g. this trip went from "74%" to "64%" SoC. If I naively use 10%, I get 4.91 kWh / 10% = 49.1 kWh capacity (usable? actual? projected?). Of course that 10% could be anywhere from 9.0001% to 10.9999% due to the fact "74%" could be 73.5% to 74.499% and likewise for "64%" ... and now I get a range with a wide range [;)] of 44.6kWh to 54.6kWh :)

Having a longer trip that uses more "%" would help I suppose. Or I could use the change in rated km instead of %, hmm...

Ok, so ya, this trip used 38 km on the range meter ... whether that's actual rated, or estimated, or rated-based-on-degraded-battery, or rated-based-on-degraded-and-temperature, or something else?? I am not sure. For the first few weeks I had the car it was exactly 'rated', but it changed at some point after that. e.g. 90% used to be 347km (of the 386 SR+ rated range). Now 90% might be 337, 338, or 339 depending on the day implying my range is 374-377km, not 386km :)

Anyways, using "38km", as being 37.500-38.499km, as a % of 386km that is 9.715-9.974% used for this trip. If I use the 376km reduced range number, it is 9.973-10.239%.

Those give me capacity numbers of 49.23-50.54 kWh (using 386km) or 47.95-49.23 kWh (using 376km).

I guess that's as close as I'm going to get without a longer trip to make the rounding errors smaller. So what is this telling me ... my actual ideal battery capacity is 49.23-50.54kWh, but my currently estimated capacity is less, and 48-49-ish kWh?


I'd be curious if anyone has a longer trip stats if their numbers match up to 'advertised' battery capacity (not actually advertised, but seems people have concluded by whatever means that SR+ is 50 kWh, and LR is 75 kWh, or 'ish').

NOTE:
My understanding from reading the forums is the trip meters only 'run' while driving, but your range meter will drop while parked and on, or asleep due to vampire drain, so for this method to be meaningful (for however meaningful it may be) you would need to run the numbers on a snapshot of right before/after a trip excluding any parked time.
 

darth_vad3r

Well-Known Sith
May 6, 2019
1,574
1,123
Canada
I neglected to show the range in error in the first calculation e = d * c, but the km is fairly precisely displayed down to 100m +/- 50m, and the Wh/km is also fairly precisely displayed.

Still, there are rounding errors there ... using them gives a range of 4.89-4.93 kWh vs my original "4.91 kWh" number (which is still more precise than the trip meter shows at "5 kWh").

For longer trips this error would get relatively small.
 

derotam

Member
Oct 31, 2018
825
700
Oak Hill, VA
Someone on a battery usage thread got me thinking to look at this method a bit closer for myself.


TL;DR if you have a long enough trip with data points at the start/end, you can use the trip meter info to back-calculate what the car's drop in displayed % or km range equals in actual energy with a more precise "kWh" figure than "5 kWh" (e.g. 4.91 kWh). Using this number you can see how many kWh the car thinks "100%" is.


For a trip from point A to B (with no "park" time at all so vampire drain of any sort is not an issue), if you take the distance (d) in km (or mi) and the consumption (c) in Wh/km (or Wh/mi) you can calculate a more precise amount of energy used (e) than what is displayed by the trip meters. e.g.
d = 34.1 km
c = 144 Wh/km
e = d * c = 4,910.4 Wh = 4.91 kWh (vs displayed on trip meter as just "5 kWh")​

I was angling at trying to use this more precise consumption info to extrapolate the capacity the car thinks it has ... but unfortunately the lack of sig figs in the reported % SoC 'estimates' and the fact you have to subtract two of them to get % used for a trip makes for a pretty wide range there :(

e.g. this trip went from "74%" to "64%" SoC. If I naively use 10%, I get 4.91 kWh / 10% = 49.1 kWh capacity (usable? actual? projected?). Of course that 10% could be anywhere from 9.0001% to 10.9999% due to the fact "74%" could be 73.5% to 74.499% and likewise for "64%" ... and now I get a range with a wide range [;)] of 44.6kWh to 54.6kWh :)

Having a longer trip that uses more "%" would help I suppose. Or I could use the change in rated km instead of %, hmm...

Ok, so ya, this trip used 38 km on the range meter ... whether that's actual rated, or estimated, or rated-based-on-degraded-battery, or rated-based-on-degraded-and-temperature, or something else?? I am not sure. For the first few weeks I had the car it was exactly 'rated', but it changed at some point after that. e.g. 90% used to be 347km (of the 386 SR+ rated range). Now 90% might be 337, 338, or 339 depending on the day implying my range is 374-377km, not 386km :)

Anyways, using "38km", as being 37.500-38.499km, as a % of 386km that is 9.715-9.974% used for this trip. If I use the 376km reduced range number, it is 9.973-10.239%.

Those give me capacity numbers of 49.23-50.54 kWh (using 386km) or 47.95-49.23 kWh (using 376km).

I guess that's as close as I'm going to get without a longer trip to make the rounding errors smaller. So what is this telling me ... my actual ideal battery capacity is 49.23-50.54kWh, but my currently estimated capacity is less, and 48-49-ish kWh?


I'd be curious if anyone has a longer trip stats if their numbers match up to 'advertised' battery capacity (not actually advertised, but seems people have concluded by whatever means that SR+ is 50 kWh, and LR is 75 kWh, or 'ish').

NOTE:
My understanding from reading the forums is the trip meters only 'run' while driving, but your range meter will drop while parked and on, or asleep due to vampire drain, so for this method to be meaningful (for however meaningful it may be) you would need to run the numbers on a snapshot of right before/after a trip excluding any parked time.

So yeah you are on the right track here, and yes a longer trip will help narrow the values. I do support the idea of using the rated range value as the base for figuring out the % value for the calculations. What I have done in the past was charge to 100% to get what the rated range is at 100%. I think that is the most important data point as the lower %'s should match respectively to the drop in rated range, but you can always get a 50% reading to add some verification to that. Once you have that, the rated range will give you more granularity than the % as you have already said.

People don't like the rated range value for some reason, but it is useful.
 
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Daniel in SD

Well-Known Member
Jan 25, 2018
6,331
8,996
San Diego
But how can you be sure that the Wh/km is accurate? You can't. :p You'll need to install a current and voltage meter directly to the battery and even then you won't know if how much you're losing in the internal battery pack wiring.
 

darth_vad3r

Well-Known Sith
May 6, 2019
1,574
1,123
Canada
But how can you be sure that the Wh/km is accurate? You can't. :p You'll need to install a current and voltage meter directly to the battery and even then you won't know if how much you're losing in the internal battery pack wiring.

LOL, well for that matter we can’t trust the accuracy of the odometer reading on distance either, right? Could be off by a percent or more. I guess we could calibrate that.

Anyways...

We can work with what we’ve got, easily, in the car ... or add some more tracker apps or CAN bus devices and go for more data at still “easily” but added cost, or ya ... get into the wiring ... but that’s beyond my level of dedication to data :D
 
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AlanSubie4Life

Efficiency Obsessed Member
Oct 22, 2018
9,644
11,554
San Diego
LOL, well for that matter we can’t trust the accuracy of the odometer reading on distance either, right? Could be off by a percent or more. I guess we could calibrate that.

Anyways...

We can work with what we’ve got, easily, in the car ... or add some more tracker apps or CAN bus devices and go for more data at still “easily” but added cost, or ya ... get into the wiring ... but that’s beyond my level of dedication to data :D


FWIW, in a P3D, using only the numbers available in the car, I consistently arrive at 232Wh/rmi, meaning:

So if the trip meter says I have used 232Wh, then the rated miles will be reduced by 1 count.

This implies about 71kWh for a full discharge. Use it how you see fit! ;)

As mentioned above, the actual accuracy of the trip meter is unknown. The distance traveled (and odometer accuracy) is really not unknown, as it can be measured concurrently with GPS. I have and it is within 1%.

Since the trip meter is just a number, the actual available energy from the battery could be higher than 71kWh (the meter might just be reading low and making you think you have awesome efficiency).

I think the only thing the EPA cares about is that the end user can access the same amount of energy that was accessed during the EPA test. Note that the EPA test documents (linked elsewhere here, not going to look up the link right now - check @Zoomit posts and my posts) for the AWD vehicle indicate that about 79kWh were drawn from the battery before it was completely dead (which ends the test).

In the end the only thing that matters is how many miles you can go before the battery is dead - so, the number (Wh/mi) in the trip meter is just a guide for relative efficiency performance - it may not be accurate in an absolute sense. But to me it appears you take the kWh it says you have used, divide by 232Wh/mi, and it should align with the rated miles decrement.
 
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willow_hiller

Active Member
Apr 3, 2019
3,151
15,014
Maryland
This might be a good place to ask about those recent Alex on Autos videos. Have you guys seen them?

Really good reviews, but somehow he only manages 192 miles out of a theoretical 100-0% test in the SR+.

First one here and follow up after criticisms here.

I guess 192 out of a highway-heavy route isn't unreasonable, but in the second video he shows his lifetime wh/mi is 267. That strikes me as a bit high! Going to email him a snapshot of my lifetime 200 wh/mi after work.
 

AlanSubie4Life

Efficiency Obsessed Member
Oct 22, 2018
9,644
11,554
San Diego
This might be a good place to ask about those recent Alex on Autos videos. Have you guys seen them?

Really good reviews, but somehow he only manages 192 miles out of a theoretical 100-0% test in the SR+.

First one here and follow up after criticisms here.

I guess 192 out of a highway-heavy route isn't unreasonable, but in the second video he shows his lifetime wh/mi is 267. That strikes me as a bit high! Going to email him a snapshot of my lifetime 200 wh/mi after work.

No I hadn’t. I am actually really surprised at how badly he managed to do with his SR+. I would have expected a lot better, and 267Wh/mi lifetime is awful for the SR+. I wonder if there is something wrong with his car.
 
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Zoomit

Active Member
Sep 1, 2015
2,196
4,114
SoCal
No I hadn’t. I am actually really surprised at how badly he managed to do with his SR+. I would have expected a lot better, and 267Wh/mi lifetime is awful for the SR+. I wonder if there is something wrong with his car.
In the video Alex states that he routinely goes over a 2000’ pass for his commute. I wouldn’t read anything into the 267 Wh/mi number.
 

willow_hiller

Active Member
Apr 3, 2019
3,151
15,014
Maryland
Oops, past the point of editing my last post and two slight corrections. My lifetime is 218 wh/mi and Alex on Auto's screen showed 263 wh/mi.

Good point on the mountain pass commute @Zoomit . I wonder if he has an average speed for the range test. If it's an average speed of 70 MPH or so I could see 192 miles being realistic. And speed aside, I think acceleration and overall driving style has a big impact. Gunning it a little bit to pass slower drivers in the Model 3 might not increase your average speed, but could impact consumption.
 

AlanSubie4Life

Efficiency Obsessed Member
Oct 22, 2018
9,644
11,554
San Diego
In the video Alex states that he routinely goes over a 2000’ pass for his commute. I wouldn’t read anything into the 267 Wh/mi number.

Was just going to look it up...but since you are here :) Do you have the link to the SR+ EPA testing document?

EDIT:
Well, I found one, not quite what I wanted:
https://iaspub.epa.gov/otaqpub/display_file.jsp?docid=46968&flag=1

Ah...here it is (page 21 of this PDF):
https://iaspub.epa.gov/otaqpub/display_file.jsp?docid=46583&flag=1

Shows 62kWh for full recharge event, with battery capacity of 54.5kWh.

End edit...

Non-video link from Alex:

Model 3 Standard Range Plus Range Test – Explained

Here, he claims 51kWh from the wall for a full recharge on the SR+. Which I find difficult to believe (contradicted above).
"The 54-55 kWh capacity that has been talked about isn’t a reality. How do we know? Because we have discharged our Model 3 SR+ down to below 5% and recharged to 100%. Charging at around 72 degrees outside with a 220V EVSE (32A capable) the car wolfed down about 51.1 kWh."

Of course, he also messes up MPGe, so who knows how good he is at doing tests!:

"Another number that doesn’t add up is the EPA rating vs the EPA range. 133 MPGe translated to, you guessed it, 3.9 miles per kWh. At that efficiency number you’d need to have a 61.5 kWh battery to get 240 miles but with the 50kWh battery you’d get just 195."

(Oops! That is not how MGPe works, unless you are talking about wall kWh.)

In short, since he only seems to be able to put 83% of the energy in the battery that Tesla was able to in the SR+ EPA document, for whatever reason, I'm not surprised he is only able to get 80% of the range.
 
Last edited:
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Zoomit

Active Member
Sep 1, 2015
2,196
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SoCal
Yeah, Alex has said a number of things that make me question his background or methodologies but I do think he’s trying to be genuine (and get clicks too).

In the comments, he mentioned that they did the 3SR, Niro and Leaf e+ driving tests at the same time, so I expect at least those results to be comparable. And the Niro and Leaf got very close to their EPA combined ranges. The Model 3 did not.

A597F768-27D2-477C-BAA0-619E97D3CA8F.png
 

AlanSubie4Life

Efficiency Obsessed Member
Oct 22, 2018
9,644
11,554
San Diego
And the Niro and Leaf got very close to their EPA combined ranges. The Model 3 did not.

Yeah, it's striking. And as much as I like to poke Tesla about the 20" P3D range (it's all about the tires! (and the inefficient front motor)), I do realize that actually the RWD variants are extremely efficient, and I believe they should hit the EPA range when driven not too fast and relatively carefully (especially since the EPA range of the SR+ is actually 247mi...IIRC). So I really think there is something wrong with his car. Maybe its front tires are cross-eyed (lots of toe)? Maybe the SoC estimation is messed up?
 

willow_hiller

Active Member
Apr 3, 2019
3,151
15,014
Maryland
Yeah, Alex has said a number of things that make me question his background or methodologies but I do think he’s trying to be genuine (and get clicks too).

In the comments, he mentioned that they did the 3SR, Niro and Leaf e+ driving tests at the same time, so I expect at least those results to be comparable. And the Niro and Leaf got very close to their EPA combined ranges. The Model 3 did not.

View attachment 411313

It bothers me he says he's testing the SR, but also saying the SR has a 240 mile EPA estimated range. Tesla will eventually software lock it, and he really doesn't make that clear:
"
Anyone who orders and received a “Standard Range” model gets a “Standard Range Plus” without Auto Pilot plus a slightly slower 0-60 time. This is the only difference. Period.
"

I don't doubt he's trying to be informative, but I'm just getting confused. You really cannot use the EPA MPGe rating to figure out range. If the EPA MPGe is 133 (253 wh/mi), then by definition the battery-to-wheels efficiency must be something less than 250, right? Let's say that 230 wh/mi is typical. Even if the usable battery is only 50 kWh, he should get 217 miles of range. And I was pretty sure the usable battery capacity was a bit higher than 50 kWh. More like 52, maybe?
 

AlanSubie4Life

Efficiency Obsessed Member
Oct 22, 2018
9,644
11,554
San Diego
It bothers me he says he's testing the SR,

Yeah, that was a confusing quote, I'm not sure why he bothered to say it. In the end, though, he was testing an SR+. Unless he was not. I really have no idea what he was testing, other than it was a dog.

And I was pretty sure the usable battery capacity was a bit higher than 50 kWh. More like 52, maybe?

For the SR+, the usable battery is 54.5kWh for the article tested for the EPA. You will likely have to go below 0 rated miles to access all of this. And you should not use the trip meter displayed Wh/mi (or lifetime Wh/mi) to calculate this value (these meters appear to read low by about 4%, at least in P3D vehicles). You should also not determine what range is achievable with this capacity by taking 54.5kWh and dividing by your Wh/mi. (As initially stated at the beginning of this thread.)


The procedure for determining range in an accessible way is to determine how many Wh/mi (indicated on the trip meter) it takes to reduce your rated range by 1 mile. For this, as stated above, for accuracy, you have to do a fairly long trip.

For my P3D, it is 232Wh (indicated) /rmi. I know that if I am doing better than this according to the trip meter, I will exceed the rated range. (This never happens of course for the P3D+ unless it is all downhill.)

What the Wh/rmi is in the SR+, I do not know. Do a long trip, note the rated miles used (being careful to note them immediately before putting in drive and immediately after putting in park - you'll also want to START with a warm battery (so in warm conditions do a modest drive before starting the experiment) and end with the same warm battery), calculate the kWh from your trip meter (ideally over 100 mile trip), divide that kWh by rmi used. That's the constant. And then you can extrapolate that to whether you can do more than the rated range or less, depending on whether your Wh/mi indicated are higher or lower than that constant.

There may be errors at extremes of the range due to BMS/SoC nonlinearity, but I haven't seen them. It seems to be surprisingly linear, at least for 40+ rmi changes.
 
Last edited:

Zoomit

Active Member
Sep 1, 2015
2,196
4,114
SoCal
Maybe the SoC estimation is messed up?
This is what I was wondering too, but it’d need to be pretty far off to drop it from 240 to 192.

But it seems like in all Model 3 there’s definitely some weirdness going on with the screen indication of what’s usable verses what the EPA application says. No one is seeing 55kWh nor 78kWh.
 

AlanSubie4Life

Efficiency Obsessed Member
Oct 22, 2018
9,644
11,554
San Diego
But it seems like in all Model 3 there’s definitely some weirdness going on with the screen indication of what’s usable verses what the EPA application says. No one is seeing 55kWh nor 78kWh.

Agreed. But, as you know, that is just a meter and it may not be accurate. The trip meter does not say anything about how much energy is actually being taken out of the battery.

Part of the error (if you do try to use the trip meter) is that there are ~5 rated miles of range below zero rated miles accessible to all users, which is accessed in the EPA test (they go until the car cannot comply with the test). But that is only part of the error. As mentioned somewhere above there does seem to be an alternate universe BMS available over the bus, but I don't have much interest in accessing that. It's not necessary if you can figure out your own personal scalar for your trip meter.
 

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