# Model 3 drive unit (motor, inverter etc) is 5.7% more efficient than Model S



## Troy (Sep 18, 2017)

Hi. After the recent EPA documents, we have more data to compare. I've calculated that the Model 3 drivetrain is 5.7% more efficient than the Model S. With the Model 3, they are now pretty close to the limits of what's possible in terms of efficiency.

The EPA documents have two numbers we can use: road load horsepower numbers from coastdown tests and dyno range numbers. Here is a table that shows what type of energy loss each number includes. I have used information from this Tesla blog post to create this table.








We have these two numbers for the Model 3 80 (aka Model 3 LR):

Road Load HP @ 50mph = 9.95 HP (Source: Page 16)
Highway dyno score = 454.64 miles (Source: Page 7)

9.95 HP means, this is the amount of power you need to apply for the car to continue going at 50 mph. During the coastdown test, the car is in neutral. Therefore drivetrain losses (motor, inverter, gearbox, motor controller and high power wire losses) are not included. During the dyno test, air drag is included because they have entered that into the dyno settings. To do that, they do the coastdown test, take some readings, convert that to a mathematical curve represented by a formula that looks like AV+BV^2+CV^3 and then they enter the A, B, C coefficients to the dyno. In other words, the dyno is able to compensate for air drag and rolling resistance at any speed for that particular vehicle.

We can find out the drivetrain losses by subtracting road load numbers from dyno test numbers. The problem is, the road load and dyno test numbers are in different units. One is horsepower and the other is miles. To solve this issue, I've came up with two methods. I don't know which is more accurate but both have similar results. The first shows 5.7% difference. The second shows 5.8%.

*Method 1:* Calculating miles from road load horsepower.
9.95 HP is 7.42 kW. We also know from the EPA dyno document that the Model 3 80 has 78.27 kWh usable capacity. Therefore if we continued to apply power for the car to coast at 50 mph until the total energy consumption is 78.27 kWh, we would have to continue doing that for 78.27 kWh / 7.42 kW = 10.55 hours. The coastdown HP number is at 50 mph. Therefore, the range would be 10.55 hours * 50 miles/hours= 527.45 miles.

In other words, imagine the Model 3 is in neutral and some other force is pushing the car so it continues to coast at 50 mph. Also, imagine this other force happens to have the exact same energy as the Model 3 80 battery which is 78.27 kWh. In this scenario, the car would go 527.45 miles.

However, instead of some other force pushing the car, if the car drives using its own motor, then it would drive for 454.64 miles. Therefore, 1- 454.64/527.45= 13.80% energy is lost in the motor, inverter, power electronics and wires. This might seem like a lot but it is actually pretty good because these components are in series. For example, if the inverter is 95% efficient, then 100 units energy is reduced to 95 units. If the motor is 94% efficient, now you need to take 94% of 95 units which is 0.95*0.94= 89%. Using this method, the numbers look like this:










In this table, the Model S 60 and 75 require the same power to overcome the road load because they are the same car. This is the software limited 60.

Looking at these numbers, I've noticed two interesting details:
1. The Model 3 80 drivetrain is 5.7% more efficient than the Model S 75.
2. The Model S 75D is 2.2% more efficient than the Model S 75.

*Method 2:* Converting road load and dyno range to kWh:
Model 3 highway dyno score was 454.64 miles (source: page 7). The average speed for that test is 48.4 mph. See the test details tab here. Therefore, the duration of that test should be 454.64 miles / 48.4 miles/hours= 9.39 hours.

We also know that the road load is 9.95 HP (7.42 kW). Pushing the car for 9.39 hours at 50 mph would consume 9.39 hours * 7.42 kW= 69.70 kWh. However, when the car drives itself it consumes the entire 78.27 kWh which means drivetrain losses are 78.27 kWh - 69.70 kWh= 8.57 kWh. That's 8.57/78.27= 10.95% of consumption. The whole table for this method looks like this:










The result is similar to the previous method. The Model 3 80 drivetrain appears to be 5.8% more efficient than Model S 75.

Another interesting detail is that when the Model S switches to the Model 3 technology, the real world range of the Model S 75D should increase from 235 miles to 235*1.057= 248 miles.


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## Frank99 (Aug 3, 2017)

Great analysis. If they've actually switched to a PM motor, perhaps the efficiency gain is the reason.

I do take exception with one item in your first table - because Tesla's don't have a "neutral" gear, I would say that the gearbox losses are included in the road load/coast down test. This doesn't impact your conclusion, however.


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## KarenRei (Jul 27, 2017)

~6% greater efficiency is about what I'd expect with a PM motor vs. induction.


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## Insaneoctane (May 10, 2017)

@Troy, interesting work. I have a few questions though.

Both of these methods seem to ignore energy used to accelerate the vehicle. Specifically, the road load at 50 mph is steady state, so when you compare that to the test cycle data, which is not steady state, you are ignoring the energy required to accelerate and decelerate the vehicle. I don't think that the regenerative breaking is as efficient as acceleration so you can't assume that they are net zero, especially if you consider the vehicles are fully charged for the test and have zero regenerative braking for the beginning of the cycle. Since the MS/MX have more mass and F=ma (a=F/m), the missing loss due to acceleration and deceleration is incorrectly part of your inefficiency calculation
Several of Tesla's EPA results show the road load at 50mph exactly equal to the coast down coefficient calculation. Some do and some don't. (see the reddit discussion here where the author argues the opposite of your usage and that there should not be any difference) We would need to understand why this is before subtracting them for calculations would be representative
Thanks again for the discussion.


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## Troy (Sep 18, 2017)

Hi, @Insaneoctane.

1. The aim here is to compare Model 3 drivetrain losses to the Model S. It's not to measure drivetrain losses precisely. Therefore the fact that one number represents a steady drive at 50 mph and the other fluctuates with an average of 48.3 mph is not important because it affects both the Model S and Model X.










2. That's me on Reddit. My username there is /u/Teslike. The direct link to the discussion is here. I have checked the data again and I don't see an error in the Model X numbers. Here is a screenshot. You can duplicate this tab if you want. There is an issue with the Model S P100D. The A,B,C numbers and the road load numbers Tesla published for that car don't match. When we try to calculate road load from the A,B,C coefficients, the calculation doesn't match but that's not important because the formula works fine for the other 13 cars. I have added the Model X to column G here and it looks fine.


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## Insaneoctane (May 10, 2017)

@Troy, I understand your answer to point #1. I still believe that the mass differences between the MS and M3 at the beginning of the cycle due to no regenerative braking is a factor, but I can't estimate if it is significant without doing some calculations (maybe later today)
For point #2, I mentioned on reddit that some of the road HP numbers match the EPA abc coefficient equation and some don't. I don't know why, but the inconsistencies make me a little weary of what is inaccurate in the data.

Nonetheless, good analysis and these calculations as they stand shows that the vehicles are far more efficient than I would have expected.


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## Troy (Sep 18, 2017)

Insaneoctane said:


> I mentioned on reddit that some of the road HP numbers match the EPA abc coefficient equation and some don't. I don't know why, but the inconsistencies make me a little weary of what is inaccurate in the data.


Hi. There are some minor rounding errors and a big error with the Model S P100D. In the table below, see the last column that compares published numbers versus calculated numbers. However, generally speaking, I don't see an issue. All published numbers seem OK except the Model S P100D.

In case others are wondering what this is about, here is an example: If you open the document here and look at page 5, it shows these 4 numbers under Model X 75D:
a=37.68
b=0.0486
c= 0.02143
Road load @50 mph= 12.49 HP

The interesting thing here is that the 12.49 HP number can be calculated from the a, b, c numbers as follows:
Road Load HP= AV + BV^2 + CV^3= (37.68 * 50 + 0.0486 * 50^2 + 0.02143 * 50^3 )/375= 12.49
V=Speed. 50^3 means 50*50*50

The calculation is a way to double check that the road load HP numbers are correct. Also with this formula, it is possible to calculate the road load at any speed, which is rather useful. Road load does not include drivetrain losses. AWD Teslas have lower drivetrain losses than RWD and the Model 3 has lower losses than the Model S.


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## Insaneoctane (May 10, 2017)

@Troy, Here's the issue I was seeing. Looking at the MX data (page 5), many don't match, you'll notice all the subconfiguration 1's (22 inch wheels) are at almost 50% error:


```
+----------------------+---------+---------+---------+----------+-----------+---------+---------+----------+----------+-----------+
| Unit/Model           | X 60D 0 | X 75D 0 | X 90D 0 | X P90D 0 | X P100D 0 | X 60D 1 | X 75D 1 | X 90D 1  | X P90D 1 | X P100D 1 |
+----------------------+---------+---------+---------+----------+-----------+---------+---------+----------+----------+-----------+
| A (N)                | 37.68   | 37.68   | 37.6807 | 38.9081  | 45.71     | 98.18   | 98.18   | 98.18    | 99.4     | 106.21    |
+----------------------+---------+---------+---------+----------+-----------+---------+---------+----------+----------+-----------+
| B N/kph)             | 0.0486  | 0.0486  | 0.0486  | 0.1197   | -0.0555   | 0.2604  | 0.2604  | 0.2604   | 0.3315   | 0.2673    |
+----------------------+---------+---------+---------+----------+-----------+---------+---------+----------+----------+-----------+
| C (N/kph2)           | 0.02143 | 0.02143 | 0.0214  | 0.02     | 0.0216    | 0.02393 | 0.02393 | 0.02393  | 0.0225   | 0.0241    |
+----------------------+---------+---------+---------+----------+-----------+---------+---------+----------+----------+-----------+
| Road Load HP @ 50mph | 12.49   | 12.49   | 12.48   | 12.65    | 13.12     | 15.3    | 15.3    | 15.29    | 15.46    | 16.18     |
+----------------------+---------+---------+---------+----------+-----------+---------+---------+----------+----------+-----------+
| kW                   | 9.31754 | 9.31754 | 9.31008 | 9.4369   | 9.78752   | 11.4138 | 11.4138 | 11.40634 | 11.53316 | 12.07028  |
+----------------------+---------+---------+---------+----------+-----------+---------+---------+----------+----------+-----------+
| Formula Result       | 12.49   | 12.49   | 12.48   | 12.65    | 12.92     | 22.80   | 22.80   | 22.80    | 22.96    | 23.98     |
+----------------------+---------+---------+---------+----------+-----------+---------+---------+----------+----------+-----------+
|  Percent Error       | 0.01%   | 0.01%   | 0.01%   | 0.02%    | -1.49%    | 49.04%  | 49.04%  | 49.14%   | 48.53%   | 48.19%    |
+----------------------+---------+---------+---------+----------+-----------+---------+---------+----------+----------+-----------+
```


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## Troy (Sep 18, 2017)

Hi, @Insaneoctane. Now I see what you mean. Indeed a few sections on the Model X file on page 5 here seem to be wrong. I have shown the wrong sections in red. For example, if we look at the red box on the top right, which is for the Model X P100D, those 3 coefficient numbers, a=45.71, b=-0.0555, c= 0.02160, are wrong because the result is not 13.12. The numbers should be a=46.87 b=-0.0518 c=0.02166. When you use these numbers, the calculation is 13.12.

I found the correct numbers inside an EPA spreadsheet here. If you want to download it, right click to the 2017 link, select "Save link as ...", then open the file in Excel or upload it to Google Sheets. Unfortunately, this file doesn't show subconfigurations. Therefore the numbers for the Model X with 22" wheels are not listed here.

Probably what happened was, they copied the correct HP numbers but the wrong A,B,C coefficient numbers when submitting the data for the MX document. Maybe they had metric units in a different column. The EPA spreadsheet has these imperial units: Target Coef A (lbf), Target Coef B (lbf/mph), Target Coef C (lbf/mph^2) but in the screenshot below, it shows metric units: A (N), B (N/kph), C (N/kph2). Either way, this is not very important. You just have to ignore the coefficients shown in red.


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## Insaneoctane (May 10, 2017)

Thanks for confirming my findings. I find your reddit comment ironic in this light..... 
"With the HP number, they can now identify the incompetent manufacturers who submit wrong numbers. It is a sneaky method to detect inconsistency within the data. EPA is not doing any of these tests."


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## roflwaffle (Sep 25, 2017)

Troy said:


> *Method 1:* Calculating miles from road load horsepower.
> 9.95 HP is 7.42 kW. We also know from the EPA dyno document that the Model 3 80 has 78.27 kWh usable capacity. Therefore if we continued to apply power for the car to coast at 50 mph until the total energy consumption is 78.27 kWh, we would have to continue doing that for 78.27 kWh / 7.42 kW = 10.55 hours. The coastdown HP number is at 50 mph. Therefore, the range would be 10.55 hours * 50 miles/hours= 527.45 miles.
> 
> In other words, imagine the Model 3 is in neutral and some other force is pushing the car so it continues to coast at 50 mph. Also, imagine this other force happens to have the exact same energy as the Model 3 80 battery which is 78.27 kWh. In this scenario, the car would go 527.45 miles.
> ...


When you say efficiency, you mean the energy lost in the drivetrain less the energy regained from regen braking, right? Using the 55mph test from the last page (SS1) and Tesla's RLHP coefficients, I'm getting 76% drivetrain efficiency, which is a lot lower than what you're getting.

Over 301.26 miles/5.48 hours, the total energy used was 65.3717kWh/.75(hp/kWh) = 87.16hphr. From Tesla's coefficients, RLHP at 55mph is 12.14hp, which puts energy over the 301.26 miles at 66.5hphr, and drivetrain efficiency at 76% (66.5hphr/87.16hphr). Granted, it's kind of late, so I might have made a mistake, but I'm not sure what it is offhand.


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## Troy (Sep 18, 2017)

@roflwaffle, you skipped a few steps in your message that made it difficult to follow. It took me a while to realize that SS1 refers to one of the test sections on the last page here. I don't know what SS means so I checked it. It could mean steady-state test at 55 mph based on page 8 here. Assuming this is correct, the range of Model 3 LR at 55 mph would be 78270 Wh * 301.26 mi / 65371.7 Wh= 360.70 miles if the car drives normally.

However, if an external force pushes the car, then the power required at 55 mph is 9.05 kW. Pushing the car for 360.7 miles at 55 mph would take 360.7 mi / 55mph= 6.56 hours and the energy required would be 6.56h * 9.05 kW= 59.35 kWh. Therefore only 59.35 kWh out of 78.27 kWh reach the wheels. That means 75.83% efficiency for the motor + inverter + drive electronics.

In short, we agree on the 76%. Like I said in message #5, I wasn't trying to measure drivetrain losses precisely. I was comparing Model 3 drivetrain losses to the Model S. Comparing steady state at 55 mph is a better idea than comparing EPA highway scores but I don't have steady state numbers for the Model S. Check out the Model S file here. The SS1 number we saw in the Model 3 file doesn't exist here.

By the way, the steady state at 55 mph could be useful. How did you find out about the 55 mph?


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## roflwaffle (Sep 25, 2017)

Yeah, I pulled it from the same document. I agree that the efficiency of 3 and S can be compared using the UDDS/HWFET, but I don't think that translates into specific efficiency figures.

FWIW, I'm seeing about 55% efficiency on the UDDS, which makes sense because of more braking/regen and idle energy consumption being a larger portion of overall energy consumption. At the same time, I'm getting 83% efficiency on the HWFET, which didn't seem right initially, since it's substantially above the 55mph SS1 efficiency.

I dug around a little, and found a reference to the J1634 incorporating the "5-cycle" testing, which I imagine means HVAC use is included.

www.sae.org/events/pdf/hybridev/2017_hybridev_guide.pdf



> Also discussed are the efficiency and range testing procedures for BEVs, SAE J1634. It recently underwent an update in order to accommodate "5-Cycle" testing.


My feeling is that 83+% efficiency is a good baseline with minimal braking/no HVAC, 76% corresponds to that, plus HVAC use, and 55% use is greater braking plus idle power consumption at a lower average speed. It's a little complicated, but I think accurate, and it may be possible to use this to accurate calculate range across many different situations.


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