How to improve the electric car

The electric car is about to replace cars with combustion engines, but range anxiety is one of the big reasons why people still don’t dare to switch. What can be done about it?

With battery technology coming to plateau, improving efficiency is one of the most promising areas for future improvements. Battery and electric motor need to be within an optimal temperature and power window to perform most efficiently.

But temperature inside the motor and torque delivery are hard to measure in a moving vehicle and here Data Science comes in handy.

Scientists from the University of Paderborn measured several “outside” parameters like ambient temperature or currents and voltages of an electric motor while running through different power cycles. Of course motor temperature and torque delivery was measured as well and now the question arises: Are there correlations between the explanatory variables and the target variables power and torque? Can we predict our target variables with the explanatory variables? Is more data always better or do we need to stick to fixed power regimes for our model?

The data can be downloaded here:

Electric Motor Temperature

1. Are there correlations between outside parameters like coolant temperature or currents to motor temperature and torque?

What we are interested in here is if one sensor result A correlates with another sensor result B. If it does, B could help explain why A behaves as it does. We can do this with all 12 sensors and get 144 pairwise correlations. Such a correlation matrix for our data is shown in figure 1.

Figure 1: Correlation matrix for one particular test run.

The matrix in figure 1 looks at first glance chaotic, but if we just look at the values related to torque, we see that the current i_q fully correlates with torque (this means it is +1), while u_d has shows a large anti-correlation (this means it is >0 and <-1).

For motor temperature pm the situation is a lot more chaotic and it seems we should include a lot of sensor data in our model to fit it.

What is our conclusion: Torque seems to be easy. Just measure the current i_q and voltage u_d and you should be fine. Motor temperature? Messy.

2. Are those sensor data sufficient to predict motor temperature and torque?

We can build a simple linear regression model to fit both target values and see what happens. And what happens is shown in figure 2 for motor temperature.

Figure 2: Components of linear regression for motor temperature

We see in figure 2 that if motor temperature goes up, coolant temperature does as well — who knew? But more tricky is the fact that at the same time current i_q and voltages u_q and u_d go down. i_d and ambient are both small and when dropping them still roughly 58% of the variance of motor temperature can be explained with only those five parameters.

That is quite ok, but of course not sufficient to accurately fit motor temperature. But ok given the simplicity of our model.

Now what about torque? The correlation matrix in figure 1 suggested a big influence of i_q and u_d. The components of linear regression for torque are shown in figure 3 and confirm our suggestions …

Figure 2: Components of linear regression for torque

… partially. Current i_q is in fact very important for explaining torque, but u_d does not seem to be important at all. In fact, those seven components in figure 3 explain 99.96% of the variance of torque, but the awesome fact is, that i_q alone explains already 99.66% of the variance of torque!

So torque is really easy. Just measure current i_q and you know the torque delivered by the electric motor.

So now we are up to question 3:

3. Can we improve our results with more data?

First, this is only relevant for motor temperature. Torque is already so well explained by current i_q that we don’t care anymore (ok, we care, but we focus on motor temperature).

Second, OF COURSE! Remember the law of large numbers?

But here we need to be careful. When collecting the data the engine performed different driving cycles, which “denote random walks in the speed-torque-plane in order to imitate real world driving cycles to a more accurate degree than constant excitations and ramp-ups and -downs would.”

Previously we only looked at data for one driving cycle. Now we try to mix them and the result is:

1. For motor temperature the explained variance drops from 58% to 34%
2. For torque the explained variance drops from 99.66% to 99.32%

So here you have it, more data does not always lead to better models!

Conclusion

Drivetrain efficiency is crucial for electric cars and to optimize efficiency also motor temperature and torque need to be controlled. Since they are tough to measure in a driving vehicle we were interested if data that is easy to measure can predict both target values.

For torque it seems that just the measurement of current i_q is sufficient to predict torque of the motor.

But for motor temperature more parameters need to be included in a model and those given by the researchers of Paderborn University explain just 58% of the variance of motor temperature. A more sophisiticated model than linear regression may help to improve the result. Or more sensor data.

But be careful here. Different driving cycles with different mappings decrease our results of predicting motor temperature. Also here a more complicated model may help.