The use of modeling based on fractional order calculus could improve the accuracy of range estimations provided in electric vehicles — through the suppression of “errors normally observed in methods for estimating charge.”

As this is not my area of expertise, I’ll just go ahead and post the explanation of context provided in a recent piece about the research:

*It’s virtually impossible to know the exact interior state of batteries as they powers devices like phones, laptops or cars. Batteries can’t be opened without killing power. And even if it were possible, there are complex chemical interactions, temperature effects and mechanical changes to consider. That’s why researchers use more roundabout ways of estimating charge. These methods typically involve measuring external properties such as voltage or current to derive the charge. Each measurement, however, carries a small amount of error, and because many measurements are made per second, such errors quickly pile up. Although more advanced methods, such as Kalman filtering, use mathematical models to reduce these inaccuracies, they still produce errors of greater than 1%. The problem is that the underlying equations, which are based on integer order calculus, don’t fully capture the complex electrochemical reactions that occur in a battery. These processes are better described with fractional order calculus. And by using this more exotic form, researchers developed a more accurate technique for estimating the amount of charge left in a battery while it’s in use.*

This was accomplished by the researchers through:

- first taking measurements of actual battery behavior during charge/discharge;
- creating a simple circuit model that allowed replication of this observed behavior; and then
- formulating fractional order equations to “describe the activity of each element in the circuit.”

Following testing of the model, the researchers determined that the charge estimations were much closer to the truth than as with other methods — being only 0.5% off. This compares to differences of as much as 3% when utilizing integer order calculus.

Obviously, these findings are preliminary and will need to be tested a good deal further before seeing potential wide-scale utilization.

Irrespective of which EV you own or are planning to buy, the human brain can, usually, work out the capacity of any system after a few times use. Otherwise your in trouble…

The estimate would be helped a lot by having three additional pieces of data:

The location of the car (and therefore what road it is on).

The elevation of the car at any given moment (and therefore the rise / drop on the current road).

The current air temperature, giving a good estimation of the aerodynamic drag on the car, and whether or not HVAC will be needed.