B Using battery energy to heat a battery…

[Devin-M]

TL;DR Summary

Thermodynamics of using a battery to heat itself…

Problem: You’re an Uber driver with a Tesla Model 3. Today’s low: 30F, high: 65F.
You want to reach a USD$ profit target in the least number of hours, but your choices could have added cost. Do you preheat the battery only when you are headed to the charging station (to increase the charging rate by warming the battery — however the battery might not be “warm enough” when your reach the charger and thus slower charging rates), or do you always “navigate to the charger” the entire day (which preheats the battery), so that the car maintains the battery at the optimal temperature for the entire day (thus always giving peak charge speed on arrival to the supercharger, but using more power). This option uses more energy to maintain battery at near constant temp, and the charging rate is increased so less time charging, downtime is reduced (more time available to earn). What is the optimal strategy for least time to a certain dollar profit target, considering charging costs $0.45USD/kwh?

 

[Devin-M]

PS… It isn’t necessary to fully charge the battery each time. As seen above, with the battery pre-warmed, two separate 15 minute charging sessions with driving in between provides more energy and range than a single 30 minute session.

*EDIT: When I initially viewed this chart I thought it showed pre-warmed vs not prewarmed, but I believe this chart only shows the battery with initial cell temp close to 40C, the solid line is the cell temps and the dashed line is the power into the pack. What isn’t shown by this graph is if the cells are in freezing temperatures, this initial charging power will be much lower.

 

[Devin-M]

This graph supposedly shows 30F weather, initial 10% state of charge, temperature preconditioned (grey) vs not preconditioned (green:

Source: https://insideevs.com/news/699912/supercharging-tesla-winter-preconditioned-vs-cold-battery-test/

 

[Devin-M]

I took some measurements today. The temp was constant 55f. A full preconditioning took 3.3kWh. Then after 2 hours of driving and 61 miles traveled, maintaining the constant preconditioning took a further 1.3kWh. In the pictures below, the preconditioning energy use is shown in miles. These miles can be multiplied by the rated 222Wh/mi to get the Wh used.