Using battery energy to heat a battery…

[Devin-M]

TL;DR

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.

 

[Devin-M]

I finally got a somewhat decent cold temperature measurement. The car is a 2022 standard range Tesla model 3.

I started preconditioning the battery in the morning when the outside and car were approximately 29F. Battery state of charge 167mi remaining (37074Wh).

After 1hr 53min of driving while preconditioning (50 actual miles driven) and 75mi remaining state of charge the battery conditioning use was 31.6 miles equivalent or 7015 watt hours when I reached the charging station.

Initial charging rate was 106kW at 8:49am…

Charging was terminated at 9:03am after adding 108mi range (24976W/h) total 14 mins…

At 10:58am, after 1hr and 55mins of driving after the previous charge, maintaining precondition temperature for the entire time took 7.3mi range equivalent or 1620Wh…

 

[DaveC426913]

Frunk? :)

 

[Devin-M]

The following morning it was 49F and the battery had 83 miles (18426Wh) remaining. The charging station was 5 minutes away. I planned to measure how long it took to add 100 miles (22200Wh) of range while only preconditioning the battery for the 5 minutes it took to reach the charging station. This 5 minutes of battery conditioning consumed 1.9 miles (421Wh) of effective range.

Charging commenced at 5:16am and finished at 5:46am taking 30 minutes to add about 100 miles (22200Wh) of effective range (as opposed to 14 minutes the previous day).

 

[Devin-M]

Can I solve this as follows:
In 2 charge cycles, 8.6kWh was invested heating the battery, at $0.45/kWh costing $3.87. This saved 30 minutes of charging time. If an Uber driver makes $30/hr while in motion, $15 extra dollars were earned in the time saved while charging.

$15 > $3.87 therefore the Uber driver makes more $/hr by keeping the battery heated (preconditioning) at all times with these assumptions.