### Why does the cell capacity not change when I use different c-rates for charging?

· 2 · 338 #### Ilona Glatt

•     • Posts: 6 ##### Why does the cell capacity not change when I use different c-rates for charging?
« on: April 28, 2021, 09:14:13 AM »
When I run a charging simulation in BatteryDict the cell capacity in the result file is independent of the charge rate. In an experiment, the charge rate does influence the effective cell capacity. Can someone please help me sort out this apparent contradiction? #### Aaron Widera

• Math2Market Employee
•     • Posts: 17
• Position: Sales Engineer Digital Material R&D ##### Re: Why does the cell capacity not change when I use different c-rates for charging?
« Reply #1 on: May 20, 2021, 02:05:58 PM »
Hallo, first of all welcome here to the forum. Nice to have questions here :)

Let me try to summarize answers here:
1. As in real experiments, the capacity reached by the charging simulation depends on the criterium that stops the time evolution of the battery.
2. For a constant C-rate the most important stopping criteria are:
a) Reaching a user-defined final Cell SOC (implemented in BatteryDict2018 as “Battery’s State-ofCharge Range” or “Range of the Cell State of Charge”)
b) Reaching a user-defined final cell potential (this will be implemented in BatteryDict 2022)
3. The stopping criterion (b) will result in different reached capacities depending on the user-defined C rate.
4. For any constant C Rate, the stopping criteria (a) will result in the same reached capacity, if the cell potential does not diverge during the simulation.
5. One can reproduce the result of the stopping criterion (b) with the stopping critertion (a) using a certain trick.

The trick I mentioned is:
1. Definition of settings in ChargeBattery for stopping criterium with final cell SOC:
a) $$SOC_{start}$$: User-defined initial cell SOC.
b) $$SOC_{endt}$$: User-defined final cell SOC.
c) $$C\text{-}rate$$: user-defined charge rate.
2. Known from analyzing the battery structure and using the material settings:
a) $$C_{theo}$$: theoretical capacity of the full battery including unconnected active material, see result map in GDR: “Battery:TotalCapacity”
3. By the definition of the cell state of charge, we already know:
a) $$C_{reached} = | SOC_{end} - SOC_{start} | * C_{theo}$$
4. Additionally, we can determine the time for charging the battery cell:
a) $$reached\text{ }time = | SOC_{end} - SOC_{start} | * \frac{3600 s}{C\text{-}rate}$$
b) (Example 1: the C-rate=1 charges 100% of $$C_{theo}$$ within one hour (3600 s).
(Example 2: The C-rate=3 charges 50% of  $$C_{theo}$$  within a sixth of an hour (600 s).
5. We know this without having done any simulation with BatteryDict.
6. This comes directly from the chosen stopping criterion and does not depend on the rest of the algorithm.