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Thermal modelling of an equivalent Lithium cell battery pack

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I'm trying to model a 4parallel and 80series battery pack through a single 2RC model in order to speed up the identification procedure and easily estimate R1,R2,C1,C2 and R0 using experimental discharge curves. The model easily matches the experimental curve with the simulated one by adjusting the values of those parameters but I would like also to model the correct thermal behaviour of the battery pack with an equivalent compact model.
Currently I'm considering that the model temperature can be computed by solving the heat equation of a homogeneous body exchanging heat with the environment (using temperature data of the environment where the battery pack is located). With the proper experimental data the model gives back a temperature of 27 °C while the correct battery pack temperature (collected from the BMS) is shown in the figure with values rangin from 23.8°C to 28°C during the discharge phase (the phase I'm considering with a negative quasi constant current for the discharge).
How can I actually model this behaviour with a compact thermal model considering the fact that the battery pack is successfuly modelled with a 2RC circuit in relation to the discharge voltage curves?
Thank you a lot for your time.
Following there are the pictures of (1) Correct temperature of the battery pack from the BMS as a function of the discharge time in sec (2) My thermal model of the equivalent circuit where T is the temperature of the model (as I mentioned befor is stable at 27°C).

Accepted Answer

Joel Van Sickel
Joel Van Sickel on 7 Nov 2022
This example incorporate thermal and might be a good place to start, although it looks like you want a more reduced order model so this approach is probably more complex than you want:
For a reduced order model, your model is TOO reduced. First, you are putting your heat flow directly into a thermal mass. This means that your temperature instantaneously changes when the battery discharges energy. This is not how it works in the real world. For a reduced order mode, at least put a thermal resistance between your heat flow and thermal mass. However, that is only a 1st order system and will likely not recreate your dynamic response correctly. You will want at least a 2nd or 3rd order thermal model to match the plot you shared. Since you are just fitting to experimental data, how you accomplish the model is not that relevant. Maybe you can use the prebuilt cauer or foster thermal models in simscape electrical. The new tool simscape battery may also be useful in creating more detailed models to have a compairson point to your reduced order model.
slow_hand on 7 Nov 2022
Yes the battery pack is exchanging heat with the external environment (air).
So for example I can use the foster or cauer thermal model in addition to the one I've presented (or introduce a thermal resistance) and tune it with the parameters estimation tool by comparing the real temperature with the one from the model?
Joel Van Sickel
Joel Van Sickel on 8 Nov 2022
yes, that would be a good first attempt at trying to get something that is useful without explicitly calculating system thermal parameters.

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