Adding a custom submodel for LAM

[DarioSlaifsteinSk]

Hi,
I have a reduced order model (ROM) for loss of active material (LAM) in the anode and I want to incorporate it to an SPM model.
The model is from Jin (2022) with the following Eqs.:

$$ Q_{AM,t} = Q_{Li, 0} . \int_0^t k_{AM}.e^{\frac{-E_{AM}}{R.T}}.SoC_{t}.|i_{t}| .dt $$

where:

$$ k_{\text{AM}}=\frac{k_{\text{AM}}^0}{\varepsilon_{\text{AM}, 0}} $$

$$ SoC_t = \frac{x_{100} - x_t }{x_{100} - x_{0}} $$

the parameters are only $k_{\text{AM}}$ in [1/Ah] and $E_{\text{AM}}$.
I checked this notebook but i don't really get the logic of it.

I'm guessing that I should do something like the following:

# initialize the models
model = pybamm.lithium_ion.SPM() # cell model
LAMmodel = pybamm.active_material.BaseModel()

# LAM model parameters
kAM = pybamm.Parameter("LAM Reaction rate constant [1 .A-1.h-1]")
EAM = pybamm.Parameter("LAM Activation energy [J.mol-1]")

# LAM model variables
QAM = pybamm.Variable("Capacity loss of active material [A.h]")
dQAMdt = kAM * pybamm.exp(-EAM / (pybamm.constants.R * T) ) * abs(Iapp) * Cell_SOC * Q0;

LAMmodel.rhs = {QAM: dQAMdt}
model.submodels["negative primary active material"] = LAMmodel

The cell current Iapp, the initial capacity Q0, the cell temperature T, the state of charge Cell_SOC and the lost capacity QAM should all come from the cell model. But... I have no idea how to do it. 😅

I'm "using" the "reaction rate" option for LAM in the SPM but I have no reference values for my cell so all my results are kinda dubious.

Thanks in advance,

[valentinsulzer]

If you haven't done this yet I would start by making a copy of BasicSPM and adding the new equations in directly https://github.com/pybamm-team/PyBaMM/blob/develop/pybamm/models/full_battery_models/lithium_ion/basic_spm.py

It won't work with experiments but we're working on making that possible in the next release

[DarioSlaifsteinSk]

Well I literally needed it for that so...
A little context, I´m using PBROMs (performance and ageing) for control and I wanted to investigate the effect of using old and fresh batteries, which is one of the main advantages of the models.

I wanted to have a good/realistic aged battery dataset for the initial conditions of the cell and controller.

I´ll use what I can find in the literature then and wait for the new features. If these are incorporated that´d be great.