Cyclable lithium capacity is greater than electrode capacity when varying the electrode thickness

[tGisbertz]

Hello all,

I'm playing with pybamm and an optimization wrt energy density by varying the electrode thicknesses. For some values of the electrode thicknesses however I get the this warning from the electrode_soh script: warnings.warn(f"Q_Li={Q_Li:.4f} Ah is greater than Q_p={Q_p:.4f} Ah.") (e.g. when the positive electrode thickness is lower than in the original parameter set: UserWarning: Q_Li=8.4028 Ah is greater than Q_p=7.9900 Ah).
My understanding is, that at least Qn and Qp have to be given for the esoh calculation, but but i dont really understand/find how/where those values are calculated since they are not given in the parameter set.
What would be the best way to avoid having QLi outside of Qn and Qp when varying the thicknesses and / how can i calculate QLi?

Thanks in advance!

[valentinsulzer]

The relevant calculations for this are in

PyBaMM/pybamm/parameters/lithium_ion_parameters.py

Lines 489 to 514 in c63671d

	self.epsilon_s = pybamm.FunctionParameter(
	f"{pref}{Domain} electrode active material volume fraction",
	{"Through-cell distance (x) [m]": x},
	)
	self.c_init = pybamm.FunctionParameter(
	f"{pref}Initial concentration in {domain} electrode [mol.m-3]",
	{
	"Radial distance (r) [m]": r,
	"Through-cell distance (x) [m]": pybamm.PrimaryBroadcast(
	x, f"{domain} {phase_name}particle"
	),
	},
	)
	self.c_init_av = pybamm.xyz_average(pybamm.r_average(self.c_init))
	self.sto_init_av = self.c_init_av / self.c_max
	eps_c_init_av = pybamm.xyz_average(
	self.epsilon_s * pybamm.r_average(self.c_init)
	)
	self.n_Li_init = eps_c_init_av * self.domain_param.L * main.A_cc
	self.Q_Li_init = self.n_Li_init * main.F / 3600
	self.epsilon_s_av = pybamm.xyz_average(self.epsilon_s)
	self.elec_loading = (
	self.epsilon_s_av * self.domain_param.L * self.c_max * main.F / 3600
	)
	self.Q_init = self.elec_loading * main.A_cc

Q_n and Q_p are linearly proportional to thickness.

Then Q_Li = Q_Li_n + Q_Li_p = Q_n * x_100 + Q_p * y_100, where x_100 and y_100 are initial stoichiometries. So you need to find the values of x_100 and y_100 that give the Q_Li you want. You can use the ElectrodeSOHSolver to do this.

[valentinsulzer]

Based on your discussions raised I'd be interested in talking more with you to find out how you are using PyBaMM. Can you email me [email protected]

[tGisbertz]

Sure I'll get in touch with you, also thanks for your quick response!