Source code for pybop.pybamm.parameter_utils
import pybamm
from pybamm import LithiumIonParameters, Parameter, ParameterValues, Symbol
[docs]
def set_formation_concentrations(parameter_values: ParameterValues) -> None:
"""
Compute the concentration of lithium in the positive electrode assuming that
all lithium in the active material originated from the positive electrode.
Only perform the calculation if an initial concentration exists for both
electrodes, i.e. it is not a half cell.
Parameters
----------
parameter_values : pybamm.ParameterValues
A PyBaMM parameter set containing standard lithium ion parameters.
"""
param_key = "Initial concentration in negative electrode [mol.m-3]"
if param_key in parameter_values.keys():
# Obtain the total amount of lithium in the active material
Q_Li_particles_init = parameter_values.evaluate(
LithiumIonParameters().Q_Li_particles_init
)
# Convert this total amount to a concentration in the positive electrode
c_init = parameter_values.evaluate(
(Q_Li_particles_init * 3600)
/ (
Parameter("Positive electrode active material volume fraction")
* Parameter("Positive electrode thickness [m]")
* electrode_area()
* pybamm.constants.F.value
)
)
# Set the ratio between the cyclable and theoretical formation concentrations
c_p_max = parameter_values.evaluate(
Parameter("Maximum concentration in positive electrode [mol.m-3]")
)
parameter_values.update(
{
"Initial cyclable lithium inventory to positive electrode capacity ratio": c_init
/ c_p_max
}
)
# Define the maximum theoretical lithium inventory [A.h]
Q_Li_particles_max = (
pybamm.Parameter("Maximum concentration in positive electrode [mol.m-3]")
* Parameter("Positive electrode active material volume fraction")
* Parameter("Positive electrode thickness [m]")
* electrode_area()
* pybamm.constants.F.value
) / 3600
# Define an initial lithium inventory that scales with the maximum theoretical lithium inventory
Q_Li_particles_init = (
pybamm.Parameter(
"Initial cyclable lithium inventory to positive electrode capacity ratio"
)
* Q_Li_particles_max
)
def set_initial_state_from_formation(
initial_value,
parameter_values,
direction=None,
param=None,
known_value="cyclable lithium capacity",
inplace=True,
options=None,
inputs=None,
tol=1e-6,
):
if known_value != "cyclable lithium capacity":
raise ValueError(
"The known value must be cyclable litihum capacity to use formation concentrations."
)
if param is not None and not isinstance(param, LithiumIonParameters):
raise TypeError(
"Expecting param to be an instance of PyBaMM's LithiumIonParameters class."
)
# Employ the scalable definition of the cyclable lithium inventory
param = param or LithiumIonParameters()
param.Q_Li_particles_init = Q_Li_particles_init
return pybamm.lithium_ion.set_initial_state(
initial_value=initial_value,
parameter_values=parameter_values,
direction=direction,
param=param,
known_value=known_value,
inplace=inplace,
options=options,
inputs=inputs,
tol=tol,
)
parameter_values._set_initial_state = set_initial_state_from_formation # noqa: SLF001
[docs]
def electrode_area() -> Symbol:
"""
An expression for the cross-sectional area of the electrode.
"""
return Parameter("Electrode height [m]") * Parameter("Electrode width [m]")
[docs]
def cell_volume() -> Symbol:
"""
An expression for the total cell volume in m3.
This method defines the total cell volume as the product of the electrode
cross-sectional area and the total thickness of the cell including electrodes,
eparator, and current collectors.
"""
cell_thickness = (
Parameter("Positive electrode thickness [m]")
+ Parameter("Negative electrode thickness [m]")
+ Parameter("Separator thickness [m]")
+ Parameter("Positive current collector thickness [m]")
+ Parameter("Negative current collector thickness [m]")
)
return electrode_area() * cell_thickness
[docs]
def cell_mass() -> Symbol:
"""
An expression for the total cell mass in kilograms.
This method defines the total mass as the sum of the components masses,
including the electrodes, separator, and current collectors, based on their
densities, porosities, and thicknesses.
"""
def mass_density(
active_material_vol_frac,
density,
porosity,
electrolyte_density,
carbon_binder_domain_density,
):
return (
(active_material_vol_frac * density)
+ (porosity * electrolyte_density)
+ (1.0 - active_material_vol_frac - porosity) * carbon_binder_domain_density
)
def area_density(thickness, mass_density):
return thickness * mass_density
# Mass densities
positive_mass_density = mass_density(
Parameter("Positive electrode active material volume fraction"),
Parameter("Positive electrode active material density [kg.m-3]"),
Parameter("Positive electrode porosity"),
Parameter("Electrolyte density [kg.m-3]"),
Parameter("Positive electrode carbon-binder density [kg.m-3]"),
)
negative_mass_density = mass_density(
Parameter("Negative electrode active material volume fraction"),
Parameter("Negative electrode active material density [kg.m-3]"),
Parameter("Negative electrode porosity"),
Parameter("Electrolyte density [kg.m-3]"),
Parameter("Negative electrode carbon-binder density [kg.m-3]"),
)
# Areal densities
positive_area_density = area_density(
Parameter("Positive electrode thickness [m]"), positive_mass_density
)
negative_area_density = area_density(
Parameter("Negative electrode thickness [m]"), negative_mass_density
)
separator_area_density = area_density(
Parameter("Separator thickness [m]"),
Parameter("Separator density [kg.m-3]"),
)
positive_cc_area_density = area_density(
Parameter("Positive current collector thickness [m]"),
Parameter("Positive current collector density [kg.m-3]"),
)
negative_cc_area_density = area_density(
Parameter("Negative current collector thickness [m]"),
Parameter("Negative current collector density [kg.m-3]"),
)
total_area_density = (
positive_area_density
+ negative_area_density
+ separator_area_density
+ positive_cc_area_density
+ negative_cc_area_density
)
return electrode_area() * total_area_density