#
# Base battery model class
#
import pybamm
import warnings
class Options(pybamm.FuzzyDict):
"""
Attributes
----------
options: dict
A dictionary of options to be passed to the model. The options that can
be set are listed below. Note that not all of the options are compatible with
each other and with all of the models implemented in PyBaMM. Each option is
optional and takes a default value if not provided.
* "cell geometry" : str
Sets the geometry of the cell. Can be "pouch" (default) or
"arbitrary". The arbitrary geometry option solves a 1D electrochemical
model with prescribed cell volume and cross-sectional area, and
(if thermal effects are included) solves a lumped thermal model
with prescribed surface area for cooling.
* "convection" : str
Whether to include the effects of convection in the model. Can be
"none" (default), "uniform transverse" or "full transverse".
Must be "none" for lithium-ion models.
* "current collector" : str
Sets the current collector model to use. Can be "uniform" (default),
"potential pair" or "potential pair quite conductive".
* "dimensionality" : int
Sets the dimension of the current collector problem. Can be 0
(default), 1 or 2.
* "electrolyte conductivity" : str
Can be "default" (default), "full", "leading order", "composite" or
"integrated".
* "external submodels" : list
A list of the submodels that you would like to supply an external
variable for instead of solving in PyBaMM. The entries of the lists
are strings that correspond to the submodel names in the keys
of `self.submodels`.
* "interfacial surface area" : str
Sets the model for the interfacial surface area. Can be "constant"
(default) or "varying". Not currently implemented in any of the models.
* "lithium plating" : str, optional
Sets the model for lithium plating. Can be "none" (default),
"reversible" or "irreversible".
* "loss of active material" : str
Sets the model for loss of active material. Can be "none" (default),
"positive", "negative" or "both" to enable it for the specific
electrode.
* "operating mode" : str
Sets the operating mode for the model. Can be "current" (default),
"voltage" or "power". Alternatively, the operating mode can be
controlled with an arbitrary function by passing the function directly
as the option. In this case the function must define the residual of
an algebraic equation. The applied current will be solved for such
that the algebraic constraint is satisfied.
* "particle" : str
Sets the submodel to use to describe behaviour within the particle.
Can be "Fickian diffusion" (default), "uniform profile",
"quadratic profile", or "quartic profile".
* "particle shape" : str
Sets the model shape of the electrode particles. This is used to
calculate the surface area to volume ratio. Can be "spherical"
(default), "user" or "no particles". For the "user" option the surface
area per unit volume can be passed as a parameter, and is therefore not
necessarily consistent with the particle shape.
* "particle cracking" : str
Sets the model to account for mechanical effects and particle
cracking. Can be "none", "no cracking", "negative", "positive" or
"both".
All options other than "none" account for the effects of swelling
of electrode particles, cell thickness change, and stress-assisted
diffusion. The options "negative", "positive" or "both" additionally
account for crack propagation in the negative, positive or both
electrodes, respectively.
* "SEI" : str
Set the SEI submodel to be used. Options are:
- "none": :class:`pybamm.sei.NoSEI` (no SEI growth)
- "constant": :class:`pybamm.sei.Constant` (constant SEI thickness)
- "reaction limited": :class:`pybamm.sei.ReactionLimited`
- "solvent-diffusion limited":\
:class:`pybamm.sei.SolventDiffusionLimited`
- "electron-migration limited": \
:class:`pybamm.sei.ElectronMigrationLimited`
- "interstitial-diffusion limited": \
:class:`pybamm.sei.InterstitialDiffusionLimited`
- "ec reaction limited": \
:class:`pybamm.sei.EcReactionLimited`
* "SEI film resistance" : str
Set the submodel for additional term in the overpotential due to SEI.
The default value is "none" if the "SEI" option is "none", and
"distributed" otherwise. This is because the "distributed" model is more
complex than the model with no additional resistance, which adds
unnecessary complexity if there is no SEI in the first place
- "none": no additional resistance\
.. math::
\\eta_r = \\frac{F}{RT} * (\\phi_s - \\phi_e - U)
- "distributed": properly included additional resistance term\
.. math::
\\eta_r = \\frac{F}{RT}
* (\\phi_s - \\phi_e - U - R_{sei} * L_{sei} * j)
- "average": constant additional resistance term (approximation to the \
true model). This model can give similar results to the \
"distributed" case without needing to make j an algebraic state\
.. math::
\\eta_r = \\frac{F}{RT}
* (\\phi_s - \\phi_e - U - R_{sei} * L_{sei} * \\frac{I}{aL})
* "SEI porosity change" : str
Whether to include porosity change due to SEI formation, can be "false"
(default) or "true".
* "side reactions" : list
Contains a list of any side reactions to include. Default is []. If this
list is not empty (i.e. side reactions are included in the model), then
"surface form" cannot be 'false'.
* "surface form" : str
Whether to use the surface formulation of the problem. Can be "false"
(default), "differential" or "algebraic".
* "thermal" : str
Sets the thermal model to use. Can be "isothermal" (default), "lumped",
"x-lumped", or "x-full".
* "total interfacial current density as a state" : str
Whether to make a state for the total interfacial current density and
solve an algebraic equation for it. Default is "false", unless "SEI film
resistance" is distributed in which case it is automatically set to
"true".
**Extends:** :class:`dict`
"""
def __init__(self, extra_options):
self.possible_options = {
"surface form": ["false", "differential", "algebraic"],
"convection": ["none", "uniform transverse", "full transverse"],
"current collector": [
"uniform",
"potential pair",
"potential pair quite conductive",
],
"dimensionality": [0, 1, 2],
"interfacial surface area": ["constant", "varying"],
"thermal": ["isothermal", "lumped", "x-lumped", "x-full"],
"cell geometry": ["arbitrary", "pouch"],
"SEI": [
"none",
"constant",
"reaction limited",
"solvent-diffusion limited",
"electron-migration limited",
"interstitial-diffusion limited",
"ec reaction limited",
],
"SEI film resistance": ["none", "distributed", "average"],
"SEI porosity change": ["true", "false"],
"lithium plating": ["none", "reversible", "irreversible"],
"loss of active material": ["none", "negative", "positive", "both"],
"operating mode": ["current", "voltage", "power"],
"particle cracking": [
"none",
"no cracking",
"negative",
"positive",
"both",
],
"particle": [
"Fickian diffusion",
"fast diffusion",
"uniform profile",
"quadratic profile",
"quartic profile",
],
"particle shape": ["spherical", "user", "no particles"],
"electrolyte conductivity": [
"default",
"full",
"leading order",
"composite",
"integrated",
],
"total interfacial current density as a state": ["true", "false"],
}
default_options = {
"operating mode": "current",
"dimensionality": 0,
"surface form": "false",
"convection": "none",
"side reactions": [],
"interfacial surface area": "constant",
"current collector": "uniform",
"particle": "Fickian diffusion",
"particle shape": "spherical",
"electrolyte conductivity": "default",
"thermal": "isothermal",
"cell geometry": "none",
"external submodels": [],
"SEI": "none",
"lithium plating": "none",
"SEI porosity change": "false",
"loss of active material": "none",
"working electrode": "none",
"particle cracking": "none",
"total interfacial current density as a state": "false",
}
# Change the default for cell geometry based on which thermal option is provided
extra_options = extra_options or {}
thermal_option = extra_options.get("thermal", "none")
# return "none" if option not given
if thermal_option in ["none", "isothermal", "lumped"]:
default_options["cell geometry"] = "arbitrary"
else:
default_options["cell geometry"] = "pouch"
# The "cell geometry" option will still be overridden by extra_options if
# provided
# Change the default for SEI film resistance based on which SEI option is
# provided
# extra_options = extra_options or {}
sei_option = extra_options.get("SEI", "none")
# return "none" if option not given
if sei_option == "none":
default_options["SEI film resistance"] = "none"
else:
default_options["SEI film resistance"] = "distributed"
# The "SEI film resistance" option will still be overridden by extra_options if
# provided
options = pybamm.FuzzyDict(default_options)
# any extra options overwrite the default options
for name, opt in extra_options.items():
if name in default_options:
options[name] = opt
else:
raise pybamm.OptionError(
"Option '{}' not recognised. Best matches are {}".format(
name, options.get_best_matches(name)
)
)
# If "SEI film resistance" is "distributed" then "total interfacial current
# density as a state" must be "true"
if options["SEI film resistance"] == "distributed":
options["total interfacial current density as a state"] = "true"
# Check that extra_options did not try to provide a clashing option
if (
extra_options.get("total interfacial current density as a state")
== "false"
):
raise pybamm.OptionError(
"If 'sei film resistance' is 'distributed' then 'total interfacial "
"current density as a state' must be 'true'"
)
# Some standard checks to make sure options are compatible
if options["SEI porosity change"] in [True, False]:
raise pybamm.OptionError(
"SEI porosity change must now be given in string format "
"('true' or 'false')"
)
if options["dimensionality"] == 0:
if options["current collector"] not in ["uniform"]:
raise pybamm.OptionError(
"current collector model must be uniform in 0D model"
)
if options["convection"] == "full transverse":
raise pybamm.OptionError(
"cannot have transverse convection in 0D model"
)
if options["particle"] == "fast diffusion":
raise NotImplementedError(
"The 'fast diffusion' option has been renamed. "
"Use 'uniform profile' instead."
)
if options["thermal"] == "x-lumped" and options["dimensionality"] == 1:
warnings.warn(
"1+1D Thermal models are only valid if both tabs are "
"placed at the top of the cell."
)
for option, value in options.items():
if (
option == "side reactions"
or option == "external submodels"
or option == "working electrode"
):
pass
elif value not in self.possible_options[option]:
if not (option == "operating mode" and callable(value)):
raise pybamm.OptionError(
f"\n'{value}' is not recognized in option '{option}'. "
f"Possible values are {self.possible_options[option]}"
)
super().__init__(options.items())
def print_options(self):
for key, value in self.items():
if key in self.possible_options.keys():
print(f"{key!r}: {value!r} (possible: {self.possible_options[key]!r})")
else:
print(f"{key!r}: {value!r}")
def print_detailed_options(self):
print(self.__doc__)
[docs]class BaseBatteryModel(pybamm.BaseModel):
"""
Base model class with some default settings and required variables
**Extends:** :class:`pybamm.BaseModel`
"""
def __init__(self, options=None, name="Unnamed battery model"):
super().__init__(name)
self.options = options
self.submodels = {}
self._built = False
self._built_fundamental_and_external = False
@property
def default_parameter_values(self):
# Default parameter values
# Lion parameters left as default parameter set for tests
return pybamm.ParameterValues(chemistry=pybamm.parameter_sets.Marquis2019)
@property
def default_geometry(self):
return pybamm.battery_geometry(
current_collector_dimension=self.options["dimensionality"]
)
@property
def default_var_pts(self):
var = pybamm.standard_spatial_vars
base_var_pts = {
var.x_n: 20,
var.x_s: 20,
var.x_p: 20,
var.r_n: 30,
var.r_p: 30,
var.y: 10,
var.z: 10,
}
# Reduce the default points for 2D current collectors
if self.options["dimensionality"] == 2:
base_var_pts.update({var.x_n: 10, var.x_s: 10, var.x_p: 10})
return base_var_pts
@property
def default_submesh_types(self):
base_submeshes = {
"negative electrode": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"separator": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"positive electrode": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"negative particle": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"positive particle": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
}
if self.options["dimensionality"] == 0:
base_submeshes["current collector"] = pybamm.MeshGenerator(pybamm.SubMesh0D)
elif self.options["dimensionality"] == 1:
base_submeshes["current collector"] = pybamm.MeshGenerator(
pybamm.Uniform1DSubMesh
)
elif self.options["dimensionality"] == 2:
base_submeshes["current collector"] = pybamm.MeshGenerator(
pybamm.ScikitUniform2DSubMesh
)
return base_submeshes
@property
def default_spatial_methods(self):
base_spatial_methods = {
"macroscale": pybamm.FiniteVolume(),
"negative particle": pybamm.FiniteVolume(),
"positive particle": pybamm.FiniteVolume(),
}
if self.options["dimensionality"] == 0:
# 0D submesh - use base spatial method
base_spatial_methods[
"current collector"
] = pybamm.ZeroDimensionalSpatialMethod()
elif self.options["dimensionality"] == 1:
base_spatial_methods["current collector"] = pybamm.FiniteVolume()
elif self.options["dimensionality"] == 2:
base_spatial_methods["current collector"] = pybamm.ScikitFiniteElement()
return base_spatial_methods
@property
def options(self):
return self._options
@options.setter
def options(self, extra_options):
options = Options(extra_options)
# Options that are incompatible with models
if isinstance(self, pybamm.lithium_ion.BaseModel):
if options["convection"] != "none":
raise pybamm.OptionError(
"convection not implemented for lithium-ion models"
)
if (
options["thermal"] in ["x-lumped", "x-full"]
and options["cell geometry"] != "pouch"
):
raise pybamm.OptionError(
options["thermal"] + " model must have pouch geometry."
)
if isinstance(self, pybamm.lead_acid.BaseModel):
if options["thermal"] != "isothermal" and options["dimensionality"] != 0:
raise pybamm.OptionError(
"Lead-acid models can only have thermal "
"effects if dimensionality is 0."
)
if options["SEI"] != "none" or options["SEI film resistance"] != "none":
raise pybamm.OptionError("Lead-acid models cannot have SEI formation")
if options["lithium plating"] != "none":
raise pybamm.OptionError("Lead-acid models cannot have lithium plating")
if (
isinstance(self, (pybamm.lead_acid.LOQS, pybamm.lead_acid.Composite))
and options["surface form"] == "false"
):
if len(options["side reactions"]) > 0:
raise pybamm.OptionError(
"""must use surface formulation to solve {!s} with side reactions
""".format(
self
)
)
self._options = options
def set_standard_output_variables(self):
# Time
self.variables.update(
{
"Time": pybamm.t,
"Time [s]": pybamm.t * self.timescale,
"Time [min]": pybamm.t * self.timescale / 60,
"Time [h]": pybamm.t * self.timescale / 3600,
}
)
# Spatial
var = pybamm.standard_spatial_vars
L_x = self.param.L_x
L_z = self.param.L_z
self.variables.update(
{
"x": var.x,
"x [m]": var.x * L_x,
"x_n": var.x_n,
"x_n [m]": var.x_n * L_x,
"x_s": var.x_s,
"x_s [m]": var.x_s * L_x,
"x_p": var.x_p,
"x_p [m]": var.x_p * L_x,
}
)
if self.options["dimensionality"] == 1:
self.variables.update({"z": var.z, "z [m]": var.z * L_z})
elif self.options["dimensionality"] == 2:
# Note: both y and z are scaled with L_z
self.variables.update(
{"y": var.y, "y [m]": var.y * L_z, "z": var.z, "z [m]": var.z * L_z}
)
# Initialize "total reaction" variables
# These will get populated by the "get_coupled_variables" methods, and then used
# later by "set_rhs" or "set_algebraic", which ensures that we always have
# added all the necessary variables by the time the sum is used
self.variables.update(
{
"Sum of electrolyte reaction source terms": 0,
"Sum of negative electrode electrolyte reaction source terms": 0,
"Sum of positive electrode electrolyte reaction source terms": 0,
"Sum of x-averaged negative electrode "
"electrolyte reaction source terms": 0,
"Sum of x-averaged positive electrode "
"electrolyte reaction source terms": 0,
"Sum of interfacial current densities": 0,
"Sum of negative electrode interfacial current densities": 0,
"Sum of positive electrode interfacial current densities": 0,
"Sum of x-averaged negative electrode interfacial current densities": 0,
"Sum of x-averaged positive electrode interfacial current densities": 0,
}
)
def build_fundamental_and_external(self):
# Get the fundamental variables
for submodel_name, submodel in self.submodels.items():
pybamm.logger.debug(
"Getting fundamental variables for {} submodel ({})".format(
submodel_name, self.name
)
)
self.variables.update(submodel.get_fundamental_variables())
# Set the submodels that are external
for sub in self.options["external submodels"]:
self.submodels[sub].external = True
# Set any external variables
self.external_variables = []
for submodel_name, submodel in self.submodels.items():
pybamm.logger.debug(
"Getting external variables for {} submodel ({})".format(
submodel_name, self.name
)
)
external_variables = submodel.get_external_variables()
self.external_variables += external_variables
self._built_fundamental_and_external = True
def build_coupled_variables(self):
# Note: pybamm will try to get the coupled variables for the submodels in the
# order they are set by the user. If this fails for a particular submodel,
# return to it later and try again. If setting coupled variables fails and
# there are no more submodels to try, raise an error.
submodels = list(self.submodels.keys())
count = 0
# For this part the FuzzyDict of variables is briefly converted back into a
# normal dictionary for speed with KeyErrors
self._variables = dict(self._variables)
while len(submodels) > 0:
count += 1
for submodel_name, submodel in self.submodels.items():
if submodel_name in submodels:
pybamm.logger.debug(
"Getting coupled variables for {} submodel ({})".format(
submodel_name, self.name
)
)
try:
self.variables.update(
submodel.get_coupled_variables(self.variables)
)
submodels.remove(submodel_name)
except KeyError as key:
if len(submodels) == 1 or count == 100:
# no more submodels to try
raise pybamm.ModelError(
"Missing variable for submodel '{}': {}.\n".format(
submodel_name, key
)
+ "Check the selected "
"submodels provide all of the required variables."
)
else:
# try setting coupled variables on next loop through
pybamm.logger.debug(
"Can't find {}, trying other submodels first".format(
key
)
)
# Convert variables back into FuzzyDict
self._variables = pybamm.FuzzyDict(self._variables)
def build_model_equations(self):
# Set model equations
for submodel_name, submodel in self.submodels.items():
if submodel.external is False:
pybamm.logger.debug(
"Setting rhs for {} submodel ({})".format(submodel_name, self.name)
)
submodel.set_rhs(self.variables)
pybamm.logger.debug(
"Setting algebraic for {} submodel ({})".format(
submodel_name, self.name
)
)
submodel.set_algebraic(self.variables)
pybamm.logger.debug(
"Setting boundary conditions for {} submodel ({})".format(
submodel_name, self.name
)
)
submodel.set_boundary_conditions(self.variables)
pybamm.logger.debug(
"Setting initial conditions for {} submodel ({})".format(
submodel_name, self.name
)
)
submodel.set_initial_conditions(self.variables)
submodel.set_events(self.variables)
pybamm.logger.debug(
"Updating {} submodel ({})".format(submodel_name, self.name)
)
self.update(submodel)
self.check_no_repeated_keys()
def build_model(self):
# Check if already built
if self._built:
raise pybamm.ModelError(
"""Model already built. If you are adding a new submodel, try using
`model.update` instead."""
)
pybamm.logger.info("Start building {}".format(self.name))
if self._built_fundamental_and_external is False:
self.build_fundamental_and_external()
self.build_coupled_variables()
self.build_model_equations()
pybamm.logger.debug("Setting voltage variables ({})".format(self.name))
self.set_voltage_variables()
pybamm.logger.debug("Setting SoC variables ({})".format(self.name))
self.set_soc_variables()
# Massive hack for consistent delta_phi = phi_s - phi_e with SPMe
# This needs to be corrected
if isinstance(self, pybamm.lithium_ion.SPMe):
for domain in ["Negative", "Positive"]:
phi_s = self.variables[domain + " electrode potential"]
phi_e = self.variables[domain + " electrolyte potential"]
delta_phi = phi_s - phi_e
s = self.submodels[domain.lower() + " interface"]
var = s._get_standard_surface_potential_difference_variables(delta_phi)
self.variables.update(var)
self._built = True
pybamm.logger.info("Finish building {}".format(self.name))
[docs] def new_empty_copy(self):
""" See :meth:`pybamm.BaseModel.new_empty_copy()` """
new_model = self.__class__(name=self.name, options=self.options, build=False)
new_model.use_jacobian = self.use_jacobian
new_model.convert_to_format = self.convert_to_format
new_model.timescale = self.timescale
new_model.length_scales = self.length_scales
return new_model
[docs] def set_external_circuit_submodel(self):
"""
Define how the external circuit defines the boundary conditions for the model,
e.g. (not necessarily constant-) current, voltage, etc
"""
if self.options["operating mode"] == "current":
self.submodels["external circuit"] = pybamm.external_circuit.CurrentControl(
self.param
)
elif self.options["operating mode"] == "voltage":
self.submodels[
"external circuit"
] = pybamm.external_circuit.VoltageFunctionControl(self.param)
elif self.options["operating mode"] == "power":
self.submodels[
"external circuit"
] = pybamm.external_circuit.PowerFunctionControl(self.param)
elif callable(self.options["operating mode"]):
self.submodels[
"external circuit"
] = pybamm.external_circuit.FunctionControl(
self.param, self.options["operating mode"]
)
def set_tortuosity_submodels(self):
self.submodels["electrolyte tortuosity"] = pybamm.tortuosity.Bruggeman(
self.param, "Electrolyte"
)
self.submodels["electrode tortuosity"] = pybamm.tortuosity.Bruggeman(
self.param, "Electrode"
)
def set_thermal_submodel(self):
if self.options["thermal"] == "isothermal":
thermal_submodel = pybamm.thermal.isothermal.Isothermal(self.param)
elif self.options["thermal"] == "lumped":
thermal_submodel = pybamm.thermal.Lumped(
self.param,
cc_dimension=self.options["dimensionality"],
geometry=self.options["cell geometry"],
)
elif self.options["thermal"] == "x-lumped":
if self.options["dimensionality"] == 0:
# With 0D current collectors x-lumped is equivalent to lumped pouch
thermal_submodel = pybamm.thermal.Lumped(self.param, geometry="pouch")
elif self.options["dimensionality"] == 1:
thermal_submodel = pybamm.thermal.pouch_cell.CurrentCollector1D(
self.param
)
elif self.options["dimensionality"] == 2:
thermal_submodel = pybamm.thermal.pouch_cell.CurrentCollector2D(
self.param
)
elif self.options["thermal"] == "x-full":
if self.options["dimensionality"] == 0:
thermal_submodel = pybamm.thermal.OneDimensionalX(self.param)
elif self.options["dimensionality"] == 1:
raise NotImplementedError(
"""X-full thermal submodels do not
yet support 1D current collectors"""
)
elif self.options["dimensionality"] == 2:
raise NotImplementedError(
"""X-full thermal submodels do
not yet support 2D current collectors"""
)
self.submodels["thermal"] = thermal_submodel
def set_current_collector_submodel(self):
if self.options["current collector"] in ["uniform"]:
submodel = pybamm.current_collector.Uniform(self.param)
elif self.options["current collector"] == "potential pair":
if self.options["dimensionality"] == 1:
submodel = pybamm.current_collector.PotentialPair1plus1D(self.param)
elif self.options["dimensionality"] == 2:
submodel = pybamm.current_collector.PotentialPair2plus1D(self.param)
self.submodels["current collector"] = submodel
def set_voltage_variables(self):
ocp_n = self.variables["Negative electrode open circuit potential"]
ocp_p = self.variables["Positive electrode open circuit potential"]
ocp_n_av = self.variables[
"X-averaged negative electrode open circuit potential"
]
ocp_p_av = self.variables[
"X-averaged positive electrode open circuit potential"
]
ocp_n_dim = self.variables["Negative electrode open circuit potential [V]"]
ocp_p_dim = self.variables["Positive electrode open circuit potential [V]"]
ocp_n_av_dim = self.variables[
"X-averaged negative electrode open circuit potential [V]"
]
ocp_p_av_dim = self.variables[
"X-averaged positive electrode open circuit potential [V]"
]
ocp_n_left = pybamm.boundary_value(ocp_n, "left")
ocp_n_left_dim = pybamm.boundary_value(ocp_n_dim, "left")
ocp_p_right = pybamm.boundary_value(ocp_p, "right")
ocp_p_right_dim = pybamm.boundary_value(ocp_p_dim, "right")
ocv_av = ocp_p_av - ocp_n_av
ocv_av_dim = ocp_p_av_dim - ocp_n_av_dim
ocv = ocp_p_right - ocp_n_left
ocv_dim = ocp_p_right_dim - ocp_n_left_dim
# overpotentials
eta_r_n_av = self.variables[
"X-averaged negative electrode reaction overpotential"
]
eta_r_n_av_dim = self.variables[
"X-averaged negative electrode reaction overpotential [V]"
]
eta_r_p_av = self.variables[
"X-averaged positive electrode reaction overpotential"
]
eta_r_p_av_dim = self.variables[
"X-averaged positive electrode reaction overpotential [V]"
]
delta_phi_s_n_av = self.variables["X-averaged negative electrode ohmic losses"]
delta_phi_s_n_av_dim = self.variables[
"X-averaged negative electrode ohmic losses [V]"
]
delta_phi_s_p_av = self.variables["X-averaged positive electrode ohmic losses"]
delta_phi_s_p_av_dim = self.variables[
"X-averaged positive electrode ohmic losses [V]"
]
delta_phi_s_av = delta_phi_s_p_av - delta_phi_s_n_av
delta_phi_s_av_dim = delta_phi_s_p_av_dim - delta_phi_s_n_av_dim
eta_r_av = eta_r_p_av - eta_r_n_av
eta_r_av_dim = eta_r_p_av_dim - eta_r_n_av_dim
# SEI film overpotential
eta_sei_n_av = self.variables[
"X-averaged negative electrode SEI film overpotential"
]
eta_sei_p_av = self.variables[
"X-averaged positive electrode SEI film overpotential"
]
eta_sei_n_av_dim = self.variables[
"X-averaged negative electrode SEI film overpotential [V]"
]
eta_sei_p_av_dim = self.variables[
"X-averaged positive electrode SEI film overpotential [V]"
]
eta_sei_av = eta_sei_n_av + eta_sei_p_av
eta_sei_av_dim = eta_sei_n_av_dim + eta_sei_p_av_dim
# TODO: add current collector losses to the voltage in 3D
self.variables.update(
{
"X-averaged open circuit voltage": ocv_av,
"Measured open circuit voltage": ocv,
"X-averaged open circuit voltage [V]": ocv_av_dim,
"Measured open circuit voltage [V]": ocv_dim,
"X-averaged reaction overpotential": eta_r_av,
"X-averaged reaction overpotential [V]": eta_r_av_dim,
"X-averaged SEI film overpotential": eta_sei_av,
"X-averaged SEI film overpotential [V]": eta_sei_av_dim,
"X-averaged solid phase ohmic losses": delta_phi_s_av,
"X-averaged solid phase ohmic losses [V]": delta_phi_s_av_dim,
}
)
# Battery-wide variables
V = self.variables["Terminal voltage"]
V_dim = self.variables["Terminal voltage [V]"]
eta_e_av_dim = self.variables["X-averaged electrolyte ohmic losses [V]"]
eta_c_av_dim = self.variables["X-averaged concentration overpotential [V]"]
num_cells = pybamm.Parameter(
"Number of cells connected in series to make a battery"
)
self.variables.update(
{
"X-averaged battery open circuit voltage [V]": ocv_av_dim * num_cells,
"Measured battery open circuit voltage [V]": ocv_dim * num_cells,
"X-averaged battery reaction overpotential [V]": eta_r_av_dim
* num_cells,
"X-averaged battery solid phase ohmic losses [V]": delta_phi_s_av_dim
* num_cells,
"X-averaged battery electrolyte ohmic losses [V]": eta_e_av_dim
* num_cells,
"X-averaged battery concentration overpotential [V]": eta_c_av_dim
* num_cells,
"Battery voltage [V]": V_dim * num_cells,
}
)
# Variables for calculating the equivalent circuit model (ECM) resistance
# Need to compare OCV to initial value to capture this as an overpotential
ocv_init = self.param.U_p(
self.param.c_p_init(1), self.param.T_init
) - self.param.U_n(self.param.c_n_init(0), self.param.T_init)
ocv_init_dim = (
self.param.U_p_ref
- self.param.U_n_ref
+ self.param.potential_scale * ocv_init
)
eta_ocv = ocv - ocv_init
eta_ocv_dim = ocv_dim - ocv_init_dim
# Current collector current density for working out euiqvalent resistance
# based on Ohm's Law
i_cc = self.variables["Current collector current density"]
i_cc_dim = self.variables["Current collector current density [A.m-2]"]
# ECM overvoltage is OCV minus terminal voltage
v_ecm = ocv - V
v_ecm_dim = ocv_dim - V_dim
# Current collector area for turning resistivity into resistance
A_cc = self.param.A_cc
# Hack to avoid division by zero if i_cc is exactly zero
# If i_cc is zero, i_cc_not_zero becomes 1. But multiplying by sign(i_cc) makes
# the local resistance 'zero' (really, it's not defined when i_cc is zero)
i_cc_not_zero = ((i_cc > 0) + (i_cc < 0)) * i_cc + (i_cc >= 0) * (i_cc <= 0)
i_cc_dim_not_zero = ((i_cc_dim > 0) + (i_cc_dim < 0)) * i_cc_dim + (
i_cc_dim >= 0
) * (i_cc_dim <= 0)
self.variables.update(
{
"Change in measured open circuit voltage": eta_ocv,
"Change in measured open circuit voltage [V]": eta_ocv_dim,
"Local ECM resistance": pybamm.sign(i_cc)
* v_ecm
/ (i_cc_not_zero * A_cc),
"Local ECM resistance [Ohm]": pybamm.sign(i_cc)
* v_ecm_dim
/ (i_cc_dim_not_zero * A_cc),
}
)
# Cut-off voltage
self.events.append(
pybamm.Event(
"Minimum voltage",
V - self.param.voltage_low_cut,
pybamm.EventType.TERMINATION,
)
)
self.events.append(
pybamm.Event(
"Maximum voltage",
V - self.param.voltage_high_cut,
pybamm.EventType.TERMINATION,
)
)
# Power
I_dim = self.variables["Current [A]"]
self.variables.update({"Terminal power [W]": I_dim * V_dim})
[docs] def set_soc_variables(self):
"""
Set variables relating to the state of charge.
This function is overriden by the base battery models
"""
pass
[docs] def process_parameters_and_discretise(self, symbol, parameter_values, disc):
"""
Process parameters and discretise a symbol using supplied parameter values
and discretisation. Note: care should be taken if using spatial operators
on dimensional symbols. Operators in pybamm are written in non-dimensional
form, so may need to be scaled by the appropriate length scale. It is
recommended to use this method on non-dimensional symbols.
Parameters
----------
symbol : :class:`pybamm.Symbol`
Symbol to be processed
parameter_values : :class:`pybamm.ParameterValues`
The parameter values to use during processing
disc : :class:`pybamm.Discretisation`
The discrisation to use
Returns
-------
:class:`pybamm.Symbol`
Processed symbol
"""
# Set y slices
if disc.y_slices == {}:
variables = list(self.rhs.keys()) + list(self.algebraic.keys())
disc.set_variable_slices(variables)
# Set boundary condtions (also requires setting parameter values)
if disc.bcs == {}:
self.boundary_conditions = parameter_values.process_boundary_conditions(
self
)
disc.bcs = disc.process_boundary_conditions(self)
# Process
param_symbol = parameter_values.process_symbol(symbol)
disc_symbol = disc.process_symbol(param_symbol)
return disc_symbol