#
# Base class for open-circuit potential
#
import pybamm
from pybamm.models.submodels.interface.base_interface import BaseInterface
[docs]
class BaseOpenCircuitPotential(BaseInterface):
"""
Base class for open-circuit potentials
Parameters
----------
param : parameter class
The parameters to use for this submodel
domain : str
The domain to implement the model, either: 'Negative' or 'Positive'.
reaction : str
The name of the reaction being implemented
options: dict
A dictionary of options to be passed to the model. See
:class:`pybamm.BaseBatteryModel`
phase : str, optional
Phase of the particle (default is "primary")
x_average : bool
Whether the particle concentration is averaged over the x-direction. Default is False.
"""
def __init__(
self, param, domain, reaction, options, phase="primary", x_average=False
):
super().__init__(param, domain, reaction, options=options, phase=phase)
self.x_average = x_average
def _alias_ocp_as_equilibrium(self, variables):
"""Publish the "equilibrium open-circuit potential [V]" variables as
aliases of the main OCP variables. For OCP models without hysteresis
(single OCP, MSMR) the equilibrium OCP equals the OCP, and the shapes
are already handled by :meth:`_get_standard_ocp_variables`.
"""
domain, Domain = self.domain_Domain
domain_options = getattr(self.options, domain)
phase_name = self.phase_name
variables.update(
{
f"{Domain} electrode {phase_name}equilibrium open-circuit potential [V]": variables[
f"{Domain} electrode {phase_name}open-circuit potential [V]"
],
f"X-averaged {domain} electrode {phase_name}equilibrium open-circuit potential [V]": variables[
f"X-averaged {domain} electrode {phase_name}open-circuit potential [V]"
],
}
)
if domain_options["particle size"] == "distribution":
variables.update(
{
f"{Domain} electrode {phase_name}equilibrium open-circuit potential distribution [V]": variables[
f"{Domain} electrode {phase_name}open-circuit potential distribution [V]"
],
f"X-averaged {domain} electrode {phase_name}equilibrium open-circuit potential distribution [V]": variables[
f"X-averaged {domain} electrode {phase_name}open-circuit potential distribution [V]"
],
}
)
def _get_standard_ocp_variables(self, ocp_surf, ocp_bulk, dUdT):
domain, Domain = self.domain_Domain
reaction_name = self.reaction_name
# Update size variables then size average.
if ocp_surf.domain in [
["negative particle size"],
["positive particle size"],
["negative primary particle size"],
["positive primary particle size"],
["negative secondary particle size"],
["positive secondary particle size"],
]:
variables = self._get_standard_size_distribution_ocp_variables(
ocp_surf, dUdT
)
ocp_surf = pybamm.size_average(ocp_surf)
dUdT = pybamm.size_average(dUdT)
else:
variables = {}
# Average, and broadcast if necessary
dUdT_av = pybamm.x_average(dUdT)
ocp_surf_av = pybamm.x_average(ocp_surf)
if self.options.electrode_types[domain] == "planar":
# Half-cell domain, ocp_surf should not be broadcast
pass
elif ocp_surf.domain == []:
ocp_surf = pybamm.FullBroadcast(
ocp_surf, f"{domain} electrode", "current collector"
)
elif ocp_surf.domain == ["current collector"]:
ocp_surf = pybamm.PrimaryBroadcast(ocp_surf, f"{domain} electrode")
# Particle overpotential is the difference between the average(U(c_surf)) and
# U(c_bulk), i.e. the overpotential due to concentration gradients in the
# particle
eta_particle = ocp_surf_av - ocp_bulk
variables.update(
{
f"{Domain} electrode {reaction_name}"
"open-circuit potential [V]": ocp_surf,
f"X-averaged {domain} electrode {reaction_name}"
"open-circuit potential [V]": ocp_surf_av,
f"{Domain} electrode {reaction_name}"
"bulk open-circuit potential [V]": ocp_bulk,
f"{Domain} {reaction_name}particle concentration "
"overpotential [V]": eta_particle,
}
)
if self.reaction in ["lithium-ion main", "lead-acid main"]:
variables.update(
{
f"{Domain} electrode {reaction_name}entropic change [V.K-1]": dUdT,
f"X-averaged {domain} electrode {reaction_name}entropic change [V.K-1]": dUdT_av,
}
)
return variables
def _get_standard_size_distribution_ocp_variables(self, ocp, dUdT):
domain, Domain = self.domain_Domain
reaction_name = self.reaction_name
# X-average or broadcast to electrode if necessary
if ocp.domains["secondary"] != [f"{domain} electrode"]:
ocp_av = ocp
ocp = pybamm.SecondaryBroadcast(ocp, f"{domain} electrode")
else:
ocp_av = pybamm.x_average(ocp)
if dUdT.domains["secondary"] != [f"{domain} electrode"]:
dUdT_av = dUdT
dUdT = pybamm.SecondaryBroadcast(dUdT, f"{domain} electrode")
else:
dUdT_av = pybamm.x_average(dUdT)
variables = {
f"{Domain} electrode {reaction_name}"
"open-circuit potential distribution [V]": ocp,
f"X-averaged {domain} electrode {reaction_name}"
"open-circuit potential distribution [V]": ocp_av,
}
if self.reaction_name == "":
variables.update(
{
f"{Domain} electrode entropic change "
"(size-dependent) [V.K-1]": dUdT,
f"X-averaged {domain} electrode entropic change "
"(size-dependent) [V.K-1]": dUdT_av,
}
)
return variables
def _get_stoichiometry_and_temperature(self, variables):
domain, Domain = self.domain_Domain
domain_options = getattr(self.options, domain)
phase_name = self.phase_name
sto_bulk = variables[f"{Domain} electrode {phase_name}stoichiometry"]
T = variables[f"{Domain} electrode temperature [K]"]
T_bulk = pybamm.xyzs_average(T)
# For "particle-size distribution" models, take distribution version
# of sto_surf that depends on particle size.
if domain_options["particle size"] == "distribution":
sto_surf = variables[
f"{Domain} {phase_name}particle surface stoichiometry distribution"
]
# If variable was broadcast, take only the orphan
if isinstance(sto_surf, pybamm.Broadcast) and isinstance(
T, pybamm.Broadcast
):
sto_surf = sto_surf.orphans[0]
T = T.orphans[0]
T = pybamm.PrimaryBroadcast(T, [f"{domain} {phase_name}particle size"])
else:
sto_surf = variables[f"{Domain} {phase_name}particle surface stoichiometry"]
# If variable was broadcast, take only the orphan
if isinstance(sto_surf, pybamm.Broadcast) and isinstance(
T, pybamm.Broadcast
):
sto_surf = sto_surf.orphans[0]
T = T.orphans[0]
return sto_surf, sto_bulk, T, T_bulk
