Electrode SOH models

class pybamm.lithium_ion.ElectrodeSOHSolver(parameter_values, param=None, known_value='cyclable lithium capacity', options=None)

Class used to check if the electrode SOH model is feasible, and solve it if it is.

Parameters:

• parameter_values (pybamm.ParameterValues.Parameters) – The parameters of the simulation

• param (pybamm.LithiumIonParameters, optional) – Specific instance of the symbolic lithium-ion parameter class. If not provided, the default set of symbolic lithium-ion parameters will be used.

• known_value (str, optional) – The known value needed to complete the electrode SOH model. Can be “cyclable lithium capacity” (default) or “cell capacity”.

• options (dict-like, optional) – A dictionary of options to be passed to the model, see pybamm.BatteryModelOptions.

get_initial_ocps(initial_value, tol=1e-06)

Calculate initial open-circuit potentials to start off the simulation at a particular state of charge, given voltage limits, open-circuit potentials, etc defined by parameter_values

Parameters:

• initial_value (float) – Target SOC, must be between 0 and 1.

• tol (float, optional) – Tolerance for the solver used in calculating initial stoichiometries.

Returns:

The initial open-circuit potentials at the desired initial state of charge

Return type:

Un, Up

get_initial_stoichiometries(initial_value, tol=1e-06, inputs=None)

Calculate initial stoichiometries to start off the simulation at a particular state of charge, given voltage limits, open-circuit potentials, etc defined by parameter_values

Parameters:

• initial_value (float) – Target initial value. If integer, interpreted as SOC, must be between 0 and 1. If string e.g. “4 V”, interpreted as voltage, must be between V_min and V_max.

• tol (float, optional) – The tolerance for the solver used to compute the initial stoichiometries. A lower value results in higher precision but may increase computation time. Default is 1e-6.

Returns:

The initial stoichiometries that give the desired initial state of charge

Return type:

x, y

get_min_max_ocps()

Calculate min/max open-circuit potentials given voltage limits, open-circuit potentials, etc defined by parameter_values

Returns:

The min/max ocps

Return type:

Un_0, Un_100, Up_100, Up_0

get_min_max_stoichiometries(inputs=None)

Calculate min/max stoichiometries given voltage limits, open-circuit potentials, etc defined by parameter_values

Returns:

The min/max stoichiometries

Return type:

x_0, x_100, y_100, y_0

pybamm.lithium_ion.get_initial_stoichiometries(initial_value, parameter_values, param=None, known_value='cyclable lithium capacity', options=None, tol=1e-06, inputs=None)

Calculate initial stoichiometries to start off the simulation at a particular state of charge, given voltage limits, open-circuit potentials, etc defined by parameter_values

Parameters:

• initial_value (float) – Target initial value. If integer, interpreted as SOC, must be between 0 and 1. If string e.g. “4 V”, interpreted as voltage, must be between V_min and V_max.

• parameter_values (pybamm.ParameterValues) – The parameter values class that will be used for the simulation. Required for calculating appropriate initial stoichiometries.

• param (pybamm.LithiumIonParameters, optional) – The symbolic parameter set to use for the simulation. If not provided, the default parameter set will be used.

• known_value (str, optional) – The known value needed to complete the electrode SOH model. Can be “cyclable lithium capacity” (default) or “cell capacity”.

• options (dict-like, optional) – A dictionary of options to be passed to the model, see pybamm.BatteryModelOptions.

• tol (float, optional) – The tolerance for the solver used to compute the initial stoichiometries. A lower value results in higher precision but may increase computation time. Default is 1e-6.

Returns:

The initial stoichiometries that give the desired initial state of charge

Return type:

x, y

pybamm.lithium_ion.get_min_max_stoichiometries(parameter_values, param=None, known_value='cyclable lithium capacity', options=None)

Calculate min/max stoichiometries given voltage limits, open-circuit potentials, etc defined by parameter_values

Parameters:

• parameter_values (pybamm.ParameterValues) – The parameter values class that will be used for the simulation. Required for calculating appropriate initial stoichiometries.

• param (pybamm.LithiumIonParameters, optional) – The symbolic parameter set to use for the simulation. If not provided, the default parameter set will be used.

• known_value (str, optional) – The known value needed to complete the electrode SOH model. Can be “cyclable lithium capacity” (default) or “cell capacity”.

• options (dict-like, optional) – A dictionary of options to be passed to the model, see pybamm.BatteryModelOptions.

Returns:

The min/max stoichiometries

Return type:

x_0, x_100, y_100, y_0

pybamm.lithium_ion.get_initial_ocps(initial_value, parameter_values, param=None, known_value='cyclable lithium capacity', options=None)

Calculate initial open-circuit potentials to start off the simulation at a particular state of charge, given voltage limits, open-circuit potentials, etc defined by parameter_values

Parameters:

• initial_value (float) – Target initial value. If integer, interpreted as SOC, must be between 0 and 1. If string e.g. “4 V”, interpreted as voltage, must be between V_min and V_max.

• parameter_values (pybamm.ParameterValues) – The parameter values class that will be used for the simulation. Required for calculating appropriate initial stoichiometries.

• param (pybamm.LithiumIonParameters, optional) – The symbolic parameter set to use for the simulation. If not provided, the default parameter set will be used.

• known_value (str, optional) – The known value needed to complete the electrode SOH model. Can be “cyclable lithium capacity” (default) or “cell capacity”.

• options (dict-like, optional) – A dictionary of options to be passed to the model, see pybamm.BatteryModelOptions.

Returns:

The initial electrode OCPs that give the desired initial state of charge

Return type:

Un, Up

pybamm.lithium_ion.get_min_max_ocps(parameter_values, param=None, known_value='cyclable lithium capacity', options=None)

Calculate min/max open-circuit potentials given voltage limits, open-circuit potentials, etc defined by parameter_values

Parameters:

• parameter_values (pybamm.ParameterValues) – The parameter values class that will be used for the simulation. Required for calculating appropriate initial open-circuit potentials.

• param (pybamm.LithiumIonParameters, optional) – The symbolic parameter set to use for the simulation. If not provided, the default parameter set will be used.

• known_value (str, optional) – The known value needed to complete the electrode SOH model. Can be “cyclable lithium capacity” (default) or “cell capacity”.

• options (dict-like, optional) – A dictionary of options to be passed to the model, see pybamm.BatteryModelOptions.

Returns:

The min/max OCPs

Return type:

Un_0, Un_100, Up_100, Up_0