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def calculate_computing_parameters(step_current_parameters, Hgdl, Hmpl, Hacl):
    """This function is used to set the computing parameters of the fuel cell system.

    Parameters
    ----------
    step_current_parameters : dict
        Parameters for the step current density function.
    Hgdl : float
        Thickness of the gas diffusion layer in meters.
    Hmpl : float
        Thickness of the microporous layer in meters.
    Hacl : float
        Thickness of the anode catalyst layer in meters.

    Returns
    -------
    nb_gdl : int
        Number of model nodes placed inside each GDL.
    nb_mpl : int
        Number of model nodes placed inside each MPL.
    nb_tl : int
        Number of model nodes placed inside each transition layer.
    t_purge : tuple
        Time parameters for purging the system.
        It is a tuple containing the purge time 'purge_time' in seconds, and the time between two purges
        'delta_purge' in seconds.
        delta_t_dyn_step : float
    rtol : float
        Relative tolerance for the system of ODEs solver.
    atol : float
        Absolute tolerance for the system of ODEs solver.
    step_current_parameters : dict
        Parameters for the step current density. It is a dictionary containing:
        - 'delta_t_ini_step': the initial time (in seconds) at zero current density for the stabilisation of the
        internal states,
        - 'delta_t_load_step': the loading time (in seconds) for the step current density function, from 0 to
        i_step,
        - 'delta_t_break_step': the time (in seconds) at i_step current density for the stabilisation of the
        internal states,
        - 'i_step': the current density (in A.m-2) for the step current density function,
        - 'delta_t_dyn_step': the time (in seconds) for dynamic display of the step current density function.
    """

    # Calculation of the minimum thickness of the model node
    H_node_min = Hacl  # m. It is the minimum thickness of the model node.

    # Setting the number of model points placed inside each layer:
    nb_gc = 1  # It is the number of model points placed inside each gas channel.
    nb_gdl = max(1, int(Hgdl / H_node_min / 4))  # It is the number of model points placed inside each GDL.
    nb_mpl = max(1, int(Hmpl / H_node_min / 3))  # It is the number of model points placed inside each MPL.

    print('nb_gdl: ', nb_gdl, ' nb_mpl: ', nb_mpl)

    # Setting the purging parameters of the system and the dynamic display of the step current density function:
    t_purge = 0.6, 15  # (s, s). It is the time parameters for purging the system.
    delta_t_dyn_step = 2 * 60  # (s). Time for dynamic display of the step current density function.

    # Setting the tolerances for the system of ODEs solver:
    rtol = 1e-3  # Relative tolerance for the system of ODEs solver.
    atol = 1e-6  # Absolute tolerance for the system of ODEs solver.

    # Update the step current parameters.
    step_current_parameters['delta_t_dyn_step'] = delta_t_dyn_step
    return nb_gc, nb_gdl, nb_mpl, t_purge, rtol, atol

def calculate_current_density_parameters(type_current=None):
    """This function is used to set the parameters of the current density which is imposed to the fuel cell system.

    Parameters
    ----------
    type_current : str
        Type of current density which is imposed to the fuel cell system. It can be "step", "polarization" or "EIS".

    Returns
    -------
    step_current_parameters : dict
        Parameters for the step current density. It is a dictionary containing:
        - 'delta_t_ini_step': the initial time (in seconds) at zero current density for the stabilisation of the
        internal states,
        - 'delta_t_load_step': the loading time (in seconds) for the step current density function, from 0 to
        i_step,
        - 'delta_t_break_step': the time (in seconds) at i_step current density for the stabilisation of the
        internal states,
        - 'i_step': the current density (in A.m-2) for the step current density function,
        - 'delta_t_dyn_step': the time (in seconds) for dynamic display of the step current density function.
    pola_current_parameters : dict
        Parameters for the polarization current density. It is a dictionary containing:
        - 'delta_t_ini_pola': the initial time (in seconds) at zero current density for the stabilisation of the
        internal states,
        - 'delta_t_load_pola': the loading time (in seconds) for one step current of the polarisation current
        density function,
        - 'delta_t_break_pola': the breaking time (in seconds) for one step current, for the stabilisation of the
        internal states,
        - 'delta_i_pola': the current density step (in A.m-2) for the polarisation current density function.
        - 'i_max_pola': the maximum current density (in A.m-2) for the polarization curve.
    pola_current_for_cali_parameters : dict
        Parameters for the polarization current density for calibration. It is a dictionary containing:
        - 'delta_t_ini_pola_cali': the initial time (in seconds) at zero current density for the stabilisation of
        the internal states,
        - 'delta_t_load_pola_cali': the loading time (in seconds) for one step current of the polarisation current
        density function,
        - 'delta_t_break_pola_cali': the breaking time (in seconds) for one step current, for the stabilisation of
        the internal states.
    i_EIS : float
        Parameters for the EIS curve. It is the current for which a perturbation is added.
    ratio_EIS : float
        Parameters for the EIS curve. It is the ratio of the current for which a perturbation is added.
    f_EIS : tuple
        Frequency parameters for the EIS_current density function.
        It is a tuple containing the power of the initial frequency 'f_power_min_EIS'
        (f_min_EIS = 10**f_power_min_EIS), the power of the final frequency 'f_power_max_EIS', the number of
        frequencies tested 'nb_f_EIS', and the number of points calculated per specific period 'nb_points_EIS'.
    t_EIS : tuple
        Time parameters for the EIS_current density function.
        It is a tuple containing the initial EIS time after stack equilibrium 't0_EIS' in seconds, a list of time
        parameters which gives the beginning of each frequency change 't_new_start_EIS' in seconds, the final time
        'tf_EIS' in seconds, a list of time parameters which gives the estimated time for reaching equilibrium at each
        frequency 'delta_t_break_EIS' in seconds, and a list of time parameters which gives the estimated time for
        measuring the voltage response at each frequency 'delta_t_measurement_EIS' in seconds.
    current_density : function, optional.
        Current density function.
    """

    # Setting the parameters of the step current density function
    delta_t_ini_step = 30 * 60 # (s). Initial time at zero current density for the stabilisation of the internal states (standard value).
    delta_t_load_step = 30 # (s). Loading time for the step current density function, from 0 to i_step.
    delta_t_break_step = 15 * 60  # (s). Time at i_step current density for the stabilisation of the internal states.
    i_step = 2.0e4 # (A.m-2). Current density for the step current density function.
    step_current_parameters = {'delta_t_ini_step': delta_t_ini_step, 'delta_t_load_step': delta_t_load_step,
                               'delta_t_break_step': delta_t_break_step,'i_step': i_step}

    # Setting the parameters of the polarization current density function
    delta_i_pola = 0.05e4  # (A.m-2). Current density step for the polarisation current density function.
    delta_t_ini_pola = 120 * 60 # (s). Initial time at zero current density for the stabilisation of the internal states.
    v_load_pola = 0.01  # (A.m-2.s-1). Loading rate for one step current of the polarisation current density function.
    delta_t_load_pola = delta_i_pola / v_load_pola # (s). Loading time for one step current of the polarisation current density function.
    delta_t_break_pola = 15 * 60 # (s). Breaking time for one step current, for the stabilisation of the internal states.
    pola_current_parameters = {'delta_i_pola': delta_i_pola, 'delta_t_ini_pola': delta_t_ini_pola,
                               'delta_t_load_pola': delta_t_load_pola, 'delta_t_break_pola': delta_t_break_pola}

    # Setting the parameters of the polarization for calibration current density function
    delta_t_ini_pola_cali = 120 * 60  # (s). Initial time at zero current density for the stabilisation of the internal states.
    delta_t_load_pola_cali = 30  # (s). Loading time for one step current of the polarisation current density function.
    delta_t_break_pola_cali = 10 * 60  # (s). Breaking time for one step current, for the stabilisation of the internal states.
    pola_current_for_cali_parameters = {'delta_t_ini_pola_cali': delta_t_ini_pola_cali,
                                        'delta_t_load_pola_cali': delta_t_load_pola_cali,
                                        'delta_t_break_pola_cali': delta_t_break_pola_cali}

    # Setting the parameters of the EIS current density function
    i_EIS, ratio_EIS = 1.0e4, 5/100  # (A/m², ). Parameters for the EIS curve.
    f_EIS = -3, 5, 90, 50 # Frequency parameters for the EIS_current density function.
    t_EIS = EIS_parameters(f_EIS)  # Time parameters for the EIS_current density function.

    # Setting the current density function:
    if type_current == "step": current_density = step_current
    elif type_current == "polarization": current_density = polarization_current
    elif type_current == "polarization_for_cali": current_density = polarization_current_for_calibration
    elif type_current == "EIS": current_density = EIS_current
    elif type_current is None: current_density = None  # No current density function is set.
    else: raise ValueError('You have to specify a type_current which is on the list.')

    return (step_current_parameters, pola_current_parameters, pola_current_for_cali_parameters,
            i_EIS, ratio_EIS, f_EIS, t_EIS, current_density)

def calculate_operating_inputs(pola_current_parameters, type_fuel_cell, voltage_zone):
    """This function is used to set the operating inputs of the fuel cell system.

    Parameters
    ----------
    pola_current_parameters : dict
        Parameters for the polarization current density function.
    type_fuel_cell : str
        Type of fuel cell system.
    voltage_zone : str
        Zone of the polarization curve which is considered. It can be 'full' or 'before_voltage_drop'.

    Returns
    -------
    T_des : float
        Desired fuel cell temperature in Kelvin.
    Pa_des : float
        Desired anode pressure in Pascal.
    Pc_des : float
        Desired cathode pressure in Pascal.
    Sa : float
        Stoichiometric ratio of hydrogen.
    Sc : float
        Stoichiometric ratio of oxygen.
    Phi_a_des : float
        Desired anode relative humidity.
    Phi_c_des : float
        Desired cathode relative humidity.
    pola_current_parameters : dict
        Parameters for the polarization current density. It is a dictionary containing:
        - 'delta_t_ini_pola': the initial time (in seconds) at zero current density for the stabilisation of the
        internal states,
        - 'delta_t_load_pola': the loading time (in seconds) for one step current of the polarisation current
        density function,
        - 'delta_t_break_pola': the breaking time (in seconds) for one step current, for the stabilisation of the
        internal states,
        - 'delta_i_pola': the current density step (in A.m-2) for the polarisation current density function.
        - 'i_max_pola': the maximum current density (in A.m-2) for the polarization curve.
    """

    if type_fuel_cell == "manual_setup": # Setup which are not stored in "stored_operating_inputs".
        T_des = 74 + 273.15  # K. It is the desired fuel cell temperature.
        Pa_des, Pc_des = 2.0e5, 2.0e5  # Pa. It is the desired pressure of the fuel gas (at the anode/cathode).
        Sa, Sc = 1.2, 2.0  # It is the stoichiometric ratio (of hydrogen and oxygen).
        Phi_a_des, Phi_c_des = 0.4, 0.6  # It is the desired relative humidity.
        y_H2_in = 1 # It is the molar fraction of H2 in the dry anode gas mixture (H2/N2) injected at the inlet.
        i_max_pola = 3.0e4  # A.m-2. It is the maximum current density for the polarization curve.
    elif type_fuel_cell is None:
        T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, y_H2_in, i_max_pola = None, None, None, None, None, None, None, None, None
    else: # Stored setup in "stored_operating_inputs".
        T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, y_H2_in, i_max_pola = stored_operating_inputs(type_fuel_cell, voltage_zone)

    pola_current_parameters['i_max_pola'] = i_max_pola  # Update the maximum current density for the polarization curve.
    return T_des, Pa_des, Pc_des, Sa, Sc, Phi_a_des, Phi_c_des, y_H2_in, pola_current_parameters

def calculate_physical_parameters(type_fuel_cell):
    """This function is used to set the physical parameters of the fuel cell system.

    Parameters
    ----------
    type_fuel_cell : str
        Type of fuel cell system.

    Returns
    -------
    Hacl : float
        Thickness of the anode catalyst layer in meters.
    Hacl : float
        Thickness of the cathode catalyst layer in meters.
    epsilon_mc : float
        Volume fraction of ionomer in the catalyst layer.
    Hmem : float
        Thickness of the membrane in meters.
    Hgdl : float
        Thickness of the gas diffusion layer in meters.
    epsilon_gdl : float
        Anode/cathode GDL porosity.
    epsilon_c : float
        Compression ratio of the GDL.
    Hmpl : float
        Thickness of the microporous layer in meters.
    epsilon_mpl : float
        Porosity of the microporous layer.
    Hagc : float
        Thickness of the anode gas channel in meters.
    Hcgc : float
        Thickness of the cathode gas channel in meters.
    Wagc : float
        Width of the anode gas channel in meters.
    Wcgc : float
        Width of the cathode gas channel in meters.
    Lgc : float
        Length of the gas channel in meters.
    Aact : float
        Active area of the catalyst layer in meters squared.
    nb_cell : int
        Number of cell in the stack.
    A_T_a : float
        Exhaust anode manifold throttle area in m².
    A_T_c : float
        Exhaust cathode manifold throttle area in m².
    Vasm : float
        Supply manifold volume at the anode in m³.
    Vcsm : float
        Supply manifold volume at the cathode in m³.
    Vaem : float
        Exhaust manifold volume at the anode in m³.
    Vcem : float
        Exhaust manifold volume at the cathode in m³.
    V_endplate_a : float
        Anode endplate volume in m³.
    V_endplate_c : float
        Cathode endplate volume in m³.
    V_man_agc : float
        Volume connecting the anode manifold to the gas channel in m³.
    V_man_cgc : float
        Volume connecting the cathode manifold to the gas channel in m³.
    e : float
        Capillary exponent.
    i0_c_ref : float
        Reference exchange current density at the cathode in A.m-2.
    kappa_co : float
        Crossover correction coefficient in mol.m-1.s-1.Pa-1.
    kappa_c : float
        Overpotential correction exponent.
    a_slim : float
        One of the limit liquid saturation coefficients: the slop of slim function.
    b_slim : float
        One of the limit liquid saturation coefficients: the intercept of slim function.
    a_switch : float
        One of the limit liquid saturation coefficients: the slop of s_switch function.
    C_dl : float
        Volumetric double layer capacitance in F.m-3.
    """

    if type_fuel_cell == "manual_setup": # Setup which are not stored in "stored_physical_parameters".
        # Fuel cell physical parameters: 𝜔 (which are not controllable by the system)
        # Global
        Aact = 279.72e-4  # m². It is the MEA active area.
        nb_cell = 1  # . It is the number of cell in the stack.
        #   Catalyst layer
        Hacl = 8.089e-6  # m. It is the thickness of the anode catalyst layer.
        Hccl = Hacl  # m. It is the thickness of the cathode catalyst layer.
        epsilon_cl = 0.25  # It is the porosity of the catalyst layer, without units.
        epsilon_mc = 0.3949198274842546  # It is the volume fraction of ionomer in the CL.
        #   Membrane
        Hmem = 2e-5  # m. It is the thickness of the membrane.
        #   Gas diffusion layer
        Hgdl = 2e-4  # m. It is the thickness of the gas diffusion layer.
        epsilon_gdl = 0.7011156494971454  # It is the anode/cathode GDL porosity.
        epsilon_c = 0.27052745219052654  # It is the compression ratio of the GDL.
        #   Microporous layer
        Hmpl = 3e-5  # m. It is the thickness of the microporous layer.
        epsilon_mpl = 0.4  # It is the porosity of the microporous layer.
        #   Gas channel
        Hagc = 5e-4  # m. It is the thickness of the anode gas channel.
        Hcgc = Hagc  # m. It is the thickness of the cathode gas channel.
        Wagc = 4.5e-4  # m. It is the width of the anode gas channel.
        Wcgc = Wagc  # m. It is the width of the cathode gas channel.
        Lgc = 144e-3  # m. It is the length of one channel in the bipolar plate.
        nb_channel_in_gc = 67  # . It is the number of channels in the bipolar plate.
        Ldist = 5e-2  # m. It is the estimated length of the distributor, which is the volume between the gas channel and the manifold.
        #   Auxiliaries
        Lm = 25.8e-3  # m. It is the length of the manifold.
        L_endplate = 46.8e-3  # m. It is the length of the endplate.
        A_T_a = 11.8e-4  # m². It is the inlet/exhaust anode manifold throttle area
        A_T_c = A_T_a  # m². It is the inlet/exhaust cathode manifold throttle area
        Vasm, Vcsm = 7000e-6, 7000e-6  # m3. It is the supply manifold volume.
        Vaem, Vcem = 2400e-6, 2400e-6  # m-3. It is the exhaust manifold volume.
        V_endplate_a = 33.6e-6  # m3. It is the anode endplate volume.
        V_endplate_c = 86.6e-6  # m3. It is the cathode endplate volume.
        #   Interaction parameters between water and PEMFC structure
        e = 5.0  # It is the capillary exponent
        #   Voltage polarization
        Re = 1e-06  # Ω.m². It is the electron conduction resistance of the circuit.
        i0_d_c_ref = 14.43  # A.m-2. It is the dry reference exchange current density at the cathode.
        i0_l_c_ref = 1.0e3  # A.m-2. It is the fully humidified reference exchange current density at the cathode.
        kappa_co = 29.793535549174077  # mol.m-1.s-1.Pa-1. It is the crossover correction coefficient.
        kappa_c = 1.6136446641573106  # It is the overpotential correction exponent.
        a_slim, b_slim, a_switch = 0.0555312850726664, 0.10514269908118055, 0.6365424991141914  # It is the limit
        #                                                               liquid saturation coefficients.
        C_scl = 2e7  # F.m-3. It is the volumetric space-charge layer capacitance.
    else: # Stored setup in "stored_physical_parameters".
        (Hacl, Hccl, epsilon_mc, Hmem, Hgdl, epsilon_gdl, epsilon_cl, epsilon_c, Hmpl, epsilon_mpl, Hagc, Hcgc, Wagc,
         Wcgc, Lgc, nb_channel_in_gc, Ldist, Lm, A_T_a, A_T_c, Vasm, Vcsm, Vaem, Vcem, Aact, nb_cell, e, Re, i0_d_c_ref,
         i0_h_c_ref, kappa_co, kappa_c, a_slim, b_slim, a_switch, C_scl) = stored_physical_parameters(type_fuel_cell)

    return (Hacl, Hccl, epsilon_mc, Hmem, Hgdl, epsilon_gdl, epsilon_cl, epsilon_c, Hmpl, epsilon_mpl, Hagc, Hcgc, Wagc,
            Wcgc, Lgc, nb_channel_in_gc, Ldist, Lm, A_T_a, A_T_c, Vasm, Vcsm, Vaem, Vcem, Aact, nb_cell, e, Re, i0_d_c_ref,
            i0_h_c_ref, kappa_co, kappa_c, a_slim, b_slim, a_switch, C_scl)