RCAIDE.Library.Methods.Powertrain.Converters.Fuel_Cells.Proton_Exchange_Membrane.compute_fuel_cell_performance
compute_fuel_cell_performance#
- compute_fuel_cell_performance(fuel_cell_stack, state, bus, coolant_lines, t_idx, delta_t)[source]#
Computes the performance of a PEM fuel cell stack.
- Parameters:
fuel_cell_stack (RCAIDE.Components.Energy.Converters.Fuel_Cell_Stack) – The fuel cell stack object containing cell properties and configuration
state (RCAIDE.Framework.Mission.Common.State) – Container for mission segment conditions
bus (RCAIDE.Components.Energy.Distribution.Electric_Bus) – The electric bus to which the fuel cell stack is connected
coolant_lines (list) – List of coolant line components for thermal management
t_idx (int) – Current time index in the simulation
delta_t (float) – Time step size [s]
- Returns:
stored_results_flag (bool) – Flag indicating that results have been stored for potential reuse
stored_fuel_cell_stack_tag (str) – Tag identifier of the fuel cell stack with stored results
Notes
This function implements a detailed electrochemical model for PEM fuel cells that accounts for activation losses, ohmic losses, and concentration losses. It iteratively determines the current density required to match the power demand from the electric bus.
The function also models the compressor-expander module (CEM) that supplies air to the fuel cell, accounting for parasitic power losses.
Temperature effects are considered through a thermal model that updates the stack temperature based on heat generation.
- Major Assumptions
Uniform temperature distribution across all cells
Hydrogen is supplied at constant pressure
Air composition is standard atmospheric (21% oxygen)
Water management is ideal (no flooding or membrane dehydration)
Theory
The PEM fuel cell voltage is calculated as:
\[V_{cell} = E_{cell} - \eta_{act} - \eta_{ohmic} - \eta_{conc} - degradation\]- where:
E_{cell} is the Nernst potential
η_{act} is the activation loss
η_{ohmic} is the ohmic loss
η_{conc} is the concentration loss
degradation accounts for cell degradation over time
The thermal model uses:
\[\frac{dT}{dt} = \frac{Q_{gross}}{m_{stack} \cdot c_p}\]where Q_{gross} is the heat generated by the stack.
References
[1] O’Hayre, R., Cha, S. W., Colella, W., & Prinz, F. B. (2016). Fuel Cell Fundamentals (3rd ed.). John Wiley & Sons.
See also
RCAIDE.Library.Methods.Powertrain.Converters.Fuel_Cells.Proton_Exchange_Membrane.evaluate_PEM,RCAIDE.Library.Methods.Powertrain.Converters.Fuel_Cells.Proton_Exchange_Membrane.evaluate_CEM
- evaluate_PEM(fuel_cell_stack, fuel_cell_conditions, t_idx)[source]#
Determines the fuel cell state of the PEM fuel cell
Parameters:#
- i: float
The current density to evaluate the cell voltage at (A/cm^2)
- stack_temperature: Temperature
Temperature of the fuel cell
- P_H2_input: Pressure
Pressure of the hydrogen stream
- FC_air_p: Pressure
Pressure of the hydrogen air entering the fuel cell
- RH: float
Relative humidity of the air and hydrogen streams (0-1)
- air_excess_ratio: float
Air excess ratio (above stoichometric)
- thermo_state_in: ThermoState
Conditions of air entering the compressor
- degradation: float
The voltage drop due to degradation (V) optional, defaults to 0 V
Returns:#
- float:
Hydrogen Mass flow (kg/s)
- float:
Net Power (W)
- float:
Gross power (W)
- float:
Gross heat (W)
- float:
Compressor Power (W)
- float:
mdot_air_in (kg/s)
- evaluate_CEM(fuel_cell_stack, fuel_cell_conditions, t_idx)[source]#
Evaluates the power required by the CEM (compressor-expander module)
Parameters:#
- FC_air_p: float
Air pressure after the humidifier entering the fuel cell (bar)
- thermo_state_in: ThermoState
Air thermostate entering the compressor
- mdot_air_in: float
Mass flow of air entering the fuel cell and compressor (kg/s)
- air_excess_ratio: float
Oxygen excess ratio (above stoichometric)
- p_drop_hum: float
The pressure drop (bar) through the humidifier
- pressure_drop: float
The pressure drop (bar) through the fuel cell
Returns:#
- float:
The power required to run the CEM at the given operating conditions (W)
- calculate_voltage(i, fuel_cell_stack, fuel_cell_conditions, t_idx)[source]#
Calculates the output voltage of the fuel cell by subtracting the activation, ohmic, and concentration voltage losses from the reversible Nernst voltage, E_cell.
Parameters:#
- i: float
The current density to evaluate the cell voltage at (A/m^2)
- stack_temperature: float
Temperature of the fuel cell (K)
- P_H2_input: float
Pressure of the hydrogen stream (bar)
- P_air: float
Pressure of the incoming air (bar)
- RH: float
Relative humidity of the air and hydrogen streams (0-1)
- air_excess_ratio: float
Air excess ratio (above stoichometric)
- pressure_drop: float
Pressure drop of the fuel cell at the rated current density (bar)
- degradation: float
The percent of maximumm degradation to evaluate divided by 100 optional, defaults to 0 (0% of fuel_cell.maximum_deg)
Returns:#
- float:
Output voltage of the fuel cell (V)
- set_rated_current_density(fuel_cell_stack, rated_current_density, rated_power_density)[source]#
Sets the rated cd and pd of the fuel cell system
Parameters:#
- rated_CD: float
The current density (A/cm2) to set
- rated_power_density: float
The power density (W/cm2) to set
- calculate_P_drop_hum(fuel_cell_stack, i)[source]#
Calculates the pressure drop across the humidifier for the rated current
Parameters:#
- i: float
Current Density (Acm2) to calculate the pressure drop
Returns:#
- float
The Humidifier pressure drop in bar
- calculate_P_drop_stack(fuel_cell_stack, i)[source]#
Calculates the pressure drop across the stack for the rated current
Parameters:#
- i: float
Current Density (Acm2) to calculate the pressure drop
Returns:#
- float
The stack pressure drop in bar
- calculate_P_O2(fuel_cell_stack, P_air, stack_temperature, RH, air_excess_ratio, P_drop, i)[source]#
Calculate the partial pressure of oxygen at the fuel cell cathode
Parameters:#
- P_air: float
The input air pressure to the fuel cell (bar)
- stack_temperature: float
The fuel cell stack temperature (K)
- RH: float
The relative humidity of the oxygen stream (0-1)
- air_excess_ratio: float
The oxygen excess ratio (above stoichometric)
- P_drop: float
The pressure drop (bar) across the fuel cell cathode
- i: float
The current density (Acm2) to calculate the partial pressure at
Returns:#
- float
The oxygen partial pressure (bar)
- calculate_P_H2(fuel_cell_stack, P_H2_input, stack_temperature, RH, i)[source]#
Calculate the partial pressure of hydroen at the fuel cell anode
Parameters:#
- P_H2_input: float
The input hydrogen pressure to the fuel cell (bar)
- stack_temperature: float
The fuel cell stack temperature (K)
- RH: float
The relative humidity of the oxygen stream (0-1)
- i: float
The current density (Acm2) to calculate the partial pressure at
Returns:#
- float
The hydrogen partial pressure (bar)
- calculate_E_cell(fuel_cell_stack, stack_temperature, P_H2, P_O2)[source]#
Calculates the reversible Nernst Voltage of the cell
Parameters:#
- stack_temperature: float
The fuel cell stack temperature (K)
- P_H2: float
The hydrogen partial pressure (bar)
- P_O2: float
The oxygen partial pressure (bar)
Returns:#
- float
The reversible cell potential (V)
- calculate_activation_losses(fuel_cell_stack, stack_temperature, P_O2, i)[source]#
calculation of activation losses for both high temperature and low temperature fuel cells
Parameters:#
- stack_temperature: float
Stack Temperature (K)
- P_O2: float
Oxygen Partial Pressure (bar)
- i: float
Current density to evaluate activation losses (A/cm2)
Returns:#
- float:
Activation voltage loss (V)
- calculate_ohmic_losses_LT(fuel_cell_stack, stack_temperature, i)[source]#
Calculation of ohmic losses for low temperature fuel cells
Parameters:#
- stack_temperature: float
Stack Temperature (K)
- i: float
Current density to evaluate activation losses (A/cm2)
Returns:#
- float:
Ohmic voltage loss (V)
- calculate_ohmic_losses_HT(fuel_cell_stack, stack_temperature, i)[source]#
Calculation of ohmic losses for high temperature fuel cells
Parameters:#
- stack_temperature: float
Stack Temperature (K)
- i: float
Current density to evaluate activation losses (A/cm2)
Returns:#
- float:
Ohmic voltage loss (V)
- calculate_concentration_losses_LT(fuel_cell_stack, stack_temperature, P_O2, RH, air_excess_ratio, P_drop, i)[source]#
Calculation of concentration losses for low temperature fuel cells
Parameters:#
- stack_temperature: float
Stack Temperature (K)
- P_O2: float
Oxygen partial pressure (bar)
- RH: float
Relative humidity of the oxygen stream (0-1)
- air_excess_ratio: float
Oxygen excess ratio (above stoichometric)
- P_drop: float
Pressure drop across the fuel cell stack (bar)
- i: float
Current density to evaluate activation losses (A/cm2)
Returns:#
- float:
Concentration voltage loss (V)
- calculate_limiting_current_density_LT(fuel_cell_stack, stack_temperature, P_O2, RH, air_excess_ratio, P_drop, i, **kwargs)[source]#
Calculation of the limiting current density for LT-PEM
Parameters:#
- stack_temperature: float
Stack Temperature (K)
- P_O2: float
Oxygen partial pressure (bar)
- RH: float
Relative humidity of the oxygen stream (0-1)
- air_excess_ratio: float
Oxygen excess ratio (above stoichometric)
- P_drop: float
Pressure drop across the fuel cell stack (bar)
- i: float
Current density to evaluate activation losses (A/cm2)
Returns:#
- float:
limiting current density (A/cm^2)
- calculate_concentration_losses_HT(fuel_cell_stack, stack_temperature, P_O2, RH, air_excess_ratio, P_drop, i)[source]#
Calculation of concentration losses for high temperature fuel cells
Parameters:#
- stack_temperature: float
Stack Temperature (K)
- P_O2: float
Oxygen partial pressure (bar)
- RH: float
Relative humidity of the oxygen stream (0-1)
- air_excess_ratio: float
Oxygen excess ratio (above stoichometric)
- P_drop: float
Pressure drop across the fuel cell stack (bar)
- i: float
Current density to evaluate activation losses (A/cm2)
Returns:#
- float:
Concentration voltage loss (V)
- calculate_limiting_current_density_HT(fuel_cell_stack, stack_temperature, P_O2, RH, air_excess_ratio, P_drop, i)[source]#
Calculation of the limiting current density for HT-PEM
Parameters:#
- stack_temperature: float
Stack Temperature (K)
- P_O2: float
Oxygen partial pressure (bar)
- RH: float
Relative humidity of the oxygen stream (0-1)
- air_excess_ratio: float
Oxygen excess ratio (above stoichometric)
- P_drop: float
Pressure drop across the fuel cell stack (bar)
- i: float
Current density to evaluate activation losses (A/cm2)
Returns:#
- float:
limiting current density (A/cm^2)