Fuel Cell

The electrical system of the fuel cell.

blockType: AcausalElectricPowerSystems.Sources.FuelCell

Path in the library:

/Physical Modeling/Electrical/Sources/Fuel Cell

Description

Block Fuel Cell simulates a fuel cell that converts the chemical energy of hydrogen into electrical energy.

This chemical reaction determines the electrical transformation.:

The chemical reaction occurs as a result of the following anodic and cathodic half reactions:

fuel cell 1

Block Fuel Cell It consists of several fuel cells connected in series. An equivalent circuit of one of the block elements is shown below:

fuel cell 2

where

– cell voltage;
– corresponds to the parameter Internal resistance;
– corresponds to the parameter Sum of activation and concentration resistance;
– parallel RC capacitance, which takes into account the dynamics of time in the cell.

The equations

Use the parameter Model fidelity to allow one of two levels of simulation accuracy Fuel Cell:

Simplified - nominal conditions – The unit calculates the Nernst voltage under nominal temperature and pressure conditions.
Detailed with signal inputs – the unit calculates the Nernst voltage, taking into account the pressure and consumption of fuel and air.

The simplified electrical model

If for the parameter Model fidelity the value is set Simplified - nominal conditions, block Fuel Cell calculates the Nernst voltage, , under nominal temperature and pressure conditions, according to the equations:

where

– corresponds to the value of the parameter Open-circuit voltage;
– corresponds to the value of the parameter Number of cells per module;
– the current generated by the fuel cell;
– voltage at the terminals of the fuel cell;
– corresponds to the value of the parameter Module units (Series);
– voltage drop that takes into account the dynamics of the fuel cell;
– corresponds to the value of the parameter Tafel slope, in volts;
– corresponds to the value of the parameter Nominal exchange current;
.

The detailed electrical model

If for the parameter Model fidelity the value is set Detailed with signal inputs, the fuel cell unit calculates the Nernst voltage, considering the pressure and fuel and air consumption.

In this mode, the rate of hydrogen utilization is, , and oxygen, , are defined by the equations:

where

– thermal stress at room temperature;
– fuel supply pressure in bar;
– fuel consumption;
– the concentration of hydrogen in the fuel, as a percentage;
– air supply pressure in bar;
– air consumption;
– oxygen concentration in the air, as a percentage.

The partial pressure values are determined by the equations:

where – the concentration of vapors in the air, in percent.

The block then calculates the Nernst voltage as:

where

;
– electrokinetic member for activation;
– electrokinetic member for concentration;
;
– constant voltage at the rated operating mode;
– the operating temperature of the fuel cell;
– corresponds to the value of the parameter Nominal temperature;
– the number of moving electrons per second;
– the number of moving electrons per second for a given parameter value Nominal exchange current;
– Faraday’s constant;
– universal gas constant;
– nominal pressure of hydrogen in bar;
– nominal oxygen pressure in bar;
– Taffeta tilt depending on temperature;
– corresponds to the value of the parameter Collapse current;
Voltage 1.229 represents the standard cell potential for the Nernst equation.

The unit calculates the power dissipation or heat generated in a fuel cell using the following equation:

where

– the total velocity of electron circulation in mol/s;
– change in the entropy of the fuel cell reaction in kJ/(mol⋅s) at the operating temperature of the fuel cell;
– the change in the Gibbs free energy of the total reaction of the fuel cell in kJ/mol at the operating temperature of the fuel cell.

Assumptions and limitations

Block Fuel Cell It is not intended for modeling electrolysis.

Variables

Use the parameter group Initial Targets to set the priority and initial target values for the block parameter variables before modeling. For more information, see Configuring physical blocks using target values.

Ports

Conserving

# + — favourable
electricity

Details

A non-directional port representing the positive terminal of the fuel cell.

Program usage name

p

# - — negative
electricity

Details

A non-directional port representing the negative terminal of the fuel cell.

Program usage name

n

# H — heat port
heat

Details

Heat port.

Dependencies

To use this port, set the parameters Model fidelity to Detailed with signal inputs.

Program usage name

thermal_port

Input

# pfuel — absolute pressure of fuel supply, Pa
scalar

Details

Input port that defines the absolute pressure of the fuel supplied to the unit in Pa.

Dependencies

To use this port, set the parameter Model fidelity to the value of Detailed with signal inputs.

Data types	`Float64`.
Complex numbers support	No

# pair — air overpressure, Pa
scalar

Details

An input port that determines the gauge air pressure in Pa.

Dependencies

To use this port, set the parameter Model fidelity to the value of Detailed with signal inputs.

Data types	`Float64`.
Complex numbers support	No

# qfuel — fuel consumption, m³/s
scalar

Details

An input port that defines the volumetric fuel flow rate of the unit in m³/c.

Dependencies

To use this port, set the parameter Model fidelity to Detailed with signal inputs.

Data types	`Float64`.
Complex numbers support	No

# qair — air flow rate, m³/s
scalar

Details

An input port that defines the air flow rate of the unit in m³/s.

Dependencies

To use this port, set the parameters Model fidelity to Detailed with signal inputs.

Data types	`Float64`.
Complex numbers support	No

Parameters

Main

# Model fidelity — accuracy of the fuel cell model
Simplified - nominal conditions | Detailed with signal inputs

Details

The level of accuracy of the fuel cell model.

Values	`Simplified - nominal conditions` \| `Detailed with signal inputs`
Default value	`Detailed with signal inputs`
Program usage name	`model`
Evaluatable	No

# Open-circuit voltage — open circuit voltage
V | uV | mV | kV | MV

Details

Open circuit voltage.

If the flow is low or close to zero and the fuel and air pressures are nominal, the fuel cell output voltage is equal to the open circuit voltage multiplied by the number of module units. The current flowing out of the fuel cell is negligible.

Units	`V` \| `uV` \| `mV` \| `kV` \| `MV`
Default value	`65.0 V`
Program usage name	`E_oc`
Evaluatable	Yes

# Tafel slope — Tafel slope
V | uV | mV | kV | MV

Details

The amount of excess potential required to increase the reaction rate by a factor of ten.

Units	`V` \| `uV` \| `mV` \| `kV` \| `MV`
Default value	`0.23 V`
Program usage name	`A`
Evaluatable	Yes

# Internal resistance — internal resistance
Ohm | mOhm | kOhm | MOhm | GOhm

Details

Internal resistance.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`0.05 Ohm`
Program usage name	`R_internal`
Evaluatable	Yes

# Nominal exchange current — rated exchange current
A | pA | nA | uA | mA | kA | MA

Details

Exchange current at rated temperature.

At the nominal exchange current, the fuel cell leaves the activation polarisation region and enters the ohmic polarisation region.

Units	`A` \| `pA` \| `nA` \| `uA` \| `mA` \| `kA` \| `MA`
Default value	`80.0 A`
Program usage name	`i0`
Evaluatable	Yes

# Collapse current — collapse current
A | pA | nA | uA | mA | kA | MA

Details

The value of current at which the voltage across the fuel cell becomes zero. When the fuel cell enters the region of concentration polarisation and the current continues to rise, the voltage starts to drop faster.

Dependencies

To use this parameter, set the parameter Model fidelity to the value of Detailed with signal inputs.

Units	`A` \| `pA` \| `nA` \| `uA` \| `mA` \| `kA` \| `MA`
Default value	`200.0 A`
Program usage name	`i_limit`
Evaluatable	Yes

# Number of cells per module — number of cells per module

Details

Number of cells per module.

The value of the number of cells in this block corresponds to the fuel cell delivering the maximum power output for the given flow and pressure values .

Default value	`65`
Program usage name	`cell_count`
Evaluatable	Yes

# Module units (Series) — stack of modules in series

Details

A stack of modules connected in series.

Connecting modules in series to increase the voltage. For example, 10 modules connected in series with an open circuit voltage of 65 V produce a voltage of 650 V.

Default value	`10`
Program usage name	`unit_count`
Evaluatable	Yes

Supply

# Nominal H2 pressure — nominal hydrogen pressure
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Excess hydrogen pressure at nominal temperature.

Dependencies

To use this parameter, set the parameters Model fidelity to . Detailed with signal inputs.

Units	`Pa` \| `uPa` \| `hPa` \| `kPa` \| `MPa` \| `GPa` \| `kgf/m^2` \| `kgf/cm^2` \| `kgf/mm^2` \| `mbar` \| `bar` \| `kbar` \| `atm` \| `ksi` \| `psi` \| `mmHg` \| `inHg`
Default value	`1.5e5 Pa`
Program usage name	`p_H2_nominal`
Evaluatable	Yes

# Nominal O2 pressure — nominal oxygen pressure
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

Oxygen overpressure at rated temperature.

Dependencies

To use this parameter, set the parameters Model fidelity to . Detailed with signal inputs.

Units	`Pa` \| `uPa` \| `hPa` \| `kPa` \| `MPa` \| `GPa` \| `kgf/m^2` \| `kgf/cm^2` \| `kgf/mm^2` \| `mbar` \| `bar` \| `kbar` \| `atm` \| `ksi` \| `psi` \| `mmHg` \| `inHg`
Default value	`1.0e5 Pa`
Program usage name	`p_O2_nominal`
Evaluatable	Yes

# Concentration H2 in fuel (%) — hydrogen concentration in fuel

Details

Molar concentration of hydrogen in fuel.

The unit of measurement is per cent.

Dependencies

To use this parameter, set the Model fidelity parameters to . Detailed with signal inputs.

Default value	`99.0`
Program usage name	`C_H2`
Evaluatable	Yes

# Concentration O2 in air (%) — fuel oxygen concentration

Details

Molar concentration of oxygen in fuel.

The units of measurement are per cent.

Dependencies

To use this parameter, set the Model fidelity parameters to . Detailed with signal inputs.

Default value	`21.0`
Program usage name	`C_O2`
Evaluatable	Yes

# Concentration vapor in air (%) — airborne vapour concentration

Details

Molar concentration of vapours in air.

The unit of measurement is per cent.

Dependencies

To use this parameter, set the Model fidelity parameters to . Detailed with signal inputs.

Default value	`1.0`
Program usage name	`C_w`
Evaluatable	Yes

Dynamics

# Model activation delay — activation delay modelling option

Details

Check this parameter if you want to model the activation delay of the fuel cell.

Default value	`false (switched off)`
Program usage name	`activation_delay`
Evaluatable	No

# Sum of activation and concentration resistance — sum of activation and concentration resistance
Ohm | mOhm | kOhm | MOhm | GOhm

Details

The sum of activation resistance and concentration resistance.

Dependencies

To use this parameter, select the checkbox Model activation delay.

Units	`Ohm` \| `mOhm` \| `kOhm` \| `MOhm` \| `GOhm`
Default value	`0.005 Ohm`
Program usage name	`R_dynamic`
Evaluatable	Yes

# Time constant — time constant
s | ns | us | ms | min | hr | d

Details

Time constant.

Dependencies

To use this parameter, select the check box Model activation delay.

Units	`s` \| `ns` \| `us` \| `ms` \| `min` \| `hr` \| `d`
Default value	`10.0 s`
Program usage name	`tau`
Evaluatable	Yes

Thermal

Details

The temperature at which the nominal parameters are measured.

Dependencies

To use this parameter, set the parameters Model fidelity to . Detailed with signal inputs.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`T_nominal`
Evaluatable	Yes

# Thermal mass — thermal mass associated with the heat port
J/K | kJ/K

Details

Thermal mass associated with the heat port H.

This value represents the energy required to raise the temperature of the heat port by one degree.

Dependencies

To use this parameter, set the Model fidelity parameters to Detailed with signal inputs.

Units	`J/K` \| `kJ/K`
Default value	`30000.0 J/K`
Program usage name	`thermal_mass`
Evaluatable	Yes