Fuel Cell

The electrical system of the fuel cell.

blockType: AcausalElectricPowerSystems.Sources.FuelCell

Path in the library:

/Physical Modeling/Electrical/Sources/Fuel Cell

Description

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

This chemical reaction determines the electrical conversion:

The chemical reaction results from the following anodic and cathodic half-reactions:

fuel cell 1

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

fuel cell 2

where

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

Equations

Use the parameters Model fidelity, to one of two levels of modelling accuracy Fuel Cell:

Simplified - nominal conditions - block calculates the Nernst stress under nominal temperature and pressure conditions.
Detailed with signal inputs - the unit calculates the Nernst stress with regard to pressure and fuel and air flow.

Simplified electrical model

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

where

- corresponds to the value of the parameters Open-circuit voltage;
- corresponds to the value of the parameter Number of cells per module;
- current generated by the fuel cell;
- voltage at the fuel cell terminals;
- 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;
.

Detailed electrical model

If the parameter Model fidelity is set to a value of Detailed with signal inputs, the fuel cell unit calculates the Nernst voltage, , taking into account the pressure and flow rate of fuel and air.

In this mode, the utilisation rates of hydrogen, , and oxygen, , are determined by the equations:

where

- is the thermal stress at room temperature;
- fuel supply pressure in bar;
- fuel flow rate;
- hydrogen concentration in fuel, in per cent;
- air supply pressure in bar;
- air flow rate;
- oxygen concentration in air, in per cent.

The partial pressure values are determined by the equations:

where is the vapour concentration in air, in percent.

The unit then calculates the Nernst stress as:

where

;
- electrokinetic term for activation;
- electrokinetic term for concentration;
;
- voltage constant at nominal operation mode;
- operating temperature of the fuel cell;
- corresponds to the value of the parameters Nominal temperature;
- number of moving electrons per second;
- number of moving electrons per second for a given value of the parameter Nominal exchange current;
- Faraday constant;
- universal gas constant;
- nominal pressure of hydrogen in bar;
- nominal pressure of oxygen in bar;
- Tafel slope as a function of temperature;
- corresponds to the value of the parameters Collapse current;
The voltage 1.229 represents the standard cell potential for the Nernst equation.

The unit calculates the power dissipated or heat released in the fuel cell using the following equation:

where

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

Assumptions and limitations

The Fuel Cell block is not intended for modelling electrolysis.

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

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

Details

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

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

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

Details

Internal resistance.

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

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

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

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

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` \| `MA` \| `kA` \| `mA` \| `nA` \| `pA` \| `uA`
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 | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Excess hydrogen pressure at nominal temperature.

Dependencies

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

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`1.5e5 Pa`
Program usage name	`p_H2_nominal`
Evaluatable	Yes

# Nominal O2 pressure — nominal oxygen pressure
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Oxygen overpressure at rated temperature.

Dependencies

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

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
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 | GOhm | MOhm | kOhm | mOhm

Details

The sum of activation resistance and concentration resistance.

Dependencies

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

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

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

Details

Time constant.

Dependencies

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

Units	`d` \| `s` \| `hr` \| `ms` \| `ns` \| `us` \| `min`
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