Fuel Cell
The electrical system of the fuel cell.
blockType: AcausalElectricPowerSystems.Sources.FuelCell
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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:
A Fuel Cell unit consists of several fuel cells connected in series. The equivalent circuit of one of the elements of the unit is shown below:
where
-
- cell voltage;
-
- corresponds to the Internal resistance parameter;
-
- corresponds to the parameter Sum of activation and concentration resistances;
-
- parallel RC-capacitance, which takes into account time dynamics in the cell.
Equations
Use the Model fidelity parameter to one of two levels of Fuel Cell modelling fidelity:
-
Simplified - nominal conditions- the unit calculates the Nernst stress under nominal temperature and pressure conditions. -
Detailed with physical inputs- the block calculates the Nernst stress taking into account pressure and fuel and air flow rates.
Simplified electrical model
If Model fidelity is set to Simplified - nominal conditions, the Fuel Cell unit calculates the Nernst voltage, , under nominal temperature and pressure conditions, according to the equations:
where
-
- corresponds to the value of the Open-circuit voltage parameter;
-
- corresponds to the value of parameter Number of cells per module;
-
- current generated by the fuel cell;
-
- voltage on the fuel cell terminals;
-
- corresponds to the value of the parameter Module units (Series);
-
- voltage drop that takes into account the fuel cell dynamics;
-
- corresponds to the value of the Tafel slope parameter, in volts;
-
- corresponds to the value of the parameter Nominal exchange current;
-
.
Detailed electrical model
If Model fidelity is set to Detailed with physical 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 hydrogen, , and oxygen, , utilisation rates are determined by the equations:
where
-
- is the thermal stress at room temperature;
-
- is the fuel supply pressure, in
bar; -
- fuel flow rate;
-
- hydrogen concentration in the 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 Nominal temperature parameter;
-
- number of moving electrons per second;
-
- number of moving electrons per second for a given value of the Nominal exchange current parameter;
-
- Faraday constant;
-
- universal gas constant;
-
- nominal hydrogen pressure, in `bar';
-
- nominal pressure of oxygen, in `bar';
-
- Tafel slope as a function of temperature;
-
- corresponds to the value of the Collapse current parameter;
-
The voltage
1.229represents the standard cell potential for the Nernst equation.
The block 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 in entropy of the fuel cell reaction, in
kJ/(mol*K), 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.
Variables
To set priority and initial target values for block variables before simulation, use the Initial Targets section of the block dialogue box.
Use nominal values to set the expected values of a model variable. Using system scaling based on nominal values increases the robustness of the simulation. Nominal values can be obtained from a variety of sources. One such source is the Nominal Values section of the block dialogue box.
Ports
Input
pfuel - absolute pressure of fuel supply, bar
scalar
Input port defining the absolute pressure of the fuel supplied to the unit, in bar.
Dependencies
To enable this port, set Model fidelity to `Detailed with signal inputs'.
pair - air overpressure, bar
scalar
Input port that determines the gauge air pressure, in bar.
Dependencies
To enable this port, set Model fidelity to `Detailed with signal inputs'.
qfuel - fuel consumption, litres/minute
scalar
Input port that defines the volumetric fuel flow rate in the block.
Dependencies
To enable this port, set Model fidelity to `Detailed with signal inputs'.
qair - air flow rate, litres/minute
scalar
Input port that defines the air flow rate of the unit.
Dependencies
To enable this port, set Model fidelity to `Detailed with signal inputs'.
Non-directional
+ - positive
electricity.
A non-directional port representing the positive terminal of the fuel cell.
- is negative
electricity
A non-directional port representing the negative terminal of the fuel cell.
H - heat port
heat
Heat Port.
Dependencies
To enable this port, set the Model fidelity parameter to Detailed with signal inputs.
Parameters
Main
Model fidelity - fuel cell fidelity
Detailed with signal inputs (by default)| Simplified - nominal conditions
Fuel cell model fidelity level.
Open-circuit voltage - open-circuit voltage
65 V (By default) | Positive scalar
Open circuit voltage.
When 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 units of the module. The current flowing out of the fuel cell is negligible.
Tafel slope - Tafel slope
0.23 V (by default) | positive scalar
The amount of excess potential required to increase the reaction rate by a factor of ten.
Internal resistance - internal resistance.
0.05 Ohm (by default) | `positive scalar'.
Internal resistance.
Nominal exchange current - nominal exchange current
80 A (By default) | Positive scalar
Exchange current at nominal temperature.
At nominal exchange current, the fuel cell leaves the activation polarisation region and enters the ohmic polarisation region.
Collapse current - collapse current
200 A (By default) | Positive scalar
The value of the current at which the voltage on 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 enable this parameter, set Model fidelity to `Detailed with signal inputs'.
Number of cells per module - number of cells per module
65 (By default) | positive scalar
Number of cells per module.
The value of the number of cells in this block corresponds to the fuel cell producing the maximum power output for the specified flow and pressure values .
Module units (Series) - stack of modules in series
10 (By default) | positive scalar
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.
Supply
To enable this parameter group, set the Model fidelity parameter to Detailed with signal inputs.
Nominal H2 pressure - Nominal hydrogen pressure
1.5e5 Pa (by default) | positive scalar.
Excess hydrogen pressure at nominal temperature.
Dependencies
To enable this parameter, set Model fidelity to `Detailed with signal inputs'.
Nominal O2 pressure - nominal oxygen pressure
1.0e5 Pa (by default) | `positive scalar'.
Excess oxygen pressure at nominal temperature.
Dependencies
To enable this parameter, set Model fidelity to `Detailed with signal inputs'.
Concentration H2 in fuel (%) - hydrogen concentration in fuel
99 (By default) | an integer between 0 and 100.
Molar concentration of hydrogen in fuel.
The unit of measurement is per cent.
Dependencies
To enable this parameter, set Model fidelity to Detailed with signal inputs.
Concentration O2 in fuel (%) - Oxygen concentration in fuel
21 (By default) | an integer between 0 and 100.
Molar concentration of oxygen in fuel.
The unit of measurement is per cent.
Dependencies
To enable this parameter, set Model fidelity to Detailed with signal inputs.
Concentration vapour in air (%) - concentration of vapour in air
1 (By default) | an integer between 0 and 100.
Molar concentration of vapour in air.
The units of measurement are per cent.
Dependencies
To enable this parameter, set Model fidelity to Detailed with signal inputs.
Dynamics
Model activation delay - activation delay modelling option
off (by default) | on
Check this option if you want to model the fuel cell activation delay.
Sum of activation and concentration resistance - sum of activation and concentration resistance
0.005 Ohm (by default) | `positive scalar'.
Sum of activation and concentration resistance.
Dependencies
To enable this parameter, enable the Model activation delay parameter.
Time constant - time constant
10 s (by default) | `positive scalar'.
Time constant.
Dependencies
To enable this parameter, switch on the Model activation delay parameter.
Thermal
To enable this parameter, set Model fidelity to Detailed with signal inputs.
Nominal temperature - Nominal temperature
293.15 K (By default) | scalar.
The temperature at which the nominal parameters are measured.
Dependencies
To enable this parameter, set Model fidelity to `Detailed with signal inputs'.
Thermal mass is the thermal mass associated with the thermal port, H
30000 J/K (by default) | positive scalar.
Thermal mass associated with the thermal port, H.
This value represents the energy required to raise the temperature of the thermal port by one degree.
Dependencies
To enable this parameter, set Model fidelity to `Detailed with signal inputs'.
Initial Targets
Current
Priority - priority
None (by default) | Higt | Low
Current priority.
Value - current value
0 A (By default) | scalar
Current value.
The unit of measurement is A.
References
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Do, T.C., et al. "Energy Management Strategy of a PEM Fuel Cell Excavator with a Supercapacitor/Battery Hybrid Power Source". Energies 12, no. 22, (November 2019). DOI.org (Crossref), doi:10.3390/en13010136.
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Motapon, Souleman N., O. Tremblay and L. Dessaint, "A generic fuel cell model for the simulation of fuel cell vehicles." 2009 IEEE Vehicle Power and Propulsion Conference, Dearborn, MI, 2009, pp. 1722-1729, doi:10.1109/VPPC.2009.5289692
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Hirschenhofer, J. H.,, D. B. Stauffer, R.R. Engleman, and M.G. Klett. "Fuel Cell Handbook" (4th Ed). U.S. Department of Energy Office of Fossil Energy, 1988.
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Larminie, James, and Andrew Dicks. "Fuel Cell Systems Explained". West Sussex, England: John Wiley & Sons, Ltd, 2003. https://doi.org/10.1002/9781118878330.