Modeling and simulation of proton-exchange membrane fuel cells (PEMFC) may work as a powerful tool in the research & development of renewable energy sources. The Open-Source PEMFC Simulation Tool (OPEM) is a modeling tool for evaluating the performance of proton exchange membrane fuel cells. This package is a combination of models (static/dynamic) that predict the optimum operating parameters of PEMFC. OPEM contained generic models that will accept as input, not only values of the operating variables such as anode and cathode feed gas, pressure and compositions, cell temperature and current density, but also cell parameters including the active area and membrane thickness. In addition, some of the different models of PEMFC that have been proposed in the OPEM, just focus on one particular FC stack, and some others take into account a part or all auxiliaries such as reformers. OPEM is a platform for collaborative development of PEMFC models.
Fig1. OPEM Block Diagram
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CMD
(Windows) or Terminal
(UNIX)opem
or python -m opem
(or run OPEM.exe
)Enter PEM cell parameters (or run standard test vectors)
Amphlett Static Model
Input | Description | Unit |
T | Cell operation temperature | K |
PH2 | Partial pressure | atm |
PO2 | Partial pressure | atm |
i-start | Cell operating current start point | A |
i-step | Cell operating current step | A |
i-stop | Cell operating current end point | A |
A | Active area | cm^2 |
l | Membrane thickness | cm |
lambda | An adjustable parameter with a min value of 14 and max value of 23 | -- |
R(*Optional) | R-Electronic | ohm |
JMax | Maximum current density | A/(cm^2) |
N | Number of single cells | -- |
Larminie-Dicks Static Model
Input | Description | Unit |
E0 | Fuel cell reversible no loss voltage | V |
A | The slope of the Tafel line | V |
T | Cell operation temperature | K |
i-start | Cell operating current start point | A |
i-step | Cell operating current step | A |
i-stop | Cell operating current end point | A |
i_n | Internal current | A |
i_0 | Exchange current at which the overvoltage begins to move from zero | A |
i_L | Limiting current | A |
RM | The membrane and contact resistances | ohm |
N | Number of single cells | -- |
Chamberline-Kim Static Model
Input | Description | Unit |
E0 | Open circuit voltage | V |
b | Tafel's parameter for the oxygen reduction | V |
R | Resistance | ohm.cm^2 |
i-start | Cell operating current start point | A |
i-step | Cell operating current step | A |
i-stop | Cell operating current end point | A |
A | Active area | cm^2 |
m | Diffusion's parameters | V |
n | Diffusion's parameters | (A^-1)(cm^2) |
N | Number of single cells | -- |
Padulles Dynamic Model I
Input | Description | Unit |
E0 | No load voltage | V |
T | Fuel cell temperature | K |
KH2 | Hydrogen valve constant | kmol.s^(-1).atm^(-1) |
KO2 | Oxygen valve constant | kmol.s^(-1).atm^(-1) |
tH2 | Hydrogen time constant | s |
tO2 | Oxygen time constant | s |
B | Activation voltage constant | V |
C | Activation constant parameter | A^(-1) |
Rint | Fuel cell internal resistance | ohm |
rho | Hydrogen-Oxygen flow ratio | -- |
qH2 | Molar flow of hydrogen | kmol/s |
N0 | Number of cells | -- |
i-start | Cell operating current start point | A |
i-step | Cell operating current step | A |
i-stop | Cell operating current end point | A |
Padulles Dynamic Model II
Input | Description | Unit |
E0 | No load voltage | V |
T | Fuel cell temperature | K |
KH2 | Hydrogen valve constant | kmol.s^(-1).atm^(-1) |
KH2O | Water valve constant | kmol.s^(-1).atm^(-1) |
KO2 | Oxygen valve constant | kmol.s^(-1).atm^(-1) |
tH2 | Hydrogen time constant | s |
tH2O | Water time constant | s |
tO2 | Oxygen time constant | s |
B | Activation voltage constant | V |
C | Activation constant parameter | A^(-1) |
Rint | Fuel cell internal resistance | ohm |
rho | Hydrogen-Oxygen flow ratio | -- |
qH2 | Molar flow of hydrogen | kmol/s |
N0 | Number of cells | -- |
i-start | Cell operating current start point | A |
i-step | Cell operating current step | A |
i-stop | Cell operating current end point | A |
Padulles-Hauer Dynamic Model
Input | Description | Unit |
E0 | No load voltage | V |
T | Fuel cell temperature | K |
KH2 | Hydrogen valve constant | kmol.s^(-1).atm^(-1) |
KH2O | Water valve constant | kmol.s^(-1).atm^(-1) |
KO2 | Oxygen valve constant | kmol.s^(-1).atm^(-1) |
tH2 | Hydrogen time constant | s |
tH2O | Water time constant | s |
tO2 | Oxygen time constant | s |
t1 | Reformer time constant | s |
t2 | Reformer time constant | s |
B | Activation voltage constant | V |
C | Activation constant parameter | A^(-1) |
CV | Conversion factor | -- |
Rint | Fuel cell internal resistance | ohm |
rho | Hydrogen-Oxygen flow ratio | -- |
qMethanol | Molar flow of methanol | kmol/s |
N0 | Number of cells | -- |
i-start | Cell operating current start point | A |
i-step | Cell operating current step | A |
i-stop | Cell operating current end point | A |
Padulles-Amphlett Dynamic Model
Input | Description | Unit |
E0 | No load voltage | V |
T | Fuel cell temperature | K |
KH2 | Hydrogen valve constant | kmol.s^(-1).atm^(-1) |
KH2O | Water valve constant | kmol.s^(-1).atm^(-1) |
KO2 | Oxygen valve constant | kmol.s^(-1).atm^(-1) |
tH2 | Hydrogen time constant | s |
tH2O | Water time constant | s |
tO2 | Oxygen time constant | s |
t1 | Reformer time constant | s |
t2 | Reformer time constant | s |
A | Active area | cm^2 |
l | Membrane thickness | cm |
lambda | An adjustable parameter with a min value of 14 and max value of 23 | -- |
R(*Optional) | R-Electronic | ohm |
JMax | Maximum current density | A/(cm^2) |
CV | Conversion factor | -- |
rho | Hydrogen-Oxygen flow ratio | -- |
qMethanol | Molar flow of methanol | kmol/s |
N0 | Number of cells | -- |
i-start | Cell operating current start point | A |
i-step | Cell operating current step | A |
i-stop | Cell operating current end point | A |
Chakraborty Dynamic Model
Input | Description | Unit |
E0 | No load voltage | V |
T | Cell operation temperature | K |
KH2 | Hydrogen valve constant | kmol.s^(-1).atm^(-1) |
KH2O | Water valve constant | kmol.s^(-1).atm^(-1) |
KO2 | Oxygen valve constant | kmol.s^(-1).atm^(-1) |
rho | Hydrogen-Oxygen flow ratio | -- |
Rint | Fuel cell internal resistance | ohm |
N0 | Number of cells | -- |
u | Fuel utilization ratio | -- |
i-start | Cell operating current start point | A |
i-step | Cell operating current step | A |
i-stop | Cell operating current end point | A |
Model_Name
folder Amphlett Static Model
>>> from opem.Static.Amphlett import Static_Analysis
>>> Test_Vector={"T": 343.15,"PH2": 1,"PO2": 1,"i-start": 0,"i-stop": 75,"i-step": 0.1,"A": 50.6,"l": 0.0178,"lambda": 23,"N": 1,"R": 0,"JMax": 1.5,"Name": "Amphlett_Test"}
>>> data=Static_Analysis(InputMethod=Test_Vector,TestMode=True,PrintMode=False,ReportMode=False)
Key | Description | Type |
Status | Simulation status | Bool |
P | Power | List |
I | Cell operating current | List |
V | FC voltage | List |
EFF | Efficiency | List |
Ph | Thermal power | List |
V0 | Linear-Apx intercept | Float |
K | Linear-Apx slope | Float |
Eta_Active | Eta activation | List |
Eta_Conc | Eta concentration | List |
Eta_Ohmic | Eta ohmic | List |
VE | Estimated FC voltage | List |
Larminie-Dicks Static Model
>>> from opem.Static.Larminie_Dicks import Static_Analysis
>>> Test_Vector = {"A": 0.06,"E0": 1.178,"T": 328.15,"RM": 0.0018,"i_0": 0.00654,"i_L": 100.0,"i_n": 0.23,"N": 23,"i-start": 0.1,"i-stop": 98,"i-step": 0.1,"Name": "Larminiee_Test"}
>>> data=Static_Analysis(InputMethod=Test_Vector,TestMode=True,PrintMode=False,ReportMode=False)
Key | Description | Type |
Status | Simulation status | Bool |
P | Power | List |
I | Cell operating current | List |
V | FC voltage | List |
EFF | Efficiency | List |
Ph | Thermal power | List |
V0 | Linear-Apx intercept | Float |
K | Linear-Apx slope | Float |
VE | Estimated FC voltage | List |
Chamberline-Kim Static Model
>>> from opem.Static.Chamberline_Kim import Static_Analysis
>>> Test_Vector = {"A": 50.0,"E0": 0.982,"b": 0.0689,"R": 0.328,"m": 0.000125,"n": 9.45,"N": 1,"i-start": 1,"i-stop": 42.5,"i-step": 0.1,"Name": "Chamberline_Test"}
>>> data=Static_Analysis(InputMethod=Test_Vector,TestMode=True,PrintMode=False,ReportMode=False)
Key | Description | Type |
Status | Simulation status | Bool |
P | Power | List |
I | Cell operating current | List |
V | FC voltage | List |
EFF | Efficiency | List |
Ph | Thermal power | List |
V0 | Linear-Apx intercept | Float |
K | Linear-Apx slope | Float |
VE | Estimated FC voltage | List |
Padulles Dynamic Model I
>>> from opem.Dynamic.Padulles1 import Dynamic_Analysis
>>> Test_Vector = {"T": 343,"E0": 0.6,"N0": 88,"KO2": 0.0000211,"KH2": 0.0000422,"tH2": 3.37,"tO2": 6.74,"B": 0.04777,"C": 0.0136,"Rint": 0.00303,"rho": 1.168,"qH2": 0.0004,"i-start": 0,"i-stop": 100,"i-step": 0.1,"Name": "PadullesI_Test"}
>>> data=Dynamic_Analysis(InputMethod=Test_Vector,TestMode=True,PrintMode=False,ReportMode=False)
Key | Description | Type |
Status | Simulation status | Bool |
P | Power | List |
I | Cell operating current | List |
V | FC voltage | List |
EFF | Efficiency | List |
PO2 | Partial pressure | List |
PH2 | Partial pressure | List |
Ph | Thermal power | List |
V0 | Linear-Apx intercept | Float |
K | Linear-Apx slope | Float |
VE | Estimated FC voltage | List |
Padulles Dynamic Model II
>>> from opem.Dynamic.Padulles2 import Dynamic_Analysis
>>> Test_Vector = {"T": 343,"E0": 0.6,"N0": 5,"KO2": 0.0000211,"KH2": 0.0000422,"KH2O": 0.000007716,"tH2": 3.37,"tO2": 6.74,"tH2O": 18.418,"B": 0.04777,"C": 0.0136,"Rint": 0.00303,"rho": 1.168,"qH2": 0.0004,"i-start": 0.1,"i-stop": 100,"i-step": 0.1,"Name": "Padulles2_Test"}
>>> data=Dynamic_Analysis(InputMethod=Test_Vector,TestMode=True,PrintMode=False,ReportMode=False)
Key | Description | Type |
Status | Simulation status | Bool |
P | Power | List |
I | Cell operating current | List |
V | FC voltage | List |
EFF | Efficiency | List |
PO2 | Partial pressure | List |
PH2 | Partial pressure | List |
PH2O | Partial pressure | List |
Ph | Thermal power | List |
V0 | Linear-Apx intercept | Float |
K | Linear-Apx slope | Float |
VE | Estimated FC voltage | List |
Padulles-Hauer Dynamic Model
>>> from opem.Dynamic.Padulles_Hauer import Dynamic_Analysis
>>> Test_Vector = {"T": 343,"E0": 0.6,"N0": 5,"KO2": 0.0000211,"KH2": 0.0000422,"KH2O": 0.000007716,"tH2": 3.37,"tO2": 6.74,"t1": 2,"t2": 2,"tH2O": 18.418,"B": 0.04777,"C": 0.0136,"Rint": 0.00303,"rho": 1.168,"qMethanol": 0.0002,"CV": 2,"i-start": 0.1,"i-stop": 100,"i-step": 0.1,"Name": "Padulles_Hauer_Test"}
>>> data=Dynamic_Analysis(InputMethod=Test_Vector,TestMode=True,PrintMode=False,ReportMode=False)
Key | Description | Type |
Status | Simulation status | Bool |
P | Power | List |
I | Cell operating current | List |
V | FC voltage | List |
EFF | Efficiency | List |
PO2 | Partial pressure | List |
PH2 | Partial pressure | List |
PH2O | Partial pressure | List |
Ph | Thermal power | List |
V0 | Linear-Apx intercept | Float |
K | Linear-Apx slope | Float |
VE | Estimated FC voltage | List |
Padulles-Amphlett Dynamic Model
>>> from opem.Dynamic.Padulles_Amphlett import Dynamic_Analysis
>>> Test_Vector = {"A": 50.6,"l": 0.0178,"lambda": 23,"JMax": 1.5,"T": 343,"N0": 5,"KO2": 0.0000211,"KH2": 0.0000422,"KH2O": 0.000007716,"tH2": 3.37,"tO2": 6.74,"t1": 2,"t2": 2,"tH2O": 18.418,"rho": 1.168,"qMethanol": 0.0002,"CV": 2,"i-start": 0.1,"i-stop": 75,"i-step": 0.1,"Name": "Padulles_Amphlett_Test"}
>>> data=Dynamic_Analysis(InputMethod=Test_Vector,TestMode=True,PrintMode=False,ReportMode=False)
Key | Description | Type |
Status | Simulation status | Bool |
P | Power | List |
I | Cell operating current | List |
V | FC voltage | List |
EFF | Efficiency | List |
PO2 | Partial pressure | List |
PH2 | Partial pressure | List |
PH2O | Partial pressure | List |
Ph | Thermal power | List |
V0 | Linear-Apx intercept | Float |
K | Linear-Apx slope | Float |
Eta_Active | Eta activation | List |
Eta_Conc | Eta concentration | List |
Eta_Ohmic | Eta ohmic | List |
VE | Estimated FC voltage | List |
Chakraborty Dynamic Model
>>> from opem.Dynamic.Chakraborty import Dynamic_Analysis
>>> Test_Vector = {"T": 1273,"E0": 0.6,"u":0.8,"N0": 1,"R": 3.28125 * 10**(-3),"KH2O": 0.000281,"KH2": 0.000843,"KO2": 0.00252,"rho": 1.145,"i-start": 0.1,"i-stop": 300,"i-step": 0.1,"Name": "Chakraborty_Test"}
>>> data=Dynamic_Analysis(InputMethod=Test_Vector,TestMode=True,PrintMode=False,ReportMode=False)
Key | Description | Type |
Status | Simulation status | Bool |
P | Power | List |
I | Cell operating current | List |
V | FC voltage | List |
EFF | Efficiency | List |
PO2 | Partial pressure | List |
PH2 | Partial pressure | List |
PH2O | Partial pressure | List |
Ph | Thermal power | List |
Nernst Gain | Nernst Gain | List |
Ohmic Loss | Ohmic Loss | List |
V0 | Linear-Apx intercept | Float |
K | Linear-Apx slope | Float |
VE | Estimated FC voltage | List |
TestMode
: Active test mode and get/return data as dict
, (Default : False
)ReportMode
: Generate reports(.csv
,.opem
,.html
) and print result in console, (Default : True
)PrintMode
: Control printing in console, (Default : True
)Folder
: Reports folder, (Default : os.getcwd()
)dict
/start
command to OPEM BOTOPEM can be used online in interactive Jupyter Notebooks via the Binder service! Try it out now! :
.ipynb
files in Documents
folderTest_Vector
in Full Run
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or send an email to opem@ecsim.site.
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1- J. C. Amphlett, R. M. Baumert, R. F. Mann, B. A. Peppley, and P. R. Roberge. 1995. "Performance Modeling of the Ballard Mark IV Solid Polymer Electrolyte Fuel Cell." J. Electrochem. Soc. (The Electrochemical Society, Inc.) 142 (1): 9-15. doi: 10.1149/1.2043959.
2- Jeferson M. Correa, Felix A. Farret, Vladimir A. Popov, Marcelo G. Simoes. 2005. "Sensitivity Analysis of the Modeling Parameters Used in Simulation of Proton Exchange Membrane Fuel Cells." IEEE Transactions on Energy Conversion (IEEE) 20 (1): 211-218. doi:10.1109/TEC.2004.842382.
3- Junbom Kim, Seong-Min Lee, Supramaniam Srinivasan, Charles E. Chamberlin. 1995. "Modeling of Proton Exchange Membrane Fuel Cell Performance with an Empirical Equation." Journal of The Electrochemical Society (The Electrochemical Society) 142 (8): 2670-2674. doi:10.1149/1.2050072.
4- I. Sadli, P. Thounthong, J.-P. Martin, S. Rael, B. Davat. 2006. "Behaviour of a PEMFC supplying a low voltage static converter." Journal of Power Sources (Elsevier) 156: 119–125. doi:10.1016/j.jpowsour.2005.08.021.
5- J. Padulles, G.W. Ault, J.R. McDonald. 2000. "An integrated SOFC plant dynamic model for power systems simulation." Journal of Power Sources (Elsevier) 86 (1-2): 495-500. doi:10.1016/S0378-7753(99)00430-9.
6- Hauer, K.-H. 2001. "Analysis tool for fuel cell vehicle hardware and software (controls) with an application to fuel economy comparisons of alternative system designs." Ph.D. dissertation, Transportation Technology and Policy, University of California Davis.
7- A. Saadi, M. Becherif, A. Aboubou, M.Y. Ayad. 2013. "Comparison of proton exchange membrane fuel cell static models." Renewable Energy (Elsevier) 56: 64-71. doi:dx.doi.org/10.1016/j.renene.2012.10.012.
8- Diego Feroldi, Marta Basualdo. 2012. "Description of PEM Fuel Cells System." Green Energy and Technology (Springer) 49-72. doi:10.1007/978-1-84996-184-4_2
9- Gottesfeld, Shimshon. n.d. The Polymer Electrolyte Fuel Cell: Materials Issues in a Hydrogen Fueled Power Source. http://physics.oregonstate.edu/~hetheriw/energy/topics/doc/electrochemistry/fc/basic/The_Polymer_Electrolyte_Fuel_Cell.htm
10- Mohamed Becherif, Aïcha Saadi, Daniel Hissel, Abdennacer Aboubou, Mohamed Yacine Ayad. 2011. "Static and dynamic proton exchange membrane fuel cell models." Journal of Hydrocarbons Mines and Environmental Research 2 (1)
11- Larminie, J., Dicks, A., & McDonald, M. S. 2003. Fuel cell systems explained (Vol. 2, pp. 207-225). Chichester, UK: J. Wiley. doi: 10.1002/9781118706992.
12- Rho, Y. W., Srinivasan, S., & Kho, Y. T. 1994. ''Mass transport phenomena in proton exchange membrane fuel cells using o 2/he, o 2/ar, and o 2/n 2 mixtures ii. Theoretical analysis.'' Journal of the Electrochemical Society, 141(8), 2089-2096. doi: 10.1149/1.2055066.
13- U. Chakraborty, A New Model for Constant Fuel Utilization and Constant Fuel Flow in Fuel Cells, Appl. Sci. 9 (2019) 1066. https://doi.org/10.3390/app9061066.
If you use OPEM in your research , please cite this paper :
@article{Haghighi2018, doi = {10.21105/joss.00676}, url = {https://doi.org/10.21105/joss.00676}, year = {2018}, month = {jul}, publisher = {The Open Journal}, volume = {3}, number = {27}, pages = {676}, author = {Sepand Haghighi and Kasra Askari and Sarmin Hamidi and Mohammad Mahdi Rahimi}, title = {{OPEM} : Open Source {PEM} Cell Simulation Tool}, journal = {Journal of Open Source Software} }
Download OPEM.bib(BibTeX Format)
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