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Shunt Currents in an Alkaline Electrolyzer Stack
Introduction
In an alkaline electrolyzer stack, all cells share the same electrolyte. As a result of all cells being in ionic contact, parasitic shunt currents flow between the cells through the manifolds and the electrolyte channels, on both the inlet and outlet side.
This example models a secondary current distribution in a stack comprising 20 cells. The electricity-to-hydrogen coulombic and energy efficiencies for the stack are computed, as well as the individual shunt currents entering or exiting each cell.
Model Definition
Figure 1: Model stack geometry.
Figure 1 shows the full model geometry. The stack consists of two end plates and 20 repeating unit cells, shown in Figure 2.
Figure 2: Repeating cell unit. Scaled ten times in the x direction.
The endplates and the bipolar plates are made of steel. The electrolyte is 6 M KOH.
The model is set up using the Water Electrolyzer interface. The electrode surfaces are modeled using Butler–Volmer kinetics and ohmic losses both in the electrode and electrolyte phases are included, but and any effects due to gas phase mass transport limitations are neglected (this is also known as a secondary current distribution model). The model is isothermal, with the stack set to operate at 85°C.
The effective electrolyte conductivity in the electrolyte compartment on each side of the separate is set to depend on the electrolyte volume fraction according to
(1)
where σl,bulk is the bulk conductivity of 6.0 KOH. Due to gas evolution in the cell electrolyte compartments, the electrolyte volume fraction εl is defined to vary linearly with z from 100% at the bottom of the electrode active surface area to 50% at the exit to the upper manifolds.
The model is solved using an auxiliary sweep, sweeping the average cell voltage from 1.3 V to 1.8 V.
Results and Discussion
Figure 3 shows the electric potential in the end plates and bipolar plates of the stack for an average cell voltage of 1.8 V.
Figure 3: Electrode phase potential.
Figure 4 and Figure 5 show the electrolyte phase potential in the stack, and the corresponding electrolyte current streamlines in the inlet/outlet channels and manifolds, for an average cell voltage of 1.8 V, respectively.
Figure 4: Electrolyte phase potential.
Figure 5: Current streamlines in the inlet and outlet channels and manifolds.
Figure 6: Entering or exiting shunt current per cell at an average cell voltage of 1.3 V.
Figure 7: Entering or exiting shunt current per cell at an average cell voltage of 1.8 V.
The shunt current streamlines in Figure 5 can be integrated over the internal boundary between each manifold and the corresponding electrolyte compartment to compute the individual entry/exit shunt currents of each cell. This is shown in Figure 6 and Figure 7 for the average cell voltages of 1.3 and 1.8 V. The lower effective electrolyte conductivity in the upper channels, due to lower electrolyte volume fraction (Equation 1) results in lower shunt currents for the outlet channels compared to the inlet channels. It is also seen that the shunt currents are more pronounced toward the end of the stack. The higher stack voltage results in generally higher shunt currents in Figure 7, compared to Figure 6.
Figure 8 shows a polarization plot for the stack, where the total current on the x-axis was computed by integrating the current density over one of the end plates of the stack. The plot also show the open circuit and thermoneutral cell voltage for the operating conditions. The thermoneutral cell voltage is of particular interest since additional heat would be required to heat the stack when operating the electrolyzer below this voltage.
Figure 8: Polarization plot for the stack.
We can also compute the coloumbic efficiency for hydrogen production in the stack. This efficiency measure is defined as the total hydrogen evolution current density in all cells, divided by the stack current times the number of cells. The coloumbic efficiency is plotted in Figure 9. The interplay between different polarization effects results in the efficiency being lower at lower stack currents.
Figure 9: Current-to-hydrogen coloumbic efficiency.
Finally, we can also have a look at the energy efficiency of the stack for different current levels in Figure 10. For a system of this kind there are various ways of defining the energy efficiency. Here we base the efficiency measure on the Gibbs free energy of the produced hydrogen, and define the efficiency as the maximum possible energy (per time unit) which would be possible to produce in a fuel cell operating at the same conditions (I112 × Eeq), divided by the electrical energy required to produce it in the stack (Istack × Estack). The energy efficiency first increases, as a result of the increasing coloumbic efficiency (Figure 9), to reach at maximum around 1400 A. The decrease seen after 1400 A is due to an increasing stack voltage at higher currents (Figure 8).
Figure 10: Electrical energy-to-hydrogen energy (Gibbs) efficiency.
Notes About the COMSOL Implementation
A Global Evaluation Sweep is used to compute the table values plotted in Figure 6 and Figure 7. To update these plots and the corresponding table after recomputing the model, the global evaluation sweep needs to be reevaluated.
Application Library path: Fuel_Cell_and_Electrolyzer_Module/Electrolyzers/aec_shunt_currents
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Electrochemistry>Water Electrolyzers>Hydroxide Exchange (we).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select Preset Studies for Selected Physics Interfaces>Stationary with Initialization.
6
Click  Done.
Geometry 1
Load the geometry sequence from a file.
1
In the Geometry toolbar, click Insert Sequence and choose Insert Sequence.
2
Browse to the model’s Application Libraries folder and double-click the file aec_shunt_currents_geom_sequence.mph.
3
In the Geometry toolbar, click  Build All.
4
In the Model Builder window, collapse the Geometry 1 node.
Definitions
The stack geometry has a high aspect ratio, with the cell thicknesses being very small in relation to the cross-sectional area. To facilitate setting up the physics, add a view with scaling in the x direction as follows:
View 20
1
In the Model Builder window, expand the Component 1 (comp1)>Definitions node.
2
Right-click Definitions and choose View.
Camera
1
In the Model Builder window, expand the View 20 node, then click Camera.
2
In the Settings window for Camera, locate the Camera section.
3
From the View scale list, choose Manual.
4
In the x scale text field, type 10.
5
Click  Update.
You can now toggle between the two views at any time.
6
Click the  Go to Default View button in the Graphics toolbar.
7
In the Graphics window toolbar, clicknext to  Go to Default View, then choose Go to View 1.
8
In the Graphics window toolbar, clicknext to  Go to Default View, then choose Go to View 20.
Global Definitions
Geometry Parameters
Some parameters were loaded with the geometry sequence.
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, type Geometry Parameters in the Label text field.
Add some more parameters from a text file.
Physics Parameters
1
In the Home toolbar, click  Parameters and choose Add>Parameters.
2
In the Settings window for Parameters, type Physics Parameters in the Label text field.
3
Locate the Parameters section. Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file aec_shunt_currents_physics_parameters.txt.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
This model uses the Materials node to define the properties of the bipolar plates, end plates, and electrolyte.
2
Go to the Add Material window.
3
In the tree, select Built-in>Steel AISI 4340.
4
Right-click and choose Add to Component 1 (comp1).
5
In the tree, select Fuel Cell and Electrolyzer>Aqueous Alkali>Potassium Hydroxide, KOH.
6
Right-click and choose Add to Component 1 (comp1).
7
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Steel AISI 4340 (mat1)
1
In the Settings window for Material, locate the Geometric Entity Selection section.
2
From the Selection list, choose Current Conductors.
Potassium Hydroxide, KOH (mat2)
1
In the Model Builder window, click Potassium Hydroxide, KOH (mat2).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Electrolyte Compartments.
Definitions
Variables 1
1
In the Model Builder window, under Component 1 (comp1) right-click Definitions and choose Variables.
Add some variable expressions from a text file. Most of these will be used during postprocessing of the solution.
2
In the Settings window for Variables, locate the Variables section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file aec_shunt_currents_variables.txt.
Note that some expressions are marked in orange, indicating unknown operators. Add these operators as follows:
Integration 1 (intop1)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, type intop_point_h2 in the Operator name text field.
3
Locate the Source Selection section. From the Geometric entity level list, choose Point.
4
Select Point 15 only.
Integration 2 (intop2)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, type intop_point_o2 in the Operator name text field.
3
Locate the Source Selection section. From the Geometric entity level list, choose Point.
4
Select Point 57 only.
Integration 3 (intop3)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, type intop_h2_electrodes in the Operator name text field.
3
Locate the Source Selection section. From the Geometric entity level list, choose Boundary.
4
From the Selection list, choose H2 Electrodes.
Integration 4 (intop4)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, type intop_cc in the Operator name text field.
3
Locate the Source Selection section. From the Geometric entity level list, choose Boundary.
4
Select Boundary 1 only.
Integration 5 (intop5)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, type intop_upper in the Operator name text field.
3
Locate the Source Selection section. From the Geometric entity level list, choose Boundary.
4
From the Selection list, choose Upper Manifold - Active Cell Boundaries.
Integration 6 (intop6)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, type intop_lower in the Operator name text field.
3
Locate the Source Selection section. From the Geometric entity level list, choose Boundary.
4
From the Selection list, choose Lower Manifold - Active Cell Boundaries.
Variables 1
All variable expressions should now have turned black.
Water Electrolyzer (we)
You are now ready to start defining the physics.
1
In the Model Builder window, under Component 1 (comp1) click Water Electrolyzer (we).
2
In the Settings window for Water Electrolyzer, locate the H2 Gas Mixture section.
3
Clear the H2O check box.
4
Find the Reactions subsection. Select the Include H2O(l) in reaction stoichiometry check box.
5
Locate the O2 Gas Mixture section. Clear the H2O check box.
6
Select the Include H2O(l) in reaction stoichiometry check box.
Separator 1
1
In the Physics toolbar, click  Domains and choose Separator.
2
In the Settings window for Separator, locate the Domain Selection section.
3
From the Selection list, choose Separators.
4
Locate the Effective Electrolyte Charge Transport section. In the εl text field, type epsl_sep.
Current Collector 1
1
In the Physics toolbar, click  Domains and choose Current Collector.
2
In the Settings window for Current Collector, locate the Domain Selection section.
3
From the Selection list, choose Current Conductors.
4
Locate the Electrode Charge Transport section. From the σs list, choose From material.
H2 Gas-Electrolyte Compartment 1
1
In the Physics toolbar, click  Domains and choose H2 Gas-Electrolyte Compartment.
2
In the Settings window for H2 Gas-Electrolyte Compartment, locate the Domain Selection section.
3
From the Selection list, choose H2 Gas Electrolyte Compartments.
4
Locate the Effective Electrolyte Charge Transport section. In the εl text field, type epsl.
O2 Gas-Electrolyte Compartment 1
1
In the Physics toolbar, click  Domains and choose O2 Gas-Electrolyte Compartment.
2
In the Settings window for O2 Gas-Electrolyte Compartment, locate the Domain Selection section.
3
From the Selection list, choose Oxygen Gas Electrolyte Compartments.
4
Locate the Effective Electrolyte Charge Transport section. In the εl text field, type epsl.
Internal H2 Electrode Surface 1
1
In the Physics toolbar, click  Boundaries and choose Internal H2 Electrode Surface.
2
In the Settings window for Internal H2 Electrode Surface, locate the Boundary Selection section.
3
From the Selection list, choose H2 Electrodes.
H2 Electrode Reaction 1
1
In the Model Builder window, click H2 Electrode Reaction 1.
2
In the Settings window for H2 Electrode Reaction, locate the Stoichiometric Coefficients section.
3
In the νH2O(l) text field, type -1.
4
Locate the Electrode Kinetics section. From the Exchange current density type list, choose Lumped multistep.
5
In the i0,ref(T) text field, type i0_ref_h2.
6
From the Pressure dependence list, choose Cathodic reaction orders.
7
In the ξc,H2 text field, type 1.
Internal O2 Electrode Surface 1
1
In the Physics toolbar, click  Boundaries and choose Internal O2 Electrode Surface.
2
In the Settings window for Internal O2 Electrode Surface, locate the Boundary Selection section.
3
From the Selection list, choose O2 Electrodes.
O2 Electrode Reaction 1
1
In the Model Builder window, click O2 Electrode Reaction 1.
2
In the Settings window for O2 Electrode Reaction, locate the Stoichiometric Coefficients section.
3
In the νH2O(l) text field, type -1.
4
Locate the Electrode Kinetics section. From the Exchange current density type list, choose Lumped multistep.
5
In the i0,ref(T) text field, type i0_ref_o2.
6
From the Pressure dependence list, choose Anodic reaction orders.
7
In the ξa,O2 text field, type 1.
Electronic Conducting Phase 1
In the Model Builder window, under Component 1 (comp1)>Water Electrolyzer (we) click Electronic Conducting Phase 1.
Electric Ground 1
1
In the Physics toolbar, click  Attributes and choose Electric Ground.
2
Select Boundary 1 only.
Electronic Conducting Phase 1
In the Model Builder window, click Electronic Conducting Phase 1.
Electric Potential 1
1
In the Physics toolbar, click  Attributes and choose Electric Potential.
2
Select Boundary 1610 only.
3
In the Settings window for Electric Potential, locate the Electric Potential section.
4
In the φs,bnd text field, type E_stack.
Electrolyte Phase 1
The electrolyte properties need input from the physics with regards to the electrolyte concentration and the temperature.
1
In the Model Builder window, under Component 1 (comp1)>Water Electrolyzer (we) click Electrolyte Phase 1.
2
In the Settings window for Electrolyte Phase, locate the Model Input section.
3
From the c list, choose User defined.
The model input variables can be defined locally on this node or as a Common model input. In the associated text field, type c_KOH.
Global Definitions
Default Model Inputs
1
In the Model Builder window, under Global Definitions click Default Model Inputs.
2
In the Settings window for Default Model Inputs, locate the Browse Model Inputs section.
3
In the tree, select General>Temperature (K) - minput.T.
4
Find the Expression for remaining selection subsection. In the Temperature text field, type T.
Also, the pressure needs to be set since the equilibrium potentials of the electrode reactions depend on the pressure.
5
In the tree, select General>Pressure (Pa) - minput.pA.
6
In the Pressure text field, type p_abs.
Mesh 1
This model requires a manual mesh. The geometry has been set up in such a way that it can easily be swept in the x direction. For good accuracy when computing the shunt currents, a more well-resolved mesh is needed in the manifolds and channels.
Size 1
1
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose Size.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
From the Selection list, choose Upper/Lower Manifold and Active Area Boundaries (for Meshing).
5
Locate the Element Size section. From the Predefined list, choose Extra fine.
Size 2
1
In the Model Builder window, right-click Mesh 1 and choose Size.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Channels.
5
Locate the Element Size section. From the Predefined list, choose Finer.
Swept 1
In the Mesh toolbar, click  Swept.
Distribution 1
1
Right-click Swept 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Domain Selection section.
3
From the Selection list, choose H2 Gas Electrolyte Compartments.
Distribution 2
1
In the Model Builder window, right-click Swept 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Domain Selection section.
3
From the Selection list, choose Current Conductors.
4
Locate the Distribution section. In the Number of elements text field, type 1.
Distribution 3
1
Right-click Swept 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Domain Selection section.
3
From the Selection list, choose Oxygen Gas Electrolyte Compartments.
Distribution 4
1
Right-click Swept 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Domain Selection section.
3
From the Selection list, choose Separators.
4
Locate the Distribution section. In the Number of elements text field, type 2.
Swept 1
Right-click Swept 1 and choose Build Selected.
Boundary Layers 1
The local current densities on the electrode surfaces are higher in the regions close to the manifolds. Add boundary layer meshes there in order to improve the shunt current accuracy further.
1
In the Mesh toolbar, click  Boundary Layers.
2
In the Settings window for Boundary Layers, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Active Cell Volume.
5
Click to expand the Transition section. Clear the Smooth transition to interior mesh check box.
Boundary Layer Properties
1
In the Model Builder window, click Boundary Layer Properties.
2
In the Settings window for Boundary Layer Properties, locate the Boundary Selection section.
3
From the Selection list, choose Upper/Lower Active Area Boundaries (for Meshing).
4
Locate the Layers section. In the Number of layers text field, type 5.
5
From the Thickness specification list, choose First layer.
6
In the Thickness text field, type D_o2/3.
Boundary Layers 2
1
In the Mesh toolbar, click  Boundary Layers.
2
In the Settings window for Boundary Layers, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Manifolds.
5
Locate the Transition section. Clear the Smooth transition to interior mesh check box.
Boundary Layer Properties
1
In the Model Builder window, click Boundary Layer Properties.
2
In the Settings window for Boundary Layer Properties, locate the Boundary Selection section.
3
From the Selection list, choose Manifold - Active Cell Boundaries.
4
Locate the Layers section. In the Number of layers text field, type 2.
5
From the Thickness specification list, choose First layer.
6
In the Thickness text field, type D_o2/3.
7
Click  Build All.
The model is now ready for solving. Use an auxiliary sweep for sweeping the average cell voltage from 1.3 to 1.8 V.
Study 1
Step 2: Stationary
1
In the Model Builder window, under Study 1 click Step 2: Stationary.
2
In the Settings window for Stationary, click to expand the Study Extensions section.
3
Select the Auxiliary sweep check box.
4
Click  Add.
5
In the table, click to select the cell at row number 1 and column number 3.
6
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
E_cell (Cell voltage (varied in sweep))
range(1.3,0.1,1.8)
V
7
In the Home toolbar, click  Compute.
Results
Electrode Potential with Respect to Ground
Reproduce the plots from the Results and Discussion section as follows.
1
In the Settings window for 3D Plot Group, type Electrode Potential with Respect to Ground in the Label text field.
2
In the Model Builder window, expand the Electrode Potential with Respect to Ground node.
Arrow Volume 1, Multislice 1
1
In the Model Builder window, under Results>Electrode Potential with Respect to Ground, Ctrl-click to select Multislice 1 and Arrow Volume 1.
2
Right-click and choose Disable.
Surface 1
1
In the Model Builder window, right-click Electrode Potential with Respect to Ground and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type we.phis.
4
In the Electrode Potential with Respect to Ground toolbar, click  Plot.
5
In the Graphics window toolbar, clicknext to  Go to Default View, then choose Go to View 1.
Electrode Potential with Respect to Ground
1
In the Model Builder window, click Electrode Potential with Respect to Ground.
2
In the Settings window for 3D Plot Group, locate the Plot Settings section.
3
Clear the Plot dataset edges check box.
4
In the Electrode Potential with Respect to Ground toolbar, click  Plot.
Electrolyte Potential
1
In the Model Builder window, under Results click Electrolyte Potential (we).
2
In the Settings window for 3D Plot Group, type Electrolyte Potential in the Label text field.
3
Locate the Plot Settings section. Clear the Plot dataset edges check box.
4
In the Model Builder window, expand the Electrolyte Potential node.
Arrow Volume 1, Multislice 1
1
In the Model Builder window, under Results>Electrolyte Potential, Ctrl-click to select Multislice 1 and Arrow Volume 1.
2
Right-click and choose Disable.
Surface 1
1
In the Model Builder window, right-click Electrolyte Potential and choose Surface.
2
In the Electrolyte Potential toolbar, click  Plot.
Shunt Current Streamlines
1
In the Home toolbar, click  Add Plot Group and choose 3D Plot Group.
2
In the Settings window for 3D Plot Group, type Shunt Current Streamlines in the Label text field.
3
Locate the Plot Settings section. Clear the Plot dataset edges check box.
Streamline 1
1
Right-click Shunt Current Streamlines and choose Streamline.
2
In the Settings window for Streamline, locate the Streamline Positioning section.
3
In the Number text field, type 100.
4
Locate the Selection section. From the Selection list, choose Manifold - Active Cell Boundaries.
5
Locate the Coloring and Style section. Find the Point style subsection. From the Type list, choose Arrow.
Selection 1
1
Right-click Streamline 1 and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Channels and Manifolds.
Color Expression 1
1
In the Model Builder window, right-click Streamline 1 and choose Color Expression.
2
In the Settings window for Color Expression, click to expand the Title section.
3
From the Title type list, choose Automatic.
4
Locate the Coloring and Style section. Click  Change Color Table.
5
In the Color Table dialog box, select Aurora>AuroraBorealis in the tree.
6
Click OK.
Surface 1
1
In the Model Builder window, right-click Shunt Current Streamlines and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type 1.
4
Click to expand the Title section. From the Title type list, choose None.
Material Appearance 1
Right-click Surface 1 and choose Material Appearance.
Surface 2
1
In the Model Builder window, right-click Shunt Current Streamlines and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type 1.
4
Locate the Title section. From the Title type list, choose None.
Material Appearance 1
1
Right-click Surface 2 and choose Material Appearance.
2
In the Settings window for Material Appearance, locate the Appearance section.
3
From the Material list, choose Potassium Hydroxide, KOH (mat2).
Transparency 1
1
In the Model Builder window, right-click Surface 2 and choose Transparency.
2
In the Settings window for Transparency, locate the Transparency section.
3
Set the Transparency value to 0.9.
4
In the Shunt Current Streamlines toolbar, click  Plot.
Polarization Plot
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Polarization Plot in the Label text field.
Global 1
1
Right-click Polarization Plot and choose Global.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Global definitions>Parameters>E_cell - Cell voltage (varied in sweep) - V.
3
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Definitions>Variables>Eeq_cell - Cell equilibrium voltage - V.
4
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Definitions>Variables>Etherm_cell - Cell thermoneutral voltage - V.
5
Locate the x-Axis Data section. From the Parameter list, choose Expression.
6
Click Replace Expression in the upper-right corner of the x-Axis Data section. From the menu, choose Component 1 (comp1)>Definitions>Variables>I_stack - Stack current - A.
7
Click to expand the Coloring and Style section. Find the Line style subsection. From the Line list, choose Cycle.
8
Click to expand the Legends section. From the Legends list, choose Manual.
9
In the table, enter the following settings:
Legends
E<sub>cell</sub>
E<sub>ocv</sub>
E<sub>therm</sub>
Polarization Plot
1
In the Model Builder window, click Polarization Plot.
2
In the Settings window for 1D Plot Group, locate the Legend section.
3
From the Position list, choose Upper left.
4
Locate the Plot Settings section.
5
Select the y-axis label check box. In the associated text field, type Voltage (V).
6
Click to expand the Title section. From the Title type list, choose None.
7
In the Polarization Plot toolbar, click  Plot.
Coulombic Efficiency
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Coulombic Efficiency in the Label text field.
Global 1
1
Right-click Coulombic Efficiency and choose Global.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Definitions>Variables>Eff_coulombic - Current-to-hydrogen coloumbic efficiency.
3
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
Eff_coulombic
%
Current-to-hydrogen coloumbic efficiency
4
Locate the x-Axis Data section. From the Parameter list, choose Expression.
5
Click Replace Expression in the upper-right corner of the x-Axis Data section. From the menu, choose Component 1 (comp1)>Definitions>Variables>I_stack - Stack current - A.
6
Locate the Legends section. Clear the Show legends check box.
Coulombic Efficiency
1
In the Model Builder window, click Coulombic Efficiency.
2
In the Settings window for 1D Plot Group, locate the Title section.
3
From the Title type list, choose None.
4
In the Coulombic Efficiency toolbar, click  Plot.
Energy Efficiency
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Energy Efficiency in the Label text field.
Global 1
1
Right-click Energy Efficiency and choose Global.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Definitions>Variables>Eff_energy - Electrical energy-to-hydrogen energy efficiency.
3
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
Eff_energy
%
Electrical energy-to-hydrogen energy efficiency
4
Locate the x-Axis Data section. From the Parameter list, choose Expression.
5
Click Replace Expression in the upper-right corner of the x-Axis Data section. From the menu, choose Component 1 (comp1)>Definitions>Variables>I_stack - Stack current - A.
6
Locate the Legends section. Clear the Show legends check box.
Energy Efficiency
1
In the Model Builder window, click Energy Efficiency.
2
In the Settings window for 1D Plot Group, locate the Title section.
3
From the Title type list, choose None.
4
In the Energy Efficiency toolbar, click  Plot.
Global Evaluation Sweep 1
1
In the Results toolbar, click  More Derived Values and choose Other>Global Evaluation Sweep.
2
In the Settings window for Global Evaluation Sweep, locate the Data section.
3
From the Parameter value (E_cell (V)) list, choose 1.3.
4
Locate the Parameters section. In the table, enter the following settings:
Parameter name
Parameter value list
Cell
range(1,1,N_cells)
5
Locate the Expressions section. Click  Load from File.
6
Browse to the model’s Application Libraries folder and double-click the file aec_shunt_currents_global_sweep_evaluation_expressions.txt.
7
Click  Evaluate.
Shunt Currents per Cell
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Shunt Currents in the Label text field.
3
In the Label text field, type Shunt Currents per Cell.
Table Graph 1
1
Right-click Shunt Currents per Cell and choose Table Graph.
2
In the Settings window for Table Graph, click to expand the Legends section.
3
Select the Show legends check box.
4
In the Shunt Currents per Cell toolbar, click  Plot.
5
Locate the Coloring and Style section. Find the Line style subsection. From the Line list, choose None.
6
Find the Line markers subsection. From the Marker list, choose Cycle.
Shunt Currents per Cell
1
In the Model Builder window, click Shunt Currents per Cell.
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
Select the y-axis label check box. In the associated text field, type Current (A).
4
Locate the Legend section. From the Position list, choose Upper left.
5
In the Shunt Currents per Cell toolbar, click  Plot.
Global Evaluation Sweep 1
1
In the Model Builder window, under Results>Derived Values click Global Evaluation Sweep 1.
2
In the Settings window for Global Evaluation Sweep, locate the Data section.
3
From the Parameter value (E_cell (V)) list, choose 1.8.
4
Click  Evaluate.
Table Graph 1
1
In the Model Builder window, under Results>Shunt Currents per Cell click Table Graph 1.
2
In the Shunt Currents per Cell toolbar, click  Plot.