Method for revising a polarization curve that defines the current/voltage relationship of a fuel cell stack
View Patent ↗A method for revising a reference polarization curve of a fuel cell stack that identifies the relationship between the voltage and the current of the stack over time. When the stack is operating at a low load where kinetic voltage losses of the stack dominate, a first adaptation value is revised as the difference between the actual stack voltage and the stack voltage of the reference polarization curve. When the stack is operating at higher loads where ohmic voltage losses of the stack dominate, a second adaptation value is revised as the difference between the actual stack voltage and the stack voltage of the reference polarization curve.
1. A method for revising a polarization curve that defines the current/voltage relationship of a fuel cell stack, said method comprising:
defining a reference polarization curve at a first point in time;
revising the reference polarization curve at a later point in time to match the actual polarization curve of the stack when the stack current density is below a predetermined threshold by changing a first adaptation value; and
revising the reference polarization curve at a later point in time to match the actual polarization curve of the stack when the stack current density is above the predetermined threshold by changing a second adaptation value, wherein the first adaptation value defines an absolute voltage difference between the predicted average cell voltage of fuel cells in the stack and the average cell voltage of the reference polarization curve for a particular stack current density, and the second adaptation value defines a current dependent voltage difference between the predicted average of cell voltage of fuel cells in the stack and the average cell voltage of the reference polarization curve for the particular stack current density.
2. The method according to claim 1 wherein the predetermined threshold defines a transition between where kinetic voltage losses are dominant and where ohmic voltage losses are dominant, where the kinetic voltage losses are dominant below the threshold and the ohmic voltage losses are dominant above the threshold.
3. The method according to claim 2 wherein the predetermined threshold is about 0.2 A/cm 2 .
4. The method according to claim 1 wherein the first point in time is when the stack is new.
5. The method according to claim 1 wherein the fuel cell stack is part of a fuel cell system that also includes a rechargeable energy storage device to supplement the fuel cell stack power.
6. The method according to claim 1 further comprising preventing the reference polarization curve from being revised when the stack is operating in a region of the reference polarization curve where mass transport voltage losses are dominant.
7. The method according to claim 1 wherein the reference polarization curve is stored as a plurality of values in a look-up table.
8. The method according to claim 1 wherein the reference polarization curve is stored as an arithmetric expression.
9. The method according to claim 1 wherein revising the reference polarization curve includes using the equation:
U model ( I )= U Reference ( I )+ C 1 +C 2 *I
where U model is the revised reference polarization curve, U Reference is the reference polarization curve, C 1 is the first adaptation value, C 2 is the second adaptation value and I is current.
10. The method according to claim 1 wherein the reference polarization curve and the revised reference polarization curve are defined by the arithmetric expression:
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where V e is the voltage at current i e , V 0 is the open circuit voltage, T is the absolute temperature, p is the total pressure, p O 2 is the partial pressure of oxygen, φ is humidity, and b, R, m and n are empirical equation constants.
11. The method according to claim 1 wherein defining a reference polarization curve at a first point in time includes defining a reference polarization curve for a first fuel cell stack of a series of fuel cell stacks being manufactured, where the reference polarization curve is used for all of the stacks in the series.
12. A method for revising a polarization curve that defines the current/voltage relationship of a fuel cell stack, said method comprising:
defining a reference polarization curve at a first point in time; and
revising the reference polarization curve to match an actual polarization curve of the stack over time when the stack current density is either below or above a predetermined threshold, wherein the predetermined threshold defines a transition between where kinetic and voltage losses are dominate and where ohmic voltage losses are dominate, where the kinetic voltage losses are dominate below the threshold and the ohmic voltage losses are dominate above the threshold.
13. The method according to claim 12 wherein revising the reference polarization curve includes revising the reference polarization curve when the stack is experiencing only static voltage loses or when the stack is experiencing additional linear voltage loses.
14. A method for revising a polarization curve that defines the current/voltage relationship of a fuel cell stack, said method comprising:
defining a reference polarization curve at a first point in time;
revising the reference polarization curve at a later point in time to match an actual polarization curve of the stack when the stack current density is below a predetermined threshold by changing a first adaptation value; and
revising the reference polarization curve at a later point in time to match the actual polarization curve of the stack when the stack current density is above the predetermined threshold by changing a second adaptation value, wherein the predetermined threshold defines a transition between where kinetic voltage loses are dominate and where ohmic voltage loses are dominate, where the kinetic voltage loses are dominate below the threshold and the ohmic voltage loses are dominate above the threshold.
15. The method according to claim 14 wherein the predetermined threshold is about 0.2 A/cm 2 .
16. The method according to claim 14 further comprising preventing the reference polarization curve from being revised when the stack is operating in a region of the reference polarization curve where mass transport voltage losses are dominant.
17. The method according to claim 14 wherein the reference polarization curve is stored as a plurality of values in a look-up table.
18. The method according to claim 14 wherein the reference polarization curve is stored as an arithmetic expression.
19. The method according to claim 14 wherein revising the reference polarization curve includes using the equation:
U model ( I )= U Reference ( I )+ C 1 +C 2 *I
where U model is the revised reference polarization curve, U Reference is the reference polarization curve, C 1 is the first adaptation value, C 2 is the second adaptation value and I is current.
20. The method according to claim 14 wherein defining a reference polarization curve at a first point in time includes defining a reference polarization curve for a first fuel cell stack of a series of fuel cell stacks being manufactured, where the reference polarization curve is used for all of the stacks in the series.