US2017005350A1PendingUtilityA1
Systems and methods for acquisition, parameterization, and validation of fuel cell polarization data
Est. expiryJul 2, 2035(~9 yrs left)· nominal 20-yr term from priority
H01M 8/04992H01M 8/04544H01M 8/04641H01M 8/04574Y02E60/50
45
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Claims
Abstract
Methods, systems, and techniques are provided for acquiring fuel cell polarization data, obtaining fuel cell polarization parameters from the fuel cell polarization data, and validating the reliability of the obtained data and parameters. In some aspects methods for acquiring and parameterizing proton exchange membrane fuel cell polarization data include measuring at least one current-voltage point for an operating fuel cell, and determining at least one polarization parameter of the fuel cell by evaluating a closed form solution using the at least one current-voltage point.
Claims
exact text as granted — not AI-modifiedWhat is claimed is:
1 . A method for acquiring and parameterizing proton exchange membrane fuel cell polarization data, the method comprising:
(a) controlling operation of a fuel cell at an initial cathode pressure and, while the fuel cell is operating at the initial cathode pressure, determining at least one voltage and corresponding current density; and (b) determining, by a processor, at least one polarization parameter of the fuel cell by evaluating a closed form solution using the at least one voltage and corresponding current density.
2 . The method of claim 1 wherein controlling operation of a fuel cell at an initial cathode pressure and, while the fuel cell is operating at the initial cathode pressure, determining at least one voltage and corresponding current density comprises:
controlling operation of the fuel cell in a low current density region of a fuel cell polarization curve and, while the fuel cell is operating in the low current density region, determining an open circuit voltage, a first voltage and corresponding first current density, and a second voltage and corresponding second current density;
and wherein determining, by a processor, at least one polarization parameter of the fuel cell by evaluating a closed form solution using the at least one voltage and corresponding current density comprises:
determining, by the processor, the at least one polarization parameter by evaluating, the closed form solution using the open circuit voltage, the first voltage and corresponding first current density, and the second voltage and corresponding second current density.
3 . The method of claim 2 wherein controlling operation of the fuel cell in a low current density region of a fuel cell polarization curve comprises controlling operation of the fuel cell within a voltage range between the open circuit voltage and 150 mV less than the open circuit voltage.
4 . The method of claim 2 wherein determining, by a processor, at least one polarization parameter of the fuel cell comprises determining Tafel slope, permeation current density, and exchange current density.
5 . The method of claim 4 , wherein the method comprises determining the permeation current density, then determining the Tafel slope using the permeation current density, and then determining the exchange current density using the Tafel slope and the permeation current density.
6 . The method of claim 4 , wherein the method comprises determining the permeation current density using the open circuit voltage, the first voltage and corresponding first current density, and the second voltage and corresponding second current density.
7 . The method of claim 6 wherein the processor determines permeation current density using
(
i
1
-
i
P
)
α
-
i
P
α
-
i
2
i
P
α
-
1
=
0
;
a
=
V
2
-
V
oc
V
1
-
V
oc
wherein i p is the permeation current density, i 1 and i 2 are the first and second current densities, respectively, V OC is the open circuit voltage, and V 1 and V 2 are the first and second voltages, respectively.
8 . The method of claim 4 wherein determining Tafel slope comprises using either the first voltage and corresponding first current density, or the second voltage and corresponding second current density, and using the open circuit voltage and the permeation current density.
9 . The method of claim 8 wherein the processor determines the Tafel slope using
V
=
V
OC
-
A
ln
(
1
+
i
i
P
)
wherein V and i are the first voltage and current density or the second voltage and current density, V OC is the open circuit voltage, i p is the permeation current density, and A is the Tafel slope.
10 . The method of claim 4 , wherein the method comprises determining the exchange current density using the permeation current density, the open circuit voltage, an equilibrium voltage of the fuel cell, and the Tafel slope.
11 . The method of claim 10 wherein the processor determines the exchange current density using
i
0
=
i
P
V
oc
-
V
eq
A
wherein i 0 is the exchange current density, V eq is the equilibrium voltage, V OC is the open circuit voltage, i p is the permeation current density, and A is the Tafel slope.
12 . The method of claim 1 , wherein controlling operation of a fuel cell at an initial cathode pressure and, while the fuel cell is operating at the initial cathode pressure, determining at least one voltage and corresponding current density comprises:
controlling operation of the fuel cell in a medium current density region of a fuel cell polarization curve and, while the fuel cell is operating in the medium current density region, determining an open circuit voltage, a voltage and corresponding current density; and wherein determining, by a processor, at least one polarization parameter of the fuel cell by evaluating a closed form solution using the at least one voltage and corresponding current density comprises: determining, by the processor, cell resistance of the fuel cell by evaluating the closed form solution using the open circuit voltage, the voltage and corresponding current density, an equilibrium voltage of the fuel cell, a permeation current density of the fuel cell, an exchange current density of the fuel cell, and a Tafel slope of the fuel cell.
13 . The method of claim 12 wherein controlling operation of the fuel cell in a medium current density region of a fuel cell polarization curve comprises controlling operation of the fuel cell within a voltage range between 150 mV less than the open circuit voltage of the fuel cell and 500 mV.
14 . The method of claim 12 wherein the processor determines the cell resistance using
r
=
V
eq
-
V
-
A
ln
(
i
+
i
P
i
0
)
i
wherein r is the cell resistance, V eq is the equilibrium voltage, V and i are the voltage and current density, respectively, i 0 is the exchange current density, A is the Tafel slope, and i p is the permeation current density.
15 . The method of claim 5 further comprising:
(c) controlling operation of the fuel cell in a medium current density region of a fuel cell polarization curve and, while the fuel cell is operating in the medium current density region, determining a third voltage and corresponding third current density; and
(d) determining, by a processor, cell resistance of the fuel cell by evaluating a closed form solution using the open circuit voltage, the third voltage and third current density, an equilibrium voltage of the fuel cell, the permeation current density, the exchange current density, and the Tafel slope.
16 . The method of claim 15 wherein the processor evaluates a closed form solution to determine each of the permeation current density, exchange current density, and Tafel slope.
17 . The method of claim 16 wherein the processor determines the cell resistance using
r
=
V
eq
-
V
3
-
A
ln
(
i
3
+
i
P
i
0
)
i
3
wherein r is the cell resistance, V eq is the equilibrium voltage, V 3 and i 3 are the third voltage and current density, respectively, i 0 is the exchange current density, A is the Tafel slope, and i p is the permeation current density.
18 . The method of claim 17 wherein the processor determines:
(i) the permeation current density using
(
i
1
-
i
P
)
α
-
i
P
α
-
i
2
i
P
α
-
1
=
0
;
a
=
V
2
-
V
oc
V
1
-
V
oc
wherein i p is the permeation current density, i 1 and i 2 are the first and second current densities, respectively, V OC is the open circuit voltage, and V 1 and V 2 are the first and second voltages, respectively,
(ii) the Tafel slope using
V
=
V
OC
-
A
ln
(
1
+
i
i
P
)
wherein V and i are the first voltage and current density or the second voltage and current density, and A is the Tafel slope, and
(iii) the exchange current density using
i
0
=
i
P
V
oc
-
V
eq
A
wherein i 0 is the exchange current density and V eq is an equilibrium voltage of the fuel cell.
19 . The method of claim 16 further comprising iteratively re-determining, by the processor, the permeation current density, Tafel slope, exchange current density, and cell resistance, until the permeation current density, Tafel slope, exchange current density, and cell resistance each converges, wherein the processor re-determines the permeation current density for a current iteration using a closed form solution comprising the cell resistance, the open circuit voltage, and the first and second voltages and current densities from a previous iteration.
20 . The method of claim 19 wherein the processor re-determines the permeation current density using
(
i
1
-
i
P
)
a
-
i
P
a
-
i
2
i
P
a
-
1
=
0
a
=
V
2
+
ri
2
-
V
oc
V
1
+
ri
1
-
V
oc
wherein i p is the permeation current density, i 1 and i 2 are the first and second current densities, respectively, V OC is the open circuit voltage, and V 1 and V 2 are the first and second voltages, respectively, and r is the cell resistance.
21 . The method of claim 16 further comprising:
(e) controlling operation of the fuel cell at a secondary cathode pressure and in the low current density region; and
(d) while the fuel cell is operating at the secondary cathode pressure in the low current density region, re-determining, by the processor, the permeation current density, Tafel slope, exchange current density, and cell resistance at the secondary cathode pressure.
22 . The method of claim 21 further comprising iteratively re-determining, by the processor, the permeation current density, Tafel slope, exchange current density, and cell resistance for the secondary cathode pressure until the permeation current density, Tafel slope, exchange current density, and cell resistance for the secondary cathode pressure each converges, and wherein the processor re-determines the permeation current density for the secondary cathode pressure for a current iteration using a closed form solution comprising the cell resistance, the open circuit voltage, and the first and second voltages and current densities for the secondary cathode pressure from a previous iteration.
23 . The method of claim 21 further comprising determining a reaction order, by the processor, using the initial and secondary cathode pressures and the exchange current densities at the initial and secondary cathode pressures.
24 . The method of claim 23 wherein the processor determines the reaction order using
γ
=
ln
(
i
0
*
i
0
)
ln
(
P
*
P
0
)
wherein γ is the reaction order, P 0 is the initial cathode pressure, P* is the secondary cathode pressure, i 0 is the exchange current density at P 0 , and i 0 * is the exchange current density at P*.
25 . The method of claim 1 wherein controlling operation of a fuel cell at an initial cathode pressure and, while the fuel cell is operating at the initial cathode pressure, determining at least one voltage and corresponding current density comprises:
controlling operation of the fuel cell in a high current density region of a fuel cell polarization curve and, while the fuel cell is operating in the high current density region, determining a voltage and corresponding current density;
and wherein determining, by a processor, at least one polarization parameter of the fuel cell by evaluating a closed form solution using the at least one voltage and corresponding current density comprises:
determining, by the processor, a diffusion resistance of the fuel cell by evaluating the closed form solution using the voltage and corresponding current density, a permeation current density of the fuel cell, an exchange current density of the fuel cell, a Tafel slope of the fuel cell, a reaction order of the fuel cell, an equilibrium voltage of the fuel cell, a cell resistance of the fuel cell, a partial pressure of oxygen in a cathode of the fuel cell, and a pressure in the cathode of the fuel cell corresponding to the exchange current density.
26 . The method of claim 25 wherein controlling operation of the fuel cell in a high current density region of a fuel cell polarization curve comprises controlling operation of the fuel cell within a voltage range between 0 mV and 500 mV.
27 . The method of claim 25 wherein the processor determines the diffusion resistance using
R
d
(
i
)
=
4
sFP
0
i
RT
(
P
c
P
0
-
(
i
+
i
p
i
0
)
1
γ
V
+
ri
-
V
eq
A
γ
)
wherein R d is the diffusion resistance, s is a cell area of the fuel cell, F is the Faraday constant, P 0 is the pressure in the cathode of the fuel cell corresponding to the exchange current density, V and i are the voltage and corresponding current density, respectively, R is the universal gas constant, T is a temperature of the fuel cell, P c is the partial pressure of oxygen in the cathode of the fuel cell, i p is the permeation current density, i 0 is the exchange current density, A is the Tafel slope, γ is the reaction order, r is the cell resistance, and V eq is the equilibrium voltage.
28 . The method of claim 16 further comprising:
(e) controlling operation of the fuel cell in a high current density region of a fuel cell polarization curve and, while the fuel cell is operating in the high current density region, determining a fourth voltage and corresponding fourth current density; and
(f) determining, by a processor, diffusion resistance of the fuel cell by evaluating the closed form solution using the fourth voltage and fourth current density, a permeation current density of the fuel cell, an exchange current density of the fuel cell, a Tafel slope of the fuel cell, a reaction order of the fuel cell, an equilibrium voltage of the fuel cell, a cell resistance of the fuel cell, a partial pressure of oxygen in a cathode of the fuel cell, and a pressure in the cathode of the fuel cell corresponding to the exchange current density.
29 . The method of claim 28 wherein the processor determines the diffusion resistance using
R
d
(
i
)
=
4
sFP
0
i
RT
(
P
c
P
0
-
(
i
+
i
p
i
0
)
1
γ
V
+
ri
-
V
eq
A
γ
)
wherein R d is the diffusion resistance, s is a cell area of the fuel cell, F is the Faraday constant, P 0 is the pressure in the cathode of the fuel cell corresponding to the exchange current density, V and i are the fourth voltage and corresponding current density, respectively, R is the universal gas constant, T is a temperature of the fuel cell, P c is the partial pressure of oxygen in the cathode of the fuel cell, i p is the permeation current density, i 0 is the exchange current density, A is the Tafel slope, γ is the reaction order, r is the cell resistance, and V eq is the equilibrium voltage.
30 . The method of claim 28 further comprising:
(g) determining, by the processor, a partial pressure of oxygen in a cathode catalyst layer of the fuel cell using the partial pressure of oxygen in the cathode, the fourth current density, and the diffusion resistance; and
(h) re-determining, by the processor, the equilibrium voltage using the partial pressure of oxygen in the cathode catalyst layer;
(i) iteratively re-determining, by the processor, the diffusion resistance, partial pressure of oxygen in the cathode catalyst layer, and equilibrium voltage until the diffusion resistance converges.
31 . The method of claim 30 wherein the processor determines:
(i) the partial pressure of oxygen in the cathode catalyst layer using
P
ccl
=
P
c
-
iRTR
d
4
sF
;
wherein P ccl is the partial pressure of oxygen in the cathode catalyst layer, P c is the partial pressure of oxygen in the cathode, i is the fourth current density, R is the universal gas constant, T is temperature of the fuel cell, R d is the diffusion resistance, s is cell area of the fuel cell, and F is Faraday's constant, and
(ii) the equilibrium voltage using
V eq =1.482−0.0000431 T ln( P H2 P ccl 0.5 )
wherein P H2 is hydrogen pressure of the fuel cell and V eq is the equilibrium voltage.
32 . The method of claim 16 further comprising:
(e) while the fuel cell is operating in a medium current density region of the fuel cell polarization curve, measuring a validation voltage and a validation current density;
(f) determining, by the processor, a predicted voltage at the validation current density, the predicted voltage predicted from the equilibrium voltage, Tafel slope, permeation current, exchange current density, cell resistance, and validation current density; and
(g) comparing, by the processor, the validation voltage to the predicted voltage.
33 . The method of claim 32 wherein the processor determines the predicted voltage using
V
=
V
eq
-
A
ln
(
i
+
i
P
i
0
)
-
ri
wherein V is the predicted voltage, i is the validation current density, V eq is the equilibrium voltage, A is the Tafel slope, i p is the permeation current density, i 0 is the exchange current density, and r is the cell resistance.
34 . A supervisory control and data acquisition system for acquiring and parameterizing proton exchange membrane fuel cell polarization data, the system comprising:
a load bank for connecting electrically in series with the fuel cell; a voltmeter for connecting electrically across the fuel cell; an ammeter for connecting electrically in series with the load bank and the fuel cell; and a controller communicatively coupled to the load bank, the voltmeter, and the ammeter, the controller configured to operate the fuel cell at an initial cathode pressure and, while the fuel cell is operating at the initial cathode pressure, the controller configured to:
determine at least one voltage and corresponding current density; and
determine at least one polarization parameter of the fuel cell by evaluating a closed form solution using the at least one voltage and current density.
35 . A non-transitory computer readable medium having encoded thereon computer program code that is executable by a processor and that, when executed by the processor, causes the processor to acquire and parameterize proton exchange membrane fuel cell polarization data by operating the fuel cell at an initial cathode pressure and, while the fuel cell is operating at the initial cathode pressure causes the processor to:
determine at least one voltage and corresponding current density; and determine at least one polarization parameter of the fuel cell by evaluating a closed form solution using the at least one voltage and current density.Cited by (0)
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