Method for optimization of fuel cells operating conditions using hybrid model
Provided is a method for optimization of fuel cells operating conditions using a hybrid model, and more particularly, a method for optimization of fuel cells operating conditions using a hybrid model which generates a life prediction model determined by time and temperature based on a theoretical performance model and an empirical durability model and estimates an optimal operation temperature in a target life based on the life prediction model.
1. A method for adjusting operating conditions of a fuel cell with an aid of a computing device including an empirical durability model generating unit, an optimal operation temperature estimating unit, and a memory including executable instructions stored thereon, the method comprising:
obtaining a potential difference depending on a current density of a cell based on a thermodynamics reversible voltage, an activity loss, a resistance loss, and a concentration loss of a high temperature proton-exchange membrane fuel cell (PEMFC) including a polybenzimidazole (PBI) membrane with which phosphoric acid is doped (S 10 );
generating an empirical durability model which predicts a reduction in cell voltage over an operation time at a predetermined temperature (S 20 ) at the empirical durability model generating unit;
determining an optimal operation temperature at a target life based on the potential difference depending on a current density of the PEMFC (S 10 ) and the durability model generated in the generating of the empirical durability model (S 20 ) (S 40 ) at the optimal operation temperature estimating unit; and
adjusting an operation temperature of the PEMFC to the optimal operation temperature,
wherein the generating of the durability model (S 20 ) includes:
generating a draft model predicting the reduction in cell voltage over the operation time at the predetermined various temperatures while ruling out an effect of the operation time (S 21 );
performing a durability test of the PEMFC which detects the reduction in cell voltage for a predetermined period at the predetermined various temperatures;
estimating coefficients of the draft model over various times generated in the generating of the draft model (S 21 ) based on the reduction in cell voltage detected in the durability test of the PEMFC (S 22 ); and
generating a third-order non-linear function depending on the operation time and temperature using the coefficients estimated in the estimating of the coefficient (S 22 ) (S 23 ), and
wherein for each of the predetermined various temperatures, the draft model in the generating of the draft model (S 21 ) predicts the reduction in cell voltage over the operation time using the draft model corresponding to the following Equation:
VD ( t )= x 1 t 3 −x 2 t 2 +x 3 t+x 4 , and
a final model which is used at the durability model is to fit the four coefficients x 1 , x 2 , x 3 , and x 4 of the draft model depending on the operation temperature.
2. The method of claim 1 , wherein the potential difference depending on a current density of the PEMFC is obtained by subtracting the activity loss, the resistance loss, and the concentration loss from the thermodynamics reversible voltage based on the following Equation:
E cell =E rev −η act −η ohm −η conc
In the above Equation, E cell represents the potential difference depending on a current density of the PEMFC, E rev represents the thermodynamics reversible voltage, η act represents the activity loss, η ohm represents the resistance loss and η conc represents the concentration loss.
3. The method of claim 2 , wherein the thermodynamics reversible voltage is calculated based on the following Equation,
E
ref
=
-
Δ
g
rnx
ref
n
F
.
In the above Equation, Δg rnx ref represents Gibbs' free energy and F represents a Faraday constant and n represents number of transfer electrons,
the thermodynamics reversible voltage at a given temperature T is calculated based on the following Equation by introducing a change in entropy depending on temperature,
E
T
=
E
ref
+
Δ
s
n
F
(
T
-
T
ref
)
.
In the above Equation, Δs represents the change in entropy depending on the temperature and T ref represents reference temperature,
when a concentration of chemical species is specified, the thermodynamics reversible voltage is calculated based on the following Equation by introducing activity, and
E
rev
=
E
ref
-
RT
n
F
ln
a
H
2
O
a
H
2
a
O
2
0.5
.
In the above Equation, R represents an abnormal gas constant and a represents activity, and
at the given temperature T and concentration c, the thermodynamics reversible voltage is calculated based on the following Equation
E
rev
=
E
ref
+
Δ
s
n
F
(
T
-
T
ref
)
-
RT
n
F
ln
a
H
2
O
a
H
2
a
O
2
0.5
.
4. The method of claim 2 , wherein the activity loss is calculated by the following Equation:
j
gross
=
j
0
(
e
α
n
F
η
c
/
RT
-
e
-
(
1
-
α
)
n
F
η
c
/
RT
)
j
gross
=
j
0
e
α
n
F
η
c
/
RT
η
c
=
RT
α
n
F
ln
j
+
j
leak
j
0
j
0
=
j
0
ref
S
Pt
eff
(
c
O
2
c
o
2
ref
)
γ
e
Δ
b
act
RT
(
1
-
T
T
ref
)
.
In the above Equation, n represents number of transfer electrons and a represents a transfer coefficient, a total of current density j gross includes an operating current density j, an internal current, and a loss current j leak occurring due to a leakage of reactants, by being focused on a high current density area in which a reverse reaction is disregarded, a second exponential term of the right terms representing the reverse reaction is disregarded, an exchange current density j 0 ref is corrected depending on a concentration and a temperature value, a reference exchange current density j 0 ref measured based on a reference temperature T ref and a reference oxygen concentration c O 2 ref , S Pt eff represents an effective platinum surface area, c O 2 represents an oxygen concentration in the catalyst layer, and γ represents a reaction order, j 0 ref and S Pt eff are estimated based on the experimental data, and an activity barrier energy Δb act uses 7.24·104 Jmol −1 .
5. The method of claim 2 , wherein the resistance loss is represented by the following Equations:
η
okm
=
j
δ
m
κ
m
κ
m
=
AB
T
e
-
b
act
RT
b
act
=
-
619.6
DL
+
21750
A
=
168
DL
2
-
6324
DL
2
+
65750
DL
+
8460
B
=
1
+
(
0.1432
T
-
56.89
)
RH
eff
.
In the above Equation, δ m and k m each represent the thickness and ion conductivity of the membrane, the ion conductivity of the PBI membrane relies on a doping level (DL) of the phosphoric acid, relative humidity (RH), and temperature T, temperature dependency of ion conductivity relies on an Arrhenius law, A and B are pre-exponential coefficients describing an effect of the phosphoric acid doping level and the relative humidity, respectively, b act represents the activation energy of the membrane.
6. The method of claim 1 , wherein in the generating of the draft model (S 21 ), a pretreatment process of converting each coefficient into a log value prior to fitting is performed to improve a prediction ability of the draft model.
7. The method of claim 1 , wherein in the of the operating condition (S 40 ), when the target life is maximal, the operation temperature is kept at 150 to 160° C.
8. The method of claim 1 , wherein in the performing the durability test of the PEMFC, the PEMFC is heated from room temperature to the predetermined temperature as purged with nitrogen, and then dry hydrogen and dry air which are heated up to the predetermined temperature by a line heater in a hydrogen and oxygen supply pipe are supplied to an anode and a cathode of the PEMFC, respectively.