Download Aalborg Universitet Fuel Cell Equivalent Electric Circuit Parameter Mapping

Aalborg Universitet
Fuel Cell Equivalent Electric Circuit Parameter Mapping
Jeppesen, Christian; Zhou, Fan; Andreasen, Søren Juhl
Publication date:
2014
Document Version
Early version, also known as pre-print
Link to publication from Aalborg University
Citation for published version (APA):
Jeppesen, C., Zhou, F., & Andreasen, S. J. (2014). Fuel Cell Equivalent Electric Circuit Parameter Mapping.
Poster session presented at 4th CARISMA conference 2014, Cape Town, South Africa.
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Fuel Cell Equivalent Electric Circuit
Parameter Mapping
Christian Jeppesen† , Fan Zhou, Søren Juhl Andreasen
Department of Energy Technology, Aalborg University, Denmark
†
[email protected]
Introduction
System Analysis
Current mapping
In this work a simple model for a fuel cell is
investigated for diagnostic purpose. The fuel
cell is characterized, with respect to the electrical impedance of the fuel cell at non-faulty
conditions and under variations in load current.
Based on this the equivalent electrical circuit
parameters can be estimation as a function of
the load current.
The data is based on an experiment conducted
using a single BASF prototype Celtec P2100
HTPEM fuel cell (45 cm2 ) operated at 160 C,
installed in a Greenlight fuel cell test station.
In order to determine how the EEC parameters
vary, for the circuit given in Fig. 1 at different operating conditions, an experiment is carried out.
The EEC parameter values depends on different parameters such as the current, temperature, contamination of the anode and cathode
gas, etc. as shown in [1]. The purpose of this
experiment is to establish a characterization of
a fuel cell, for diagnostic purposes. The temperature effect on the EEC parameter is neglected,
and the system is in this work only be analyzed
for changing current.
The current and voltage profile from the characterization experiment is shown in Fig. 2. In the
experiment an EIS measurement is conducted
every 10 min.
For the averaged EEC parameters shown in
Fig. 3, a function can be fitted, in order to establish an estimation between the current and
the EEC parameters. The data is fitted utilizing
the power function given in eq. 2, where I is the
steady state fuel cell load current.
-5
Experimental impedance data
Equivalent electric circuit model
-4
L1
R1
-3
0.4
0
0
50
100
150
200
250
0.006
0.008
0.01
0.012
Re(z) [+]
Fig. 1: Equivalent electric circuit model fitted to measured impedance data, using a Differential evolution
optimization algorithm with a Least Squares objective function.
Based on the impedance data, the parameters
of an equivalent electric circuit (EEC) network
can be fitted, and thereby the impedance data
can be quantified into electric component parameters. Many different EECs have been proposed, for PEM fuel cells, and some of the have
been adopted for HTPEM fuel cells as in [1]. In
this paper, a simplified Randle’s EEC is utilized,
where only one arc is included. This is done
since the impedance response is rather simple
for the fuel cell used in this work. A simpler
EEC also reduces the fitting time, which is convenient for online diagnostic purposes.
In order to get a suitable fit of the EEC for diagnostic purpose, a simplified Randle’s model
is used. The model is implemented with a constant phase element (CPE), with the impedance
implemented as shown in eq. 1.
1
zCPE (!, C1 , ↵) =
C1 · (j!)↵
For every individual EIS measurement, the EEC
parameters are estimated using a DE optimization algorithm. For every current setpoint, all
the EEC parameters are averaged, giving values for each current set point. The average
EEC parameters is shown in Fig. 3.
0.04
0.02
0
0
5
10
15
20
25
8
Avg. C1
Fit
6
4
2
The power function parameters giving the mapping between the steady state current and the
EEC parameters, are listed in Table 1.
For this mapping to be accurate, it is important
that the current used in Eq. 2 is the steady state
current. It is therefore suggested that the current is averaged over a suitable window size.
The relationship between the EEC parameters
and the load current are established in eq. 2 using the parameters given in Table 1. This yields
a baseline for the EEC parameters under nonfaulty condition.
R1
R2
C1
↵
a
b
c
0.006204
0.03421
5.583
-1.631
-0.09585
-0.9097
0.1774
0.04947
-0.001004
0.004472
-3.215
2.485
If EEC parameters under operation differ from
the values estimated using eq. 2, will this indicate abnormal operation. The estimation can
thereby be used for diagnostic purpose.
For further development of this method for diagnostic purpose, the system must be analyzed
for different faults, in order to classify faults for
a fault isolation and detection algorithm. This
method could be coupled with other identification methods or sensor input, in order to isolate
the fault root.
I In this work a mapping between the fuel cell
load current and the parameters of an EEC
is established, by experimental characterization.
I The EEC parameter estimation can be utilized for a baseline, to specify normal fuel
cell operation. A deviation from these EEC
parameters indicate a system fault or other
abnormal fuel cell operation.
References
0
5
10
15
20
25
0.9
Avg. ,
Fit
0.8
0.7
0.6
0.5
(2)
Final Remarks
0.01
(1)
It was shown in [2] that EEC parameter estimation for batteries can be done effectively
by evolutionary optimization algorithms such as
Differential evolution (DE) [3]. The Differential
evolution optimization algorithm is in this work
adapted, to fit the acquired impedance data for
a fuel cell to fit the EEC. An example of this is
shown in Fig 1.
Avg. R1
Fit
Avg. R2
Fit
0.03
{R1 , R2 , C1 , ↵} = a · I + c
Table 1: Parameters for the current mapping of the
EEC model mapping.
Fig. 2: The voltage polarization profile from the EEC
parameters mapping experiment. The experiment is
conducted at 160 C with H2 = 2.5 and air = 4.
R2
0.004
10
C1 [F ]
0.002
0.6
,
R1
0
20
Time [hr]
-1
0
0.8
R2
CPE
-2
1
Voltage
Current
R1 , R2 [+]
Im(z) [+]
-6
#10-3
30
Current [A]
For characterization of fuel cells the most popular method by far, based on the number of publications, is electrochemical impedance spectroscopy (EIS). From the frequency data, the
impedance can be calculated, and plotted in a
Nyquist plot, as shown in Fig. 1.
1
Voltage [V]
Fuel Cell Characterization
and Equivalent model
b
0
5
10
15
20
25
Current [A]
Fig. 3: The EEC parameters as function of the current.
[1] Søren Andreasen, Jesper Jespersen and
Erik Schaltz and Søren Kær: Characterisation and Modelling of a High Temperature
PEM Fuel Cell Stack using Electrochemical
Impedance Spectroscopy, Fuel Cells, 2009
[2] Guangya Yang: Battery parameteriastion
based on differential evolution via boundary evolution strategy, International Journal
Power Sources, 2014
[3] Rainer Storn and Kenneth Price: Differential Evolution - A Simple and Efficient
Heuristic for Global Optimization over Continuous Spaces, Journal of Global Optimization, 1997