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Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters
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Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters Arafet Bouaicha a,*, Hatem Allagui a, El-Hassane Aglzim b, Amar Rouane c, Adelkader Mami a a
Laboratory LACS-ENIT/FST, Faculty of Sciences of Tunis, University Tunis El Manar, Tunis, Tunisia Laboratory DRIVE, University of Bourgogne, Nevers, France c University of Lorraine, Nancy, France b
article info
abstract
Article history:
In this paper, we present a new methodology for determining the complex impedance
Received 1 August 2016
parameters for a Proton Exchange Membrane (PEM) Fuel Cell in order to have a general
Received in revised form
model for embedded diagnosis. The modelling of Fuel Cells is a very important phase
18 January 2017
because it contributes to a better understanding and representation of the internal phe-
Accepted 19 January 2017
nomena in this type of generator. After obtaining the experimental results of the complex
Available online xxx
impedance using a realized test bench for Proton Exchange Membrane (PEM) Fuel Cell using an electrochemical method which is the electrochemical impedance spectroscopy
Keywords:
(EIS), we treat these results with an identification algorithm based on least squares method
Proton exchange membrane (PEM)
in the objective to determine the variations laws of the complex impedance parameters
fuel cell
then implement in a PEM Fuel Cell model with Matlab/Simulink software. The established
Test bench
model of the complex impedance is based on electrical components and takes into account
Modeling
the mathematical equations of the different elements. The simulation results of this
Complex impedance
implemented model inform us about the state of the PEM Fuel Cell and validate the choice
Least square method
of the parameters. The validation of this choice is done by a comparative study using re-
On-board diagnosis
sidual analysis method between the experimental and the simulation results. The general model is obtained from the superposition of the measured and theoretical results. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Proton Exchange Membrane (PEM) Fuel Cell is an electrochemical device; its study requires multidisciplinary knowledge. Using this device is particularly complicated due to the large number of internal and external parameters to be controlled simultaneously (gas flow, operating temperature,
humidification membranes…). The influence of all these parameters makes a complex modelling for PEM Fuel Cell. The modelling plays an important part in the development of Fuel Cells as it facilitates a better understanding of the physicochemical phenomena and parameters affecting a performance of Fuel Cells systems. This modelling presents a very important phase because it contributes to a better understanding and representation of the internal phenomena.
* Corresponding author. E-mail address: [email protected] (A. Bouaicha). http://dx.doi.org/10.1016/j.ijhydene.2017.01.114 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114
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The building of a model usually depends on the use to which it is intended, a model can be used to design, understand, or ordering. The developed models for PEM Fuel Cells can provide a significant level of details; the possibly problem is the identification and validation of these models. All of the used approaches for modelling pass necessarily with a long and difficult experimental stage. These are probably the physical models requires the largest number of tests, including in domains applications such in electrical engineering. Also, management of Fuel Cells systems is difficult because of the many internal physical parameters such as the current required by the load, the temperature of the stack, pressures and flow rates. All of these parameters have an impact on the progress of the system that are often particularly difficult to estimate and to express clearly. In reality, these parameters are expressed by nonlinear relationships, generally it is difficult to model since they are dependent on each other. In terms of literature, many researchers used algorithms to identify these variables according to the desired objectives for the development of each model, sometimes the variables are limited or difficult to implement in a validation procedure. The electrochemical impedance spectroscopy (EIS) method plays an important role for determining the parameters of the model. This method is used in several research studies [1e13] to model the complex impedance of a PEM Fuel Cell. A. Saadi et al. [1] using an experimental strategy based on the results of the study in order to predict three static models of a PEM Fuel Cell, and validated experimentally with identification of the static model parameters using EIS. In the study of S. Chevalier et al. [2], the authors presented a multi-physical modelling of a PEM Fuel Cell using the same method for the detection of the degradation of the cells. Another study by S.H. Yang et al. [3] using the EIS method to diagnose a Direct Methanol Fuel Cell (DMFC), and presented a comparison between the results obtained at the anode and the cathode. Y.H. Lee et al. [4] used a real-time diagnosis procedure using the principle of superposition and the EIS method to characterize the performances of a PEM Fuel Cell. A modelling study using Bond Graph is presented by D. Mzoughi et al. [5], they presented a model using Bond Graph and the EIS method for Nexa PEM Fuel Cell. In this study, we present a new simple approach methodology to identify the variables of the internal phenomena of the PEM Fuel Cell, which are validated by comparing the experimental results with those of simulation using the EIS method. Then, we present the different modelling approaches using the experimental data obtained using the Nexa PEM Fuel Cell system. After exposing the modelling approach of the different obtained parameters in the PEM Fuel Cell, we present the global model. Next, we detail the explanation of the methodology used for determining the complex impedance parameters. Finally, we present and discuss the obtained results.
Test bench description Experimental test bench One way to know the state of the membranes of the Proton Exchange Membrane (PEM) Fuel Cell is the measure of its
complex impedance, the advantage of this method is to better understand the physical effects occurring in this system. The method for measuring the complex impedance is the electrochemical impedance spectroscopy (EIS), this method consists to superimposing a perturbing signal to a value of the DC current at the input and analyzing the response signal [6e11]. This method allows us to make a real-time measurement during the operation of the PEM Fuel Cell. To make the measurement of the complex impedance, we must design and implement a test bench which supports a DC current supplied by the PEM Fuel Cell. To use the EIS method, the DC current response should be linear compared to the Fuel Cell voltage. The PEM Fuel Cell is a priori a nonlinear and non-stationary system, so we can determine the complex impedance using low-amplitude perturbations around an operating point that is assumed stationary [8,9,12]. The experimental test bench is designed around the Nexa Ballard [14] PEM Fuel Cell and a realized electronic load. In addition, a measuring electronic board based on the STM32F4 microcontroller connected to a computer to collect data that are saved and processed by a measurement application developed with LabVIEW software. LabVIEW software is used to control various devices and also can analyze and save the results of the complex impedance measurement in a data file that can be used to display and analyze the results found by an acquisition card which performs acquiring data. The electronic load realized to the impedance measurement must impose a DC current to be supplied by the Nexa PEM Fuel Cell during measurement, in our case, we realized an electronic load [15e17] which supports 750 W power that is a 25 A DC current to a 30 V voltage. Fig. 1 shows the schematic of the proposed test bench that is used to measure the complex impedance of the PEM Fuel Cell. This test bench is mainly composed with the electronic load designed and constructed in our laboratory, the Nexa Ballard PEM Fuel Cell system [14], a function generator for injecting the perturbing signal, the data acquisition system and the computer that integrates applications developed using LabVIEW and Matlab/Simulink. In all of the realized tests, we injected a sinusoidal signal of frequency ranging from 0.1 Hz to 12 kHz and 250 mVPeP amplitude which is provided using a function generator, usually for a PEM Fuel Cell the frequency spectrum is selected between 1 Hz and 10 kHz [18]. The proposed test bench is for instrumentation dedicated to the PEM Fuel Cell. The obtained results are in the form of the complex impedance diagrams and they are usually done into the Nyquist plan presented by the imaginary part as a function of the real part. The progress of a complex impedance measurement using this test bench is presented by the following steps. First, we impose the static parameter of the measure using the control card and the electronic load which is the DC current flow through the Nexa PEM Fuel Cell. After a short stabilization time, the Fuel Cell voltage and the DC current are measured and saved using the developed LabVIEW application. Next, we inject the sinusoidal perturbation signal into the imposed signal using the electronic load. The electronic measuring system using the microcontroller acquisition module
Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114
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Fig. 1 e Schematic of the proposed test bench for Nexa PEM Fuel Cell.
STM32F4 runs complicated calculations in order to obtain the desired results. After measuring the spectrum of frequencies (from 0.1 Hz to 12 kHz), the obtained results are saved in a file created by the developed LabVIEW application. Finally, this file is used to analyze the founded results in the form of frequencies, real parts and imaginary parts that present the essential elements to calculate the PEM Fuel Cell complex impedance parameters. The modelling of the Nexa Ballard PEM Fuel Cell system [14] takes into account the auxiliary elements (electronic boards, humidifier, compressor, etc.). This system can provide a power of 1200 W at the voltage of 26 V under load. The stacking is composed with 47 cells that can supply the voltage of 42 V without load. An on-board control card allows system safety by controlling certain parameters using integrated sensors (leakage of hydrogen, increase of temperature, drop of voltage, etc.).
experimental test bench. We implemented the model for this measurement test bench in a simulation environment that is Matlab/Simulink. This model is composed with the electrical elements in Simulink libraries. These are connected together in parallel or in series; the value of each parameter is then calculated using the equations of the chosen model. We have chosen to model the Nexa PEM Fuel Cell system, this system is generally composed with the stacking of anodes, membranes and cathodes. We chose modelling this system with the tools of Matlab/Simulink. Fig. 2 shows the schematic diagram of the modelling system using Matlab/Simulink. This system is composed by the test bench elements, the impedance measurement system of the complex impedance and the Nexa PEM Fuel Cell model. This modelling system with Matlab/Simulink is composed of three main blocks: a block which includes the model elements of the Nexa PEM Fuel Cell, a block for measuring and
Test bench modelling using Matlab/Simulink Matlab/Simulink is a powerful tool for scientific calculation and process simulation; it provides rapid solutions for scientific applications. It is software for simulating, modelling and analyzing physical systems; it has a dynamic simulation environment for complex systems described by differential and polynomial equations. The modelling of the PEM Fuel Cell complex impedance in this work is based on an approach called equivalent electrical circuits; the complex impedance is achieved using assembling the various electrical components such as resistors, capacitors and inductors. To validate the results obtained by the
Fig. 2 e Schematic diagram of the modelling system.
Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114
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displaying the complex impedance using Matlab/Simulink and a measuring block using the principle of the impedance spectroscopy method which is presented with the test bench system. The details are represented in Figs. 3e5. Fig. 3 shows the schematic diagram of the impedance measurement system using Matlab/Simulink. The impedance measurement system block with Matlab/ Simulink allowed us to export the simulation results of the mathematical equations of the different model parameters to Matlab environment “Workspace” in order to draw the Nyquist plots. Fig. 4 shows the schematic diagram of the Test Bench system using Matlab/Simulink. The Test Bench system presents the principle of the electrochemical impedance spectroscopy (EIS) method in Matlab/ Simulink that allowed us to simulate the principle of this chosen method that injects a sinusoidal perturbing signal to be superimposed on the DC current (IFC) and sampling the voltage (VFC) across the model of the Nexa PEM Fuel Cell. We used this block in the same principle of controlling the current of the experimental test bench which is constituted by the model of N-MOSFET transistor and the model of the operational amplifier in Matlab/Simulink.
The integration of the PEM Fuel Cell in an electric environment requires knowledge of its electric model. The models can be built using static physical relationships; they present a static model. If the models are based on parametric identification techniques; then they present a dynamic model. Various models can be developed according to the objective. In this work, the model must be simple, accurate and describes the electrical behavior of the Nexa PEM Fuel Cell system in dynamic mode. The assumptions for modelling the Nexa PEM Fuel Cell system in this work are:
Parameters determination of the complex impedance model
Fig. 5 shows the structure of the model in the form of an equivalent circuit diagram consisting with electric elements translating physical phenomena considered. The elements of the chosen model of the Nexa PEM Fuel Cell with Matlab/ Simulink are composed by resistors, capacitors, inductors and a DC voltage source. Obtaining the result of the complex impedance has many benefits because it provides access to inaccessible internal parameters when measurement is running. Many researchers [10,11,26e29] used this model, and it can be considered as the nearest model of the Nexa PEM Fuel Cell system. With:
Complex impedance model of Nexa PEM fuel cell Many models have been presented for the electrochemical reactions of the PEM Fuel Cell; the goal of these models is to understand the reaction mechanisms in this system. To analyze the internal behavior of the PEM Fuel Cell such that the influence of humidification, drying membranes and observing the performance of the PEM Fuel Cell in the presence of carbon monoxide in hydrogen [19,20], the EIS is considered an adequate method for the study of electrochemical devices. It is used extensively for modelling batteries [21,22] and Fuel Cells [23e25]. This modelling is presented by equivalent electrical circuits that are based on experimental testing of the impedance spectra, reflecting the behavior of the PEM Fuel Cell. The equivalent impedances are used to determine the electrochemical parameters of the complex impedance; it is the modelling using the complex impedance.
The gases are pure hydrogen and pure oxygen. The gas supplies are expected at constant rates. The electrodes, catalytic layers and the membrane are homogeneous and isotropic. Gas pressures are considered uniform in the supply lines (no losses in the gas supply channel). The membrane is fully humidified so that the ionic conductivity is constant. The components of the model are all the Nexa PEM Fuel Cell system and its auxiliaries. No parasitic reaction and the aging of the electrochemical cells are not considered.
CDC: double layer capacity placed in parallel with the representative impedance of the electrochemical phenomena, it is due to the presence of positive charges on the surface of the membrane and negative charges on the electrode surface. RT: Resistance characterizes the transfer phenomena charges to the electrodes.
Fig. 3 e Impedance measurement system in Matlab/Simulink. Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114
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Fig. 4 e Test Bench system in Matlab/Simulink.
Fig. 5 e Electric schematic of the Nexa PEM Fuel Cell model.
RM: Membrane resistance. Cf and Rf: elements that represent the faradaic impedance. They have the concentration of each species in the anode, it is the Warburg impedance noted W [27,29,30]. LZ and RZ: different impedances connection with the PEM Fuel Cell (connecting wire, electrical contacts, etc.).
ZðuÞ ¼
RZ þ juLZ juLZ RZ
i h R R RTa þ Rf , 1 þ juCf RTaTaþRf f þ RM þ 1 RTa Rf CDCa Cf u2 þ ju, RTa þ Rf CDCa þ Rf Cf þ
The total impedance of the model is constituted by the impedance of the anode and cathode in addition to the impedance of the membrane and the connections of the PEM Fuel Cell. The expression of the corresponding impedance is expressed as follows:
RTc 1 þ juRTc CDCc (1)
This model is used to analyze the results of impedance spectroscopy found by experimental test bench, eventually we establish the variation laws of the different parameters
Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114
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forming this chosen model from the measuring results. The mathematical expressions of the different parameters are implemented in this model of Matlab/Simulink.
Optimization methodology of the complex impedance parameters After obtaining measurement results with the Proton Exchange Membrane (PEM) Fuel Cell using the experimental test bench, we must pass through the analysis phase. For this, we determine the parameters expressions of the model according to the measurement results. The obtained parameters inform us the state of the PEM Fuel Cell in real time. Fig. 6 shows the flowchart of the methodology for extraction the complex impedance parameters of the Nexa PEM Fuel Cell. This methodology consists to calculate the numerical values for each parameter of the model using the results of experimental tests. After, we calculate the optimal value for each parameter by minimizing the difference between the theoretical and the measured value. The obtained values for each parameter are used to find the mathematical expression of the model parameters chosen using the least squares method. In the last step, these obtained functions will be used in Matlab/ Simulink to validate the choice of the simulation model.
Variation laws of the complex impedance parameters The idea is to compare the experimental tests with those of simulation model defined above, and then adjust the values of these parameters in the model until a very small difference between the two curves. We find to obtain the optimal
Fig. 6 e Flowchart of the extraction methodology.
parameter set that minimizes the difference between the calculated and measured values for each point. We used the least squares method to minimize this difference. The principle to determine the parameters is presented by the steps in the flowchart in Fig. 7. The criterion (J) to minimize which is the difference between the experimental point (Remes(Z), Immes(Z)) and a calculated point (Recal(Z), Imcal(Z)) and it is expressed as follows: J¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðRemes ðZÞ Recal ðZÞÞ2 þ ðImmes ðZÞ Imcal ðZÞÞ2
(2)
When one of the stop conditions for optimizing is executed, we get a set of the optimal parameters. After optimization of all parameters model for different values of the measured currents, we obtain a table with the calculated parameters from the experimental measured values of the current, frequency, real and imaginary part. Table 1 shows the experimental values of the model parameters extracted for different current values. Remember that the measurements were made on a Nexa PEM Fuel Cell system in a DC current range from 1 to 20 A and a frequency range from 0.1 Hz to 12 kHz. From these numerical values, we extract a valid general law variation for all current values for each model parameter CDCa, RTa, Cf, Rf, CDCc, RTc, LZ, RZ, RM et VFC in terms of the supplied currents. In fact, they founded expressions for each parameter of the model allows us to calculate the numerical value of this parameter according to each current value. Equations (3)e(12) are obtained with “Matlab Curve Fitting Toolbox” using the least squares method for calculating the coefficients of the found equations. This method allows us to see the influence of the current on the complex impedance of the PEM Fuel Cell and the behavior of each element separately. An interpolation approximation allows us to achieve the following mathematical functions of the different parameters of the complex impedance for the PEM Fuel Cell as follows: CDCa ¼ 0:000161 ðIÞ2 0:00254 ðIÞ þ 0:0607
(3)
RTa ¼ 0:15 lnðIÞ þ 0:645
(4)
Cf ¼ 0:0043 ðIÞ2 0:038 ðIÞ þ 0:3386
(5)
Rf ¼ 0:163 lnðIÞ þ 0:5624
(6)
CDCc ¼ 0:000233 ðIÞ þ 0:0168
(7)
RTc ¼ 0:00837 lnðIÞ þ 0:0895
(8)
RM ¼ 0:000911 ðIÞ þ 0:1304
(9)
LZ ¼ 2:28 E09 ðIÞ þ 1:59 E06
(10)
RZ ¼ 3:41 E04 ðIÞ þ 1:23 E01
(11)
UPAC ¼ 39; 239 ðIÞ0;08
(12)
Equations (3)e(12) are implemented in the simulation model to obtain a general and valid model for all current
Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114
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Fig. 7 e Flowchart of the complex impedance parameters optimization.
Table 1 e Experimental values of the complex impedance model parameters in terms of the supplied currents. IFC (A)
CDCa(F)
CDCc(F)
Cf(F)
RM(U)
RTa(U)
Rf(U)
RTc(U)
RZ(U)
LZ(H)
VFC (V)
1 2 3 4 5 6 7 8 9 10 12 14 16 18 20
0.061143 0.056302 0.054816 0.054264 0.047706 0.048648 0.051383 0.049911 0.056625 0.05783 0.055016 0.049911 0.053518 0.071536 0.076122
0.02093 0.018424 0.018328 0.018456 0.017087 0.017723 0.017876 0.018059 0.018122 0.021779 0.018228 0.020434 0.022194 0.020633 0.020912
0.3213 0.2808 0.2748 0.24958 0.19777 0.2667 0.30232 0.27049 0.43719 0.48216 0.45627 0.47241 0.73616 1.3192 1.1733
0.1309 0.1269 0.1257 0.1251 0.12564 0.12225 0.12229 0.12184 0.1241 0.12294 0.12436 0.12284 0.12654 0.10523 0.10555
0.54314 0.50314 0.49741 0.45412 0.36815 0.37814 0.36021 0.31425 0.32791 0.30696 0.26459 0.24265 0.2489 0.20622 0.20837
0.46632 0.39632 0.38464 0.36751 0.33931 0.27634 0.22015 0.20783 0.15792 0.14277 0.14371 0.14548 0.1287 0.096056 0.11701
0.09728 0.087063 0.086081 0.083514 0.06468 0.0713 0.07373 0.063883 0.077198 0.079895 0.068361 0.055887 0.055211 0.07686 0.070228
0.1305 0.1225 0.11813 0.12356 0.11844 0.127 0.12783 0.12847 0.12986 0.13132 0.13246 0.13466 0.13171 0.12334 0.12348
1.60E06 1.52E06 1.54E06 1.59E06 1.49E06 1.60E06 1.59E06 1.60E06 1.57E06 1.58E06 1.61E06 1.62E06 1.58E06 1.48E06 1.51E06
39.05 36.99 36.99 36.02 35.56 35.23 34.89 34.38 34.08 33.58 32.90 32.10 31.52 30.74 30.08
Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114
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values. It can calculate and simulate the values of parameters according to each current value.
Results and discussion In this part, we compare the simulation results of the complex impedance model to experimental tests from impedance spectroscopy. The results of the simulation model of the Proton Exchange Membrane (PEM) Fuel Cell using Matlab/ Simulink helped us to obtain the Nyquist plots for a current range from 1 to 20 A. The frequency range used for simulation varies from 0.1 Hz to 12 kHz with a 0.3 Hz step. Fig. 8 shows the simulation results by Nyquist plots of the complex impedance for different current values. We see in Fig. 8 that the different Nyquist plots are constituted by two lobes; each lobe corresponds to an operation area of the PEM Fuel Cell complex impedance. Low frequencies are located on the right of the curves while high frequencies are on the left. These lobes correspond to losses in the cells, large lobes which are located in the right of the curves represent the sum of the polarization and transfer charges losses that occurring at the anode and the cathode while the small lobes which are on the left represent the total ohmic losses of the cells from the PEM Fuel Cell [15,17,31,32]. Losses at the connections from cables appear at high frequencies for values greater than that of the ohmic losses. Our objective is to compare the model simulation results with the experimental results obtained by the experimental test bench. In fact we evaluate if the followed different parameters from the least squares method to find the signatures of different conditions from cell degradation. In this case, the method of analysis is to compare diagnostic results based on
measured values to the simulation results for the diagnosis of the PEM Fuel Cell model. To determine the error between simulation results and experimental results, we performed a residual analysis which consists to study the differences between the output predicted by a model and the output measured from the entire validation data. The residues represent the portion of experimental data which are not described by the model; in our case we studied the difference in results between simulation Nyquist diagram and experimental Nyquist diagram for a 10 A current. For this type of analysis, we used the “Matlab Residual Analysis tool”. Fig. 9 represents the superposition of the Nyquist diagram by simulation and experimental measurements for a 10 A current. We observe a small difference between the results of two curves for some frequencies values. Fig. 10 shows the results of the residual analysis of the real and the imaginary part as a function of frequency for the Nyquist plots for a 10 A current. The results are in direct percent to the differences values between the simulation and experimental results. Following this analysis, it is observed that there is a small difference due to a calculation error between simulation results and experimental results. For the real and imaginary parts, the error rate varies depending on the frequency. It is noted that large error rates are at low frequencies presented in the Nyquist diagram by the big lobe representing the activation losses. For the real part we note that the maximum error rate does not exceed 1% and for the imaginary part the maximum error rate does not exceed 4%. The Nexa PEM Fuel Cell system operates at a temperature of 65 C [14]. This temperature does not influence the operation of the system because an on-board electronic card ensures the monitoring of the temperature rise. A study by K.S.
Fig. 8 e Nyquist diagrams for different current values. Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114
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Fig. 9 e Superposition of Nyquist plots for 10 A.
Fig. 10 e Results of Residual analysis for spectrum 10 A.
Choi et al. [33] discusses the effect of temperature and humidity on the performance of the Nexa PEM fuel cell system. According to the results of this study, the temperature does not affect the power delivered by the Nexa PEM Fuel Cell and its complex impedance.
Conclusion In this work, we described the new methodology to determine the complex impedance parameters for Proton Exchange
Membrane (PEM) Fuel Cell model. The modelling of the complex impedance established is based on electrical components such as resistors, inductor and capacitors. This model takes into account the mathematical equations parameters which are derived from results of the experimental test bench and algorithm identification based on the least squares method. We implemented this model and simulated in Matlab/Simulink. Simulation results are presented in the Nyquist diagrams allowing us identifying the different phenomena occurring inside the PEM Fuel Cell. In addition, we conducted a residual analysis to observe the correlation between the different
Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114
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results. Our contribution through the results obtained in this work, is that this proposed a new modelling approach and describes the dynamic operation of the Nexa PEM Fuel Cell system in load. This complete model allows us to predict the PEM Fuel Cell operation. These results can be used in order to obtain a generalized model for On-Board Diagnostics (OBD) of the PEM Fuel Cell vehicles.
Acknowledgment This work is supported by the Faculty of Sciences of Tunis (FST) in Tunis Tunisia, DRIVE Laboratory of the ISAT in Nevers France and Institute Jean Lamoure in Nancy France.
Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.ijhydene.2017.01.114.
references
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[12] Asghari S, Mokmeli A, Samavati M. Study of PEM fuel cell performance by electrochemical impedance spectroscopy. Int J Hydrogen Energy Sep 2010;35(17):9283e90. [13] Lai CM, Lin JC, Hsueh KL, Hwang CP, Tsay KC, Tsai LD, et al. On the electrochemical impedance spectroscopy of direct methanol fuel cell. Int J Hydrogen Energy December 2007;32(17):4381e8. [14] Nexa Power Module User’s Manuel, Ballard Power Systems, 2003. [15] Bouaicha A, Allegui H, Rouane A, Aglzim EH, Mami A. Design and realization of an electronic load for a PEM fuel cell‘. World Acad Sci Eng Technol Jan 2014;8(1):202e7. [16] A. Bouaicha, H. Allagui, A. Mami and A. Rouane, Study of an electronic load for measuring the internal impedance of a PEM fuel cell. In: 10th International Multi-Conferences on Systems, Signals & Devices 2013 (SSD13), Tunisia, pp. 1e5, 2013. [17] Bouaicha A, Allegui H, Aglzim EH, Rouane A, Mami A. Study and validation of a PEM fuel cell complex impedance measurement system. Indian J Sci Technol December 2016;9(45):1e9. [18] Raposa G. Performing AC impedance measurements on fuel cells. Fuel Cell Magazine-Agilent Technologies. 2003. [19] Bu¨chi Felix N, Srinivasan Supramaniam. Operating protons exchange membrane fuel cells without external humidification of the reactant gases. J Electrochem Soc Aug 1997;144(8):2767e72. [20] Wagner N, Gu¨lzow E. Change of electrochemical impedance spectra (EIS) with time during CO-poisoning of the Pt-anode in a membrane fuel cell. J Power Sources Eighth Ulmer Electrochem Tage Mar 2004;127:341e7. € ki M, Momma T. Influence of [21] Osaka T, Nakade S, Rajama capacity fading on commercial lithium-ion battery impedance. J Power Sources June 2003;119e121:929e33. [22] Nelatury Sudarshan Rao, Singh Pritpal. Equivalent circuit parameters of nickel/metal hydride batteries from sparse impedance measurements. J Power Sources May 2004;132:309e14. [23] Springer TE, Zawodzinski TA, Wilson MS, Gottesfeld S. Characterization of polymer electrolyte fuel cells using AC impedance spectroscopy. J Electrochem Soc Feb 1996;143(2):587e99. [24] Eikerling M, Kornyshev AA. Electrochemical impedance of the cathode catalyst layer in polymer electrolyte fuel cells. J Electroanal Chem Oct 1999;475:107e23. [25] Bultel Y, Genies L, Antoine O, Ozil P, Durand R. Modeling impedance diagrams of active layers in gas diffusion electrodes: diffusion, ohmic drop effects and multistep reactions. J Electroanal Chem May 2002;527:143e55. [26] Outeiro MT, Chibante R, Carvalho AS, de Almeida AT. A parameter optimized model of a proton exchange membrane fuel cell including temperature effects. J Power Sources Dec 2008;185(2):952e60. [27] Tao WQ, Min CH, Liu XL, He YL, Yin BH, Jiang W. Parameter sensitivity examination and discussion of PEM fuel cell simulation model validation Part I. Current status of modeling research and model development. J Power Sources Sep 2006;160(1):359e73. [28] Aglzim EH. Characterization by impedance spectroscopy the complex impedance of a load fuel cell: evaluation of the influence of moisture. Thesis. France: University Henri Nancy; 2009. Poincare [29] Fontes G, Turpin C, Astier S, Meynard TA. Interactions between fuel cells and power converters: influence of current harmonics on a fuel cell stack. In: IEEE transactions on power electronicsvol. 22; March 2007. p. 670e8. 2. [30] J. Garnier, M.C. Pera, D. Hissel, F. Harel, D. Candusso, N. Glandut, et al. Dynamic PEM fuel cell modeling for
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automotive applications’, 2003 IEEE 58th Vehicular Technology Conference, VTC 2003-Fall, Vol. 5, pp. 3284e3288, October 2003. [31] Diard JP, Le Gorrec B, Montella C. EIS study of electrochemical battery discharge on constant load. J power Sources 1998;70:78e84. rez-page M, Pe rez-Herranz V. Study of the electrochemical [32] Pe behaviour of a 300 W PEM fuel cell stack by electrochemical
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impedance spectroscopy. Int J Hydrogen Energy Mar 2014;39(8):4009e15. [33] Choi KS, Kim HM, Yoon HC, Forrest ME, Erickson PA. Effects of ambient temperature and relative humidity on the performance of Nexa fuel cell. Energy Convers Manag December 2008;49(12):3505e4351.
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Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters Arafet Bouaicha a,*, Hatem Allagui a, El-Hassane Aglzim b, Amar Rouane c, Adelkader Mami a a
Laboratory LACS-ENIT/FST, Faculty of Sciences of Tunis, University Tunis El Manar, Tunis, Tunisia Laboratory DRIVE, University of Bourgogne, Nevers, France c University of Lorraine, Nancy, France b
article info
abstract
Article history:
In this paper, we present a new methodology for determining the complex impedance
Received 1 August 2016
parameters for a Proton Exchange Membrane (PEM) Fuel Cell in order to have a general
Received in revised form
model for embedded diagnosis. The modelling of Fuel Cells is a very important phase
18 January 2017
because it contributes to a better understanding and representation of the internal phe-
Accepted 19 January 2017
nomena in this type of generator. After obtaining the experimental results of the complex
Available online xxx
impedance using a realized test bench for Proton Exchange Membrane (PEM) Fuel Cell using an electrochemical method which is the electrochemical impedance spectroscopy
Keywords:
(EIS), we treat these results with an identification algorithm based on least squares method
Proton exchange membrane (PEM)
in the objective to determine the variations laws of the complex impedance parameters
fuel cell
then implement in a PEM Fuel Cell model with Matlab/Simulink software. The established
Test bench
model of the complex impedance is based on electrical components and takes into account
Modeling
the mathematical equations of the different elements. The simulation results of this
Complex impedance
implemented model inform us about the state of the PEM Fuel Cell and validate the choice
Least square method
of the parameters. The validation of this choice is done by a comparative study using re-
On-board diagnosis
sidual analysis method between the experimental and the simulation results. The general model is obtained from the superposition of the measured and theoretical results. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Proton Exchange Membrane (PEM) Fuel Cell is an electrochemical device; its study requires multidisciplinary knowledge. Using this device is particularly complicated due to the large number of internal and external parameters to be controlled simultaneously (gas flow, operating temperature,
humidification membranes…). The influence of all these parameters makes a complex modelling for PEM Fuel Cell. The modelling plays an important part in the development of Fuel Cells as it facilitates a better understanding of the physicochemical phenomena and parameters affecting a performance of Fuel Cells systems. This modelling presents a very important phase because it contributes to a better understanding and representation of the internal phenomena.
* Corresponding author. E-mail address: [email protected] (A. Bouaicha). http://dx.doi.org/10.1016/j.ijhydene.2017.01.114 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114
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The building of a model usually depends on the use to which it is intended, a model can be used to design, understand, or ordering. The developed models for PEM Fuel Cells can provide a significant level of details; the possibly problem is the identification and validation of these models. All of the used approaches for modelling pass necessarily with a long and difficult experimental stage. These are probably the physical models requires the largest number of tests, including in domains applications such in electrical engineering. Also, management of Fuel Cells systems is difficult because of the many internal physical parameters such as the current required by the load, the temperature of the stack, pressures and flow rates. All of these parameters have an impact on the progress of the system that are often particularly difficult to estimate and to express clearly. In reality, these parameters are expressed by nonlinear relationships, generally it is difficult to model since they are dependent on each other. In terms of literature, many researchers used algorithms to identify these variables according to the desired objectives for the development of each model, sometimes the variables are limited or difficult to implement in a validation procedure. The electrochemical impedance spectroscopy (EIS) method plays an important role for determining the parameters of the model. This method is used in several research studies [1e13] to model the complex impedance of a PEM Fuel Cell. A. Saadi et al. [1] using an experimental strategy based on the results of the study in order to predict three static models of a PEM Fuel Cell, and validated experimentally with identification of the static model parameters using EIS. In the study of S. Chevalier et al. [2], the authors presented a multi-physical modelling of a PEM Fuel Cell using the same method for the detection of the degradation of the cells. Another study by S.H. Yang et al. [3] using the EIS method to diagnose a Direct Methanol Fuel Cell (DMFC), and presented a comparison between the results obtained at the anode and the cathode. Y.H. Lee et al. [4] used a real-time diagnosis procedure using the principle of superposition and the EIS method to characterize the performances of a PEM Fuel Cell. A modelling study using Bond Graph is presented by D. Mzoughi et al. [5], they presented a model using Bond Graph and the EIS method for Nexa PEM Fuel Cell. In this study, we present a new simple approach methodology to identify the variables of the internal phenomena of the PEM Fuel Cell, which are validated by comparing the experimental results with those of simulation using the EIS method. Then, we present the different modelling approaches using the experimental data obtained using the Nexa PEM Fuel Cell system. After exposing the modelling approach of the different obtained parameters in the PEM Fuel Cell, we present the global model. Next, we detail the explanation of the methodology used for determining the complex impedance parameters. Finally, we present and discuss the obtained results.
Test bench description Experimental test bench One way to know the state of the membranes of the Proton Exchange Membrane (PEM) Fuel Cell is the measure of its
complex impedance, the advantage of this method is to better understand the physical effects occurring in this system. The method for measuring the complex impedance is the electrochemical impedance spectroscopy (EIS), this method consists to superimposing a perturbing signal to a value of the DC current at the input and analyzing the response signal [6e11]. This method allows us to make a real-time measurement during the operation of the PEM Fuel Cell. To make the measurement of the complex impedance, we must design and implement a test bench which supports a DC current supplied by the PEM Fuel Cell. To use the EIS method, the DC current response should be linear compared to the Fuel Cell voltage. The PEM Fuel Cell is a priori a nonlinear and non-stationary system, so we can determine the complex impedance using low-amplitude perturbations around an operating point that is assumed stationary [8,9,12]. The experimental test bench is designed around the Nexa Ballard [14] PEM Fuel Cell and a realized electronic load. In addition, a measuring electronic board based on the STM32F4 microcontroller connected to a computer to collect data that are saved and processed by a measurement application developed with LabVIEW software. LabVIEW software is used to control various devices and also can analyze and save the results of the complex impedance measurement in a data file that can be used to display and analyze the results found by an acquisition card which performs acquiring data. The electronic load realized to the impedance measurement must impose a DC current to be supplied by the Nexa PEM Fuel Cell during measurement, in our case, we realized an electronic load [15e17] which supports 750 W power that is a 25 A DC current to a 30 V voltage. Fig. 1 shows the schematic of the proposed test bench that is used to measure the complex impedance of the PEM Fuel Cell. This test bench is mainly composed with the electronic load designed and constructed in our laboratory, the Nexa Ballard PEM Fuel Cell system [14], a function generator for injecting the perturbing signal, the data acquisition system and the computer that integrates applications developed using LabVIEW and Matlab/Simulink. In all of the realized tests, we injected a sinusoidal signal of frequency ranging from 0.1 Hz to 12 kHz and 250 mVPeP amplitude which is provided using a function generator, usually for a PEM Fuel Cell the frequency spectrum is selected between 1 Hz and 10 kHz [18]. The proposed test bench is for instrumentation dedicated to the PEM Fuel Cell. The obtained results are in the form of the complex impedance diagrams and they are usually done into the Nyquist plan presented by the imaginary part as a function of the real part. The progress of a complex impedance measurement using this test bench is presented by the following steps. First, we impose the static parameter of the measure using the control card and the electronic load which is the DC current flow through the Nexa PEM Fuel Cell. After a short stabilization time, the Fuel Cell voltage and the DC current are measured and saved using the developed LabVIEW application. Next, we inject the sinusoidal perturbation signal into the imposed signal using the electronic load. The electronic measuring system using the microcontroller acquisition module
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Fig. 1 e Schematic of the proposed test bench for Nexa PEM Fuel Cell.
STM32F4 runs complicated calculations in order to obtain the desired results. After measuring the spectrum of frequencies (from 0.1 Hz to 12 kHz), the obtained results are saved in a file created by the developed LabVIEW application. Finally, this file is used to analyze the founded results in the form of frequencies, real parts and imaginary parts that present the essential elements to calculate the PEM Fuel Cell complex impedance parameters. The modelling of the Nexa Ballard PEM Fuel Cell system [14] takes into account the auxiliary elements (electronic boards, humidifier, compressor, etc.). This system can provide a power of 1200 W at the voltage of 26 V under load. The stacking is composed with 47 cells that can supply the voltage of 42 V without load. An on-board control card allows system safety by controlling certain parameters using integrated sensors (leakage of hydrogen, increase of temperature, drop of voltage, etc.).
experimental test bench. We implemented the model for this measurement test bench in a simulation environment that is Matlab/Simulink. This model is composed with the electrical elements in Simulink libraries. These are connected together in parallel or in series; the value of each parameter is then calculated using the equations of the chosen model. We have chosen to model the Nexa PEM Fuel Cell system, this system is generally composed with the stacking of anodes, membranes and cathodes. We chose modelling this system with the tools of Matlab/Simulink. Fig. 2 shows the schematic diagram of the modelling system using Matlab/Simulink. This system is composed by the test bench elements, the impedance measurement system of the complex impedance and the Nexa PEM Fuel Cell model. This modelling system with Matlab/Simulink is composed of three main blocks: a block which includes the model elements of the Nexa PEM Fuel Cell, a block for measuring and
Test bench modelling using Matlab/Simulink Matlab/Simulink is a powerful tool for scientific calculation and process simulation; it provides rapid solutions for scientific applications. It is software for simulating, modelling and analyzing physical systems; it has a dynamic simulation environment for complex systems described by differential and polynomial equations. The modelling of the PEM Fuel Cell complex impedance in this work is based on an approach called equivalent electrical circuits; the complex impedance is achieved using assembling the various electrical components such as resistors, capacitors and inductors. To validate the results obtained by the
Fig. 2 e Schematic diagram of the modelling system.
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displaying the complex impedance using Matlab/Simulink and a measuring block using the principle of the impedance spectroscopy method which is presented with the test bench system. The details are represented in Figs. 3e5. Fig. 3 shows the schematic diagram of the impedance measurement system using Matlab/Simulink. The impedance measurement system block with Matlab/ Simulink allowed us to export the simulation results of the mathematical equations of the different model parameters to Matlab environment “Workspace” in order to draw the Nyquist plots. Fig. 4 shows the schematic diagram of the Test Bench system using Matlab/Simulink. The Test Bench system presents the principle of the electrochemical impedance spectroscopy (EIS) method in Matlab/ Simulink that allowed us to simulate the principle of this chosen method that injects a sinusoidal perturbing signal to be superimposed on the DC current (IFC) and sampling the voltage (VFC) across the model of the Nexa PEM Fuel Cell. We used this block in the same principle of controlling the current of the experimental test bench which is constituted by the model of N-MOSFET transistor and the model of the operational amplifier in Matlab/Simulink.
The integration of the PEM Fuel Cell in an electric environment requires knowledge of its electric model. The models can be built using static physical relationships; they present a static model. If the models are based on parametric identification techniques; then they present a dynamic model. Various models can be developed according to the objective. In this work, the model must be simple, accurate and describes the electrical behavior of the Nexa PEM Fuel Cell system in dynamic mode. The assumptions for modelling the Nexa PEM Fuel Cell system in this work are:
Parameters determination of the complex impedance model
Fig. 5 shows the structure of the model in the form of an equivalent circuit diagram consisting with electric elements translating physical phenomena considered. The elements of the chosen model of the Nexa PEM Fuel Cell with Matlab/ Simulink are composed by resistors, capacitors, inductors and a DC voltage source. Obtaining the result of the complex impedance has many benefits because it provides access to inaccessible internal parameters when measurement is running. Many researchers [10,11,26e29] used this model, and it can be considered as the nearest model of the Nexa PEM Fuel Cell system. With:
Complex impedance model of Nexa PEM fuel cell Many models have been presented for the electrochemical reactions of the PEM Fuel Cell; the goal of these models is to understand the reaction mechanisms in this system. To analyze the internal behavior of the PEM Fuel Cell such that the influence of humidification, drying membranes and observing the performance of the PEM Fuel Cell in the presence of carbon monoxide in hydrogen [19,20], the EIS is considered an adequate method for the study of electrochemical devices. It is used extensively for modelling batteries [21,22] and Fuel Cells [23e25]. This modelling is presented by equivalent electrical circuits that are based on experimental testing of the impedance spectra, reflecting the behavior of the PEM Fuel Cell. The equivalent impedances are used to determine the electrochemical parameters of the complex impedance; it is the modelling using the complex impedance.
The gases are pure hydrogen and pure oxygen. The gas supplies are expected at constant rates. The electrodes, catalytic layers and the membrane are homogeneous and isotropic. Gas pressures are considered uniform in the supply lines (no losses in the gas supply channel). The membrane is fully humidified so that the ionic conductivity is constant. The components of the model are all the Nexa PEM Fuel Cell system and its auxiliaries. No parasitic reaction and the aging of the electrochemical cells are not considered.
CDC: double layer capacity placed in parallel with the representative impedance of the electrochemical phenomena, it is due to the presence of positive charges on the surface of the membrane and negative charges on the electrode surface. RT: Resistance characterizes the transfer phenomena charges to the electrodes.
Fig. 3 e Impedance measurement system in Matlab/Simulink. Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114
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Fig. 4 e Test Bench system in Matlab/Simulink.
Fig. 5 e Electric schematic of the Nexa PEM Fuel Cell model.
RM: Membrane resistance. Cf and Rf: elements that represent the faradaic impedance. They have the concentration of each species in the anode, it is the Warburg impedance noted W [27,29,30]. LZ and RZ: different impedances connection with the PEM Fuel Cell (connecting wire, electrical contacts, etc.).
ZðuÞ ¼
RZ þ juLZ juLZ RZ
i h R R RTa þ Rf , 1 þ juCf RTaTaþRf f þ RM þ 1 RTa Rf CDCa Cf u2 þ ju, RTa þ Rf CDCa þ Rf Cf þ
The total impedance of the model is constituted by the impedance of the anode and cathode in addition to the impedance of the membrane and the connections of the PEM Fuel Cell. The expression of the corresponding impedance is expressed as follows:
RTc 1 þ juRTc CDCc (1)
This model is used to analyze the results of impedance spectroscopy found by experimental test bench, eventually we establish the variation laws of the different parameters
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forming this chosen model from the measuring results. The mathematical expressions of the different parameters are implemented in this model of Matlab/Simulink.
Optimization methodology of the complex impedance parameters After obtaining measurement results with the Proton Exchange Membrane (PEM) Fuel Cell using the experimental test bench, we must pass through the analysis phase. For this, we determine the parameters expressions of the model according to the measurement results. The obtained parameters inform us the state of the PEM Fuel Cell in real time. Fig. 6 shows the flowchart of the methodology for extraction the complex impedance parameters of the Nexa PEM Fuel Cell. This methodology consists to calculate the numerical values for each parameter of the model using the results of experimental tests. After, we calculate the optimal value for each parameter by minimizing the difference between the theoretical and the measured value. The obtained values for each parameter are used to find the mathematical expression of the model parameters chosen using the least squares method. In the last step, these obtained functions will be used in Matlab/ Simulink to validate the choice of the simulation model.
Variation laws of the complex impedance parameters The idea is to compare the experimental tests with those of simulation model defined above, and then adjust the values of these parameters in the model until a very small difference between the two curves. We find to obtain the optimal
Fig. 6 e Flowchart of the extraction methodology.
parameter set that minimizes the difference between the calculated and measured values for each point. We used the least squares method to minimize this difference. The principle to determine the parameters is presented by the steps in the flowchart in Fig. 7. The criterion (J) to minimize which is the difference between the experimental point (Remes(Z), Immes(Z)) and a calculated point (Recal(Z), Imcal(Z)) and it is expressed as follows: J¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðRemes ðZÞ Recal ðZÞÞ2 þ ðImmes ðZÞ Imcal ðZÞÞ2
(2)
When one of the stop conditions for optimizing is executed, we get a set of the optimal parameters. After optimization of all parameters model for different values of the measured currents, we obtain a table with the calculated parameters from the experimental measured values of the current, frequency, real and imaginary part. Table 1 shows the experimental values of the model parameters extracted for different current values. Remember that the measurements were made on a Nexa PEM Fuel Cell system in a DC current range from 1 to 20 A and a frequency range from 0.1 Hz to 12 kHz. From these numerical values, we extract a valid general law variation for all current values for each model parameter CDCa, RTa, Cf, Rf, CDCc, RTc, LZ, RZ, RM et VFC in terms of the supplied currents. In fact, they founded expressions for each parameter of the model allows us to calculate the numerical value of this parameter according to each current value. Equations (3)e(12) are obtained with “Matlab Curve Fitting Toolbox” using the least squares method for calculating the coefficients of the found equations. This method allows us to see the influence of the current on the complex impedance of the PEM Fuel Cell and the behavior of each element separately. An interpolation approximation allows us to achieve the following mathematical functions of the different parameters of the complex impedance for the PEM Fuel Cell as follows: CDCa ¼ 0:000161 ðIÞ2 0:00254 ðIÞ þ 0:0607
(3)
RTa ¼ 0:15 lnðIÞ þ 0:645
(4)
Cf ¼ 0:0043 ðIÞ2 0:038 ðIÞ þ 0:3386
(5)
Rf ¼ 0:163 lnðIÞ þ 0:5624
(6)
CDCc ¼ 0:000233 ðIÞ þ 0:0168
(7)
RTc ¼ 0:00837 lnðIÞ þ 0:0895
(8)
RM ¼ 0:000911 ðIÞ þ 0:1304
(9)
LZ ¼ 2:28 E09 ðIÞ þ 1:59 E06
(10)
RZ ¼ 3:41 E04 ðIÞ þ 1:23 E01
(11)
UPAC ¼ 39; 239 ðIÞ0;08
(12)
Equations (3)e(12) are implemented in the simulation model to obtain a general and valid model for all current
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Fig. 7 e Flowchart of the complex impedance parameters optimization.
Table 1 e Experimental values of the complex impedance model parameters in terms of the supplied currents. IFC (A)
CDCa(F)
CDCc(F)
Cf(F)
RM(U)
RTa(U)
Rf(U)
RTc(U)
RZ(U)
LZ(H)
VFC (V)
1 2 3 4 5 6 7 8 9 10 12 14 16 18 20
0.061143 0.056302 0.054816 0.054264 0.047706 0.048648 0.051383 0.049911 0.056625 0.05783 0.055016 0.049911 0.053518 0.071536 0.076122
0.02093 0.018424 0.018328 0.018456 0.017087 0.017723 0.017876 0.018059 0.018122 0.021779 0.018228 0.020434 0.022194 0.020633 0.020912
0.3213 0.2808 0.2748 0.24958 0.19777 0.2667 0.30232 0.27049 0.43719 0.48216 0.45627 0.47241 0.73616 1.3192 1.1733
0.1309 0.1269 0.1257 0.1251 0.12564 0.12225 0.12229 0.12184 0.1241 0.12294 0.12436 0.12284 0.12654 0.10523 0.10555
0.54314 0.50314 0.49741 0.45412 0.36815 0.37814 0.36021 0.31425 0.32791 0.30696 0.26459 0.24265 0.2489 0.20622 0.20837
0.46632 0.39632 0.38464 0.36751 0.33931 0.27634 0.22015 0.20783 0.15792 0.14277 0.14371 0.14548 0.1287 0.096056 0.11701
0.09728 0.087063 0.086081 0.083514 0.06468 0.0713 0.07373 0.063883 0.077198 0.079895 0.068361 0.055887 0.055211 0.07686 0.070228
0.1305 0.1225 0.11813 0.12356 0.11844 0.127 0.12783 0.12847 0.12986 0.13132 0.13246 0.13466 0.13171 0.12334 0.12348
1.60E06 1.52E06 1.54E06 1.59E06 1.49E06 1.60E06 1.59E06 1.60E06 1.57E06 1.58E06 1.61E06 1.62E06 1.58E06 1.48E06 1.51E06
39.05 36.99 36.99 36.02 35.56 35.23 34.89 34.38 34.08 33.58 32.90 32.10 31.52 30.74 30.08
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values. It can calculate and simulate the values of parameters according to each current value.
Results and discussion In this part, we compare the simulation results of the complex impedance model to experimental tests from impedance spectroscopy. The results of the simulation model of the Proton Exchange Membrane (PEM) Fuel Cell using Matlab/ Simulink helped us to obtain the Nyquist plots for a current range from 1 to 20 A. The frequency range used for simulation varies from 0.1 Hz to 12 kHz with a 0.3 Hz step. Fig. 8 shows the simulation results by Nyquist plots of the complex impedance for different current values. We see in Fig. 8 that the different Nyquist plots are constituted by two lobes; each lobe corresponds to an operation area of the PEM Fuel Cell complex impedance. Low frequencies are located on the right of the curves while high frequencies are on the left. These lobes correspond to losses in the cells, large lobes which are located in the right of the curves represent the sum of the polarization and transfer charges losses that occurring at the anode and the cathode while the small lobes which are on the left represent the total ohmic losses of the cells from the PEM Fuel Cell [15,17,31,32]. Losses at the connections from cables appear at high frequencies for values greater than that of the ohmic losses. Our objective is to compare the model simulation results with the experimental results obtained by the experimental test bench. In fact we evaluate if the followed different parameters from the least squares method to find the signatures of different conditions from cell degradation. In this case, the method of analysis is to compare diagnostic results based on
measured values to the simulation results for the diagnosis of the PEM Fuel Cell model. To determine the error between simulation results and experimental results, we performed a residual analysis which consists to study the differences between the output predicted by a model and the output measured from the entire validation data. The residues represent the portion of experimental data which are not described by the model; in our case we studied the difference in results between simulation Nyquist diagram and experimental Nyquist diagram for a 10 A current. For this type of analysis, we used the “Matlab Residual Analysis tool”. Fig. 9 represents the superposition of the Nyquist diagram by simulation and experimental measurements for a 10 A current. We observe a small difference between the results of two curves for some frequencies values. Fig. 10 shows the results of the residual analysis of the real and the imaginary part as a function of frequency for the Nyquist plots for a 10 A current. The results are in direct percent to the differences values between the simulation and experimental results. Following this analysis, it is observed that there is a small difference due to a calculation error between simulation results and experimental results. For the real and imaginary parts, the error rate varies depending on the frequency. It is noted that large error rates are at low frequencies presented in the Nyquist diagram by the big lobe representing the activation losses. For the real part we note that the maximum error rate does not exceed 1% and for the imaginary part the maximum error rate does not exceed 4%. The Nexa PEM Fuel Cell system operates at a temperature of 65 C [14]. This temperature does not influence the operation of the system because an on-board electronic card ensures the monitoring of the temperature rise. A study by K.S.
Fig. 8 e Nyquist diagrams for different current values. Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114
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Fig. 9 e Superposition of Nyquist plots for 10 A.
Fig. 10 e Results of Residual analysis for spectrum 10 A.
Choi et al. [33] discusses the effect of temperature and humidity on the performance of the Nexa PEM fuel cell system. According to the results of this study, the temperature does not affect the power delivered by the Nexa PEM Fuel Cell and its complex impedance.
Conclusion In this work, we described the new methodology to determine the complex impedance parameters for Proton Exchange
Membrane (PEM) Fuel Cell model. The modelling of the complex impedance established is based on electrical components such as resistors, inductor and capacitors. This model takes into account the mathematical equations parameters which are derived from results of the experimental test bench and algorithm identification based on the least squares method. We implemented this model and simulated in Matlab/Simulink. Simulation results are presented in the Nyquist diagrams allowing us identifying the different phenomena occurring inside the PEM Fuel Cell. In addition, we conducted a residual analysis to observe the correlation between the different
Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114
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results. Our contribution through the results obtained in this work, is that this proposed a new modelling approach and describes the dynamic operation of the Nexa PEM Fuel Cell system in load. This complete model allows us to predict the PEM Fuel Cell operation. These results can be used in order to obtain a generalized model for On-Board Diagnostics (OBD) of the PEM Fuel Cell vehicles.
Acknowledgment This work is supported by the Faculty of Sciences of Tunis (FST) in Tunis Tunisia, DRIVE Laboratory of the ISAT in Nevers France and Institute Jean Lamoure in Nancy France.
Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.ijhydene.2017.01.114.
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Please cite this article in press as: Bouaicha A, et al., Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.01.114