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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. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. ? Users may download and print one copy of any publication from the public portal for the purpose of private study or research. ? You may not further distribute the material or use it for any profit-making activity or commercial gain ? You may freely distribute the URL identifying the publication in the public portal ? Take down policy If you believe that this document breaches copyright please contact us at [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from vbn.aau.dk on: September 17, 2016 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