A simple transient model for a high temperature PEM fuel cell impedance

2014

A transient one-dimensional model for the coupled performance of the cathode catalyst layer (CCL) and the gas-diffusion layer (GDL) in a PEM fuel cell is linearized and an exact analytical solution for the cathode side impedance Z is derived. The solution is valid at a low current density, when the proton and oxygen transport losses in the CCL are not large. The zero-frequency resistance contains the faradaic term, the terms due to the proton and oxygen transport in the CCL and due to the oxygen transport in the GDL. The analytical equation for Z is fast enough for least-squares fitting of experimental spectra, which yields the GDL oxygen diffusivity, the Tafel slope of the oxygen reduction reaction, and the CCL proton conductivity and oxygen diffusivity. As an example, the model is fitted to three measured spectra of a high-temperature PEMFC; the fitting parameters are discussed. Polymer electrolyte membrane fuel cells (PEMFCs) are close to commercialization: leading car manufacturers claim beginning of mass production of fuel cell cars within the next few years. Yet, a lot of research has to be done to improve PEMFC durability and performance.One of the most powerful in situ techniques for fuel cell characterisation is electrochemical impedance spectroscopy (EIS).1 In a working fuel cell, the transport and kinetic processes affect the cell impedance, as all these processes are linked to the charges production and consumption in electrochemical reactions. A great advantage of EIS is that it nicely separates potential losses corresponding to the processes with different time scales, whereas the cell polarization curve shows only the sum of these losses. Interpretation of EIS spectra requires modeling.Historically, EIS has been developed for electrochemical studies on a plane single-crystal electrode surface immersed in a liquid electrolyte.1,2 A number of classic solutions for the impedance of this system in different conditions has been derived e.g., Warburg transport impedance, Gerischer impedance for the system with transport and chemical reaction in the electrolyte 3 etc. The Gerischer impedance has been used for analysis of impedance spectra of SOFC anode, in which the electrochemical conversion occurs at the anode/electrolyte interface. 4,5 However, PEMFC electrode is a porous system with the reaction distributed over the electrode depth. It can be shown that the impedance of this system is not equivalent to the Gerischer impedance of a planar electrode (see below).Analytical solutions for impedance of a single cylindrical pore have been derived by Lasia.6,7 DeLevie suggested a transmission line model for the porous electrode and discussed a physical model for the electrode impedance.8 However, the transmission line of deLevie does not include oxygen transport elements and equivalence of this simple model to the physical model resulting from the conservation equations has not been rigourously proofed.Every physical impedance model is a tool for fitting experimental impedance spectra in order to obtain phys...

“…The MEA parameters required for fitting are given in the caption to Table I; the cell operating parameters and other relevant experimental information is reported in Ref. 31.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

One-Dimensional Impedance of the Cathode Side of a PEM Fuel Cell: Exact Analytical Solution

2014

“…17 must also be fulfilled, we finally get the following condition for the regular frequencies, at which |Z ∞ gdl | is small: [21] With the data in Tables I, II, Eq. 21 holds for the frequencies f > 10 Hz.…”

Section: For Detailed Discussion)mentioning

confidence: 90%

Comparison of Two Physical Models for Fitting PEM Fuel Cell Impedance Spectra Measured at a Low Air Flow Stoichiometry

Reshetenko

2016

Local impedance spectra of a segmented PEM fuel cell operated at an air flow stoichiometry of λ = 2 are measured. The local spectra are fitted with the recent 1D and quasi-2D (q2D) physical models for PEMFC impedance. The q2D model takes into account oxygen transport in the gas channel, while the 1D model ignores this transport assuming infinite stoichiometry of the air flow. Analysis of the q2D expression for the GDL impedance Z ∞ gdl at λ → ∞ shows that the contribution of Z ∞ gdl to the total cell impedance rapidly decays with the frequency growth. We derive an equation for the boundary frequency f lim , above which this contribution is small. We show that the 1D model can be fitted to the high-frequency part ( f > f lim ) of a spectrum acquired at λ 2, ignoring the low-frequency arc due to the oxygen transport in the channel. Comparison of fitting parameters resulted from the 1D and q2D models confirms this idea. Polymer electrolyte membrane fuel cells (PEMFCs) generate electricity due to splitting the hydrogen-oxygen combustion reaction into two half-reactions producing and consuming charged particles. Understanding transport and kinetic potential losses in these cells is crucial for cell design. Electrochemical impedance spectroscopy (EIS) provides a unique opportunity to separate contributions of different processes into the total potential loss in a cell.1,2 Deciphering experimental impedance spectra requires modeling though.The simplest and fastest way to rationalize the spectra is the transmission line modeling (TLM). This approach aims at construction of equivalent electric circuit, which has a spectrum close to the measured one. The circuit is usually assembled out of R, C and L-elements, and out of a number of elements representing classic impedances of electrochemical systems. Two well-known examples are the Warburg element, 3 which describes impedance of a transport layer attached to a planar electrode, and Gerischer element 4 representing impedance of a transport layer with the distributed chemical reaction. The TLM has been widely used in fuel cell studies (see e.g. Refs. 5 and 6); however, validity of this approach cannot be rigorously proved. First, there is no guarantee, that the selected equivalent circuit is unique. Second, the classic solutions for impedance of a system with the planar electrode 3,4 are, in general, not applicable to a porous catalyst layer with the distributed electrochemical reaction. 7,8 In addition, determination of the cell physical transport and kinetic parameters from the equivalent circuit elements is usually beyond the scope of the TLM.This explains growing interest in physical modeling of PEMFC impedance.9-22 Generally, a physical impedance model can be obtained from any transient performance model of a cell by making a standard procedure of linearization and Fourier-transform (see e.g. Ref. 23 for mathematical details). The resulting system of linear equations for the perturbation amplitudes is, in general, a complex-valued boundary-value problem (BVP), which ca...

“…17. As can be seen, the quality of fitting is very high: the fitted and experimental points shown for the same frequencies practically overlap.…”

Section: Resultsmentioning

confidence: 76%

“…25 spectra of a high-temperature PEM fuel cell. 17 The spectrum has been measured at the cell current density of 60 mA cm −2 , cell temperature of 160…”

Section: Resultsmentioning

confidence: 99%

A Fast Low-Current Model for Impedance of a PEM Fuel Cell Cathode at Low Air Stoichiometry

2017

We report a physics-based analytical model for low-current PEM fuel cell impedance, which takes into account oxygen transport in the channel. The model is fast: fitting the model impedance to the experimental Nyquist spectrum takes about 2 minutes on a 2-GHz notebook. In addition to the transport and kinetic parameters of the catalyst layer, fitting returns the oxygen diffusion coefficient in the gas-diffusion layer and the resistivity due to oxygen transport in the channel. Maple worksheet with the fitting procedure is available for download.