Dynamic modeling of proton exchange membrane fuel cell using non-integer derivatives

The modeling of proton exchange membrane fuel cells (PEMFC) may work as a powerful tool in the development and widespread testing of alternative energy sources in the next decade. In order to obtain a suitable PEMFC model, which can be used in the analysis of fuel cell-based power generation systems, it is necessary to define the values of a specific group of modeling parameters. In this paper, the authors propose a dynamic model of PEMFC, the originality of which lays on the use of non-integer derivatives to model diffusion phenomena. This model has the advantage of having least number of parameters while being valid on a wide frequency range and allows simulating an accurate dynamic response of the PEMFC.

In this model, the fuel cell is represented by an equivalent circuit, whose components are identified with the experimental technique of electrochemical impedance spectroscopy (EIS). This identification process is applied to a commercially available air-breathing PEMFC and its relevance is validated by comparing model simulations and laboratory experiments. Finally, the dynamic response derived from this fractional model is studied and validated experimentally.     

Design modeling of lithium-ion battery performance

A computer design modeling technique has been developed for lithium-ion batteries to assist in setting goals for cell components, assessing materials requirements, and evaluating thermal management strategies. In this study, the input data for the model included design criteria from Quallion, LLC for Gen-2 18650 cells, which were used to test the accuracy of the dimensional modeling. Performance measurements on these cells were done at the electrochemical analysis and diagnostics laboratory (EADL) at Argonne National Laboratory. The impedance and capacity related criteria were calculated from the EADL measurements. Five batteries were designed for which the number of windings around the cell core was increased for each succeeding battery to study the effect of this variable upon the dimensions, weight, and performance of the batteries. The lumped-parameter battery model values were calculated for these batteries from the laboratory results, with adjustments for the current collection resistance calculated for the individual batteries.     

Experimental measurement and analysis methods of electrochemical impedance spectroscopy for lithium batteries

电化学阻抗谱是一种重要的电化学测试方法,在电化学领域尤其是锂离子电池领域具有广泛的应用,如电导率、表观化学扩散系数、SEI的生长演变、电荷转移及物质传递过程的动态测量。本文介绍了电化学阻抗谱的基本原理、测试方法、测试注意事项、常用电化学阻抗测量设备及测试流程,并结合实际案例,具体分析了电化学阻抗谱在锂离子电池中的应用。     

Validation of a methodology for determining the PEM fuel cell complex impedance modelling parameters

In this paper, we present a new methodology for determining the complex impedance parameters for a Proton Exchange Membrane (PEM) Fuel Cell in order to have a general model for embedded diagnosis. The modelling of Fuel Cells is a very important phase because it contributes to a better understanding and representation of the internal phenomena in this type of generator. After obtaining the experimental results of the complex impedance using a realized test bench for Proton Exchange Membrane (PEM) Fuel Cell using an electrochemical method which is the electrochemical impedance spectroscopy (EIS), we treat these results with an identification algorithm based on least squares method in the objective to determine the variations laws of the complex impedance parameters then implement in a PEM Fuel Cell model with Matlab/Simulink software. The established model of the complex impedance is based on electrical components and takes into account the mathematical equations of the different elements. The simulation results of this implemented model inform us about the state of the PEM Fuel Cell and validate the choice of the parameters. The validation of this choice is done by a comparative study using residual analysis method between the experimental and the simulation results. The general model is obtained from the superposition of the measured and theoretical results.     

Estimation of fuel cell operating time for predictive maintenance strategies

Durability is one of the limiting factors for spreading and commercialization of fuel cell technology. That is why research to extend fuel cell durability is being conducted world wide. A pattern-recognition approach aiming to estimate fuel cell operating time based on electrochemical impedance spectroscopy measurements is presented here. It is based on extracting the features from the impedance spectra. For that purpose, two approaches have been investigated. In the first one, particular points of the spectrum are empirically extracted as features. In the second approach, a parametric modeling is performed to extract features from both the real and the imaginary parts of the impedance spectrum. In particular, a latent regression model is used to automatically split the spectrum into several segments that are approximated by polynomials. The number of segments is adjusted taking into account the a priori knowledge about the physical behavior of the fuel cell components. Then, a linear regression model using different subsets of extracted features is employed for an estimate of the fuel cell operating time. The effectiveness of the proposed approach is evaluated on an experimental dataset. Allowing the estimation of the fuel cell operating time, and consequently its remaining duration life, these results could lead to interesting perspectives for predictive fuel cells maintenance policy.     

Ageing behaviour of electrochemical double layer capacitors: Part I. Experimental study and ageing model

Different types of commercially available electrochemical double layer capacitors (EDLCs) were analysed in accelerated ageing tests by impedance spectroscopy. From these measurements the parameters of an impedance model were determined. The characteristic change of the impedance parameters is discussed and an ageing model for EDLCs is developed.     

Impedance characterization of high temperature proton exchange membrane fuel cell stack under the influence of carbon monoxide and methanol vapor

This work presents a comprehensive mapping of electrochemical impedance measurements under the influence of CO and methanol vapor contamination of the anode gas in a high temperature proton exchange membrane fuel cell, at varying load current. Electrical equivalent circuit model parameters based on experimental evaluation of electrochemical impedance spectroscopy measurements were used to quantify the changes caused by different contamination levels. The changes are generally in good agreement with what is found in the literature. It is shown that an increased level of CO contamination resulted in an increase in the high frequency and intermediate frequency impedances. When adding CO and methanol to the anode gas, the low frequency part of the impedance spectrum is especially affected at high load currents, which is clearly seen as a result of the high load current resolution used in this work. The negative effects of methanol vapor are found to be more pronounced on the series resistance. When CO and methanol vapor are both present in anode gas, the entire frequency spectrum and thereby all the equivalent circuit model parameters are affected. It is also shown that the trends of contamination effects are similar for all the test cases, namely, CO alone, methanol alone and a mix of the two, suggesting that effects of methanol may include oxidation into CO on the catalyst layer.     

Characterisation of a PEM electrolyser using the current interrupt method

A method is proposed to model the electrochemical characteristics of a Proton Exchange Membrane (PEM) electrolyser. The electrochemical characteristics, which include the Ohmic, activation and concentration losses, are modelled by means of an equivalent electric circuit impedance. The equivalent electric circuit impedance under consideration is the Randles–Warburg (RW) cell and the parameters are obtained through the current interrupt (CI) method. The CI method consists of two parts, 1) the natural voltage response (NVR) method to model the Ohmic losses, and 2) the current switching (CS) method to model the activation and concentration losses. A simulation model of the RW cell is used to verify and validate the CI method. Thereafter, the CI method is practically implemented and the results presented. Results show that the Ohmic losses correlates well with existing literature. The paper furthermore illustrates the capability of the CI method to visually illustrate the RW impedance through Nyquist diagrams. Nyquist diagrams are used to illustrate the concentration losses and indicate the degradation state of the PEM at specific operating conditions. Results show that the concentration losses decrease with an increase in the operating current density and temperature.     

An electrochemical impedance spectroscopy method for prediction of the state of charge of a nickel-metal hydride battery at open circuit and during discharge

A multivariate method for predicting state of charge, from electrochemical data, of a nickel-metal hydride (NiMH)-battery is presented. Partial least square (PLS) regression is used to evaluate electrochemical impedance spectra and predict state of charge. The impedance spectra are analysed in the frequency range 239–0.6 Hz. The impedance is measured for different states of charge at open-circuit conditions and during continuous discharge at loads ranging between 0.2 C and 0.8 C. When measuring the impedance during discharge, the AC-current signal is imposed on the DC-current. The predictive capability of the method is tested by a cross validation procedure and the root mean square error of prediction is 7% when using the outlier identification capability of the PLS-regression method. The state of charge is evaluated with a single model, independently of whether the cell is subjected to open-circuit or polarised conditions. The predictive performance of the present model decreases at state of charge values less than 10%.     

Simplified calculation of the area specific impedance for battery design

Battery design is a critical aspect of material and system development that leads to the commercialization of effective electrochemical energy storage systems. Successful modeling of battery designs relies upon accurate calculation of the area specific impedance (ASI). A simplified calculation of the ASI is presented that accounts for physical limitations without performing computationally expensive calculations. The limiting currents for transport within the electrolyte and within the intercalation materials are implemented into a linear form of the Butler-Volmer equation to calculate the interfacial impedance. Lithium-ion batteries are then designed to examine the effect of power to energy ratio on battery dimensions. A large ASI is shown to be detrimental to battery design regardless if the increase in impedance results from mass transport limitations or a reduction in electrochemical active area due to small electrode loadings. The smaller electrochemical active area does not increase the voltage losses of a battery when a constant C-rate is maintained. However, the higher ASI values from low electrode loadings require a larger separator and current collector area resulting in a greater battery volume and weight to achieve similar energy and power requirements when compared to a system with a lower ASI.     

On the electrochemical impedance spectroscopy of direct methanol fuel cell

The direct methanol fuel cell (DMFC) was operated under a variety of current densities to monitor the electrochemical impedance spectroscopy (EIS) for understanding its reaction mechanism. Based on the EIS analysis, the impedance of the cell reaction is divided into three components, two of them are current dependent and the remainder is current independent. Through detailed exploration of the impedance components, the high-frequency impedance was attributed to interfacial behavior, the medium-frequency impedance to electrochemical reactions, and the low-frequency impedance to the adsorption/relaxation of CO. Based on EIS analysis, a qualitative model is proposed to delineate the reaction mechanisms of DMFC, which is confirmed quantitatively by one set of equivalent circuit elements. The experimental data are satisfactorily consistent with the results simulated from the proposed model.     

Electrochemical modeling of lithium polymer batteries

An electrochemical model for lithium polymer cells was developed and a parameter set for the model was measured using a series of laboratory experiments. Examples are supplied to demonstrate the capabilities of the electrochemical model to obtain the concentration, current, and potential distributions in lithium polymer cells under complex cycling protocols. The modeling results are used to identify processes that limit cell performance and for optimizing cell design. Extension of the electrochemical model to examine two-dimensional studies is also described.     

Numerical analysis of the electrochemical impedance spectra of the cathode of direct methanol fuel cells

A mathematical model is developed to simulate the electrochemical impedance spectra (EIS) of the cathode of a direct methanol fuel cell (DMFC) based on the electrode kinetics and mass transports. Successful simulation of the impedance spectra confirms the usefulness of the model as a diagnostic tool for interpreting the impedance characteristics of the cathode. Numerically, the capacitive semicircle in the impedance pattern is ascribed to the charge transfer process and the inductive semicircle is mainly due to the CO adsorption relaxation. Results show that the impedance pattern is strongly dependent on the electrode potential, which can be used as a criterion for judging the relative effect of the methanol permeation on the cathode. Another capacitive semicircle appears and the charge transfer resistance is changed when the oxygen transport is limited. The effects of the methanol permeation on the impedance pattern are also delineated, indicating that the methanol permeation often leads to larger oxygen transport impedance and the charge transfer resistance of the DMFC cathode depends on the methanol permeation rate.     

Catalyst degradation diagnostics of proton exchange membrane fuel cells using electrochemical impedance spectroscopy

A previously validated equivalent circuit model, in which two resonant circuits were inserted to represent the processes in the catalyst layers, is applied to fit the electrochemical impedance spectroscopy results of a single proton exchange membrane fuel cell exposed to accelerated stress test targeting catalyst degradation. The simulation results of the applied equivalent circuit model show very good agreement with the experimental data. The applied model is able to extract contributions of each of the model elements to the cell degradation. The obtained results indicate that the cathode catalyst layer resonant loop parameters, together with the cathode charge transfer resistance and cathode double-layer capacitance, change the most during the accelerated stress test. If each of the elements of the cathode resonant loop can be associated with physical processes inside the catalyst layer, the model may be used to give more insight into the degradation effects on functioning of the catalyst layer. From the conducted electrochemical impedance spectroscopy analysis, it seems that the low-frequency intercept in Nyquist plot shows the most significant change with degradation, so it may be used directly as a sufficient indicator of fuel cell performance degradation due to catalyst layer degradation.     

Impedance studies of nickel hydroxide microencapsulated by cobalt

Nickel hydroxide is used as an active material in pasted-type nickel hydroxide electrodes for rechargeable alkaline batteries. The electrochemical impedance spectroscopes of different nickel hydroxide electrodes were measured. The results were analyzed using a standard equivalent circuit model including a Warburg impedance term. The Nyquist plots were used to interpret the characteristics of the different electrodes. The nickel hydroxide electrode deposited by cobalt has shown lower charge transfer resistance and higher electronic and protonic conductivity. © 1999 International Association for Hydrogen Energy. Published by Elsevier Science Ltd. All rights reserved.     

Non-dimensional analysis of PEM fuel cell phenomena by means of AC impedance measurements

AC impedance or electrochemical impedance spectroscopy (EIS) is becoming a fundamental technique used by researchers and scientists in proton exchange membrane (PEM) fuel cell analysis and development. In this work, in situ impedance measurements are presented for a series of operating conditions in a 50 cm² fuel cell. The electrode charge transfer resistance was determined from the corresponding arcs of the Nyquist diagrams. The analyses were performed for H₂/O₂ and H₂/air operation at different stoichiometric factors and reactant gases humidification. Characteristic time scales of charge transfer processes at the different operating conditions were estimated from the corresponding Bode plots. These values were used for a non-dimensional analysis of the different fuel cell electrochemical and transport processes, namely electrochemical reaction versus GDL reactant transport. Fuel cell adapted Damkhöler numbers are thus presented, where the results indicate that the GDL diffusion transport is the limiting process for the cases under analysis, especially when air is used as oxidant. Additional analysis of channel convective mass transport versus GDL diffusive mass transport is also presented.     

Development of a method to estimate the lifespan of proton exchange membrane fuel cell using electrochemical impedance spectroscopy

This paper proposes a new method for estimating the state and lifespan of fuel cells in operation by fuel cell equivalent impedance modeling by electrochemical impedance spectroscopy (EIS) and observing degradation. The performance change of fuel cells takes place in the form of changes in each parameter value comprising an equivalent AC impedance circuit; monitoring such changes allows for the prediction of the state and lifespan of a fuel cell. In the experiments, the AC impedance of high-temperature proton exchange membrane (PEM) fuel cells was measured at constant time intervals during their continuous operation for over 2200 h. The expression for the lifespan of a fuel cell was deduced by curve fitting the changes in each parameter to a polynomial. Electric double layer capacitance and charge transfer resistance, which show the reduction reaction of the cathode, were used as major parameters for judging the degradation; a method of using time constants is proposed to more accurately estimate the degree of degradation. In addition, an algorithm that can evaluate the soundness and lifespan of a fuel cell is proposed; it compares the measured time constant of the fuel cell being tested with that of average lifespan fuel cell.     

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

We develop a pseudo two-dimensional, isothermal transient model for a high temperature proton exchange membrane fuel cell. It takes into account the dynamic change of oxygen concentration in the cathode gas diffusion layer and in the cathode channel. The model can be used to simulate and analyze electrochemical impedance spectra of the cell in both potentiostatic and galvanostatic modes, current interrupt results and step changes in the cell current or potential. The model is validated by fitting experimental data.     

Non-destructive delamination detection in solid oxide fuel cells

A finite element model has been developed to simulate the steady state and impedance behaviour of a single operating solid oxide fuel cell (SOFC). The model results suggest that electrode delamination can be detected minimally-invasively by using electrochemical impedance spectroscopy. The presence of cathode delamination causes changes in the cell impedance spectrum that are characteristic of this type of degradation mechanism. These changes include the simultaneous increase in both the series and polarization resistances, in proportion to the delaminated area. Parametric studies show the dependence of these changes on the extent of delamination, on the operating point, and on the kinetic characteristics of the fuel cell under study.