Fractional order model for diagnosis of flooding and drying of the proton exchange membrane fuel cell

The diagnosis and control of PEMFCs hydration states depend on the reliable models and methods of monitoring of system operating. Impedance spectroscopy was generally used to describe fuel cell systems and derived impedance models. This study investigated the characterization and diagnosis of fuel cells by using fractional order impedance model as an explicit transfer function and factor design methodology (DOE) to determine the model parameters. The physical parameters appeared very sensitive to humidity and then used for monitoring and diagnosing of fuel cells. The proposed model is suitable to represent Randles impedance model equivalent electrical circuit enhanced by CPE, with the ability to generate the Nyquist impedance spectra easily for all conditions of relative humidity and operating time.The comparison between the literature experimental impedance spectra in both cases (drying and flooding), and the spectra simulated by the explicit fractional order impedance model demonstrated that the proposed model was robust and reliable and can, therefore, be integrated into the PEMFCs water management system.     

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.     

Dynamic modeling of electrical characteristics of solid oxide fuel cells using fractional derivatives

An efficient controller is greatly important for the quick load-following response of solid oxide fuel cell (SOFC) power systems, which is vital for the fuel utilization and the life of the stack. To design such a controller, an accurate dynamic model of SOFC electrical characteristics is critical. Here an integer order dynamic model is established by a transient equivalent circuit, and then a fractional order dynamic model is done in the perspective of the fractional derivatives theory. The parameters of the dynamic models then are optimized via genetic algorithms according to electrochemical impedance spectroscopy (EIS) experimental data. Finally, the dynamic response experiments from the models are studied. The results show that the fractional order dynamic model has higher accuracy for representing the dynamics of the SOFC electrical characteristics, which lays a solid foundation for the controller based on the accurate model.     

基于ALMBO算法的PEMFC分数阶时域子空间模型研究

针对质子交换膜燃料电池（PEMFC）发电过程复杂难以建模的问题,考虑PEMFC系统的分数阶特性,提出一种基于优化的分数阶时域子空间辨识方法,并建立PEMFC的分数阶状态空间模型。首先,将分数阶微分理论与子空间时域辨识方法相结合,采用Poisson滤波器对输入输出信号进行滤波处理,并引入权重矩阵提高辨识的精度;其次,对Poisson滤波器以及辨识的分数阶阶次寻优,提出一种变异反向学习的自适应帝王蝶优化算法（ALMBO）,在迁移算子中引入变异反向学习策略、并融入自适应权重来提高寻优的精度,防止陷入局部最优解。最后,通过仿真结果验证算法的有效性,所得的PEMFC辨识模型能准确描述PEMFC的动态过程。     

Electrochemical parameter identification—An efficient method for fuel cell impedance characterisation

Electrochemical parameter identification (EPI) is a novel, application-oriented characterisation method for fuel cell impedances. EPI strictly works in the time domain, with a model of the fuel cell impedance and measurements of the excitation and the response in the time domain. This approach reduces the measurement time considerably in comparison to frequency domain measurements for electrochemical impedance spectroscopy. The use of a superimposed signal as system excitation leads to less interference of the fuel cell operation than a current interrupt. Short measurement time and little interference enable an online application of the method during the operation of the fuel cell. A simple discrete-time model describing the dynamic electrical behaviour of the fuel cell is depicted as an equivalent circuit which consists of a voltage source and the impedance as internal resistance. The model parameters are identified by a hybrid optimisation algorithm using the sampled excitation and response signals. A comparison of measured impedance spectra at various operation conditions with impedance models identified by EPI shows very good agreement over a wide frequency range and emphasizes the reliability of EPI.     

Electrochemical AC impedance model of a solid oxide fuel cell and its application to diagnosis of multiple degradation modes

A finite element model of the impact of diverse degradation mechanisms on the impedance spectrum of a solid oxide fuel cell is presented as a tool for degradation mode identification. Among the degradation mechanisms that cause electrode active area loss, the attention is focused on electrode delamination and uniformly distributed surface area loss, which were found to cause distinct and specific changes in the impedance spectrum. Degradation mechanisms resulting in uniformly distributed reactive surface area loss include sintering, sulphur poisoning, and possibly incipient coke formation at the anode, and chromium deposition at the cathode. Parametric studies reveal the extent and limits of applicability of the model and detectability of the different degradation modes, as well as the influence of different cell geometries on the change in impedance behaviour resulting from the loss of active area. It is expected that this technique could form the basis of a useful diagnostic tool for both solid oxide fuel cell developers and users.     

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.     

Model based PEM fuel cell state-of-health monitoring via ac impedance measurements

The present paper deals with monitoring of flooding and drying out of a proton exchange membrane (PEM) fuel cell using a model-based approach coupled with ac impedance measurements. A study of the impedance response of a 150 cm² six-cell air/H₂ PEM fuel cell as a function of inlet gas relative humidity was carried out. Parameters of a Randles-like equivalent circuit were then fitted to the data. In order to improve the quality of the fit, the classical Randles cell was extended by changing the standard plane capacitor into a constant phase element (CPE). It was found that monitoring the evolution of the three resistances of this modified Randles model was an efficient and robust way of monitoring the state-of-health (SOH) of the fuel cell with respect to the water content of the membrane electrode assembly. Moreover, the non-integer power of the CPE was found to be statistically constant over a wide range of operating conditions, thus comforting the assumption that it has a physical meaning. Qualitative interpretation of the variation of the parameters as a function of the SOH is proposed in both flooded and dry conditions.     

Electric circuit modeling of fuel cell system including compressor effect and current ripples

This study aims to investigate the development of an Electrical Circuit Model (ECM) that represents the behavior of a PEM fuel cell system. The ECM parameters are identified based on sets of impedance data obtained by using a characterization process known as Electrochemical Impedance Spectroscopy (EIS). In this process, a small magnitude of alternating current sweeping a broad spectrum of frequencies is superimposed on a DC current drawn from the fuel cell while measuring the resulting voltage response. The measured impedance is fitted to an ECM using a nonlinear least-square fitting method. The proposed ECM is able to reflect the voltage response of the system to current ripples and represent the effect of the compressor. The proposed model is validated using a commercial fuel cell power module. In general, such model representation is useful for analyzing the effects of the operating conditions on the fuel cell performance, efficiency and durability. It also helps in comprehending the effects of current ripple on the fuel cell while operating with power-conditioning units     

A new parameter extraction method for accurate modeling of PEM fuel cells

In this paper, a new parameter extraction method for accurate modeling of proton exchange membrane (PEM) fuel cell systems is presented. The main difficulty in obtaining an accurate PEM fuel cell dynamical model is the lack of manufacturer information about the exact values of the parameters needed for the model. In order to obtain a realistic dynamic model of the PEM system, the electrochemical considerations of the system are incorporated into the model. Although many models have been reported in the literature, the parameter extraction issue has been neglected. However, model parameters must be precisely identified in order to obtain accurate simulation results. The main contribution of the present work is the application of the simulated annealing (SA) optimization algorithm as a method for identification of PEM fuel cell model parameter identification. The major advantage of SA is its ability to avoid becoming trapped in local minimum, as well as its flexibility and robustness. The parameter extraction and performance validation are carried out by comparing experimental and simulated results. The good agreement observed confirms the usefulness of the proposed extraction approach together with adopted PEM fuel cell model as an efficient tool to help design of power fuel cell power systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Study of the electrochemical behaviour of a 300 W PEM fuel cell stack by Electrochemical Impedance Spectroscopy

Electrochemical Impedance Spectroscopy (EIS) is a suitable and powerful diagnostic testing method for fuel cells because it is non-destructive and provides useful information about fuel cell performance and its components. In this work, EIS measurements were carried out on a 300 W stack with 20 elementary cells. Electrochemical impedance spectra were recorded either on each cell or on the stack. Parameters of a Randles-like equivalent circuit were fitted to the experimental data. In order to improve the quality of the fit, the classical Randles cell was extended by changing the standard plane capacitor into a constant phase element (CPE). The effects of output current, cell position, operating temperature and humidification temperature on the impedance spectra were studied.     

An EIS alternative for impedance measurement of a high temperature PEM fuel cell stack based on current pulse injection

In this paper a method for estimating the fuel cell impedance is presented, namely the current pulse injection (CPI) method, which is well suited for online implementation. This method estimates the fuel cell impedance and unlike electrochemical impedance spectroscopy (EIS), it is simple to implement at a low cost. This makes it appealing as a characterization method for on-line diagnostic algorithms. In this work a parameter estimation method for estimation of equivalent electrical circuit (EEC) parameters, which is suited for on-line use is proposed. Tests on a 10 cell high temperature PEM fuel cell show that the method yields consistent results in estimating EEC parameters for different current pulse at different current loads, with a low variance. A comparison with EIS shows that despite its simplicity the response of CPI can reproduce well the impedance response of the high and intermediate frequencies.     

2D modeling of a defective PEMFC

A dysfunctioning of the heart of the fuel cell might affect the whole system, and thus the demand of electric power. To be able to estimate the damage of the fuel cell, the default has to be detected precisely. As it is well known, the physico-chemical processes involved in proton exchange membrane fuel cell (PEMFC) are strongly coupled, as such that putting apart a phenomenon by experimental measurement can be quite difficult. To this end, simulations of an online or offline diagnosis, for instance by electrochemical impedance spectroscopy (EIS) method are interesting. It can help also to analyze what happens locally in the heart of cell. The main aim of the presented work is to highlight the interest of using PEMFC dynamic model as a diagnosis tool. To illustrate this potential, EIS method has been implemented in 2D dynamic single cell in both simulated cases of defective and healthy cells.     

Short-stack modeling of degradation in solid oxide fuel cells: Part I. Contact degradation

As the first part of a two paper series, we present a two-dimensional impedance model of a working solid oxide fuel cell (SOFC) to study the effect of contact degradation on the impedance spectrum for the purpose of non-invasive diagnosis. The two dimensional modeled geometry includes the ribbed interconnect, and is adequate to represent co- and counter-flow configurations. Simulated degradation modes include: cathode delamination, interconnect oxidation, and interconnect-cathode detachment. The simulations show differences in the way each degradation mode impacts the impedance spectrum shape, suggesting that identification is possible. In Part II, we present a sensitivity analysis of the results to input parameter variability that reveals strengths and limitations of the method, as well as describing possible interactions between input parameters and concurrent degradation modes.     

Degradation prediction model for proton exchange membrane fuel cells based on long short-term memory neural network and Savitzky-Golay filter

Proton exchange membrane fuel cell (PEMFC) as a promising green power source, can be applied to vehicles, ships, and buildings. However, the lifetime of the fuel cell needs to be prolonged in order to achieve a wide range of applications. Consequently, the prediction of the health state draws attention lately and is critical to improving the reliability of the fuel cell. Since the degradation mechanism of the fuel cell is not fully understood, the data-driven method is very suitable for designing degradation prediction models. However, the data-driven method usually requires a lot of data, which is difficult to be obtained. To solve the issues, we propose a degradation prediction model for PEMFC based on long short-term memory neural network (LSTM) and Savitzky-Golay filter in this paper. First, we select the monitoring parameters for building the degradation prediction model by analyzing the degradation phenomenon of the fuel cell. Then, Savitzky-Golay filter is utilized to smooth out the selected data, and the sliding time window is used to generate training samples. Finally, the LSTM is applied to establish the degradation prediction model. Moreover, the dropout layer and mini-batch method are adopted to improve the model generalization ability. We use an actual aging data of the fuel cell to verified the proposed degradation prediction model. The results demonstrate that the proposed model can precisely predict the fuel cell degradation. It is worth mentioning that the determination coefficient (R²) of the test set based on the model trained by 25% of data is 0.9065.     

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.     

AC impedance technique in PEM fuel cell diagnosis—A review

Because the AC impedance technique, also known as electrochemical impedance spectroscopy (EIS), is being utilized by more and more researchers in proton exchange membrane (PEM) fuel cell studies, the technique has developed into a primary tool in such research. In this paper the recent work on PEM fuel cells using the AC impedance technique is reviewed. Both in situ and ex situ impedance measurements are discussed, with primary focus on the in situ measurements. Within the domain of in situ studies, various methods for measuring the impedance of a PEM fuel cell are examined, and typical impedance spectra in several common scenarios are presented. Representative applications of the AC impedance technique in PEM fuel cell research are also discussed. Finally, the necessity of a time domain rapid AC impedance technique is briefly discussed.     

PEMFC impedance spectroscopy using synthetic wide-band signals

The “state of health” of a fuel cell can be determined by the study of its complex impedance in a frequency domain, usually using impedance spectroscopy (IS) method. In our days, to characterize a PEM using this method, a sine signal sweep is used. The IS is based on the complex measurement of the impedance of a cell along a frequency domain, depending on the electrochemical state of the cell. The main advantage of the IS is the faithfulness between its results and the theoretical ones. These results are analyzed using the electrical Randles model. Our work presents an innovative method to measure the IS. It introduces a system to dramatically reduce the measurement time using as an alternative of the sine signal, a frequency domain synthetic wide-band signal. During the tests, a theoretical wide-band signal is built in the frequency domain. The signal is converted into a temporal one and is used as a stimulus for the fuel cell. The response in terms of cell voltage is captured and the impedance measured. This answer is defined in the same frequency range than the stimulus. The time required for the measurement corresponds to the time of the stimulus and it is in the range of the lower cut-off frequency. The system used as test-bench is composed by an electronic circuit and a PC based software for the signal analysis. This system was built and tested with good results using a PEMFC.