Electrochemical low-frequency impedance spectroscopy algorithm for diagnostics of PEM fuel cell degradation

Prognostics and health management for fuel cells in real-world applications are important for optimization of lifetime and operation. A parameter that has been shown to indicate the state of ageing is the low-frequency intercept with the real axis of the Nyquist diagram in a fuel cell's impedance spectrum. This article presents a method for direct identification of this parameter, without the need to carry out a full electrochemical impedance spectroscopy, and with an algorithm that can be realized within a typical fuel-cell control system. The proposed method is based on relay excitation feedback, a proven solution from controller tuning.     

Analysis of the electrochemical behaviour of polymer electrolyte fuel cells using simple impedance models

The analysis of the electrochemical behaviour of polymer electrolyte fuel cells (PEFC) both in time and frequency domain requires appropriate impedance models. Simple impedance models with lumped parameters as resistances and capacitances or Warburg impedances do have limitations: often the validity is limited to a certain frequency range, effects at very low or very high frequencies can not be described properly.     

Electrochemical impedance diagnosis of micro porous layer in polymer electrolyte membrane fuel cell electrodes

In the present study, Electrochemical Impedance Spectroscopy (EIS) is used to evaluate two different types of gas diffusion electrodes for Polymer Electrolyte Membrane Fuel Cells (PEMFC). The over potential losses due to the components are determined without any reference electrode using symmetric gas supply of hydrogen or oxygen at various conditions viz., open circuit potential (OCP), various load up to 0.7 A cm⁻², and various humidity conditions. Though it is very clear that the cathode impedance is a major contributor for voltage loss, it is observed that the two type of electrodes with different micro-porous layers (DSGDL and SSGDL), show different behavior with respect to operating conditions like dry gas operation, humid condition etc., The DSGDL is favorable for operating the cell at higher temperature and relative humidity while SSGDL is favorable under dry gas operation. However at higher current density and with humidity, Nernst diffusion plays a major contribution. The Nernst diffusion coefficient decreases with increasing current density for DSGDL and increasing for SSGDL, suggesting that the gas diffusion electrodes need to be engineered depending on the operating conditions and current density.     

High temperature PEM fuel cell performance characterisation with CO and CO2 using electrochemical impedance spectroscopy

In this work, extensive electrochemical impedance measurements have been conducted on a 45 cm² BASF Celtec P2100 high temperature PEM MEA. The fuel cell performance has been examined subject to some of the poisoning effects experienced when running on a reformate gas. The impedance is measured at different temperatures, currents, and different content of CO, CO₂ and H₂ in the anode gas. The impedance spectrum at each operating point is fitted to an equivalent circuit and an analysis to identify the different mechanisms governing the impedance is performed. The trends observed, when varying the operating conditions under pure H₂, generally show good agreement with results from the literature. When adding CO and CO₂ to the anode gas the entire frequency spectrum is affected, and especially the measurements conducted at low temperatures and high CO concentrations reveal undesirable transient effects.     

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 fault diagnosis model for proton exchange membrane fuel cell based on impedance identification with differential evolution algorithm

An effective online fault diagnosis system is of great significance to improve the reliability of fuel cell vehicles. In this paper, a fault diagnosis model for proton exchange membrane fuel cells is proposed. Firstly, the tests of electrochemical impedance spectroscopy under different fault types (flooding, drying, air starvation) and fault degrees (minor, moderate, severe) are carried out, and each polarization loss of the fuel cell is denoted by an equivalent circuit model (ECM). Then, the parameters of the ECM are identified by the proposed random mutation differential evolution algorithm. Furthermore, the parameters identified under different fault conditions are used to train and test a probabilistic neural network-based fault diagnosis model. The fault diagnosis model achieves diagnosis accuracies of 100% for the fault type and 96.67% for the fault degree. By setting operating conditions with different fault degrees, the fault diagnosis model proposed in this paper can realize the fault type and fault degree diagnosis, effectively avoiding the misjudgment of fault types, and is effective for improving the reliability of the fuel cell system.     

A semi-empirical method for electrically modeling of fuel cell: Executed on a direct methanol fuel cell

In this paper, a novel semi-empirical modeling method to mathematically derive a nonlinear equivalent circuit from a special group of impedance fuel cell models is proposed. As an example, a 5-cm² direct methanol fuel cell (DMFC) was modeled by this method. The derived equivalent circuit is composed of lumped nonlinear resistors, capacitors and an inductor. The nonlinear circuit has an impedance equivalent to the target fuel cell in various operating conditions and provides a good approximation of the static and transient behaviors of the fuel cell. The equivalent circuit fuel cell model was validated by comparing its numerical simulation results with its polarization curve and the dynamic behavior of the target DMFC. These comparisons were performed while the DMFC was operating under square current pulses with different upper and low current levels.     

Analytic parameter identification of proton exchange membrane fuel cell catalyst layer using electrochemical impedance spectroscopy

A finite transmission line is proposed for proton exchange membrane fuel cell reaction layer, when the faradic current is absent due to purging of Inert gas at the back of cathode and anode. Also a finite transmission line is presented when a charge transfer accrued among catalyst and electrolyte interface. The electrochemical impedances of finite transmission lines are computed using MATLAB software. Relative to the orders and types of the evaluated impedances, some relations to determine and identify the parameters of the proposed models are derived. In first model, it is shown that the electrical elements of transmission line can be extracted explicitly from the Nyquist and Bode diagrams whereas for the second one, some of the parameters cannot directly be investigated. However, using a numerical procedure, some valuable results about parameter variations are obtained.     

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.     

An impedance-based predictive control strategy for the state-of-health of PEM fuel cell stacks

This work presents a control strategy for PEM fuel cell systems based on simultaneous impedance measurements on single cells. This control strategy distinguishes between flooding and drying of the cells in a stack and helps to run the stack at an optimal operating point. In the presented experiments, it has been found that impedance measurements can detect flooding phenomena in single cells minutes before they can be seen in related polarisation curves. It is shown that impedance measurements at two specific frequencies, one high and one low frequency impedance, are sufficient to predict voltage drops caused by flooding and drying. In flooding mode, the imaginary part of the low frequency impedance changes while the high frequency impedance remains stable and vice versa in drying mode. This technique reduces measuring time compared to the measurement of whole impedance spectra, without losing important information for the control of the system.     

Performance and endurance of a high temperature PEM fuel cell operated on methanol reformate

This paper analyzes the effects of methanol and water vapor on the performance of a high temperature proton exchange membrane fuel cell (HT-PEMFC) at varying temperatures, ranging from 140 °C to 180 °C. For the study, a H₃PO₄ – doped polybenzimidazole (PBI) – based membrane electrode assembly (MEA) of 45 cm² active surface area from BASF was employed. The study showed overall negligible effects of methanol-water vapor mixture slips on performance, even at relatively low simulated steam methanol reforming conversion of 90%, which corresponds to 3% methanol vapor by volume in the anode gas feed. Temperature on the other hand has significant impact on the performance of an HT-PEMFC. To assess the effects of methanol-water vapor mixture alone, CO₂ and CO are not considered in these tests. The analysis is based on polarization curves and impedance spectra registered for all the test points. After the performance tests, endurance test was performed for 100 h at 90% methanol conversion and an overall degradation rate of −55 μV/h was recorded.     

Investigating the effects of methanol-water vapor mixture on a PBI-based high temperature PEM fuel cell

This paper investigates the effects of methanol and water vapor on the performance of a high temperature proton exchange membrane fuel cell (HT-PEMFC). A H₃PO₄-doped polybenzimidazole (PBI) membrane electrode assembly (MEA), Celtec P2100 of 45 cm² of active surface area from BASF was employed. A long-term durability test of around 1250 h was performed, in which the concentrations of methanol-water vapor mixture in the anode feed gas were varied. The fuel cell showed a continuous performance decay in the presence of vapor mixtures of methanol and water of 5% and 8% by volume in anode feed. Impedance measurements followed by equivalent circuit fitting revealed that the effects were most significant for intermediate-high frequency resistances, implying that charge transfer losses were the most significant losses. Vapor mixture of 3% in feed, however, when introduced after operation at 8%, showed positive or no effect on the cell's performance in these tests.     

Simplified model for evaluating ripple effects on commercial PEM fuel cell

In this paper a simple model for evaluating current ripple effects on commercial PEM fuel cells is presented. The model is formulated starting from the Randles equivalent circuit and extending it assuming a dielectric relaxation of the material to represent dynamic processes in the frequency range typical of inverter current ripple. The proposed equivalent circuit is experimentally validated on a 14 kW commercial Morphic PEM fuel cell at the frequencies of interest. Finally the effects of current ripple on losses and fuel cell efficiency are discussed.     

Performance of high temperature fuel cells with different types of PBI membranes as analysed by impedance spectroscopy

In order to study how PBI membranes influence the operation of HT-PEFC cathode we analyse the performance of HT-PEFC based on three different PBI membrane types (meta-PBI, ABPBI and PBI-O-PhT) by means of stationary voltamperometry and impedance spectroscopy. For impedance spectra interpretation we use an equivalent circuit containing transmission line distributed element. This approach allows us to measure the distributed ohmic resistance of proton transport inside cathode catalyst layer. It is shown that this resistance depends on the membrane type used and has even more pronounced influence on the FC performance than ohmic resistance of the membrane itself.     

Application of the improved chaotic grey wolf optimization algorithm as a novel and efficient method for parameter estimation of solid oxide fuel cells model

In this paper, important functional parameters of solid oxide fuel cells are identified by introducing a novel high-speed optimization method, namely adaptive chaotic grey wolf optimization algorithm. The suggested optimization method is obtained by combining the adaptive grey wolf optimization and chaotic grey wolf optimization algorithms. The chaotic algorithm is applied to the basic grey wolf optimization to achieve higher convergence speed, keep the population's diversity, and provide an initial population with uniform distribution. Besides, a nonlinear convergence factor is defined for balancing the global and local exploration abilities. Employing the improved convergence factor resulted in a new version of the grey wolf optimization algorithm, namely adaptive grey wolf optimization algorithm. Adaptive chaotic grey wolf optimization algorithm adopts the advantages of both chaotic grey wolf optimization and adaptive grey wolf optimization methods simultaneously. The adaptive grey wolf optimization algorithm is applied to a 5 kW dynamic tubular stack. The results of the simulation report the lowest values of mean squared error, higher accuracy, higher robustness, and high convergence speed for the adaptive grey wolf optimization algorithm compared to some well-known optimization methods. Besides, the proposed method shows a good agreement with experimental results with lower computational difficulty.     

Electrochemical characterisation of solid oxide cell electrodes for hydrogen production

Oxygen electrodes and steam electrodes are designed and tested to develop improved solid oxide electrolysis cells for H₂ production with the cell support on the oxygen electrode. The electrode performance is evaluated by impedance spectroscopy testing of symmetric cells at open circuit voltage (OCV) in a one-atmosphere set-up. For the oxygen electrode, nano-structured La_0.75Sr_0.25MnO₃ (LSM25) is impregnated into a LSM25/yttria stabilised zirconia (YSZ) composite, whereas for the steam electrode, nano-structured Ni and Ce_0.8Gd_0.2O_2−δ (CGO) is impregnated into a Sr_0.94Ti_0.9Nb_0.10O_3−δ (STN) backbone. In the present study, the best performing oxygen electrode is a LSM25-YSZ composite with 20% porosity and impregnated with a LSM25 solution measuring a polarisation resistance (R_p) of 0.12 Ω cm² at 850 °C in oxygen. For the steam electrode, the best performance is obtained for a STN backbone, sintered at 1200 °C and impregnated with CGO/Ni, with an R_p of 0.08 Ω cm² at 850 °C in 3% H₂O/H₂.     

An improved TLBO with elite strategy for parameters identification of PEM fuel cell and solar cell models

Clean and renewable energy generation and supply has drawn much attention worldwide in recent years, the proton exchange membrane (PEM) fuel cells and solar cells are among the most popular technologies. Accurately modeling the PEM fuel cells as well as solar cells is critical in their applications, and this involves the identification and optimization of model parameters. This is however challenging due to the highly nonlinear and complex nature of the models. In particular for PEM fuel cells, the model has to be optimized under different operation conditions, thus making the solution space extremely complex. In this paper, an improved and simplified teaching-learning based optimization algorithm (STLBO) is proposed to identify and optimize parameters for these two types of cell models. This is achieved by introducing an elite strategy to improve the quality of population and a local search is employed to further enhance the performance of the global best solution. To improve the diversity of the local search a chaotic map is also introduced. Compared with the basic TLBO, the structure of the proposed algorithm is much simplified and the searching ability is significantly enhanced. The performance of the proposed STLBO is firstly tested and verified on two low dimension decomposable problems and twelve large scale benchmark functions, then on the parameter identification of PEM fuel cell as well as solar cell models. Intensive experimental simulations show that the proposed STLBO exhibits excellent performance in terms of the accuracy and speed, in comparison with those reported in the literature.     

Online impedance spectrum measurement of fuel cells based on Morlet wavelet transform

An online impedance calculation method for fuel cells is proposed in this paper. A periodic square wave is selected as the standard excitation current and injected into a fuel cell. Then, the impedance spectrum is obtained by converting the excitation current and response voltage to the frequency domain with the Morlet wavelet. The accuracy of the calculated impedance is firstly tested offline under the stand excitation current condition, and the relative errors of the real part and imaginary part are within 5% and 10%, respectively. To calculate the impedance automatically, a search method is proposed to locate the position of the translation parameters autonomously. Besides, this paper investigates the effects of the stable time and the excitation current form on the calculation results and recommends the excitation current parameters. Finally, an implementation scheme for online impedance measurement is given.     

Design of experiment techniques for fuel cell characterisation and development

Designs of Experiments (DoE) can be of immediate relevance for various research works conducted in the Fuel Cell (FC) area. DoE techniques allow efficient test definitions for rapid conceptions and well-organised characterisations of FC materials and components, individual cells, stacks or even complete generators. In the DoE method, some statistic-based models can be proposed in pre-stages of physical models. The statistical/numerical relations are used to predict the behaviour of the investigated systems as a function of various operating parameters. Some control strategies can also be developed to optimise relevant criteria like FC voltage, fuel consumption, and maximal electrical power or stack lifetime.