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.     

Water content diagnosis for proton exchange membrane fuel cell based on wavelet transformation

The fuel cell reliability and durability are still the main factors limiting the large scale commercialization. To a certain degree, water content, transportation, distribution and state in the fuel cell influence the fuel cell State of Health (SOH). However, it's very difficult to measure water content inside fuel cell directly. The PEMFC system voltage fluctuate during hydrogen purging process, due to the removal of liquid water will affect the reactants transformation. Different internal water content will cause different voltage fluctuations. For this characteristic, The Energy Intensity of Reconstructed Vibrating Voltage (EIV) based on wavelet transformation is proposed and validated in this paper. The boundary value of EIV is determined to be 0.1 through experiments. The results show that the fuel cell voltage drop is reduced to 0.32 V/h from 1.39 V/h by using this method to avoid anode flooding. By several PEMFC system experiment results in test bench, this method can diagnosis the water content in PEMFC properly.     

Collaborative simulation for dynamical PEMFC power systems

In this paper a collaborative simulation platform for proton exchange membrane fuel cell (PEMFC) power systems is presented, where the stack is simulated by a two-phase distributed parameter model and the auxiliary units by lumped parameter models. By exchanging the dynamic data between the external load/auxiliary units and PEMFC stack, dynamic simulation of PEMFC stack has been carried out during the load changes for various states associated with different characteristic variables. The internal states of the stack can be observed due to variation of external load/auxiliary units. Numerical experiments are provided for a special case with multiple cycles of load changes derived from an acceleration mode of a fuel cell vehicle. The numerical results demonstrate that the “undershoot” of output voltage is due to the response lag of the auxiliary units and liquid water accumulation in the fuel cell stack.     

Disclosure of the internal transport phenomena in an air-cooled proton exchange membrane fuel cell—part III: Performance research based on qualitative comparisons between modeling and experimental results

The validation of a computational fluid dynamics model for a proton exchange membrane fuel cell (PEMFC) is normally conducted by the experimental I–V performance curve. However, it seems this method is not solid enough. In the meantime, it's difficult to conduct the item-to-item quantitative comparisons between the internal distributions acquired from numerical and testing results. Therefore, in this paper, as the first attempt, qualitative comparisons between the modeling and experimental results are conducted based on the three important parameters of an air-cooled PEMFC (air stoichiometric ratio, air relative humidity, cathode flow field design) to explore the trends of the related fuel cell I–V performance curves and internal resistances. The internal resistances are tested using the EIS technique and differentiated by an equivalent circuit model. Conclusions show that the qualitative comparisons between the numerical and testing results support each other well and new results are found based on the comparisons. Finally, discussions on the sensitivity based on the experimental EIS results are conducted to explore the response degree of the total resistance to the air stoichiometric ratio, the air relative humidity and the cathode flow field design.     

Model parameters identification of the PEMFCs using an improved design of Crow Search Algorithm

There is an increasing trend for fuel cell systems applications in electricity generation systems instead of traditional power generation systems because of their advantages such as high efficiency and almost no environmental pollution, desirable dynamic response, and reliability. Due to this reason, herein, a new method has been presented for optimum identification of the model of the proton exchange membrane fuel cell (PEMFC) model. The major concept is to lessen the sum of squared error (SSE) amount of the observed output voltage and the output voltage of the PEMFC stack by an improved version of Crow Search optimizer (ICSO). To validate the suggested technique, it is applied to two studied cases and the achievements are put in comparison with several newest optimizers, which are Genetic algorithm (GA), Grasshopper Optimizer (GHO), and Salp Swarm Optimizer (SSO). The achievements show that the suggested ICSO gives a better superiority to the other comparative algorithms for optimum estimation of the PEMFC model.     

Dynamic modeling of a proton exchange membrane fuel cell system with a shell-and-tube gas-to-gas membrane humidifier

The proton exchange membrane fuel cell (PEMFC) system with a shell-and-tube gas-to-gas membrane humidifier is considered to be a promising PEMFC system because of its energy-efficient operation. However, because the relative humidity of the dry air flowing into the stack depends on the stack exhaust air, this system can be unstable during transients. To investigate the dynamic behavior of the PEMFC system, a system model composed of a lumped dynamic model of an air blower, a two-dimensional dynamic model of a shell-and-tube gas-to-gas membrane humidifier, and a one-dimensional dynamic model of a PEMFC system is developed. Because the water management during transient of the PEMFC system is one of the key challenges, the system model is simulated at the step change of current. The variations in the PEMFC system characteristics are captured. To confirm the superiority of the system model, it is compared with the PEMFC component model during transients.     

A novel densely connected neural network for proton exchange membrane fuel cell fault diagnosis

It is of great significance to perform proton exchange membrane fuel cell (PEMFC) fault diagnosis and take action timely to mitigate or even eliminate the faults, which can strengthen PEMFC reliability and durability. In previous studies, cell voltage is extensively used for PEMFC fault diagnosis. However, there exists similar cell voltage drop phenomenon as different PEMFC faults occur, especially for faults like flooding and air starvation having extremely similar voltage dynamic variation, which makes it difficult to capture the features sensitive to faults. Moreover, cell voltages collected from different MEAs follow different distributions even in the same operation condition, which challenges the diagnosis consistency of fault diagnosis methods. In this paper, in order to break through the hindrances, a novel densely connected neural network codenamed Inc-DenseNet is proposed for PEMFC fault diagnosis, which integrates advantages of InceptionNet and DenseNet to extract more specific and robust features from cell voltage. In the analysis, the collected PEMFC voltage signal is transformed into 2D image data, which is then used to train the Inc-DenseNet. Results demonstrate that with the trained Inc-DenseNet, the diagnostic accuracy for four PEMFC states of health (normal, flooding, dehydration, air starvation) can reach 95.3%, especially for flooding and air starvation. In addition, by using the voltage datasets collected from two different MEAs, the generalization capacity of the Inc-DenseNet is proved. With the findings, the proposed network Inc-DenseNet can not only achieve high-precision fault diagnosis, but also has a high computing efficiency, which makes it promising in real-time PEMFC fault diagnosis in the future.     

Investigation of PEMFC fault diagnosis with consideration of sensor reliability

Despite the wide range of applications for the polymer electrolyte membrane fuel cell (PEMFC), its reliability and durability are still major barriers for further commercialization. As a possible solution, PEMFC fault diagnosis has received much more attention in the last few decades. Due to the difficulty of developing an accurate PEMFC model incorporating various failure mode effects, data-driven approaches are widely used for diagnosis purposes. These methods depend largely on the quality of sensor measurements from the PEMFC. Therefore, it is necessary to investigate sensor reliability when performing PEMFC fault diagnosis.In this study, sensor reliability is investigated by proposing an identification technique to detect abnormal sensors during PEMFC operation. The identified abnormal sensors will be removed from the analysis in order to guarantee reliable diagnostic performance. Moreover, the effectiveness of the proposed technique is investigated using test data from a PEMFC system, where fuel cell flooding is observed. During the test, due to accumulation of liquid water inside the PEMFC, the humidity sensors will give misleading readings, and flooding cannot be identified correctly with inclusion of these humidity sensors in the analysis. With the proposed technique, the abnormal humidity measurements can be detected at an early stage. Results demonstrate that by removing the abnormal sensors, flooding can be identified with the remaining sensors, thus reliable health monitoring can be guaranteed during the PEMFC operation.     

Effect of channel-rib width ratio and relative humidity on performance of a single serpentine PEMFC based on electrochemical impedance spectroscopy

The geometry configuration of proton exchange membrane fuel cell (PEMFC) which is considered as a promising energy conversion device has great influence on PEMFC performance. In this paper, effect of channel-to-rib width ratio and relative humidity of reactant gas on the performance are compared based on two single PEMFCs. The EIS testing results below 50 A are given and analyzed. The results obtained from polarization curves, power density curves and EIS fitting results prove that: 1. Compared with cell 3:4, the anode high humidification has a greater addition to the performance of cell 1:1; 2. PEMFCs with different geometry configurations of flow field have their own suitable working condition ranges; 3. The charge transfer resistance is the dominating factor when current loading is below 2.0 A cm^?2.     

Coupling RTD and EIS modelling to characterize operating non-uniformities on PEM cathodes

Large PEM cells will be used in future proton exchange membrane fuel cell (PEMFC) power plants and appropriate tools are therefore be needed to study their behaviour. One approach to understanding single cell behaviour involves using mathematical models. The numerous techniques used in this work to describe PEM electrode behaviour require different scientific disciplines: chemical engineering and electrochemistry. This study proposes combining residence time distribution (RTD) and electrochemical impedance spectroscopy (EIS). The investigation focuses on cathodic DC and AC responses where over-voltage is critical. Results demonstrate that although gas distribution does not cause additional loops on impedance diagrams, it is strongly related to both the shape and amplitude of these diagrams. The simulations have drawn attention to operating conditions that can threaten the life of the PEM cell: under these setting points EIS method is not sufficient to detect this risk.     

Impedance-based diagnosis of polymer electrolyte membrane fuel cell failures associated with a low frequency ripple current

This work deals with a diagnosis of cathode flooding and membrane drying associated with a low frequency ripple current of a polymer electrolyte membrane fuel cell (PEMFC) based on impedance measurement on 12 single cells using electrochemical impedance spectroscopy (EIS). Average values of the identified model parameters obtained from direct measurement of the impedance curves of 12 single cells obtained after cycling for hours at variable frequencies, it has been found that impedance magnitude of a fuel cell injecting a low frequency ripple current (100 Hz) increased when compared with those injecting high frequency ripple currents (1 kHz and 10 kHz). Based on these investigations, additional impedance measurements are directly conducted to gain insight into cathode flooding and membrane drying concerning a low frequency ripple current. Regardless of operating frequency of ripple current, two PEMFC failures lead to an increase in the impedance magnitude in comparison with that of a fresh cell. Specifically, it is shown that a low frequency ripple current more accelerates the PEMFC degradation associated with two PEMFC failures.     

Characterization and experimental results in PEM fuel cell electrical behaviour

A control oriented electrochemical static model of a proton exchange membrane fuel cell (PEMFC) stack is developed in this paper. Even though its validation is performed on a specific 7-cell PEMFC stack fed by humidified air and pure hydrogen, the methodology and fit parameters can be applied to different fuel cell systems with minor changes. The fuel cell model was developed combining theoretical considerations and semi-empirical analysis based on the experimental data. The proposed model can be successfully included into a larger dynamic subsystem to complete the power generation system.     

The optimal performance estimation for an unknown PEMFC based on the Taguchi method and a generic numerical PEMFC model

In this paper, a new approach to estimate the optimal performance of an unknown proton exchange membrane fuel cell (PEMFC) has been proposed. This proposed approach combines the Taguchi method and the numerical PEMFC model. Simulation results obtained using the Taguchi method help to determine the value of control factors that represent the tested unknown PEMFC. The objective of reducing both fuel consumption and operation cost can be achieved by determining the parameters for the unknown PEMFC. In addition, the optimal operation power for the tested unknown PEMFC can also be predicted. Experimental results on the test equipment show that the proposed approach is effective in optimal performance estimation for the tested unknown PEMFC, thus demonstrating the success achieved by combining the Taguchi method and the numerical PEMFC model.     

Adaptive thermal control for PEMFC systems with guaranteed performance

Proton exchange membrane fuel cell (PEMFC) s are faced with dynamical load scenario in practical applications, and the resulting temperature variation will decrease the performance and consequently shorten the fuel cell lifetime. To address this problem, a control strategy for regulating the stack temperature is proposed in this paper. Firstly, a thermal management-oriented dynamic model of a water-cooled PEMFC system is built to facilitate the control design. Secondly, considering that the stack temperature should be maintained in a certain range regardless of the dynamical changing current demand, a Barrier Lyapunov function is employed to construct a feedback error of the stack temperature. Thirdly, a set of adaptation laws is designed to estimate the unknown parameters related to the gas flow rates in the flow fields. Particularly, a dynamic inversion tracking methodology is applied to design the non-affine input. A Lyapunov method based analysis demonstrates the stability and convergence of the closed-loop properties. Simulation results are provided to show that the proposed control strategy can satisfy all the control objectives and enhance the control performance compared to the proportional-integral controlled case.     

Degradation prediction of proton exchange membrane fuel cell using auto-encoder based health indicator and long short-term memory network

As durability of proton exchange membrane fuel cell (PEMFC) remains as the main obstacle for its larger scale commercialization, predicting PEMFC degradation progress is thus an effective way to extend its lifetime. To realize reliable prediction, a novel health indicator (HI) extraction method based on auto-encoder is proposed in this paper, with which PEMFC future voltage can be predicted by long short-term memory network (LSTM). The effectiveness and robustness of proposed approach is investigated with test data simulating vehicle operation conditions, and accurate prediction performance can be observed, with the maximum root mean square error (RMSE) of 0.003513. Moreover, by comparing with two commonly prognostic methods including attention-based gated recurrent unit network and polarization model-LSTM, the proposed method can provide better predictions under various operating conditions. Furthermore, with the proposed method, the degradation mechanism of PEMFC can also be analyzed. Therefore, the proposed prognostic method can predict reliable PEMFC degradation progress and its corresponding degradation mechanisms, which will be beneficial in practical PEMFC systems for taking appropriate strategies to guarantee PEMFC durability.     

Preparation of microporous layer for proton exchange membrane fuel cell by using polyvinylpyrrolidone aqueous solution

A new method of preparing microporous layer (MPL) for proton exchange membrane fuel cell (PEMFC) was presented in this paper. Considering the bad dispersion of PTFE aqueous suspension in the carbon slurry based on ethanol, polyvinylpyrrolidone (PVP) aqueous solution was used to prepare carbon slurry for microporous layer. The prepared gas diffusion layers (GDLs) were characterized by scanning electron microscopy, contact angle system and pore size distribution analyzer. It was found that the GDL prepared with PVP aqueous solution had higher gas permeability, as well as more homogeneous hydrophobicity. Moreover, the prepared GDLs were used in the cathode of fuel cell and evaluated with fuel cell performance and EIS analysis, and the GDL prepared with PVP aqueous solution indicated better fuel cell performance and lower ohmic resistance and mass transfer resistance.     

Simultaneous fault diagnosis of proton exchange membrane fuel cell systems based on an Incremental Multi-label Classification Network

Fault diagnosis plays an important role in the operation of proton exchange membrane fuel cell (PEMFC) systems. In some certain working conditions, multiple faults can occur simultaneously. And, to the best of our knowledge, very few studies have yet to design an algorithm specifically for simultaneous fault diagnosis in PEMFC systems. Therefore, a novel simultaneous fault diagnosis algorithm, based on multi-label classifier chain named Incremental Multi-label Classification Network (IMCN), is proposed. To develop and optimize IMCN, a PEMFC model is constructed based on the commercial software AVL CURISE M to simulate data when simultaneous multiple faults occur. To further verify the generalization performance and practical effect of IMCN, a bench experiment using a high-power PEMFC system is conducted, which has similar boundary conditions as the boundary conditions embedded in simulation model. And, whether in experiment or simulation, corresponding verification methods are adopted to verify the success of simultaneous multiple faults embedding. Experimental data testing shows that, the subset accuracy, Hamming loss, Jaccard index, precision and recall of IMCN reaches 0.973, 0.029, 0.921, 0.961 and 0.956 respectively (better than Multi-Label MLP classifier, Label powerset MLP classifier, etc.), and the proposed simultaneous fault diagnosis method has achieved excellent results.     

Online electrochemical impedance spectroscopy detection integrated with step-up converter for fuel cell electric vehicle

Declining reserves of the crude oil and increasingly serious environmental pollution have emphasized the requirement of a suitable substitute to our actual petroleum-based automobile market. An environmentally-friendly and efficient power generation device based on a sustainable energy source is attractive to settle this issue and realize cleaner production. Proton Exchange Membrane Fuel Cell (PEMFC), which achieves zero emission, modular construction, high energy conversion ratio and etc., has been treated as one of the most promising solution for automobile applications. Nevertheless, many technical restrictions such as relatively short life cycle have still to be conquered before satisfying the requirements of large-scale commercialization.Electrochemical Impedance Spectroscopy (EIS) is an effective technique for fault detection of electrochemical system. This paper presents an on-line EIS detection strategy based on the proposed fuel cell stack connected step-up converter. No additional equipment is required compared with conventional detection process. Furthermore, the proposed 6-phase Interleaved Boost Converter (IBC) based on Silicon Carbide (SiC) semiconductors and inverse coupled inductors has achieved low input current ripple, high efficiency, high voltage gain ratio, high compactness and high redundancy. Benefiting from these advantages, the lifespan of fuel cell stack can be extended. The proposed online EIS detection has been realized and the results have been compared with theoretical analysis.