PEM Fuel Cell Model Research Articles

Parameter optimization of polymer electrolyte membrane fuel cell using moment-based uncertainty evaluation technique

Finding the optimal operational parameters of polymer electrolyte membrane (PEM) fuel cells is very critical for improving its efficiency. The incorporation of uncertainties in the operational parameters during the optimization process is very important to ensure that the fuel cell can operate reliably in real-life deployment. Unfortunately, no attention has been given thus far on studying the effects of parameter uncertainties on the fuel cell performance. In this paper, the output power and hydrogen flow rate are being optimized under uncertain conditions of the stack current, stack temperature, oxygen excess ratio, hydrogen excess ratio and inlet air humidity of the PEM fuel cell. The effective application of a new analytical moment-based uncertainty evaluation technique proposed in combination with response surface methodology provides an accurate and numerically efficient evaluation of the fuel cell performance. The paper has demonstrated that the optimal mean output power under uncertainty is 1329.56W and its corresponding operating point is different from that of the optimal output power 1545.25W calculated assuming all parameters are fixed. The results show that, for the selected PEM fuel cell model, meeting probabilistic constraints makes the fuel cell less susceptible to input variations, but this can only be achieved at the expense of optimal output power. The useful framework, analyses and discussions presented in the paper can be adapted into any fuel cell performance evaluation and design optimization.

Distributed parameter model-based control of water activity and concentration of reactants in a polymer electrolyte membrane fuel cell

Water management is still a key challenge for optimal performance and durability of polymer electrolyte membrane (PEM) fuel cells. Water levels along the channel in a PEM fuel cell present important spatial variations that should be taken into account to avoid both local flooding and local drying. In this work, a decentralised model predictive control scheme is designed to maintain the water activity on both anode and cathode sides of the PEM at appropriate levels. The proposed strategy tackles the accumulation of liquid water on the surface of the catalyst layers, and the possibility of local drying, by controlling observed water activity spatial profiles. Classic PEM fuel cell issues like reactant starvation are also considered. High control performance is achieved. The strategy is applied to a validated distributed parameter PEM fuel cell model. Results show increased cell power density in comparison to non-spatial control strategies.

Numerical Simulation and Experimental Comparison of Single, Double and Triple Serpentine Flow Channel Configuration on Performance of a PEM Fuel Cell

In this study, the effect of single (1-S), double (2-S) and triple (3-S) serpentine flow field configuration on the performance of PEM fuel cell (PEMFC) was investigated both numerically and experimentally. First, a complete 3-D PEMFC model was developed, and simulations were carried out to examine the effect of 1-S, 2-S and 3-S flow field configuration on the performance of PEMFC using commercial CFD code ANSYS FLUENT. Along with the cell performance, important parameters such as pressure distribution, mass fraction of hydrogen, oxygen, liquid water activity, current flux density distribution and the membrane water content have been presented. Next, an experimental study is carried out with a PEMFC by changing 1-S, 2-S and 3-S flow field configurations to verify the numerical predictions. Finally numerically and experimentally obtained performance curves have been compared, and 1-S flow channel fuel cell is found to exhibit the best electrochemical performance compared with the 2-S and 3-S flow channel fuel cells.

Non-uniform control volume sizing methodology for relative humidity control of proton exchange membrane fuel cells

Real-time water management is a major ongoing challenge for PEM fuel cell technologies. Given the inherently distributed nature of the system, local conditions can change significantly from cell-to-cell. To compensate for this variance, a control-oriented PEM fuel cell model that is capable of capturing localized differences in operating conditions in real time is needed. To fulfill this need, the authors previously investigated the use of multiple, equally sized control volumes (CVs) to represent the cathode channel. This modification to the modeling architecture greatly improved the accuracy over a one CV model, which was incapable of capturing the stack vapor dynamics. However, because the relative humidity distribution in the stack is non-linear, equally sized CVs do not optimize the additional information gained from the multiple cathode CV approach.In this paper, an algorithm to optimally size CVs based on an analytical solution of the relative humidity profile in the cathode channel is presented. The analytical solution was found based on the vapor mass conservation equation in the cathode. This conservation equation includes consideration of electro-osmotic drag, concentration gradient based diffusion, vapor generation, and bulk fluid flow. The solution was validated by correcting the one CV model to match experimental data using the result of the analysis. After applying the analytical adjustment strategy to the one CV model, the dewpoint temperature predicted by the augmented one CV model was in good agreement with experimental results.The solution also revealed a coefficient that relates the current, flow rate, and membrane diffusion in a single term. This coefficient could be used for control decisions to avoid flooding issues in the stack. Furthermore, using the analytical RH profile equation, CVs can be optimally, unevenly sized to improve the modeling of local operating conditions.

Dynamic Modeling and Fractional Order PIλDμ Control of PEM Fuel Cell

Dynamic Modeling and Fractional Order PIλDμ Control of PEM Fuel Cell

PEMFC modeling based on characterization of effective diffusivity in simulated cathode catalyst layer

Oxygen diffusion in the cathode catalyst layer (CCL) is crucial to the high performance of polymer electrolyte membrane fuel cells (PEMFCs), especially in high current density or concentration loss regions. Recently, PEMFC performance has been reported to be enhanced by increasing CCL pore size and pore volume due to the reduction of diffusion resistance by capillary water equilibrium [Yim et al., Electrochimica Acta 56 (2011) 9064–9073]. Herein, we simulate these experimental results utilizing a new one-dimensional PEMFC model considering the effects of accumulated water film in CCL on oxygen diffusion. Two CCL microstructures were numerically generated based on agglomerate models to examine the experimental results obtained for two membrane electrode assembly (MEA) samples with different CCL porosity. The effective diffusivity of oxygen in the CCL was estimated by performing auxiliary simulations of oxygen concentration in CCL microstructures covered by a film of liquid water, with exponential correlation obtained between effective diffusivity and the thickness of the above film. Polarization curves predicted by the present model were in good agreement with experimental results. In agreement with the results of Yim et al., the present model predicts that the MEA featuring a CCL with smaller pores (which are more easily filled by liquid water) should exhibit a larger concentration loss at high current densities.

Effective parameters’ identification for polymer electrolyte membrane fuel cell models using grey wolf optimizer

The aim of this paper is to develop an accurate model for the polymer electrolyte membrane fuel cell (PEMFC), that can precisely mimic and simulate the electrical characteristics of actual PEMFC stacks at different operating conditions. Models of PEMFC are empirical, multi-variables and have many non-linear terms that should be estimated accurately to ensure appropriate modeling. In this paper, a novel application based-on a nature-inspired metaheuristic optimization algorithm namely, the grey wolf optimizer (GWO) to identify PEMFC model parameters is addressed. The GWO relies on the principles of metaheuristic techniques, exploration and exploitation phases, in order to avoid sticking in local optima and getting better solution. The proposed GWO-based method is tested on five commercial PEMFCs. Many investigations and performance tests are made to prove the effectiveness of the algorithm to simulate the electrical behavior of those commercial PEMFC stacks based-on experimental data. In addition, parametric and non-parametric statistical tests are in place to assess the effectiveness of the proposed method. For more validation, PEMFC model based-on GWO is compared with other challenging algorithms published in literature, and very competitive results are reported.

Microscopy Supported Multi-Scale Modeling of PEM Fuel Cells

Proton exchange membrane fuel cells (PEMFCs) are being developed as alternative energy sources for both residential and automotive applications. For this technology to reach its full commercial potential, however, a significant reduction in cost is still required while the performance and durability of PEMFCs being maintained or improved. The key in this process is continuous improvement of membrane electrode assembly (MEA) through both the development of new materials and the optimization of the 3D structural arrangement of individual MEA components [1,2] . Structural optimization of MEA remains to be challenging due to multiple materials interacting across 6 orders of magnitude in their characteristic length scales, from several nanometers for the catalyst particle size to hundreds of micrometers for carbon fibers in porous transport layer. In recent years, several microscopy techniques have become widely available to characterize the three-dimensional (3D) structure of PEMFC catalyst layers. Due to the heterogeneous nature of the PEMFCs sample, a correlative, multi-scale imaging protocol is developed in this work. The following technology is used where their corresponding resolution limit is pushed. Transmission Electron Microscope tomography, TEMt [3] (0.60nm X 0.60nm X 0.60nm Voxel Size) Focussed Ion Beam - Scanning Electron Microscope tomography, FIB-SEM [4] (2.5nm X 2.5nm X20 nm Voxel Size) Micro and Nano X-ray Computed Tomography, NanoCT [5] (367nm X 367nm X 367nm Voxel Size) Each technique by itself supports valuable insight to be obtained on the investigated structure at the corresponding length scale. By combining 3D imaging data at multiple scales, an unified structural characterization workflow is developed. Furthermore, an up scaling approach is developed based on TEMt, SEM and NanoCT reconstruction of catalyst layer, micro-porous layer and porous gas transport layer of a PMEFC cathode. Structural properties and effective transport properties are computed at each scale via image-based numerical simulation. Effective transport properties are up-scaled. MEA performances are predicted based on the obtained effective quantities at micro-scale.

Prospects for Validation of PEM Fuel Cell Models Using Current Distribution

Complex systems have a lot to gain from computational models, as they provide information out of reach of most individual experimental techniques. The possibility of providing full control over variables and parameters of a given system, as well as enabling the comparison of mathematical approaches, are a few of the many advantages of employing a well-developed computational model. Such is the case for fuel cells, notorious for its complex interactions between micro, meso and macro-scale components, and difficulty in obtaining reliable information from its dynamics. However, it is of high importance that the models be continuously improved and validated, not only against the already established empirical data, but also against new techniques that provide furtherinsights in the system. In this context, an ongoing work is being developed to provide robust data from current distribution, a rather unused technique when it comes to PEM fuel cell model validation, in order to further improve model development and provide a complementary dataset for validation. It is seen that, when using a simple 3D model of a 50 cm2 PEM fuel cell, with a well-established mathematical formulation, it is possible to reproduce most of the experimental polarization curve, within one deviation, despite the uncertainties on material properties (upper graph in Figure). On the other hand, the current distribution greatly differs between the experimental and computational results, even qualitatively (lower graph in Figure: applied current 3.0 A, current values normalized by sum over all collection points). In general, the same behavior is observed throughout the polarization curve and for different inlet flow rates. Although the lack of proper characterization of the electrode materials may be partially to blame, the consistent differences in the spatial distribution of the current points to broader issues: i) the polarization curve is rather insensitive to finer properties of the system, being a poor result for validation; and ii) the lack of accuracy of widely used mathematical formulations in describing the spatial dependency of variables of interest, in this case current, even in a relatively small device and conservative conditions. These preliminary results and the observed tendencies add to the growing consensus that greater efforts are needed in order to develop and validate useful fuel cell models. In particular, it is suggested that current distribution results, if available, provide more information and greater constraints for fuel cell development and validation, than when relying solely on polarization curves. Figure 1

PEM fuel cell model and simulation in Matlab–Simulink based on physical parameters

An advanced PEM fuel cell mathematical model is described and realised in four ancillaries in the Matlab–Simulink environment. Where possible, the model is based on parameters with direct physical meaning, with the aim of going beyond empirically describing the characteristics of the fuel cell. The model can therefore be used to predict enhanced performance owing to, for instance, improved electrode materials, and to relate changes in the measured performance to internal changes affecting influential physical parameters. Some simplifying assumptions make the model fairly light in computational demand and therefore amenable to extension to simulate an entire fuel-cell stack as part of an energy system. Despite these assumptions, the model emulates experimental data well, especially at high current density. The influences of pressure, temperature, humidification and reactant partial pressure on cell performance are explored. The dominating effect of membrane hydration is clearly revealed.

Reduced-order model of cascade-type PEM fuel cell stack with integrated humidifiers and water separators

In this paper, model order reduction (MOR) of cascade-type polymer electrolyte membrane (PEM) fuel cell stack with integrated humidifiers and water separators is investigated. The purpose of this work is to attain orders of magnitude improvement in numerical simulation speed. Both the anode and the cathode of stack operate in a dead-end mode. The reduced-order model (ROM) is developed for continuous and discrete form of the cascade-type PEM fuel cell models. The obtained ROM is verified with the full nonlinear model, which full-order model itself is validated using experimental data from cascade-type 4-cells PEM fuel cell stack. Responses of different orders of ROMs are compared to those of full-order model to determine the minimum order of the model that approximates the behavior of the original model properly. The results predicted by the developed reduced-order model nearly follow the full nonlinear model and experimental results. According to the low computational cost of ROM, the derived model can be further used for real-time control and diagnostic applications.

Development and Experimental Validation of a Physics-Based PEM Fuel Cell Model for Cathode Humidity Control Design

In large polymer electrolyte membrane (PEM) fuel cell stacks, monitoring and control of the local changes in membrane humidity inside the cathode channel is critical. In this study, a control-oriented dynamic model capable of describing the spatial distribution of voltage and relative humidity (RH) in a large fuel cell stack is developed and experimentally validated. The model tracks energy and mass flow inside the cathode, anode, and coolant channels, as well as the fuel cell stack body. Validation tests show that the model agrees well with the experimental data. The new modeling framework developed in this study can be used to predict the localized effects of humidity on the performance of a fuel cell stack. Also, given its accurate prediction of RH in the stack, this model can be used as an observer to predict local humidity variations that are, otherwise, not available. This capability would allow PEM fuel cells to avoid membrane damage due to low operating humidities as well as efficiency losses due to catalyst layer flooding.

Modeling of PEM Fuel Cell Based Power Generation System

Modeling of PEM Fuel Cell Based Power Generation System

(Invited) Numerical Modeling of the Growth of Fatigue Cracks in PFSA Membranes

The initiation and propagation of cracks in polymer electrolyte membranes is not well understood but it is generally considered to be caused by a combination of chemical, mechanical and hygrothermal stressors resulting in combined effects which can accelerate degradation. One such effect is the chemical decomposition of ionomer causing local defects, which can act as crack-initiation sites and can grow under mechanical stresses, leading to enhanced crossover and higher rates of chemical decomposition. It has recently been shown that defect-growth is a good metric to monitor the membrane’s lifetime and fatigue behavior since there exists a correlation between the gas crossover and defect size in membranes. Thus, investigation of crack-growth mechanisms due to mechanical stresses during RH cycling is of great interest for understanding the factors controlling chemical/mechanical durability and developing strategies for improved membrane stability. The mechanical stresses in the membrane are associated with swelling and shrinkage as a result of environmental changes inside the cell during operation. Hydration and heating lead to hygrothermal swelling strains in the membrane. However, the membranes are generally constrained in the fuel cell system by gas diffusion layers (GDL), bipolar plates and gaskets, preventing the membrane from expanding. Consequently, significant compressive stresses can develop. If these stresses exceed the elastic limit, residual tensile stresses may develop during dehydration shrinkage in the membrane. In these cases, the membrane is subjected to cyclical compressive and tensile stresses during the cyclical hydration-dehydration and heating-cooling occurring during fuel cell operation. Such loading is typically referred as fatigue loading and can cause crack propagation. Thus, with the combination of the cyclic fatigue loading and the environmental factors, microcracks can easily initiate and grow into through-thickness cracks, increasing the gas crossover through the membrane and causing the eventual catastrophic failure of the PEM fuel cells. Characterizing this fatigue crack growth under RH cycling is essential for understanding and improving the mechanical durability of PEM fuel cells. Currently, there is very little work on modelling in-situ crack growth in polymer electrolyte membrane and thus far, no attempt has been made to model the in-situ crack-propagation in a membrane using time-dependent viscoelastic-plastic membrane mechanical properties, which is important for an accurate representation of damage accumulation with time. However, considerable research has been devoted to modeling fatigue crack growth in other materials. In 1967, Rice first suggested the use of plastically dissipated energy as a criterion to study fatigue crack propagation in ductile materials. Following the work of Rice, there have been a number of analytical, experimental and numerical investigations into the application of plastically dissipated energy in predicting fatigue crack propagation. In the numerical investigations, the accumulation of plastically dissipated energy under cyclical loading is calculated in a defined region ahead of the crack tip and compared to a critical value, presumed to be a material parameter. Once the accumulation reaches the critical value, the crack propagates via a node release algorithm. In the present work, we develop a numerical simulation to study in-situ crack growth in the through-thickness direction under humidity cycling in a PEM fuel cell model. The temperature-humidity-time-dependent viscoelastic-plastic membrane properties used in the simulation are taken from separate mechanical characterization experiments conducted in our lab. We show that the plastically dissipated energy criterion can qualitatively capture a range of well-established phenomena seen experimentally and in operating fuel cells. Namely; (1) crack propagation in unreinforced perfluorosulfonic acid (PFSA) membrane, (2) crack propagation in expanded polytetrafluoroethylene (ePTFE) reinforced PFSA membrane, (3) the differences between the two, 4) the differences between crack propagation under the channel and land regions in a typical flow channel architecture, (5) the effect of fuel cell clamping pressure on membrane cracking.

An effective mesh strategy for CFD modelling of polymer electrolyte membrane fuel cells

Computational fluid dynamics (CFD) is a major tool in PEM fuel cell research. Typical three-dimensional PEM fuel cell models involve more than 106 mesh elements. This makes the computation very intense and necessitates a methodology to mesh the computational domain that can keep the number of elements to a minimum while maintaining good accuracy. In this study, the effect of computational mesh in each direction on the accuracy of the solution is investigated in a systematic way. It is found that the mesh in different directions has a different degree of influence on the solution suggesting that the mesh in one direction can be coarser than the other. The proposed mesh strategy is capable of greatly reducing the number of mesh elements, hence computation time, while preserving the characteristics of important flow-field variables. Moreover, it is applicable to a wide range of cell sizes and flow-field configurations and should be used as a guideline for mesh generation.

Vibration Modeling of PEM Fuel Cell for Prediction of Cell Number Effects by Experimental Data

AbstractOne of the most important challenges in increasing the performance, reliability and lifetime of fuel cells is the mechanical load effects that occur on real applications. Therefore, the vibration model of fuel cell that predicts the behavior of various fuel cell layouts is very useful. The fuel cell is made up of different adjacent layers that may have semi opposite mechanical properties. This special structure leads to occurrence of non‐linear behavior of fuel cell under dynamic mechanical vibrations and so, a black box method is selected for modeling of its vibration behavior. In this study, the mechanical load experiments in various shape and axes were applied on five layouts of proposed fuel cell and the vibration of its body measure by some accelerometers. The NNARXM neural network is created and trained with the experimental data of three layouts of the fuel cell. Then, the prediction error of this neural network, validated with the two other experimental data of fuel cell layouts, by correlation coefficients and histogram of prediction errors. Neural network validation shows the well prediction of both untrained layout and suitable estimation for any desired layout.

Application of PEM Fuel Cell for Stand-alone Based on a Fuzzy PID Control

Due to increasing concerns on environmental pollution and depleting fossil fuels, fuel cell (FC) has received considerable attention as an alternative to the conventional energy systems. Fuel cells have numerous stand-alone and grid-connected applications. This paper presents the control of the stand-alone application based on fuzzy PID (FPID) controller. The aim of the paper is to achieve the control of the fuel cell for stand-alone with suitable power conditioning unit (PCU) that consists of the two stages of DC/DC converter and DC/AC inverter. An analysis of cascade structure based on FPID controller for a single phase inverter is done and comprises two feedback control loops. The inductor current and capacitor voltage are measured and feedback to the inner loop and the outer loop, respectively. The analytical models of the h PEM fuel cells is designed and simulated by developing a detailed simulation software using Matlab, Simulink and SimPowerSystems Blockset for portable applications. The PEM fuel cell model is validated with NexaTM Power Module MAN5100078 by Ballard Power Systems at 80°C. In this paper shown that the proposed controller shows a robust behavior and good transient response.

Investigation of contact pressure distribution over the active area of PEM fuel cell stack

Contact pressure distribution over the active area of proton exchange membrane fuel cell (PEMFC) has significant effects on the performance of PEMFCs. Even clamping pressure over the membrane electrode assembly (MEA) affects contact resistance, characteristics of porous media and sealing task. This paper develops a PEM fuel cell model to study the contact pressure distribution over the membrane electrode assembly using finite element model. At first, the three-dimensional model of a single cell was reduced to a two-dimensional model to decrease the calculation time. After validation of the obtained results via the pressure sensitive films, the effect of some parameters such as thickness and material of the end plates, sealant hardness, number of the stack's cells and position of the cell on the contact pressure distribution over the MEA were investigated. The results reveal that optimizing mentioned parameters leads to design PEM fuel cells with proper contact pressure distribution over the MEA.

Proton exchange membrane fuel cell degradation: A parametric analysis using Computational Fluid Dynamics

A Polymer Electrolyte Membrane (PEM) fuel cell is numerically investigated both as fresh and as degraded with the help of observed degradation patterns reported in the literature. The fresh fuel cell model is validated and verified with the data from the literature. Modifying the model by varying the parameters affected by degradation, a degraded PEM fuel cell model is created. The degraded fuel cell is parametrically analyzed by using a commercial Computational Fluid Dynamics (CFD) software. The investigated parameters are the membrane equivalent weight, the Catalyst Layer (CL) porosity and viscous resistance, the Gas Diffusion Layer (GDL) porosity and viscous resistance, and the bipolar plate contact resistance. It is shown for the first time that PEM fuel cell overall degradation can be numerically estimated by combining experimental data from degraded individual components. By comparing the simulation results for the fresh and the degraded PEM fuel cells for two years of operation, it is concluded that the effects of overall degradation on cell potential is significant – estimated to be 17% around the operating point of the fuel cell at 0.95 V open circuit voltage and 70 °C operating temperature.

Three Dimensional, High Resolution MPL Generation for Thermal and Mass Transport Modeling of PEM Fuel Cells

A stochastically generated microporous layer (MPL) model has been numerically simulated for studying their thermal and mass transport properties. In this work, the MPLs have been generated with a particle diameter of 50 nm and a filling radius of 15 nm. The resulting structure has a bulk porosity of 0.6, a PTFE content of 31 wt. %, and has been generated at a resolution of 2.5 nm/voxel. The high resolution structure allows the particle to particle contact region to be studied, which is critically important for heat transfer studies. Both the thermal conductivity and effective diffusion coefficient were calculated. Thermal conductivity has been calculated to 17.6 W/m-K using an iterative form of the Fourier heat conduction equation. The effective diffusion coefficient of oxygen has been found to be 7.6 mm2/s using OpenPNM, which is an open source pore network modeling platform.