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.     

Low power proton exchange membrane fuel cell system identification and adaptive control

This paper proposes a systematic method of system identification and control of a proton exchange membrane (PEM) fuel cell. This fuel cell can be used for low-power communication devices involving complex electrochemical reactions of nonlinear and time-varying dynamic properties. From a system point of view, the dynamic model of PEM fuel cell is reduced to a configuration of two inputs, hydrogen and air flow rates, and two outputs, cell voltage and current. The corresponding transfer functions describe linearized subsystem dynamics with finite orders and time-varying parameters, which are expressed as discrete-time auto-regression moving-average with auxiliary input models for system identification by the recursive least square algorithm. In the experiments, a pseudo-random binary sequence of hydrogen or air flow rate is fed to a single fuel cell device to excite its dynamics. By measuring the corresponding output signals, each subsystem transfer function of reduced order is identified, while the unmodeled, higher-order dynamics and disturbances are described by the auxiliary input term. This provides a basis of adaptive control strategy to improve the fuel cell performance in terms of efficiency, as well as transient and steady state specifications. Simulation shows that adaptive controller is robust to the variation of fuel cell system dynamics, and it has proved promising from the experimental results.     

Statistical design of experiment approach for modeling and optimization of PEM fuel cell

Polymer electrolyte membrane (PEM) fuel cell has many input factors and it is very difficult to find which input factor affects response or output factor significantly. The general method of changing one factor at a time is statistically not correct because the interaction of the factors also affects the response in most of the cases. Mathematical and simulation models are important tools for designing and analysis of fuel cell-based systems. In this paper, first, a protocol for development of a 25-cm² active area, high performance, PEM fuel cell is presented and then its simulation model is developed using the first principle in MATLAB SIMULINK. Full factorial statistical design of experiment methodology is used to develop first- and second-order Metamodels (Mathematical model of simulation model) for PEM fuel cell to find which input factors affect the response variables significantly. Validation of the Metamodels is checked by various statistical tests, viz, normality, regression analysis, analysis of variance, and lack of fit. Steepest ascent method is used to find the maximum power delivered by PEM fuel cell within the defined ranges of input factors.     

A parameter optimized model of a Proton Exchange Membrane fuel cell including temperature effects

An electrical equivalent circuit model of the proton exchange membrane (PEM) fuel cell system with parameters extracted through optimization is presented in this paper. The analytical formulation of the fuel cell behavior is based on a set of equations which enables to estimate his overall performance in terms of operation conditions without extensive calculations. The approach uses a set of parametrical equations and related parameters in order to characterize and predict the voltage–current characteristics of the fuel cell operation without examining in depth all physical/chemical phenomena, but including within the model different components and forms of energy actuating in the generation process. 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 this work is the application of Simulated Annealing (SA) as optimization method focused on the extraction of the PEM model parameters. Model validation is carried out comparing experimental and simulated results. The good agreement between the simulation and experimental results shows that the proposed model provides an accurate representation of the static and dynamic behavior for the PEM fuel cell. Therefore, the approach allows at getting the set of parameters within analytical formulation of any fuel cell. In consequence, fuel cell performance characteristics are well described as they are carried out through a methodology that simultaneously calibrates the model.     

An application of indirect model reference adaptive control to a low-power proton exchange membrane fuel cell

Nonlinearity and the time-varying dynamics of fuel cell systems make it complex to design a controller for improving output performance. This paper introduces an application of a model reference adaptive control to a low-power proton exchange membrane (PEM) fuel cell system, which consists of three main components: a fuel cell stack, an air pump to supply air, and a solenoid valve to adjust hydrogen flow. From the system perspective, the dynamic model of the PEM fuel cell stack can be expressed as a multivariable configuration of two inputs, hydrogen and air-flow rates, and two outputs, cell voltage and current. The corresponding transfer functions can be identified off-line to describe the linearized dynamics with a finite order at a certain operating point, and are written in a discrete-time auto-regressive moving-average model for on-line estimation of parameters. This provides a strategy of regulating the voltage and current of the fuel cell by adaptively adjusting the flow rates of air and hydrogen. Experiments show that the proposed adaptive controller is robust to the variation of fuel cell system dynamics and power request. Additionally, it helps decrease fuel consumption and relieves the DC/DC converter in regulating the fluctuating cell voltage.     

Effects of inlet humidification on PEM fuel cell dynamic behaviors

The dynamic behaviors of a proton exchange membrane (PEM) fuel cell have been studied both experimentally and numerically. The objective of this paper is to investigate the effects of cathode inlet humidification on PEM fuel cell load change operations and the fuel cell performance during a simulated start‐up process. The PEM fuel cell was found to respond quickly and reproducibly to load changes. It was also found that an increase in the cathode inlet humidification significantly influences the start‐up performance of a PEM fuel cell. The cathode inlet relative humidity (RH) under 30% significantly dropped the cell dynamic performance. Extensive numerical simulations, with the transient processes of load jump and gradual changes considered, were performed to characterize dynamic responses of a singe‐channel PEM fuel cell under different inlet humidification levels. The results showed that the response time for a fuel cell to reach steady state depends on water accumulation in the membrane, which is consistent with the experimental results. Copyright © 2010 John Wiley & Sons, Ltd.     

Design of an optical thermal sensor for proton exchange membrane fuel cell temperature measurement using phosphor thermometry

Internal temperatures in a proton exchange membrane (PEM) fuel cell govern the ionic conductivities of the polymer electrolyte, influence the reaction rate at the electrodes, and control the water vapor pressure inside the cell. It is vital to fully understand thermal behavior in a PEM fuel cell if performance and durability are to be optimized. The objective of this research was to design, construct, and implement thermal sensors based on the principles of the lifetime-decay method of phosphor thermometry to measure temperatures inside a PEM fuel cell. Five sensors were designed and calibrated with a maximum uncertainty of ±0.6 °C. Using these sensors, surface temperatures were measured on the cathode gas diffusion layer of a 25 cm² PEM fuel cell. The test results demonstrate the utility of the optical temperature sensor design and provide insight into the thermal behavior found in a PEM fuel cell.     

Prediction performance of PEM fuel cells by gene expression programming

In the present study, gene expression programming has been utilized to evaluate the output voltage of different PEM fuel cells as the performance symbol of these structures. A total number of 843 data were collected from the literature, randomly divided into 682 and 161 sets, and then trained and tested, respectively by different models. The used data as input parameters were consisted of current density, fuel cell temperature, anode humidification temperature, cathode humidification temperature, operating pressures, fuel cell type, O₂ flow rate, air flow rate and active surface area of the PEM fuel cells. According to these input parameters, in the gene expression programming models, the voltage of each PEM fuel cell in different conditions was predicted. The training and testing results in the gene expression programming model have shown an acceptable potential for predicting voltage values of the PEM fuel cells in the considered range.     

Study of the characteristics of temperature rise and coolant flow rate control during malfunction of PEM fuel cells

In actual PEM fuel cell systems, the coolant flow rate is generally controlled to maintain a preset temperature at the coolant outlet. This implies that a change in coolant supply flow rate is a good early indicator of a malfunctioning PEM fuel cell stack and system components. In this study, various fuel cell malfunctions are simulated based on the practical coolant flow control strategy by using a three-dimensional, two-phase, multiscale PEM fuel cell model developed in our previous studies. The focus is on analysis of the characteristics of coolant flow rate change along with voltage degradation in various fuel cell malfunction cases. The model predictions show that in general, the coolant flow rate tends to increase proportionally with the degree of voltage degradation, but the increase in temperature inside the membrane electrode assembly (MEA) is not always related to the voltage drop and is influenced more directly by local current density distribution. Although the present numerical comparison between the normal and malfunctioning cases is conducted at the low current density of 0.3 A cm^?2, the general cell behavior will not be altered at higher current densities due to inverse relationship between cell performance and waste heat generation. The present work elucidates the complex interplay among increase in coolant flow rate, increase in MEA temperature, voltage drop, and change in local current density distribution when a PEM fuel cell malfunctions.     

Analysis and control of a fuel delivery system considering a two-phase anode model of the polymer electrolyte membrane fuel cell stack

The fuel delivery system using both an ejector and a blower for a PEM fuel cell stack is introduced as a fuel efficiency configuration because of the possibility of hydrogen recirculation dependent upon load states.A high pressure difference between the cathode and anode could potentially damage the thin polymer electrolyte membrane. Therefore, the hydrogen pressure imposed to the stack should follow any change of the cathode pressure. In addition, stoichiometric ratio of the hydrogen should be maintained at a constant to prevent a fuel starvation at abrupt load changes.Furthermore, liquid water in the anode gas flow channels should be purged out in time to prevent flooding in the channels and other layers. The purging control also reduces the impurities concentration in cells to improve the cell performance.We developed a set of control oriented dynamic models that include a anode model considering the two-phase phenomenon and system components The model is used to design and optimize a state feedback controller along with an observer that controls the fuel pressure and stoichiometric ratio, whereby purging processes are also considered. Finally, included is static and dynamic analysis with respect to tracking and rejection performance of the proposed control.     

Modelling and simulation of the steady-state and dynamic behaviour of a PEM fuel cell

The performance of a fuel cell can be expressed by the voltage–load current (V–I) characteristics. In this study, two mathematical modelling for computing the steady-state and dynamic voltage–current (V–I) characteristics of PEM fuel cell stacks have been developed. For determining the humidity of the membrane in steady-state conditions, mathematical and theoretical equations are considered. This value is not an adjustable parameter. The goal of dynamic modelling is to find the response of the system against the load variations. In this research, in addition to the charge double layer phenomenon, the effects of temperature and gas flows are taken into account, then the fuel cell system is divided into three control volumes and thus a lumped-parameter model for these sub-systems is established using the mass and heat transfer equations. The proposed models are implemented in Matlab/Simulink environment. Additionally, these models were tested for the SR-12Modular PEM Generator, the Ballard Mark V FC, the BCS 500-W stack and various experimental data in open literature. They exhibit excellent agreement with other simulation and experimental results.     

A novel P systems based optimization algorithm for parameter estimation of proton exchange membrane fuel cell model

Accurate kinetic models are of great significance for the simulation and analysis for hydrogen fuel cells. The proton exchange membrane (PEM) fuel cell is a complex nonlinear, multi-variable system. The mathematical modeling of PEM fuel cell usually leads to nonlinear parameter estimation problems which often contain more than one minimum. In this paper, a novel bio-inspired P systems based optimization algorithm, named BIPOA, is proposed to solve PEM fuel cell model parameter estimation problems. In BIPOA, the nested membrane structure and new rules such as adaptive mutation rule, partial migration rule and autophagy rule are combined to improve the algorithm's global search capacities and convergence accuracy. Studies on some benchmark test functions indicate that the BIPOA outperforms the other two methods (PSOPS and GAs) in both convergence speed and accuracy. In addition, experimental results reveal that the model predictive outputs are in better agreement with the actual experimental data. Therefore, the BIPOA is a helpful and reliable technique for estimating the PEM fuel cell model parameters and is available to other complex parameter estimation problems of fuel cell models.     

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.     

重力对PEM燃料电池性能的影响

水对质子交换膜(PEM)燃料电池的性能有极其重要的影响,良好的水管理是PEM燃料电池保持高性能的必要条件.通过试验,观察了在重力作用下液态水对PEM燃料电池性能及其内部传质的影响,分析了PEM燃料电池单体电极的不同摆放位置对其性能的影响.试验结果发现:在电流密度较小时,重力对PEM燃料电池性能的影响不明显,电流密度较大时,重力对PEM燃料电池性能的影响比较明显.试验结果对优化PEM燃料电池的结构和水管理有一定的参考价值.     

Maximum equivalent efficiency and power output of a PEM fuel cell/refrigeration cycle hybrid system

With the help of the current models of proton exchange membrane (PEM) fuel cells and three-heat-source refrigeration cycles, the general model of a PEM fuel cell/refrigeration cycle hybrid system is originally established, so that the waste heat produced in the PEM fuel cell may be availably utilized. Based on the theory of electrochemistry and non-equilibrium thermodynamics, expressions for the efficiency and power output of the PEM fuel cell, the coefficient of performance and cooling rate of the refrigeration cycle, and the equivalent efficiency and power output of the hybrid system are derived. The curves of the equivalent efficiency and power output of the hybrid system varying with the electric current density and the equivalent power output versus efficiency curves are represented through numerical calculation. The general performance characteristics of the hybrid system are discussed. The optimal operation regions of some parameters in the hybrid system are determined. The advantages of the hybrid system are revealed.     

Evaluating the impact of enhanced anode CO tolerance on performance of proton-exchange-membrane fuel cell systems fueled by liquid hydrocarbons

Recent advances in anode electrocatalysts for low-temperature PEM fuel cells are increasing tolerance for CO in the H₂-rich anode stream. This study explores the impact of potential improvements in CO-tolerant electrocatalysts on the system efficiency of low-temperature Nafion-based PEM fuel cell systems operating in conjunction with a hydrocarbon autothermal reformer and a preferential CO oxidation (PROx) reactor for CO clean-up. The incomplete H₂ clean-up by PROx reactors with partial CO removal can present conditions where CO-tolerant anode electrocatalysts significantly improve overall system efficiency. Empirical fuel cell performance models were based upon voltage-current characteristics from single-cell MEA tests at varying CO concentrations with new Pt-Mo alloy reformate-tolerant electrocatalysts tested in conjunction with this study. A system-level model for a liquid-fueled PEM fuel cell system with a 5 kW full power output is used to study the trade-offs between the improved performance with decreased CO concentration and the increased penalties from the air supply to the PROx reactor and associated reduction in H₂ partial pressures to the anode. As CO tolerance is increased over current state-of-the-art Pt alloy catalysts, system efficiencies improve due primarily to higher fuel cell voltages and to a lesser extent to reductions in parasitic loads. Furthermore, increasing CO tolerance of anode electrocatalysts allows for the potential for reduced system costs with minimal efficiency penalty by reducing PROx reactor size through reduced CO conversion requirements.     

Design of a mobile PEM power backup system through detailed dynamic and control analysis

In this paper we present a one dimensional dynamic model of a PEM fuel cell applied to the design of a mobile backup system for uninterruptable power units. The fuel cell is modeled using a finite difference approach where mass and energy balance equations are applied locally together with the pertinent equations of the electrochemical model yielding the profiles of any relevant thermodynamic and electrochemical cell variable. An accurate analysis of the membrane humidification is included based on state of the art models available in literature.     

Modeling of an automotive fuel cell thermal system

This work develops an 8th order, non-linear thermal model of an automotive proton exchange membrane (PEM) fuel cell system. Subsystem models are developed from first principals where ever possible and validated against data from a physical system. The system model is validated against data from an automotive 120 kW fuel cell system, with good agreement. Next, a reduced order model is constructed from the full model and the performance of the two models are compared. The reduced order linear model provided an acceptable representation of the full non-linear model.     

Characterization of the dynamic response of proton exchange membrane fuel cells – A numerical study

The dynamic response of PEM (Proton exchange membrane) fuel cells is a complex phenomenon which is affected by numerous factors related to their designs and operating conditions. Despite that experimental data is available in the literature, a systematic numerical study to explain the dynamic behavior of PEM fuel cells is currently unavailable. In this paper, a one-dimensional, two-phase, dynamic model of PEM fuel cell is developed to achieve this principal objective. Transient profiles of cell voltage, activation and ohmic over-potentials, saturation level of liquid water, oxygen concentration, and membrane water content are predicted under various operating conditions. Under constant fuel and air flow rates, it is found that the cell voltage exhibits undershoot behavior following a step increase in current density due to the inherent time delay experienced by the redistribution of membrane water content with a response time of ∼50 s. The undershoot is followed by an overshoot in the presence of flooding with a significantly longer predicted response time of ∼150–200 s. It is found that the various operating conditions mainly affect the specific details of the undershoot and overshoot profiles without changing their general behavioral forms.     

A combined methanol autothermal steam reforming and PEM fuel cell pilot plant unit: Experimental and simulation studies

An integrated system for hydrogen production via autothermal steam reforming of methanol and consequent power generation in a polymer electrolyte membrane (PEM) fuel cell has been developed and operated at C.P.E.R.I. The pilot plant comprises an autothermal reforming reactor to produce hydrogen, a preferential oxidation reactor (PROX) to reduce CO concentration below 50 ppm and a PEM fuel cell for power generation.The present paper deals with the study of this system, both from an experimental and a theoretical point of view. The experimental work aims to: (a) examine the effect of the reforming temperature on methanol conversion and on the effluent stream concentration, (b) investigate the effect of reaction temperature and O₂/CO ratio on the performance of the PROX reactor, and (c) evaluate the operation of a 10-cell PEM fuel cell, using pure hydrogen and air at three temperature levels. The experimental data are subsequently utilized for the validation of one-dimensional pseudo-homogeneous models that have been developed for the two reactors and also for the identification of the voltage–current characteristic curve of the PEM fuel cell. The validated models are then used to investigate the behavior and explore the interactions, both static and dynamic, among the various process subsystems.