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.     

Parameter identification for proton exchange membrane fuel cell model using particle swarm optimization

The accurate mathematical model is an extremely useful tool for simulation and design analysis of fuel cell power systems. Particle swarm optimization (PSO) is a recently invented high-performance algorithm. In this work, a PSO-based parameter identification technique of proton exchange membrane (PEM) fuel cell models was proposed in terms of the voltage–current characteristics. Using the simulated and experimental voltage–current data, the validity of the proposed method has been confirmed. The results indicate that the PSO is an effective technique for identifying the parameters of PEM fuel cell models even in the presence of measuring noise. Moreover, the proposed method does not particularly necessitate initial guesses as close as possible to the solutions, required only is a broad range specified for each of the parameters. Therefore, the PSO method outperforms the GA and traditional optimization methods.     

Theory,modelling and performance measurement of unitised regenerative fuel cells

Unitised Regenerative Fuel Cells (URFCs) based on Proton Exchange Membrane (PEM) technology provide a promising opportunity for reducing the cost of the hydrogen subsystem used in renewable-energy hydrogen systems for remote area power supply. A general theoretical relationship between cell potential and current density of a single-cell URFC operating in both fuel-cell and electrolyser modes is derived using the Butler–Volmer equation for both oxygen and hydrogen electrodes, and accounting for membrane resistance and mass transport losses. Modifying the standard Butler–Volmer equation with a denominator term containing two additional ‘saturation’ parameters to reflect mass transport constraints generates voltage–current curves that are much closer to experimentally obtained polarisation curves in both modes. The theoretical relationship is used to construct a computer model based on Excel and Visual Basic to generate voltage–current curves in both electrolyser and fuel cell modes for URFCs with a range of membrane electrode assembly characteristics. Hence the influence of key factors such as exchange current densities and charge transfer coefficients on cell performance is analysed. Experimental results for voltage–current curves from singe-cell URFCs with a number of different oxygen-side catalysts are reported, and compared to the theoretically modelled curves. Generally values have been found for exchange current densities, charge transfer coefficients, and saturation current densities that give a close fit between the empirical and theoretically generated curves. The values found conform well to expectations based on the catalyst loadings, in partial confirmation of the validity of the modelling approach. The model thus promises to be a useful tool in identifying electrodes with materials and structures, together with optimal catalyst types and loadings that will improve URFC performance.     

A diagnosis method for identification of the defected cell(s) in the PEM fuel cells

Incorrect controlling of the pressure, temperature, flow rate and humidity levels of reactant gases can inflict severe and sometimes irreversible damages on the PEM fuel cells. Most important damage is leakage between the two sides of cathode and anode that may lead to physical defects in the stack. Usage of neutral gas method only reveals the overall leakage and does not show the exact location of the defected cell in the stack. This research seeks to determine the exact location of the defective cell using a method that is based on the data received from the voltage–time graphs of the stack under hydrogen sudden stop condition when the stacks are operating in the open circuit voltage condition. This method has been used with respect to two fuel cell stacks with different powers in different working conditions. Also the stack voltage drop due to leakage has been considered theoretically.     

An experimental and modelling study of a photovoltaic/proton-exchange membrane electrolyser system

An experimental model of a photovoltaic (PV) module-proton exchange membrane (PEM) electrolyser system has been built. A model has been developed for each device separately based on the experimental results. Output current–voltage (I–V) characteristics of the PV module are modelled in respect to different irradiance and temperature conditions by experimental tests. Similarly, input I–V characteristic and hydrogen formation characteristic of the PEM electrolyser are measured and modelled. After these studies, combined PV module–PEM electrolyser system model is defined. There is a good agreement between model predictions and measurements. At 18–100% irradiance interval, operating points of PEM electrolyser on the PV module are predicted with relative errors of 0.1–0.8%. Furthermore, the study shows that these simple model system devices can easily be defined in MATLAB/Simulink and used to model similar systems of different size.     

Characterization of flooding and two-phase flow in polymer electrolyte membrane fuel cell stacks

A partially flooded gas diffusion layer (GDL) model is proposed and solved simultaneously with a stack flow network model to estimate the operating conditions under which water flooding could be initiated in a polymer electrolyte membrane (PEM) fuel cell stack. The models were applied to the cathode side of a stack, which is more sensitive to the inception of GDL flooding and/or flow channel two-phase flow. The model can predict the stack performance in terms of pressure, species concentrations, GDL flooding and quality distributions in the flow fields as well as the geometrical specifications of the PEM fuel cell stack. The simulation results have revealed that under certain operating conditions, the GDL is fully flooded and the quality is lower than one for parts of the stack flow fields. Effects of current density, operating pressure, and level of inlet humidity on flooding are investigated.     

Modelling of polymer electrolyte membrane fuel cell stacks based on a hydraulic network approach

Polymer electrolyte membrane (PEM) fuel cells convert the chemical energy of hydrogen and oxygen directly into electrical energy. Waste heat and water are the reaction by‐products, making PEM fuel cells a promising zero‐emission power source for transportation and stationary co‐generation applications. In this study, a mathematical model of a PEM fuel cell stack is formulated. The distributions of the pressure and mass flow rate for the fuel and oxidant streams in the stack are determined with a hydraulic network analysis. Using these distributions as operating conditions, the performance of each cell in the stack is determined with a mathematical, single cell model that has been developed previously. The stack model has been applied to PEM fuel cell stacks with two common stack configurations: the U and Z stack design. The former is designed such that the reactant streams enter and exit the stack on the same end, while the latter has reactant streams entering and exiting on opposite ends. The stack analysed consists of 50 individual active cells with fully humidified H₂ or reformate as fuel and humidified O₂ or air as the oxidant. It is found that the average voltage of the cells in the stack is lower than the voltage of the cell operating individually, and this difference in the cell performance is significantly larger for reformate/air reactants when compared to the H₂/O₂ reactants. It is observed that the performance degradation for cells operating within a stack results from the unequal distribution of reactant mass flow among the cells in the stack. It is shown that strategies for performance improvement rely on obtaining a uniform reactant distribution within the stack, and include increasing stack manifold size, decreasing the number of gas flow channels per bipolar plate, and judicially varying the resistance to mass flow in the gas flow channels from cell to cell. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

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.     

Modelling a PEM fuel cell stack with a nonlinear equivalent circuit

A nonlinear circuit model of a polymer electrolyte membrane (PEM) fuel cell stack is presented. The model allows the simulation of both steady-state and dynamic behaviour of the stack on condition that the values of some of its parameters are changed in the two operating conditions. The circuit parameters can be obtained by means of simple experimental tests and calculations. A commercial PEM fuel cell stack is modelled as seen from the power conditioning system side, without requiring parameters necessary for complex mathematical models and not easily obtainable by the majority of users. A procedure of parameter determination is developed and a comparison between the simulated and experimental results for both steady-state and dynamic behaviour of the PEM stack is shown.     

Operation-relevant modeling of an experimental proton exchange membrane fuel cell

A current–voltage (I–V) curve, also known as a polarization curve, is generally used to express the characteristics of a proton exchange membrane (PEM) fuel cell system. The behavior of a PEM fuel cell is highly nonlinear and it is important to incorporate process nonlinearity for control system design and process optimization. Therefore, it is essential to generate the I–V curve from the model as the operating condition changes. A first principle one-dimensional water and thermal management model is developed to generate the I–V curve. The model considers the effects of water transport across the membrane, activation overpotential, ohmic overpotential, concentration overpotential, pressure drops, and current density distribution along the channel of a PEM fuel cell. Design and modeling parameters are obtained via regression from four sets of experimental data. They are further validated as operating conditions (e.g., fuel cell temperature, anode pressure, cathode pressure, hydrogen stoichiometric ratio, air stoichiometric ratio, hydrogen humidification temperature, and air humidification temperature) change. A sensitivity analysis example is used to illustrate the usefulness of the predictive model.     

Modeling and simulation of a PEM fuel cell stack considering temperature effects

Management of the water and heat ejected as byproducts in an operating PEM fuel cell stack are crucial factors in their optimal design and safe operations. Models currently available for a PEM fuel cell are based on either empirical or 3-D computational fluid dynamics (CFD). Both models do not fully meet the need to represent physical behavior of a stack because of either their simplicity or complexity. We propose a highly dynamic PEM fuel cell stack model, taking into account the most influential property of temperature affecting performance and dynamics. Simulations have been conducted to analyze start-up behaviors and the performance of the stack in conjunction with the cells. Our analyses demonstrate static and dynamic behaviors of a stack. Major results presented are as follows: (1) operating dependent temperature gradient across through-plane direction of the fuel cell stack, (2) endplate effects on the temperature profile during start-up process, (3) temperature profile influences on the output voltage of individual cells and the stack, (4) temperature influence on the water content in membranes of different cells, and (5) cathode inlet relative humidity influence on the temperature profile of the stack.     

Exergoeconomic analysis of a vehicular PEM fuel cell system

In this study, we deal with the exergoeconomic analysis of a proton exchange membrane (PEM) fuel cell power system for transportation applications. The PEM fuel cell performance model, that is the polarization curve, is previously developed by one of the authors by using the some derived and developed equations in literature. The exergoeconomic analysis includes the PEM fuel cell stack and system components as compressor, humidifiers, pressure regulator and the cooling system. A parametric study is also conducted to investigate the system performance and cost behaviour of the components, depending on the operating temperature, operating pressure, membrane thickness, anode stoichiometry and cathode stoichiometry. For the system performance, energy and exergy efficiencies and power output are investigated in detail. It is found that with an increase of temperature and pressure and a decrease of membrane thickness the system efficiency increases which leads to a decrease in the overall production cost. The minimization of the production costs is very crucial in commercialization of the fuel cells in transportation sector.     

Parametric analysis of a hybrid power system using organic Rankine cycle to recover waste heat from proton exchange membrane fuel cell

Using fuel cell systems for distributed generation (DG) applications represents a meaningful candidate to conventional plants due to their high power density and the heat recovery potential during the electrochemical reaction. A hybrid power system consisting of a proton exchange membrane (PEM) fuel cell stack and an organic Rankine cycle (ORC) is proposed to utilize the waste heat generated from PEM fuel cell. The system performance is evaluated by the steady-state mathematical models and thermodynamic laws. Meanwhile, a parametric analysis is also carried out to investigate the effects of some key parameters on the system performance, including the fuel flow rate, PEM fuel cell operating pressure, turbine inlet pressure and turbine backpressure. Results show that the electrical efficiency of the hybrid system combined by PEM fuel cell stack and ORC can be improved by about 5% compared to that of the single PEM fuel cell stack without ORC, and it is also indicated that the high fuel flow rate can reduce the PEM fuel cell electrical efficiency and overall electrical efficiency. Moreover, with an increased fuel cell operating pressure, both PEM fuel cell electrical efficiency and overall electrical efficiency firstly increase, and then decrease. Turbine inlet pressure and backpressure also have effects on the performance of the hybrid power system.     

Performance and cost modelling taking into account the uncertainties and sensitivities of current and next-generation PEM water electrolysis technology

This paper presents a bottom-up approach to the assessment of model performance and costs of a proton-exchange-membrane electrolysis considering cell, stack and process levels. The cell voltage is modelled dependent on current density and detailed models for stack, investment and hydrogen costs are developed. Taking into account current research on PEM electrolysis, such as the use of thinner membranes or low precious metal loading on the electrodes, allows the prediction of next generation's efficiency and costs. By comparison of a current and next-generation PEM electrolysis, the effectiveness of individual development steps was assessed and remaining space for efficiency and cost improvement was identified. This can help to prioritize and to focus on development steps which are most effective.In the next generation, efficiency will be increased even at higher current density operation. Thus, specific stack costs will drop to less than half of present day costs which is decisive to achieve lower hydrogen production costs in the next generation. Specific installed costs and hydrogen production costs of the current and next generation are calculated for plant sizes up to 100 MW_DC and reveal significant cost decrease for plant capacities up to 25 MW_DC while only changing slightly for capacities larger than this.Costs are always subject to uncertainties due to model assumptions and boundary conditions that need to be defined. Uncertainties and the sensitivities of the model are estimated and assessed to provide an indication of the actual cost range. Main cost model uncertainties are identified to arise from membrane electrode and stack assembly costs, civil engineering and construction surcharge as well as the electrical system. Hydrogen costs are dominated by operating costs and therefore are highly sensitive to the annual operating hours and the electricity price, which have a greater impact on the hydrogen costs than the model assumptions for capital costs.     

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.     

Assembly pressure and membrane swelling in PEM fuel cells

Assembly pressure and membrane swelling induced by elevated temperature and humidity cause inhomogeneous compression and performance variation in proton exchange membrane (PEM) fuel cells. This research conducts a comprehensive analysis on the effects of assembly pressure and operating temperature and humidity on PEM fuel cell stack deformation, contact resistance, overall performance and current distribution by advancing a model previously developed by the authors. First, a finite element model (FEM) model is developed to simulate the stack deformation when assembly pressure, temperature and humidity fields are applied. Then a multi-physics simulation, including gas flow and diffusion, proton transport, and electron transport in a three-dimensional cell, is conduced. The modeling results reveal that elevated temperature and humidity enlarge gas diffusion layer (GDL) and membrane inhomogeneous deformation, increase contact pressure and reduce contact resistance due to the swelling and material property change of the GDL and membrane. When an assembly pressure is applied, the fuel cell overall performance is improved by increasing temperature and humidity. However, significant spatial variation of current distribution is observed at elevated temperature and humidity.     

Equivalent circuit elements for PSpice simulation of PEM stacks at pulse load

The PEFC stack in a commercial power system was operated with room air and pure hydrogen. After the system reached a steady temperature, an ac impedance test was conducted on the fuel cell power system. The impedance data were real-time response generated by the ac sinusoidal excitation. Data for a single PEM stack and PEM stacks operating in parallel and series were collected with or without an embedded system controller board and electronic devices. The equivalent circuit model with three time constants and the non-linear least square fitting program (NLLS) were applied for fitting the stack impedance spectrum. The Levenberg–Marquardt algorithm utilized in the NLLS fitting process automatically adjusted the parameter values of the physical elements in the model to find the best fit result. From the preliminary results, data interpretation and the equivalent circuit model identified the physical elements, the related electrochemical processes, and the phenomenon inside the fuel cells or stacks. Losses from ohmic conduction, anode activation, cathode activation, and mass transfer were separated and analyzed. Further PSpice simulation curves using these equivalent circuit elements demonstrate good agreement with the pulse testing data measured from the PEFC power system.     

An experimental study on the dynamic process of PEM fuel cell stack voltage

The dynamic characteristics of the proton exchange membrane (PEM) fuel cell are of great importance in its design and applications. In this paper, the dynamic process of stack voltage is analyzed when the current is step inputted. We discuss the process from the following four aspects: voltage variation rate, initial value of dynamic voltage, time to reach steady state and dynamic resistance factor. The analysis results show that the dynamic process of stack voltage responding to current step-up is different from that to current step-down. Additionally, the operating current values also have significant influence on the dynamic characteristics of stack voltage.     

Data driven models for a PEM fuel cell stack performance prediction

The operating principles of polymer electrolyte membrane (PEM) fuel cells system involve electrochemistry, thermodynamics and hydrodynamics theory for which it is not always easy to establish a mathematical model. In this paper two different methods to model a commercial PEM fuel cell stack are discussed and compared. The models presented are nonlinear, derived from a black-box approach based on a set of measurable exogenous inputs and are able to predict the output voltage and cathode temperature of a 5 kW module working at the CNR-ITAE. A PEM fuel cell stack fed with H₂ rich gas is employed to experimentally investigate the dynamic behaviour and to reveal the most influential factors. The performance obtained using a classical Neural Networks (NNs) model are compared with a number of stacking strategies. The results show that both strategies are capable of simulating the effects of different stoichiometric ratio in the output variables under different working conditions.