Channel geometry optimization using a 2D fuel cell model and its verification for a polymer electrolyte membrane fuel cell

This paper studies the optimization method of channel geometries for a proton exchange membrane fuel cell (PEMFC) using a genetic algorithm (GA). The channel and rib widths and channel height are selected as geometry variables. The fuel cell output power is chosen as the cost function for the optimization. In this paper, an in-house genetic algorithm is constructed, and the fuel cell output power is obtained using an interfacing program connected to a commercial computational fluid dynamics (CFD) tool, COMSOL, in a Matlab environment. The 2D PEMFC is used to calculate the performance cost function for computational time and cost. The calculated output power of the PEMFC is delivered to the in-house GA program to check for optimality. After the optimality is checked, the new geometry data is fed back to the COMSOL to calculate the PEMFC output power until the optimization process is finished. Experiments are conducted to support the optimized results using three different channel geometries: channel-to-rib width ratios of 0.5:1, 1:1, and 2:1. A full 3D PEMFC CFD model is constructed using COMSOL to support the 2D CFD optimization results. This paper shows the possibility of applying the geometry optimization process to sophisticated electrochemical reaction systems, such as a PEMFC, using a GA and a commercial CFD tool on the Matlab platform. The geometries and materials can be optimized using this approach to obtain the most efficient performance of an electrochemical system.     

Optimization of PEMFC model parameters with a modified particle swarm optimization

In this paper, an electrochemical‐based proton exchange membrane fuel cell (PEMFC) model suitable for engineering applications is presented. In order to improve the accuracy of this model so that it can reflect the actual PEMFC performance better, its parameters are optimized by means of a modified particle swarm optimization (MPSO). The MPSO is a modified method for the PSO's inertia weight. The proposed inertia weight is calculated according to the distance of the particle's current position from the best solution of the entire swarm. The obtained results of the PEMFC model with optimized parameters agree with experimental data well. Therefore, the MPSO is a helpful and reliable technique for optimizing the model parameters and can be used to solve other complex parameter optimization problems of fuel cell models. Copyright © 2010 John Wiley & Sons, Ltd.     

The optimal design for PEMFC modeling based on Taguchi method and genetic algorithm neural networks

This paper has presented a new approach to estimate the output voltage of proton exchange membrane fuel cell (PEMFC) accurately by combining the use of a genetic algorithm neural networks (GANN) model and the Taguchi method. Using the PEMFC experimental data measured from performance test equipment of PEMFC, the GANN model could be trained and constructed for obtaining the steady state output voltage of PEMFC. Furthermore, in order to determine the important parameters in GANN, the Taguchi method is used for parameter optimization, with the goal of reducing the estimation error. The test equipment of PEMFC is accurate enough for acquiring the output voltage of PEMFC, and is quite useful for teaching purpose. However, taking the high cost, complicated operation procedure and environment safety into consideration, it is necessary to develop a simulation model of PEMFC to benefit teaching and R&D. Therefore, this paper will present an approach for constructing a GANN model with precise accuracy for the output voltage of PEMFC. For achieving the GANN model with high precision, a troublesome work has to be taken care of, that is, to determine all the parameters required in GANN. We will introduce Taguchi method to solve this problem as well. Finally, to show the superiority of proposed model, this approach has compared the estimation values of output voltage for PEMFC from GANN and BPNN models without using Taguchi method. One can easily find that the error of the proposed method is much smaller than that of the GANN model without Taguchi method and of the BPNN model; that is, the proposed approach has better performance on estimation for PEMFC output voltages.     

Parameter optimization for tubular solid oxide fuel cell stack based on the dynamic model and an improved genetic algorithm

The tubular solid oxide fuel cell (SOFC) stack has important parameters that need to be identified and optimized for the control of high performance. In this paper, a simple SOFC electrochemical model which its parameters need to be optimized is introduced to implement stack control for high output power. A dynamic SOFC model is built based on three sub-models to provide a large numbers simulated data and different condition for optimization. Unlike the traditional parameter optimization method--simple genetic algorithm (SGA), an improved genetic algorithm (IGA) is introduced. The proposed method shows more accuracy and validity by comparing the different results using SGA and IGA methods, the simulated data, and experimental data. The models and IGA method are adapted to control processes.     

Novel dynamic semiempirical proton exchange membrane fuel cell model incorporating component voltages

This paper introduces a novel dynamic semiempirical model for the proton exchange membrane fuel cell (PEMFC). The proposed model not only considers the stack output voltage but also provides valid waveforms of component voltages, such as the no‐load, activation, ohmic, and concentration voltages of the PEMFC stack system. Experiments under no‐load, ramping load, and dynamic load conditions are performed to obtain various voltage components. According to experimental results, model parameters are optimised using the lightning search algorithm by providing valid theoretical ranges of parameters to the lightning search algorithm code. In addition, the correlation between the vapour and water pressures of the PEMFC is obtained to model the component voltages. Finally, all component voltages and the stack output voltage are validated by using the experimental/theoretical waveforms mentioned in previous research. The proposed model is also compared with a recently developed semiempirical model of PEMFC through particle swarm optimisation. The proposed dynamic model may be used in future in‐depth studies on PEMFC behaviour and in dynamic applications for health monitoring and fault diagnosis.     

A study of operation strategy of cooling module with dynamic fuel cell system model for transportation application

A fuel cell system model with detailed cooling module model was developed to evaluate the control algorithms of cooling module which is used for the thermal management of a proton exchange membrane fuel cell (PEMFC) system. The system model is composed of a dynamic fuel cell stack model and a detailed dynamic cooling module model. To extend modeling flexibility, the fuel cell stack model utilizes analytic approach to capture the transient behavior of the stack temperature corresponding to the change of the coolant temperature and the flow rate during load follow-up. The cooling module model integrated model of fan, water pump, coolant passage, and electric motors so that the model is capable of investigation of operating strategy of pump and fan.The fuel cell system model is applied to the investigation of the control logics of the cooling module. Since, it is necessary for the control of cooling module to define the reference conditions such as coolant temperature and fuel cell stack temperature, this study presents such thermal management criteria. Finally, two control algorithms were compared, a conventional control algorithm and a feedback control algorithm. As a consequence, the feedback control algorithm was found to be more suitable for the cooling module of the PEMFC stack, as they consume less parasitic power while producing more stack power compared to a conventionally controlled cooling module.     

Modeling and thermal management of proton exchange membrane fuel cell for fuel cell/battery hybrid automotive vehicle

The proton exchange membrane fuel cell (PEMFC) stack is a key component in the fuel cell/battery hybrid vehicle. Thermal management and optimized control of the PEMFC under real driving cycle remains a challenging issue. This paper presents a new hybrid vehicle model, including simulations of diver behavior, vehicle dynamic, vehicle control unit, energy control unit, PEMFC stack, cooling system, battery, DC/DC converter, and motor. The stack model had been validated against experimental results. The aim is to model and analyze the characteristics of the 30 kW PEMFC stack regulated by its cooling system under actual driving conditions. Under actual driving cycles (0–65 kW/h), 33%–50% of the total energy becomes stack heat; the heat dissipation requirements of the PEMFC stack are high and increase at high speed and acceleration. A PID control is proposed; the cooling water flow rate is adjusted; the control succeeded in stabilizing the stack temperature at 350 K at actual driving conditions. Constant and relative lower inlet cooling water temperature (340 K) improves the regulation ability of the PID control. The hybrid vehicle model can provide a theoretical basis for the thermal management of the PEMFC stack in complex vehicle driving conditions.     

A hybrid multi-variable experimental model for a PEMFC

A hybrid model composed of a least square support vector machine (LS-SVM) model and a pressure-incremental model is developed to dispose operation conditions of current, temperature, cathode and anode gas pressures, which have major impacts on a proton exchange membrane fuel cell's (PEMFC) performance. The LS-SVM model is built to incorporate current and temperature and a particle swarm optimization (PSO) algorithm is used to improve its performance. The optimized LS-SVM model fits the experimental data well, with a mean squared error of 0.0002 and a squared correlation coefficient of 99.98%. While a pressure-incremental model with only one empirical coefficient is constructed to for anode and cathode pressures with satisfactory results. Combining these two models together makes a powerful hybrid multi-variable model that can predict a PEMFC's voltage under any current, temperature, cathode and anode gas pressure. This black-box hybrid PEMFC model could be a competitive solution for system level designs such as simulation, real-time control, online optimization and so on.     

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.     

Constructal PEM fuel cell stack design

This paper describes a structured procedure to optimize the internal structure (relative sizes, spacings), single cells thickness, and external shape (aspect ratios) of a polymer electrolyte membrane fuel cell (PEMFC) stack so that net power is maximized. The constructal design starts from the smallest (elemental) level of a fuel cell stack (the single PEMFC), which is modeled as a unidirectional flow system, proceeding to the pressure drops experienced in the headers and gas channels of the single cells in the stack. The polarization curve, total and net power, and efficiencies are obtained as functions of temperature, pressure, geometry and operating parameters. The optimization is subjected to fixed stack total volume. There are two levels of optimization: (i) the internal structure, which accounts for the relative thicknesses of two reaction and diffusion layers and the membrane space, together with the single cells thickness, and (ii) the external shape, which accounts for the external aspect ratios of the PEMFC stack. The flow components are distributed optimally through the available volume so that the PEMFC stack net power is maximized. Numerical results show that the optimized single cells internal structure and stack external shape are “robust” with respect to changes in stoichiometric ratios, membrane water content, and total stack volume. The optimized internal structure and single cells thickness, and the stack external shape are results of an optimal balance between electrical power output and pumping power required to supply fuel and oxidant to the fuel cell through the stack headers and single-cell gas channels. It is shown that the twice maximized stack net power increases monotonically with total volume raised to the power 3/4, similarly to metabolic rate and body size in animal design.     

An integrated simulation model for PEM fuel cell power systems with a buck DC-DC converter

Fuel cell powered systems generally have a high current and a low voltage. Therefore, the output voltage of the fuel cell must be stepped-down using a DC-DC buck converter. However, since the fuel cell and converter have different dynamics, they must be suitably coordinated in order to satisfy the demanded load. Accordingly, this study commences by constructing a MATLAB/Simulink model of a proton exchange membrane fuel cell (PEMFC) system comprising a PEMFC stack, an air/fuel supply system, and a temperature control system. The validity of the PEMFC model is demonstrated by comparing the simulation results obtained for the polarzation curves of a single fuel cell with the corresponding experimental curves. A model is then constructed of the DC-DC buck converter used to step-down the PEMFC output voltage. In addition, a sliding mode control (SMC) scheme is proposed for the DC-DC buck converter which guarantees a low and stable output voltage given transient variations in the output voltage of the PEMFC. Finally, a model is constructed of a DC-AC inverter with a pulse width modulated (PWM) control scheme which enables the PEMFC stack to supply the grid or power AC applications directly. Overall, the combined PEMFC/DC-DC buck converter/DC-AC inverter model provides a powerful and versatile tool for the design and development of a wide range of PEMFC power systems.     

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.     

A novel surrogate model for channel geometry optimization of PEM fuel cell based on Bagging-SVM Ensemble Regression

Channel structure plays an important role on the performance of proton exchange membrane fuel cell (PEMFC). In this study, the channel geometry of a PEMFC is optimized through genetic algorithm to obtain better performance. For the first time, a machine learning method called Bagging Ensemble Regression is employed as the surrogate model to calculate the fitness value of the algorithm, which accelerates the optimization process. First, a three-dimensional PEMFC simulation model is developed as the optimization prototype through CFD technology. Second, the Bagging ensemble model is trained through training data obtained from the CFD model. Then the Bagging ensemble model is integrated into the genetic algorithm to conduct the optimization process. Finally, the optimal model obtained is compared with the optimization prototype in terms of polarization curves, pressure drop, and reactant distribution, and the advantages of using Bagging ensemble model are discussed. Results show that the optimal model has a smaller pressure drop and a more uniform reactant distribution than the basic model at the expense of just a little power density. The presented surrogate model shows high prediction accuracy with only a small amount of training data, which is superior to the commonly used surrogate models.     

A model of PEMFC-battery system to evaluate inner operating status and energy consumption under different energy management strategies

A hybrid system with jointed battery and PEMFC is popular and of great potential in New Energy Vehicle (NEV) application. However, reliability and efficiency remain to be improved for commercial products. To reflect the complicated physics inside the proton exchange membrane fuel cell (PEMFC), the PEMFC model consisting of inner muti-physics process and other accessories was built, then a complete hybrid system was established when a matched battery, DC/DC, regenerative braking were taken into consideration. Based on the above model, the stack state and system performance under standard cycle for heavy duty vehicle-CWTVC were obtained. According to the simulation results, fuel cell states such as pressure, water content and voltage suffers severe oscillation with external load, especially in the highway cycle. Membrane electrode assembly (MEA) suffers from pressure impact with average value of more than 24 kPa in highway cycle. In the aspect of relative humidity, the PEMFC stack is most threatened in road cycle. As for the hybrid system, its efficiency and state of charge (SOC) fluctuation perform worst in urban cycle and road cycle respectively, while its highest efficiency occurs in road test. Operating mode of fuel cell has influence on hybrid system. When 3-level mode of fuel cell output was applied, the efficiency increased to its peak value at medium level of 28 kW and then declined gradually. H₂ consumption had an opposite trend compared to efficiency. In the aspect of battery SOC, it declines in operating process and its fluctuations decreases when medium level got bigger. The 3-level mode and 4-level mode were compared using this model. It can be concluded that although 3-level mode performs slightly better in hybrid system efficiency, H₂ consumption, pressure impact, it does not have absolute advantage over 4-level mode in other indicators.     

Modelling,simulation and control of a proton exchange membrane fuel cell (PEMFC) power system

Fuel cell power systems are emerging as promising means of electrical power generation on account of the associated clean electricity generation process, as well as their suitability for use in a wide range of applications. During the design stage, the development of a computer model for simulating the behaviour of a system under development can facilitate the experimentation and testing of that system's performance. Since the electrical power output of a fuel cell stack is seldom at a suitable fixed voltage, conditioning circuits and their associated controllers must be incorporated in the design of the fuel cell power system. This paper presents a MATLAB/Simulink model that simulates the behaviour of a Proton Exchange Membrane Fuel Cell (PEMFC), conditioning circuits and their controllers. The computer modelling of the PEMFC was based on adopted mathematical models that describe the fuel cell's operational voltage, while accounting for the irreversibilities associated with the fuel cell stack. The conditioning circuits that are included in the Simulink model are a DC–DC converter and DC–AC inverter circuits. These circuits are the commonly utilized power electronics circuits for regulating and conditioning the output voltage from a fuel cell stack. The modelling of the circuits is based on relationships that govern the output voltage behaviour with respect to their input voltages, switching duty cycle and efficiency. In addition, this paper describes a Fuzzy Logic Controller (FLC) design that is aimed at regulating the conditioning circuits to provide and maintain suitable electrical power for a wide range of applications. The model presented demonstrates the use of the FLC in conjunction with the PEMFC Simulink model and that it is the basis for more in-depth analytical models.     

Multi-objective topology optimization of end plates of proton exchange membrane fuel cell stacks

End plates of the proton exchange membrane fuel cell (PEMFC) need to be well designed because their strength and rigidity directly affect the clamping pressure distribution and thus affect the performance and lifetime of fuel cell stacks. In this paper, a multi-objective topology optimization model of the end plates in a PEMFC stack with nonlinear contact boundary conditions was established to obtain an optimized structural design. It was found that the design improved with topology optimization is not only light but also meets manufacturability requirements. This provides good guidance for the design of a high-performance end plate.     

Neuro-evolutionary approach applied for optimizing the PEMFC performance

A multi-objective optimization strategy, based on stacked neural network–genetic algorithm (SNN–GA) hybrid approach, was applied to study the C/PBI content on a high temperature PEMFC performance. The operating conditions of PEMFC were correlated with power density and electrochemical active surface area for electrodes. The structure of the stack was determined in an optimal form related to the contribution of individual neural networks, after applying an interpolation based procedure. Multi-objective optimization using SNN as model and GA as solving procedure provides optimal working conditions which lead to a high PEMFC performance. Simulation results were in agreement with experimental data, both for model validation and system optimization (the C/PBI content in the range of 17–21%).     

Exergy analysis and optimization of a HT-PEMFC using developed Manta Ray Foraging Optimization Algorithm

This paper analyzes the efficiency of a high-temperature proton exchange membrane fuel cell (HT-PEMFC) by calculating the output voltage of the cell in different working conditions, using the semi-experimental relationships. The irreversibility and the exergy efficiency of the fuel cell is calculated under different working conditions and the effect of temperature and pressure has been studied. To achieve optimal design for the PEMFC, its parameters are optimized based on irreversibility, exergy efficiency, and its work. The system optimization is applied by a modified version of the Manta Ray Foraging Optimization Algorithm. The suggested algorithm is then compared with other algorithms from the literature and also simulation results and showed a high agreement between the suggested algorithm and the simulation results.