Nonlinear D-optimal design of experiments for polymer–electrolyte–membrane fuel cells

Using empirical models, parameters have to be estimated from experimental data. Experimental characterization of fuel cell stacks is an expensive and time-consuming task. Therefore it is very important to choose an experimental design, which maximizes the statistical quality of the resulting information. Box and Lucas (Biometrika 46 (1959)) showed that it is possible to optimize nonlinear experimental designs by the minimization of the covariance matrix of the least squares estimate. The aim of this work is to adopt this general method in order to investigate its ability for application in polymer–electrolyte–membrane fuel cell (PEMFC) characterization. Based on an empirical PEMFC model a D-optimal design criterion has been developed and validated. Numerical methods, evolutionary and heuristic are investigated with respect to fast and robust evaluation of the design criterion. For a given set of experimental data best results are achieved using a heuristic approach, a so-called sequential search. Based on that result an algorithm to obtain an optimal design of experiments (DoE) in a nondeterministic operating area is introduced. The proposed algorithm is able to take into account experimental limitations due to test facilities or examinee. The algorithm further allows to include existing and for reference needed experiments.     

Multi-input and multi-output neural model of the mechanical nonlinear behaviour of a PEM fuel cell system

A fuel cell system model is necessary to prepare and analyse vibration tests. However, in the literature, the mechanical aspect of the fuel cell systems is neglected. In this paper, a neural network modelling approach for the mechanical nonlinear behaviour of a proton exchange membrane (PEM) fuel cell system is proposed. An experimental set is designed for this purpose: a fuel cell system in operation is subjected to random and swept-sine excitations on a vibrating platform in three axes directions. Its mechanical response is measured with three-dimensional accelerometers. The raw experimental data are exploited to create a multi-input and multi-output (MIMO) model using a multi-layer perceptron neural network combined with a time regression input vector. The model is trained and tested. Results from the analysis show good prediction accuracy. This approach is promising because it can be extended to further complex applications. In the future, the mechanical fuel cell system controller will be implemented on a real-time system that provides an environment to analyse the performance and optimize mechanical parameters design of the PEM fuel system and its auxiliaries.     

Model-based analysis of thermal and geometrical effects in a microscale methanol fuel cell

This paper reports the development of a mathematical model to predict the performance of a microscale methanol fuel cell with a single fuel/electrolyte channel. Performance of the cell is investigated as a function of fuel stream inlet temperature and catalyst deposition geometry. The model is fit to experimental data by maximizing the coefficient of determination, R². Results show that peak power density with regard to total exposed catalyst surface area is inversely proportional to catalyst deposition width and proportional to fuel stream temperature. For both parameters, the mathematical model was found to compare well with experimental results in the operating regime preceding and including maximum power density. The model presented here can be used to optimize these parameters during the design phase.     

Modeling of an anode-supported Ni-YSZ|Ni-ScSZ|ScSZ| LSM-ScSZ multiple layers SOFC cell: Part II. Simulations and discussion

In part I of the present study, a two-dimensional isothermal mechanistic model of a composite yttria/scandia stabilized zirconia anode-supported multiple layers solid oxide fuel cell (Ni-YSZ|Ni-ScSZ|ScSZ|LSM-ScSZ) was developed, calibrated and validated using a button cell setup. In this paper, the model was further validated for extended operating conditions of fuel and oxidant compositions, which confirmed the robustness of the model. Since an important attribute of this model is its ability to accurately describe the effect of cell microstructure on cell performance, a large section of part II is devoted to sensitivity analysis of various microstructure parameters (cathode area, porosity, layer thickness and particle radius) on cell performance. In particular, the simulation results have shown how the button cell microstructure should be modified to optimize its performance. The proposed model could be used as a bridge between micro-scale electrode models and macro-scale unit cell simulation, thus being a useful tool for electrode design.     

Analysis and optimization of high temperature proton exchange membrane (HT-PEM) fuel cell based on surrogate model

The stoichiometric ratio and flow channel geometry play a vital role in the performance of high temperature proton exchange membrane (HT-PEM) fuel cells. Because of the high cost of experiments or simulations, most analyses and optimization of the stoichiometric ratio and flow channel geometry are limited to several points in the entire design domain. In this study, an analysis and optimization method for HT-PEM fuel cells based on the surrogate model was proposed. Surrogate models were constructed using some of the available budgets of samples to analyze and optimize the entire design domain. With this method, it was indicated that the effect of the cathode stoichiometric ratio is more significant to the cell performance than the anode stoichiometric ratio and there are significant nonlinear interactions among the flow channel geometry parameters. At the fixed operating voltage, the flow channel geometry with the maximum current density and that with the maximum real power were obtained. Compared with the base design, the designs obtained by the surrogate model improve the current density and real power by 10.54% and 3.93%, respectively. Thus, this analysis and optimization method is demonstrated to be helpful and deserves attention in future research.     

Design optimization for the hybrid power system of a green building

This paper proposes an optimal design procedure for a green building equipped with renewable energy, energy storages, and proton exchange membrane fuel cells (PEMFCs). First, we introduce the hybrid power system of the green building and construct a simulation model using Matlab/SimPowerSystem?. The model parameters are tuned so that the system responses can be estimated without extensive experiments in the optimization processes. Second, we define the cost and reliability indexes to optimize the system design using three steps: component selection, component sizing, and power management (PM) adjustment. We further define the safety index to evaluate the system's sustainability under extreme conditions when no renewable energy is available. Last, we apply the proposed procedures to the green building and demonstrate the benefits of the optimal design. The proposed method can be directly applied to develop customized hybrid power systems in the future.     

Cooling strategy for effective automotive power trains: 3D thermal modeling and multi-faceted approach for integrating thermoelectric modules into proton exchange membrane fuel cell stack

The 3D Thermal modeling utilizes a Finite Differencing heat alteration method augmented with empirical boundary conditions is employed to develop 3D thermal model for the integration of thermoelectric modules with proton exchange membrane fuel cell stack. Hardware-in-Loop was designed under pre-defined drive cycle to obtain fuel cell performance parameters along with anode and cathode gas flow-rates and surface temperatures. The fuel cell model is used to conjugate the experimental boundary conditions with the Finite Differencing code, which implemented heat generation across the stack to depict the chemical composition process. The structural and temporal temperature contours obtained from this model are in compliance with the actual recordings obtained from the infrared detector and thermocouples. The model is harmonized with thermo-electric modules with a modeling strategy, which enables optimize better temporal profile across the stack. This study presents the improvement of a 3D thermal model for proton exchange membrane fuel cell stack along with the interfaced thermo-electric module. The model provided a virtual environment using a model-based design approach to assist the design engineers to manipulate the design correction earlier in the process and eliminate the need for costly and time consuming prototypes.     

An adaptive RNA genetic algorithm for modeling of proton exchange membrane fuel cells

The accurate mathematical model is the key issue to simulation and design of the fuel cell power systems. Aiming at estimating the proton exchange membrane fuel cell (PEMFC) model parameters, an adaptive RNA genetic algorithm (ARNA-GA) which is inspired by the mechanism of biological RNA is proposed. The ARNA-GA uses the RNA strands to represent the potential solutions and new genetic operators are designed for improving the global searching ability. In order to maintain the population diversity and avoid premature convergence, on the basis of the dissimilarity coefficient, the adaptive genetic strategy that allows the algorithm dynamically select crossover operation or mutation operation to execute is proposed. Numerical experiments have been conducted on some benchmark functions with high dimensions. The results indicate that ARNA-GA has better search capability and a higher quality of solutions. Finally, the proposed approach has been applied for the parameter estimation of PEMFC model and the satisfactory results are reached.     

Analysis of design parameters in anodic recirculation system based on ejector technology for PEM fuel cells: A new approach in designing

In this study, the anodic recirculation system (ARS) based on ejector technology in polymer electrolyte membrane PEM fuel cell is studied with employing a theoretical model. A practical method is presented for selecting or designing the ejector in an ARS, that offers the best selection or design. A comprehensive parametric study is performed on the design parameters of a PEM fuel cell stack and an ARS ejector. Four geometrical parameters consist of cell active area, cell number, nozzle throat diameter, and mixing chamber diameter in the design of ARS are intended. The effect of each contributes to the overall system performance parameters is studied. In this parametric study, the correlation between stack design parameters and ejector design parameters are studied. Eventually, based on the results, two dimensionless parameters are useful in the design process are proposed.     

Surrogate model for proton exchange membrane fuel cell (PEMFC)

The main goal of this work is to realize a PEMFC model that can be used efficiently for the global modelling of the fuel cell system. The modelling method proposed in the paper is an approach from an empirical point of view that allows a PEMFC model of “black-box” class to be developed. Moving least squares (MLS) have therefore been employed to approximate the cell voltage characteristics V, using an experimental dataset measured in determinate conditions. The MLS approach appears to present a good balance of response surface accuracy, smoothness, robustness, and ease of use. This kind of numerical model offers good perspectives for the systems identification, the simulation of the systems, the design and the optimization of process control, etc. The results prove that the method is suitable for predicting and describing the fuel cell behaviour in all the points of the approximation domain. The proposed model can be included in a numerical application to optimize the operation of an existing fuel cell system.     

Fuel sensor-less control of a liquid feed fuel cell system under steady load for portable applications

This study presents a novel fuel sensor-less control scheme for a liquid feed fuel cell system that does not rely on a fuel concentration sensor. The proposed approach simplifies the design and reduces the cost and complexity of a liquid feed fuel cell system, and is especially suited to portable power sources, of which the volume and weight are important. During the reaction of a fuel cell, the cell's operating characteristics, such as potential, current and power are measured to control the supply of fuel and regulate its concentration to optimize performance. Experiments were conducted to verify that the fuel sensor-less control algorithm is effective in the liquid feed fuel cell system.     

Experimentally and numerically investigating cell performance and localized characteristics for a high-temperature proton exchange membrane fuel cell

This paper is to experimentally and numerically investigate the cell performance and the localized characteristics associated with a high-temperature proton exchange membrane fuel cell (PEMFC). Three experiments are carried out in order to study the performance of the PEMFC with different operating conditions and to validate the numerical simulation model. The model proposed herein is a three-dimensional (3-D) computational fluid dynamics (CFD) non-isothermal model that essentially consists of thermal–hydraulic equations and electrochemical model. The performance curves of the PEMFC predicted by the present model agree with the experimental measured data. In addition, both the experiments and the predictions precisely demonstrate the enhanced effects of inlet gas temperature and system pressure on the PEMFC performance. Based on the simulation results, the localized characteristics within a PEMFC can be reasonably captured. These parameters include the fuel gas distribution, liquid water saturation distribution, membrane conductivity distribution, temperature variation, and current density distribution etc. As the PEMFC is operated at the higher current density, the fuel gas would be insufficiently supplied to the catalyst layer, consequently causing the decline in the generation of power density. This phenomenon is so called mass transfer limitation, which can be precisely simulated by the present CFD model.     

Optimization and parametric analysis of PEMFC based on an agglomerate model for catalyst layer

A one-dimensional, non-isothermal, single-phase, steady-state comprehensive model is developed to investigate the effects of different parameters of catalyst layer and operational case as relative humidity on the proton exchange membrane fuel cell (PEMFC) performance, then to optimize the design and operation of PEMFC. The agglomerate model with thin film of polymer and liquid water was employed to describe electrochemical reaction in catalyst layers. The model considers the effect of different production ratio of water vapor and liquid water in the reaction on the fuel cell performance. The effects of operational case as temperature, relative humidity of reactants and catalyst layer structure parameters as Pt loading, agglomerate radius and Pt radius on cell performance are computed and discussed in detail. The results indicate that agglomerate radius, Pt loading and Pt particle radius, operation temperature and pressure have different kinds of effects on performance, and the performance can be improved by suitable operational case and catalyst layer structure. Results can provide good reference for optimization design of the catalyst layer and the whole cell.     

Analysis and optimization of solid oxide fuel cell-based auxiliary power units using a generic zero-dimensional fuel cell model

Fuel-cell-based auxiliary power units can help to reduce fuel consumption and emissions in transportation. For this application, the combination of solid oxide fuel cells (SOFCs) with upstream fuel processing by autothermal reforming (ATR) is seen as a highly favorable configuration. Notwithstanding the necessity to improve each single component, an optimized architecture of the fuel cell system as a whole must be achieved. To enable model-based analyses, a system-level approach is proposed in which the fuel cell system is modeled as a multi-stage thermo-chemical process using the “flowsheeting” environment PRO/II™. Therein, the SOFC stack and the ATR are characterized entirely by corresponding thermodynamic processes together with global performance parameters. The developed model is then used to achieve an optimal system layout by comparing different system architectures. A system with anode and cathode off-gas recycling was identified to have the highest electric system efficiency. Taking this system as a basis, the potential for further performance enhancement was evaluated by varying four parameters characterizing different system components. Using methods from the design and analysis of experiments, the effects of these parameters and of their interactions were quantified, leading to an overall optimized system with encouraging performance data.     

A new cost-minimizing power-allocating strategy for the hybrid electric bus with fuel cell/battery health-aware control

The two primary challenges preventing the commercialization of fuel cell hybrid electric vehicles (FCHEV) are their high cost and limited lifespan. Improper use usage can could also hasten the breakdown of proton exchange membrane fuel cell (PEMFC). This paper proposes a new cost-minimizing power-allocating technique with fuel cell/battery health-aware control to optimize the economic potential of fuel cell/battery hybrid buses. The proposed framework quantifies the fuel cell (FC) deterioration of the whole working zone in a real hybrid electric bus using a long short-term memory network (LSTM), which reduces the time required to get the key lifetime parameters. A new FC lifespan model is embedded into the control framework, together with a battery aging model, to balance hydrogen consumption and energy source durability. In addition, in the speed prediction step, an enhanced online Markov prediction approach with stochastic disturbances is presented to increase the forecast accuracy for future disturbances. Finally, comparative analysis is used to verify the efficacy of the suggested approach, which shows that when compared to the benchmark method, the proposed strategy may extend the FC lifetime and lower operating costs by 5.04% and 3.76%, respectively.     

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.     

Network based optimization model for pin-type flow field of polymer electrolyte membrane fuel cell

The flow field of a bipolar plate distributes reactants for polymer electrolyte membrane (PEM) fuel cells and removes the produced water from the fuel cells. It greatly influences the performance of fuel cells, especially the concentration losses. Pin-type design, as one of the widely utilized flow field configurations, has the advantage of low pressure drop but the disadvantage of uneven flow distribution and stagnant areas. In this paper, a network-based optimization model was developed to optimize the pin-type flow field configuration. Two optimization cases, uniform flow distribution with and without considering reactant consumption along flow channels, were investigated and the corresponding optimized designs were developed. Three-dimensional numerical simulations of PEM fuel cell were conducted to validate the proposed optimization model and also to compare the performance of the fuel cells using the optimized designs and the regular pin-type design. The numerical results verified the designs generated with the present optimization model. Both the optimized designs exhibited substantially higher fuel cell performance compared to the regular pin-type configuration. Moreover, the optimized design with considering reactant consumption performed even better than the one without considering the consumption, emphasizing the significance of reactant consumption in the flow field optimization model.     

Integration of a fuel cell into the power system using an optimal controller based on disturbance accommodation control theory

In this paper, the integration of a fuel cell into the power system is treated as a load frequency control (LFC) problem with the fuel cell acting as a load disturbance source. The integration of a fuel cell into the power system results into a change in real power. But changes in real power affect the system frequency. Thus, the integration will result into a change of frequency of the synchronous machines. Hence, we need to design a control scheme for keeping the system in the steady state. An optimal controller based on the disturbance accommodation control (DAC) theory is proposed for this load frequency control problem. For demonstrating the effectiveness of the proposed controller, we have considered a two-area power system with the fuel cell introduced in area 1. The fuel cell is considered as an external disturbance to each subsystem. A mathematical model is derived for each subsystem and based upon these models controllers are designed for keeping each subsystem stable, which in turn stabilizes the overall system. So, the proposed controller is decentralized in nature. To account for the modeling uncertainties, an observer is designed to estimate each subsystem’s own and interfacing variables. The controller uses these estimates to optimize a given performance index and allocate generating unit outputs according to the requirements.     

The modeling of a standalone solid-oxide fuel cell auxiliary power unit

In this research, a Simulink model of a standalone vehicular solid-oxide fuel cell (SOFC) auxiliary power unit (APU) is developed. The SOFC APU model consists of three major components: a controller model; a power electronics system model; and an SOFC plant model, including an SOFC stack module, two heat exchanger modules, and a combustor module. This paper discusses the development of the nonlinear dynamic models for the SOFC stacks, the heat exchangers and the combustors. When coupling with a controller model and a power electronic circuit model, the developed SOFC plant model is able to model the thermal dynamics and the electrochemical dynamics inside the SOFC APU components, as well as the transient responses to the electric loading changes. It has been shown that having such a model for the SOFC APU will help design engineers to adjust design parameters to optimize the performance. The modeling results of the SOFC APU heat-up stage and the output voltage response to a sudden load change are presented in this paper. The fuel flow regulation based on fuel utilization is also briefly discussed.     

Three-dimensional computational fluid dynamics modeling of anode-supported planar SOFC

Modeling plays a very important role in the development of fuel cells and fuel cell systems. The aim of this work is to investigate the electrochemical processes of a Solid Oxide Fuel Cell (SOFC) and to evaluate the performance of the proposed SOFC design. For this aim a three-dimensional Computational Fluid Dynamics (CFD) model has been developed for an anode-supported planar SOFC with corrugated bipolar plates serving as gas channels and current collector. The conservation of mass, momentum, energy and species is solved by using the commercial CFD code FLUENT in the developed model. The add-on FLUENT SOFC module is implemented for modeling the electrochemical reactions, loss mechanisms and related electric parameters throughout the cell. The distributions of temperature, flow velocity, pressure and gaseous (fuel and air) concentrations through the cell structure and gas channels is investigated. The relevant fuel cell variables such as the potential and current distribution over the cell and fuel utilization are calculated and studied. The modeling results indicate that, for the proposed SOFC design, reasonably uniform distributions of current density over the active cell area can be achieved. The geometry of the cathode gas channel has a substantial effect on the oxygen distribution and thus the overall cell performance. Methods for arriving at improved cell designs are discussed.