Hybrid artificial bee colony algorithm for parameter estimation of proton exchange membrane fuel cell

The accurate electrochemical model plays an important role in design and analysis of hydrogen fuel cell systems. For the purpose of estimating parameters of the proton exchange membrane fuel cell (PEMFC) model, and inspired by the foraging behavior of bacteria and bees, a hybrid artificial bee colony (HABC) algorithm is proposed. The HABC uses an improved solution search equation that mimics the chemotactic effect of bacteria to enhance the local search ability. To avoid premature convergence and improve search accuracy, the adaptive Boltzmann selection scheme is adopted, which adjusts selective probabilities in different stages. Performance testing has been conducted on some typical benchmark functions. The results demonstrate that the HABC outperforms other methods (BIPOA, PSOPS and two improved GAs) in both convergence speed and accuracy. The proposed approach is applied to estimate the PEMFC model parameters and the satisfactory model predictive curves are obtained. More experimental results in different search ranges and validate strategies indicate that HABC is an efficient technique for the parameter estimation problem of PEMFC.     

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.     

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.     

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.     

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.     

Parameter estimation of fuel cell polarization curve using BMO algorithm

Polarization curves of proton exchange membrane fuel cells (PEMFCs) are affected by various parameters. The relative importance and effect of each parameter on the polarization curve is different. This paper studies estimation of parameters with the most influence on the electrochemical model. In order to evaluate the obtained results, the model accuracy is compared with that model in which all the parameters are estimated. Because PEMFCs parameter estimation is a complex optimization problem, a recently invented nature-inspired algorithm, bird mating optimizer (BMO), is proposed. For this aim, two real systems, the SR-12 Modular PEM Generator and the Ballard Mark V FC, are considered. The obtained results show that when the whole parameters are estimated, the accuracy of the model increases. Also, BMO algorithm yields better results than the other studied methods in terms of precision and robustness.     

Sensor fault estimation of PEM fuel cells using Takagi Sugeno fuzzy model

This paper presents a sensor fault estimation scheme for polymer electrolyte membrane (PEM) fuel cells using Takagi Sugeno (TS) fuzzy model. First, PEM fuel cell systems with sensor faults are modelled by TS fuzzy model. Next, by adding a first order filter, an augmented TS fuzzy system with actuator fault is obtained. Then, for the augmented system, an unknown input observer (UIO) and a fault estimator are developed. The UIO gains are computed by solving linear matrix equalities (LMEs) and linear matrix inequalities (LMIs). The UIO convergence and stability are analyzed and the performances of the proposed fault estimation scheme is demonstrated by numerical simulations for a PEM fuel cell system with return manifold pressure and hydrogen mass sensors.     

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.     

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.     

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.     

Data-driven parameterization of polymer electrolyte membrane fuel cell models via simultaneous local linear structured state space identification

In order to mitigate the degradation and prolong the lifetime of polymer electrolyte membrane fuel cells, advanced, model-based control strategies are becoming indispensable. Thereby, the availability of accurate yet computationally efficient fuel cell models is of crucial importance. Associated with this is the need to efficiently parameterize a given model to a concise and cost-effective experimental data set. A challenging task due to the large number of unknown parameters and the resulting complex optimization problem. In this work, a parameterization scheme based on the simultaneous estimation of multiple structured state space models, obtained by analytic linearization of a candidate fuel cell stack model, is proposed. These local linear models have the advantage of high computational efficiency, regaining the desired flexibility required for the typically iterative task of model parameterization. Due to the analytic derivation of the local linear models, the relation to the original parameters of the non-linear model is retained. Furthermore, the local linear models enable a straight-forward parameter significance and identifiability analysis with respect to experimental data. The proposed method is demonstrated using experimental data from a 30 kW commercial polymer electrolyte membrane fuel cell stack.     

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.     

Enhancing reliability and lifespan of PEM fuel cells through neural network-based fault detection and classification

In order to maximise fuel cell reliability of operation and useful life span, an accurate online health assessment of the fuel cell system is essential. Existing algorithms for fault detection in fuel cell systems are based on sensing elements, control methods, and statistical/probabilistic models. In this paper, an artificial neural network (ANN) will be developed to detect and classify faults in proton-exchange membrane (PEM) fuel cell systems. As the ANN model developed within the PEM system relies on the input and output current and voltage, additional sensing devices are not required within the system. Based on an experimental setup using a 3-kW fuel cell system, it was found that the proposed model was able to detect faults associated with the reduction/increase of fuel pressure, H₂ consumption rate, and voltage regulation changes in the dc-dc converter with >90% accuracy. In the proposed model, historical data is required to train and validate the ANN algorithm, but after this is complete, no human intervention is required afterward.     

An algorithm for estimation of membrane water content in PEM fuel cells

Available humidity sensing techniques are often intrusive, and of limited practical interest for real-time control applications due to their cost, size, and inadequate response time and accuracy. In this study, we present a novel method for estimation of PEM fuel cell humidity by exploiting its effect on cell resistive voltage drop. This voltage loss is discerned from mass transport, concentration, activation losses and open circuit voltage by a well-known fuel cell voltage model. The proposed scheme makes use of measurements of voltage, current, temperature, and total pressure values in the anode and cathode. It also incorporates dynamic estimators for hydrogen and oxygen partial pressures, adapted from [M. Arcak, H. Gorgun, L.M. Pedersen, S. Varigonda, A nonlinear observer design for fuel cell hydrogen estimation, IEEE Trans. Control Syst. Technol. 12 (1) (2004) 101–110]. The membrane resistance thus obtained is then used to estimate membrane water content following functional characterizations presented in [T.E. Springer, T.A. Zawodzinski, S. Gottesfeld, Polymer electrolyte fuel cell model, J. Electrochem. Soc. 138 (8) (1991) 2334–2342]. Experiments with this estimation technique, performed at the Connecticut Global Fuel Cell Center, are presented and discussed.     

A micro-scale model for predicting contact resistance between bipolar plate and gas diffusion layer in PEM fuel cells

Contact resistance between the bipolar plate (BPP) and the gas diffusion layer (GDL) in a proton exchange membrane (PEM) fuel cell constitutes a significant portion of the overall fuel cell electrical resistance under the normal operation conditions. Most current methods for contact resistance estimation are experimental and there is a lack of well developed theoretical methods. A micro-scale numerical model is developed to predict the electrical contact resistance between BPP and GDL by simulating the BPP surface topology and GDL structure and numerically determining the status for each contact spot. The total resistance and pressure are obtained by considering all contact spots as resistances in parallel and summing the results together. This model shows good agreements with experimental results. Influences of BPP surface roughness parameters on contact resistance are also studied. This model is beneficial in understanding the contact behavior between BPP and GDL and can be integrated with other fuel cell simulations to predict the overall performance of PEM fuel cells.     

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.     

Modeling of ion and water transport in the polymer electrolyte membrane of PEM fuel cells

Ion and water transport phenomena in the polymer electrolyte membrane (PEM) play a significant role in the energy conversion process of a PEM fuel cell, as they provide the closure for the electric and mass transport in the PEM fuel cells. A mathematical model for the transport of ion and water in the PEM is formulated in this study, based on the non-equilibrium thermodynamics and the Generalized Stefan–Maxwell equations. The physical constants of the model, such as the binary diffusion coefficients in the Generalized Stefan–Maxwell equations, are determined from experimental data available in literature for membrane-water diffusion and conductivity. The electrolyte transport model is incorporated into a model for the entire PEM fuel cell; water transport in the electrolyte and in the other cell components are coupled and solved in a single computational domain. It is shown that the present generalized formulation is advantageous to other formulations for the macroscopic analysis of transport phenomena through the membrane electrolyte.     

Feedback-Linearization-Based Nonlinear Control for PEM Fuel Cells

This paper presents a dynamic nonlinear model for polymer electrolyte membrane fuel cells (PEMFCs). A nonlinear controller is designed based on the proposed model to prolong the stack life of the PEM fuel cells. Since it is known that large deviations between hydrogen and oxygen partial pressures can cause severe membrane damage in the fuel cell, feedback linearization is applied to the PEM fuel cell system so that the deviation can be kept as small as possible during disturbances or load variations. A dynamic PEM fuel cell model is proposed as a nonlinear, multiple-input multiple-output system so that feedback linearization can be directly utilized. During the control design, hydrogen and oxygen inlet flow rates are defined as the control variables, and the pressures of hydrogen and oxygen are appropriately defined as the control objectives. The details of the design of the control scheme are provided in the paper. The proposed dynamic model was tested by comparing the simulation results with the experimental data previously published. The simulation results show that PEMFCs equipped with the proposed nonlinear controls have better transient performances than those with linear controls.     

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.     

Importance and applications of DOE/optimization methods in PEM fuel cells: A review

Although proton exchange membrane (PEM) fuel cells are seen as one of the energy conversion technologies of the future due to their high energy conversion efficiency, low levels of emissions, low temperature operation, and compact systems, studies continue to reduce their cost, which is the biggest obstacle to commercialization. Design of experiment (DOE) methods are frequently used in optimization of PEM fuel cells to reduce their cost by decreasing experimental runs. This paper reviews the main gains subsuming the usage of several DOE and optimization methods in PEM fuel cell components, design, operation conditions, and model parameters. It firstly focuses on the Taguchi method and response surface methodology (RSM) known to be applied usually in PEM fuel cell studies. In addition to these known methods, other experimental design and optimization methods used in PEM fuel cells are discussed, and the results are summarized.