A metaheuristic-based methodology for efficient system identification of the Proton Exchange Membrane Fuel Cell stacks

In this study, a new procedure for optimum and effective system identification of Proton Exchange Membrane Fuel Cell (PEMFC) stacks is introduced. The present study proposes a method to obtain the optimum amount of the uncertain parameters of the PEMFC design to deliver the uppermost confirmation with the real output voltage value. To do so, the integral of the absolute error (IAE) between the real and model outputted voltage values is considered an objective function. To minimize this function, a modified design of the emperor penguin optimizer has been suggested. The method has been then investigated by performing two real case study models and its achievements are put in comparison with several latest techniques to show the method's productivity. The achievements show that the suggested technique has a higher ability for parameter estimation of the PEMFC models.     

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.     

Adaptive estimation of PEMFC stack model parameters - An experimental verification

The growing popularity of using proton-exchange membrane fuel cells (PEMFCs) stacks in stationary, portable, and transportation applications is driving researchers to develop proper dynamic models for PEMFCs. These models are used to accurately capture the electrical characteristics and runtime performance. This work proposes a well-known equivalent circuit model of a battery, to be modified and used as a model for a PEMFC stacks voltage-current characteristics. This model is modified by finding suitable functions to model the open circuit voltage and the series resistance, required to model the electrical performance of a 200-W PEMFC stack. The paper also shows that the existing adaptive parameters estimation (APE) technique for Li-ion battery parameters estimation is also able to estimate parameters of the PEMFC stack's model. The model parameters are estimated using the APE technique that requires only five experiments. The model is validated experimentally under different load conditions for a 200-W PEMFC stack supplied from a hydrogen cylinder (voltage error ?0.2 V to 0.5 V), and a 30-W PEMFC stack supplied from a fuel stick (voltage error ?0.2 V–0.4 V). The results show that the parameters estimation methodology works well across PEMFC stacks of different sizes with different input fuel intake configurations, with a minimal terminal voltage estimation error in the order of millivolts. Open circuit voltage measurements (OCV) show that the OCV curve starts at a little lower than 31 V, declines slowly to around 30 V for a normalized hydrogen flow rate of 0.6, after which there is a sudden linear decline in OCV was observed. Most of the data has absolute estimation error less than 0.1 V. In fact, the terminal voltage estimation error across all tests, with different current discharge profiles, lies between ?0.2 and 0.2 V only. Also, 95.84% of the error samples lie between ±0.1% error.     

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.     

Neural network model of 100 W portable PEM fuel cell and experimental verification

The inherent properties of artificial neural networks (ANNs) such as low sensitivity to noise and incomplete information make the ANN a promising candidate to model the fuel cell system. In this paper, an ANN-based model of 100 W portable direct hydrogen fed proton exchange membrane fuel cell (PEMFC) is presented. The model is built based on experimentally collected data from a portable 100 W direct hydrogen fed PEMFC in the authors’ laboratory. A multilayer feedforward ANN with back-propagation training algorithm is used to model the portable PEMFC. The ANN consists of fully connected four layers network with two hidden layers. The PEMFC ANN model is trained using extracted data from experimentally measured and calculated parameters. To validate the model, the outputs of the PEMFC ANN are compared against experimental data and results from a dynamic model of portable direct hydrogen fed PEMFC. In addition, three statistical indices to measure variations, unbiasedness (precision), and accuracy in voltage, power, and hydrogen flow are used to evaluate the PEMFC ANN model performance. The indices indicate that the maximum variations, unbiasedness, and accuracy of the voltage, power, and hydrogen flow are 1.45%, 2.04%, and 1.90%, respectively, which shows a close agreement between the outputs of the PEMFC ANN and the experimental results.     

Optimal parameter identification of PEMFC stacks using Adaptive Sparrow Search Algorithm

In this paper, a new optimization algorithm called Adaptive Sparrow Search Algorithm (ASSA) is proposed for optimal model parameters identification of the proton exchange membrane fuel cell (PEMFC) stacks. The proposed ASSA is utilized for minimizing the sum of squared error (SSE) between the empirical stack voltage and the calculated stack voltage by optimal selection of the mentioned parameters in the PEMFC stack. The method is then performed to three case studies including Ballard Mark V, Horizon H-12, and NedStack PS6 under different operating conditions and give 0.82, 5.14, and 0.097 of SEE which is the least value for all three case studies. The results of the algorithm are compared with some reported works in the literature including CGOA, GRA, and basic SSA to show the method prominence. The final results indicated that the proposed ASSA has the best efficiency toward the others.     

Design of proton exchange membrane fuel cell grid-connected system based on resonant current controller

Because of its high efficiency, low pollution and good stability, proton exchange membrane fuel cell (PEMFC) is considered as one of the most promising technologies for a wide range of applications, such as distributed power generation, transportation, portable power source and automobile. In a PEMFC grid-connected system, the proportion integration (PI) regulator can achieve zero error for the dc components in the rotating frame, but cannot achieve zero error for the ac components in the rotating frame. Hence, the PEMFC grid-connected system will produce a large number of harmonics. In order to overcome this shortcoming, a proportion integration resonant (PIR) controller is utilized to realize zero magnitude error and selective disturbance rejection. Instead of the PIR controller, a vector proportion integration (VPI) controller is designed to quickly and accurately regulate current which achieve zero both amplitude and phase frequency response at the resonant frequency simultaneously. In this paper, the PEMFC grid-connected system based on PIR and VPI controllers are developed according to the operating characteristics of a PEMFC generation system, then analyze and compare the performance of compensation harmonics between them. The total harmonic distortion (THD) of grid-connected voltage and current are measured by means of the criterion of IEEE Std1547-2003. This proposed grid-connected method will provide a novel approach for the design of advanced PEMFC grid-connected control system.     

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.     

Fractional order modeling and two loop control of PEM fuel cell for voltage regulation considering both source and load perturbations

The growing demand for renewable energy sources has favored attention towards fuel cell and in particular towards Polymer Electrolyte Membrane Fuel Cell (PEMFC) as an alternative energy source. Despite the advantage of possessing high current density, standalone isolated fuel cell operate at low voltage and the output is heavily dependent on the operating condition. This demands the integration of fuel cells with suitable power conditioning units. The present work aims at designing a controller which achieves the objective of regulated output voltage irrespective of variation in both load and source operating condition. The design and integration of the converter with PEMFC necessitates the development of a mathematical model, which can represent the PEMFC dynamics under different operating conditions. PEMFCs are known to exhibit distributed dynamics and possess long term memory, which are more accurately represented by fractional calculus. In this regard, a hybrid optimization based approach for fractional order modeling of PEMFC has been proposed. Further using the model, a fractional order Proportional Integral (FOPI) controller has been designed for regulating the load voltage. The presence of an extra tuning parameter in FOPI allows greater flexibility in achieving the system specification as compared to the classical Integer Order Proportional Integral (IOPI) controller. The effectiveness of the proposed FOPI controller for PEMFC fed PWM DC/DC converter has been validated under varying operating condition of the PEMFC and load perturbations in real time environment.     

Optimal parameter estimation for PEMFC using modified monarch butterfly optimization

The present study develops a new optimization method called monarch butterfly optimization algorithm for optimal parameter estimation of the polymer electrolyte membrane fuel cell (PEMFC). After designing the proposed methodology, it is implemented to 250 MW PEMFC stack under different operating conditions to show the system efficiency and the results are compared with some state-of-the-art methods including Grass Fibrous Root Optimization Algorithm, hybrid Teaching Learning Based Optimization-Differential Evolution Algorithm, and the basic MBO algorithm. Two operational conditions in 3/5 bar and 80°C and 2.5/3 bar, 70°C are used for model verification. The main idea is to minimize the sum of square error (SSE) between the estimated and the actual data. Simulation results in the first condition give an SSE of value 7.277667729 with 9.28434e−16 SD value and in the second condition, an SSE of value 4.52810115 with 0.043581628 standard deviations has been reached as the minimum value among the other compared methods that indicate the accuracy and the robustness of the suggested method toward the analyzed methods. The algorithm also gives a convergence speed of 540 iterations and 370 iterations for conditions 1 and 2, respectively that are the fastest in the study.     

Degradation prediction of proton exchange membrane fuel cell using auto-encoder based health indicator and long short-term memory network

As durability of proton exchange membrane fuel cell (PEMFC) remains as the main obstacle for its larger scale commercialization, predicting PEMFC degradation progress is thus an effective way to extend its lifetime. To realize reliable prediction, a novel health indicator (HI) extraction method based on auto-encoder is proposed in this paper, with which PEMFC future voltage can be predicted by long short-term memory network (LSTM). The effectiveness and robustness of proposed approach is investigated with test data simulating vehicle operation conditions, and accurate prediction performance can be observed, with the maximum root mean square error (RMSE) of 0.003513. Moreover, by comparing with two commonly prognostic methods including attention-based gated recurrent unit network and polarization model-LSTM, the proposed method can provide better predictions under various operating conditions. Furthermore, with the proposed method, the degradation mechanism of PEMFC can also be analyzed. Therefore, the proposed prognostic method can predict reliable PEMFC degradation progress and its corresponding degradation mechanisms, which will be beneficial in practical PEMFC systems for taking appropriate strategies to guarantee PEMFC durability.     

Membrane-hydration-state detection in proton exchange membrane fuel cells using improved ambient-condition-based dynamic model

Proton-exchange-membrane fuel cells (PEMFCs) are a popular source of alternative energy because of their operational reliability and compactness. This paper presents an improved model to represent the semi-empirical voltage of PEMFCs to overcome the limitations of existing models. The proposed model considers variations in ambient conditions, such as the ambient temperature and relative humidity, to obtain the accurate output voltage that corresponds to variations in dynamic and static loads. The proposed model was developed by conducting several experiments on the Horizon PEMFC system under normal, humid, and dry ambient conditions. Subsequently, the model parameters corresponding to each case were optimised using the quantum lightning search algorithm (QLSA). Parameters demonstrating significant variations with ambient conditions were finally represented as a function of the ambient temperature and relative humidity via statistical regression analysis. The voltage obtained using the modified model was verified by conducting experiments on both the Horizon and NEXA PEMFC systems by varying the ambient temperature and relative humidity with root mean square error (RMSE) less than 0.5. As observed, the results we obtained using the modified model closely approximated those obtained using PEMFCs under various operating conditions, and in both cases, the PEMFC voltage was observed to vary with the ambient and load conditions. The inherent advantages of the proposed PEMFC model include its ability to determine the membrane-water content and water pressure inside PEMFCs. The membrane-water content provides clear indications regarding the occurrence of drying and flooding faults. Under normal conditions, this membrane water content ranges from 11 to 7 for both the Horizon and NEXA PEMFC system. The simulation results suggested using the threshold membrane-water-content level as a possible indicator of fault occurrence under extreme ambient conditions. The limits of the said threshold were observed to be useful for fault diagnosis within PEMFC systems.     

Portable direct hydrogen fed PEM fuel cell model and experimental verification

This paper focuses on the experimental verification of an electrochemical model of 100 W portable direct hydrogen fed proton exchange membrane (PEM) fuel cell (FC). The model is built based on the relationship between the FC terminal voltage and the partial pressures of hydrogen and oxygen. The model is then used to predict the output voltage and study the transient response of a PEMFC when subjected to rapid changes in the load. To validate the model, the measurements obtained from a commercially available 100 W FC are compared against the model results. Three different scenarios are considered for testing the model and the actual FC. In the first two scenarios, a step change in the load is used. In the third scenario, the load is replaced by a laptop computer. Results show a close agreement between the voltage and the power responses of the proposed model and the actual PEM FC. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

The optimal performance estimation for an unknown PEMFC based on the Taguchi method and a generic numerical PEMFC model

In this paper, a new approach to estimate the optimal performance of an unknown proton exchange membrane fuel cell (PEMFC) has been proposed. This proposed approach combines the Taguchi method and the numerical PEMFC model. Simulation results obtained using the Taguchi method help to determine the value of control factors that represent the tested unknown PEMFC. The objective of reducing both fuel consumption and operation cost can be achieved by determining the parameters for the unknown PEMFC. In addition, the optimal operation power for the tested unknown PEMFC can also be predicted. Experimental results on the test equipment show that the proposed approach is effective in optimal performance estimation for the tested unknown PEMFC, thus demonstrating the success achieved by combining the Taguchi method and the numerical PEMFC model.     

Fuel cell diagnosis method based on multifractal analysis of stack voltage signal

Measuring local singularities on voltage signal transmits valuable information about the evolving dynamics of non-stationary and nonlinear processes in fuel cell systems. This paper deals with wavelet transform combined with multifractal formalism proposed for PEMFC behavior analysis. The proposed method combines the capability of wavelet transform to produce high coefficients on the singular points of signals and the ability of multifractal formalism to measure the singularity strength via the wavelet coefficients. This method is applied in order to discriminate the voltage signals acquired on a PEMFC operated in different conditions. The average multifractal spectrum estimated on voltage signals acquired at nominal operating conditions is compared to those measured for poor operating conditions considered as fault modes.     

A review of polymer electrolyte membrane fuel cell stack testing

This paper presents an overview of polymer electrolyte membrane fuel cell (PEMFC) stack testing. Stack testing is critical for evaluating and demonstrating the viability and durability required for commercial applications. Single cell performance cannot be employed alone to fully derive the expected performance of PEMFC stacks, due to the non-uniformity in potential, temperature, and reactant and product flow distributions observed in stacks. In this paper, we provide a comprehensive review of the state-of-the art in PEMFC testing. We discuss the main topics of investigation, including single cell vs. stack-level performance, cell voltage uniformity, influence of operating conditions, durability and degradation, dynamic operation, and stack demonstrations. We also present opportunities for future work, including the need to verify the impact of stack size and cell voltage uniformity on performance, determine operating conditions for achieving a balance between electrical efficiency and flooding/dry-out, meet lifetime requirements through endurance testing, and develop a stronger understanding of degradation.     

Experimental study of dynamic performance of defective cell within a PEMFC stack

Defective cell in a PEMFC stack may reduce durability and reliability of the stack and even damage the stack. However, the dynamic performance of defective cell within a PEMFC stack is not clear. In this paper, the dynamic characteristics of the defective cell under different load conditions are analyzed. The results reveal that the defective cell has slower dynamic response rate than other single fuel cells, and the defective cell causes a poor voltage uniformity of the stack. The increased frequency of load change makes the voltage change rate of defective cell higher. The increased amplitude of load change has a more negative impact than the increased frequency of load change, and makes the defective cell more prone to flooding. Furthermore, impedance spectrum shows that these load conditions have greater negative effect for the defective cell than other cells. Finally, according to the experimental results and practical application, recommends related to control strategy of PEMFC stack are proposed to extend lifetime.     

Application of flower pollination algorithm for enhanced proton exchange membrane fuel cell modelling

Modelling of Proton Exchange Membrane Fuel Cell (PEMFC) characteristics assumes importance in view of better understanding, analysis and design of high efficient fuel cell systems. Limited by its complexity, strongly coupled behaviour and multivariate characteristics; optimization techniques are attempted to model PEMFC characteristics. Influenced by convergence speed, computational efficiency, level of complexity, dependency on initial solution and ability to locate global optimum; recently evolved Flower Pollination Algorithm is utilized in this work for PEMFC modelling. This method is applied to derive unknown model parameters of fuel cells having different characteristics and rating. Further, to illustrate the superiority of the method, results obtained are compared with some of the recent works. Moreover, to showcase its efficiency; comprehensive comparison is made in terms of model parameter values, sum of squared error, individual absolute error and relative error values.     

Parallel serpentine-baffle flow field design for water management in a proton exchange membrane fuel cell

In a proton exchange membrane fuel cell (PEMFC) water management is one of the critical issues to be addressed. Although the membrane requires humidification for high proton conductivity, water in excess decreases the cell performance by flooding. In this paper an improved strategy for water management in a fuel cell operating with low water content is proposed using a parallel serpentine-baffle flow field plate (PSBFFP) design compared to the parallel serpentine flow field plate (PSFFP). The water management in a fuel cell is closely connected to the temperature control in the fuel cell and gases humidifier. The PSBFFP and the PSFFP were evaluated comparatively under three different humidity conditions and their influence on the PEMFC prototype performance was monitored by determining the current density–voltage and current density–power curves. Under low humidification conditions the PEMFC prototype presented better performance when fitted with the PSBFFP since it retains water in the flow field channels.