Computationally efficient modeling of the dynamic behavior of a portable PEM fuel cell stack

A numerically efficient mathematical model of a proton exchange membrane fuel cell (PEMFC) stack is presented. The aim of this model is to study the dynamic response of a PEMFC stack subjected to load changes under the restriction of short computing time. This restriction was imposed in order for the model to be applicable for nonlinear model predictive control (NMPC). The dynamic, non-isothermal model is based on mass and energy balance equations, which are reduced to ordinary differential equations in time. The reduced equations are solved for a single cell and the results are upscaled to describe the fuel cell stack. This approach makes our calculations computationally efficient. We study the feasibility of capturing water balance effects with such a reduced model. Mass balance equations for water vapor and liquid water including the phase change as well as a steady-state membrane model accounting for the electro-osmotic drag and diffusion of water through the membrane are included. Based on this approach the model is successfully used to predict critical operating conditions by monitoring the amount of liquid water in the stack and the stack impedance. The model and the overall calculation method are validated using two different load profiles on realistic time scales of up to 30 min. The simulation results are used to clarify the measured characteristics of the stack temperature and the stack voltage, which has rarely been done on such long time scales. In addition, a discussion of the influence of flooding and dry-out on the stack voltage is included. The modeling approach proves to be computationally efficient: an operating time of 0.5 h is simulated in less than 1 s, while still showing sufficient accuracy.     

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.     

Experimental analysis of the performance of the air supply system in a 120 kW polymer electrolyte membrane fuel cell system

For analyzing the performance of 120 kW polymer electrolyte membrane fuel cell (PEMFC) system and its air supply system, an air system test bench was built, then applied on a 120 kW PEMFC system test bench composed of air supply subsystem, hydrogen supply subsystem, stack, cooling subsystem and electronic control subsystem. The strategy composed of feedforward table and Piecewise proportional integral (PI) feedback control strategy is employed to regulate the flow rate and pressure of air supply system. Firstly, the air compressor map and the mapping relationship between the speed of air compressor, opening of back-pressure valve and stack current are obtained by carrying out experiments on the PEMFC air system bench. Then, the max output performance, steady-state performance, the startup performance, the dynamic response abilities of PEMFC system are tested, respectively. During the experiments, performances under different test conditions were analyzed by comparing parameters such as voltage inconsistency, average voltage, minimum voltage, voltage range, net power of the PEMFC system, and stack power. The test results show that the air supply system can provide qualified flow rate and pressure for the PEMFC stack. The peak power of the stack is 120 kW and net power of the system is 97 kW when the current is 538 A. The response time from rated net power to idle net power is 12 s and from idle net power to rated net power is 23 s. The overshoot of average voltage and minimum voltage in the process of increasing load is both 0.01 V, which are 0.015 V and 0.02 V lower than that when the load is decreased, respectively. The dynamic response speed and stability of the PEMFC system in the process of decreasing the load are better than those in the process of increasing the load.     

Diagnosis of PEM fuel cell stack dynamic behaviors

In this study, the steady-state performance and dynamic behavior of a commercial 10-cell Proton Exchange Membrane (PEM) fuel cell stack was experimentally investigated using a self-developed PEM fuel cell test stand. The start-up characteristics of the stack to different current loads and dynamic responses after current step-up to an elevated load were investigated. The stack voltage was observed to experience oscillation at air excess coefficient of 2 due to the flooding/recovery cycle of part of the cells. In order to correlate the stack voltage with the pressure drop across the cathode/anode, fast Fourier transform was performed. Dominant frequency of pressure drop signal was obtained to indicate the water behavior in cathode/anode, thereby predicting the stack voltage change. Such relationship between frequency of pressure drop and stack voltage was found and summarized. This provides an innovative approach to utilize frequency of pressure drop signal as a diagnostic tool for PEM fuel cell stack dynamic behaviors.     

Experimental investigation on the dynamic performance of a hybrid PEM fuel cell/battery system for lightweight electric vehicle application

A hybrid system combining a 2 kW air-blowing proton exchange membrane fuel cell (PEMFC) stack and a lead–acid battery pack is developed for a lightweight cruising vehicle. The dynamic performances of this PEMFC system with and without the assistance of the batteries are systematically investigated in a series of laboratory and road tests. The stack current and voltage have timely dynamic responses to the load variations. Particularly, the current overshoot and voltage undershoot both happen during the step-up load tests. These phenomena are closely related to the charge double-layer effect and the mass transfer mechanisms such as the water and gas transport and distribution in the fuel cell. When the external load is beyond the range of the fuel cell system, the battery immediately participates in power output with a higher transient discharging current especially in the accelerating and climbing processes. The DC–DC converter exhibits a satisfying performance in adaptive modulation. It helps rectify the voltage output in a rigid manner and prevent the fuel cell system from being overloaded. The dynamic responses of other operating parameters such as the anodic operating pressure and the inlet and outlet temperatures are also investigated. The results show that such a hybrid system is able to dynamically satisfy the vehicular power demand.     

Numerical study for diagnosing various malfunctioning modes in PEM fuel cell systems

The proton exchange membrane fuel cell (PEMFC) is promising technology for efficient power generation and has wide applications. In PEMFC development, it is important to diagnose malfunctions in a system with defective components and a PEMFC stack can act as an effective sensor to detect the various malfunctioning modes. Hence, the focus of this study is to analyze the response of a PEMFC under various malfunction conditions including humidifier, air blower, and coolant pump, catalyst layer degradation, and membrane aging based on 3D PEMFC simulations. Except for the coolant supply malfunction, other malfunctions exhibit similar behavior in terms of voltage drop and temperature rise, requiring more detailed measurement techniques such as Electrochemical Impedance Spectroscopy to identify the cause of malfunctions. In addition, measuring the relative humidity of the outlet gas may not provide sufficient information to distinguish the malfunction of the anode or cathode humidifier. The results of the study suggest fault detection and isolation methods under these malfunction conditions to prevent more severe failure of the PEMFC stack and system. An extensive multi-dimensional contour comprising temperature, relative humidity, liquid saturation, water content, and current density is also provided for the better analyzation of system malfunctioning behaviors.     

基于PEMFC分布式发电系统的动态特性分析

分析了质子交换膜燃料电池(PEMFC)的机理模型,在此基础上运用MATLAB的Simulink仿真工具,建立了PEMFC发电系统带负载模型。通过仿真,分析了负载对PEMFC电堆的各项动态特性(燃料的流量、效率、输出电压等)的影响,以及DC/DC、负载端的电压响应。仿真结果中负载电压呈三相交流正弦波形,表明搭建的整个PEMFC发电系统是基本正确的,为实现PEMFC并网的实时分析和动态优化提供了理论依据和参考方法。     

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.     

Control-orientated thermal model for proton-exchange membrane fuel cell systems

A lumped parameter dynamic model is developed for predicting the stack temperature, temperatures of the exit reactant gases and coolant water outlet in a proton-exchange membrane fuel cell (PEMFC) system. A dynamic model for a water pump is also developed and can be used along with the thermal model to control the stack temperature. The thermal and water pump models are integrated with the air flow compressor and PEMFC stack current–voltage models developed by Pukrushpan et al. to study the fuel cell system under open and closed-loop conditions. The results obtained for the aforementioned variables from open-loop simulation studies are found to be similar to the experimental values reported in the literature. Closed-loop simulations using the model are carried out to study the effect of stack temperature on settling times of other variables such as stack voltage, air flow rate, oxygen excess ratio and net power of the stack. Further, interaction studies are performed for selecting appropriate input–output pairs for control purpose. Finally, the developed thermal model can assist the designer in choosing the required number of cooling plates to minimize the difference between the cooling water outlet temperature and stack temperature.     

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.     

Effects of operating conditions on the performances of individual cell and stack of PEM fuel cell

In this study, experiments were carried out to study the effects on the performances of individual cell and stack of PEM fuel cell. In the experiment, there are four key operating conditions that affect the cell performance, and they are gas humidification temperature, cell temperature, assembled torsion, and gas flow rate. A 5-cell stack of PEMFC was used to measure the voltage and current density for individual cell in this experiment. Results reveal that the performances of the center fuel cells are relatively lower than those of the cells on both sides of the stack. It is also shown that stack performance increases with the increase in the anode humidification temperature as well as the center cell of the stack. As for the effect of cell temperature, results indicate that stack performance increases with the increase in cell temperature. It is also disclosed that the performances of individual cell and stack do not change with the increase in the anode gas stoichiometric ratio, but increase with the increase in the cathode gas stoichiometric ratio. In addition, the experiment results also show that the whole stack's performance is enhanced with the increase in the assembling torsion.     

Energy processing from fuel-cell systems using a high-gain power dc-dc converter: Analysis,design, and implementation

The electrolyte membrane fuel cell (PEMFC) is characterized by a low and unregulated output voltage; thus, an interface between source and load is required for processing the generated energy by the PEMFC. In this paper, a solution for processing the energy generated by a PEMFC is given. A switching regulator is developed by using a quadratic boost converter with a single switch (QBC-SS). The controller for the QBC-SS is designed using average current-mode (ACM) control, which is easy to implement using analog circuits. The proposed switching regulator ensures high conversion ratios, output voltage regulation, adequate dynamic performance, and stability. On the other hand, a model with static characteristics for the PEMFC electrical behavior is proposed, which can be used for modeling and control purposes. This model consists of three parameters, which are computed using experimental data of the PEMFC stack. A laboratory prototype of 400 W is used to verify the analytical results. As an input source, a PEMFC system is used. The output voltage of the PEMFC stack ranges from 41 V to 24 V, which depends on the generated current. Experimental results applying load step changes and frequency response analysis are shown.     

Dynamic fuel cell stack model for real-time simulation based on system identification

The authors have been developing an empirical mathematical model to predict the dynamic behaviour of a polymer electrolyte membrane fuel cell (PEMFC) stack. Today there is a great number of models, describing steady-state behaviour of fuel cells by estimating the equilibrium voltage for a certain set of operating parameters, but models capable of predicting the transient process between two steady-state points are rare. However, in automotive applications round about 80% of operating situations are dynamic. To improve the reliability of fuel cell systems by model-based control for real-time simulation dynamic fuel cell stack model is needed. Physical motivated models, described by differential equations, usually are complex and need a lot of computing time. To meet the real-time capability the focus is set on empirical models. Fuel cells are highly nonlinear systems, so often used auto-regressive (AR), output-error (OE) or Box-Jenkins (BJ) models do not accomplish satisfying accuracy. Best results are achieved by splitting the behaviour into a nonlinear static and a linear dynamic subsystem, a so-called Uryson-Model. For system identification and model validation load steps with different amplitudes are applied to the fuel cell stack at various operation points and the voltage response is recorded. The presented model is implemented in MATLAB environment and has a computing time of less than 1 ms per step on a standard desktop computer with a 2.8 MHz CPU and 504 MB RAM. Lab tests are carried out at DaimlerChrysler R&D Centre with DaimlerChrysler PEMFC hardware and a good agreement is found between model simulations and lab tests.     

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.     

Experimental investigation of self-regulating capability of open-cathode PEMFC under different fan working conditions

Self-regulation capability of the open-cathode PEMFC generally means that the stack itself can adjust its state to response to different operating conditions to achieve better performance when the external control strategy remains unchanged. In this paper, self-regulating capability of the stack are analyzed when its cooling fan works under blow or suction mode at different voltages. The result of output voltage shows that the stack achieves better self-regulation when the fan operates at 8.5 V in both blow mode and suction mode. Analysis of impedance spectra reveals that the stack can realize self-regulating function by adjusting activation resistance and ohmic resistance, and the cathode activation resistance is dominant. Furthermore, the result of a cycle load test indicates that the stack can better reflect the self-regulating capability in fan suction mode than in blow mode, and the stack can achieve better water and heat regulation in suction mode. Finally, according to the air velocity distribution and temperature change, it is found that self-regulating capability in suction mode play a better role due to more uniform heat remove. A suitable fan operating voltage and mode are critical for the self-regulating capability of the open-cathode PEMFC stack to maintain a water-heat balance.     

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.     

Power assisted fuel cell

A hybrid fuel cell demonstrated pulse power capability at pulse power load simulations synonymous with electronics and communications equipment. The hybrid consisted of a 25.0 W Proton Exchange Membrane Fuel Cell (PEMFC) stack in parallel with a two-cell lead-acid battery. Performance of the hybrid PEMFC was superior to either the battery or fuel cell stack alone at the 18.0 W load. The hybrid delivered a flat discharge voltage profile of about 4.0 V over a 5 h radio continuous transmit mode of 18.0 W.     

Development and characteristics of a 400 W-class direct methanol fuel cell stack

In this study, a 400 W-class direct methanol fuel cell (DMFC) stack is developed for large size portable applications and its operating behaviors under the various conditions are monitored. The DMFC stack comprising of 42-cells is assembled with graphite bipolar plates and membrane–electrode assemblies (MEAs) having an active area of 138 cm² per each. The stack is operated by varying the concentrations of methanol, stoichiometry (λ), and the electric load. In addition, other associated factors, such as voltage and temperature distributions along the individual unit cells, pressure drops inside the stack, voltage behaviors in response to the dynamic change of the electric load and the pHs of the effluent solutions from the outlets of both electrodes, are also studied in a detailed manner. The stack produces a power of 400 W under an operating condition of feeding 0.8 M methanol and 34 l/min air at 1 atm, and uniform distributions of temperature and voltage prevail in all the 42 unit cells. A long-term operation coupled with performance restoration processes shows that a typical single cell used in this stack is able to run with a good stability for more than 500 h without any substantial degradation in the performance.     

Rapid degradation characteristics of an air-cooled PEMFC stack

Durability is one of the obstacles to the large-scale commercialization of proton exchange membrane fuel cell (PEMFC) stacks. Understanding its decay behavior is a prerequisite for improving durability. In this study, rapid degradation characteristics of an air-cooled PEMFC stack are investigated. Due to the simultaneous presence of various degradation sources, the maximum power of the PEMFC stack has been reduced by 39.6% after just 74.6 h of operations. Performance degradation characteristics are sought by analyzing the cell voltage, temperature distribution, ion chromatography, and surface morphology of the gas diffusion layer. The result shows that abnormal cell voltage and temperature distribution can reflect the problematic location. The fluoride ion emission rate is 0.111 mg/day, which proves that the membrane has been seriously degraded. Contact angle reduction and impurities attached to the surface of the gas diffusion layer lead to the water management failure. It is also found that the main factor for performance degradation could be different under different current conditions. And more information can be found under higher current conditions during monitoring the decay of PEMFCs. This study helps to deepen the understanding of performance degradation characteristics.