Quasi-three dimensional dynamic model of a proton exchange membrane fuel cell for system and controls development

A first principles dynamic model of the physical, chemical, and electrochemical processes at work in a proton exchange membrane fuel cell has been developed. The model solves the dynamic equations that govern the physics, chemistry and electrochemistry for time scales greater than about 10 ms. The dynamic equations are solved for a typical but simplified quasi-three dimensional geometric representation of a single cell repeat unit of a fuel cell stack. The current approach captures spatial and temporal variations in the important physics of heat transfer and water transport in a manner that is simple enough to make the model amenable to PEMFC system simulations and controls development. Comparisons of model results to experimental data indicate that the model can well predict steady state voltage–current relationships as well as the oxygen, water, and nitrogen spatial distribution within the fuel cell. In addition, the model gives dynamic insight into the distribution of current, water flux, species mole fractions, and temperatures within the fuel cell. Finally, a control system test is demonstrated using the simplified dynamic model.     

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.     

Model predictive control of water management in PEMFC

Water management is critical for Proton Exchange Membrane Fuel Cells (PEMFC). An appropriate humidity condition not only can improve the performances and efficiency of the fuel cell, but can also prevent irreversible degradation of internal composition such as the catalyst or the membrane. In this paper we built the model of water management systems which consist of stack voltage model, water balance equation in anode and cathode, and water transport process in membrane. Based on this model, model predictive control mechanism was proposed by utilizing Recurrent Neural Network (RNN) optimization. The models and model predictive controller have been implemented in the MATLAB and SIMULINK environment. Simulation results showed that this approach can avoid fluctuation of water concentration in cathode and can extend the lifetime of PEM fuel cell stack.     

Determination of fuel utilisation and recirculated gas composition in dead-ended PEMFC systems

This work presents a fundamental theory and methods for understanding the gas composition dynamics in PEMFC anode fuel supply compartments operated dead-ended with recirculation. The methods are applied to measurement data obtained from a PEMFC system operated with a 1 kW short stack.We show how fuel utilisation and stack efficiency, two key factors determining how well a fuel supply system performs, are coupled through the anode gas composition.The developed methods allow determination of the anode fuel supply molar balance, giving access to the membrane crossover rates and the extent of recirculated gas exchanged to fresh fuel during a purge. A methane tracer gas is also evaluated for estimating fuel impurity enrichment ratios.The above theory and methods may be applied in modelling and experimental research activities related to defining hydrogen fuel quality standards, as well as for developing more efficient and robust PEMFC system operation strategies.     

Experimental and modeling study on water dynamic transport of the proton exchange membrane fuel cell under transient air flow and load change

Water management is important in the proton exchange membrane fuel cell (PEMFC) operations, especially for those cells based on sulfonic acid polymers due to the depending of the conductivity on water. This paper aims at illustrating the effect of the change in membrane water content on cell potential response. For this purpose, the cell potential response has been investigated experimentally and computationally under transient air flow and load change of a PEMFC. From the experimental and computational results, an undershoot behavior of cell potential as well as the great influence of the relative humidity on the magnitude of undershoot is observed. It is found that the magnitude of cell potential undershoot increases as the relative humidity decreases. By carrying out a transient simulation on the water content of the membrane, the undershoot phenomena could be well explained. It is also found from the computational prediction that the time scale for the cell potential to reach its steady state is about 20 s, in agreement with experimental results. The model prediction also suggests that the dynamic behavior of PEMFC is critically dependent on the water content in the membrane.     

Thermal analysis and management of proton exchange membrane fuel cell stacks for automotive vehicle

The thermal management of a proton exchange membrane fuel cell (PEMFC) is crucial for fuel cell vehicles. This paper presents a new simulation model for the water-cooled PEMFC stacks for automotive vehicles and cooling systems. The cooling system model considers both the cooling of the stack and cooling of the compressed air through the intercooler. Theoretical analysis was carried out to calculate the heat dissipation requirements for the cooling system. The case study results show that more than 99.0% of heat dissipation requirement is for thermal management of the PEMFC stack; more than 98.5% of cooling water will be distributed to the stack cooling loop. It is also demonstrated that controlling cooling water flow rate and stack inlet cooling water temperature could effectively satisfy thermal management constraints. These thermal management constraints are differences in stack inlet and outlet cooling water temperature, stack temperature, fan power consumption, and pump power consumption.     

Analysis of a PEMFC durability test under low humidity conditions and stack behaviour modelling using experimental design techniques

A polymer electrolyte membrane fuel cell (PEMFC) stack has been operated under low humidity conditions during 1000 h. The fuel cell characterisation is based both on polarisation curves and electrochemical impedance spectra recorded for various stoichiometry rates, performed regularly throughout the ageing process. Some design of experiment (DoE) techniques, and in particular the response surface methodology (RSM), are employed to analyse the results of the ageing test and to propose some numerical/statistical laws for the modelling of the stack performance degradation. These mathematical relations are used to optimise the fuel cell operating conditions versus ageing time and to get a deeper understanding of the ageing mechanisms. The test results are compared with those obtained from another stack operated in stationary regime at roughly nominal conditions during 1000 h (reference test). The final objective is to ensure for the next fuel cell systems proper operating conditions leading to extended lifetimes.     

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

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

Development of a novel portable-size PEMFC short stack with electrodeposited Pt hydrogen diffusion anodes

This paper presents, for the first time, a five-cell polymer electrolyte membrane fuel cell (PEMFC) short stack with electrodeposited hydrogen diffusion anodes. The anodes were manufactured by means of galvanostatic pulse electrodeposition and the cathodes by air-brushing. Nafion^® 212 was employed as a solid polymer electrolyte membrane in all cases. The short stack, whose cells had an active geometric area of 14 cm², was assembled and tested under different operating conditions. A peak power of about 11 W was obtained at 50 °C and atmospheric pressure using hydrogen and air feed, whereas a smaller value of 8.6 W was obtained from a five-cell short PEMFC stack with conventional hydrogen diffusion anodes under the same operating conditions. The better performance of the cells described in this paper has been assigned to the higher utilization of the platinum in the electrodeposited anodes compared to the conventional ones.     

Monodimensional modeling and experimental study of the dynamic behavior of proton exchange membrane fuel cell stack operating in dead-end mode

The dynamic behavior of a five cells proton exchange membrane fuel cell (PEMFC) stack operating in dead-end mode has been studied at room temperature, both experimentally and by simulation. Its performances in “fresh” and “aged” state have been compared. The cells exhibited two different response times: the first one at about 40 ms, corresponding to the time needed to charge the double-layer capacitance, and the second one at about 15–20 s. The first time response was not affected by the ageing process, despite the decrease of the performances, while the second one was. Our simulations indicated that a high amount of liquid water was present in the stack, even in “fresh” state. This liquid water is at the origin of the performances decrease with ageing, due to its effect on decreasing the actual GDL porosity that in turn cause the starving of the active layer with oxygen. As a consequence, it appears that water management issue in a fuel cell operating in dead-end mode at room temperature mainly consists in avoiding pore flooding instead of providing enough water to maintain membrane conductivity.     

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.     

Performance of a proton exchange membrane fuel cell stack with thermally conductive pyrolytic graphite sheets for thermal management

This work experimentally investigates the effects of the pyrolytic graphite sheets (PGS) on the performance and thermal management of a proton exchange membrane fuel cell (PEMFC) stack. These PGS with the features of light weight and high thermal conductivity serve as heat spreaders in the fuel cell stack for the first time to reduce the volume and weight of cooling systems, and homogenizes the temperature in the reaction areas. A PEMFC stack with an active area of 100 cm² and 10 cells in series is constructed and used in this research. Five PGS of thickness 0.1 mm are cut into the shape of flow channels and bound to the central five cathode gas channel plates. Four thermocouples are embedded on the cathode gas channel plates to estimate the temperature variation in the stack. It is shown that the maximum power of the stack increase more than 15% with PGS attached. PGS improve the stack performance and alleviate the flooding problem at low cathode flow rates significantly. Results of this study demonstrate the feasibility of application of PGS to the thermal management of a small-to-medium-sized fuel cell stack.     

Continuous bubble humidification and control of relative humidity of H2 for a PEMFC system

The proton conductivity of perfluorinated ionomer membrane used in a proton exchange membrane fuel cell (PEMFC) depends largely on the extent of hydration state of the membrane. Sufficient membrane hydration is achieved typically through the humidification of gases prior to feeding them into the fuel cell. Further, hydrogen humidification is known to have a larger impact on the performance of a PEMFC than the oxygen humidification. Bubble humidification has been a widely used method to externally humidify hydrogen. However, to-date a continuous bubble humidification system, which is essential to the continuous operation of the PEMFC system, has not been implemented. The main contributions of this work are (i) a design for continuous humidification of hydrogen for the PEMFC system and (ii) a method to maintain the RH of hydrogen between 93 and 95% (at desired temperature) over a wide range of gas flow rates. One of the key advantages of the proposed design is the flexibility of using recirculated stack coolant water to increase the energy efficiency of the PEMFC system. The design is first tested off-line and then online with a 1 kW stack. Results obtained from both the off-line and online tests indicate that the design successfully meets the demands of an online operation. It is observed that with the use of the proposed humidification scheme, the stack efficiency in terms of power output increases by about 6–19% of the power obtained under dry hydrogen conditions.     

车用PEMFC氢气系统建模及其排放特性研究

建立基于尾氢再循环的车用PEMFC氢气系统的集总参数模型和质子交换膜燃料电池堆的二维CFD模型,瞬态模拟研究额定功率工况下尾氢排放对系统及电堆工作特性的影响。结果表明：排放过程中,阳极进气压力和进气流量等参数出现显著的波动现象,且波动幅度和波动时间与排放持续时间存在直接关系;电堆性能在排放过程中有所下降,排放结束后能迅速恢复到排放前的水平;阳极内部的水气分布在排放过程中得到明显改善。     

Dynamic modeling of a proton exchange membrane fuel cell system with a shell-and-tube gas-to-gas membrane humidifier

The proton exchange membrane fuel cell (PEMFC) system with a shell-and-tube gas-to-gas membrane humidifier is considered to be a promising PEMFC system because of its energy-efficient operation. However, because the relative humidity of the dry air flowing into the stack depends on the stack exhaust air, this system can be unstable during transients. To investigate the dynamic behavior of the PEMFC system, a system model composed of a lumped dynamic model of an air blower, a two-dimensional dynamic model of a shell-and-tube gas-to-gas membrane humidifier, and a one-dimensional dynamic model of a PEMFC system is developed. Because the water management during transient of the PEMFC system is one of the key challenges, the system model is simulated at the step change of current. The variations in the PEMFC system characteristics are captured. To confirm the superiority of the system model, it is compared with the PEMFC component model during transients.     

Effects of water induced pore blockage and mitigation strategies in low temperature PEM fuel cells – A simulation study

Ineffective water management in proton exchange membrane fuel cells (PEMFCs) can cause performance degradation. A simple mathematical model capturing the effect of water on the overall performance of the fuel cell system is of immense use in developing tools for water management. In this work, a computationally efficient first principles dynamic model for PEMFC system simulations and concomitant water management studies are developed. The steady-state version of this model is validated with experimental data. The effect of various operating conditions and design parameters on the performance of the fuel cell is studied using this model. Various control strategies for improving fuel cell performance in the presence of flooding are evaluated using the model. The simplicity and adequate predictive capability of the model make it amenable to be used in a model-based feedback control framework for online water management.     

Constructal PEM fuel cell stack design

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

Modeling of the Ballard-Mark-V proton exchange membrane fuel cell with power converters for applications in autonomous underwater vehicles

This paper studies the transient response of the output voltages of a Ballard-Mark-V 35-cell 5 kW proton exchange membrane fuel cell (PEMFC) stack with power conversion for applications in autonomous underwater vehicles (AUVs) under load changes. Four types of pulse-width modulated (PWM) dc-dc power converters are employed to connect to the studied fuel cell in series for converting the unregulated fuel cell stack voltage into the desired voltage levels. The fuel cell model in this paper consists of the double-layer charging effect, gases diffusion in the electrodes, and the thermodynamic characteristic; PWM dc-dc converters are assumed to operate in continuous-conduction mode with a voltage-mode control compensator. The models of the study's fuel cell and PWM dc-dc converters have been implemented in a Matlab/SIMULINKTM environment. The results show that the output voltages of the studied PEMFC connected with PWM dc-dc converters during a load change are stable. Moreover, the model can predict the transient response of hydrogen/oxygen out flow rates and cathode and anode channel temperatures/pressures under sudden change in load current.