Modeling and control of air stream and hydrogen flow with recirculation in a PEM fuel cell system—I. Control-oriented modeling
Introduction
Fuel cells provide an environmentally friendly high-efficiency power source without Carnot's limitation of efficiency. The proton exchange membrane fuel cell (PEMFC) is considered to be the most promising candidate for electric vehicles by virtue of its high power density, zero pollution, low operating temperature, quick startup capability and long lifetime. The American “Freedom CAR” and Chinese “Fuel Cell City Bus Project” are two examples for the mobile applications of fuel cells.
There are three major subsystems in a typical pure-hydrogen fuel cell system: air supply system, fuel supply and recirculation system, water and thermal management system (including humidification). Reasonable flow rate and pressure are controlled to avoid oxygen starvation and excessive auxiliary power consumption in the air supply subsystem. Anode recirculation is used to reduce the hydrogen waste, maintain the pressure difference between the anode and the cathode, and run the fuel in the anode to get better water management. Water and thermal management is essential to the health of FCS. The dynamic response of fuel cell system is important for vehicular applications, where power demand fluctuates, and the fuel cell and all other subsystems do not usually operate at the optimal steady states designed by the manufacturer. Creating a control-oriented dynamic model of the overall system is an essential first step not only for the understanding of the system behavior but also for the development and design of model-based control methodologies.
Up to now, a number of fuel cell models have been built to predict the polarization [1], [2], [3], [4], [5], [6], [7]. While supplying good understanding of the fuel cell fundamental, these contributions in cell level are not suitable for the control study. Models of fuel cell system are mainly designed for component sizing and parameter optimization [8], [9], [10]. Compared to these steady-state works, a few dynamic models of fuel cell systems are published. Xue's lumped-parameter model [11] is a dynamic system-level model for the stack body. Golbert's distributed-parameter model [12] in single-cell level is focused on the effect of the temperature on the electric power. Amphlett [13] predicted the transient response of the stack temperature for thermal management. Lukas [14] built a dynamic model for internally reformed molten carbonate fuel cell stack. Pischinger [15] raised a lot of interests on the system dynamics including compressor, fuel cell and reformer but not a clear set of equations are in open literature in his study. Rodatz [16] built a reduced model for the control of flow rate and pressure in the air supply system. Pukrushpan [17] developed a system-level model that includes compressor, supply and return manifolds, humidifier, and anode and cathode channel. This state-of-the-art work is for the air system without including the anode recirculation.
Compared to the above dynamic models which are mainly only for a certain subsystem, this paper is focused to develop a control-oriented dynamic model for integrated control study of the air stream, fuel flow with recirculation in a pure-hydrogen PEM fuel cell system. In addition to the requirement of the essential control of stream pressures and flow rates, the water transport is also needed to be described in this dynamic model for the future humidity estimation and control. Considering the phenomena of electrochemical reaction, mechanical revolution and mass and heat transfer, there are multi-scale time constants in a fuel cell system. The time constant in the range of is taken into account in this paper, which is the typical time range of manifold filling dynamics, flow control of devices and variation of mechanical revolution. So, the stack temperature is considered as constant because of its relative slow response. On the other hand, the electrochemical reaction, mass transfer and water transport in the cell body are considered fast and described by a steady-state analytical fuel cell model. In addition to the mathematical models of main components including compressor and motor, supply and return manifolds, humidifier and lumped-parameter anode and cathode channel, a static model of injection pump is embedded to describe the anode recirculation. So, all the transient behaviors of reactant partial pressure and water content in PEM can be captured. By introducing an analytical fuel cell model, another advantage of this system-level model is that it can also be easily polished to reflect the water flooding in the cathode gas diffusion layer.
Section snippets
Fuel cell system model
Fig. 1 shows the schematic configuration of air supply subsystem, hydrogen supply and recirculation subsystem in a PEMFCS. This is the prototype of high-pressure FCS in a Chinese fuel cell city bus. A screw compressor driven by a motor is used to obtain the proper air flow. At the end of outlet manifold in the cathode, a proportional back-pressure valve supplies the freedom to regulate the cathode pressure. In the anode loop, three injection pumps cooperate to realize the anode recirculation.
Analysis
Table 1 lists the parameters in this dynamic model. This is a configuration with a stack of 150 kW and the rated net power of FCS is about 100 kW. Fig. 6 shows the realization in MATLAB/SIMULINK environment.
The focus of the air supply system in a FCS is to avoid oxygen starvation. Corresponding to a specific electric load, the excess amount of reactant is described by the stoichiometric ratio which is defined as the ratio of reactant supplied to the reactant reacted. As the dominant consumer of
Conclusion
In this paper, a control-oriented dynamic model of air stream, hydrogen flow with recirculation in a PEM fuel cell system was build. Unlike other models only for the air supply subsystem, the fuel recirculation is integrated by an analytical model of injection pump. The transient phenomena in FCS are captured by the mechanical inertia of the compressor and flow filling dynamics of the manifolds, lumped anode and cathode. Considering the mass transfer and water transport in MEA, the analytical
Acknowledgment
The financial support of the Fuel Cell City Bus project in China 863 Electric Vehicle Program under contract 2003AA501100 is gratefully acknowledged.
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