Conclusion and outlook

An analysis of the dynamic behavior of a PEMFC stack is given based on a novel stack model. The mathematical formulation of the stack model is a coupled differ-ential algebraic equation system. Ordinary differdiffer-ential equations in time describe the transport phenomena, and the oxygen reduction at the cathode is modeled by an algebraic relation. The model is physically detailed and considers the impor-tant couplings among the transport phenomena and the electrochemical reaction.

At the same time, the model is computationally efficient.

The realistic simulation results show that the modeling approach is appropriate for

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time [min]

voltage [V]

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current [A]

simulated stack voltage measured stack voltage measured current

Figure 5.12: Comparison of simulated and measured stack voltage. The simulated stack voltage shows good agreement with the results of the measurement. The deviations be-tween simulated and measured values are due to the occurrence of liquid water in the PEMFC stack. Until the highest current density is reached, the temperature of the stack is low enough to allow for the generation and accumulation of liquid water. Hence, the protonic conductivity of the MEA increases and leads to an increase of the stack voltage during each current step. When the current density is decreased the stack is still heating up. Eventually, this causes the MEA to dry out and the stack voltage to decrease during each step.

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time [s]

stack voltage [V]

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current density [A/cm2 ]

stack voltage current density

Figure 5.13: Simulation of a step in the current density on a short time scale. Using a high time-resolution it becomes evident that the stack voltage does not follow instantaneously upon a change in the current density. The stack voltage reaches a minimum value and subsequently relaxes to the new equilibrium value. This behavior is explained in Fig. 5.14

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time [s]

molar flow [mol/s]

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current density [A/cm2 ]

molar flow of H2Ov at anode outlet molar flow of H2Ov at cathode outlet current density

Figure 5.14: The same current step as in Fig. 5.13 is shown. The red and green curves indicate the molar flux of water vapor at the outlet of the cathode and the anode side, respectively. The humidity of both the anode and the cathode off-gas increases due to the increased generation rate of water vapor at higher current density. The humidity of the anode off-gas is delayed with respect to the step change of the current density. The water that is generated at the cathode side has to be transferred to the anode gas channels via the membrane. The water vapor concentration of both the anode and the cathode side influence the water content of the membrane. Thus, the protonic conductivity and, hence, the stack voltage increase delayed with respect to the step change of the current density.

the dynamic description of a PEMFC stack. The model can predict the stack volt-age and the molar fluxes of hydrogen, oxygen, and water vapor given an arbitrary load profile. Moreover, the temperature of the off-gas and of the stack itself is calculated. The stack temperature is coupled with all other phenomena that occur in a fuel cell stack. For example, the protonic conductivity is treated as a function of the temperature, and its evolution is calculated.

A thorough understanding of the dynamic response of a PEMFC stack is cru-cial for the operation control of integrated fuel cell systems. The stack model is suitable for control applications, since the convergence behavior is excellent, as shown by the simulation of a current-step-profile. This model property allows one to examine a wide parameter range and to simulate different operating scenarios.

Moreover, the model is computationally efficient. In a computing time of less than one second the dynamic response of the stack to varying load can be predicted for an operation time of more than one hour.

The model is validated by the comparison of the simulated and the measured stack temperature. A PEMFC stack constructed for use in portable applications was op-erated under constant load. The input parameters of the model were controlled by the software of the test stand. The simulation results agree with the results of the measurement.

The identification of the dominant time-dependent physical processes under chang-ing load conditions and for different operatchang-ing regimes is a capability of the stack model. For example the influence of the humidity of the inlet gases, or the heat flux that should be removed via the surface of the stack, can be simulated. By inte-grating the stack model into a system simulation environment, it can be utilized to study the dynamic interaction between the fuel cell stack and its peripheral com-ponents like pumps, fans, and valves. From the results of such a study guidelines for the optimization of fuel cell systems can be derived. The most important ap-plication is the model-based development of a control algorithm. Currently, the control of fuel cell systems is usually managed by algorithms that are based on empirical observations and practical experience. By developing a control scheme that is based on a physical fuel cell stack model the performance of fuel cell sys-tems can be improved.