Numerical stiffness study of multi-physical solid oxide fuel cell model for real-time simulation applications

Real-time fuel cell model and simulations can help to develop the fuel cell system, especially for the effective implementation of the advanced online diagnostic tool by the multi-dimensional multi-physical approach. However, the strong numeric stiffness observed in the physical equations of the high dimensional real-time model can lead to an overrun error for real-time simulation, which could be critical for online diagnosis accuracy, or even cause control failure. In this paper, the real-time simulation of a two-dimensional tubular solid oxide fuel cell model is developed. Moreover, the stiff issues of the control-oriented real-time fuel cell model are analyzed thoroughly through the calculations and comparisons of the time constants and eigenvalues for the dynamic ordinary differential equations of the nonlinear fuel cell model. An appropriate solving approach with second-order accuracy is then proposed to reduce the influence of the specific stiffness issue during the real-time simulation. The proposed solving algorithm is proofed to be L-stable and thus can make the stiff fuel cell model executed with a reduced computation time. The experimental results show that the developed multi-physical tubular fuel cell model can be effectively executed in real-time within milliseconds range with over hundreds of control volumes.