In this paper, a control-oriented model of a solid oxide fuel cell system is formulated and analyzed in detail. First, a lumped model based on first principle laws is formulated and tuned using experimental data coming from a real solid oxide fuel cell system test bench. The model calibration is carried out based on an optimization approach to minimize the error between the experimental data and the model one. To systematically analyze the system behavior, an equilibrium point analysis is formulated and developed. The analysis results show the maximum steady-state electrical power under each constant stack temperature. This will allow to appropriately select operation points during the system operation. Secondly, Lyapunov's theory is used to characterize the local stability of the equilibrium points. The results show that the equilibrium points are locally stable. Besides, comparison between the initial nonlinear model with the linearized model is performed to show the efficacy of the linearised model analysis. Finally, the frequency response of the linearized model is performed. This analysis provides key information about control system design in order to efficiently operate the solid oxide fuel cell system.