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Identifying the degradation mechanisms at the early stage of operation is important for the long-term operation of solid oxide fuel cells (SOFCs). Compared to conventional methods, total harmonic distortion analysis (THDA) can significantly reduce the test time for identifying performance degradation during SOFC operation. In this study, a one-dimensional transient elementary reaction kinetic model of an SOFC fueled with syngas is developed. The model incorporates the coupling effect of elementary chemical and electrochemical reactions, the electrode microstructure, the charge and mass transport processes, and the detailed evolution reaction of surface adsorbed carbon. A THDA simulation calculation method was developed and applied to determine the failure mode of anode carbon deposition. The amplitude, duration, and harmonic number of the perturbation signal are determined to improve fault detection for THDs. The results show that the use of THD can not only detect carbon accumulation behavior at the early stage of SOFC operation but also distinguish the specific degradation mechanism caused by carbon deposition: the hindered SOFC charge transfer reaction can be detected in the frequency range of 100–4000 Hz, and the hindered gas diffusion process inside the anode can be detected in the frequency range of 0.01–10 Hz.