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Solid oxide fuel cell (SOFC) technology is recognized as a promising solution to address global climate change, due to its broad fuel tolerance and strong heat integration capability. When connected to the natural gas grid, micro combined heat and power (μ-CHP) SOFC system can be installed indoors to provide both electricity and hot water. Two main commercial technologies have been released in the field: (1) Ni-YSZ based anode-supported cell, and (2) Ni-GDC based electrolyte-supported cell (ESC). Recently, Ni-GDC cermet negatrode has gained significant interest due to its superior performance and impurity tolerance compared to the Ni-YSZ negatrode. Ensuring stable operation of commercial SOFC system has been essential to prolong the system lifespan and improve the techno-economic performance. Consequently, multiple state-of-health diagnosis methods have been employed to real-time monitor the system and avoid faulty conditions, including chronopotentiometry, electrochemical impedance spectroscopy (EIS), and total harmonic distortion (THD) analysis. EIS measurements have been extensively applied to the Ni-GDC based single ESCs to investigate the individual electrochemical processes, via distribution of relaxation times (DRT) method, equivalent circuit model (ECM) and complex non-linear least square (CNLS) fit. A comprehensive parametric study has been conducted to investigate the response of different electrochemical processes to the temperature, current density, air utilization, fuel utilization (FU), O 2 partial pressure, H 2 partial pressure and H 2 O partial pressure. Five processes were identified: (1) gas conversion (0.1-1 Hz), (2) O 2- surface exchange in GDC (0.1-10 Hz), (3) electrode gas diffusion (1-50 Hz coupled with partial O 2- surface exchange), (4) positrode charge transfer (50-150 Hz), and (5) negatrode charge transfer (> 150 Hz). In the syngas environment, the O 2- surface exchange process could be split into two parts and merge with gas conversion and electrode gas diffusion, respectively. THD analysis has been used in cell level to detect the nonlinear electrochemical response under fuel starvation condition, featured with a higher THD index at low frequencies than that under nominal operating conditions. Notably, THD measurement takes less than 10 minutes, which is much shorter than an accurate EIS measurement (30 minutes). At the stack and system levels, most EIS measurements focused on the nominal operating conditions, while cell-level research on faulty condition detection often overlooked potential non-uniformities in gas and temperature distribution after scaling up. The impact of the non-uniform mass and heat distribution on the entire stack integrated into a complete system, as well as the identification of specific cells affected under fuel starvation via state-of-health monitoring tools, remains an area that requires further research. Additionally, the effectiveness of rapid diagnostics using THD tool still needs to be