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This study investigates one of the most fundamental issues of integrating fuel cell (FC) generation into power systems - its effect on power system small-signal stability when it operates jointly with conventional power generation. The study first presents a comprehensive mathematical model of the solid oxide fuel cell (SOFC) power plant integrated with the single-machine infinite-bus power system. Based on the model, conventional damping torque analysis is carried out to study the effect of SOFC power generation on power system small-signal stability. The analysis concludes that system small-signal stability can be affected either positively or negatively by the SOFC power plant when system operating conditions change. Two examples of power systems with gird-connected SOFC power plants are presented. Small-signal stability of the first example of single-machine power system was examined when the power system operated at different load conditions and levels of mixtures of conventional and FC power generation. The second example is a four-machine two-area power system where the power supplied by the gird-connected SOFC power plant is variable. Results of simulation using full non-linear model of the power systems and the SOFC power plants are given. All the results from the example power systems confirm and further demonstrate the analysis presented and conclusions obtained.