This study proposes novel simulation methods to model the power delivery function of a parallel-connected solid-oxide-fuel-cell stack system. The proposed methods are then used to investigate the possible thermal runaway induced by the performance mismatch between the employed stacks. A challenge in this modeling study is to achieve the same output voltage but different output current for each employed stack. Conventional fuel-cell models cannot be used, because they employ fuel flow rates and stack currents as the input variables. These two variables are unknown in the parallel-connected stack systems. The proposed method solves the aforementioned problems by integrating the fuel supply dynamics with the conventional stack models and then arranging them in a multiple-feedback-loop configuration for conducting simulations. The simulation results indicate that the proposed methods can model the transient response of the parallel-connected stack system. Moreover, for the dynamics of the power distribution, there exists an unstable positive feedback loop between employed stacks when the stack temperatures are low, and a stable negative feedback loop when the stack temperatures are high. A thermal runaway could be initiated when the dynamics of the stack temperature is slower than that of the current distribution.