The first part of this two-part-paper develops a comprehensive nonlinear dynamic model of a solid-oxide fuel cell (SOFC) that can be used for dynamic and transient stability studies. The model based on electrochemical and thermal equations, accounts for temperature dynamics and output voltage losses. The output voltage response of a stand-alone fuel-cell plant to a step load change, a fuel flow step change, and fast load variations are simulated to illustrate the dynamic behavior of SOFC for fast and slow perturbations. A method for interfacing the proposed fuel-cell models to a power system stability package is developed.