Dynamic modeling and analysis of solid oxide fuel cell systems can provide insight towards meeting transient response application requirements and enabling an expansion of the operating envelope of these high temperature systems. SOFC modeling for system studies are accomplished with channel-level interface charge transfer models, which implement dynamic conservation equations coupled with additional submodels to capture the porous media mass transport and electrochemistry of the cell. Many of these models may contain simplifications in order to decouple the mass transport, fuel reforming, and electrochemical processes enabling the use of a 1-D model. The reforming reactions distort concentration profiles of the species within the anode, where hydrogen concentration at the triple-phase boundary may be higher or lower than that of the channel altering the local Nernst potential and exchange current density. In part one of this paper series, the modeling equations for the 1-D and 'quasi' 2-D models are presented, and verified against button cell electrochemical and channel-level reforming data. Steady-state channel-level modeling results indicate a 'quasi' 2-D SOFC model predicts a more uniform temperature distribution where differences in the peak cell temperature and maximum temperature gradient are experienced. The differences are most prominent for counter-flow cell with high levels of internal reforming. The transient modeling comparison is discussed in part two of this paper series. (C) 2015 Elsevier B.V. All rights reserved.