The aim of this study is to elucidate the transient behavior of thermodynamic variables in a solid oxide fuel cell (SOFC) upon electrical load change, which can be used for optimizing cell microstructure and developing a reliable SOFC stack design. To overcome the insufficient durability and large performance degradation, SOFC technologies still need reliable cell microstructure and stack design prior to their market deployment. This is of significant concerns when considering actual operating conditions, in particular, sudden and severe electrical load change. Enhancing the dynamic stability of SOFC is essential to improve its durability under the electrical load change. To meet the needs, the local thermodynamic state and thermo-fluid environment should be examined in detail, which requires high-fidelity numerical simulations. In this study, a physical model is developed to resolve temporally and spatially reactions and transport phenomena taking place inside planar, anode-supported SOFC stacks. The model is validated by using in-house experimental measurements of a current response profile upon electrical load change. Then, the dynamic response of thermodynamic variables upon electrical load change is investigated by assuming potentiodynamic conditions. The results of this study show that the electrical current responds excessively to the potential steps and recovers its magnitude asymptotically to the quasi-steady state. A relaxation time is needed for its dynamic response and recovery. This is explained by the time-dependent variation of the electrochemical reaction zone and species transport in the anode. The former reacts quickly to electrical load change, influencing the hydrogen concentration, while the latter shows time-delay, affecting the diffusion of hydrogen between the reaction zone and fuel channel. The time-delay required for the response of hydrogen diffusion corresponds to the relaxation time needed for the electrical current response. These results indicate that the overall transient behavior is predominantly governed by species diffusion in the anode. The pressure field also shows similar trend of time-dependent variations, whereas the temperature does not change as much as other variables, implying that it needs much longer time to adjust itself to a new operating condition.