A promising solution to the storage of intermittent renewable energy is to integrate solid oxide electrolysis cells (SOEC) with solar/wind power. This trend necessitates comprehensive, quantitative investigations on the transient characteristics of SOEC, especially under varying power-supply conditions. For this purpose, a highresolution, 3-dimensional, transient numerical model, as well as an adaptive time-stepping strategy, is proposed in this study. This study analyzes the electrical, gaseous, and thermal responses of SOEC to voltage ramps with different ramp rates and ramp magnitudes. The results show that electrical undershoots or overshoots occur after fast voltage changes. This phenomenon reflects the discrepancies between the steady and transient current–voltage characteristics and may lead to unsteady hydrogen production rates in practice. The electrical undershoots or overshoots are caused by the different transfer rates in SOEC – electronic/ionic transfer rate is faster than mass transfer rate, and mass transfer rate is faster than heat transfer rate. Furthermore, the electrical undershoots or overshoots can be divided into two parts. One part is related to mass-transfer lag, and the other part is related to heat-transfer lag. The former can be alleviated or eliminated by simply slowing down the voltage ramp, while the latter needs a more effective control strategy other than merely adjusting the voltage ramps. Apart from the electrical conditions, cell structure also has significant impacts on the electrical responses, e.g., the rib and the length of channel are related to the non-uniform electrical responses in the functional layer. Finally, via a quantitative technique developed from linear time-invariant systems, it is shown that the electrical responses of SOEC are governed by two time constants in the functional layer, namely the mass-transfer time constant (estimated as 0.00723 s) and the heat-transfer time constant (estimated as 180 s).