The main purpose of this paper was to develop a complete dynamic model of a power generation system based on two serially connected solid oxide fuel cell stacks. The uniqueness of this study lies in a different number of fuel cells in the stacks. The model consists of the electrochemical model, mass and energy balance equations implemented in MATLAB Simulink environment. Particular attention has been paid to the analysis of the transient response of the reformers, fuel cells and the burner. The dynamic behavior of the system during transient conditions was investigated by load step changing. The model evaluates electrical and thermal responses of the system at variable drawn current. It was found that a decrease of 40% in the 1st stage and 2nd solid oxide fuel cell (SOFC) stacks drawn current caused both stacks temperature to drop by 2%. An increase of the cell voltage for the 1st and 2nd SOFC stacks led to very fast steam reformer response combined with a slight decrease in reformer temperature, while a considerable burner temperature increase of 70 K can be observed. Predictions of the model provide the basic insight into the operation of the power generation-based SOFC system during various transients and support its further design modifications.