In this paper, an application-oriented tubular Solid Oxide Fuel Cell (SOFC) mathematical model is presented. Its dynamic behaviors in complex power systems which consist of synchronous generators of different types are then investigated where SOFC transience is studied on a small (second) timescale. Based on the mathematical model of the entire power system, SOFC dynamic states estimator is designed to track and predict the behaviors of unmeasurable states inside SOFC during normal operating and electrically faulty conditions, using stochastic filtering algorithms. The proposed estimator operates on a holistic level with all generators, transmission lines and loads taken into consideration, whereas only SOFC local electrical data are needed for the dynamic state estimation. The success of estimating SOFC internal states will lead to a higher possibility of designing state-related controllers so as to regulate the behaviors of SOFC during electric faults.