This paper carries on the stable state simulation and transition condition simulation for the single phase power systems, which are without TCSC and with TCSC systems. Both without TCSC and with TCSC circuits in the single-phase power system, have been carried out a detailed steady state and transition condition simulation, and studied the influence for TCSC that on power system load voltage and load power. In addition, applies the TCSC conventional PID impedance control mode, with TCSC fuzzy PID impedance control in the electrical power system, contrasts their function that display in the electrical power system operation, and demonstrate the two controllers’ advantage and disadvantage. In the stable state simulation, establishes the systems operation separately in the two kind of situations that rated load and overload, observes the respective load voltage profile, and carries on the comparison with other, in order to study the function for TCSC that work s in the single phase power system normal operation time . In the transition condition simulation, establishment short trouble, views the system transition condition’s load voltage, makes its profile the comparison, and studies TCSC in the single phase power system transition condition function. At the same time, considered the difference for TCSC impedance control modes, as well each as the influence which produces to the TCSC performance characteristic, makes the TCSC conventional PID impedance control mode and TCSC fuzzy PID impedance control mode to apply in the single phase power system separately, and carries on the two's simulation profile in detail contrastive analysis . The simulation result indicated that TCSC has the tidal current control and the damping line power vibration, enhances the electrical power system transition condition stably many kinds of functions, in the stable state condition, TCSC can increase system's transportation power, and reduce the electric transmission loss; under the transition condition, TCSC can suppress the system power oscillation and enhance the system stability.