When the TCSC steady-state operation, the thyristor turn-on and turn-off time is definite, the changing for TCSC electric capacity voltage and thyristor electric current is with the periodicity and symmetry.Thyristor controlled series compensation technology is fixed series compensation technology foundation, which is meet the needs for adaptation electrical power system operation control developing. With changes the triggering angle for thyristor suitably, then can realize the TCSC equivalent reactance fast, continuously and adjusts smoothly, provides the controllable series compensation for the system, as to achieve increases the system transmitting capacity, enhance the transition condition stability, the damping power oscillation, and the purpose for improvement system tidal current distribution. Although in the entire time axis, obtains the analytic expression for TCSC running status variable is difficulty, but as long as had determined the analytic expression for various electrical quantity in a power frequency cycle, according to the stable state movement's symmetry and periodicity, we can determine the steady state profile that in the entire time axis, and then analyses the TCSC electric circuit’s steady-state characteristic with the time domain computation method. In this paper, topological analysis for TCSC operation established by formula, and then carries on the time domain partition to the TCSC electric circuit solution, finally obtains the steady state fundamental frequency impedance model for TCSC. This paper steady-state characteristic analysis is mainly carries on the topological analysis method to the TCSC main circuit, then establishes the stable state base frequency impedance model for TCSC, and analyses the resonance question for TCSC simultaneously. Then studies TCSC the steady- state characteristic, and with modeling and simulation on them to do further research and analysis, and utilizes the solution method for transformation territory, namely applies the Laplace transform solution equation of state. Thus can be obtained the zero-input response and zero status response formula for system.