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Moeling and simulation of transience stability on a thyristor controlled series compensation. More comprehensive mathematical equations of TCSC circuit for any period (including the whole transient processfrom firing the thyristors to a steady state) and for the steady state relating to the voltages and currents of the capacitor,inductor and thyristor components are precisely developed by using Laplace transformation. And the accurate mathematicalrelationship between the fundamental impedance of TCSC and the firing angle of the thyristors is further derived by using Fourier analysis. Via the simulation, having a good understanding of the transience stability on a thyristor controlled series compensation.