This paper studies the operational characteristics of thyristor controlled shunt compensator in a simple power t transmission system. With Fourier series representation of the thyristor switching action and the system parameters, t the thyristor current equations are derived, which transmit the required real power of the simple power transmission s system. Bisection algorithm is used to solve the thyristor current equations, which informs the thyristor firing an밍e, t the thyristor conduction an밍e, the power flows and the harmonic characteristics. The stability analysis is performed w with the theory of Poincare mapping for the nonlinear discrete periodic dynamic system. EMTP simulations at the v various operating points show the transient characteristics of the thyristor controlled shunt compensator and C correspond to the results calculated with Fourier series representation and the stability analysis.