In the traditional electromagnetic transient simulation, the computation speed of SVC (Static Var Compensator) and TCSC (Thyristor Controlled Series Compensation) is relatively slower. In order to overcome this deficiency, a new method of fast simulation for the electromagnetic transients of SVC and TCSC is proposed. For the fact that the state equations of SVC and TCSC are unchanged when the state of TCR (Thyristor Controlled Reactor) branches stay the same, the piecewise timeinvariant state equations of SVC and TCSC are developed firstly. Then, auxiliary variables are introduced and the model is transformed from a set of nonhomogeneous linear equations into homogeneous ones to obtain the unified expression suitable for varied working conditions. Finally, the scaling and squaring method is utilized to compute the matrix exponent and the response of the model is obtained. The feasibility and high efficiency of the proposed method is verified by comparing with the results from classical electromagnetic transient simulations using the PSCAD/EMTDC software package.