This study presents the theory and modelling of a novel controller based on PWM - based Series Vectorial Compensator (SVeC). This is a new series Flexible AC Transmission System (FACTS) controller for active power flow control in a transmission line and damping of low-frequency oscillations (LFO). This paper presents the basic module, steady- state operation, mathematical analysis, current injection model and dynamic model of SVeC. The main contribution of this work is that a current injection model of the SVeC for studying the effect of the SVeC on the LFO is proposed. A brief comparison of the Coordinated Control (COC) of SVeC and Power System Stabilizer (PSS) with without control is presented for dynamic series compensation of transmission lines. The multi machine network is used for comparison purpose. The performance of the proposed controller is checked through eigen-value analysis and non-linear time domain simulations under nominal load operation. The results obtained show that the proposed control is efficient for studying the effects of SVeC on the electro mechanical oscillations and it has better oscillation damping characteristics than without control.