Studies on the modeling and simulation of the railway vehicle traction system play an active role in the operation and planning phase of railway electrification. In this paper, the longitudinal dynamic of a light rail vehicle was modelled and simulated in Matlab-Simulink. The traction system consists of two parallel motor groups, each of which is composed of two seperately-excited motors connected in series. The first simulation scenario represents how the traction system works in acceleration and braking modes with respect to a given speed change profile. Within this scenario, the time dependent responses of the motor armature and excitation currents, fluxes, motor traction moment, adhesion, resistance forces and acceleration are evaluated, and the constant torque, field attenuation, operation zones and vehicle traction force curve are described. The second simulation scenario represents the slip control application, which examines the complex nonlinear relationship between the adhesion force and the slip ratio, were demonstrated. Modified super-twisting sliding mode slip control are performed under dry, wet and low wheel-rail contact conditions, which are sequentially switched. It has been confirmed by the simulation results that the proposed control strategy achieves the maximum adhesion force of the train. The main purposes of this study are to investigate the operation principles of the railway dynamics associated with acceleration or braking modes and to examine the effects of certain parameters related with the dynamical electromechanical traction system.