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A variant of application of a contact compensated chain suspension with levers and lateral current collection for a three-phase traction power supply system (TSTE) is considered. Two different-phase contact suspensions are located on different sides of the track axis. The electric rolling stock must have two current collectors that press on the contact wire from the track axis in opposite directions. The description of the design of the contact suspension as a whole and the main components, in particular, the fastening of the rods, which makes it possible to provide a vertical zigzag and limit the transverse movement of the contact wire, is made. At points at the supports, the levers are connected to the consoles and have a knot to create angular rigidity. In addition, the rotation of these levers is limited towards the axis of the path and in the opposite direction. This prevents the possibility of lashing of different-phase contact wires. In accordance with this design, a mathematical model of this contact suspension was developed based on the finite element method, which provides calculation in statics and dynamics, taking into account the current collector. To describe the pantograph, a common three-mass model is used. Based on the analysis of the results obtained using this model, the influence of the design parameters of the suspension, cross wind and the speed of the pantograph movement on the quality of the current collection is determined, the limits of applicability of the suspension under consideration, depending on the value of these parameters, are established. It has been determined that, in contrast to a conventional contact suspension with a vertical current collection, for suspensions with a lateral current collection, a side wind has a significant effect on the quality of the current collection. It is the wind speed that is the main factor limiting the possibility of using a suspension with lateral current collection.