A Mathematical Model of the Pantograph-Catenary Dynamic Interaction with Several Contact Wires

This paper presents the work carried out by CALPE team on the development of a mathematical model used in the study and simulation of the pantograph-catenary dynamic interaction in high speed railways considering two independent series of the catenary spans where the transition spans are overlapped. According to the developed mathematical model, a non lineal system of differential equations with variable constraints conditions which depend on the pantograph position has been obtained. To solve these equations, a numerical integration algorithm based on the explicit method of the central differences has been implemented. The procedure designed allows us to study the more appropriate contact wire configuration, in order to achieve a smooth transition of the pantograph between sets of spans. This procedure can be generalized considering the case of several pantographs running on the line, obtaining very realistic simulations.