Parametric model for the simulation of the railway catenary system static equilibrium problem

• A parametric nonlinear model of the railway catenary, including undeformed dropper lengths as extra-coordinates, is proposed.
• Proper General Decomposition (PGD) technique is applied to solve the high dimensional static equilibrium problem.
• The high nonlinearity of dropper slackening is also included under the PGD approach.
• A linearized formulation is presented in order to reduce the computational cost.

Dynamic simulations of pantograph–catenary interaction are nowadays essential for improving the performance of railway locomotives, by achieving better current collection at higher speeds and lower wear of the collecting parts. The first step in performing these simulations is to compute the static equilibrium of the overhead line. The initial dropper lengths play an important role in hanging the contact wire at an appropriate height. From a classical point of view, if one wants to obtain the static equilibrium configuration of the system for different combinations of dropper lengths, one static problem must be solved for each combination of lengths, which involves a prohibitive computational cost. In this paper we propose a parametric model of the catenary, including the undeformed dropper lengths as extra-coordinates of the problem. This multidimensional problem is efficiently solved by means of the Proper Generalized Decomposition (PGD) technique, avoiding the curse of dimensionality issue. The capabilities and performance of the proposed method are shown by numerical examples.