A Galerkin Approach for Modelling the Pantograph-Catenary Interaction

The pantograph-catenary interaction was modelled for high-speed electric and hybrid trains. A lumped-mass pantograph model was used and the overhead wires were modelled as Euler-Bernoulli beams. Each vertical and horizontal wire deflection was decomposed into an infinite series of spatial basis functions, which were chosen to be the eigenmodes of the Euler-Bernoulli PDE, and corresponding time functions. The boundary conditions were used to evaluate the spatial basis functions and reduce the PDEs to ODEs in terms of the time functions. Elimination of variables was used to remove the algebraic contact constraints and reduce the overall index-three DAE to an ODE. This linear, time-varying ODE was solved by integration and the elimination process was reversed in order to recover the original states. The Simulink model was validated against the 2002 and 2018 European Standards, BS:EN 50318:2002 and BS:EN 50318:2018 respectively. In both cases, the model produced accurate results with exceptional simulation speeds.