Dynamic Modelling of Overhead Power Lines for Electric Trains

The pantograph-catenary interaction has been modelled for high-speed electric trains using spectral analysis, also known as a Galerkin approach, to efficiently solve the time-varying, linear index-three differential-algebraic equation. The time solution of the Euler-Bernoulli beam equation for the overhead wires has been found by decomposing the overall solution into its spatial frequencies and using eigenvector decomposition to diagonalise the system. The algebraic constraints have been removed using elimination of variables, leading to a solvable ordinary differential equation. For optimal time efficiency, a Simulink model has been used to solve this ODE. The results have been tested against the British Standard BS:EN 50318:2002 and have proven to be sufficiently accurate. The simulation runs approximately one order of magnitude faster than competing FEM software. The main use of this software is to help design more robust overhead line equipment that will be safe at higher speeds.