SPOPS statement of methods

The Simulation Programme for Overhead contact lines – Pantograph System (SPOPS) is based on a two-dimensional finite element model of an overhead contact line and a lumped mass model for a pantograph. The SPOPS allows for a lateral change of contact points between the pantograph and the contact wire and for the rolling motions of contact strips in the pantograph model. Thus, the programme can consider the stagger of a contact wire in a dynamic simulation. Either a penalty method or a Lagrange multiplier method can be chosen to model the contact phenomenon between a pantograph and a contact wire. According to pantograph–catenary benchmark results, the simulation results obtained from the SPOPS are very close to the average values of the simulation results obtained from programmes implemented in the benchmark work in all cases, including a three-dimensional (3-D) case. These benchmark results demonstrate that the SPOPS is as accurate as other fully 3-D simulation programmes while utilising minimal computational efforts.