###### Abstract  
The effective vibration area includes most of the catenary vibration caused by pantograph-catenary interactions and is the basis of the real-time catenary model for hardware-in-the-loop simulation. However, while the length of the effective vibration area is one of the most important parameters of the real-time catenary model, it has not been fully studied at present. In this paper, the length of the effective vibration area is first investigated. A pantograph-catenary interaction model is developed based on the modal superposition method. After the validation of the model, the vibration energy distribution of the catenary is used to determine the length of the effective vibration area based on the converged total energy. The influence of vehicle velocity and contact wire tension on the vibration energy distribution and length of the effective vibration area is investigated. The obtained appropriate length of effective vibration area is validated by a real-time catenary model and online measurement data of the contact force. The investigation results show that the energy distribution of the catenary can accurately determine the length of effective vibration area, and it increases with increasing vehicle velocity but decreases with increasing contact wire tension. The appropriate length of effective vibration area should be at least 160 m (approximately three spans) in the pantograph-catenary system. pantograph-catenary interaction; effective vibration area; real-time catenary model; energy distribution +
Footnote †: journal: Medical  
The EN 50318-2018 standard [11] is also proposed based on existing investigation results as the standard of pantograph-catenary interaction simulation and experimental models. Recently, [PERSON] et al. [12] even used deep, long-short-term memory neural networks to efficiently investigate the dynamics of pantograph-catenary interactions. Traditionally, pantograph-catenary interactions are considered to influence all catenary structures, and the finite element method (FEM) [13; 14; 15] and modal superposition method (MSM) [16; 17; 18] are mainly used to model pantograph-catenary interactions with all catenary structures considered. However, the increasing train operation speed lets the pantograph continuously interact with a long catenary structure due to the long travel distance of the vehicle. With a long catenary model considered, the number of degrees of freedom (DOFs) of the whole pantograph-catenary interaction model is greatly increased, and its calculation efficiency is decreased. This is harmful to the investigation of pantograph-catenary long-term dynamic behavior and the development of pantograph-catenary hardware-in-loop simulations, where both calculation accuracy and efficiency are needed. In 2012, [PERSON] and [PERSON] [18] found that the pantograph-catenary interaction does not influence the whole catenary structure and the vibration of the catenary caused by the pantograph-catenary interaction is mainly concentrated in a small area around the moving pantograph. This small area is the effective vibration area (EVA), as shown in Figure 1. Based on the EVA, they developed a real-time catenary model for a hardware-in-the-loop pantograph-catenary interaction simulation. In the real-time catenary model, the long catenary is reduced to EVA (3-5 spans) and modeled using the MSM. When the pantograph moves near the boundary of the real-time catenary model, the whole model moves forward to let the pantograph located in the center of the model again, and the initial condition of the model after movement is derived based on the calculation results of the model before movement. Because only the EVA (3-5 spans) instead of the whole long catenary (normally 20 spans) needs to be modeled, the number of DOFs of the whole model is greatly decreased, and its calculation efficiency is improved when calculating the dynamic responses of the pantograph-catenary interaction with a long catenary considered.