###### Abstract
Later, [PERSON] [19] and [PERSON] [20] further improved this model to formulate the hardware-in-the-loop pantograph-catenary interaction test bench. The same theory is also used in train-track interaction simulation models, such as the moving element model [21; 22] and the reduced beam model [23; 24]. These new methods have proved accurate and efficient in solving pantograph-catenary interaction dynamics with long catenary structures and can be used in hardware-in-the-loop pantograph-catenary interaction simulation. It can be seen from these methods that the EVA is the basement of these methods, and the length of the EVA can directly decide the accuracy and efficiency of these methods. If the length of EVA is too short, the vibration of the catenary caused by the pantograph-catenary interaction cannot be fully included in the model, and its calculation accuracy is decreased. If the length of EVA is too long, the length of the catenary model is also long, and the DOFs of the model are increased, which further decreases the calculation efficiency of these new methods. [PERSON] et al. [25] investigated the influence of the length of EVA on the calculation accuracy of the reduced catenary model and gave the proper length of EVA of a certain pantograph-catenary interaction case. However, while the length of EVA is considered in the existing literature, the way to calculate the length of EVA and the influence of different  
Figure 1: Schematic of the effective vibration area in the pantograph–catenary interaction. key parameters on the length of EVA is not considered so far. This limits the application of the new efficient pantograph-catenary interaction model based on the EVA. Therefore, to better understand the basic theory of these new models and apply them in different pantograph-catenary interaction cases, it is necessary to investigate the length of EVA in the pantograph-catenary system and decide them before using the new models based on the EVA. In this work, the length of EVA in the pantograph-catenary system is investigated. Based on the existing model developed in [26], a pantograph-catenary interaction model with a long catenary structure (30 spans) is developed, where the whole model is validated by the EN50318:2018 standard. Then, a new method is developed based on the energy distribution to obtain the length of the EVA in the pantograph-catenary interaction system. Based on this new method, the length of EVA under the influence of different contact wire tensions and vehicle velocities is investigated. The appropriate length of EVA with respect to different vehicle velocities and contact wire tensions is obtained. Finally, the real-time catenary model is used to calculate the dynamic responses of the pantograph-catenary interaction under different lengths of EVA, and the results are compared with those from measurement data to validate the obtained appropriate length of EVA. The present research results enhance the theory of the new efficient pantograph-catenary interaction models based on EVA and can be used as a supplement to these models. The rest of this paper is organized as follows. The MSM-based pantograph-catenary model and the new method to obtain the length of the EVA are described in Section 2, and the present pantograph-catenary model is validated in Section 3. The length of EVA under different conditions is calculated and validated in Section 4. Some useful conclusions based on the study are drawn in Section 5.