## 2 Materials and Methods
### Pantograph-Catenary Electrical Contact System  
In Europe, high-speed rail networks operate at 25-27.5 kV and 50 Hz. In the majority of countries, locomotives use a transformer to adjust the voltage according to the type of motor. Reconciler-based AC-wire DC motors or newer electric locomotives use AC motor-GTO (gate turn-off thyristor) inverter systems to offer high-efficiency traction motors, as well as regenerative braking. Figure 1 shows the electrical overhead line, which has two main suspended cable wires, a messenger wire above, and a contact wire that receives energy for the electric locomotive. Droppers connect these wires, and mechanical tensioning devices at the end poles keep them in tension all over the track. The locomotive pantograph assembly represents a crucial type of modern current collector that supplies power to locomotive transformers nowadays. The pantograph-catenary system includes the pantograph, the contact wire, and the interface- pantograph slide. The pantograph slide is essential in ensuring reliable power transfer under dynamic circumstances. The pantograph-catenary system is an essential component in the purchase of electricity for electric locomotives. The train's electrical system connects to the pantograph. The conductive cables convey electrical energy, which powers the train. Pillars usually stand alongside railway tracks to support these wires. While the train is moving, the pantograph expands to make contact with the catenary cable wires. The train appears to be extending its pantograph to connect to an electrical source. As the train moves, the pantograph slides easily along the wires. When the pantograph touches the catenary wires, it transfers electricity to the train. While the train is moving, the pantograph and catenary wires remain in continuous contact, as they move in sync down the rails. The pantograph adapts itself to changes in wire height or location to provide a continuous connection. When the train arrives at the final point of the electrified track section or has to come to a stop for any reason, the pantograph descends from the catenary wires. This eliminates the electrical connection, and the train may either switch to another power source or stop using energy altogether. Figure 1: Electrical overhead lines connect to the train pantograph–catenary system. To avoid grooving and ensure the uniform wear of the CS, the contact wire is anchored in a zigzag pattern, known as stagger. This stagger is provided by a rigid arm mounted to the cantilever. The cantilever is a horizontal support attached to the pillars that holds the overhead line in place and preserves the right zigzag pattern. The stagger alternates horizontally throughout the track, using the track's axis as a reference, ensuring that the pantograph is used uniformly along its entire length, as illustrated in Figure 2. The contact wire's lateral offset from the track axis varies depending on the form of the railway route. Figure 2 shows the components and architecture of an overhead catenary system used to power electric trains. The central line of the railway track, which serves as a reference point for the overhead line's zigzag displacement, allows for a more accurate view of the zigzag value. The zigzag length value is one of the most important parameters in determining how effectively energy is transported between the contact wire and the locomotive's current collector. Reduced zigzag length values result in greater local wear on the pantograph surface, reducing component's durability. If the zigzag value is too high in extreme wind conditions [7; 12], or due to a local dropper flaw [14], the contact wire will surpass the maximum value of the functioning region of the CS hanging, causing significant damage to the pantograph-catenary equipment. Failure to strictly stick to the zigzag length could result in the 'hanging' of the catenary suspension, the breaking of the contact wire, the destruction of the pantograph, and the suspension for hundreds of meters until the train stops.