# Electrical Circuits Simulator in Null-Flux Electrodynamic Suspension Analysis
## 2 Unveiling the Inner Workings: Exploring the Principles and Model of an EDS System
### The Model Validation  
Calculations were performed to validate the presented model's accuracy and to determine the electromagnetic forces generated by the interaction of 4 SC coils on the bogie and 20 null-flux coils on the guideway. The analysis focused on the average electromagnetic forces as a speed function, ranging from \(v\) = 0 km/h to 600 km/h. The obtained results were  
Figure 14: Lift force in one 8-shaped coil fed by one SC coil for six different air gaps. Figure 15: Guidance force in one 8-shaped coil fed by one SC coil for six different air gaps. compared with the data measured from the Yamanashi test line [38]. Figure 16 displays the values of drag and levitation forces, while Figure 17 illustrates the guidance force. In Figure 16, the characteristic curves of EDS system can be observed through the levitation and drag forces. The levitation force exhibited an increasing trend with speed until it reached a maximum value. This behavior is attributed to the simultaneous increase in induced voltage in the ground coil and the coil's effective resistance, due to the metallic conductor's skin effect. Consequently, the induced current in the coil increased at a slower rate or stopped increasing, resulting in saturation of the suspension force at higher speeds. The experimental data indicated that this saturation speed occurred at approximately 100 km/h. The critical speed, which depends on the magnetic field strength in the air gap and the vehicle weight, refers to the speed at which the vertical force of the vehicle becomes positive [2]. It is also called lift-off speed. Once the system achieves levitation, it remains sustained as long as the onboard SC coils operate stably. The drag force exhibited a sharp increase up to approximately 50 km/h, followed by a gradual decrease after reaching the peak's speed of the electromagnetic drag force. This phenomenon indicates that less energy is lost as the train's speed increases. The reduction in energy loss can be attributed to the fact that if the time it takes for a SC coil to cross the null-flux coil is shorter than the current decay time of the ground coil, the null-flux coil does not have sufficient time to dissipate the stored energy within the Maglev system. Thus, the variation of the drag force with velocity, as shown in Figure 16, can be explained. Figure 17 portrays the relationship between the guidance force and speed. As speed increased, the guidance force gradually rose. However, after reaching a speed of 200 km/h, the guidance force increased at a slower rate. This behavior mirrored the relationship observed in the levitation force-speed characteristics. At higher speeds, the induced current remained relatively stable due to the skin effect, leading to a tendency for the guidance force to approach saturation. Figure 16: Levitation and drag forces as a function of displacement speed. A comparison between the model utilizing the circuit simulator and experimental measurements conducted on the Yamanashi test line. The configuration consists of four SC coils onboard and twenty 8-shaped coils on the guideway. The simulation results, as depicted in Figures 16 and 17, exhibited a notable disparity between the calculated values and the measured data, which could be attributed to the approximations made in the numerical models regarding the coil parameters. Specifically, the SC coil, originally with a racetrack shape, was approximated as a rectangle with an equivalent internal area. Similarly, the 8-shaped coil was approximated using two rectangular loops, disregarding the curved ends of the actual coil. Moreover, both coils were considered one-dimensional, that is, without thickness. Additionally, the proposed model did not consider certain aspects, such as the shield of the SC coil. As a result, discrepancies arose in the mutual inductances between the onboard and off-board coils and the induced current in the 8-shaped coil.