# Electrical Circuits Simulator in Null-Flux Electrodynamic Suspension Analysis
## 3 Discussion  
This study presents the analysis and advantages of a null-flux coil system for Maglev suspension, highlighting its potential benefits and limitations compared to previous studies and working hypotheses. One significant advantage of the null-flux coil system is its lack of dependence on a feedback control loop. Its configuration ensures it remains in a dynamic equilibrium position \(z_{0}\). This feature simplifies the overall system while maintaining effective control. Furthermore, the null-flux coil system exhibits high vertical rigidity, resulting in minimal vertical displacement of the train when transitioning from on-load to full-load states. However, this system also possesses some drawbacks, such as low lateral stiffness. This limitation restricts the system's tolerance for lateral deviations, as large lateral displacements can generate torques in the vehicle, potentially compromising its stability. To address this issue, the suspension and guidance system, known as the cross-connected null-flux system, was developed to enhance stability during operation, and is already being analyzed for a study to follow using an electrical circuit simulator. Figures 7-11 and 18 provide valuable insights into the EDS system's performance. Figure 7 confirms that induced currents become positive with increasing speed. Figure 8 shows that the method suits EDS system studies, and Figure 18 demonstrates the potential for increased system complexity. Figure 9 highlights the magnetic drag of the system, which is proportional to the electric currents in both coils and inversely proportional to the train's speed. The guidance force, which increases and decreases similarly to the levitation force, but with a much lower value, is illustrated in Figure 10. At the same time, Figure 11 depicts the lift force, which oscillates between positive and negative values at lower speeds but  
Figure 18: The electrical equivalent circuit of an 8-shaped coil powered by three SC coils, forming a null-flux EDS system at a cruising speed of \(v\) = 600 km/h, was implemented in the Ansys® Twin Builder software, which also displays the respective force curves generated as a function of time. The red, green, and blue lines represent drag, lift, and guidance forces, respectively. remains consistently positive at higher speeds, due to changes in induced current behavior. Together, these figures provide a comprehensive analysis of the EDS system's performance and potential for improvement. Figure 12 illustrates the effect of varying the lateral air gap on the induced current in the 8-shaped coils. As the distance between the coils decreases, the induced current increases. Figures 13 and 14 demonstrate that this variation has minimal impact on the drag force and negligible influence on the levitation force, respectively. Figure 15 depicts the influence of the lateral air gap on the guidance force. Figures 16 and 17 corroborate the feasibility of the proposed method. The analysis of these figures highlights the unique approach adopted in this study, which aims to simplify the research process in electrodynamic levitation. The calculation of mutual inductance and its derivatives using the Biot-Savart equation provides a solid foundation for the numerical calculation of mutual inductance as a function of magnetic flux variation. By utilizing the circuit simulator, the complexity of solving electric circuit equations and determining forces is significantly reduced. This streamlined approach simplifies the analysis and allows the exploration of a cross-connected circuit, which will be the focus of a subsequent paper, without the need for complex harmonic approximations or other intricate considerations. Moreover, the flexibility of the circuit simulator enables electrical modifications and the introduction of additional elements, which align with a research topic of a further study. Together, these factors contribute to the innovative nature of the work and its potential to simplify and advance research in electrodynamic levitation.