# Electrical Circuits Simulator in Null-Flux Electrodynamic Suspension Analysis
## 2 Unveiling the Inner Workings: Exploring the Principles and Model of an EDS System
### The Basic Principles of an EDS System  
An EDS system comprises three types of coils, as illustrated in part a of Figure 1. The SC coils are onboard, and the guideway coils include the levitation and propulsion coils. The levitation coils are figure-eight-shaped, known as 8-shaped or ground coils [36]. In the 1960s, physicists [PERSON] and [PERSON] developed suspension systems based on electromagnetic forces [40]. They patented a null-flux suspension system to minimize drag forces, requiring less propulsion power. The most common configuration is displayed in parts b and c of Figure 1.  
The 8-shaped coil is formed by connecting two coils in series, both of which are fed by the same magnetic field source, which is electrically isolated from any other element in the system. The operating principle is that the counter electromotive force generated by the upper loop (1) opposes that produced by the lower loop (2); hence, they are connected in reverse bias. The advantage is the absence of electrical current and power loss when the magnetic field source is centered relative to the coils. The 8-shaped coils are mounted vertically on both sides of a U-shaped track. This topology is known for its high lift-drag ratio, indicating high propulsion efficiency in the train [13]. An electric current is induced in the ground coil when a magnetic source passes below its center, generating the levitation force to balance the train's weight.  
The case study focuses on the JR-Maglev, developed by the Central Japan Railway Company. JR Central plans to deploy the L0 Series train on the Chuo Shinkansen rail line  
Figure 1: **(a)** Diagram of the main components of the JR–Maglev, Yamanashi test track. PC: propulsion coil. MS: mechanical suspension. SC: superconducting coil. 8C: figure-eight-shaped coil. (b) Sketch of the null-flux coils. (c) Equivalent electrical circuit. The numbers 1 and 2 refer to the upper and lower loops of the coil, respectively [41].  
between Tokyo and Osaka, which is currently under construction. This study refers to data from the MLX01 series train measured on the Yamanashi test line due to difficulty in obtaining data from the current model, as provided in Table 1[24; 25; 41]. The conventional notation used is depicted in part a of Figure 2. The Maglev's longitudinal movement aligns with the \(x\)-axis, representing the drag force, \(f_{x}\). The transverse movement, or lateral displacement, follows the \(y\)-axis direction, representing the guidance force, \(f_{y}\). Lastly, the vertical motion is associated with the \(z\)-axis, with \(f_{z}\) representing the levitation force. Position \(z_{0}\) is the equilibrium position, where the lift force equals the Maglev's weight force in magnitude, allowing it to move without touching the ground. The \(\Delta y\) and \(\Delta z\) represent the fluctuation during the train's movement in the \(y\) and \(z\) directions, respectively. The dimensions of the current SC and 8-shaped coils of the Yamanashi test track are shown in part b of Figure 2.