*2.1. Conventional Method*

As described above, in a maglev train, both propulsion and normal force fluctuate according to slip. In particular, levitation in the normal force affecting the levitation system of the train becomes a factor that can hinder the safety of the train. Therefore, to control the train, normal force must be controlled by slip. However, because the LIM is a system based on an induction motor and cannot directly control the slip, it was controlled using slip frequency that has a proportional relationship with the slip, as shown in Equation (2):

$$f\_{sl} = f\_c S \tag{2}$$

$$f\_e = f\_m + f\_{sl} \tag{3}$$

where *fe* is the synchronization frequency, which means the supply frequency of the AC voltage supplied to the stator winding; *fm* is the rotor frequency, which is the physical rotation frequency; *fsl* is the slip frequency, which is the difference between the synchronization frequency and the rotor frequency; and *S* is the slip, which is the ratio of the slip frequency to the synchronization frequency, and it can be expressed as *s* = *fsl*/ *fe*.

Table 1 shows an example of fluctuations in slip and normal force when slip frequency is fixed and the synchronous speed of the train is changed using Equation (2) and Figure 3. Figure 3 shows the normal force value derived through finite-element analysis.

**Table 1.** Correlation between elements in fixed slip-frequency control.


**Figure 3.** Normal force by slip frequency through finite-element analysis.

Table 1 shows that, as the synchronous frequency associated with the train's synchronous speed decreased, slip increased, maintaining a fixed slip frequency. As shown in Figure 3, as slip increased, vertical force changed in the direction of decreasing, increasing the safety of the train [5,13]. If the slip frequency were fixed, Equation (3) shows that the synchronous speed also had its maximal value at the point where the speed of the train was maximal, and the greatest vertical force occurred at this moment (here, the maximal synchronous speed was the maximal change speed of the magnetic field generated by the stator when the train was running at maximal speed. The greatest normal force was at the moment when the magnitude of the levitation force that made the levitation system unstable was the greatest), that is, if slip magnitude and the normal force at which the levitation did not fail at the maximal speed of the train, maximal slip frequency could be derived from the synchronous speed of the train. If the derived slip frequency were fixed, the train would be in an area where there was less

risk of accidents caused by vertical force when the train is running at full speed. This means that the risk of accidents caused by vertical force would also be low in the section where the speed of the train was decreasing. So, the train could safely run in all speed zones. For train safety, this method is applied to currently running maglev trains. However, this method ignores the train's operating conditions and uses a fixed slip frequency, which leads to low-efficiency train operation due to large slip at low speeds. Consequently, if the ratio of the fluctuations of the propulsion force and normal force of the train based on the slip frequency is known, the efficiency of the train can be improved by adjusting slip frequency within the normal force that operates safety zones according to the required propulsion force.
