**3. Simulation**

In order to perform the simulation under the same conditions as those of the actual train, the data of a train that was actually operated were used as input values, as shown in Figure 6a, through which the current command and slip required for control of the slip frequency was derived and utilized. The black waveform represents the speed pattern of the train, and the blue waveform represents the driving-force waveform of the train. For efficiency comparison, total power consumption and generated normal force were compared between the conventional method using a slip frequency of 13.5 Hz, and the proposed method in which the slip frequency fluctuated during train operation based on the operating conditions. In the proposed method, the margin rate of the limited normal force was set to vary between 9.5 and 13.5 Hz according to the applied operating conditions.

**Figure 6.** Simulation conditions and calculation blocks: (**a**) Train operation pattern (train data) and (**b**) Block diagram using train pattern.

Figure 7 compares the results of the existing control method and the proposed method. Figure 7a shows the accumulated power consumption while the train was running. The existing control method of the red curve consumed approximately 140 Wh of power while operating under the same conditions and section, whereas the proposed method of the black curve consumed approximately 116 Wh of power, an improvement of approximately 24 Wh, which is a reduction in power consumption and an efficiency improvement of approximately 19.6%. Figure 7b shows the normal force change during train operation. When a margin ratio of approximately 30% was compensated for safety from the actual train's limited normal force, the limit value was about −2.5 kN, called the critical normal force. If the normal force falls below this value, levitation fails. Looking at the waveform in Figure 7b, the maximal generated normal force of the conventional method was −2.04 kN, and the maximal generated normal force of the proposed method was −2.45 kN. Both systems were in the safe area. Therefore, when using the proposed method, efficiency increased by approximately 17.14%, but it was confirmed that the efficiency improvement of the proposed method was effective because the train was running within a safe range of normal force.

**Figure 7.** Comparison of existing and proposed condition data: (**a**) Accumulated power consumption and (**b**) Normal train force.

### **4. Experiment**

Figure 8a shows the LIM train of Incheon International Airport in Korea used for the experiment. In order to compare train efficiency, the power system installed on the train and inverter power were directly measured. Figure 8b shows the train's operating route used in the experiment. Five sections were operated over one round trip from Station 101 (the start station) to Station 106 (the end station).

**Figure 8.** Actual vehicle test conditions and used vehicle: (**a**) Experimental linear induction motor (LIM) and (**b**) Train test-run section.

Table 3 shows the specifications of the trains used in the experiment; the train was composed of 1 car and 2 trains. For comparison, the widely used 13.5 Hz slip-frequency fixed control method and the proposed slip-frequency variable-vector control method were compared. To increase the reliability of the experiment, it was conducted in triplicate, and results were calculated using the average. Lastly, the train was operated using the automatic-train-operation (ATO) method [18], an automatic train control system that propels, rides, and brakes trains according to given commands. The ATO was used for train operations because it reduces the deviation of experiment results using train drivers and quickly responds to slip-frequency fluctuations during operation.


**Table 3.** Experimental vehicle specifications.

Figures 9 and 10 show the accumulated power consumption of each part according to actual train operation. Figure 9 shows the operating results from Station 101 to Station 106, and Figure 10 shows the train operating results from Station 106 to Station 101. Figures 9 and 10a show the results of the conventional train control method, and Figures 9 and 10b show those of the proposed control method. In each curve, the green line represents the total amount of consumed power to float the train, the blue line represents the total power consumption used to propel the train, and the red line represents the sum of the power consumption of propulsion. Lastly, the black line indicates the speed of the train. The moment when the curve changed in value was when the train was running between the stations, and the moments when the curve had no value indicate the waiting time after arriving at the station. To exclude the effect of energy consumption caused by differences in waiting times at each station on the results, the consumed energy during the waiting time at each station was removed from the actual comparison. In addition, the test train was used when comparing the actual consumed energy twice as often as the measured value in the two trains.

**Figure 9.** Comparison of accumulated power consumption between existing and proposed methods (101 → 106): (**a**) Conventional method and (**b**) Proposed method.

**Figure 10.** Comparison of accumulated power consumption of existing and proposed methods (106 → 101): (**a**) Conventional method and (**b**) Proposed method.

Table 4 shows the results of comparing the two methods in consideration of the elimination of reverse waiting time, and (1) quantity and (2) schedule. When moving from Station 101 to Station 106, the total power consumption of the existing method was 27.74 kWh, and the total power consumption of the proposed method was 25.12 kWh. When using the proposed method, there was approximately 2.62 kWh (9.45%) increased efficiency. When moving from Station 106 to Station 101, the total power consumption of the existing method was 27.8 kWh, the total power consumption of the proposed method was 23.64 kWh; when using the proposed method, there was approximately 4.16 kWh (14.96%) increased efficiency. As a result, efficiency increased by approximately 6.78 kWh (12.2%) when using the proposed method, to 55.54 and 48.76 kWh, respectively, from Station 101 to Station 106.


**Table 4.** Comparison of power-consumption results.

#### **5. Conclusions**

In this study, as part of our research on improving the operating efficiency of a maglev train using an LIM, the relationship between train slip frequency, normal force, and propulsion force was analyzed through a mathematical study. Using the analytical results, the slip frequency having the optimal efficiency was derived on the basis of the train's operating conditions while limiting the normal force to the extent to which the levitation system of the train did not fail. Subsequently, slip frequency was changed according to the operating conditions of the train in real time. Through the ATO driving system, a simulation test in which slip frequency was varied on the basis of the driving conditions of the train while it was running, and an experiment using an actual train were conducted. As a result of the simulation test for one operating section in which the actual train was running, when the proposed method was used rather than the existing fixed system slip frequency of 13.5 Hz, a cumulative power-consumption decrease of approximately 24 Wh and an efficiency gain of approximately 17.14% were achieved. These results confirmed that the efficiency improvement using the proposed method was significant. In the case of the experiment, when the proposed method was compared with the existing fixed system slip frequency of 13.5 Hz, the cumulative power consumption decreased by approximately 6.78 kWh and efficiency increased by approximately 12.2%. Through this, we verified that the proposed method is more efficient than the existing method is (the proposed method uses LIM characteristics, which are suitable for low- and medium-speed types. Therefore, it is difficult to apply to maglev trains with different structures and principles, such as superconducting-repulsion or permanent-magnet types).

**Author Contributions:** Conceptualization, S.-U.P.; methodology, S.-U.P.; software, H.-U.S.; validation, S.-U.P.; formal analysis, S.-U.P.; investigation, S.-U.P.; resources, J.-W.L.; data curation, S.-U.P.; writing—original-draft preparation, S.-U.P.; writing—review and editing, H.-S.M. and S.-H.O.; visualization, S.-U.P.; supervision, H.-S.M.; project administration, S.-H.O.; funding acquisition, J.-W.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Korea Institute of Machinery and Materials (KIMM).

**Conflicts of Interest:** The authors declare no conflict of interest.
