*5.1. Speed Response Characteristics of the Propulsion Motor*

Figure 25 shows the results of the simulation on the characteristics of the propulsion motor's response to step speed reference values. The standard speed value was set as 500 rpm. Based on these results, it can be observed that the conventional AFE rectifier, 24-pulse rectifier, and improved AFE rectifier all showed relatively good speed response characteristics to the reference value.

**Figure 25.** Speed response characteristics of the propulsion motor.

#### *5.2. Comparison of the DC Output Voltage Waveform in the DC Link*

Figure 26 shows the DC output voltage in the DC link when different rectifiers are used. The 24-pulse rectifier, which uses the phase shifting transformer, had the best response characteristics to the reference DC voltage. Nevertheless, the improved AFE rectifier maintained the DC output voltage in a more stable state than the conventional AFE rectifier.

**Figure 26.** DC output voltage in the DC link.

*5.3. Comparison of the Total Harmonic Distortion in the Voltage of the Power Source*

Figure 27 shows the results of the simulation for the total harmonic distortion in the power supply at the output side. The estimated values for the electric propulsion system that used the improved AFE rectifier were about 2% better than the case wherein the conventional AFE rectifier was used. Similar results were obtained for the 24-pulse rectifier. These values satisfied the recommendation for total harmonic distortion that is included in the IEEE Standard 519-2014 [45], which specifies a total harmonic distortion of 8% in power generators under 1 kV.

**Figure 27.** Total harmonic distortion of the power source on the voltage side.

#### *5.4. Comparison of the Heat Loss in the Inverter Switching Element*

The inverter's IGBT module consists of the IGBT element and diode. Loss during power conversion can be categorized into switching loss and conduction loss in the IGBT element as well as switching loss and conduction loss in the diode element. The simulation estimated the power loss and heat loss in the inverter module's diode and IGBT element. The equation for obtaining conduction loss and switching loss is as follows. Figure 28 shows the block diagram of the apparatus used to record heat loss.

**Figure 28.** Block diagram of the apparatus used to obtain the heat loss in the inverter switching element.

Conduction losses:

$$P\_{\rm cond\\_Q} = V\_{\rm ce(sat)} \times I\_{\rm c} \times D \tag{26}$$

Switching losses:

$$\text{Turnr on } P\_{sw\\_Q\\_ov} = E\_{am} \times f \times V\_{cc} + V\_{cc\\_datasheet} \tag{27}$$

$$\text{Turn off} \, P\_{sw\\_Q\\_off} = E\_{off} \times f \times V\_{cc} \div V\_{cc\\_datasheet} \tag{28}$$

where, *Vce*(*sat*) is the transistor collector–emitter saturation voltage, *Ic* is the collector current, D is conducting duty cycle, *Eon* is the transistor turn-on energy losses, *Eoff* is the transistor turn-off energy losses, *f* is the frequency, and *Vcc* is the actual dc bus voltage.

Figure 29 shows the results of our simulations to estimate the sum of the switching and conduction losses of the diode in the inverter of a large-scale electric propulsion system using the conventional AFE rectifier, 24-pulse rectifier, and improved AFE rectifier. Table 5 lists the average of these results. It is clear from these analysis results that the system with the improved AFE rectifier shows lower switching losses than the one with the 24-pulse rectifier.

**Table 5.** Comparison of the heat losses from the inverter when using the conventional AFE rectifier, DFE rectifier and improved AFE rectifier in a large-scale electric propulsion system modeled.


**Figure 29.** *Cont*.

**Figure 29.** Comparison of the switching loss in the inverter elements.

## **6. Conclusions**

Relatively good propulsion motor speed response results were obtained for the large-scale electric propulsion systems that were modeled using each of the rectification methods. However, the large-scale electric propulsion system that used the improved AFE rectifier was able to accurately detect the phase angle of the power supply voltage using a PLL control circuit. Therefore, it was able to obtain a more stable DC link voltage output and reduced number of harmonics in the input power supply side compared with the conventional AFE rectifier. Furthermore, the improved rectifier showed similar output performance as the 24-pulse DFE rectifier, which uses a phase shifting transformer. In addition, from the simulation results, it was observed that when the proposed AFE rectifier is used, the DC output performance of the DC link in the rectifier was improved. Consequently, the switching loss of the power semiconductor of the inverter used for controlling the speed of the propulsion motor was similar to that of the 24-pulse rectifier.

So far, large-sized electric propulsion vessels have adopted the same high-power drive system of the shore, but the use of phase shifting transformers with DFE rectifiers in a limited space and heavy weight has several disadvantages. In this study, an improved AFE rectifier with superior performance compared to the 24-pulse rectifier was applied. Research findings revealed that the proposed system would mitigate the complexity of the electric converting system by reducing the number of the rectifiers to be fitted. Therefore, the optimized spatial arrangement in the engine room could contribute to increasing the cargo loading efficiency of the vessel.

Based on these simulation results, it was confirmed that it can be more effective for a large-scale electric propulsion system to use an AFE rectifier that can turn a power semiconductor switch on and off, rather than using an existing DFE rectifier employing a phase switching transformer.

**Author Contributions:** Conceptualization, J.K and K.Y.; Methodology, J.S., K.Y. and H.J.; Formal analysis, H.J.; Software, K.Y. and H.J.; Writing-original draft preparation, H.J.; Writing-review and editing, K.Y.

**Funding:** This research received no external funding.

**Acknowledgments:** We thank our colleagues from Seoung Hwan Kim who provided insight and expertise that greatly assisted the research, although they may not agree with all of the conclusions of this paper. In addition, they are indebted towards Prof. Kim for his assistance on setting-up the simulations in the PSIM environment.

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