## 3 High-Speed PMSG Characteristics with STS420-J2 Shaft Material
### Influence of Shaft Material on Electromagnetic Characteristics  
After ensuring the mechanical stability of the PMSG rotating at high speed, a design that satisfies the rated requirement output of 100 kW and line-to-line voltage of 380 V\({}_{\text{rms}}\) was developed. Subsequently, to verify the validity and reliability of the designed generator, a high-speed PMSG was manufactured, and an experiment was conducted. Figure 4 and Table 2 shows a comparison of the FEM and experimental results of the manufactured high-speed generator.  
Figure 3: Modal analysis of STS420-J2 shaft rotor.  
Figure 2: Critical speed analysis of STS420-J2 shaft rotor.  
As a result of the comparison, there was an error rate of approximately 9.19% in the case of line-to-line voltage and approximately 23.4% in phase current, leading to an end result that does not fulfill the rated output and voltage. Therefore, in this study, the causes of incompatibility with the requirements were analyzed. In general, the voltage drop of a generator is mainly caused by an increase in inductance and a decrease in magnetic flux owing to demagnetization of the magnet. However, it was confirmed that the PM used in the designed generator had no problem even if it was used at the required rated operating temperature because the maximum operating temperature was 300 \({}^{\circ}\)C. Therefore, an analysis of the generator inductance characteristics was performed. It was observed from the comparison between the inductance derived through the 3D FEM of the fabrication model and the inductance measured before heat treatment of the rotating body that the error rate was very well matched at approximately 1%. However, as shown in Table 3, by measuring the inductance after heat treatment of the rotating body, it was confirmed that the inductance increased by approximately 22%.  
This is because the paramagnetic characteristics are transformed into ferromagnetic characteristics during the heat treatment process in the assembly of the rotor. Therefore, as shown in Figure 5, a large leakage magnetic flux occurs at both ends of the shaft, which causes an increase in the synchronous reactance as the inductance increases [21]. The synchronous reactance component is located in the denominator term as follows Equations (2) and (3).  
\[V_{t}\ =\ E_{ph}\sqrt{\frac{R_{load}^{2}\ +\ X_{load}^{2}}{\left(R_{s}\ +\ R_{ load}\right)^{2}+\left(X_{ph}\right)^{2}}} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **FEM Value** & **Experiment Value** & **Percentage Error** \\ \hline Output power & 103.7 [kW] & 72.2 [kW] & 30.37\% \\ Phase current & 155.47 [A\({}_{\text{rms}}\)] & 119.05 [A\({}_{\text{rms}}\)] & 23.42\% \\ L-L voltage & 385.11 [V\({}_{\text{rms}}\)] & 349.71 [V\({}_{\text{rms}}\)] & 9.19\% \\ Efficiency & 96.72 [\%] & 95.62 [\%] & 1.13\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of STS420-J2 Shaft Material FEM and Experiment Results.  
Figure 4: Line to Line voltage and phase current characteristics of STS420-J2 shaft material at load.  
\[I_{ph}\ =\ \frac{E_{ph}}{\sqrt{\left(R_{ph}\ +\ R_{load}\right)^{2}\ +\ \left(X_{ph} \right)^{2}}} \tag{3}\]  
As the synchronous reactance increases, the voltage drop and current decrease. This voltage drop and current decrease cause an output reduction, as follows:  
\[P_{out}\ =\ 3\ \cdot\ V_{t}\ \cdot\ I_{ph} \tag{4}\]  
\(V_{t}\) is the terminal voltage, \(I_{ph}\) is the phase current, \(E_{ph}\) is the back EMF, \(R_{ph}\) is the phase resistance, \(R_{load}\) is the load resistance, and \(X_{ph}\) is the synchronous reactance (including self, mutual, and leakage reactance).