# Research on the High Reliable Electromagnetic Stirring Power Supply
## 2 Materials and Methods
### Fault Diagnosis and Reconstruction of the Back-Stage Two-Phase Quadrature Inverter
\begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **Primary Fault** & **Connection** & **First Reconstruction** \\ \hline
0 & / & TR\({}_{\text{b}}\) & / \\
1 & V\({}_{1}\) & TR\({}_{\text{w}}\) \& TR\({}_{\text{13}}\) & S\({}_{\alpha}\) (V\({}_{3}\), V\({}_{4}\)) Sv (C\({}_{1}\), C\({}_{2}\)) \\
2 & V\({}_{2}\) & TR\({}_{\text{w}}\) \& TR\({}_{\text{13}}\) & S\({}_{\alpha}\) (V\({}_{3}\), V\({}_{4}\)) Sv (C\({}_{1}\), C\({}_{2}\)) \\
3 & V\({}_{3}\) & TR\({}_{\text{w}}\) & S\({}_{\text{w}}\) (C\({}_{1}\), C\({}_{2}\)) \\
4 & V\({}_{4}\) & TR\({}_{\text{w}}\) & S\({}_{\text{w}}\) (C\({}_{1}\), C\({}_{2}\)) \\
5 & V\({}_{5}\) & TR\({}_{\text{w}}\) \& TR\({}_{\text{35}}\) & S\({}_{\beta}\) (V\({}_{3}\), V\({}_{4}\)) Sv (C\({}_{1}\), C\({}_{2}\)) \\
6 & V\({}_{6}\) & TR\({}_{\text{w}}\) \& TR\({}_{\text{35}}\) & S\({}_{\beta}\) (V\({}_{3}\), V\({}_{4}\)) Sv (C\({}_{1}\), C\({}_{2}\)) \\
7 & V\({}_{1}\) \& V\({}_{2}\) & TR\({}_{\text{w}}\) \& TR\({}_{\text{13}}\) & S\({}_{\alpha}\) (V\({}_{3}\), V\({}_{4}\)) Sv (C\({}_{1}\), C\({}_{2}\)) \\
8 & V\({}_{3}\) \& V\({}_{4}\) & TR\({}_{\text{w}}\) & S\({}_{\text{w}}\) (C\({}_{1}\), C\({}_{2}\)) \\
9 & V\({}_{5}\) \& V\({}_{6}\) & TR\({}_{\text{w}}\) \& TR\({}_{\text{35}}\) & S\({}_{\beta}\) (V\({}_{3}\), V\({}_{4}\)) Sv (C\({}_{1}\), C\({}_{2}\)) \\
18 & V\({}_{1}\) \& V\({}_{4}\) & TR\({}_{\text{w}}\) \& TR\({}_{\text{13}}\) & S\({}_{\alpha}\)(V\({}_{3}\), V\({}_{2}\)) Sv (C\({}_{1}\), C\({}_{2}\)) \\
19 & V\({}_{2}\) \& V\({}_{3}\) & TR\({}_{\text{w}}\) \& TR\({}_{\text{13}}\) & S\({}_{\alpha}\)(V\({}_{1}\), V\({}_{4}\)) Sv (C\({}_{1}\), C\({}_{2}\)) \\
20 & V\({}_{3}\) \& V\({}_{6}\) & TR\({}_{\text{w}}\) \& TR\({}_{\text{35}}\) & S\({}_{\beta}\)(V\({}_{5}\), V\({}_{4}\)) Sv (C\({}_{1}\), C\({}_{2}\)) \\
21 & V\({}_{4}\) \& V\({}_{5}\) & TR\({}_{\text{w}}\) \& TR\({}_{\text{35}}\) & S\({}_{\beta}\)(V\({}_{3}\), V\({}_{6}\)) Sv (C\({}_{1}\), C\({}_{2}\)) \\ \hline \end{tabular}
\end{table} 
Table 2: First reconfigurable inverter switching status. Figure 3: Equivalent circuit diagram. (**a**) S\({}_{\beta}\)= 1; (**b**) S\({}_{\beta}\)= \(-1\). From Figure 3b, we can get:  
\[u_{o^{\prime}o}=\frac{u_{dc}}{4}\times\frac{r_{o}+L_{o}+L_{\beta}}{2(r_{o}+L_{o} )+L_{\beta}} \tag{15}\]  
The voltage deviation at the midpoint is:  
\[u_{o^{\prime}o}-u_{\alpha oN}=\frac{u_{dc}}{2}\Bigg{(}1-\frac{r_{o}+L_{o}+L_{ \beta}}{4(r_{o}+L_{o})+2L_{\beta}}\Bigg{)}>0 \tag{16}\]  
The polarity of the midpoint voltage deviation is also positive. That is, when the fault occurs in V4, no matter whether \(S_{\beta}=1\) or \(S_{\beta}=-1\), there will be \(J_{\alpha o}=P\). In the same way, the polarity of the voltage deviation at the midpoint of the other arms can be obtained when other IGBTs fail. The secondary fault diagnosis is shown in Table 3.  
It can be seen from the reasoning process that the secondary fault diagnosis method is the same as the fault diagnosis method for the primary fault. The fault diagnosis method based on the voltage polarity at the midpoint of the bridge arm can be applied to the secondary fault diagnosis after the primary fault occurring in inverter and reconfiguration, which has the characteristic of strong versatility. When the fault is detected in V4, the inverter topology is immediately reconstructed for the second time: V4 is cut off, TRw and TR13 are kept connected, and V2 is triggered. Namely \(\alpha\)-phase is reconstructed by V3 and V2, and the DC side capacitor remains as the \(w\)-phase. The reconstruction result is shown in the Figure 4. The rest of the reconstruction status is shown in Table 4.