## 5 Transient-State Analysis for Switching from Six- to Three-Phase Operation  
In Section 4, the load characteristics in the steady state were analyzed in detail. Subsequently, it was necessary to investigate changes in voltage, current, and torque when switching from six- to three-phase operation. Here, the data obtained through transient analysis during phase switching could be used as a reference when designing the controller and inverter of the fault-tolerant system. The phase switching experiment was conducted by changing the control program for each mode.  
To switch from six- to three-phase operation as shown in Figure 16, the input and output of INV2 must be limited to zero in the controller. Here, the output variable of SVPWM, which is the input of the inverter, was set to zero, and the three-phase switch of INV2 was turned off using the trip function to prevent malfunction. At this time, according to the state of the Clarke transformation matrix of the fed-back current, operation could be divided into constant-current and constant-torque modes. In a normal six-phase operation, a six-phase Clarke transformation matrix is applied and multiplied by a scaling factor of 1/3, as shown in Equation (23). However, when converting from six to three phases, a three-phase Clarke transformation matrix must be applied as shown in Figure 16. Here, constant-current mode was controlled through Equation (24) to keep the phase current constant, and the torque was reduced by half. On the other hand, constant-torque mode was controlled to keep the MMF generated in the stator in its original state through Equation (25); subsequently, phase current was doubled.  
\[T_{c}=\frac{1}{3}\left[\begin{array}{cccccc}1&cos(\theta)&cos(4\theta)&cos(5 \theta)&cos(8\theta)&cos(9\theta)\\ 0&sin(\theta)&sin(4\theta)&sin(5\theta)&sin(8\theta)&sin(9\theta)\\ 1&cos(5\theta)&cos(8\theta)&cos(\theta)&cos(4\theta)&cos(9\theta)\\ 0&sin(5\theta)&sin(8\theta)&sin(\theta)&sin(4\theta)&sin(9\theta)\\ 1&0&1&0&1&0\\ 0&1&0&1&0&1\end{array}\right] \tag{23}\]  
\[T_{c}=\frac{2}{3}\left[\begin{array}{cccc}1&cos(4\theta)&cos(8\theta)\\ 0&sin(4\theta)&sin(8\theta)\\ 0&0&0\end{array}\right] \tag{24}\]  
\[T_{t}=\frac{1}{3}\left[\begin{array}{cccc}1&cos(4\theta)&cos(8\theta)\\ 0&sin(4\theta)&sin(8\theta)\\ 0&0&0\end{array}\right] \tag{25}\]  
First, a phase-switching experiment was conducted to stop UVW2, using Equation (24) at 480 r/min and 5 A, to obtain transient-state curves of UVW1 for constant-current mode. The result is shown in Figure 17, and changes were observed in current and torque, excluding voltage. Figure 17 shows the U1-V1 voltage, U1 current, U2 current, and torque in that order. At the beginning of the transient state of the constant-current mode, the peak current of U1 increased from 7 to 15 A, and the steady state was restored after approximately 85 ms. However, the torque did not immediately respond to the current change and started to change from 7.7 to 8.6 Nm after approximately 12 ms after the time  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Currents** & **Load Angle** & **Torque** & **Torque** & **Torque Error** & **Torque** \\
**[Arms]** & **[deg]** & **FEA [Nm]** & **Exp. [Nm]** & **[\%]** & **Constant** \\ \hline
2 & 6 & 1.6 & 1.4 & 14.3 & 0.70 \\
4 & 12 & 3.2 & 3.0 & 6.7 & 0.75 \\
5 & 15 & 4.0 & 3.8 & 6.7 & 0.75 \\
6 & 17 & 4.8 & 4.5 & 6.7 & 0.75 \\
8 & 21 & 6.5 & 6.1 & 6.6 & 0.76 \\
10 & 23 & 8.2 & 7.7 & 6.5 & 0.77 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Comparison of torque characteristics in relation to current for three-phase operation.  
The transient times for constant-current and constant-torque modes presented above were 85 and 135 ms, respectively, and the time difference between the modes from transient to steady-state during phase change was therefore 50 ms. Transient time is summarized in Table 13 by dividing it into current and torque for each mode. Here, U2 current was not included because it was immediately cut off during phase change.