## 3 Influence of PWM Pulse Frequency on Overvoltage Distribution
### The Influence of PWM Frequency on the Voltage Distribution from the End to the Ground  
The simulation waveform of the ground voltage of each turn conductor at 100 kHz frequency is shown in Figure 6.  
It can be seen from the above figure that the maximum voltage of the second pulse wave is higher than that of the first pulse voltage wave, and the maximum ground voltage will not continue to rise later. This is because when the frequency is high, the overvoltage generated by the falling edge of the first pulse wave is too late to attenuate to zero, so it \begin{table}
\begin{tabular}{c c c c c c} \hline
**Capacitor/pF** & **C1** & **C2** & **C3** & **C4** & **C5** \\ \hline C1 & 496.3 & 1046.2 & & & \\ C2 & 1046.2 & 587.7 & 1013.6 & & \\ C3 & & 1013.6 & 620.4 & 978.8 & \\ C4 & & & 978.8 & 587.8 & 938.4 \\ C5 & & & & 938.4 & 492.2 \\ \hline \end{tabular} Note: The diagonal lines in the table represent the ground capacitance of each turn conductor, and the non-diagonal elements represent the inter-turn capacitance of different conductors.  
\end{table} 
Table 1: Distributed capacitance of permanent magnet synchronous wind generator. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Inductor/\(\mu\)H** & **1 st Turn** & **2 nd Turn** & **3 rd Turn** & **4 th Turn** & **5 th Turn** \\ \hline
1 st turn & 16.0 & 15.4 & 14.9 & 14.3 & 13.8 \\
2 nd turn & 15.4 & 15.9 & 15.4 & 14.8 & 14.3 \\
3 rd turn & 14.9 & 15.4 & 15.9 & 15.4 & 14.8 \\
4 th turn & 14.3 & 14.8 & 15.4 & 15.8 & 15.4 \\
5 th turn & 13.8 & 14.3 & 14.8 & 15.4 & 15.8 \\ \hline \end{tabular} Note: The diagonal in Table 2 is the equivalent self-inductance of each conductor, and the rest is the equivalent mutual inductance between different conductors.  
\end{table} 
Table 2: Distributed inductance of permanent magnet wind turbine. Figure 6: Simulation waveform of ground voltage at 100 kHz. will be generated at the rising edge of the second pulse wave. The superposition of the overvoltage generated by the second pulse wave leads to a further increase in the ground voltage. When the third pulse wave comes, the overvoltage generated by the falling edge of the first pulse wave attenuates to zero, only affected by the overvoltage generated by the falling edge of the second pulse wave, so the maximum voltage remains unchanged. When the frequency drops to 50 kHz, the ground voltage simulation waveform of each turn conductor is shown in Figure 7.  
As shown in Figure 7, when the frequency drops to 50 kHz, the first pulse's rising edge overvoltage is the same, and the first pulse wave's falling edge overvoltage is greatly attenuated, resulting in the second pulse wave's rising edge overvoltage being lower than that at 100 kHz. When the frequency is further reduced to 10 kHz, the simulation waveform is shown in Figure 8.  
As shown in Figure 8, when the frequency drops to 10 kHz, the first pulse overvoltage is still basically the same, but the pulse wave at the falling edge is completely attenuated, which has little effect on the second rising edge pulse wave. The waveform generated by the first pulse is consistent with the waveform generated by the second pulse. In summary, the first pulse wave rising edge overvoltage waveform at each frequency is the same; the difference is in the second pulse wave overvoltage waveform, and as the frequency decreases, that is, the period increases, the second pulse's generated overvoltage will be reduced. The second pulse wave rising edge overvoltage of three frequencies is compared with the first pulse wave rising edge overvoltage, as shown in Figure 9.  
Figure 8: Simulation waveform of ground voltage at 10 kHz. Figure 7: Simulation waveform of ground voltage at 50 kHz. As shown in Figure 9, the first pulse (black) in the figure represents the overvoltage generated by the first pulse wave at different frequencies; 1-1-4-5 denotes the first turn conductor of coil 1 to the fifth turn conductor of coil 4.