# Effect of Multiple Reclosing Time Intervals on Axial Vibration of Winding
## 4 Evaluation of the Effect of Reclosing Time Interval on Short-Circuit Vibration
### Calculation of Winding Response Variation at Different Reclosing Intervals  
According to the axial dynamic formula of the winding shown in Equation (1), the vibration acceleration of the winding can reflect the magnitude of the resultant force. According to the difference in the vibration acceleration value, a quantitative analysis of the influence of different intervals on the winding is carried out.  
As the short-circuit interval changes, the axial vibration amplitude on the winding changes, as does the attenuation time. The peaks and valleys values in each cycle in the acceleration curve of Figure 10 were sampled and fitted, and the relationship curve between the acceleration amplitude of the secondary vibration and the recclosing interval was obtained, as shown in Figure 11.  
The vibration acceleration curve of closing at a 0\({}^{\circ}\) phase angle is generally larger than that of closing at a 90\({}^{\circ}\) phase angle. Table 2 was obtained by quantitative analysis of the curve in Figure 11. The sampling intervals were 50 ms, 200 ms, 400 ms, and 600 ms.  
As the short-circuit interval increases, the acceleration amplitude of the secondary vibration decreases, and the attenuation reaches a steady state at 600 ms. In a steady state, the vibration acceleration amplitude is reduced by about 40%. The acceleration at 0\({}^{\circ}\) is much greater than that at the 90\({}^{\circ}\) phase angle. For example, the amplitude at 0\({}^{\circ}\) acceleration is more than twice that of the amplitude at 90\({}^{\circ}\) in the 50-ms interval. Therefore, adjusting  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Interval** & **Angle** & **0\({}^{\circ}\)** & **90\({}^{\circ}\)** \\ \hline
50 ms & 132.02 m/s\({}^{2}\) & 61.13 m/s\({}^{2}\) \\
200 ms & 107.16 m/s\({}^{2}\) & 48.97 m/s\({}^{2}\) \\
400 ms & 92.21 m/s\({}^{2}\) & 42.19 m/s\({}^{2}\) \\
600 ms & 84.93 m/s\({}^{2}\) & 38.37 m/s\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Acceleration at different phase angles under different degrees of attenuation.  
Figure 11: Vibration acceleration at different phase angles of 0\({}^{\circ}\) and 90\({}^{\circ}\).  
Figure 10: Vibration displacement and acceleration at different closing times.  
the closing phase angle can effectively reduce the acceleration amplitude of secondary vibration.  
These results can be used to evaluate the quantitative effect of the short-circuit time interval on the transformer and the dynamic relationship between winding vibration and the electromagnetic force. Additionally, the influence of the superposition effect can be more intuitively reflected through this numerical approach. The simulation calculation yields the short-circuit current multiples at which the winding vibration acceleration reaches amplitudes of strong vibration superposition during mechanical recovery to steady state, as shown in Table 3.  
In Table 3, the amplification factor of the short-circuit current is can be expressed as the number of times that the initial short-circuit current is magnified on the basis of its original value, when the initial short-circuit vibration acceleration and the second short-circuit vibration acceleration amplitude are equal. Among these values, the short-circuit current amplification multiple is equivalent to the short-circuit current amplification. It can be seen that when the short-circuit time interval reaches 600 ms, short-circuit current amplification is already negligible.  
In conclusion, after a short circuit, the acceleration amplitude of the secondary closing decreases as the vibration interval increases. Different reclosing intervals lead to different amplitudes of disk vibration acceleration.