# Effect of Multiple Reclosing Time Intervals on Axial Vibration of Winding
## 5 Conclusions  
When a permanent short-circuit fault occurs outside the transformer, the secondary vibration response may be greater than the primary vibration due to the superposition of residual vibrations. In this paper, by establishing an axial vibration model and considering the continuous influence of vibration, the authors were able to study the effect of the reclosing time interval on the vibration response of windings under multiple short-circuit impacts and obtain the following conclusions:  
1. When the transformer is subjected to a short-circuit impact, its vibration displacement and acceleration amplitude will change, and the vibration displacement change will be slower than the vibration acceleration. In the case of damped free vibration, the amplitude of the vibration displacement will decay to a relatively low level within 30 ms, and the vibration acceleration will decay to a relatively low level within 25 ms. The vibration acceleration will initially decay at a faster rate, reaching less than 10% of the peak value, but the effect of vibration persists. 2. The response to short-circuit vibration has a period of 10 ms, which corresponds to the range of the current phase angle from 0\({}^{\circ}\) to 180\({}^{\circ}\). As the reclosing time interval changes, the amplitude of winding vibration acceleration changes in the phase-angle ranges from 0\({}^{\circ}\) to 180\({}^{\circ}\), and the winding vibration acceleration at phase angles of 0\({}^{\circ}\) and 180\({}^{\circ}\) is much greater than that at a phase angle of 90\({}^{\circ}\). Due to the continuous influence of the last short-circuit vibration, the superposition effect of winding vibration in the second short circuit is more severe than that in the first short circuit. When the reclosing time interval is 10 ms, the peak value of reclosing vibration displacement is 2.74 mm, which is greater than the peak value of the first vibration displacement. At 250 ms, the peak value of secondary vibration displacement is reduced by 20%. In the same case, the peak acceleration of the secondary vibration is reduced by 37%. 3. The equivalent amplification factor of the winding short-circuit current in the secondary closing under the superposition effect is considered by conversion. When the \begin{table}
\begin{tabular}{c c c c c c} \hline
**Interval/ms** & **50** & **200** & **400** & **600** & **1000** \\ \hline Reclose at 0\({}^{\circ}\) & 1.391 & 1.252 & 1.134 & 1.051 & 1 \\ Reclose at & 1.383 & 1.244 & 1.128 & 1.041 & 1 \\
90\({}^{\circ}\) & & & & & \\ \hline \end{tabular}
\end{table} 
Table 3: The equivalent amplification factor of short circuit current under superposition effect. short-circuit time interval is short, the secondary short-circuit impact is equivalent to the larger short-circuit current effect in the primary short circuit. When the short-circuit time interval is more than 600 ms, the equivalent amplification factor of the closing short-circuit current is less than 1.041 under the ideal closing phase angle of 90\({}^{\circ}\) and the superposition effect is negligible. When the transformer experiences multiple short-circuit reclosings, the closing time interval should not be less than 600 ms to avoid the large vibration impacts, which reduce the life of the transformer. The secondary vibration response of the transformer winding in the axial direction is analyzed in this paper. However, the influence of the continuous vibration of the transformer on the radial component of the secondary vibration of the winding has yet to be established, and the overall vibration-mechanism analysis is still inconclusive. Conceptualization, L.S. and S.G.; methodology, L.S. and Y.T. ; software, R.H.; validation, F.T., L.W. and Z.Z. ; formal analysis, J.Z. ; investigation, J.Y. ; resources, S.G.; data curation, Y.Y. ; writing--original draft preparation, L.S. ; writing--review and editing, S.G.; visualization, X.W. ; supervision, P.W. ; project administration, J.G. ; funding acquisition, L.S.