# Experimental Analysis of Transformer Core Vibration and Noise under Inter-Harmonic Excitation
## 3 Results and Discussion  
### Inter-Harmonic Frequency Influence on Core Vibration  
As the voltage gradually increases, the inter-harmonic content reaches 3%. The relationship between the peak-to-peak value of the vibration displacement of measuring point 1 and the inter-harmonic frequency contained in the excitation is shown in Figure 6. \begin{table}
\begin{tabular}{c c} \hline
**Difference between Equipment and** & **Measurement Correction Value/dB** \\
**Background Noise/dB** & \\ \hline
3 & \(-3\) \\
4–5 & \(-2\) \\
6–9 & \(-1\) \\ \hline \end{tabular}
\end{table} 
Table 2: Correction of background noise. From the overall trend analysis in the figure, it is found that the lower the inter-harmonic frequency, the greater the peak-to-peak value of the core vibration displacement, but in different frequency ranges, the increase in amplitude varies greatly. When the frequency of inter-harmonics is less than 20 Hz, the amplitude of vibration increase is much greater than when the frequency is greater than 20 Hz. For example, when the fundamental voltage amplitude is 50 V, the peak-to-peak displacement under excitation with 2 Hz inter-harmonic component is 450.3 nm, which is 1.8 times that of excitation without an inter-harmonic component. The excitation with 20 Hz inter-harmonics is only 1.05 times the peak-to-peak value of vibration without inter-harmonic excitation. Figure 7 shows the time-domain waveform of the vibration displacement of measuring point 1 without inter-harmonic excitation. It can be seen from Figure 7b that when the transformer core is in normal working conditions, the frequency spectrum is mainly concentrated on even-numbered components such as 100 Hz and 200 Hz. It also contains a small number of odd harmonics, and they are basically concentrated below 500 Hz. Due to the experimental environment and core resonance, there are some interference signals in the range of less than 20 Hz. The existence of interference signals may be caused by problems such as experimental equipment and the iron core manufacturing process. When the excitation does not contain inter-harmonics, there will be some interference signals in the spectrogram, and the difference between the interference signal and the main signal is about ten times, so it is considered that the interference signal will not affect the experimental results. Figure 6: The peak-to-peak value of core vibration displacement. Since the inter-harmonics below 20 Hz have a greater impact on vibration, the experimental results containing low-frequency inter-harmonics are mainly analyzed. Figures 8 and 9 show the time-domain waveform diagram and spectrum analysis diagram of the core vibration displacement within 1 s when the excitation contains 2 Hz and 5 Hz inter-harmonics. It can be seen from the time-domain diagram that when the excitation voltage contains single-frequency inter-harmonics, the vibration displacement forms a periodic image with \(2f_{0}\) as the single vibration frequency and \(2f_{\rm{fl}}\) as the overall vibration frequency in the time-domain. It is found from spectrum analysis that a single frequency inter-harmonic voltage will cause a large number of inter-harmonic components in the transformer core vibration. Considering that the resonant frequency of the transformer core itself is around 20 Hz and that some interference signals are brought by the experimental environment, the lower frequency components are mainly concentrated around 20 Hz. In the frequency range greater than 30 Hz, the relationship between the excitation intermediate harmonic and the vibration intermediate harmonic frequency is shown in Table 3.  
Figure 8: Vibration displacement of iron core with 2 Hz inter-harmonics in excitation; (**a**) time-domain waveform; (**b**) spectrum analysis. Figure 7: Vibration displacement of iron core without inter-harmonics; (**a**) time-domain waveform; (**b**) spectrum analysis.