# Experimental Analysis of Transformer Core Vibration and Noise under Inter-Harmonic Excitation
## 2 Experimental Methods  
### Experimental Scheme  
This paper has built a vibration measurement platform that can generate arbitrary inter-harmonic excitation. Inter-harmonics with different contents and frequencies are set, and vibration and noise measurement experiments are carried out under this excitation. The experimental flow chart is shown in Figure 1.  
The experimental circuit is shown in Figure 2, and the equipment parameters are shown in Table 1. The transformer core model is made of B27R085 silicon steel sheet, which is commonly used in distribution transformers. The winding turns on both core legs are 30 turns. The model size is shown in Figure 3.  
Figure 1: Experimental flow chart.  
In Figure 3, pure iron stack thickness is 66 mm; window height (A) is 130 mm; window width (B) is 70 mm; silicon steel sheet width (C) is 65 mm; core model stack thickness (D) is 68 mm; core overall width (E) is 200 mm; core overall height (F) is 260 mm.  
The excitation voltage is given by  
\[v(t)=V_{1}[\sin(2\pi f_{0}t)+m\sin(2\pi f_{ih}t)] \tag{1}\]  
In Equation (1), \(V_{1}\) is the voltage amplitude,\(f_{0}\) is the fundamental voltage frequency of 50 Hz, \(f_{ih}\) is the inter-harmonic voltage frequency, and \(m\) is the inter-harmonic content. The experiment studied the influence of the frequency and content of inter-harmonics on the vibration characteristics of the transformer core by changing the parameters \(f_{ih}\) and \(m\).  
The main sources of common inter-harmonics are nonlinear loads, frequency converter speed control devices, and sub-synchronous oscillations of wind turbines. According to the above main sources of inter-harmonics, this part of the experiment sets the inter-harmonic content to 3%, that is, \(m\) = 0.03 unchanged. Take \(f_{ih}\) as: 2, 5, 7, 10, 15, 17, 20, 25, 30, 40, 45,  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Experimental Equipment** & **Performance Index** \\ \hline NF WF1974 signal generator & Frequency accuracy: \(\pm\)(3 ppm + 2 pHz of set value) \\  & frequency resolution: 0.01 \(\upmu\)Hz \\  & Amplitude accuracy: \(\pm\)(1% of amplitude setting \\  & value + 2 mVp-p)/open circuit \\ \hline NF 4510 A Precision power amplifier & Rated frequency band: DC\(-\)20 kHz \\  & Rated output power: 1 kVA \\  & Voltage output accuracy: \(\pm\)0.1\% \\ \hline WT3000 power analyzer & Range accuracy: \(\pm\)0.04\% of range \\  & Basic power accuracy: \(\pm\)0.02\% \\  & Frequency range: 0.1 Hz\(\sim\)1 MHz \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of instruments.  
Figure 3: Dimensions of transformer core model.  
Figure 2: Experimental circuit.  
and 53 Hz. Under the condition of introducing different inter-harmonic frequencies, the voltage amplitude is gradually increased from 0 to 50 V. During debugging, the vibration displacement of different measuring points is recorded, and the vibration displacement is analyzed by frequency spectrum.  
In order to further analyze the influence of the inter-harmonic content on the vibration characteristics of the iron core, experiments were carried out under the conditions of inter-harmonic frequencies of 5, 20, and 40 Hz. Keep the inter-harmonic frequency constant, set the inter-harmonic content to 1%, 3%, and 5%, respectively, and compare and study the peak-to-peak variation of the core vibration under the same voltage amplitude.