# Application Study of Adaptive Tracking Algorithm in Active Noise Control System of Transformer
## 2 Substation Sound Field Characteristics
It can be seen that the noise level is close to critical noise in the standard above. Since the power system requires transformer to operate stably, the working characteristic parameters can be regarded as constant, so the radiation noise is stable and fluctuates in a small range. Figure 3 and Table 1 show that the transformer noise is in a discrete peak arrangement in the frequency domain, which is a typical tonal noise. With respect to 100 Hz to 500 Hz, the five noise components are the main transformer noise. In addition, the noise collected by the primary sensor also includes the high-frequency noise component of the transformer body noise, the noise of the transformer cooling fan, and the noise of the surrounding environment. The transformer body noise is mainly line spectrum \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Frequency** & **100 Hz** & **200 Hz** & **300 Hz** & **400 Hz** & **500 Hz** \\ \hline Sound Pressure Level(dB(A)) & 72.93 & 69.29 & 49.54 & 63.23 & 42.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The sound pressure level of five frequency components. Figure 3: The time domain and frequency spectrum at H2. (**a**) Time-domain signal; (**b**) Frequency spectrum  
Figure 2: The sound pressure variation of the transformer noise. (**a**) A9; (**b**) H2. noise, which is tonal noise. The noises of the transformer cooling fan and surrounding environment are random and broadband, which are chaotic noise [17; 18; 19]. It can be concluded that the transformer noise is complex sound waves composed of periodic noise and chaotic noise. According to the superposition principle of sound waves, complex sound waves can be expressed by Equation (1). \[P(n)=\sum\limits_{k=1}^{K}A_{k}\cos(\frac{2\pi f_{k}n}{f_{s}}-\varphi_{k})+ch(n )\ \ \ k=1,\cdots,K \tag{1}\]  
where, \(k\) is the total wave number of the single frequency component; \(ch(n)\) is the chaotic noise [18]; \(A_{k}\) is the amplitude of the \(k\)th frequency component; \(\varphi_{k}\) is the phase of the \(k\)th frequency component; \(f_{k}\) is the frequency value of the \(k\)th frequency component; \(f_{s}\) is the sampling frequency. The sound pressure level superposition formula can be expressed by Equation (2). \[ \begin{array}{ll}L_{p}&=10\lg\sum\limits_{k=1}^{K}10^{0.1L_{k}}\\ &=10\lg 10^{0.1L_{1}}+10\lg[1+10^{-0.1(L_{1}-L_{2})}+\cdots+10^{-0.1(L_{1}-L_{ K})}]\\ &=L_{1}+\Delta L\end{array}  \tag{2}\]  
where \(L_{p}\) is the sound pressure level of stacked noise and \(L_{k}\) is the sound pressure level of the \(k\)th noise frequency component. Assuming \(k\) = 2, when \(L_{1}\) = \(L_{2}\), \(\Delta L\) = 3 dB; when \(L_{1}\) - \(L_{2}\) = 10 dB, \(\Delta L\) = 0.4 dB; when \(L_{1}\) - \(L_{2}\) = 20 dB, \(\Delta L\) = 0.04 dB. The deduction shows that the total sound pressure level is equal to that of a single sound source plus 3 dB when the sound pressure level of the two sound sources are the same. The bigger the sound pressure level difference between the two sounds, the less the contribution of the lower sound pressure source to total sound pressure level. Table 1 shows the sound pressure values of five main noise components of the transformer. According to the Equation (2), the synthetic sound pressure level of these five frequency components is 65 dB and the actual noise level is 66.5 dB. The sound pressure level contribution of other noise components is 1.5 dB. Therefore, if the five noise components can be effectively suppressed, the main energy of transformer noise can be eliminated, and the purpose of noise reduction can be achieved. Taking the sound pressure level data of H series measuring points as the equivalent noise source, taking the sound pressure level data at other measuring point as reference, the noise attenuation model of substation is established. The noise distribution of substation is calculated and the substation noise contours are plotted.