# Application Study of Adaptive Tracking Algorithm in Active Noise Control System of Transformer
## 3 ANC Control Algorithm Based on an Adaptive Tracking Method  
In this work, we focused on the conclusion of transformer noise characteristics analysis, and proposed an adaptive tracking algorithm for 100 Hz to 500 Hz noise components. The five noise components belong to low frequency noise. Comparing with high-frequency noise, it is easier to achieve compensation and tracking of amplitude and phase. The adaptive tracking algorithm proposed in this paper draws on the perturbations observation method in photovoltaic power generation, which tracks the maximum power point under the dynamic change of external factors (temperature, sunshine). The algorithm is a self-optimization algorithm [20]. Its basic principle is judging the change direction of output power after adding voltage perturbations, and then adjusting the perturbations voltage to make the output power towards the maximum point. In the Equation (1), the time-varying parameters of the periodic noise of transformer noise are amplitude \(A_{k}\) and phase \(\varphi_{k}\), which can be approximately considered as a continuous variation. This paper proposed an adaptive tracking  
Figure 4: Contour distribution map. algorithm by adding perturbations of amplitude and phase. Its basic principle is judging the change direction of residual noise after adding perturbations and then adjusting the perturbations to make the residual noise towards the minimum point. When the residual noise reaches the optimum value or constraint conditions, the current amplitude and phase are output. The algorithm flow is shown in Figure 5.  
First, the five frequency noise components of 100 Hz, 200 Hz, 300 Hz, 400 Hz, and 500 Hz are picked up by low-pass filter and FFT transform of the transformer noise collected by the primary sensor, and the other noise components are not considered. Thus, Equation (6) can be expressed as:  
\[P_{\text{ref}}(n)=\sum_{k=0}^{5}A_{k\cdot\text{ref}}\cos\left(\frac{2\pi f_{k} n}{f_{\text{s}}}-\varphi_{k\cdot\text{ref}}\right)=\sum_{k=1}^{5}P_{k\cdot \text{ref}}(n) \tag{8}\]  
where \(P_{\text{ref}}(n)\) represents the reference signal; \(A_{k\cdot\text{ref}}\) is the \(k\)th noise frequency component in the reference signal; \(A_{k\cdot\text{ref}}\) is the \(k\)th noise amplitude component in the reference signal; \(\varphi_{k\cdot\text{ref}}\) is the \(k\)th noise phase component in the reference signal; \(f_{k}\) represents the signal frequency; \(k\) is the number of frequency components; \(n\) is the sampling sequence. The perturbations tracing output signal can be expressed as:  
\[P_{\text{pur}}(n)=\sum_{k=0}^{5}A_{k\cdot\text{pur}}\cos\left(\frac{2\pi f_{k} n}{f_{\text{s}}}-\varphi_{k\cdot\text{pur}}\right)=\sum_{k=1}^{5}P_{k\cdot \text{pur}}(n) \tag{9}\]  
where \(P_{\text{pur}}(n)\) represents the reference signal; \(P_{k\cdot\text{pur}}(n)\) is the \(k\)th noise frequency component in the perturbation signal; \(A_{k\cdot\text{pur}}\) is the \(k\)th noise amplitude component in the perturbation signal; \(\varphi_{k\cdot\text{pur}}\) is the \(k\)th noise phase component in the perturbation signal. The residual noise sound pressure amplitude is:  
\[A^{2}_{\text{mix}}=A^{2}_{\text{ref}}+A^{2}_{\text{pur}}+2A^{2}_{\text{ref}}A ^{2}_{\text{pur}}\cos(\varphi_{\text{ref}}-\varphi_{\text{pur}}). \tag{10}\]  
Figure 5: Algorithm flow chart. When \(A_{\text{ref}}=A_{\text{pur}}\), \(\varphi_{\text{ref}}-\varphi_{\text{pur}}\)= \(2l\pi+\pi\), \(l\) = 0,1,2,..., the sound pressure of the space sound field reaches the minimum value \(A^{2}\)mix, the space synthesis acoustic wave is:  
\[ \begin{array}{c}P_{\text{mix}}(n)=\sum\limits_{k=1}^{5}P_{k\text{-ref}}(n)+ \sum\limits_{k=1}^{5}P_{k\text{-pur}}(n)\\ =\sum\limits_{k=1}^{5}A_{k\text{-ref}}\cos(\frac{2\pi f_{k}n}{f_{k}}-\varphi_{ k\text{-ref}})\\ +\sum\limits_{k=1}^{5}A_{k\text{-pur}}\cos(\frac{2\pi f_{k}n}{f_{k}}-\varphi_{ k\text{-pur}})\ \ \ k=1,2,3,4,5\end{array}