## 2 Methods
According to the Helmholtz-Kirchhoff integral equation, the phase conjugation acoustic field is:  
\[p_{PC}(r,r_{s})=\int\left[G(r,r^{\prime})\frac{\partial p^{*}(r^{\prime},r_{s} )}{\partial\mathbf{n}}-p^{*}(r^{\prime},r_{s})\frac{\partial G(r,r^{\prime})} {\partial\mathbf{n}}\right]dS^{\prime}, \tag{2}\]  
where \(r_{s}\) is the noise source location, \(r\) represents the location of a field point, \(r^{\prime}\) is the location of an array microphone, \(S^{\prime}\) means surface microphone array, \(G(r,r_{s})=\frac{\partial^{2}\mathbf{r}}{4\pi R}\) is the Green function of free acoustic field, and \(R=|r-r^{\prime}|\), \(k=\omega/c_{0}\). Because the actual arrays are discrete, the phase conjugation acoustic field generated by a finite discrete array including \(N\) elements is:  
\[p_{\text{PC/P}}(r,r_{s})=\sum_{n=1}^{N}\left[G(r,r_{n})\frac{\partial p^{*}(r _{n},r_{s})}{\partial\mathbf{n}}S_{n}-p^{*}(r_{n},r_{s})\frac{\partial G(r,r_ {n})}{\partial\mathbf{n}}S_{n}\right], \tag{3}\]  
which is called the PC/P phase conjugation acoustic field. In addition, the PC/D phase conjugation acoustic field is:  
\[p_{\text{PC/D}}(r,r_{s})=\sum_{n=1}^{N}\left[\frac{\partial p^{*}(r_{n},r_{s} )}{\partial\mathbf{n}}\frac{\partial G(r,r_{n})}{\partial\mathbf{n}}S_{n}\right], \tag{4}\]  
and the PC/M phase conjugation acoustic field is:  
\[p_{\text{PC/M}}(r,r_{s})=\sum_{n=1}^{N}\left[G(r,r_{n})p^{*}(r_{n},r_{s})S_{n} \right]. \tag{5}\]  
The research results of [15; 16] indicate that the PC/D phase conjugation method achieves the best focusing effect when the distance \(R\) between the array and the sound source is within the range where the evanescent wave can be measured (\((0,\lambda_{\text{min}}/3]\), \(\lambda_{\text{min}}\)(m) is the minimum wavelength), and the PC/M phase conjugation method achieves better focusing effect when the distance between the array and the sound source is relatively far. Therefore, the PC/D phase conjugation method is used when the distance between the line array and the sources is less than \(\lambda_{\text{min}}/3\) while the PC/M method is adopted in other cases in the paper. 3. Equivalent point source method  
The noise level of a single piece of equipment in a substation generally does not exceed 120 dB. Therefore, it is considered that the noise in the substation satisfies linear acoustic theory [9]. From linear acoustic theory, the total sound pressure at a point can be expressed as a linear superposition of the sound pressures of each source, i.e. :  
\[p_{0}(f)=\sum_{i=1}^{m}p_{i}(f), \tag{6}\]  
where \(f\)(Hz) is the frequency. The noise source sound pressure is \(p=A\frac{\exp(\mathrm{i}kr)}{r}\), if the noise source is a point source. \(A\) is equal to \(s_{i}Q\) and \(p_{i}=s_{i}Q\frac{\exp(\mathrm{i}(kr_{i}+\theta_{i}))}{r_{i}}\) when the source intensity ratio \(s_{i}\) and phase \(\theta_{i}\) of each source is obtained by the phase conjugation method. We substitute \(p_{i}\) into Equation (6) and take the amplitude on both sides of the equation to obtain the equivalent source intensity \(Q\) (m\({}^{3}\)/s). Finally, the sound pressures \(p_{i}\) of each source at the points to be separated can be obtained by \(p_{i}=s_{i}Q\frac{\exp(\mathrm{i}(kr_{i}+\theta_{i}))}{r_{i}}\).