## 3 Results and Discussion  
### Point Source Simulation  
This subsection explains the process and error of the noise separation technique using the phase conjugation method by separating noise pressure caused by the first and second point sources from the total noise pressure generated by two sources at three test points. Figure 2 is the schematic diagram of the point source simulation: the distance of two sources is \(l_{1}=4\) m, which is greater than half of the maximum wavelength of the transformer noise sound wave to ensure the accuracy of phase conjugation and to better meet the requirements of the substation noise analysis environment. The distance of the test points is \(L_{1}=4\) m, and \(d_{1}\) and \(d_{2}\) (\(d_{1}=d_{2}=2\) m) are, respectively, array-to-sources and array-to-test-points distances. The line array is composed of 61 microphone elements, the element spacing is \(\Delta=0.1\) m, and the array aperture is \(d=6\) m, which is the best combination of array aperture and elements spacing that minimizes the separation error shown in the figures of page 2. The model shown in Figure 2 simulates acoustic field generated by two point sources in air whose density is \(\rho_{0}=1\) kg/m\({}^{3}\) and sound velocity is \(\epsilon_{0}=350\) m/s. The first and second point source intensities are \(Q_{1}=1\) m\({}^{3}\)/s and \(Q_{2}=2\) m\({}^{3}\)/s, initial phases are both 0, and frequencies are \(f=1-1000\) Hz (step length is 1 Hz). The theoretical solution of the sound field generated by a point source in the air is \(p=-\mathrm{i}\omega\rho_{0}Q\frac{\exp(\mathrm{i}kr+\mathrm{i}\theta)}{4\pi r}\). Firstly, we obtain the amplitude and phase of sound pressure and its gradient at the line microphone array according to theoretical solution of a point source in air (simulating the measurement process of the microphone array in an acoustic field), and we reconstruct the source intensity ratio and phase value of the point source using the phase conjugation method. Secondly, the sound pressure amplitudes of three test points are obtained by  
Figure 2: Schematic diagram of point source simulation. the theoretical solution of a point source in air, and the sound pressure amplitudes of the first, second, and third test points are obtained by the equivalent point source method. Finally, the theoretical A-weighting SPL (sound pressure level) of point sources 1 and 2 at three test points are compared with those obtained by the separation technique, and the comparison results are shown in Figure 3. It can be seen that the values of the theoretical equation and the separation technique are basically consistent at the analyzed frequencies but still have errors. In order to analyze the reasons for the errors, Figure 4 illustrates the results comparing the A-weighting SPL between the separation technique and the theoretical solution when the source intensity ratio and phase value are taken as the set values (\(Q_{1}:Q_{2}=1:2\), \(\theta_{1}=\theta_{2}=0\)). It can be seen that the A-weighting SPL of the separation technique and theoretical solution are completely consistent, which means that errors between the separation technique and theoretical solution originate from reconstruction errors of point source information using phase conjugation. The accuracy of phase conjugation for acoustic field reconstruction and source focusing imaging is related to array aperture and element spacing. Therefore, the present paper investigates the effect of array aperture and element spacing on the error of noise separation technique using the phase conjugation method. The array element spacing is equal to 0.1 m when studying the effect of array aperture, and the array aperture is 6 m when studying the effect of array element spacing.