# On the Control of Low-Frequency Audible Noise from Electrical Substations: A Case Study
## 3 Results and Discussion
### Before Situation
Therefore, the two values to compare are the SPL measured at the receiver purged of the background noise, and the simulated SPL at the receiver. The sound pressure level caused by the transformers alone is 47.4 \(\ominus\) 46 = 41.8 dB(A), with \(\ominus\) indicating energetic subtraction. Since the model gives a sound pressure level due to the two power transformers and without any barrier equal to 42.9 dB(A), it can be considered validated, with a difference of 1.1 dB with respect to the measured value. The analysis of the measured results obtained with the power transformers turned on highlights two tonal components in 315 Hz and 400 Hz frequency bands (spectrum of the minimum values in Figure 12). Italian legislation (Ministerial Decree 16/03/1998 [35]) prescribes that a penalization of 3 dB is added to the measured sound pressure level in this case. As a result, the overall impression level encompassing background noise and penalization is 50.4 dB(A), i.e., above or very close to the law limit. A mitigation action seems therefore appropriate. It is worth remarking that replacing the transformer with less noisy equipment is an expensive and burdensome solution, which in general is exploited in case of extremely severe disturbance when no other solution is available. In the present case, other options exist to solve the problem without changing the components. To better understand the characteristics of the disturbing tones, the impulse response generated by the software between the source and the receiver can be used. In particular, the narrow band spectrum at the receiver can be reconstructed by convolving the normalized impulse response (Figure 13) with the signal of the noise emitted by the power transformer, \(s(t)\), the latter being a WAV file recorded  
Figure 11: Spectrum of the minimum values for background noise measured at the facade of the receiver building (first floor). Figure 12: Spectrum of the minimum values for noise measured with the sources turned on at the facade of the receiver building (first floor). Dashed line: 33 phon equal loudness contour. during the sound power level measurements in a representative position along the direction towards the receiver:  
\[\left(h\ast s\right)\left(t\right)=\int_{-\infty}^{+\infty}h(\tau)\,s\left(t- \tau\right)\,\mathrm{d}\tau. \tag{7}\]  
The spectrum \(L_{\mathrm{p,1/3,norm}}\) is derived by applying the Fourier transform to the result of this operation (narrow band spectrum, \(L_{\mathrm{p,narrow,norm}}\)), and synthesizing in one-third octave bands. The noise signal obtained convolving the impulse response with the recorded signal must be scaled to emulate the sound perception at the receiver. For this reason, as a first approximation, the calculated spectrum is shifted so that it gives the same overall A-weighted SPL at the receiver as the value computed by the software in the simulation, \(L_{\mathrm{p,A,tot}}\):  
\[L_{\mathrm{p,1/3}}=L_{\mathrm{p,1/3,norm}}+\left[L_{\mathrm{p,A,tot}}-10\log_{ 10}\left(\sum 10^{\left(L_{\mathrm{p,1/3,norm}}+A\right)/10}\right)\right], \tag{8}\]  
where \(A\) is the weighting in decibels defined in IEC 61672-1 standard [36]. In this way, the impulse response can be used to evaluate several potentially disturbed points, even when they are not easily accessible for in-field measurements. The same shifting amount is applied to \(L_{\mathrm{p,narrow,norm}}\) to obtain the narrow band spectrum, \(L_{\mathrm{p,narrow}}\). In Figure 14, \(L_{\mathrm{p,narrow}}\) is compared with the equal loudness curve intersecting the highest spectrum peaks, showing which frequency components most contribute to the loudness perception at the receiver. The main contributions are related to the 300 Hz, 400 Hz, 800 Hz and 900 Hz components. It is worth noting that a noise barrier's efficiency is proportional to frequency: the higher the frequency, the stronger the attenuation.