# On the Control of Low-Frequency Audible Noise from Electrical Substations: A Case Study
## 2 Methods
### Characterization of the Sound Source  
Measurements for the characterization of the sound source have been carried out in two separate sessions. The first experimental campaign has been performed in RPS substation (Figure 1), in order to determine the sound power level of the sources and to collect recordings in prescribed confidence points for validation purpose. Sound power levels have been measured using a sound level meter and the scanning technique described in IEC EN 60076-10 [31]. According to the standard, the sound power level of a source \(L_{\text{W}}\) can be determined based on a series of measurements of the sound pressure level (SPL), \(L_{\text{p}}\), carried out on a surface enveloping the source, once the possible presence of background noise and reflections is considered:  
\[L_{\text{W}}=\left\langle L_{\text{p}}\right\rangle+10\log_{10}\frac{S}{S_{0}}, \tag{2}\]  
where \(\left\langle L_{p}\right\rangle\) is  
\[\left\langle L_{\text{p}}\right\rangle=10\log_{10}\left(10^{0.1\left\langle L _{\text{p0}}\right\rangle}-10^{0.1\left\langle L_{\text{bg}}\right\rangle} \right)-K. \tag{3}\]  
\(K\) represents the correction for the effect of reflections, which can be neglected when the measurements are performed outdoors and the difference between source-on and source-off pressure levels is above 15 dB, as in the present case. \(L_{\text{p0}}\) is the energetic average of the measured sound pressure level, \(L_{\text{bg}}\) is the background sound pressure level and \(\left\langle\cdot\right\rangle\) denotes spatial averaging. This technique is suitable to characterize the sound power level of large sources since it can uniformly collect energy on the envelope surface, thus it can fairly represent the actual average emission of the device. The two transformers TR1 and TR2 have been evaluated by temporarily switching off either device while the other one was assessed. The enveloping surface is a virtual box whose walls are at 1 m distance from the transformer's case. A challenging problem is the presence of strong electric field close to the source, which considerably limits the maximum height at which measurements can be carried out safely. This height has been estimated as 3.5 m, above which the recordings get disturbed and the operation can damage the equipment or even be dangerous for the operator. Therefore, it is impossible to measure the top surface of the enveloping box, which is the reason the procedure prescribed by the standard explicitly excludes the top surface from the evaluation, thus accepting that a part of the emitted power is neglected. The sound level meter is a Larson Davis 831-C with PCB Piezotronics Type 377B02 1/2\" microphone and windproof cover. The measured sound power levels are 101 dB for TR1 and 98 dB for TR2. The sound pressure level spectrum at 5 m from the transformer's case and the sound power spectrum are shown in Figure 3. It can be observed that as expected, the main components are in the 100, 200 and 315 Hz one-third octave bands. The spectrogram at the bottom of Figure 3 is obtained from scan measurements performed by an operator walking around the perimeter of TR1 at constant speed, so that the time-dependence illustrated in the plot can be viewed as an angle-dependence. In this respect, the spectrogram provides first evidence that noise emission from the source is not uniform and a directivity analysis is required. The directivity can be found from the directivity factor \(DF_{\theta}(f)\), defined for each frequency band \(f\) as the ratio between the sound intensity along direction \(\theta\), \(I_{\theta}(f)\), and the intensity of an omnidirectional source of the same power input \(I_{0}(f)\) at distance \(r\) from measurement point:  
\[DF_{\theta}(f)=\frac{I_{\theta}(f)}{I_{0}(f)} \tag{4}\]  
\[I_{0}(f)=\frac{W}{4\pi r^{2}} \tag{5}\]  
Figure 3: Characteristics of TR1 transformer. From top to bottom: sound pressure level spectrum at 5 m from the transformer’s case; sound power spectrum; spectrogram.