# On the Control of Low-Frequency Audible Noise from Electrical Substations: A Case Study
## 2 Methods  
### Description of the Case and Noise Control Strategy  
The case study involves a power substation for a railway south of Turin, in North-West Italy. The railway station dates back 1854 and the power substation, which henceforth will be referred to as \"RPS\", was built in 1961, when the area was rural. Over time, the urban district has gradually expanded north (1960s-1970s and after 2010) and south (2000s) of the area, for which the substation is now very close to the houses. The closest buildings are 60 m far from the north-east side of the source enveloping surface. The most recent dwellings have been evaluated noise-wise to check and limit the disturbance as much as possible. Among these, a receiver located 130 m far from the substation at a height of 4 m above the ground (Figure 1) has been considered. Given the number of buildings and their short distance from the source, reflections are expected to play an important role in noise propagation. The RPS substation has been revamped in the 1980s and the power of its two transformers increased. The transformers, TR1 and TR2, are 25,000 kVA devices with dimensions 6 m \(\times\) 4 m \(\times\) 3.5 m each, whose acoustic characterization is described in Section 2.2. The vibration of the transformer's core at twice the network frequency and its harmonics is responsible for most of the sound emission. Building a noise barrier close to the source is the most common way to mitigate this problem. However, space constraints exist that reduce the practical benefit that can be obtained with this solution: for this reason, noise masking can be exploited as complementary measure. Noise masking consists of immersing the receiver in a pleasant background noise able to conceal the tonal components of the original noise spectrum. Methods to estimate the required masking level are available in the literature see for instance [PERSON] and [PERSON] [26] and [PERSON] [27], with an outcome related to psychoacoustics and therefore subjective. In this respect, an auralization process to recreate the designed soundscape and have it evaluated by the potential receivers could be a helpful psychoacoustical tool. Considering the environment under investigation as a linear time-invariant system, Figure 2, the output signal \(y(t)\) is related to the input signal \(x(t)\) through the impulse response of the system:  
\[y(t)=\left(h*x\right)(t) \tag{1}\]  
where \(*\) indicates the convolution product. The impulse response \(h(t)\) can be obtained from the transfer function \(H(f)\) through the relationship \(H(f)=\mathcal{F}\left\{h(t)\right\}\), where \(\mathcal{F}\) is Fourier transform and the transfer function is defined between two meaningful source and recording positions. In the present case, \(h(t)\) is the impulse response of the environment and \(x(t)\) is an anechoic recording of the signal, so that \(y(t)\) is the source noise (before or after mitigation) as heard at the receiver's position. Using the impulse response approach allows the obtaining of extra information, such as the time history of the signal as a result of the contributions by reflections, which can be particularly interesting in case of urban environment. The impulse response of the environment cannot be calculated by the standard \"ray-tracing\" codes that are conventionally used to evaluate outdoor propagation and that are based on the formulas  
Figure 1: Satellite image of RPS substation. Sources circled in red; receiver in green box. Imagery ©2019 Maxar Technologies, Map data ©2019 Google. Figure 2: Linear time-invariant system. described in ISO 9613-2 standard [28], but it can be rather obtained with the same approach employed with theaters and indoor spaces. The codes developed for room acoustics simulations are primarily made to estimate sound quality parameters such as reverberation time, clarity index, gain and lateral fraction, for which the time history of the sound rays (and, therefore, the impulse response of the room) is necessary.