## 5 Experimental Results
These results confirm the effectiveness of the proposed RSF_SVPWM scheme in reducing the acoustic noise emitted by the IM. Figure 18: A-weighting curve according to IEC 61672-1/2002. The measured acoustic noise spectra where \(\rm i_{m}=1\) and \(\rm Fc=5\ kHz\) are presented in Figure 21. The same observations are valid in Figure 21d, where the acoustic noise emitted from the IM is totally spread for the RSF_SVPWM technique. In addition, for index modulation \(\rm i_{m}=1\), the acoustic noise falls down for the four proposed PWM techniques. Accordingly, the noise amplitude is \(-29.7\) dBA, \(-40.8\) dBA and \(-58.2\) dBA for SVPWM, \(-19.65\) dBA, \(-38.2\) dBA and \(-60\) dBA for RZV_SVPWM, \(-28.52\) dBA, \(-40\) dBA and \(-60\) dBA for RPP_SVPWM and \(-79.1\) dBA, \(-84.3\) dBA and \(-78\) dBA for RSF_SVPWM, respectively, at 5, 10 and 15 kHz. Generally, the mechanical behavior of the stator can be characterized by its natural modes of vibration. Each mode, corresponding to a proper frequency, represents a particular deformation of the structure. The main modes of the stator deformation are shown in Figure 3. The proper frequencies for a 0.5 kW IM for this study with 17 rotor bars, 24 stator slots and 1 pole pair for different modes (0, 1, 2, 3, 4, 5) are, respectively, 14,033, 19,845, 2878, 7624, 13,461 and 19,922 Hz. Consequently, the generation of the magnetic forces on different frequencies near to the machine's natural frequency leads the machine to vibrate and produces a higher level of noise. Generally, the noise magnitude can increase due to the resonance phenomena. For example, when \(\rm im=1\)  
Figure 19: Stator current waveforms and harmonic spectrum for (**a**) RSF_SVPWM, (**b**) SVPWM, (**c**) RZV_SVPWM and (**d**) RPP_SVPWM. and Fc = 5 kHz, and with SVPWM at frequencies 2400 Hz and 6450 Hz close to 2878 Hz and 7624 Hz for vibrational modes m = 2 and m = 3, the levels of acoustic noise are, respectively, equal to \(-\)50.11 dBA and \(-\)61.03 dBA. In addition, with RZV_SVPWM, for vibrational modes m = 2 and m = 3, at frequencies 2400 Hz and 6450 Hz, the levels of acoustic noise are, respectively, equal to \(-\)52 dBA and \(-\)55.0 dBA. Therefore, with RPP_SVPWM, the noise at 2878 Hz is equal to \(-\)50 dBA, and at 8562 Hz, it is equal to \(-\)56 dBA. In conclusion, the obtained results show that the noise magnitude is uniformly reduced with RSF_SVPWM. Figure 22 presents the time-frequency spectra corresponding, respectively, to the studied techniques where im = 1 and Fc = 5 kHz. These results show that SVPWM, RZV_SVPWM and RPP_SVPWM give practically the same characteristics in terms of current spectrogram. Moreover, RSFSVPWM gives better performance. Figure 21: Acoustic noise spectrum at im = 1, Fc = 5 kHz for (**a**) SVPWM, (**b**) RZV_SVPWM, (**c**) RPP_SVPWM and (**d**) RSF_SVPWM. \[\mathrm{L_{P}(t)}=20\log_{10}\biggl{(}\frac{p(t)}{P_{0}}\biggr{)} \tag{18}\]0 Acoustic noise spectrum at im = 0.8, Fc = 5 kHz for (**a**) SVPWM, (**b**) RZV_SVPWM, (**c**) RPP_SVPWM and (**d**) RSF_SVPWM. The current frequency spectra corresponding to the studied techniques are depicted in \[\mathrm{L_{P}(t)}=20\log_{10}\biggl{(}\frac{p(t)}{P_{0}}\biggr{)} \tag{18}\]1 The SVPWM, RZV_SVPWM and RPP_SVPWM methods generate the most significant harmonics with the highest at 5 kHz and its multiples. With RSFSVPWM, on the other hand, the spectrum is totally dispersed over the entire frequency band. Thus, according to the similarity of the numerical and experimental results, we can confirm that RSF_SVPWM is practically more adapted to minimize the harmonics of the current and the acoustic noise. Table 3 compares the SVPWM, RPWM and RSFSVPWM techniques in terms of current THD (%), and acoustic noise level (dBA) emitted by an IM. It should be remembered that for the RPWM technique developed in our previous study, the values for the current and the acoustic noise are 3.92% and \(-\)59.79 dBA, respectively.