## 4 Simulation Analysis  
A numerical simulation model of an IM fed by a two-level VSI controlled with SVPWM, RSF_SVPWM, RPP_SVPWM and RZV_SVPWM is developed and implemented on MATLAB/Simulink. In addition, the simulation results examine the characteristics of harmonic current spectra and the dynamic response of drives at different modulation indexes. The machine parameters are mentioned in Table 1. Simulation is performed under the same conditions: input voltage E = 560 V, switching frequency Fc = 5 kHz, and fundamental frequency F = 50 Hz. For all random SVPWM control, the uniform probability density function is used to perform all randomizations. For the random RSF_SVPWM control, randomness level RT plays a key role, since the distribution of harmonic spectra is affected by the parameters of the random triangular carrier. Accordingly, the RT parameter identifies the varying width of the PWM technique. The methodology to select the parameter of the triangular carrier is to make a sequence of simulation tests with different values of RT. Generally, in practice, randomness level RT does not generally exceed 0.5. We can note that if RT= 0, we have a constant switching frequency. In order to estimate the most appropriate RT parameter, a series of simulation tests are carried out to determine the Total Harmonic Distortion (THD) of the current \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Rated power & 0.5 Kw \\ \hline Motor speed & 3000 tr/min \\ \hline Stator resistance & 24 \(\Omega\) \\ \hline Stator inductance & 0.66 H \\ \hline Rotor resistance & 10.88 \(\Omega\) \\ \hline Rotor inductance & 0.66H \\ \hline Mutual inductance & 0.63 H \\ \hline Friction coefficient & 0.00159 \\ \hline Inertia moment & 0.004 Kg\(\cdot\)m\({}^{2}\) \\ \hline Pair pole number & 1 \\ \hline \end{tabular}
\end{table} 
Table 1: The 0.5 Kw IM parameters. Figure 10: Waveforms for two-level VSI of switch \(\mathbf{S_{11}}\) using **(a)** SVPWM and **(b)** RSF_SVPWM. corresponding to each R\({}_{\rm T}\) value. The results of the harmonic spectra of each randomness level signal (RT = 0.5, 0.3 and 0.1) are shown in Figure 11. For RT = 0.5, the triangular signal begins to vary randomly. In the same vein, we notice that the harmonic peak begins to attenuate with RT = 0.3. Furthermore, it is clear that RSF_SVPWM with RT = 0.1 provides a significant reduction in the THD value by 1.39% without neglecting the considerable reduction in the harmonic peak amplitude at the switching frequency and its multiples by spreading the energy spectrum over a wide frequency band. In this case, the results obtained from the RSF_SVPWM with a randomness level RT= 0.1 are more coherent and robust, and they significantly decrease the THD value compared to other cases. The acoustic PWM noise depends largely on the current noise. Figure 12 presents the stator current and its harmonic spectra waveforms, where im = 0.8 and Fc = 5 kHz, corresponding to SVPWM, RZV_SVPWM, RPP_SVPWM and RSF_SVPWM. The corresponding obtained THD values are 4.45%, 5.47%, 5.42% and 1.39%, respectively. Referring to the obtained results, it can be clearly noted that the high harmonic components are significantly generated by the SVPWM, RZV_SVPWM and RPP_SVPWM methods compared to the RSF_SVPWM. Therefore, the dominant magnitudes of the current harmonics are concentrated on the switching frequency and its multiples. In addition, the dominant harmonic magnitudes around the first switching frequency Fc are 1.66 A, 2.63 A and 1.74 A, respectively, for SVPWM, RZV_SVPWM and RPP_SVPWM. As a consequence, the harmonic magnitudes around the second switching frequency Fc are 2.17 A, 1.72 A and 1.92 A, respectively. However, for the RSF_SVPWM scheme, as depicted in the results given in Figure 12d, it is observed that there is a considerable reduction in the harmonic content. Nevertheless, the harmonic spectrum is totally spread better over the entire frequency band of the current, and the band around the switching frequency and its multiples disappear.