## 4 Simulation Analysis
Figure 11: Numerical simulation results of different carrier waveforms and FFT analysis for RSF_SVPWM control with **(a)** RT = 0.5, **(b)** RT = 0.3 and **(c)** RT = 0.1. Figure 13 represents the waveforms of the stator current and the harmonic spectra corresponding to the proposed SVPWM, RZV_SVPWM, RPP_SVPWM and RSF_SVPWM strategies, where i\({}_{\text{m}}\) = 1 and Fc = 5 kHz. Thus, the corresponding obtained THD values are 4.11%, 4.37%, 4.32% and 1.28%, respectively. In addition, it can be clearly noted that for all proposed strategies, the harmonic spectrum of the stator current is improved compared to i\({}_{\text{m}}\) = 0.8. Furthermore, for the SVPWM, RZV_SVPWM, RPP_SVPWM strategies, the dominant harmonic is located around the switching frequency and its multiples. The important harmonic appears around the first switching frequency. In addition, the dominant harmonic magnitudes around Fc are 2.06 A, 2.03 A and 2.15 A, respectively. Thereby, the harmonic magnitudes around 2 Fc are 1.18 A, 1.12 A and 0.8A, respectively. As shown by the simulation results, it is evidently noted that RSF_SVPWM control is the most effective in reducing and spreading the harmonic peaks over the entire frequency band, particularly at the first and second switching frequency Fc. Figure 12: Stator current waveforms and their harmonic spectrum for 0.5 kW at im = 0.8, Fc = 5 KHz for (**a**) SVPWM, (**b**) RZV_SVPWM, (**c**) RPP_ SVPWM and (**d**) RSF_SVPWM. Next, the four proposed PWM control methods are examined in terms of THD current and dominant harmonic peaks. Figure 14 represents the variation according to the modulation index of the THD current and the harmonic peaks. It can be seen also that the obtained results are influenced by the values of the modulation index. As illustrated in Figure 14a, it is clearly seen that when the modulation index value increases, the THD level falls for all control. Added to that, the current harmonic content of RSF_SVPWM is significantly reduced and lower compared to other schemes. The fixed SVPWM produces a lower THD compared to the RZV_SVPWM and RPP_SVPWM control. Hence, as shown in Figure 14b, the magnitude of the current harmonic is reduced significantly for RSF_SVPWM over the entire modulation range compared to other schemes. In conclusion, RSF_SVPWM is the most effective in reducing the THD current and spreading the harmonic spectra compared to the fixed SVPWM scheme, RZV_SVPWM and RPP_SVPWM. Figure 13: Stator current waveforms and their harmonic spectrum for 0.5 kW at im = 1, Fc = 5 kHz for (**a**) SVPWM, (**b**) RZV_SVPWM, (**c**) RPP_SVPWM and (**d**) RSF_SVPWM. The impact of the proposed techniques is demonstrated and verified on a 1.5 kW motor. The electrical and mechanical characteristics and parameters of this machine are provided in Table 2. Simulation is performed under the same conditions on a 0.5 kW motor: input voltage E = 560 V, switching frequency Fc = 5 kHz, and fundamental frequency F = 50 Hz. A numerical simulation model of an IM fed by a two-level VSI controlled by SVPWM, RSF_SVPWM, RPP_SVPWM and RZV_SVPWM is developed and implemented on MATLAB/Simulink. Moreover, the simulation results examine the characteristics of the harmonic current spectra and the dynamic response. The acoustic PWM noise depends largely on the current noise. Figure 15 presents the stator current and its harmonic spectra waveforms, where im = 1 and Fc =5 kHz, corresponding to the studied SVPWM, RZV_SVPWM, RPP_SVPWM and RSF_SVPWM techniques. The obtained THD values are 1.56%, 1.71%, 1.62% and 0.56%, 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 RSF_SVPWM, on a 1.5 kW motor. Hence, the dominant magnitudes of the current harmonics are concentrated on the switching frequency and its multiples for SVPWM, RZV_SVPWM and RPP_SVPWM. However, for RSF_SVPWM, it is observed that there is a considerable reduction in the harmonic content.