**7. Comparison of DTC strategies**

188 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

greatly improves the flux and torque ripples.

**Figure 29.** Sinusoidal PWM pulses generator scheme

**6.1. Simulation results** 

the same conditions.

In this proposed technique, the same flux and torque estimators and the predictive torque and flux controller as for the DTC-SVM are still used. Instead of the SVM generator, a SPWM technique is used to determine reference stator flux linkage vector. It is seen that the proposed scheme retains almost all the advantages of the DTC-SVM, such as no current control loop, constant switching frequency, low torque and flux ripple, etc. But, the main advantage of the DTC-SPWM is the simple algorithm of PWM (SPWM) used to control the VSI. Of course, the SVM algorithm needs more calculation time than SPWM and the same advantages of DTC-SVM will be obtained by using DTC-SPWM. Whatever is the load torque and speed variation, SPWM guarantees a constant switching frequency, which

The sampling period has been chosen equal to 100 µs (10 KHz) for DTC-SVM; in order to compare this strategy with basic DTC; despite the fact that the sampling time used to simulate DTC is less than that used in case of DTC-SVM. Whereas, the sampling frequencies used to simulate FDTC and DTC-SVM are equal; so as to compare these two techniques in

**Figure 30.** Stator current spectrum at 800 rpm with nominal load (on the left) and Stator flux in (α,β)

axes under load variations (on the right) in case of DTC-SPWM

To verify and to compare the four DTC strategies proposed in this chapter, digital simulations have been carried out, by using the environment Matlab/Simulink, for the same PMSM parameters and conditions, except the sampling frequency utilized to simulate basic DTC which was taken equal to 20 KHz while for the FDTC, DTC-SVM and DTC-SPWM was taken equal to 10 KHz. Taking into consideration those conditions, the strategies' performances have been compared for both regimes dynamic and steady state.

**Dynamic state:** Figures 8, 26 and 30 shows that DTC, DTC-SVM and DTC-SPWM present the same speed and torque response time. Whereas, it's seen in figure 19 that torque and speed response time was greatly improved; at start time and at load toque or speed set-point variation. Indeed, speed FLC used in FDTC improves the dynamic state performances when compared to speed PI controller used in the other strategies.

**Steady state:** Figure 10 (on the left) show the spectral analysis of current presented in figure 10, it's seen that the Total Harmonic Distortion (THD) of the current waveform under basic DTC is 13.93 %. Whereas, figure 21 show that FDTC allows to decrease the THD value to 5.27 % with a variable switching frequency as indicated in the current spectral analysis. In addition, torque and stator flux ripple are reduced in case of FDTC in comparison with basic DTC, and also the current quality was improved. Figure 28 (on the left) shows that the current THD under DTC-SVM is 3.5 %, which is smother than that of basic DTC and FDTC. Also, it's seen that torque and flux ripples are greatly reduced under DTC-SVM when compared to DTC and FDTC (compare figures 26 and 28 with figures 8, 10, 19 and 21). Figure 32 shows that the THD of the current waveform under DTC-SPWM is 3.85%, which is almost the same as DTC-SVM, also DTC-SVM guarantees a constant switching frequency; as shown in figure 32 which allow to reduce torque and flux ripple as the same as DTC-SVM. Furthermore, the calculation time of the DTC-SPWM is much inferior to the DTC-SVM, this is because SPWM algorithm is very simple than SVM. Note that the SVM symmetry used in this work eliminates the harmonics which are around the uneven switching frequency (Chikh et al., 2011a). The same performances for DTC-SVM and DTC-SPWM can be obtained if an asymmetric SVM has been used instead of symmetrical SVM.
