Voltage vectors obtained by using DSVM with three equal timeintervals per cycle period.Fig. 7. Emf range subpision in p.u. of the rated voltage.voltage vectors which determine a null value of . This lineis parallel to the direction of and its position depends on therotor speed through the dynamic emf. Each dashed line repre-sents the locus of the stator voltage vectors determining a con-stant value of .In Fig. 5, it is possible to see the influence of the rotorspeed. Note that some voltage vector directions may determinepositive torque variations at low speed and negative torquevariations at high speed. This effect should be taken intoaccount when defining a voltage vector selection strategy. Asit is possible to see in Fig. 5, at low speed two voltage vectorshaving the same magnitude and opposite direction producetorque variations with nearly the same absolute value. At highspeed the same vectors produce torque variations having quitedifferent absolute values. This behavior determines differenttorque ripple at low and at high speed, as it can be observed inbasic DTC schemes.V. DISCRETE SPACE VECTOR MODULATION TECHNIQUEThe analysis carried out in the previous Section allows oneto clearly understand the effects produced by a given voltagevector as the rotor speed changes.The possibility to compensate, at each sampling period, thetorque and flux errors is strongly dependent on the number ofavailable voltage vectors. A high number of voltage vectors canbe generated using non traditional power circuit topology as pro-posed in [16] and [17].In this paper the number of voltage vectors is increased usinga standard VSI topology and introducing a simplified spacevector modulation technique. According to the principle ofoperation, new voltage vectors can be synthesized by applying,TABLE IINEW SWITCHING TABLES FOR DSVM-DTC CONTROL SCHEME (STATOR FLUXIN SECTOR I, COUNTER-CLOCKWISE ROTOR SPEED)Fig. 8. Five-level torque hysteresis comparator.Fig. 9. Representation of the voltage vectors used by the DSVM technique inthe high emf range.at each sampling period, several voltage vectors for prefixedtime intervals. In this way a sort of Discrete Space VectorModulation (DSVM) is employed, which requires only a smallincrease of the computational time and then of the samplingperiod.The number of voltage vectors which can be generated is di-rectly related to the number of time intervals by which the sam-pling period is subpided. Higher the number of voltage vec-tors lower the amplitude of current and torque ripple. However,a high number of voltage vectors requires the definition of newand more complex switching tables. A good solution should bedefined as a compromise between a good ripple compensationand the complexity of the voltage vector selection strategy. It has been verified that subpiding the cycle period in threeequal time intervals leads to a substantial reduction of torqueand current ripple, without the need of too complex switchingtables.In basic DTC schemes, assuming the stator flux lying inSector 1, the 5 voltage vectors represented in Fig. 2 are usuallyemployed to compensate the flux and torque errors. Using theDSVM technique, with three equal time intervals, 19 voltagevectors can be used, as represented in Fig. 6. The black dotsrepresent the ends of the synthesized voltage vectors. As anexample, the label “332” denotes the voltage vector which issynthesized by using the voltage space vectors , and ,each one applied for one third of the sampling period.It should be noted that this is not equivalent to a pision of thesampling time in three, increasing the rate of the voltage vectorselection. In each sampling period the voltage vector is selectedonce only, as in basic DTC scheme. The advantage of using theDSVM technique is that one can choose among 19 voltage vec-tors instead of the five of basic DTC. As a consequence, as-suming the same sampling period in the two control schemes,the use of the DSVMtechnique improves the drive performancein terms of torque and current ripple, with an increase of the in-verter switching frequency. Then, the use of the DSVM tech-nique is very useful in applications where the maximum sam-pling frequency is limited by large computational time.A significant comparison between the two schemes canbe made assuming the same inverter switching frequency. Inorder to achieve these operating conditions it is necessary toincrease the sampling period when using the DSVM technique.With reference to the numerical examples presented in the fol-lowing, nearly the same switching frequency has been obtaineddoubling the sampling period of the control scheme based onDSVM. It has been verified that even in this case the DSVMtechnique allows the torque and current ripple to be reduced. VI.
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