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DEFINITION OF NEW SWITCHING TABLESThe voltage vector selection strategy should be defined usingall the 19 voltage vectors on the basis of the criteria discussedin the previous Sections. In particular it has been emphasizedthe large influence exerted by the dynamic emfon the torque variations produced by a voltage vector. As aconsequence, the emf value together with the actual outputsof flux and torque comparators, are used to select the voltagevector. According to this principle, seven switching tables canbe defined. For sake of simplicity, only the four related tocounter-clockwise angular speed are given in Table II. Here thestator flux is assumed to be lying in sector 1. The 19 availablevoltage vectors are denoted according to the map given inFig. 6. The first switching table is used for low values of theemf. Assuming a constant value for the stator flux this meanslow speed operation. The second table is used for mediumvalues of the emf and the last two tables are used for highvalues of the emf. The simulation and experimental resultshave been obtained with the emf ranges represented in Fig. 7.In order to avoid the chattering of the control system betweentwo switching tables it is opportune to overlap the emf rangesaccording to the hysteresis principle.In each table the synthesized voltage vectors are selected by atwo-level hysteresis band for the flux, and a five-level hysteresisband for the torque. The flux hysteresis comparator operates ac-cording to Fig. 3 and the torque hysteresis comparator accordingto Fig. 8. With reference to this last, it should be noted thatlevels 1, 0 and 1 are involved in steady state operating condi-tions and for limited torque variation demand. In these operatingconditions the 4 voltage vectors which produce limited torquevariations are selected (for instance “2ZZ,” “3ZZ,” “5ZZ,” and“6ZZ,” in the low emf switching table). Levels 2 and 2 are involved during high dynamic tran-sients, due to large torque variation demands. In these cases thecontrol algorithm selects the same voltage vector as in basicDTC scheme (i.e.: “222,” “333,” “555,” and “666”).In the high emf range two switching tables have been de-fined, each one valid for half a sector (1 and 1 ). This re-quires a 12-sector angular representation of the – plane. Twoswitching tables are necessary for high emf values to fully uti-lize the available voltage vectors. In order to explain how thesynthesized voltage vectors are selected for high emf values,we assume for the machine a counter-clockwise rotation anda torque increase demand. In this case the bold-faced line ofFig. 5 is located in the high emf range of Fig. 9, then 4 voltagevectors can be employed, i.e. “333”, “332”, “223” and “222.”Depending on whether the flux has to be reduced or increased,the first two vectors or the last two vectors respectively shouldbe selected. So, if we have to force the flux to decrease we canchoose between “333” and “332”. For the last step we have toverify the position of the flux vector. If the flux is in sector 1the vector “333” is selected, while with the flux in sector 1it is opportune to select “332”. It should be noted that it is notpossible to apply these selection criteria in the medium and lowemf ranges because the number of available voltage vectors isnot high enough.The emf value required to choose the different switching ta-bles is not critical. In sensorless applications, the emf valuegiven by can be substituted by the quantity , whereis the stator angular frequency that can be easily estimated[13].VII. SIMULATION RESULTSIn order to show the effectiveness of the proposed DSVMtechnique a numerical simulation has been carried out on a stan-dard 4 kW, 4-poles induction motor. The numerical simulationstake the effects of time discretization and delay caused by thesampling of signals into account. The sampling period has beenchosen equal to 80 s for basic DTC. When using the newswitching tables the sampling period has been doubled and thehysteresis band amplitudes adjusted in order to achieve a meanswitching frequency practically equal to that obtained with thebasic switching table.Figs. 10 and 11 show a comparison of the steady state be-havior obtained using the basic switching table and the newswitching tables. The reference values are 25 Nm for the torqueand 0.57 Wb for the stator flux. The machine is running at 100rpm. As it is possible to see in Figs. 10 and 11 an appreciablereduction of current, flux and torque ripple has been obtainedusing the DSVM technique. It should be noted that the perfor-mance improvement has been achieved with a mean switchingfrequency practically equal to that of basic DTC scheme.Figs. 12 and 13 show the numerical results of the comparisonbetween the two schemes with a rotor speed of 1000 rpm. Alsoin this case the advantages of the DSVM technique are evident.With reference to the torque behavior it can be noted that theeffects due to the crossing of sector boundaries, typical of basicDTC schemes, are avoided using the new DTC scheme.In order to show the improvement of the current waveformobtained by using the new switching tables, the harmonic anal-ysis of the motor current given in Figs. 10 and 11 has beencarried out. The results obtained are illustrated in Figs. 14 and15, where the harmonic amplitude is given in p.u. of the funda-mental component. In these Figures the -axis has been scaled toemphasize the amplitude of harmonic components. The compar-ison between Figs. 14 and 15 shows the reduction of the ampli-tude of low order harmonics obtained using the new switchingtables. In Fig. 15, it is possible to note the presence of the har-monic component corresponding to the sampling frequency.In order to verify the dynamic behavior of the two DTCschemes, a step variation from 5 to 25 Nm has been appliedto the torque command.