DSP Implementation of an Improved DTC Technique for Induction ...

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switching Table 1, dψ = 1 and dψ = 0 indicates the stator flux needs to be increased and reduced respectively. Similarly, dT = 1 indicates the motor torque needs to be increased, and dT = 0 and dT = -1 indicate the torque needs to be reduced slowly and quickly respectively. Speed control is achieved using a PI controller. In a DTC drive, as shown in Figure 1, the torque reference is also obtained from the PI speed controller. Table 1 Stator Voltage Switching Table. Induction Motor Model in the Stationary Reference Frame The stationary reference frame induction motor model, with stator and rotor fluxes as state variables, is defined by equation (1) and forms the basis for the simulation results in this paper. d dt ⎡ ⎢ ⎣ s r ⎡ Rs ⎢ − ⎤ ⎢ s ⎥ = ⎦ ⎢ Rr M ⎢ ⎣ s Lr Rs M ⎤ ⎥ s Lr ⎥ ⎡ ⎛ R ⎢ r ⎞⎥ j ⎣ ⎜ r − ⎟ ⎟⎥ ⎝ r ⎠⎦ s r ⎤ ⎡1⎤ ⎥ + ⎢ ⎥V ⎦ ⎣0⎦ where s and r are stator and rotor flux space vectors, s V is stator voltage space vector, s R and R r are the stator and rotor resistances, L s and L r are stator and rotor self-inductances, M is the mutual inductance, 2 = 1 - M Ls Lr is the leakage coefficient and r calculated from equations (2) and (3) respectively. i i ds qs 2 s is rotor angular speed. Stator dq current components are ds − md = (2) L − M s qs − mq = (3) L − M s X aq X aq X aq X aq where, md = ds + dr , mq = qs + qr L − M L − M L − M L − M s and [ ] 1 − X = ( 1/M + 1/ ( L − M ) + 1/ ( L − M ) . aq dψ dT N1 N2 N3 N4 N5 N6 1 V2(110) V3(010) V4(011) V5(001) V6(101) V1(100) 1 0 V7(111) V0(000) V7(111) V0(000) V7(111) V0(000) -1 V6(101) V1(100) V2(110) V3(010) V4(011) V5(001) 1 V3(010) V4(011) V5(001) V6(101) V1(100) V2(110) 0 0 V0(000) V7(111) V0(000) V7(111) V0(000) V7(111) -1 V5(001) V6(101) V1(100) V2(110) V3(010) V4(011) s r r s The electromagnetic torque can be expressed in terms of stator flux and current as shown in equation (4) ( i i ) ⎛ 3 ⎞⎛ P ⎞ Te = ⎜ ⎟⎜ ⎟ ds qs − ⎝ 2 ⎠⎝ 2 ⎠ qs ds where P is the number of poles in the induction motor. Compensation of the Effect of the Stator Voltage-Drop A major problem in the application of DTC at low motor speed is the effect of the IsRs voltage drop. In order to improve flux control at low speed, optimum switching vector selection and a technique that eliminates the effects of the IsRs voltage drop in the machine stator is therefore considered. Figure 2 shows the switching voltage space vectors and stator resistance voltage drop. It can be seen that at high speed, the amplitude of the stator voltage vector sh V is large and the voltage drop across R s is relatively small and can be neglected, as shown in Figure 2(a). However, it can be seen from Figure 2(b) that, at low speed, the voltage drop across s R may be the major portion of measured terminal voltage V sl . Moreover, as the temperature of the r (1) (4)
stator windings increases, the value of resistance Rs will change significantly resulting in improper flux estimation and deterioration in controller performance. sQ (a) High Speed (b) Low Speed Figure 2 Effect of the Voltage Drop on the Stator Voltage Space Vectors. Flux Estimator with Voltage-Drop Feedback In classical DTC methods the stator flux is calculated by means of the stator voltage vector and current [7] as shown in equation (5) = V R I dt s ∫ ( − ) (5) s s s This gives an accurate flux linkage estimate at high speed. However, as described in the previous section, errors in the flux estimate increase as motor speed reduces. To compensate the RsIs voltage drop at low speed, a measurement of the stator winding resistance voltage drop is incorporated into the flux estimator. It can be seen from Figure 2 that the stator voltage drop vector is the function of the stator current. The voltage drop vector can therefore be calculated from a present stator current sample and used as feedback to compensate the present voltage drop at the next sample instant. The improved flux estimator is described by equation (6). Simulation Results vqsh I α v dsh V − R I s Vsh sh α s s RsI s sD = V k R I k I k 1 dt s ∫[ ( ) − ( ( ) − ( − ))] (6) s s s s Simulation studies were carried out using the MATLAB software package. Figures 3, 4 and 5 show a comparison between the proposed compensation strategy and the classical DTC scheme. Torque and speed responses of both schemes are shown in Figure 3. It can be observed that there is no significant difference between both schemes. Figure 4(a) shows that the compensation technique results in a sinusoidal stator flux waveform whilst Figure 4(b) shows that the flux waveform obtained from the conventional DTC implementation is clearly not sinusoidal. Also, it may be seen that, with the modified DTC strategy, the actual stator flux magnitude is equal to the reference value of 0.8Wb whilst with the classical method there is a significant error between the two flux values. Figure 5(a) shows a that the stator flux vector locus is circular compared to the conventional, hexagonal flux locus of Figure 5(b). speed (rad/s) and torque (Nm) torque (Nm) 2 1 0 20 10 0 -10 0.05 0.1 0.15 time (sec.) 0.2 0.25 speed torque 0.05 0.1 0.15 0.2 time (sec.) 3 speed (rad/s), torque (Nm) torque (Nm) vqsl 2 1 sQ α vdsl Vsl V − R I sl α Is s RsI s s sD 0 0 0.05 0.1 0.15 0.2 0.25 time (sec.) 20 10 0 -10 speed torque 0.05 0.1 0.15 0.2 0.25 time (sec.) (a) Proposed Method (b) Conventional Method Figure 3 Torque and Speed Responses of Induction Motor (ωr =20 rad/s and TL=1.2 Nm).
Page 1: Abstract DSP Implementation of an I
Page 5: (a) Proposed Method (b) Conventiona

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