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Induction Motor – Direct Torque Control By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering Dr. Ungku.

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Presentation on theme: "Induction Motor – Direct Torque Control By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering Dr. Ungku."— Presentation transcript:

1 Induction Motor – Direct Torque Control By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering Dr. Ungku Anisa, July 20081EEEB443 - Control & Drives

2 Outline Introduction Switching Control Space Vector Pulse Width Modulation (PWM) Principles of Direct Torque Control (DTC) Direct Torque Control (DTC) Rules Direct Torque Control (DTC) Implementation References Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives2

3 Introduction High performance Induction Motor drives consists of: Field Orientation Control (FOC) Direct Torque Control (DTC) Direct Torque Control is IM control achieved through direct selection of consecutive inverter states This requires understanding the concepts of: Switching control (Bang-bang or Hysteresis control) Space Vector PWM for Voltage Source Inverters (VSI) Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives3

4 Switching Control A subset of sliding mode control Advantages: Robust since knowledge of plant G(s) is not necessary Very good transient performance (maximum actuation even for small errors) Disadvantage: Noisy, unless switching frequency is very high Feeding bang-bang (PWM) signal into a linear amplifier is not advisable. But it is OK if the amplifier contains switches (eg. inverters) Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives4

5 Switching Control Amplifier Plant G(s) Switching Controller Continuous Control Amplifier Plant G(s) PI Continuous Controller Limiter Switching Control

6 PWM Voltage Source Inverter – single phase Reference current compared with actual current Current error is fed to a PI controller Output of PI controller (v c ) compared with triangular waveform (v tri ) to determine duty ratio of switches v tri V dc q vcvc Pulse width modulator PI Controller i ref Dr. Ungku Anisa, July 20086EEEB443 - Control & Drives

7 Same concept is extended to three-phase VSI v a *, v b * and v c * are the outputs from closed-loop current controllers In each leg, only 1 switch is on at a certain time Leads to 3 switching variables Pulse width modulator Va*Va* Pulse width modulator Vb*Vb* Pulse width modulator Vc*Vc* Sinusoidal PWM Voltage Source Inverter Dr. Ungku Anisa, July 20087EEEB443 - Control & Drives SaSa SbSb ScSc

8 + v c - + v b - + v a - n N V dc a b c S1 S2 S3 S4 S5 S6 S1, S2, ….S6 va*va* vb*vb* vc*vc* Pulse Width Modulation Sinusoidal PWM Voltage Source Inverter Dr. Ungku Anisa, July 20088EEEB443 - Control & Drives Switching signals for the SPWM VSI

9 Sinusoidal PWM Voltage Source Inverter Three switching variables are S a, S b and S c (i.e. one per phase) One switch is on in each inverter leg at a time If both on at same time – dc supply will be shorted If both off at same time - voltage at output is undetermined Each inverter leg can assume two states only, eg: S a = 1 if S1 ON and S4 OFF S a = 0 if S1 OFF and S4 ON Total number of states = 8 An inverter state is denoted as [S a S b S c ] 2, eg: If S a = 1, S b = 0 and S c = 1, inverter is in State 5 since [101] 2 = 5 Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives9

10 Space Vector PWM Space vector representation of a three-phase quantities x a (t), x b (t) and x c (t) with space distribution of 120 o apart is given by: where: a = e j2  /3 = cos(2  /3) + jsin(2  /3) a 2 = e j4  /3 = cos(4  /3) + jsin(4  /3) ‘x’ can be a voltage, current or flux and does not necessarily has to be sinusoidal Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives10 (1)

11 Space Vector PWM Space vector of the three-phase stator voltage is: where v a, v b and v c are the phase voltages. If v a, v b and v c are balanced 3-phase sinusoidal voltage with frequency f, then the locus of  v s : circular with radius equal to the peak amplitude of the phase voltage rotates with a speed of 2  f Dr. Ungku Anisa, July EEEB443 - Control & Drives (2)

12 + v c - + v b - + v a - n N V dc a b c S1 S2 S3 S4 S5 S6 S1, S2, ….S6 va*va* vb*vb* vc*vc* We want v a, v b and v c to follow v a *, v b * and v c * Space Vector PWM Dr. Ungku Anisa, July EEEB443 - Control & Drives These voltages will be the voltages applied to the terminals of the induction motor

13 Space Vector PWM From the inverter circuit diagram: v an = v aN + v Nn v bn = v bN + v Nn v cn = v cN + v Nn v aN = V dc S a, v bN = V dc S b, v cN = V dc S c where S a, S b, S c = 1 or 0 and V dc = dc link voltage Substituting (3) – (6) into (2): (3) (4) (5) (6) (7) Dr. Ungku Anisa, July EEEB443 - Control & Drives

14 Space Vector PWM Stator voltage space vector can also be expressed in two-phase (d s q s frame). Hence for each of the 8 inverter states, a space vector relative to the d s axis is produced. Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives (8) 14

15 Space Vector PWM Example: For State 6, i.e. [110] 2 (S a = 1, S b = 1 and S c = 0) Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives vSvS dsds qsqs 15

16 Therefore, the voltage vectors for all the 8 inverter states can be obtained. Note for states [000] and [111], voltage vector is equal to zero. Space Vector PWM Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives16 [100] V1 [110] V2 [010] V3 [011] V4 [001] V5 [101] V6 (2/3)V dc (1/  3)V dc [000] V0 = 0 [111] V7 = 0 dsds qsqs Voltage Vector Inverter state [S a S b S c ] 2 V0State 0 = [000] 2 V1State 4 = [100] 2 V2State 6 = [110] 2 V3State 2 = [010] 2 V4State 3 = [011] 2 V5State 1 = [001] 2 V6State 5 = [101] 2 V7State 7 = [111] 2

17 The d s q s plane can be divided into six 60  -wide sectors, i.e. S1 to S6 as shown below(  30  from each voltage vectors) Space Vector PWM Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives17 [100] V1 [110] V2 [010] V3 [011] V4 [001] V5[101] V6 [000] V0 = 0 [111] V7 = 0 dsds qsqs S1 S2 S3 S4 S5 S6

18 Space Vector PWM Definition of Space Vector Pulse Width Modulation (PWM): modulation technique which exploits space vectors to synthesize the command or reference voltage v s * within a sampling period Reference voltage v s * is synthesized by selecting 2 adjacent voltage vectors and zero voltage vectors Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives18

19 In general: Within a sampling period T, to synthesize reference voltage v s *, it is assembled from: vector V x (to the right) vector V y (to the left) and a zero vector V z (either V0 or V7) Since T is sampling period of v s *: V x is applied for time T x V y is applied for time T y V z is applied for the rest of the time, T z Space Vector PWM Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives19 [ 100] V1 [110] V2 [010] V3 [011] V4 [001] V5 [101] V6 Note: [000] V0 = 0 [111] V7 = 0 dsds qsqs vs*vs*  = v x = v y

20 In general: Total sampling time: If  close to 0  : T x > T y If  close to 60  : T x < T y If v s * is large: more time spent at V x, V y compared to V z i.e. T x + T y > T z If v s * is small: more time spent at V z compared to V x, V y, i.e.. T x + T y < T z Space Vector PWM Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives20 [ 100] V1 [110] V2 [010] V3 [011] V4 [001] V5 [101] V6 Note: [000] V0 = 0 [111] V7 = 0 dsds qsqs vs*vs*  = v x = v y T= T x + T y + T z (9)

21 Space Vector PWM In general, if  is the angle between the reference voltage v s * and V x (vector to it’s right), then: where Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives21 [100] V1 [110] V2 [010] V3 [011] V4 [001] V5 [101] V6 Note: [000] V0 = 0 [111] V7 = 0 dsds vs*vs*  (10) qsqs (11) T z = T  T x  T y (12) Vector V x to the right of v s *

22 Space Vector PWM Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives22 [100] V1 [110] V2 [010] V3 [011] V4 [001] V5 [101] V6 Note: [000] V0 = 0 [111] V7 = 0 dsds qsqs Example: v s * is in sector S1 V x = V1 is applied for time T x V y = V2 is applied for time T y V z is applied for rest of the time, T z = v x = v y vs*vs* 

23 T T V ref is sampled V1 TxTx V2 TyTy T z /2 V0 T z /2 V7 vava vbvb vcvc Space Vector PWM Example: v s * in sector S1 Reference voltage v s * is sampled at regular intervals T, i.e. T is sampling period: V1 [100] 2 is applied for T x V2 [110] 2 is applied for T y Zero voltage V0 [000] 2 and V7 [111] 2 is applied for the rest of the time, i.e. T z T= T x + T y + T z Dr. Ungku Anisa, July EEEB443 - Control & Drives V7V2V1V0

24 Space Vector PWM Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives24 [100] V1 [110] V2 [010] V3 [011] V4 [001] V5 [101] V6 Note: [000] V0 = 0 [111] V7 = 0 dsds qsqs Example: A Space Vector PWM VSI, having a DC supply of 430 V and a switching frequency of 2kHz, is required to synthesize voltage v s * = 240  170  V. Calculate the time T x, T y and T z required. V x = ____ is applied for time T x V y = ___ is applied for time T y V z is applied for time T z Since  = ______, v s * is in sector _______ T z = T  T x  T y S1 S2 S3 S4 S5 S6

25 Space Vector Equations of IM The two-phase dynamic model of IM in the stationary d s q s frame: Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives25 (13) (14) (15) (16)

26 Direct Torque Control (DTC) – Basic Principles 1. Derivative of stator flux is equal to the stator EMF. Therefore, stator flux magnitude strongly depends on stator voltage. If voltage drop across R s ignored, change in stator flux can be obtained from stator voltage applied : Stator voltage can be changed using the space vectors of the Voltage Source Inverter (VSI). Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives26 [100]V1 [110]V2[010]V3 [011]V4 [101]V6[001]V5 (17) (18)

27 Direct Torque Control (DTC) – Basic Principles 2. Developed torque is proportional to the sine of angle between stator and rotor flux vectors  sr. Angle of  s is also dependant on stator voltage. Hence, T e can also be controlled using the stator voltage through  sr. Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives27 (19) (20)

28 Direct Torque Control (DTC) – Basic Principles 3. Reactions of rotor flux to changes in stator voltage is slower than that of stator flux. Assume  r remains constant within short time  t that stator voltage is changed. Summary DTC Basic Principles: Magnitude of stator flux and torque directly controlled by proper selection of stator voltage space vector (i.e. through selection of consecutive VSI states) Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives28

29 Direct Torque Control (DTC) – Basic Principles (example) Assuming at time t, Initial stator and rotor flux are denoted as  s (t) and  r the VSI switches to state [100]  stator voltage vector V1 generated After short time interval  t, New stator flux vector  s (t+  t) differs from  s (t) in terms of : Magnitude (increased by  s =V1(  t)) Position (reduced by  sr ) Assumption: Negligible change in rotor flux vector  r within  t Stator flux and torque changed by voltage Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives29 [100]V1 [110]V2[010]V3 [011]V4 [101]V6[001]V5  s =V1(  t)  s (t)  s (t+  t)  r dsds qsqs  sr  sr

30 Direct Torque Control (DTC) – Rules for Flux Control To increase flux magnitude: select non-zero voltage vectors with misalignment with  s (t) not exceeding  90  To decrease flux magnitude: select non-zero voltage vectors with misalignment with  s (t) that exceeds  90  V0 and V7 (zero states) do not affect  s (t), i.e. stator flux stops moving Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives30 [100]V1 [110]V2[010]V3 [011]V4 [101]V6 [001]V5  s (t)  r dsds qsqs  sr

31 Direct Torque Control (DTC) – Rules for Torque Control To increase torque: select non-zero voltage vectors which accelerates  s (t) To decrease torque: select non-zero voltage vectors which decelerates  s (t) To maintain torque: select V0 or V7 (zero states) which causes  s (t) to stop moving Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives31 [100]V1 [110]V2[010]V3 [011]V4 [101]V6 [001]V5  s (t)  r dsds qsqs  sr

32 Direct Torque Control (DTC) – Rules for Flux and Torque Control The d s q s plane can be divided into six 60  -wide sectors (S1 to S6) If  s is in sector Sk k+1 voltage vector (Vk+1) increases  s k+2 voltage vector (Vk+2) decreases  s Example: here  s is in sector 2 (S2) V3 increases  s V4 decreases  s Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives32 [100] V1 [110] V2 [010] V3 [011] V4 [001] V5[101] V6 Note: [000] V0 = 0 [111] V7 = 0 dsds qsqs S1 S2 S3 S4 S5 S6  s (t)

33 Direct Torque Control (DTC) – Rules for Flux and Torque Control Stator flux vector  s is associated with a voltage vector VK when it passes through sector K (SK) Impact of all individual voltage vectors on  s and T e is summarized in table below: Impact of VK and VK+3 on T e is ambiguous, it depends on whether  s leading or lagging the voltage vector Zero vector Vz (i.e. V0 or V7) doesn’t affect  s but reduces T e Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives33 VKVK+1VK+2VK+3VK+4VK+5Vz (V0 or V7)  s  - TeTe ?  ? 

34 Direct Torque Control (DTC) – Implementation 1. DC voltage V dc and three phase stator currents i abcs are measured 2. v sdq s and current i sdq s are determined in Voltage and Current Vector Synthesizer by the following equations: where S a, S b,S c = switching variables of VSI and Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives34 (21) (22)

35 Direct Torque Control (DTC) – Implementation 3. Flux vector  s and torque T e are calculated in the Torque and Flux Calculator using the following equations: Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives35 (23) (24) (25) (26)

36 Direct Torque Control (DTC) – Implementation 4. Magnitude of  s is compared with  s * in the flux control loop. 5. T e is compared with T e * in the torque control loop. 6. The flux and torque errors,  s and  T e are fed to respective bang-bang controllers, with characteristics shown below. Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives36 Note:  s =  s  T m =  T e b = b 

37 Direct Torque Control (DTC) – Implementation 7. Selection of voltage vector (i.e. inverter state) is based on: values of b  and b T (i.e. output of the flux and torque bang- bang controllers ) angle of flux vector  s direction of motor rotation (clockwise or counter clockwise) Specifics of voltage vector selection are provided based on Tables in Slide 37 (counterclockwise rotation) and Slide 38 (clockwise rotation) and applied in the State Selector block. Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives37 (27)

38 Direct Torque Control (DTC) – Implementation Selection of voltage vector in DTC scheme: Counterclockwise Rotation Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives38 bb 10 bTbT 1010 S1V2V7V6V3V0V5 S2V3V0V1V4V7V6 S3V4V7V2V5V0V1 S4V5V0V3V6V7V2 S5V6V7V4V1V0V3 S6V1V0V5V2V7V4 [100]V1 [110]V2[010]V3 [011]V4 [101]V6[001]V5 To minimize number of switching: V0 always follows V1, V3 and V5 V7 always follows V2, V4 and V6

39 Direct Torque Control (DTC) – Implementation Selection of voltage vector in DTC scheme: Clockwise Rotation Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives39 bb 10 bTbT 1010 S1V6V7V2V5V0V3 S2V5V0V1V4V7V2 S3V4V7V6V3V0V1 S4V3V0V5V2V7V6 S5V2V7V4Vv1V0V5 S6V1V0V3V6V7V4 [100]V1 [110]V2[010]V3 [011]V4 [101]V6[001]V5 To minimize number of switching: V0 always follows V1, V3 and V5 V7 always follows V2, V4 and V6

40 bb 10 bTbT 1010 S2V3V0V1V4V7V6 Direct Torque Control (DTC) – Implementation (Example)  s is in sector S2 (assuming counterclockwise rotation) Both flux and torque to be increased (b  = 1 and b T = 1) – apply V3 (State = [010]) Flux decreased and torque increased (b  = 0 and b T = 1) – apply V4 (State = [011]) Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives40 [100]V1 [110]V2[010]V3 [011]V4 [101]V6 [001]V5  s  r dsds qsqs  sr

41 Direct Torque Control (DTC) – Implementation EEEB443 - Control & Drives41 Flux control loop Torque control loop Eq. (21) &(22) Eq. (23), (24) &(26) Eq. (25) Eq. (27) Note: s =  s T m = T e b = b  a = S a b = S b c = S c v i = V dc v s = v sdq s i is = i sdq s ds =  sd s qs =  sq s Based on Table in Slides 37 or 38

42 References Trzynadlowski, A. M., Control of Induction Motors, Academic Press, San Diego, Asher, G.M, Vector Control of Induction Motor Course Notes, University of Nottingham, UK, Dr. Ungku Anisa, July EEEB443 - Control & Drives


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