EEEB443 Control & Drives Induction Motor – Direct Torque Control By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives Dr. Ungku Anisa, July 2008

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 2008 EEEB443 - Control & Drives

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 2008 EEEB443 - Control & Drives

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 2008 EEEB443 - Control & Drives

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

PWM Voltage Source Inverter – single phase Reference current compared with actual current Current error is fed to a PI controller Output of PI controller (vc) compared with triangular waveform (vtri) to determine duty ratio of switches vtri Vdc q vc Pulse width modulator PI Controller iref Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Sinusoidal PWM Voltage Source Inverter Same concept is extended to three-phase VSI va*, vb* and vc* 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* Sa Pulse width modulator Vb* Pulse width modulator Vc* Sb Sc Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Sinusoidal PWM Voltage Source Inverter + vc - + vb - + va - n N Vdc a b c S1 S3 S5 S4 S6 S2 Switching signals for the SPWM VSI va* vb* Pulse Width Modulation S1, S2, ….S6 vc* Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Sinusoidal PWM Voltage Source Inverter Three switching variables are Sa, Sb and Sc (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: Sa = 1 if S1 ON and S4 OFF Sa = 0 if S1 OFF and S4 ON Total number of states = 8 An inverter state is denoted as [SaSbSc]2, eg: If Sa = 1, Sb = 0 and Sc = 1, inverter is in State 5 since [101]2 = 5 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Space Vector PWM Space vector representation of a three-phase quantities xa(t), xb(t) and xc(t) with space distribution of 120o apart is given by: where: a = ej2/3 = cos(2/3) + jsin(2/3) a2 = ej4/3 = cos(4/3) + jsin(4/3) ‘x’ can be a voltage, current or flux and does not necessarily has to be sinusoidal (1) Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Space Vector PWM Space vector of the three-phase stator voltage is: where va, vb and vc are the phase voltages. If va, vb and vc are balanced 3-phase sinusoidal voltage with frequency f, then the locus of vs : circular with radius equal to the peak amplitude of the phase voltage rotates with a speed of 2f (2) Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

will be the voltages applied to the terminals of the induction motor Space Vector PWM These voltages will be the voltages applied to the terminals of the induction motor + vc - + vb - + va - n N Vdc a b c S1 S3 S5 S4 S6 S2 We want va, vb and vc to follow va*, vb* and vc* va* vb* vc* S1, S2, ….S6 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Space Vector PWM From the inverter circuit diagram: van = vaN + vNn vbn = vbN + vNn vcn = vcN + vNn vaN = VdcSa , vbN = VdcSb , vcN = VdcSc where Sa, Sb, Sc = 1 or 0 and Vdc = dc link voltage Substituting (3) – (6) into (2): (3) (4) (5) (6) (7) Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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

Space Vector PWM Example: For State 6, i.e. [110]2 (Sa = 1, Sb = 1 and Sc = 0) qs vs ds Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Inverter state [SaSbSc]2 Space Vector PWM 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. qs (1/3)Vdc Voltage Vector Inverter state [SaSbSc]2 V0 State 0 = [000] 2 V1 State 4 = [100] 2 V2 State 6 = [110] 2 V3 State 2 = [010] 2 V4 State 3 = [011] 2 V5 State 1 = [001] 2 V6 State 5 = [101] 2 V7 State 7 = [111] 2 [010] V3 [110] V2 [000] V0 = 0 [111] V7 = 0 [011] V4 [100] V1 (2/3)Vdc ds [001] V5 [101] V6 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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

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

Space Vector PWM = vy = vx In general: Within a sampling period T, to synthesize reference voltage vs*, it is assembled from: vector Vx (to the right) vector Vy (to the left) and a zero vector Vz (either V0 or V7) Since T is sampling period of vs*: Vx is applied for time Tx Vy is applied for time Ty Vz is applied for the rest of the time, Tz qs = vy [010] V3 [110] V2 vs* [011] V4  = vx [100] V1 ds Note: [000] V0 = 0 [111] V7 = 0 [001] V5 [101] V6 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Space Vector PWM In general: Total sampling time: If  close to 0 : Tx > Ty If  close to 60 : Tx < Ty If vs* is large: more time spent at Vx, Vy compared to Vz i.e. Tx + Ty > Tz If vs* is small: more time spent at Vz compared to Vx, Vy , i.e. . Tx + Ty < Tz T= Tx + Ty + Tz (9) qs [010] V3 = vy [110] V2 vs* [011] V4  [100] V1 = vx ds Note: [000] V0 = 0 [111] V7 = 0 [001] V5 [101] V6 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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

Space Vector PWM Example: vs* is in sector S1 = vy vs* qs [010] V3 = vy [110] V2 Vx = V1 is applied for time Tx vs* Vy = V2 is applied for time Ty Vz is applied for rest of the time, Tz  = vx [100] V1 ds [011] V4 Note: [000] V0 = 0 [111] V7 = 0 [001] V5 [101] V6 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Space Vector PWM Example: vs* in sector S1 Reference voltage vs* is sampled at regular intervals T, i.e. T is sampling period: V1 [100]2 is applied for Tx V2 [110]2 is applied for Ty Zero voltage V0 [000]2 and V7 [111]2 is applied for the rest of the time, i.e. Tz Vref is sampled T= Tx + Ty + Tz Tz/2 V0 V1 Tx V2 Ty Tz/2 V7 V7 V2 V1 V0 va vb vc T T Vref is sampled Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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

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

Direct Torque Control (DTC) – Basic Principles Derivative of stator flux is equal to the stator EMF. Therefore, stator flux magnitude strongly depends on stator voltage. If voltage drop across Rs 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). (17) (18) [100]V1 [110]V2 [010]V3 [011]V4 [101]V6 [001]V5 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Direct Torque Control (DTC) – Basic Principles 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, Te can also be controlled using the stator voltage through sr. (19) (20) Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Direct Torque Control (DTC) – Basic Principles 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 2008 EEEB443 - Control & Drives Dr. Ungku Anisa, July 2008

Direct Torque Control (DTC) – Basic Principles (example) [100]V1 [110]V2 [010]V3 [011]V4 [101]V6 [001]V5 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 qs s=V1(t) s(t+t) s(t) sr sr r ds Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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 qs [100]V1 [110]V2 [010]V3 [011]V4 [101]V6 [001]V5 s(t) sr r ds Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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 qs [100]V1 [110]V2 [010]V3 [011]V4 [101]V6 [001]V5 s(t) sr r ds Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Direct Torque Control (DTC) – Rules for Flux and Torque Control The dsqs 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 S3 qs [110] V2 [010] V3 s(t) [011] V4 [100] V1 ds S4 S1 [001] V5 [101] V6 S5 S6 Note: [000] V0 = 0 [111] V7 = 0 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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 Te is summarized in table below: Impact of VK and VK+3 on Te 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 Te VK VK+1 VK+2 VK+3 VK+4 VK+5 Vz (V0 or V7) s     - Te ? Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Direct Torque Control (DTC) – Implementation DC voltage Vdc and three phase stator currents iabcs are measured vsdqs and current isdqs are determined in Voltage and Current Vector Synthesizer by the following equations: where Sa, Sb ,Sc = switching variables of VSI and (21) (22) Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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

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

Direct Torque Control (DTC) – Implementation Selection of voltage vector (i.e. inverter state) is based on: values of b and bT (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. (27) Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Direct Torque Control (DTC) – Implementation [100]V1 [110]V2 [010]V3 [011]V4 [101]V6 [001]V5 Selection of voltage vector in DTC scheme: Counterclockwise Rotation b 1 bT -1 S1 V2 V7 V6 V3 V0 V5 S2 V1 V4 S3 S4 S5 S6 To minimize number of switching: V0 always follows V1, V3 and V5 V7 always follows V2, V4 and V6 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Direct Torque Control (DTC) – Implementation [100]V1 [110]V2 [010]V3 [011]V4 [101]V6 [001]V5 Selection of voltage vector in DTC scheme: Clockwise Rotation b 1 bT -1 S1 V6 V7 V2 V5 V0 V3 S2 V1 V4 S3 S4 S5 Vv1 S6 To minimize number of switching: V0 always follows V1, V3 and V5 V7 always follows V2, V4 and V6 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Direct Torque Control (DTC) – Implementation (Example) qs s is in sector S2 (assuming counterclockwise rotation) Both flux and torque to be increased (b = 1 and bT = 1) – apply V3 (State = [010]) Flux decreased and torque increased (b = 0 and bT = 1) – apply V4 (State = [011]) [100]V1 [110]V2 [010]V3 [011]V4 [101]V6 [001]V5 s sr r ds b 1 bT -1 S2 V3 V0 V1 V4 V7 V6 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

Direct Torque Control (DTC) – Implementation Note: s=s Tm= Te b= b a = Sa b = Sb c = Sc vi = Vdc vs= vsdqs iis= isdqs ds=sds qs= sqs Based on Table in Slides 37 or 38 Flux control loop Eq. (21) &(22) Eq. (25) Eq. (27) Eq. (23) , (24) &(26) Torque control loop EEEB443 - Control & Drives

References Trzynadlowski, A. M., Control of Induction Motors, Academic Press, San Diego, 2001. Asher, G.M, Vector Control of Induction Motor Course Notes, University of Nottingham, UK, 2002. Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives