Loading...

PPT – EEEB443 Control PowerPoint presentation | free to download - id: 43c1bc-Y2YzM

The Adobe Flash plugin is needed to view this content

EEEB443 Control Drives

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

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

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)

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)

Switching Control

Continuous Control

Switching Control

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

Pulse width modulator

PI Controller

iref

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

Sa

Sb

Sc

Sinusoidal PWM Voltage Source Inverter

S1

S3

S5

S2

S4

S6

Switching signals for the SPWM VSI

va

Pulse Width Modulation

vb

S1, S2, .S6

vc

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 SaSbSc2, eg
- If Sa 1, Sb 0 and Sc 1, inverter is in

State 5 since 1012 5

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)

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)

Space Vector PWM

These voltages will be the voltages applied to

the terminals of the induction motor

S1

S3

S5

S2

S4

S6

We want va, vb and vc to follow va, vb and vc

S1, S2, .S6

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)

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)

Space Vector PWM

- Example For State 6, i.e. 1102 (Sa 1, Sb

1 and Sc 0)

qs

?vs

ds

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

010 V3

Voltage Vector Inverter state SaSbSc2

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

110 V2

000 V0 0 111 V7 0

100 V1

011 V4

ds

001 V5

101 V6

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

100 V1

S4

011 V4

S1

ds

001 V5

101 V6

S5

S6

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

Space Vector PWM

- 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

vx

011 V4

?

ds

100 V1

Note 000 V0 0 111 V7 0

001 V5

101 V6

Space Vector PWM

- In general
- Total sampling time
- If ? close to 0? Tx gt Ty
- If ? close to 60? Tx lt Ty
- If vs is large more time
- spent at Vx, Vy compared
- to Vz i.e. Tx Ty gt Tz
- If vs is small more time
- spent at Vz compared
- to Vx, Vy , i.e. . Tx Ty lt Tz

T Tx Ty Tz

(9)

qs

vy

010 V3

110 V2

vs

011 V4

?

vx

ds

100 V1

Note 000 V0 0 111 V7 0

001 V5

101 V6

Space Vector PWM

Vector Vx to the right of vs

- In general, if ? is the angle between the

reference voltage vs and Vx (vector to its

right), then - where

qs

vs

110 V2

010 V3

?

(10)

100 V1

011 V4

ds

(11)

Note 000 V0 0 111 V7 0

001 V5

101 V6

Tz T ? Tx? Ty

(12)

Space Vector PWM

Example vs is in sector S1

qs

010 V3

vy

110 V2

vs

- Vx V1 is applied for time Tx

- 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

Space Vector PWM

- Example vs in sector S1
- Reference voltage vs is sampled at regular

intervals T, i.e. T is sampling period - V1 1002 is applied for Tx
- V2 1102 is applied for Ty
- Zero voltage V0 0002 and V7 1112 is applied

for the rest of the time, i.e. Tz

T Tx Ty Tz

V7

V2

V1

V0

Space Vector PWM

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

S2

- Vx ____ is applied for time Tx

S3

100 V1

S1

011 V4

S4

ds

- Vy ___ is applied for time Ty

Note 000 V0 0 111 V7 0

S6

S5

- Vz is applied for time Tz

001 V5

101 V6

Tz T ? Tx? Ty

Space Vector Equations of IM

- The two-phase dynamic model of IM in the

stationary dsqs frame

(13)

(14)

(15)

(16)

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)

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)

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)

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 ??sV1(?t))
- Position (reduced by ??sr)
- Assumption Negligible change in rotor flux

vector ??r within ?t - Stator flux and torque changed by voltage

qs

ds

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

ds

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

ds

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
- k1 voltage vector (Vk1) increases ??s
- k2 voltage vector (Vk2) decreases ??s
- Example here??s is in sector 2 (S2)
- V3 increases ??s
- V4 decreases ??s

S2

S3

qs

110 V2

010 V3

100 V1

011 V4

ds

S1

S4

001 V5

101 V6

S5

S6

Note 000 V0 0 111 V7 0

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 VK3 on Te is ambiguous, it

depends on whether ??s leading or lagging the

voltage vector - Zero vector Vz (i.e. V0 or V7) doesnt affect ??s

but reduces Te

VK VK1 VK2 VK3 VK4 VK5 Vz (V0 or V7)

??s ?? ? ? ?? ? ? -

Te ? ? ? ? ? ? ?

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)

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)

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?

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)

Direct Torque Control (DTC) Implementation

- Selection of voltage vector in DTC scheme
- Counterclockwise Rotation

b? 1 1 1 0 0 0

bT 1 0 -1 1 0 -1

S1 V2 V7 V6 V3 V0 V5

S2 V3 V0 V1 V4 V7 V6

S3 V4 V7 V2 V5 V0 V1

S4 V5 V0 V3 V6 V7 V2

S5 V6 V7 V4 V1 V0 V3

S6 V1 V0 V5 V2 V7 V4

- To minimize
- number of
- switching
- V0 always
- follows V1, V3
- and V5
- V7 always
- follows V2, V4
- and V6

Direct Torque Control (DTC) Implementation

- Selection of voltage vector in DTC scheme
- Clockwise Rotation

b? 1 1 1 0 0 0

bT 1 0 -1 1 0 -1

S1 V6 V7 V2 V5 V0 V3

S2 V5 V0 V1 V4 V7 V2

S3 V4 V7 V6 V3 V0 V1

S4 V3 V0 V5 V2 V7 V6

S5 V2 V7 V4 Vv1 V0 V5

S6 V1 V0 V3 V6 V7 V4

- To minimize
- number of
- switching
- V0 always
- follows V1, V3
- and V5
- V7 always
- follows V2, V4
- and V6

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)

ds

b? 1 1 1 0 0 0

bT 1 0 -1 1 0 -1

S2 V3 V0 V1 V4 V7 V6

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

Eq. (25)

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.