EEEB443 Control & Drives

Induction Motor – Scalar ControlByDr. Ungku Anisa Ungku AmirulddinDepartment of Electrical Power EngineeringCollege of Engineering

Dr. Ungku Anisa, July 2008 1EEEB443 - Control & Drives

OutlineIntroductionSpeed Control of Induction Motors

Pole ChangingVariable-Voltage, Constant FrequencyVariable Frequency

Constant Volts/Hz (V/f) ControlOpen-loop ImplementationClosed-loop Implementation

Constant Airgap Flux ControlReferences

Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 2

IntroductionScalar Control - control of induction machine

based on steady-state model (per phase SS equivalent circuit)


Rr’/s+

Vs

–

RsLls Llr’

+

E1

–

Is Ir’

Im

Lm

Introduction


r

s

Trated

Pull out Torque(Tmax)

Te

ssm ratedrotor

TL

Te

Intersection point (Te=TL) determines the steady –state speed

1 0

What if the load must be operated here?

rotor’

Requires speed control of motor

Speed Control of IMGiven a load T– characteristic, the steady-state speed can be

changed by altering the T– curve of the motor


fPPs 42

2

2'

2'3

lrlsr

s

s

s

re

XXs

RR

V

s

RT

Pole Changing

Varying line frequency

Varying voltage (amplitude)2

3

1

Speed Control of IMPole ChangingMachines must be specially manufactured (i.e. called pole changing

motors or multi-speed motors)Need special arrangement of stator windings

Only used with squirrel-cage motorsBecause number of poles induced in squirrel cage rotor will follow

number of stator polesTwo methods:

Multiple stator windings stator has more than one set of 3-phase windings only energize one set at a time simple, expensive

Consequent poles Discrete step change in speed


Pole ChangingConsequent poles

single winding divided into few coil groups

No. of poles changed by changing connections of coil groups

Change in pole number by factor of 2:1 only


A two-pole stator winding for pole changing. Notice the very short pitch (60 to 90) of these windings.

Speed Control of IM

Pole ChangingConsequent poles

Close up view of one phase of a pole changing winding.

In Figure (a): the 2-pole configuration, one coil is a north pole and the other is a south pole.

In Figure (b): when the connection on one of the two coils is reversed, they are both north poles, and the magnetic flux returns to the stator halfway between the two coils. The south poles are called consequent poles. Hence the winding is now 4-pole.


Speed Control of IM

Speed Control of IMVariable-Voltage (amplitude), Constant FrequencyControlled using:

Transformer (rarely used)Thyristor voltage controller

thyristors connected in anti-parallelmotor can be star or delta connected

voltage control by firing angle control(gating signals are synchronized to phase voltages and are spaced at 60 intervals)

Only for operations in Quadrant 1 and Quadrant 3 (requires reversal of phase sequence)

also used for soft start of motorsDr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 9

Speed Control of IMVariable-Voltage (amplitude), Constant FrequencyVoltage can only be reduced from rated Vs (i.e. 0 < Vs ≤ Vs,rated)From torque equation, Te Vs

2

When Vs , Te and speed reduces.If terminal voltage is reduced to bVs, (i.e. Vs = bVs,rated) :

Note: b 1Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 10

2

2'

2'3

lrlsr

s

s

s

re

XXs

RR

bV

s

RT

Speed Control of IMVariable-Voltage

(amplitude), Constant Frequency

Suitable for applications where torque demand reduces with speed (eg: fan and pump drives where TL m

2)Suitable for NEMA Class D

(high-slip, high Rr’) type motorsHigh rotor copper loss,

low efficiency motorsget appreciable speed

range


Practical speed range

Speed Control of IMVariable Voltage (amplitude),

Constant FrequencyDisadvantages:

limited speed range when applied to Class B (low-slip) motors

Excessive stator currents at low speeds high copper losses

Distorted phase current in machine and line (harmonics introduced by thyristor switching)

Poor line power factor (power factor proportional to firing angle)

Hence, only used on low-power, appliance-type motors where efficiency is not important e.g. small fan or pumps drives


Speed Control of IMVariable FrequencySpeed control above rated (base) speed

Requires the use of PWM inverters to control frequency of motorFrequency increased (i.e. s increased)Stator voltage held constant at rated valueAirgap flux and rotor current decreases Developed torque

decreases Te (1/s)

For control below base speed – use Constant Volts/Hz method


Constant Volts/Hz (V/f) ControlAirgap flux in the motor is related to the induced stator voltage

E1 :

For below base speed operation:Frequency reduced at rated Vs - airgap flux saturates

(f ,ag and enters saturation region oh B-H curve):- excessive stator currents flow- distortion of flux wave- increase in core losses and stator copper loss

Hence, keep ag = rated fluxstator voltage Vs must be reduced proportional to reduction in f

(i.e. maintaining Vs / f ratio)Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 14

f

Eag

1f

Vs Assuming small voltage drop across Rs and Lls

Constant Volts/Hz (V/f) ControlMax. torque remains almost

constantFor low speed operation:

can’t ignore voltage drop across Rs and Lls (i.e. E1 Vs)

poor torque capability(i.e. torque decreased at low speeds shown by dotted lines)

stator voltage must be boosted – to compensate for voltage drop at Rs and Lls and maintain constant ag

For above base speed operation (f > frated): stator voltage maintained at

rated valueSame as Variable Frequency

control (refer to slide 13)Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 15

s

sVT

2

max f

Eag

1f

Vs

Constant Volts/Hz (V/f) Control


Vrated

frated

Linear offset

Non-linear offset – varies with IsBoost

Vs vs. f relation in Constant Volts/Hz drivesVs

f

Linear offset curve – •for high-starting torque loads•employed for most applications

Non-linear offset curve – •for low-starting torque loads

Boost - to compensate for voltage drop at Rs and Lls

Constant Volts/Hz (V/f) Control For operation at frequency K times rated frequency:

fs = Kfs,rated s = Ks,rated (1)

(Note: in (1) , speed is given as mechanical speed)

Stator voltage: (2)

Voltage-to-frequency ratio = d = constant:

(3)


rated,

rated,

s

sVd

rated,rated,

rated,rated,

when ,

when ,

sss

ssss ffV

ffKVV


Hence, the torque produced by the motor:

(4)

where s and Vs are calculated from (1) and (2) respectively.


22

2'

2'3

lrlsr

s

s

s

re

XXKs

RR

V

s

RT


The slip for maximum torque is:

(5)

The maximum torque is then given by:

(6)

where s and Vs are calculated from (1) and (2) respectively.


222

'

max

lrlss

r

XXKR

Rs

222

2

max 2

3

lrlsss

s

s XXKRR

VT



Field Weakening Mode (f > frated)• Reduced flux (since Vs is constant)• Torque reducesConstant Power Area

(above base speed)

Constant Torque Area

(below base speed)Rated (Base) frequency

Note: Operation restricted between synchronous speed and Tmax for motoring and braking regions, i.e. in the linear region of the torque-speed curve.



Constant Power Area

Constant Torque Area

ExampleA 4-pole, 3 phase, 400 V, 50 Hz, 1470 rpm induction motor

has a rated torque of 30 Nm. The motor is used to drive a linear load with characteristic given by TL = K, such that the speed equals rated value at rated torque. If a constant Volts/Hz control method is employed, calculate:The constant K in the TL - characteristic of the load.

Synchronous and motor speeds at 0.6 rated torque.

If a starting torque of 1.2 times rated torque is required, what

should be the voltage and frequency applied at start-up? State any assumptions made for this calculation.

Answers: K = 0.195, synchronous speed = 899.47 rpm & motor speed = 881.47 rpm,

At start up: frequency = 1.2 Hz, Voltage = 9.6 VDr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 22

Constant Volts/Hz (V/f) Control – Open-loop Implementation


PWM Voltage-Source

Inverter (VSI)

Note: e= s = synchronous speed

Constant Volts/Hz (V/f) Control – Open-loop ImplementationMost popular speed control method because it is easy to

implementUsed in low-performance applications

where precise speed control unnecessary

Speed command s* - primary control variable Phase voltage command Vs* generated from V/f relation

(shown as the ‘G’ in slide 23)Boost voltage Vo is added at low speedsConstant voltage applied above base speed

Sinusoidal phase voltages (vabc*) is then generated from Vs* & s* where s* is obtained from the integral of s*

vabc* employed in PWM inverter connected to motorDr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 24

Constant Volts/Hz (V/f) Control – Open-loop ImplementationProblems in open-loop drive operation:

Motor speed not controlled precisely primary control variable is synchronous speed s

actual motor speed r is less than s due to sl

sl depends on load connected to motorsl cannot be maintained since r not measured

can lead to operation in unstable region of T- characteristic stator currents can exceed rated value – endangering inverter-

converter combinationProblems (to an extent) can be overcome by:

Open-loop Constant Volts/Hz Drive with Slip CompensationClosed-loop implementation - having outer speed loop with

slip regulationDr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 25

sls

mr

P

P

2

2



Slip Compensator

IdcVdc = Vd

sl

r*

Open-loop Constant Volts/Hz Drive with Slip Compensation- Slip speed is estimated and added to the reference speed r

*



How is sl estimated in the Slip Compensator?

Using T- curve, sl Te sl can be estimated by

estimating torque where:

(8)

(9)Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 27

Open-loop Constant Volts/Hz Drive with Slip Compensation

s

SCLin

s

age

PPPT

lossesinverter

dcdcin IVP Note: In the figure, slip= sl = slip speedsyn= s = synchronous speed

ratedslratede

esl T

T,

,

(7)

Constant Volts/Hz (V/f) Control – Closed-loop Implementation


Open-loop system (as in slide 23)

Slip Controller


Constant Volts/Hz (V/f) Control – Closed-loop ImplementationReference motor speed r* is compared to the actual speed r

to obtain the speed loop errorSpeed loop error generates slip command sl* from PI

controller and limiterLimiter ensures that the sl* is kept within the allowable slip speed

of the motor (i.e. sl* slip speed for maximum torque)sl* is then added to the actual motor speed r to generate

synchronous speed command s* (or frequency command)s* generates voltage command Vs* from V/f relation

Boost voltage is added at low speedsConstant voltage applied above base speed

Scheme can be considered open loop torque control (since T s) within speed control loop


Constant Airgap Flux ControlConstant V/f control employs the use of variable frequency

voltage source inverters (VSI)Constant Airgap Flux control employs variable frequency

current source inverters or current-controlled VSIProvides better performance compared to Constant V/f

control with Slip Compensationairgap flux is maintained at rated value through stator current

controlSpeed response similar to equivalent separately-excited dc

motor drive but torque and flux channels still coupledFast torque response means:

High-performance drive obtainedSuitable for demanding applicationsAble to replace separately-excited dc motor drives

Above only true is airgap flux remains constant at rated valueDr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 30

Constant Airgap Flux ControlConstant airgap flux in the motor means:

For ag to be kept constant at rated value, the magnetising current Im must remain constant at rated value

Hence, in this control scheme stator current Is is controlled to maintain Im at rated value


constant2

1 mmag ILf

E

Rr’/s+

Vs

–

RsLls Llr’

+

E1 Vs

–

Is Ir’

Im

Lm

maintain at rated

Controlled to maintain Im at rated

Assuming small voltage drop across Rs and Lls

Constant Airgap Flux ControlFrom torque equation (with ag kept constant at rated value),

since ss = sl and ignoring Rs and Lls,

By rearranging the equation:


2

2'

'2

1

2

2'

'2

23

23

lrsssl

r

r

sl

lrlsr

s

r

s

se

LR

REP

XXs

RR

R

s

VPT

2

2'

'

2

2

2'

'

2

2

1

23

23

lrsl

r

sl

r

age

lrsl

r

sl

r

se

LR

R

PT

LR

R

EPT

Te sl sl can be varied instantly instantaneous (fast) Te response

Constant Airgap Flux ControlConstant airgap flux requires control of magnetising current Im which is

not accessibleFrom equivalent circuit (on slide 31):

From equation (10), plot Is against sl when Im is kept at rated value. Drive is operated to maintain Is against sl relationship when frequency

is changed to control speed.Hence, control is achieved by controlling stator current Is and stator

frequency: Is controlled using current-controlled VSI

Control scheme sensitive to parameter variation (due to Tr and r)


,

11

1m

rr

rsl

rsls I

Tj

TjI

sr

ms

rs

m I

sR

LLj

sR

LjI

lr

lr

''

''

)(

relecs

elecsl

m

lrr

r

rr L

L

R

LT ,,:Note

'

'

(10)

Constant Airgap Flux Control - Implementation


Voltage Source

Inverter (VSI)

Rectifier3-phase supply IM

r*

+

+ |Is|slip

C

Current controller

s

PI

+

r

-

r

Current controller options:• Hysteresis Controller• PI controller + PWM

Equation (10) (from slide 33)

i*a

i*b

i*c

Current Controlled VSI

Hysteresis Controller

Current-Controlled VSI Implementation

Motor

+

+

+

i*a

i*b

i*c

Voltage Source

Inverter (VSI)


PI Controller + Sinusoidal PWM


Motor

+

+

+

i*a

i*b

i*c

PWM

PWM

PWM

PWM

PWM

PWM

PI

PI

PI

•Due to interactions between phases (assuming balanced conditions) actually only require 2 controllers

Voltage Source Inverter (VSI)


PI Controller + Sinusoidal PWM (2 phase)

Motor

i*a

i*b

i*c

abcdq

abcdqdq abc

PI

PI


PWMVoltage Source

Inverter (VSI)


id*

iq*

id

iq

ReferencesKrishnan, R., Electric Motor Drives: Modeling, Analysis and Control,

Prentice-Hall, New Jersey, 2001.Bose, B. K., Modern Power Electronics and AC drives, Prentice-Hall,

New Jersey, 2002.Trzynadlowski, A. M., Control of Induction Motors, Academic Press,

San Diego, 2001.Rashid, M.H, Power Electronics: Circuit, Devices and Applictions, 3rd

ed., Pearson, New-Jersey, 2004.Nik Idris, N. R., Short Course Notes on Electrical Drives,

UNITEN/UTM, 2008.Ahmad Azli, N., Short Course Notes on Electrical Drives,

UNITEN/UTM, 2008.


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EEEB443 Control & Drives