Induction Motor – Scalar Control By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering Dr. Ungku Anisa, July 2008 1 EEEB443 - Control & Drives
Dec 22, 2015
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)
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 3
Rr’/s+
Vs
–
RsLls Llr’
+
E1
–
Is Ir’
Im
Lm
Introduction
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 4
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 5
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 6
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 7
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.
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 8
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 11
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 12
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 13
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 16
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)
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 17
rated,
rated,
s
sVd
rated,rated,
rated,rated,
when ,
when ,
sss
ssss ffV
ffKVV
Constant Volts/Hz (V/f) Control For operation at frequency K times rated frequency:
Hence, the torque produced by the motor:
(4)
where s and Vs are calculated from (1) and (2) respectively.
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 18
22
2'
2'3
lrlsr
s
s
s
re
XXKs
RR
V
s
RT
Constant Volts/Hz (V/f) Control For operation at frequency K times rated frequency:
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.
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 19
222
'
max
lrlss
r
XXKR
Rs
222
2
max 2
3
lrlsss
s
s XXKRR
VT
Constant Volts/Hz (V/f) Control
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 20
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 Volts/Hz (V/f) Control
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 21
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 23
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
Constant Volts/Hz (V/f) Control – Open-loop Implementation
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 26
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
*
Note: e= s = synchronous speed
Constant Volts/Hz (V/f) Control – Open-loop Implementation
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 28
Open-loop system (as in slide 23)
Slip Controller
Note: e= s = synchronous speed
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 29
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 31
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:
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 32
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)
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 33
,
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
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 34
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)
Dr. Ungku Anisa, July 2008 35EEEB443 - Control & Drives
PI Controller + Sinusoidal PWM
Current-Controlled VSI Implementation
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)
Dr. Ungku Anisa, July 2008 36EEEB443 - Control & Drives
PI Controller + Sinusoidal PWM (2 phase)
Motor
i*a
i*b
i*c
abcdq
abcdqdq abc
PI
PI
Current-Controlled VSI Implementation
PWMVoltage Source
Inverter (VSI)
Dr. Ungku Anisa, July 2008 37EEEB443 - Control & Drives
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.
Dr. Ungku Anisa, July 2008 38EEEB443 - Control & Drives