dokumen.tips_electrical-drives-ppt.ppt

ELECTRICAL DRIVES:
An Application of Power Electronics
Dr. Nik Rumzi Nik Idris,
(Senior Member IEEE)
Department of Energy Conversion,
Universiti Teknologi Malaysia
Skudai, JOHOR

CONTENTS
Power Electronic Systems
Modern Electrical Drive Systems
Power Electronic Converters in Electrical Drives
:: DC and AC Drives
Modeling and Control of Electrical Drives
:: Current controlled Converters
:: Modeling of Power Converters
:: Scalar control of IM

What is Power Electronics ?
A field of Electrical Engineering that deals with the application of
power semiconductor devices for the control and conversion of
electric power
Power Electronics
Converters
Load
Controller
Output
- AC
- DC
Input
Source
- AC
- DC
- unregulated
Reference
POWER ELECTRONIC
CONVERTERS – the
heart of power a power
electronics system
sensors

Why Power Electronics ?
Power semiconductor devices Power switches
ON or OFF
+ vsw −
= 0
isw
+ vsw −
isw = 0
Ploss = vsw× isw = 0
Losses ideally ZERO !

-
Vak
+
ia
G
K
A
-
Vak
+
ia
K
A
-
Vak
+
ia
G
K
A

D
S
G
+
VDS
-
iD
G
C
E
+
VCE
-
ic

Passive elements High frequency
transformer
+
V1
-
+
V2
-
Inductor
+ VL -
iL
+ VC -
iC

Power Electronics
Converters
sensors
Load
Controller
Output
- AC
- DC
Input
Source
- AC
- DC
- unregulated
Reference
IDEALLY LOSSLESS !

Other factors:
• Improvements in power semiconductors fabrication
• Decline cost in power semiconductor
• Advancement in semiconductor fabrication
• ASICs • FPGA • DSPs
• Faster and cheaper to implement complex
algorithm
• Power Integrated Module (PIM), Intelligent Power
Modules (IPM)

Some Applications of Power Electronics :
Power rating of < 1 W (portable equipment)
Tens or hundreds Watts (Power supplies for computers /office equipment)
Typically used in systems requiring efficient control and conversion of
electric energy:
Domestic and Commercial Applications
Industrial Applications
Telecommunications
Transportation
Generation, Transmission and Distribution of electrical energy
kW to MW : drives
Hundreds of MW in DC transmission system (HVDC)

• About 50% of electrical energy used for drives
• Can be either used for fixed speed or variable speed
• 75% - constant speed, 25% variable speed (expanding)
• Variable speed drives typically used PEC to supply the motors
AC motors
- IM
- PMSM
DC motors (brushed)
SRM
BLDC

Classic Electrical Drive for Variable Speed Application :
• Bulky
• Inefficient
• inflexible

Power
Electronic
Converters
Load
Moto
r
Controller
Reference
POWER IN
feedback
Typical Modern Electric Drive Systems
Power Electronic Converters
Electric Energy
- Unregulated -
Electric Energy
- Regulated -
Electric Motor
Electric
Energy
Mechanical
Energy

Example on VSD application
motor pump
valve
Supply
Constant speed Variable Speed Drives
Power
In
Power loss
Mainly in valve
Power out

Power
In
Power loss
Mainly in valve
Power out
motor pump
valve
Supply
motor
PEC pump
Supply
Power
In
Power loss
Power out

Power
In
Power loss
Mainly in valve
Power out
Power
In
Power loss
Power out
motor pump
valve
Supply
motor
PEC pump
Supply

Electric motor consumes more than half of electrical energy in the US
Fixed speed Variable speed
HOW ?
Improvements in energy utilization in electric motors give large
impact to the overall energy consumption
Replacing fixed speed drives with variable speed drives
Using the high efficiency motors
Improves the existing power converter–based drive systems

DC drives: Electrical drives that use DC motors as the prime mover
Regular maintenance, heavy, expensive, speed limit
AC drives: Electrical drives that use AC motors as the prime mover
Less maintenance, light, less expensive, high speed
Overview of AC and DC drives
Easy control, decouple control of torque and flux
Coupling between torque and flux – variable spatial angle
between rotor and stator flux

Before semiconductor devices were introduced (<1950)
• AC motors for fixed speed applications
• DC motors for variable speed applications
After semiconductor devices were introduced (1960s)
• Variable frequency sources available – AC motors in variable
speed applications
• Coupling between flux and torque control
• Application limited to medium performance applications –
fans, blowers, compressors – scalar control
• High performance applications dominated by DC motors –
tractions, elevators, servos, etc

After vector control drives were introduced (1980s)
• AC motors used in high performance applications – elevators,
tractions, servos
• AC motors favorable than DC motors – however control is
complex hence expensive
• Cost of microprocessor/semiconductors decreasing –predicted
30 years ago AC motors would take over DC motors

Extracted from Boldea & Nasar

Power Electronic Converters in ED Systems
Converters for Motor Drives
(some possible configurations)
DC Drives AC Drives
DC Source
AC Source
AC-DC-DC
AC-DC
AC Source
Const.
DC
Variable
DC
AC-DC-AC AC-AC
NCC FCC
DC Source
DC-AC DC-DC-AC
DC-DC
DC-AC-DC

Converters for Motor Drives
Configurations of Power Electronic Converters depend on:
Sources available
Type of Motors
Drive Performance - applications
- Braking
- Response
- Ratings

DC DRIVES
Available AC source to control DC motor (brushed)
AC-DC-DC
AC-DC
Controlled Rectifier
Single-phase
Three-phase
Uncontrolled Rectifier
Single-phase
Three-phase
DC-DC Switched mode
1-quadrant, 2-quadrant
4-quadrant
Control Control

DC DRIVES
+
Vo
-
+
Vo
-


 cos
V
2
V m
o


 -
cos
V
3
V m
,
L
L
o
Average voltage
over 10ms
Average voltage
over 3.33 ms
50Hz
1-phase
50Hz
3-phase
AC-DC
0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44
-400
-200
0
200
400
0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44
0
5
10
0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44
-500
0
500
0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44
0
10
20
30

DC DRIVES
+
Vo
-
+
Vo
-


 cos
V
2
V m
o
90o 180o

m
V
2

- m
V
2
90o

- m
,
L
L
V
3

- - m
,
L
L
V
3


 -
cos
V
3
V m
,
L
L
o
Average voltage
over 10ms
Average voltage
over 3.33 ms
50Hz
1-phase
50Hz
3-phase
180o
AC-DC

DC DRIVES
AC-DC
Ia
Q1
Q2
Q3 Q4
Vt
3-phase
supply
+
Vt
-
ia
- Operation in quadrant 1 and 4 only

DC DRIVES
AC-DC
Q1
Q2
Q3 Q4

T
3-phase
supply
3-
phase
supply
+
Vt
-

DC DRIVES
AC-DC
Q1
Q2
Q3 Q4

T
F1
F2
R1
R2
+ Va -
3-phase
supply

DC DRIVES
AC-DC
Cascade control structure with armature reversal (4-quadrant):
Speed
controller
Current
Controller
Firing
Circuit
Armature
reversal
iD
iD,ref
iD,ref
iD,

ref + +
_
_

DC DRIVES
AC-DC-DC
control
Uncontrolled
rectifier
Switch Mode DC-DC
1-Quadrant
2-Quadrant
4-Quadrant

DC DRIVES
AC-DC-DC
control

T1 conducts  va = Vdc
Q1
Q2
Va
Ia
T1
T2
D1
+
Va
-
D2
ia
+
Vdc
-
DC DRIVES
AC-DC-DC DC-DC: Two-quadrant Converter

Q1
Q2
Va
Ia
T1
T2
D1
+
Va
-
D2
ia
+
Vdc
-
D2 conducts  va = 0
Va Eb
T1 conducts  va = Vdc
Quadrant 1 The average voltage is made larger than the back emf
DC DRIVES

Q1
Q2
Va
Ia
T1
T2
D1
+
Va
-
D2
ia
+
Vdc
-
D1 conducts  va = Vdc
DC DRIVES

Q1
Q2
Va
Ia
T1
T2
D1
+
Va
-
D2
ia
+
Vdc
-
T2 conducts  va = 0
Va
Eb
D1 conducts  va = Vdc
Quadrant 2 The average voltage is made smallerr than the back emf, thus
forcing the current to flow in the reverse direction
DC DRIVES

DC DRIVES
+
vc
2vtri
vc
+
vA
-
Vdc
0

leg A leg B
+ Va -
Q1
Q4
Q3
Q2
D1 D3
D2
D4
+
Vdc
-
va = Vdc when Q1 and Q2 are ON
Positive current
DC DRIVES
AC-DC-DC DC-DC: Four-quadrant Converter

leg A leg B
+ Va -
Q1
Q4
Q3
Q2
D1 D3
D2
D4
+
Vdc
-
va = -Vdc when D3 and D4 are ON
va = 0 when current freewheels through Q and D
Positive current
DC DRIVES

Positive current
va = Vdc when D1 and D2 are ON
Negative current
leg A leg B
+ Va -
Q1
Q4
Q3
Q2
D1 D3
D2
D4
+
Vdc
-
DC DRIVES

Positive current
va = -Vdc when Q3 and Q4 are ON
va = Vdc when D1 and D2 are ON
Negative current
leg A leg B
+ Va -
Q1
Q4
Q3
Q2
D1 D3
D2
D4
+
Vdc
-
DC DRIVES

DC DRIVES
AC-DC-DC
vAB
Vdc
-Vdc
Vdc
0
vB
vA
Vdc
0
2vtri
vc
vc
+
_
Vdc
+
vA
-
+
vB
-
Bipolar switching scheme – output
swings between VDC and -VDC

DC DRIVES
AC-DC-DC
Unipolar switching scheme – output
swings between Vdc and -Vdc
Vtri
vc
-vc
vc
+
_
Vdc
+
vA
-
+
vB
-
-vc
vA
Vdc
0
vB
Vdc
0
vAB
Vdc
0

DC DRIVES
AC-DC-DC
Bipolar switching scheme
0.04 0.0405 0.041 0.0415 0.042 0.0425 0.043 0.0435 0.044 0.0445 0.045
-200
-150
-100
-50
0
50
100
150
200
Unipolar switching scheme
0.04 0.0405 0.041 0.0415 0.042 0.0425 0.043 0.0435 0.044 0.0445 0.045
-200
-150
-100
-50
0
50
100
150
200
• Current ripple in unipolar is smaller
• Output frequency in unipolar is effectively doubled
Vdc
Vdc
Vdc
DC-DC: Four-quadrant Converter
Armature
current
Armature
current

AC DRIVES
AC-DC-AC
control
The common PWM technique: CB-SPWM with ZSS
SVPWM

• Control the torque, speed or position
• Cascade control structure
Motor
Example of current control in cascade control structure
converter
speed
controller
position
controller
-
+
*
1/s
+ +
- -
current
controller
T*
*


kT

Current controlled converters in DC Drives - Hysteresis-based
iref
+
Vdc
−
ia
iref
va
+
Va
-
ierr
ierr
q
q
• High bandwidth, simple implementation,
insensitive to parameter variations
• Variable switching frequency – depending on
operating conditions
+
_

Current controlled converters in AC Drives - Hysteresis-based
3-phase
AC Motor
+
+
+
i*a
i*b
i*c
Converter
• For isolated neutral load, ia + ib + ic = 0
control is not totally independent
• Instantaneous error for isolated neutral load can
reach double the band

id
iq
is
Dh
Dh Dh
Dh
• For isolated neutral load, ia + ib + ic = 0
control is not totally independent
• Instantaneous error for isolated neutral load can
reach double the band

powergui
Continuous
Universal Bridge 1
g
A
B
C
+
-
To Workspace1
iaref
Subsystem
c1
c2
c3
ina
inb
inc
p1
p2
p3
p4
p5
p6
Sine Wave 2
Sine Wave 1
Sine Wave
Series RLC Branch 3
Series RLC Branch 2
Series RLC Branch 1
Scope
DC Voltage Source Current Measurement 3
i
+
-
Current Measurement 2
i
+
-
i
+
-
• Dh = 0.3 A
• Sinusoidal reference current, 30Hz
• Vdc = 600V
• 10W,50mH load

0.005 0.01 0.015 0.02 0.025 0.03
-10
-5
0
5
10
Actual and reference currents Current error
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
4 6 8 10 12 14 16
x 10
-3
4
5
6
7
8
9
10

-10 -5 0 5 10
-10
-5
0
5
10
Actual current locus
0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06
-0.5
0
0.5
0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06
-0.5
0
0.5
0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06
-0.5
0
0.5
0.6A
0.6A
0.6A
Current error

vtri
Vdc
q
vc
q
Vdc
Pulse width
modulator
vc
Vdc
Pulse width
modulator
vc
iref
PI
+
-
q
Current controlled converters in DC Drives - PI-based

Motor
+
+
+
i*a
i*b
i*c
Converter
PWM
PWM
PWM
PWM
PWM
PWM
• Sinusoidal PWM
PI
PI
PI
• Interactions between phases  only require 2 controllers
• Tracking error

• Interactions between phases  only require 2 controllers
• Tracking error
• Perform the control in synchronous frame
- the current will appear as DC
• Perform the 3-phase to 2-phase transformation
- only two controllers (instead of 3) are used

Motor
i*a
i*b
i*c
Converter
PWM
+
+
+
PWM
PWM
PI
PI
PI
Current controlled converters in AC Drives - PI-based

Motor
i*a
i*b
i*c
Converter
3-2
3-2
SVM
2-3
PI
PI

id
*
iq
*
PI
controller
dqabc
abcdq
SVM
or SPWM
VSI
IM
va*
vb*
vc*
id
iq
+
+
-
-
PI
controller
Synch speed
estimator
s
s

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
-4
-2
0
2
4
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
-4
-2
0
2
4
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
0
1
2
3
4
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
0
1
2
3
4
Stationary - ia
Stationary - id
Rotating - ia Rotating - id

Modeling of the Power Converters: DC drives with Controlled rectifier
firing
circuit
controlled
rectifier

+
Va
–
vc
va(s)
vc(s)
DC motor
The relation between vc and va is determined by the firing circuit
?
It is desirable to have a linear relation between vc and va

Cosine-wave crossing control
Vm
vs
vc
0  2 3 4
Input voltage
Cosine wave compared with vc
Results of comparison trigger SCRs
Output voltage

Cosine-wave crossing control
Vm
vs
vc
0  2 3 4


Vscos(t)
Vscos() = vc









 -
s
c
1
v
v
cos
 


 cos
V
2
V m
a 
















 -
s
c
1
m
a
v
v
cos
cos
V
2
V
s
c
m
a
v
v
V
2
V


A linear relation between vc and Va

Va is the average voltage over one period of the waveform
- sampled data system
Delays depending on when the control signal changes – normally taken
as half of sampling period

s
2
T
H Ke
)
s
(
G
-

vc(s) Va(s)
s
m
V
V
2
K


Single phase, 50Hz
T=10ms
s
m
,
L
L
V
V
3
K

 -
Three phase, 50Hz
T=3.33ms
Simplified if control bandwidth is reduced to much lower than the
sampling frequency

firing
circuit
current
controller
controlled
rectifier

+
Va
–
vc
iref
• To control the current – current-controlled converter
• Torque can be controlled
• Only operates in Q1 and Q4 (single converter topology)

powergui
Continuous
Voltage Measurement4
v
+
-
v
+
-
v
+
-
v
+
-
Voltage Measurement
v
+
-
Universal Bridge
g
A
B
C
+
-
acos
To Workspace2
ir
To Workspace1
ia
To Workspace
v
Synchronized
6-Pulse Generator
alpha_deg
AB
BC
CA
Block
pulses
Step
Signal
Generator
Series RLC Branch
Scope 3
Scope 2
Scope 1
Scope
Saturation
PID Controller 1
PID
Mux
Mux
-K-
i
+
-
Current Measurement
i
+
-
Controlled Voltage Source
s
-
+
Constant 1
7
AC Voltage Source 2
AC Voltage Source 1
AC Voltage Source
• Input 3-phase, 240V, 50Hz • Closed loop current control
with PI controller

• Input 3-phase, 240V, 50Hz • Closed loop current control
with PI controller
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-500
0
500
1000
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
5
10
15
Voltage
Current
0.22 0.23 0.24 0.25 0.26 0.27 0.28
-500
0
500
1000
0.22 0.23 0.24 0.25 0.26 0.27 0.28
0
5
10
15

Modeling of the Power Converters: DC drives with SM Converters

vc
+
Va
−
vtri
Vdc
q
Switching signals obtained by comparing
control signal with triangular wave
Va(s)
vc(s)
DC motor
We want to establish a relation between vc and Va
?
AVERAGE voltage

dt
q
T
1
d
tri
T
t
t
tri



tri
on
T
t

Vdc
0
Ttri
ton
0
1




0
1
q
Vc > Vtri
Vc < Vtri
vc
dc
dT
0
dc
tri
a dV
dt
V
T
1
V
tri

 

-Vtri
Vtri
-Vtri
vc
d
vc
0.5
For vc = -Vtri  d = 0

0.5
Vtri
Vtri
vc
d
vc
-Vtri
-Vtri
For vc = 0  d = 0.5
For vc = Vtri  d = 1

0.5
vc
d
-Vtri
-Vtri
c
tri
v
V
2
1
5
.
0
d 

Vtri
Vtri
vc
For vc = 0  d = 0.5
For vc = Vtri  d = 1

Thus relation between vc and Va is obtained as:
c
tri
dc
dc
a v
V
2
V
V
5
.
0
V 

Introducing perturbation in vc and Va and separating DC and AC components:
c
tri
dc
dc
a v
V
2
V
V
5
.
0
V 

c
tri
dc
a v
~
V
2
V
v
~ 
DC:
AC:

Taking Laplace Transform on the AC, the transfer function is obtained as:
tri
dc
c
a
V
2
V
)
s
(
v
)
s
(
v

va(s)
vc(s)
DC motor
tri
dc
V
2
V

2vtri
vc
vc
vtri
+
Vdc
−
q
-Vdc
q
Vdc
+ VAB -
vAB
Vdc
-Vdc
c
tri
dc
AB
B
A v
V
V
V
V
V 

-
tri
c
A
B
V
2
v
5
.
0
d
1
d -

-

c
tri
dc
dc
B v
V
2
V
V
5
.
0
V -

vB
Vdc
0
tri
c
A
V
2
v
5
.
0
d 

c
tri
dc
dc
A v
V
2
V
V
5
.
0
V 

vA
Vdc
0

tri
dc
c
a
V
V
)
s
(
v
)
s
(
v

va(s)
vc(s)
DC motor
tri
dc
V
V

+
Vdc
−
vc
vtri
qa
Vdc
-vc
vtri
qb
Leg a
Leg b
The same average value we’ve seen for bipolar !
Vtri
vc
-vc
tri
c
A
V
2
v
5
.
0
d 

c
tri
dc
dc
A v
V
2
V
V
5
.
0
V 

vA
tri
c
B
V
2
v
5
.
0
d
-


c
tri
dc
dc
B v
V
2
V
V
5
.
0
V -

vB
c
tri
dc
AB
B
A v
V
V
V
V
V 

-
vAB

tri
dc
c
a
V
V
)
s
(
v
)
s
(
v

va(s)
vc(s)
DC motor
tri
dc
V
V

DC motor – separately excited or permanent magnet
Extract the dc and ac components by introducing small
perturbations in Vt, ia, ea, Te, TL and m
a
a
a
a
a
t e
dt
di
L
R
i
v 


Te = kt ia ee = kt 
dt
d
J
T
T m
l
e



a
a
a
a
a
t e
~
dt
i
~
d
L
R
i
~
v
~ 


)
i
~
(
k
T
~
a
E
e 
)
~
(
k
e
~
E
e 

dt
)
~
(
d
J
~
B
T
~
T
~
L
e





ac components
a
a
a
t E
R
I
V 

a
E
e I
k
T 

 E
e k
E
)
(
B
T
T L
e 


dc components

Perform Laplace Transformation on ac components
a
a
a
a
a
t e
~
dt
i
~
d
L
R
i
~
v
~ 


)
i
~
(
k
T
~
a
E
e 
)
~
(
k
e
~
E
e 

dt
)
~
(
d
J
~
B
T
~
T
~
L
e





Vt(s) = Ia(s)Ra + LasIa + Ea(s)
Te(s) = kEIa(s)
Ea(s) = kE(s)
Te(s) = TL(s) + B(s) + sJ(s)

T
k
a
a sL
R
1

)
s
(
Tl
)
s
(
Te
sJ
B
1

E
k
)
s
(
Ia )
s
(

)
s
(
Va
+
-
-
+

Tc
vtri
+
Vdc
−
q
q
+
–
kt
Torque
controller
T
k
a
a sL
R
1

)
s
(
Tl
)
s
(
Te
sJ
B
1

E
k
)
s
(
Ia )
s
(

)
s
(
Va
+
-
-
+
Torque
controller
Converter
peak
,
tri
dc
V
V
)
s
(
Te
-
+
DC motor

Design procedure in cascade control structure
• Inner loop (current or torque loop) the fastest –
largest bandwidth
• The outer most loop (position loop) the slowest –
smallest bandwidth
• Design starts from torque loop proceed towards
outer loops
Closed-loop speed control – an example

OBJECTIVES:
• Fast response – large bandwidth
• Minimum overshoot
good phase margin (>65o)
• Zero steady state error – very large DC gain
BODE PLOTS
• Obtain linear small signal model
METHOD
• Design controllers based on linear small signal model
• Perform large signal simulation for controllers verification

Ra = 2 W La = 5.2 mH
J = 152 x 10–6 kg.m2
B = 1 x10–4 kg.m2/sec
kt = 0.1
Nm/A
ke = 0.1 V/(rad/s)
Vd = 60 V Vtri = 5 V
fs = 33
kHz
• PI controllers • Switching signals from comparison
of vc and triangular waveform

Bode Diagram
Frequency (rad/sec)
-50
0
50
100
150
From: Input Point To: Output Point
Magnitude
(dB)
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
-90
-45
0
45
90
Phase
(deg)
compensated
compensated
kpT= 90
kiT= 18000
Torque controller design
Open-loop gain

Speed controller design
1
Speed
controller
sJ
B
1

* T* T 
–
+
Torque loop

Bode Diagram
Frequency (Hz)
-50
0
50
100
150
From: Input Point To: Output Point
Magnitude
(dB)
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
-180
-135
-90
-45
0
Phase
(deg)
Open-loop gain
compensated
kps= 0.2
kis= 0.14
compensated
Speed controller design

Large Signal Simulation results
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
-40
-20
0
20
40
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
-2
-1
0
1
2
Speed
Torque

Modeling of the Power Converters: IM drives
INDUCTION MOTOR DRIVES
Scalar Control Vector Control
Const. V/Hz is=f(r) FOC DTC
Rotor Flux Stator Flux Circular
Flux
Hexagon
Flux
DTC
SVM

Control of induction machine based on steady-state model (per phase SS
equivalent circuit):
Rr’/s
+
Vs
–
Rs
Lls Llr’
+
Eag
–
Is Ir’
Im
Lm

r
s
Trated
Pull out
Torque
(Tmax)
Te
s
sm rated
rotor
TL
Te
Intersection point
(Te=TL) determines the
steady –state speed

Given a load T– characteristic, the steady-state speed can be
changed by altering the T– of the motor:
Pole changing
Synchronous speed change with no.
of poles
Discrete step change in speed
Variable voltage (amplitude), frequency
fixed
E.g. using transformer or triac
Slip becomes high as voltage reduced –
low efficiency
Variable voltage (amplitude), variable
frequency (Constant V/Hz)
Using power electronics converter
Operated at low slip frequency

Variable voltage, fixed frequency
0 20 40 60 80 100 120 140 160
0
100
200
300
400
500
600
Torque
w (rad/s)
Lower speed  slip
higher
Low efficiency at low
speed
e.g. 3–phase squirrel cage IM
V = 460 V Rs= 0.25 W
Rr=0.2 W Lr = Ls =
0.5/(2*pi*50)
Lm=30/(2*pi*50)
f = 50Hz p = 4

Constant V/Hz
Approximates constant air-gap flux when Eag is large
Eag = k f ag
f
V
f
Eag


ag
 = constant
Speed is adjusted by varying f - maintaining V/f constant to avoid
flux saturation
To maintain V/Hz constant
+
V
_
+
Eag
_

0 20 40 60 80 100 120 140 160
0
100
200
300
400
500
600
700
800
900
Torque
50Hz
30Hz
10Hz
Constant V/Hz

Vrated
frated
Vs
f
Constant V/Hz

VSI
Rectifier
3-phase
supply IM
Pulse
Width
Modulator
s* +
Ramp
f
C
V
Constant V/Hz

To Workspace1
speed
To Workspace
torque
Subsystem
In1Out1
Step Slider
Gain 1
0.41147
Scope
Rate Limiter
Induction Machine
Va
Vb
Vc
isd
isq
ird
speed
Vd
irq
Vq
Te
Constant V /Hz
In1
Out1
Out2
Out3
Constant V/Hz
Simulink blocks for Constant V/Hz Control

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-100
0
100
200
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-200
0
200
400
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-100
0
100
200
Constant V/Hz
Speed
Torque
Stator phase current

Problems with open-loop constant V/f
At low speed, voltage drop across stator impedance is significant
compared to airgap voltage - poor torque capability at low speed
Solution:
1. Boost voltage at low speed
2. Maintain Im constant – constant ag

0 20 40 60 80 100 120 140 160
0
100
200
300
400
500
600
700
Torque
50Hz
30Hz
10Hz
A low speed, flux falls below
the rated value

With compensation (Is,ratedRs)
0 20 40 60 80 100 120 140 160
0
100
200
300
400
500
600
700
Torque
•Torque deteriorate at low
frequency – hence
compensation commonly
performed at low
frequency
•In order to truly
compensate need to
measure stator current –
seldom performed

With voltage boost at low frequency
Vrated
frated
Linear offset
Non-linear offset – varies with Is
Boost

Poor speed regulation
Solution:
1. Compesate slip
2. Closed-loop control
Problems with open-loop constant V/f

VSI
Rectifier
3-phase
supply IM
Pulse
Width
Modulator
Vboost
Slip speed
calculator
s*
+
+
+
+ V
Vdc Idc
Ramp
f
C

A better solution : maintain ag constant. How?
ag, constant → Eag/f , constant → Im, constant (rated)
maintain at rated
Controlled to maintain Im at rated
Rr’/s
+
Vs
–
Rs
Lls Llr’
+
Eag
–
Is
Ir’
Im
Lm

0 20 40 60 80 100 120 140 160
0
100
200
300
400
500
600
700
800
900
Torque
50Hz
30Hz
10Hz
Constant air-gap flux

s
r
m
lr
r
lr
m I
s
R
)
L
L
(
j
s
R
L
j
I






,
I
1
T
1
j
1
T
j
I
I
s
R
L
1
j
s
R
L
j
I
s
r
r
r
slip
r
slip
m
s
r
r
r
r
r
r
m
































,
I
1
T
j
1
T
1
j
I m
r
slip
r
r
r
slip
s
















• Current is controlled using current-
controlled VSI
• Dependent on rotor parameters –
sensitive to parameter variation

VSI
Rectifier
3-phase
supply IM
*
+
+ |Is|
slip
C
Current
controller
s
PI
+
r
-

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