Power_Electronics

POWER ELECTRONICS
EPE 550
CIRCUITS, DEVICES, AND APPLICATIONS
ELECTRICAL DRIVES:
An Application of Power Electronics
Eng.Mohammed Alsumady

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 in 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)

Advancement in semiconductor fabrication
• A field-programmable gate array (FPGA) is an integrated circuit designed to be configured
by the customer or designer after manufacturing—hence "field-programmable". The FPGA
configuration is generally specified using a hardware description language (HDL), similar to
that used for an application-specific integrated circuit (ASIC) circuit diagrams were
previously used to specify the configuration, as they were for ASICs, but this is increasingly
rare). FPGAs can be used to implement any logical function that an ASIC could perform. The
ability to update the functionality after shipping, partial re-configuration of the portion of the
design and the low non-recurring engineering costs relative to an ASIC design
(notwithstanding the generally higher unit cost), offer advantages for many applications.
• FPGAs contain programmable logic components called "logic blocks", and a hierarchy of
reconfigurable interconnects that allow the blocks to be "wired together"—somewhat like
many (changeable) logic gates that can be inter-wired in (many) different configurations.
Logic blocks can be configured to perform complex combinational functions, or merely
simple logic gates like AND and XOR. In most FPGAs, the logic blocks also include memory
elements, which may be simple flip-flops or more complete blocks of memory.
• In addition to digital functions, some FPGAs have analog features. The most common analog
feature is programmable slew rate and drive strength on each output pin, allowing the
engineer to set slow rates on lightly loaded pins that would otherwise ring unacceptably, and
to set stronger, faster rates on heavily loaded pins on high-speed channels that would
otherwise run too slow. Another relatively common analog feature is differential comparators
on input pins designed to be connected to differential signaling channels.

A field-programmable gate array (FPGA)
• The FPGA industry sprouted from programmable read-only
memory (PROM) and programmable logic devices (PLDs).
PROMs and PLDs both had the option of being programmed
in batches in a factory or in the field (field programmable),
however programmable logic was hard-wired between logic
gates.
• A recent trend has been to take the coarse-grained architectural
approach a step further by combining the logic blocks and
interconnects of traditional FPGAs with embedded
microprocessors and related peripherals to form a complete
"system on a programmable chip“.

A field-programmable gate array (FPGA)

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
• IM: Induction Motor
• PMSM: Permanent Magnet Synchronous Motor
• SRM: Switched Reluctance Motor
• BLDC: Brushless DC Motor
AC motors
- IM
- PMSM
DC motors (brushed)
SRM
BLDC

Permanent Magnet Synchronous Motor
 The Permanent Magnet Synchronous motor is a rotating electric machine
where the stator is a classic three phase stator like that of an induction
motor and the rotor has permanent magnets. In this respect, the PM
Synchronous motor is equivalent to an induction motor, except the rotor
magnetic field in case of PMSM is produced by permanent magnets. The
use of a permanent magnet to generate a substantial air gap magnetic flux
makes it possible to design highly efficient PM motors. Medium
construction complexity, multiple fields, delicate magnets
• High reliability (no brush wear), even at very high achievable speeds
• High efficiency
• Low EMI
• Driven by multi-phase Inverter controllers
• Sensorless speed control possible
• Higher total system cost than for DC motors
• Smooth rotation - without torque ripple
• Appropriate for position control

Permanent Magnet Synchronous Motor

Switched Reluctance (SR) Motor
 Switched reluctance (SR) motor is a brushless AC motor. It has simple
mechanical construction and does not require permanent magnet for its
operation. The stator and rotor in a SR motor have salient poles. The
number of poles presence on the stator depends on the number of phases
the motor is designed to operate in. Normally, two stator poles at opposite
ends are configured to form one phase. In this configuration, a 3-phase SR
motor has 6 stator poles. The number of rotor poles are chosen to be
different to the number of stator poles. A 3-phase SR motor with 6 stator
poles and 4 rotor poles is also known as a 6/4 3-Phase SR motor.
 SR motor has the phase winding on its stator only. Concentrated windings
are used. The windings are inserted onto the stator poles and connected in
series to form one phase of the motor. In a 3-Phase SR motor, there are 3
pairs of concentrated windings and each pair of the winding is connected in
series to form each phase respectively.

Future Electric Motors Build will be SR Motors
• The small-size SR motor was developed by Akira Chiba, professor at the
Department of Electrical Engineering, Faculty of Science & Technology,
Tokyo University of Science.
• The prototyped SR motor has the same size as the 50kW synchronous
motor equipped in the second-generation Toyota Prius. Currently all
produced Electric cars are equipped with a synchronous motor whose
rotor is embedded with a permanent magnet.
• But as the permanent magnets are getting more and more pricey (the price
has doubled or tripled) because of higher demand, the future of SR
Motors is now imminent.
• A four-phase 8/6 switched-reluctance motor is shown in cross section. In
order to produce continuous shaft rotation, each of the four stator phases is
energized and then de-energized in succession at specific positions of the
rotor as illustrated.

Future electric motors build will be SR Motors.

Brushless DC Motor
• A BLDC motor has permanent magnets which rotate, and a fixed armature,
eliminating the problems of connecting current to the moving armature. An
electronic controller replaces the brush commutator assembly of the
brushed DC motor, which continually switches the phase to the windings to
keep the motor turning. The controller performs similar timed power
distribution by using a solid-state circuit rather than the brush commutator
system.
• BLDC motors offer several advantages over brushed DC motors, including
more torque per weight, more torque per watt (increased efficiency),
increased reliability, reduced noise, longer lifetime (no brush and
commutator erosion), elimination of ionizing sparks from the commutator,
and overall reduction of electromagnetic interference (EMI). With no
windings on the rotor, they are not subjected to centrifugal forces, and
because the windings are supported by the housing, they can be cooled by
conduction, requiring no airflow inside the motor for cooling. This in turn
means that the motor's internals can be entirely enclosed and protected
from dirt or other foreign matter.

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

Example on Variable Speed Drives (VSD) application
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
Example on VSD application

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
Example on VSD application

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 Electrical Drive 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

Power Electronic Converters in ED Systems
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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