Transcript Electrical Drives: An application of Power Electronics

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
Power Electronic Systems
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
Input
Source
- AC
- DC
- unregulated
Reference
sensors
Power Electronics
Converters
Load
Output
- AC
- DC
Controller
POWER ELECTRONIC
CONVERTERS – the
heart of power a power
electronics system
Power Electronic Systems
Why Power Electronics ?
Power semiconductor devices
Power switches
isw
ON or OFF
+
vsw −
=0
isw = 0
Ploss = vsw× isw = 0
+
Losses ideally ZERO !
vsw −
Power Electronic Systems
Why Power Electronics ?
Power semiconductor devices
-
A
K
K
K
ia
Power switches
-
G
G
Vak
Vak
Vak
+
+
+
A
ia
A
ia
Power Electronic Systems
Why Power Electronics ?
Power semiconductor devices
Power switches
D
iD
C
ic
+
+
VDS
G
-
G
VCE
-
S
E
Power Electronic Systems
Why Power Electronics ?
Passive elements
+
VL
-
iL
High frequency
transformer
+
+
V1
V2
-
-
Inductor
+
iC
VC
-
Power Electronic Systems
Why Power Electronics ?
sensors
Input
Source
- AC
- DC
- unregulated
Reference
Power Electronics
Converters
IDEALLY LOSSLESS
Load !
Output
- AC
- DC
Controller
Power Electronic Systems
Why Power Electronics ?
Other factors:
• Improvements in power semiconductors fabrication
•
Power Integrated Module (PIM), Intelligent Power
Modules (IPM)
• Decline cost in power semiconductor
• Advancement in semiconductor fabrication
•
ASICs
•
Faster and cheaper to implement complex
algorithm
•
FPGA
•
DSPs
Power Electronic Systems
Some Applications of Power Electronics :
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
Power rating of < 1 W (portable equipment)
Tens or hundreds Watts (Power supplies for computers /office equipment)
kW to MW : drives
Hundreds of MW in DC transmission system (HVDC)
Modern Electrical Drive Systems
•
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
DC motors (brushed)
SRM
BLDC
AC motors
- IM
- PMSM
Modern Electrical Drive Systems
Classic Electrical Drive for Variable Speed Application :
•
Bulky
•
Inefficient
•
inflexible
Modern Electrical Drive Systems
Typical Modern Electric Drive Systems
Electric Motor
Power Electronic Converters
Electric Energy
- Unregulated -
POWER IN
Electric Energy
- Regulated -
Power
Electronic
Converters
Moto
r
feedback
Reference
Controller
Electric
Energy
Mechanical
Energy
Load
Modern Electrical Drive Systems
Example on VSD application
Variable Speed Drives
Constant speed
valve
Supply
motor
pump
Power out
Power
In
Power loss
Mainly in valve
Modern Electrical Drive Systems
Example on VSD application
Variable Speed Drives
Constant speed
valve
Supply
motor
Supply
pump
PEC
Power out
Power
In
motor
pump
Power out
Power
In
Power loss
Mainly in valve
Power loss
Modern Electrical Drive Systems
Example on VSD application
Variable Speed Drives
Constant speed
valve
Supply
motor
Supply
pump
PEC
Power out
Power
In
motor
pump
Power out
Power
In
Power loss
Mainly in valve
Power loss
Modern Electrical Drive Systems
Example on VSD application
Electric motor consumes more than half of electrical energy in the US
Fixed speed
Variable speed
Improvements in energy utilization in electric motors give large
impact to the overall energy consumption
HOW ?
Replacing fixed speed drives with variable speed drives
Using the high efficiency motors
Improves the existing power converter–based drive systems
Modern Electrical Drive Systems
Overview of AC and DC drives
DC drives: Electrical drives that use DC motors as the prime mover
Regular maintenance, heavy, expensive, speed limit
Easy control, decouple control of torque and flux
AC drives: Electrical drives that use AC motors as the prime mover
Less maintenance, light, less expensive, high speed
Coupling between torque and flux – variable spatial angle
between rotor and stator flux
Modern Electrical Drive Systems
Overview of AC and DC drives
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
Modern Electrical Drive Systems
Overview of AC and DC drives
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
Modern Electrical Drive Systems
Overview of AC and DC drives
Extracted from Boldea & Nasar
Power Electronic Converters in ED Systems
Converters for Motor Drives
(some possible configurations)
DC Drives
DC Source
AC Source
DC-AC-DC
AC-DC
AC Drives
AC-DC-DC
DC Source
AC Source
DC-DC
AC-DC-AC
Const.
DC
Variable
DC
AC-AC
NCC
FCC
DC-AC
DC-DC-AC
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
Power Electronic Converters in ED Systems
DC DRIVES
Available AC source to control DC motor (brushed)
AC-DC
AC-DC-DC
Uncontrolled Rectifier
Control
Controlled Rectifier
Single-phase
Three-phase
Single-phase
Three-phase
Control
DC-DC Switched mode
1-quadrant, 2-quadrant
4-quadrant
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC
400
200
0
+
50Hz
1-phase
Vo 
Vo
2Vm
cos 

-200
-400
0.4
0.405
0.41
0.415
0.42
0.425
0.43
0.435
0.44
0.405
0.41
0.415
0.42
0.425
0.43
0.435
0.44
0.405
0.41
0.415
0.42
0.425
0.43
0.435
0.44
0.405
0.41
0.415
0.42
0.425
0.43
0.435
0.44
10
Average voltage
over 10ms
-
5
0
0.4
500
0
50Hz
3-phase
+
Vo
-
-500
Vo 
3VL - L,m

0.4
cos
30
20
Average voltage
over 3.33 ms
10
0
0.4
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC
2 Vm

+
50Hz
1-phase
Vo 
Vo
2Vm
cos 

90o
180o
90o
180o
Average voltage
over 10ms
-
-
2 Vm

3VL - L ,m
50Hz
3-phase

+
Vo
-
Vo 
3VL - L,m

cos
Average voltage
over 3.33 ms
-
3VL - L ,m

Power Electronic Converters in ED Systems
DC DRIVES
AC-DC
ia
Vt
+
3-phase
supply
Vt
Q2
Q1
-
Q3
Q4
- Operation in quadrant 1 and 4 only
Ia
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC
3phase
supply
+
3-phase
supply
Vt
-

Q2
Q1
Q3
Q4
T
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC
R1
F1
3-phase
supply
+
Va
F2
R2

Q2
Q1
Q3
Q4
-
T
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC
Cascade control structure with armature reversal (4-quadrant):
iD

ref +
Speed
controller
_
iD,ref +
_
iD,ref
iD,
Current
Controller
Armature
reversal
Firing
Circuit
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
Uncontrolled
rectifier
control
Switch Mode DC-DC
1-Quadrant
2-Quadrant
4-Quadrant
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
control
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
DC-DC: Two-quadrant Converter
Va
+
T1
D1
ia
Vdc
-
Q2
Ia
+
T2
Q1
D2
Va
-
T1 conducts  va = Vdc
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
DC-DC: Two-quadrant Converter
Va
+
T1
D1
ia
Vdc
-
Q2
Q1
Ia
+
T2
D2
Va
-
D2 conducts  va = 0
Va
T1 conducts  va = Vdc
Eb
Quadrant 1 The average voltage is made larger than the back emf
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
DC-DC: Two-quadrant Converter
Va
+
T1
D1
ia
Vdc
-
Q2
Ia
+
T2
Q1
D2
Va
-
D1 conducts  va = Vdc
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
DC-DC: Two-quadrant Converter
Va
+
T1
D1
ia
Vdc
-
Q2
Q1
Ia
+
T2
D2
Va
-
T2 conducts  va = 0
Va
D1 conducts  va = Vdc
Eb
Quadrant 2 The average voltage is made smallerr than the back emf, thus
forcing the current to flow in the reverse direction
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
DC-DC: Two-quadrant Converter
2vtri
+
vA
vc
Vdc
-
0
+
vc
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
DC-DC: Four-quadrant Converter
leg A
+
Q1
leg B
D3
D1
+
Va
-
Q3
Vdc
-
Positive current
va = Vdc
when Q1 and Q2 are ON
Q4
D4
D2
Q2
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
DC-DC: Four-quadrant Converter
leg A
+
Q1
leg B
D3
D1
+
Va
-
Q3
Vdc
-
Q4
D4
Positive current
va = Vdc
when Q1 and Q2 are ON
va = -Vdc
when D3 and D4 are ON
va = 0
when current freewheels through Q and D
D2
Q2
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
DC-DC: Four-quadrant Converter
leg A
+
Q1
leg B
D3
D1
+
Va
-
Q3
Vdc
-
Q4
D4
Positive current
va = Vdc
when Q1 and Q2 are ON
va = -Vdc
when D3 and D4 are ON
va = 0
when current freewheels through Q and D
D2
Q2
Negative current
va = Vdc
when D1 and D2 are ON
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
DC-DC: Four-quadrant Converter
leg A
+
Q1
leg B
D3
D1
+
Va
-
Q3
Vdc
-
Q4
D4
Positive current
D2
Q2
Negative current
va = Vdc
when Q1 and Q2 are ON
va = Vdc
when D1 and D2 are ON
va = -Vdc
when D3 and D4 are ON
va = -Vdc
when Q3 and Q4 are ON
va = 0
when current freewheels through Q and D
va = 0
when current freewheels through Q and D
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
Bipolar switching scheme – output
swings between VDC and -VDC
2vtri
Vdc
+
vA
+
vB
-
-
vA
vc
Vdc
0
Vdc
vB
0
Vdc
vc
vAB
+
_
-Vdc
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
Unipolar switching scheme – output
swings between Vdc and -Vdc
vc
Vtri
-vc
Vdc
+
vA
+
vB
-
-
Vdc
vA
0
Vdc
vc
vB
+
_
-vc
0
Vdc
vAB
0
Power Electronic Converters in ED Systems
DC DRIVES
AC-DC-DC
DC-DC: Four-quadrant Converter
Armature
current
200
150
Vdc
Vdc
200
Vdc
100
100
50
50
0
0
-50
-50
-100
-100
-150
-150
-200
-200
0.04
Armature
current
150
0.0405 0.041
0.0415 0.042
0.0425 0.043
0.0435 0.044
0.0445 0.045
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
Unipolar switching scheme
•
Current ripple in unipolar is smaller
•
Output frequency in unipolar is effectively doubled
Power Electronic Converters in ED Systems
AC DRIVES
AC-DC-AC
control
The common PWM technique:
CB-SPWM with ZSS
SVPWM
Modeling and Control of Electrical Drives
•
Control the torque, speed or position
•
Cascade control structure
Example of current control in cascade control structure
*
+
*
+
-
position
controller
-
T*
speed
controller
+
-
current
controller
kT

1/s
Motor
converter

Modeling and Control of Electrical Drives
Current controlled converters in DC Drives - Hysteresis-based
+
ia
Vdc
+
iref
Va
−
va
iref
+
_
ierr
q
•
High bandwidth, simple implementation,
insensitive to parameter variations
•
Variable switching frequency – depending on
operating conditions
q
ierr
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - Hysteresis-based
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
3-phase
AC Motor
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - Hysteresis-based
iq
is
Dh Dh
id
•
For isolated neutral load, ia + ib + ic = 0
control is not totally independent
•
Instantaneous error for isolated neutral load can
reach double the band
Dh Dh
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - Hysteresis-based
Continuous
• Dh = 0.3 A
• Sinusoidal reference current, 30Hz
• Vdc = 600V
• 10W,50mH load
powergui
Scope
iaref
g
To Workspace 1
+
A
DC Voltage Source
c1
p1
c2
p2
c3
p3
ina
p4
inb
p5
inc
p6
Subsystem
Sine Wave 2
-
Measurement 3
Series RLC Branch Current
3
C
Universal Bridge 1
i
+
-
Measurement 1
Series RLC BranchCurrent
1
i
+
Sine Wave
Sine Wave 1
B
i
+
-
Series RLC BranchCurrent
2
Measurement 2
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - Hysteresis-based
Current error
Actual and reference currents
0.5
10
0.4
0.3
5
0.2
10
0.1
0
0
9
-0.1
-0.2
8
-5
-0.3
-0.4
7
-10
0.005
-0.5
0.01
0.015
6
0.02
0.025
0.03
-0.5
-0.4
5
4
4
6
8
10
12
14
16
-3
x 10
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - Hysteresis-based
Current error
Actual current locus
10
0.5
5
0
0.6A
-0.5
0
0.04
0.042
0.044
0.046
0.048
0.05
0.052
0.054
0.056
0.058
0.06
-5
0.5
-10
-10
-5
0
5
10
0.6A
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
0.6A
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
Modeling and Control of Electrical Drives
Current controlled converters in DC Drives - PI-based
Vdc
iref +
-
PI
vc
vc
vPulse
width
tri
modulator
qqq
Modeling and Control of Electrical Drives
Current controlled converters in DC Drives - PI-based
i*a
i*b
i*c
+
PI
PWM
Converter
+
PI
+
PWM
PI
PWM
• Sinusoidal PWM
• Interactions between phases  only require 2 controllers
• Tracking error
Motor
Modeling and Control of Electrical Drives
Current controlled converters in DC Drives - PI-based
• Perform the 3-phase to 2-phase transformation
- only two controllers (instead of 3) are used
• Perform the control in synchronous frame
- the current will appear as DC
• Interactions between phases  only require 2 controllers
• Tracking error
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - PI-based
i*a
i*b
i*c
+
PI
PWM
Converter
+
PI
+
PWM
PI
PWM
Motor
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - PI-based
i*a
PI
i*b
SVM
2-3
3-2
Converter
PI
i*c
3-2
Motor
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - PI-based
va*
id*
PI
controller
+
-
iq* +
-
iq
id
dqabc
PI
controller
vb*
SVM
or SPWM
VSI
vc*
s
Synch speed
estimator
s
abcdq
IM
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - PI-based
Stationary - ia
4
2
3
0
2
-2
1
-4
0
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
0.01
Rotating - ia
4
0
3
0
2
-2
1
0
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
0
0.01
0
0.002 0.004 0.006 0.008
0.01
0.012 0.014 0.016 0.018
0.02
0.01
0.012 0.014 0.016 0.018
0.02
Rotating - id
4
2
-4
Stationary - id
4
0
0.002 0.004 0.006 0.008
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
+
vc

firing
circuit
controlled
rectifier
Va
–
vc(s)
?
va(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
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
Cosine-wave crossing control
Vm
0
vc

3
2
vs
Input voltage
4
Cosine wave compared with vc
Results of comparison trigger SCRs
Output voltage
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
Cosine-wave crossing control
cos(t)= vc
Vscos()
Vm
0

2
vc
3
v 
  cos -1  c 
 vs 
4
vs

2Vm v c  -1  v c  
   
coscos
Va 
 vs 
 vs 

A linear relation between vc and Va
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
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
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
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
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
G H (s)  Ke
T
- s
2
Single phase, 50Hz
vc(s)
Va(s)
K
2Vm
Vs
T=10ms
Three phase, 50Hz
K
3VL - L ,m
Vs
T=3.33ms
Simplified if control bandwidth is reduced to much lower than the
sampling frequency
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
+
iref
current
controller
vc
firing
circuit
 controlled
rectifier
Va
–
• To control the current – current-controlled converter
• Torque can be controlled
• Only operates in Q1 and Q4 (single converter topology)
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
•
•
Input 3-phase, 240V, 50Hz
Closed loop current control
with PI controller
Scope 3
+
- v
Continuous
Voltage Measurement4
i
+
-
AC Voltage Source
powergui
Scope 2
Current Measurement 1
Step
AC Voltage Source 1
+
g
A
AC Voltage Source 2
+
s
v
Controlled Voltage Source
Series RLC Branch
To Workspace
B
+
- v
C
Universal Bridge
Voltage Measurement2
+
- v
Voltage Measurement
-
i
- +
ia
Current Measurement
To Workspace1
+
- v
alpha_deg
Voltage Measurement3
Mux
AB
BC
+
- v
Voltage Measurement1
Scope
pulses
CA
Block
Synchronized
Mux
6-Pulse Generator
Scope 1
ir
To Workspace2
PID
Signal
PID Controller Saturation
1
Generator
7
Constant 1
acos
-K -
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
•
•
Input 3-phase, 240V, 50Hz
Closed loop current control
with PI controller
1000
1000
500
500
Voltage
0
0
-500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-500
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.25
0.26
0.27
0.28
15
15
10
10
5
Current
5
0
0.22
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.23
0.24
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Vdc
Switching signals obtained by comparing
control signal with triangular wave
+
Va
−
vtri
q
vc
We want to establish a relation between vc and Va
AVERAGE voltage
vc(s)
?
Va(s)
DC motor
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Ttri
1
q
0
vc
1
0
1
d
Ttri
Vc > Vtri
Vc < Vtri

t
t  Ttri
q dt
t on

Ttri
ton
Vdc
1 dTtri
Va   Vdc dt  dVdc
Ttri 0
0
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
d
0.5
vc
-Vtri
Vtri
vc
-Vtri
For vc = -Vtri  d = 0
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
d
0.5
vc
-Vtri
-Vtri
Vtri
vc
Vtri
For vc = -Vtri  d = 0
For vc = 0 
d = 0.5
For vc = Vtri 
d=1
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
d
0.5
-Vtri
-Vtri
vc
Vtri
Vtri
vc
1
d  0.5 
vc
2Vtri
For vc = -Vtri  d = 0
For vc = 0 
d = 0.5
For vc = Vtri 
d=1
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Thus relation between vc and Va is obtained as:
Va  0.5Vdc 
Vdc
vc
2Vtri
Introducing perturbation in vc and Va and separating DC and AC components:
DC:
Vdc
Va  0.5Vdc 
vc
2Vtri
AC:
Vdc ~
~
va 
vc
2Vtri
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Taking Laplace Transform on the AC, the transfer function is obtained as:
v a ( s)
Vdc

v c ( s) 2Vtri
vc(s)
Vdc
2Vtri
va(s)
DC motor
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Bipolar switching scheme
Vdc
-Vdc
q
vtri
vc
2vtri
+
Vdc
vA
Vdc
+ VAB
0
-
−
vc
Vdc
vB
0
q
Vdc
v
d A  0.5  c
2Vtri
VA  0.5Vdc 
Vdc
vc
2Vtri
v
dB  1 - d A  0.5 - c
2Vtri
VB  0.5Vdc -
Vdc
vc
2Vtri
vAB
-Vdc
VA - VB  VAB 
Vdc
vc
Vtri
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Bipolar switching scheme
v a ( s) Vdc

v c ( s) Vtri
vc(s)
Vdc
Vtri
va(s)
DC motor
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Vdc
Unipolar switching scheme
vc
Leg b
Vtri
-vc
+
vtri
Vdc
qa
vc
−
vA
Leg a
vtri
d A  0.5 
vB
qb
-vc
vc
2Vtri
VA  0.5Vdc 
Vdc
vc
2Vtri
dB  0.5 
VB  0.5Vdc -
- vc
2Vtri
Vdc
vc
2Vtri
vAB
VA - VB  VAB 
The same average value we’ve seen for bipolar !
Vdc
vc
Vtri
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Unipolar switching scheme
v a ( s) Vdc

v c ( s) Vtri
vc(s)
Vdc
Vtri
va(s)
DC motor
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
DC motor – separately excited or permanent magnet
dia
v t  ia Ra  L a
 ea
dt
Te = kt ia
Te  Tl  J
dm
dt
e e = kt 
Extract the dc and ac components by introducing small
perturbations in Vt, ia, ea, Te, TL and m
ac components
~
d
i
~
~
v t  ia R a  L a a  ~
ea
dt
~
~
Te  k E ( ia )
dc components
Vt  Ia R a  E a
Te  k E Ia
~
~)
e e  k E (
Ee  k E
~)
d(
~
~
~
Te  TL  B  J
dt
Te  TL  B()
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
DC motor – separately excited or permanent magnet
Perform Laplace Transformation on ac components
~
d
i
~
~
v t  ia R a  L a a  ~
ea
dt
Vt(s) = Ia(s)Ra + LasIa + Ea(s)
~
~
Te  k E ( ia )
Te(s) = kEIa(s)
~
~)
e e  k E (
Ea(s) = kE(s)
~)
d(
~
~
~
Te  TL  B  J
dt
Te(s) = TL(s) + B(s) + sJ(s)
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
DC motor – separately excited or permanent magnet
Tl (s )
Va (s )
+
-
1
R a  sL a
Ia (s )
kT
-
Te (s )
1
B  sJ
+
kE
(s )
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
q
vtri
Torque
controller
Tc
+
+
Vdc
–
−
q
kt
DC motor
Tl (s )
Converter
Te (s )
Torque
controller
+
-
Vdc
Vtri ,peak
Ia (s )
1
R a  sL a
Va (s )
+
kT
-
Te (s )
+
-
kE
1
B  sJ
(s )
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Closed-loop speed control – an example
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
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Closed-loop speed control – an example
OBJECTIVES:
•
Fast response – large bandwidth
•
Minimum overshoot
good phase margin (>65o)
•
BODE PLOTS
Zero steady state error – very large DC gain
METHOD
•
Obtain linear small signal model
•
Design controllers based on linear small signal model
•
Perform large signal simulation for controllers verification
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Closed-loop speed control – an example
Ra = 2 W
La = 5.2 mH
B = 1 x10–4 kg.m2/sec
J = 152 x 10–6 kg.m2
ke = 0.1 V/(rad/s)
kt = 0.1
Nm/A
Vd = 60 V
Vtri = 5 V
fs = 33
kHz
• PI controllers
• Switching signals from comparison
of vc and triangular waveform
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Torque controller design
Open-loop gain
Bode Diagram
From: Input Point To: Output Point
150
kpT= 90
Magnitude (dB)
100
compensated
kiT= 18000
50
0
-50
90
Phase (deg)
45
0
compensated
-45
-90
-2
10
-1
10
0
10
1
10
2
10
Frequency (rad/sec)
3
10
4
10
5
10
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Speed controller design
*
+
–
T*
Speed
controller
Torque loop
1
T
1
B  sJ

Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Speed controller design
Open-loop gain
Bode Diagram
From: Input Point To: Output Point
150
kps= 0.2
Magnitude (dB)
100
kis= 0.14
50
compensated
0
-50
0
Phase (deg)
-45
-90
-135
compensated
-180
-2
10
-1
10
0
10
1
10
Frequency (Hz)
2
10
3
10
4
10
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Large Signal Simulation results
40
20
Speed
0
-20
-40
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
2
1
Torque
0
-1
-2
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
INDUCTION MOTOR DRIVES
Scalar Control
Const. V/Hz
Vector Control
is=f(r)
FOC
Rotor Flux
Stator Flux
DTC
Circular
Flux
Hexagon
Flux
DTC
SVM
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Control of induction machine based on steady-state model (per phase SS
equivalent circuit):
Rs
Is
Llr’
Lls
+
Vs
–
Lm
+
Eag
Im
Ir ’
–
Rr’/s
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Te
Pull out
Torque
(Tmax)
Te
TL
Trated
s
Intersection point
(Te=TL) determines the
steady –state speed
sm
rated
rotors
r
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
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), variable
frequency (Constant V/Hz)
Using power electronics converter
Operated at low slip frequency
Variable voltage (amplitude), frequency
fixed
E.g. using transformer or triac
Slip becomes high as voltage reduced –
low efficiency
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Variable voltage, fixed frequency
e.g. 3–phase squirrel cage IM
600
Torque
V = 460 V
Rs= 0.25 W
500
Rr=0.2 W Lr = Ls =
0.5/(2*pi*50)
400
Lm=30/(2*pi*50)
f = 50Hz
300
Lower speed  slip
higher
Low efficiency at low
speed
200
100
0
p=4
0
20
40
60
80
w (rad/s)
100
120
140
160
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Constant V/Hz
To maintain V/Hz constant
Approximates constant air-gap flux when Eag is large
+
V
+
Eag
_
_
ag = constant
Eag = k f ag

E ag
f

V
f
Speed is adjusted by varying f - maintaining V/f constant to avoid
flux saturation
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Constant V/Hz
900
800
50Hz
700
30Hz
Torque
600
500
10Hz
400
300
200
100
0
0
20
40
60
80
100
120
140
160
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Constant V/Hz
Vs
Vrated
frated
f
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Constant V/Hz
Rectifier
3-phase
supply
VSI
IM
C
f
Ramp
s*
+
V
Pulse
Width
Modulator
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Constant V/Hz
In1 Out 1
Subsystem
isd
Va
isq
Out1
ird
speed
0.41147
Step
Slider
Gain 1
In 1
Rate Limiter
Out2
Vb
Vd
Scope
irq
Out3
Constant V /Hz
Vq
Vc
Te
speed
Induction Machine
To Workspace 1
torque
To Workspace
Simulink blocks for Constant V/Hz Control
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Constant V/Hz
200
100
Speed
0
-100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
400
200
Torque
0
-200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
200
100
Stator phase current
0
-100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
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
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
700
600
50Hz
A low speed, flux falls below
the rated value
Torque
500
400
30Hz
300
10Hz
200
100
0
0
20
40
60
80
100
120
140
160
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
With compensation (Is,ratedRs)
700
• Torque deteriorate at low
frequency – hence
compensation commonly
performed at low
frequency
600
Torque
500
400
• In order to truly
compensate need to
measure stator current –
seldom performed
300
200
100
0
0
20
40
60
80
100
120
140
160
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
With voltage boost at low frequency
Vrated
Linear offset
Boost
Non-linear offset – varies with Is
frated
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Problems with open-loop constant V/f
Poor speed regulation
Solution:
1. Compesate slip
2. Closed-loop control
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Rectifier
3-phase
supply
VSI
IM
C
f
Ramp
s*
+
+
+
Slip speed
calculator
Vdc
Idc
V
+
Vboost
Pulse
Width
Modulator
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
A better solution : maintain ag constant. How?
ag, constant → Eag/f , constant → Im, constant (rated)
Rs
Is
Controlled to maintain Im at rated
Lls
Llr’
Ir ’
+
+
Vs
–
Lm
maintain at rated
Im
Eag
–
Rr’/s
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Constant air-gap flux
900
800
50Hz
700
30Hz
Torque
600
500
10Hz
400
300
200
100
0
0
20
40
60
80
100
120
140
160
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Constant air-gap flux
Im 
Im 
Im 
j L lr 
Rr
s
Is
R
j (L lr  L m )  r
s
j L r 
Rr
s
  
R
j  r L r  r
s
 1  r 
jslipTr  1
  
jslip  r Tr  1
 1  r 
Is
Is ,
 r 
Tr  1
jslip 
1  r 

Is 
Im ,
jslipTr  1
• Current is controlled using currentcontrolled VSI
• Dependent on rotor parameters –
sensitive to parameter variation
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Constant air-gap flux
3-phase
supply
VSI
Rectifier
IM
C
Current
controller
*
+
PI
-
slip
+
r
+
|Is|
s
THANK YOU