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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 2Vm
+ 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
dqabc PI controller
vb*
SVM or SPWM VSI
vc*
s
Synch speed estimator
s
abcdq
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 coscos 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 2 Vtri
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
v t ia R a L a
di a ea dt
Te = kt ia
d m Te Tl J 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 Ea Te k E Ia
~ ~) ee 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)
~ ~) ee 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,pe ak
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 rotors
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 jslipTr 1 jslip r Tr 1 1 r
Is
Is ,
jslip r Tr 1 1 r Is Im , jslipTr 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
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 2Vm
+ 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
dqabc PI controller
vb*
SVM or SPWM VSI
vc*
s
Synch speed estimator
s
abcdq
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 coscos 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 2 Vtri
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
v t ia R a L a
di a ea dt
Te = kt ia
d m Te Tl J 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 Ea Te k E Ia
~ ~) ee 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)
~ ~) ee 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,pe ak
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 rotors
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 jslipTr 1 jslip r Tr 1 1 r
Is
Is ,
jslip r Tr 1 1 r Is Im , jslipTr 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
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