1.
Power Electronics and Drives
–Modeling & Simulation
A Problem Based and Project Oriented
Learning
B.Chitti Babu
Member IEEE (USA), Student Member IET (UK)
Department of Electrical Engineering,
National Institute of Technology,Rourkela
bcbabunitrkl@ieee.org
B Chitti Babu,
14 August 2009 1
EE NIT Rourkela
2.
CONTENTS
Pre Requisite of Power Electronics System
Power Electronic 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
B Chitti Babu,
14 August 2009 2
EE NIT Rourkela
3.
Power ElectronicsAn Enabling Technology
Energy System
REFRIGERATOR
SOLAR CELLS TELEVISION
DC
AC
SOLAR LIGHT
ENERGY TRANSFORMER
3 3 3 13 MOTOR
POWER STATION TRANSFORMER PUMP
FACTS
ROBOTICS
COMPEN
SATOR
INDUSTRY
TRANSFORMER FUEL DC
CELLS AC
☯
3 POWER SUPPLY
a d
WIND TURBINE ~
FUEL =
COMMUNICATION
TRANSPORT
COMBUSTION
ENGINE
B Chitti Babu,
14 August 2009 Courtesy:
EE NIT Rourkela
Aalborg University,Denmark
3
4.
Implementation of problemoriented and
projectorganised education
Literature Lectures Group
studies
Problem Problem Report
analysis solving
Field work/ Experiments/
Tutorials Simulation Prototyping
B Chitti Babu,
14 August 2009 4
EE NIT Rourkela
5.
Prerequisite for Power Electronics
• Study of Second Order System, Control
Concepts and Mathematics
• Role of Passive Elements
• Physics concepts of Devices
• Device Selection
………………………………
• Modeling and Simulation
• Build and Evaluate
• Design & Development
• Research and Innovate
B Chitti Babu,
14 August 2009 5
EE NIT Rourkela
6.
Modeling & Simulation?
• Modeling here refers to the process of analysis and syntheses to arrive at a suitable
mathematical description that encompasses the relevant dynamic characteristics of the
component, preferably in terms of parameters that can be easily determined in practice
• Model supposely imitates or reproduces certain essential characteristics or conditions of
the actualThis is called SIMULATION.
• Modeling & SimulationSimulation is a technique that involves setting up a model of a real
situation and performing experiments on the model.
• Simulation to be an experiment with logical and mathematical models, especially
mathematical representations of the dynamic kind that are characterized by a mix of
differential and algebraic equations.
B Chitti Babu,
14 August 2009 6
EE NIT Rourkela
7.
Simulation Formulation
• Observing the Physical system.
• Formulating the hypotheses or mathematical model to
explain the observation.
• Predicting the behavior of the system from solutions
or properties of the mathematical model.
• Testing the validity of the Hypotheses or
Mathematical Model.
B Chitti Babu,
14 August 2009 7
EE NIT Rourkela
8.
Mathematical Models
• Linear or Nonlinear
• Lumped or Distributed parameters
• Static & Dynamic
• Continuous or Discrete
• Deterministic or Stochastic
Courtesy: Dynamic Simulation of Electric Machinery
By Chee Mun Ong
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14 August 2009 8
EE NIT Rourkela
9.
Simulation Packages
1)General Purpose:
Equation Oriented in that they require input in the form of
differential or algebraic equations. Eg:IESL, SABER, IMSL,
ODEPAK & DASSL etc.
2)ApplicationSpecific Packages:
Ready to use models of commonly used components for a specific
applications. Eg:SPICE2, EMTP, PSCAD etc.
MATLAB & SIMULINK:They are Registered
Trade mark of the THE MATHWORKS. Inc.,
USA
B Chitti Babu,
14 August 2009 9
EE NIT Rourkela
10.
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
sensors
Input Power
Source Electronics Load
 AC
 DC Converters Output
 unregulated  AC
 DC
POWER ELECTRONIC
CONVERTERS – the
Reference
Controlle heart of power a power
r electronics system
B Chitti Babu,
14 August 2009 10
EE NIT Rourkela
11.
Power Electronic Systems
Why Power Electronics ?
Power semiconductor devices Power switches
isw
ON or OFF
+ vsw −
=0
isw = 0
Ploss = vsw× isw = 0
+ vsw −
Losses ideally ZERO !
B Chitti Babu,
14 August 2009 11
EE NIT Rourkela
12.
Power Electronic Systems
Why Power Electronics ?
Power semiconductor devices Power switches
K K K
− − −
G G
Vak Vak Vak
+ + +
ia ia ia
A A A
B Chitti Babu,
14 August 2009 12
EE NIT Rourkela
13.
Power Electronic Systems
Why Power Electronics ?
Power semiconductor devices Power switches
D
C
iD
+ ic
+
VDS G
G VCE
−
−
S
E
B Chitti Babu,
14 August 2009 13
EE NIT Rourkela
14.
Power Electronic Systems
Why Power Electronics ?
Passive elements High frequency
+ VL transformer
−
i
L
+ +
Inductor
V V2
1
+ VC −
− −
i
C
B Chitti Babu,
14 August 2009 14
EE NIT Rourkela
15.
Passive Elements In Power Electronics
• Resistors
• Capacitors
• Inductors
• Transformers
• Filters
• Integrated Magnetics
B Chitti Babu,
14 August 2009 15
EE NIT Rourkela
16.
Resistors in
Power Electronics
• Resistors are mostly used in Power
Electronics to dissipate the trapped
energy from other components as well to
provide damping.
• Thus, resistors can carry significant
amount of high frequency currents.
• Resistors can carry fundamental ac
component currents in ac circuits and also
carry dc component currents under steady
state.
• No resistor is ideal, so their behavior
depends upon the applied frequency The
peak temperature rise depends on the
energy dissipated in the resistors.
B Chitti Babu,
14 August 2009 16
EE NIT Rourkela
17.
Capacitors in
Power Electronics
• Capacitors are mostly used in Power
Electronics to bypass high frequency
components of voltages and currents.
• Thus, capacitors can carry significant
amount of high frequency currents
Capacitors can carry fundamental ac
component.
• currents in ac circuits but cannot carry dc
component currents under steady state.
• No capacitor is ideal, so their behavior
depends upon the applied frequency
• The breakdown voltage depends on the peak
voltage charge
B Chitti Babu,
14 August 2009 17
EE NIT Rourkela
18.
Inductors in
Power Electronics
• Inductors are mostly used in Power
Electronics to block the flow of high
frequency components of currents.
• Thus, inductors can drop significant
amount of high frequency voltages.
• Inductors can have fundamental ac
component voltage drop in ac circuits but
cannot drop dc component voltages under
steady state.
• No inductor is ideal, so their behavior
depends upon the applied frequency
• The peak flux density depends on the peak
instantaneous current.
Courtesy: Dr.Sujit K. Biswas, Lecture Notes, Jadavpur University
B Chitti Babu,
14 August 2009 18
EE NIT Rourkela
19.
Power Electronic Systems
Why Power Electronics ?
sensors
Input Power
Source Electronics Load
IDEALLY
 AC
Converters LOSSLESS !
Output
 DC
 unregulated  AC
 DC
Reference
Controlle
r
B Chitti Babu,
14 August 2009 19
EE NIT Rourkela
20.
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 • FPGA • DSPs
• Faster and cheaper to implement
complex algorithm
B Chitti Babu,
14 August 2009 20
EE NIT Rourkela
21.
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)
B Chitti Babu,
14 August 2009 21
EE NIT Rourkela
22.
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) AC motors
SRM  IM
BLDC  PMSM
B Chitti Babu,
14 August 2009 22
EE NIT Rourkela
23.
Modern Electrical Drive Systems
Classic Electrical Drive for Variable Speed Application :
• Bulky
• Inefficient
• inflexible
B Chitti Babu,
14 August 2009 23
EE NIT Rourkela
24.
Modern Electrical Drive Systems
Typical Modern Electric Drive Systems
Power Electronic Converters Electric Motor
Electric Energy Electric Energy Electric Mechanical
 Unregulated   Regulated  Energy Energy
POWER IN Power
Moto Loa
Electronic d
r
Converters
feedback
Reference
Controller
B Chitti Babu,
14 August 2009 24
EE NIT Rourkela
25.
Modern Electrical Drive Systems
Example on VSD application
Constant speed Variable Speed Drives
valve
Supply
motor pump
Power out
Power
In
Power loss
Mainly in valve
B Chitti Babu,
14 August 2009 25
EE NIT Rourkela
26.
Modern Electrical Drive Systems
Example on VSD application
Constant speed Variable Speed Drives
valve
Supply Supply
motor pump motor
PEC pump
Power out
Power out
Power
Power
In
In
Power loss
Power loss
Mainly in valve
B Chitti Babu,
14 August 2009 26
EE NIT Rourkela
27.
Modern Electrical Drive Systems
Example on VSD application
Constant speed Variable Speed Drives
valve
Supply Supply
motor pump motor
PEC pump
Power out
Power out
Power
Power
In
In
Power loss
Power loss
Mainly in valve
B Chitti Babu,
14 August 2009 27
EE NIT Rourkela
28.
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
B Chitti Babu,
14 August 2009 28
EE NIT Rourkela
29.
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
B Chitti Babu,
14 August 2009 29
EE NIT Rourkela
30.
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
B Chitti Babu,
14 August 2009 30
EE NIT Rourkela
31.
Modern Electrical Drive Systems
Overview of AC and DC drives
Courtesy: Electrical Drives by Ion Boldea ,CRC Press
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14 August 2009 31
EE NIT Rourkela
32.
Power Electronic Converters in ED Systems
Converters for Motor Drives
(some possible configurations)
DC Drives AC Drives
AC Source DC Source AC Source DC Source
DCAC
DCDC
DC
ACDC ACDC DCDC
ACDC ACAC DCAC
DC AC AC
Const. Variable NCC FCC
DC
DCChitti Babu,
B
14 August 2009 32
EE NIT Rourkela
33.
Power Electronic Converters in ED Systems
DC DRIVES
Available AC source to control DC motor (brushed)
ACDC
ACDC DC
Uncontrolled Rectifier
Singlephase Control
Control
Threephase
Controlled Rectifier DCDC Switched mode
Singlephase 1quadrant, 2quadrant
Threephase 4quadrant
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14 August 2009 33
EE NIT Rourkela
34.
Power Electronic Converters in ED Systems
DC DRIVES
ACDC
400
200
0
+ 2 Vm
Vo = cos α
200
π
400
0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44
50Hz Vo 10
1phase Average voltage
5
over 10ms
−
0
0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44
500
0
50Hz
+ 500
3phase 0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44
3VL − L , m
Vo Vo = cos α
π
30
20
− Average voltage
10
over 3.33 ms
0
B Chitti Babu, 0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44
14 August 2009 34
EE NIT Rourkela
35.
Power Electronic Converters in ED Systems
DC DRIVES
ACDC
2 Vm
π
+ 2 Vm
Vo = cos α
π
50Hz Vo 90o 180o
1phase Average voltage
over 10ms
− 2 Vm
−
π
3VL − L , m
π
50Hz
+
3phase
3VL − L , m
Vo Vo = cos α
π 90o 180o
− Average voltage
over 3.33 ms 3VL − L , m
−
π
B Chitti Babu,
14 August 2009 35
EE NIT Rourkela
36.
Power Electronic Converters in ED Systems
DC DRIVES
ACDC
ia
+
Vt
3phase
Vt Q2 Q1
supply
− Q3 Q4 Ia
 Operation in quadrant 1 and 4 only
B Chitti Babu,
14 August 2009 36
EE NIT Rourkela
37.
Power Electronic Converters in ED Systems
DC DRIVES
ACDC
+
3
phase 3phase
Vt supply
supply
−
ω
Q2 Q1
Q3 Q4
T
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14 August 2009 37
EE NIT Rourkela
38.
Power Electronic Converters in ED Systems
DC DRIVES
ACDC
F1 R1
3phase
supply
+ Va 
R2 F2
ω
Q2 Q1
Q3 Q4
T
B Chitti Babu,
14 August 2009 38
EE NIT Rourkela
39.
Power Electronic Converters in ED Systems
DC DRIVES
ACDC
Cascade control structure with armature reversal (4quadrant):
iD
ω
ωref + Speed iD,ref + Current
Firing
control Control Circuit
ler _ ler
_
iD,ref
Armature
iD, reversal Babu,
B Chitti
14 August 2009 39
EE NIT Rourkela
40.
Power Electronic Converters in ED Systems
DC DRIVES
ACDCDC
Uncontrolled control
rectifier
Switch Mode DCDC
1Quadrant
2Quadrant
4Quadrant
B Chitti Babu,
14 August 2009 40
EE NIT Rourkela
41.
Power Electronic Converters in ED Systems
DC DRIVES
ACDCDC
control
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14 August 2009 41
EE NIT Rourkela
42.
Power Electronic Converters in ED Systems
DC DRIVES
ACDCDC DCDC: Twoquadrant Converter
Va
T1 D1
+
ia
Vdc Q2 Q1
+ Ia
− D2
T2
Va

T1 conducts → va = Vdc
B Chitti Babu,
14 August 2009 42
EE NIT Rourkela
43.
Power Electronic Converters in ED Systems
DC DRIVES
ACDCDC DCDC: Twoquadrant Converter
Va
T1 D1
+
ia
Vdc Q2 Q1
+ Ia
− D2
T2
Va

D2 conducts → va = 0 T1 conducts → va = Vdc
Va Eb
Quadrant 1 The average voltage is made larger than the back emf
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14 August 2009 43
EE NIT Rourkela
44.
Power Electronic Converters in ED Systems
DC DRIVES
ACDCDC DCDC: Twoquadrant Converter
Va
T1 D1
+
ia
Vdc Q2 Q1
+ Ia
− D2
T2
Va

D1 conducts → va = Vdc
B Chitti Babu,
14 August 2009 44
EE NIT Rourkela
45.
Power Electronic Converters in ED Systems
DC DRIVES
ACDCDC DCDC: Twoquadrant Converter
Va
T1 D1
+
ia
Vdc Q2 Q1
+ Ia
− D2
T2
Va

T2 conducts → va = 0 D1 conducts → va = Vdc
Va Eb
Quadrant 2 The average voltage is made smallerr than the back emf, thus
forcing the current to flow in the reverse direction
B Chitti Babu,
14 August 2009 45
EE NIT Rourkela
46.
Power Electronic Converters in ED Systems
DC DRIVES
ACDCDC DCDC: Twoquadrant Converter
vc
2vtri
+
vA Vdc

0
+
vc
B Chitti Babu,
14 August 2009 46
EE NIT Rourkela
47.
Power Electronic Converters in ED Systems
DC DRIVES
ACDCDC DCDC: Fourquadrant Converter
leg A leg B
+ D1 D3
Q1 Q3
+ Va −
Vdc
− D4 D2
Q4 Q2
Positive current
va = Vdc when Q1 and Q2 are ON
B Chitti Babu,
14 August 2009 47
EE NIT Rourkela
48.
Power Electronic Converters in ED Systems
DC DRIVES
ACDCDC DCDC: Fourquadrant Converter
leg A leg B
+ D1 D3
Q1 Q3
+ Va −
Vdc
− D4 D2
Q4 Q2
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
B Chitti Babu,
14 August 2009 48
EE NIT Rourkela
49.
Power Electronic Converters in ED Systems
DC DRIVES
ACDCDC DCDC: Fourquadrant Converter
leg A leg B
+ D1 D3
Q1 Q3
+ Va −
Vdc
− D4 D2
Q4 Q2
Positive current 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 = 0 when current freewheels through Q and D
B Chitti Babu,
14 August 2009 49
EE NIT Rourkela
50.
Power Electronic Converters in ED Systems
DC DRIVES
ACDCDC DCDC: Fourquadrant Converter
leg A leg B
+ D1 D3
Q1 Q3
+ Va −
Vdc
− D4 D2
Q4 Q2
Positive current 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
B Chitti Babu,
14 August 2009 50
EE NIT Rourkela
51.
Power Electronic Converters in ED Systems
DC DRIVES
Bipolar switching scheme – output
ACDCDC swings between VDC and VDC
vc
2vtri
Vdc
Vdc
+ + vA
vA vB 0
  Vdc
vB
0
vc Vdc
+ vAB
_ Vdc
B Chitti Babu,
14 August 2009 51
EE NIT Rourkela
52.
Power Electronic Converters in ED Systems
DC DRIVES
Unipolar switching scheme – output
ACDCDC swings between Vdc and Vdc
vc
Vtri
vc
Vdc
+ + Vdc
vA vB
vA

0

Vdc
vc vB
0
+
Vdc
_
vAB
0
vc
B Chitti Babu,
14 August 2009 52
EE NIT Rourkela
53.
Power Electronic Converters in ED Systems
DC DRIVES
ACDCDC DCDC: Fourquadrant Converter
Armature
200 current 200
150 150 Armature
Vdc 100 Vdc 100 current
50 50
0 0
50 50
Vdc 100 100
150 150
200 200
0.04 0.0405 0.041 0.0415 0.042 0.0425 0.043 0.0435 0.044 0.0445 0.045 0.04 0.0405 0.041 0.0415 0.042 0.0425 0.043 0.0435 0.044 0.0445 0.045
Bipolar switching scheme Unipolar switching scheme
• Current ripple in unipolar is smaller
• Output frequency in unipolar is effectively doubled
B Chitti Babu,
14 August 2009 53
EE NIT Rourkela
54.
Power Electronic Converters in ED Systems
AC DRIVES
ACDCAC
control
The common PWM technique: CBSPWM with ZSS
14 August 2009 SVPWM
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54
EE NIT Rourkela
55.
Modeling and Control of Electrical Drives
• Control the torque, speed or position
• Cascade control structure
Example of current control in cascade control structure
θ* ω* T*
+ + +
− − −
position speed current
controller controller controller converter Motor
kT
ω
θ
1/s
B Chitti Babu,
14 August 2009 55
EE NIT Rourkela
56.
Modeling and Control of Electrical Drives
Current controlled converters in DC Drives  Hysteresisbased
+
ia
Vdc
+
iref
− Va
−
va
iref + ierr q
_ q
• High bandwidth, simple implementation,
insensitive to parameter variations
ierr
• Variable switching frequency – depending on
operating conditions B Chitti Babu,
14 August 2009 56
EE NIT Rourkela
57.
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives  Hysteresisbased
i*a +
Converter
i*b +
i*c +
• For isolated neutral load, ia + ib + ic = 0
∴control is not totally independent 3phase
• Instantaneous error for isolated neutral load can
AC Motor
reach double the band
B Chitti Babu,
14 August 2009 57
EE NIT Rourkela
58.
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives  Hysteresisbased
iq
is
Δh Δh Δh Δh
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
B Chitti Babu,
14 August 2009 58
EE NIT Rourkela
59.
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives  Hysteresisbased
• Δh = 0.3 A • Vdc = 600V
Con u s
tin ou • Sinusoidal reference current, 30Hz load
• 10Ω, 50mH
powergui
Scope
iaref
TW
o orkspace1 g
+ i
A + 
D Voltage Source
C B Series R BranchC
LC 3urrent Measurem 3
ent
c1 p1 
C
i
c2 p2 + 
U ersal Bridge 1
niv
c3 p3 Series R Branch urrent M
LC C1 easurem 1
ent
ina p4 i
+ 
Sine W e
av
inb p5 Series R Branch urrent M
LC C2 easurem 2
ent
inc p6
Subsystem
Sine W e 1
av
Sine W e 2
av
B Chitti Babu,
14 August 2009 59
EE NIT Rourkela
60.
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives  Hysteresisbased
Actual and reference currents Current error
0.5
10
0.4
0.3
5
0.2
10
0.1
0 0
9
0.1
0.2
5 8
0.3
7 0.4
10
0.5
0.005 0.01 6
0.015 0.02 0.025 0.03
0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5
5
4
4 6 8 10 12 14 16
3
x 10
B Chitti Babu,
14 August 2009 60
EE NIT Rourkela
61.
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives  Hysteresisbased
Actual current locus Current error
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 0.6A
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 0.6A
0.5
0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06
B Chitti Babu,
14 August 2009 61
EE NIT Rourkela
62.
Modeling and Control of Electrical Drives
Current controlled converters in DC Drives  PIbased
Vdc
iref + vc vPulse width
tri
PI vc modulator
q
q
q
−
B Chitti Babu,
14 August 2009 62
EE NIT Rourkela
63.
Modeling and Control of Electrical Drives
Current controlled converters in DC Drives  PIbased
i*a +
PI PWM
Converter
i*b +
PI PWM
i*c + PWM
PI
• Sinusoidal PWM
Motor
• Interactions between phases → only require 2 controllers
• Tracking error
B Chitti Babu,
14 August 2009 63
EE NIT Rourkela
64.
Modeling and Control of Electrical Drives
Current controlled converters in DC Drives  PIbased
• Perform the 3phase to 2phase 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
B Chitti Babu,
14 August 2009 64
EE NIT Rourkela
65.
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives  PIbased
i*a +
PI PWM
Converter
i*b +
PI PWM
i*c + PWM
PI
Motor
B Chitti Babu,
14 August 2009 65
EE NIT Rourkela
66.
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives  PIbased
i*a
PI
SVM Converter
i*b
32 23
PI
i*c
32
Motor
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14 August 2009 66
EE NIT Rourkela
67.
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives  PIbased
va*
id* + PI
controller
−
vb*
id dq→abc SVM
or SPWM IM
iq* + VSI
PI vc*
− iq controller
ωs
Synch speed
ωs
estimator
abc→dq
B Chitti Babu,
14 August 2009 67
EE NIT Rourkela
68.
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives  PIbased
Stationary  ia Stationary  id
4 4
2 3
0 2
2 1
4 0
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
4 Rotating  ia 4 Rotating  id
2 3
0 2
2 1
4 0
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
B Chitti Babu,
14 August 2009 68
EE NIT Rourkela
69.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
+
vc firing α controlled
circuit rectifier Va
–
vc(s) va(s)
? DC motor
The relation between vc and va is determined by the firing circuit
B Chitti Babu,
14 August 2009 69
It is desirable to have a linear NIT Rourkela
EE relation between vc and va
70.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
Cosinewave crossing control
Vm
Input voltage
0 π 2π 3π 4π
vc vs
Cosine wave compared with vc
Results of comparison trigger SCRs
Output voltage
B Chitti Babu,
14 August 2009 70
EE NIT Rourkela
71.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
Cosinewave crossing control
cos(ωt)
Vscos(α) = vc
Vm
⎛v ⎞
0 π 2π 3π 4π α = cos −1 ⎜ c ⎟
⎜v ⎟
⎝ s⎠
vc vs
α
2Vm v c ⎛ −1 ⎛ v c ⎞ ⎞
Va = cos⎜α ) ⎜ ⎟ ⎟
(
π vs ⎝ ⎜ cos ⎜ v ⎟ ⎟
⎝ s ⎠⎠
α
A linear relation between vc and Va
B Chitti Babu,
14 August 2009 71
EE NIT Rourkela
72.
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
B Chitti Babu,
14 August 2009 72
EE NIT Rourkela
73.
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
B Chitti Babu,
14 August 2009 73
EE NIT Rourkela
74.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
T
− s
G H (s) = Ke 2
Single phase, 50Hz
vc(s) Va(s)
2Vm
K= T=10ms
πVs
Three phase, 50Hz
3VL − L ,m
K= T=3.33ms
πVs
Simplified if control bandwidth is reduced to much lower than the
sampling frequency
B Chitti Babu,
14 August 2009 74
EE NIT Rourkela
75.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
+
iref current vc firing α controlled
controller Va
circuit rectifier
–
• To control the current – currentcontrolled converter
• Torque can be controlled
• Only operates in Q1 and Q4 (single converter topology)
B Chitti Babu,
14 August 2009 75
EE NIT Rourkela
76.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
• Input 3phase, 240V, 50Hz • Closed loop current control
with PI controller
Scope3
+
 v Continuous
Voltage Measurement4
+ i powergui
 Scope2
AC Voltage Source Current Measurement 1 Step
s
AC Voltage Source1 +
g 
+ v
A Controlled Voltage Source
Series RLC Branch
AC Voltage Source2 B To Workspace
+  i
 v C  + ia
Voltage Measurement2 Universal Bridge Current Measurement To Workspace1
+ +
 v  v
alpha_deg
Voltage Measurement Voltage Measurement3
AB ux Scope
BC pulses
+
 v
CA
Block
Voltage Measurement1
Synchronized Mu
6Pulse Generator
Scope1 ir
To Workspace2
PID acos K
Signal
PID Controller Saturation
1
Generator
7
Constant 1
B Chitti Babu,
14 August 2009 76
EE NIT Rourkela
77.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with Controlled rectifier
• Input 3phase, 240V, 50Hz • Closed loop current control
with PI controller
1000
1000
500
500
0
Voltage
0
500 500
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.22 0.23 0.24 0.25 0.26 0.27 0.28
15 15
10
10
5
Current
5
0
0.22 0.23 0.24 0.25 0.26 0.27 0.28
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
B Chitti Babu,
14 August 2009 77
EE NIT Rourkela
78.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
B Chitti Babu,
14 August 2009 78
EE NIT Rourkela
79.
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
B Chitti Babu,
14 August 2009 79
EE NIT Rourkela
80.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Ttri
⎧1 Vc > Vtri
q=⎨
vc
⎩0 Vc < Vtri
1 t + Ttri
d=
Ttri ∫ t
q dt
1
t on
=
0 Ttri
ton
Vdc
1 dTtri
Va = ∫ Vdcdt = dVdc
Ttri 0
B Chitti Babu,
14 August 2009 0
EE NIT Rourkela
80
81.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
d
0.5
vc
Vtri
Vtri
Vtri vc
For vc = Vtri → d = 0
B Chitti Babu,
14 August 2009 81
EE NIT Rourkela
82.
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
14 August 2009
EE NIT
→ Rourkela
For vc = VtriChitti d = 1
B Babu,
82
83.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
d
0.5
vc
Vtri Vtri
Vtri vc
1
d = 0.5 + vc
2Vtri
Vtri
For vc = Vtri → d = 0
For vc = 0 → d = 0.5
14 August 2009
EE NIT
→ Rourkela
For vc = VtriChitti d = 1
B Babu,
83
84.
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:
V dc
V a = 0 . 5 V dc + vc
2 V tri
Introducing perturbation in vc and Va and separating DC and AC components:
V dc
DC: V a = 0 . 5 V dc + vc
2 V tri
AC: ~ = V dc ~
va vc
2 V tri
B Chitti Babu,
14 August 2009 84
EE NIT Rourkela
85.
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) V dc
=
v c ( s ) 2 V tri
vc(s) V dc va(s)
DC motor
2 V tri
B Chitti Babu,
14 August 2009 85
EE NIT Rourkela
86.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Bipolar switching scheme
Vdc
vc
2vtri
Vdc
q
vtri
+
Vdc
Vdc vA
+ VAB −
0
−
vc Vdc
vB
0
q
Vdc
vAB
v v
d A = 0.5 + c dB = 1 − d A = 0.5 − c Vdc
2Vtri 2Vtri
Vdc Vdc Vdc
VA = 0.5Vdc + vc VB = 0.5Vdc − vc VA − VB = VAB = vc
2Vtri 2Vtri Vtri
B Chitti Babu,
14 August 2009 86
EE NIT Rourkela
87.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Bipolar switching scheme
v a ( s ) V dc
=
v c (s) V tri
vc(s) V dc va(s)
DC motor
V tri
B Chitti Babu,
14 August 2009 87
EE NIT Rourkela
88.
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
vc qb vB
vc − vc vAB
d A = 0.5 + dB = 0.5 +
2Vtri 2Vtri
Vdc Vdc Vdc
VA = 0.5Vdc + vc VB = 0.5Vdc − vc VA − VB = VAB = vc
2Vtri 2Vtri Vtri
The same average value we’ve seen for bipolar !
B Chitti Babu,
14 August 2009 88
EE NIT Rourkela
89.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Unipolar switching scheme
v a ( s ) V dc
=
v c (s) V tri
vc(s) V dc va(s)
DC motor
V tri
B Chitti Babu,
14 August 2009 89
EE NIT Rourkela
90.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
DC motor – separately excited or permanent magnet
dia dωm
v t = ia R a + L a + ea Te = Tl + J
dt dt
Te = kt ia ee = kt ω
Extract the dc and ac components by introducing small
perturbations in Vt, ia, ea, Te, TL and ωm
ac components dc components
~
~ = ~ R + L d ia + ~
v t ia a ea Vt = Ia R a + E a
a
dt
~ ~
Te = k E ( ia ) Te = k E Ia
~ = k (ω )
ee ~ Ee = k Eω
E
~
~ ~ ~ + J d(ω )
Te = TL + B ω Te = TL + B(ω)
14 August 2009 dt B Chitti Babu,
90
EE NIT Rourkela
91.
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
~
~
~ = i R +L d ia ~ Vt(s) = Ia(s)Ra + LasIa + Ea(s)
vt a a a + ea
dt
~ ~ Te(s) = kEIa(s)
Te = k E ( ia )
~ = k (ω )
ee ~ Ea(s) = kEω(s)
E
~
~ ~ ~ + J d(ω )
Te = TL + B ω Te(s) = TL(s) + Bω(s) + sJω(s)
dt
B Chitti Babu,
14 August 2009 91
EE NIT Rourkela
92.
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 ) I a (s ) Te (s ) ω (s )
1 1
kT
+ Ra + sL a +
B + sJ

kE
B Chitti Babu,
14 August 2009 92
EE NIT Rourkela
93.
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
T e (s ) Torque V dc Va (s ) 1 I a (s ) Te (s ) 
1 ω (s )
kT
controller Ra + sL a B + sJ
+ V tri ,peak + +
 
kE
B Chitti Babu,
14 August 2009 93
EE NIT Rourkela
94.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Closedloop 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
B Chitti Babu,
14 August 2009 94
EE NIT Rourkela
95.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: DC drives with SM Converters
Closedloop 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
B Chitti Babu,
14 August 2009 95
EE NIT Rourkela
96.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
INDUCTION MOTOR DRIVES
Scalar Control Vector Control
Const. V/Hz is=f(ωr) FOC DTC
Rotor Flux Stator Flux
Circular Hexagon DTC
Flux Flux SVM
B Chitti Babu,
14 August 2009 96
EE NIT Rourkela
97.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Control of induction machine based on steadystate
model (per phase SS equivalent circuit):
Is Lls Llr’
Rs Ir’
+
+
Lm
Vs Rr’/s
Eag
– Im –
B Chitti Babu,
14 August 2009 97
EE NIT Rourkela
98.
Modeling and Control of Electrical Drives
Modeling of the Power Converters: IM drives
Te
Pull out
Torque Intersection point
(Tmax) (Te=TL) determines the
Te
steady –state speed
Trated TL
sm ωratedrotorωs
ω ωr
s
B Chitti Babu,
14 August 2009 98
EE NIT Rourkela
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