Power Electronics
-
Upload
guestcfebed3 -
Category
Technology
-
view
6.433 -
download
4
description
Transcript of Power Electronics
14 August 2009B Chitti Babu, EE NIT Rourkela
1
Power Electronics and Drives Power Electronics and Drives ––Modeling & SimulationModeling & Simulation
B.Chitti BabuB.Chitti BabuMember IEEE (USA), Student Member IET (UK)Member IEEE (USA), Student Member IET (UK)Department of Electrical Engineering,Department of Electrical Engineering,
National Institute of Technology,RourkelaNational Institute of Technology,[email protected]@ieee.org
A Problem Based and Project Oriented A Problem Based and Project Oriented LearningLearning
14 August 2009B Chitti Babu, EE NIT Rourkela
2
CONTENTSCONTENTS
Power Electronic SystemsPower Electronic Systems
Power Electronic Converters in Electrical DrivesPower Electronic Converters in Electrical Drives:: DC and AC Drives:: DC and AC Drives
Modeling and Control of Electrical DrivesModeling and Control of Electrical Drives:: Current controlled Converters :: Current controlled Converters :: Modeling of Power Converters :: Modeling of Power Converters :: Scalar control of IM:: Scalar control of IM
Pre Requisite of Power Electronics SystemPre Requisite of Power Electronics System
14 August 2009B Chitti Babu, EE NIT Rourkela
3
Power Electronics-An Enabling Technology
Energy System
POWER STATION
SOLAR CELLS
WIND TURBINE
MOTOR
PUMP
ROBOTICS
REFRIGERATOR
TELEVISION
LIGHT
TRANSFORMER
TRANSFORMER
INDUSTRY
=
POWER SUPPLYa d
TRANSFORMER
COMPEN - SATOR
FACTS
FUELCELLS FUEL☯
COMMUNICATION COMBUSTION
ENGINE
SOLAR ENERGY
TRANSPORT
3 3 3 1-3
3
DC AC
~
Energy System
POWER STATION
SOLAR CELLS
WIND TURBINE
MOTOR
PUMP
ROBOTICS
REFRIGERATOR
TELEVISION
LIGHT
TRANSFORMER
TRANSFORMER
INDUSTRY
=
POWER SUPPLYa d
TRANSFORMER
COMPEN - SATOR
FACTS
FUELCELLS FUEL☯
COMMUNICATION COMBUSTION
ENGINE
SOLAR ENERGY
TRANSPORT
3 3 3 1-3
3
DC AC
~
DCAC
DCAC
Courtesy: Aalborg University,Denmark
14 August 2009B Chitti Babu, EE NIT Rourkela
4
Implementation of problem-oriented andproject-organised education
Literature Lectures Groupstudies
Experiments/Fieldwork/Tutorials
Problemanalysis
Problemsolving Report
PrototypingSimulation
14 August 2009B Chitti Babu, 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
14 August 2009B Chitti Babu, 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 actual-This is called SIMULATION.
• Modeling & Simulation-Simulation 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.
14 August 2009B Chitti Babu, 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.
14 August 2009B Chitti Babu, 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
14 August 2009B Chitti Babu, EE NIT Rourkela
9
Simulation Packages1)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)Application-Specific 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
14 August 2009B Chitti Babu, 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
Power ElectronicsConverters
Power ElectronicsConverters
LoadLoad
Controller
Controller
Output- AC- DC
InputSource- AC- DC- unregulated
Reference
POWER ELECTRONIC CONVERTERS – the heart of power a power electronics system
sensors
14 August 2009B Chitti Babu, EE NIT Rourkela
11
Power Electronic Systems
Why Power Electronics ?
Power semiconductor devices Power switches
+ vsw −= 0
ON or OFF
isw
+ vsw −
isw = 0
Ploss = vsw× isw = 0
Losses ideally ZERO !
14 August 2009B Chitti Babu, EE NIT Rourkela
12
Power Electronic Systems
Why Power Electronics ?
Power semiconductor devices Power switches
−
Vak
+ia
G
K
A
−
Vak
+ia
K
A
−
Vak
+ia
G
K
A
14 August 2009B Chitti Babu, EE NIT Rourkela
13
Power Electronic Systems
Why Power Electronics ?
Power semiconductor devices Power switches
D
S
G
+
VDS
−
iD
G
C
E
+
VCE
−
ic
14 August 2009B Chitti Babu, EE NIT Rourkela
14
Power Electronic Systems
Why Power Electronics ?
Passive elements High frequencytransformer
+
V
1
−
+
V2
−
Inductor
+ VL−
i
L
+ VC−
i
C
14 August 2009B Chitti Babu, EE NIT Rourkela
15
Passive Elements In Power Electronics
• Resistors• Capacitors• Inductors• Transformers• Filters• Integrated Magnetics
14 August 2009B Chitti Babu, EE NIT Rourkela
16
Resistors inPower 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.
14 August 2009B Chitti Babu, EE NIT Rourkela
17
Capacitors inPower Electronics
• Capacitors are mostly used in Power Electronics to by-pass 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
14 August 2009B Chitti Babu, EE NIT Rourkela
18
Inductors inPower 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
14 August 2009B Chitti Babu, EE NIT Rourkela
19
Power Electronic Systems
Why Power Electronics ?
Power ElectronicsConverters
Power ElectronicsConverters
sensors
LoadLoad
Controller
Controller
Output- AC- DC
InputSource- AC- DC- unregulated
Reference
IDEALLY LOSSLESS !IDEALLY
LOSSLESS !
14 August 2009B Chitti Babu, EE NIT Rourkela
20
Power Electronic Systems
Why Power Electronics ?
Other factors:
• Improvements in power semiconductors• fabrication
• Decline cost in power semiconductor
• Advancement in semiconductor fabrication
• ASICs • FPGA • DSPs
• Faster and cheaper to implement complex algorithm
• Power Integrated Module (PIM), Intelligent Power Modules (IPM)
14 August 2009B Chitti Babu, EE NIT Rourkela
21
Power Electronic Systems
Some Applications of Power Electronics :
Power rating of < 1 W (portable equipment)
Tens or hundreds Watts (Power supplies for computers /office equipment)
Typically used in systems requiring efficient control and conversion of electric energy:
Domestic and Commercial ApplicationsIndustrial ApplicationsTelecommunicationsTransportationGeneration, Transmission and Distribution of electrical energy
kW to MW : drives
Hundreds of MW in DC transmission system (HVDC)
14 August 2009B Chitti Babu, 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
AC motors- IM
- PMSM
DC motors (brushed)
SRMBLDC
14 August 2009B Chitti Babu, EE NIT Rourkela
23
Modern Electrical Drive Systems
Classic Electrical Drive for Variable Speed Application :
• Bulky
• Inefficient
• inflexible
14 August 2009B Chitti Babu, EE NIT Rourkela
24
Modern Electrical Drive Systems
PowerElectronicConverters
PowerElectronicConverters
LoadLoad
Motor
Motor
ControllerControllerReference
POWER IN
feedback
Typical Modern Electric Drive Systems
Power Electronic ConvertersElectric Energy- Unregulated -
Electric Energy- Regulated -
Electric MotorElectric Energy
Mechanical Energy
14 August 2009B Chitti Babu, EE NIT Rourkela
25
Modern Electrical Drive SystemsExample on VSD application
motor pump
valve
Supply
Constant speed Variable Speed Drives
PowerIn
Power lossMainly in valve
Power out
14 August 2009B Chitti Babu, EE NIT Rourkela
26
Modern Electrical Drive SystemsExample on VSD application
PowerIn
Power lossMainly in valve
Power out
motor pump
valve
SupplymotorPEC pump
Supply
Constant speed Variable Speed Drives
PowerIn
Power loss
Power out
14 August 2009B Chitti Babu, EE NIT Rourkela
27
Modern Electrical Drive Systems
PowerIn
Power lossMainly in valve
Power out
PowerIn
Power loss
Power out
motor pump
valve
SupplymotorPEC pump
Supply
Constant speed Variable Speed Drives
Example on VSD application
14 August 2009B Chitti Babu, EE NIT Rourkela
28
Modern Electrical Drive Systems
Electric motor consumes more than half of electrical energy in the US
Fixed speed Variable speed
HOW ?
Improvements in energy utilization in electric motors give largeimpact to the overall energy consumption
Replacing fixed speed drives with variable speed drives
Using the high efficiency motors
Improves the existing power converter–based drive systems
Example on VSD application
14 August 2009B Chitti Babu, EE NIT Rourkela
29
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
14 August 2009B Chitti Babu, EE NIT Rourkela
30
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
14 August 2009B Chitti Babu, EE NIT Rourkela
31
Overview of AC and DC drives
Courtesy: Electrical Drives by Ion Boldea ,CRC Press
Modern Electrical Drive Systems
14 August 2009B Chitti Babu, EE NIT Rourkela
32
Power Electronic Converters in ED Systems
Converters for Motor Drives(some possible configurations)
DC Drives AC Drives
DC SourceAC Source
AC-DC-DC
AC-DC-DCAC-DCAC-DC
AC Source
Const. DC
Variable DC
AC-DC-AC
AC-DC-AC AC-ACAC-AC
NCC FCC
DC Source
DC-ACDC-AC DC-DC-AC
DC-DC-AC
DC-DCDC-DCDC-AC-DC
DC-AC-DC
14 August 2009B Chitti Babu, EE NIT Rourkela
33
Power Electronic Converters in ED SystemsDC DRIVES
Available AC source to control DC motor (brushed)
AC-DC-DC
AC-DC-DCAC-DCAC-DC
Controlled RectifierSingle-phaseThree-phase
Uncontrolled RectifierSingle-phaseThree-phase
DC-DC Switched mode1-quadrant, 2-quadrant
4-quadrant
Control Control
14 August 2009B Chitti Babu, EE NIT Rourkela
34
Power Electronic Converters in ED SystemsDC DRIVES
+
Vo
−
+
Vo
−
απ
= cosV2V mo
απ
= − cosV3
V m,LLo
50Hz3-phase
Average voltage over 10ms
Average voltage over 3.33 ms
50Hz1-phase
AC-DCAC-DC
0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44-400
-200
0
200
400
0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.440
5
10
0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44
-500
0
500
0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.440
10
20
30
14 August 2009B Chitti Babu, EE NIT Rourkela
35
Power Electronic Converters in ED SystemsDC DRIVES
+
Vo
−
+
Vo
−
απ
= cosV2V mo
90o 180o
πmV2
π− mV2
90o
π− m,LLV3
π− − m,LLV3
απ
= − cosV3
V m,LLo
50Hz3-phase
Average voltage over 10ms
Average voltage over 3.33 ms
50Hz1-phase
180o
AC-DCAC-DC
14 August 2009B Chitti Babu, EE NIT Rourkela
36
Power Electronic Converters in ED SystemsDC DRIVESAC-DCAC-DC
Ia
Q1Q2
Q3 Q4
Vt
3-phasesupply
+
Vt
−
ia
- Operation in quadrant 1 and 4 only
14 August 2009B Chitti Babu, EE NIT Rourkela
37
Power Electronic Converters in ED SystemsDC DRIVESAC-DCAC-DC
Q1Q2
Q3 Q4
ω
T
3-phasesupply
3-phasesupply
+
Vt
−
14 August 2009B Chitti Babu, EE NIT Rourkela
38
Power Electronic Converters in ED SystemsDC DRIVESAC-DCAC-DC
Q1Q2
Q3 Q4
ω
T
F1
F2
R1
R2+ Va -
3-phasesupply
14 August 2009B Chitti Babu, EE NIT Rourkela
39
Power Electronic Converters in ED SystemsDC DRIVESAC-DCAC-DC
Cascade control structure with armature reversal (4-quadrant):
Speedcontrol
ler
Speedcontrol
ler
CurrentControl
ler
CurrentControl
ler
FiringCircuitFiringCircuit
Armature reversalArmature reversal
iD
iD,ref
iD,ref
iD,
+ +
_
ω
ωref
_
14 August 2009B Chitti Babu, EE NIT Rourkela
40
Power Electronic Converters in ED SystemsDC DRIVESAC-DC-DCAC-DC-DC
controlUncontrolled rectifier
Switch Mode DC-DC1-Quadrant2-Quadrant4-Quadrant
14 August 2009B Chitti Babu, EE NIT Rourkela
41
Power Electronic Converters in ED SystemsDC DRIVESAC-DC-DCAC-DC-DC
control
14 August 2009B Chitti Babu, EE NIT Rourkela
42
T1 conducts → va = Vdc
Q1Q2
Va
Ia
T1
T2
D1
+
Va
-
D2
ia
+
Vdc
−
DC DRIVESAC-DC-DCAC-DC-DC DC-DC: Two-quadrant Converter
Power Electronic Converters in ED Systems
14 August 2009B Chitti Babu, EE NIT Rourkela
43
Q1Q2
Va
Ia
T1
T2
D1
+
Va
-
D2
ia
+
Vdc
−
D2 conducts → va = 0
Va Eb
T1 conducts → va = Vdc
Quadrant 1 The average voltage is made larger than the back emf
DC DRIVESAC-DC-DCAC-DC-DC DC-DC: Two-quadrant Converter
Power Electronic Converters in ED Systems
14 August 2009B Chitti Babu, EE NIT Rourkela
44
Q1Q2
Va
Ia
T1
T2
D1
+
Va
-
D2
ia
+
Vdc
−
D1 conducts → va = Vdc
DC DRIVESAC-DC-DCAC-DC-DC DC-DC: Two-quadrant Converter
Power Electronic Converters in ED Systems
14 August 2009B Chitti Babu, EE NIT Rourkela
45
Q1Q2
Va
Ia
T1
T2
D1
+
Va
-
D2
ia
+
Vdc
−
T2 conducts → va = 0
VaEb
D1 conducts → va = Vdc
Quadrant 2 The average voltage is made smallerr than the back emf, thus forcing the current to flow in the reverse direction
DC DRIVESAC-DC-DCAC-DC-DC DC-DC: Two-quadrant Converter
Power Electronic Converters in ED Systems
14 August 2009B Chitti Babu, EE NIT Rourkela
46
DC DRIVESAC-DC-DCAC-DC-DC DC-DC: Two-quadrant Converter
+vc
2vtrivc
+vA
-
Vdc
0
Power Electronic Converters in ED Systems
14 August 2009B Chitti Babu, EE NIT Rourkela
47
leg A leg B
+ Va −Q1
Q4
Q3
Q2
D1 D3
D2D4
+
Vdc
−
va = Vdc when Q1 and Q2 are ON
Positive current
Power Electronic Converters in ED SystemsDC DRIVESAC-DC-DCAC-DC-DC DC-DC: Four-quadrant Converter
14 August 2009B Chitti Babu, EE NIT Rourkela
48
leg A leg B
+ Va −Q1
Q4
Q3
Q2
D1 D3
D2D4
+
Vdc
−
va = -Vdc when D3 and D4 are ONva = Vdc when Q1 and Q2 are ON
va = 0 when current freewheels through Q and D
Positive current
Power Electronic Converters in ED SystemsDC DRIVESAC-DC-DCAC-DC-DC DC-DC: Four-quadrant Converter
14 August 2009B Chitti Babu, EE NIT Rourkela
49
va = -Vdc when D3 and D4 are ONva = Vdc when Q1 and Q2 are ON
va = 0 when current freewheels through Q and D
Positive current
va = Vdc when D1 and D2 are ON
Negative current
leg A leg B
+ Va −Q1
Q4
Q3
Q2
D1 D3
D2D4
+
Vdc
−
Power Electronic Converters in ED SystemsDC DRIVESAC-DC-DCAC-DC-DC DC-DC: Four-quadrant Converter
14 August 2009B Chitti Babu, EE NIT Rourkela
50
va = -Vdc when D3 and D4 are ONva = Vdc when Q1 and Q2 are ON
va = 0 when current freewheels through Q and D
Positive current
va = -Vdc when Q3 and Q4 are ONva = Vdc when D1 and D2 are ON
va = 0 when current freewheels through Q and D
Negative current
leg A leg B
+ Va −Q1
Q4
Q3
Q2
D1 D3
D2D4
+
Vdc
−
Power Electronic Converters in ED SystemsDC DRIVESAC-DC-DCAC-DC-DC DC-DC: Four-quadrant Converter
14 August 2009B Chitti Babu, EE NIT Rourkela
51
Power Electronic Converters in ED SystemsDC DRIVESAC-DC-DCAC-DC-DC
vAB
Vdc
-Vdc
Vdc
0vB
vAVdc
0
2vtrivc
vc
+
_
Vdc+vA
-
+vB
-
Bipolar switching scheme – output swings between VDC and -VDC
14 August 2009B Chitti Babu, EE NIT Rourkela
52
Power Electronic Converters in ED SystemsDC DRIVESAC-DC-DCAC-DC-DC
Unipolar switching scheme – output swings between Vdc and -Vdc
Vtri
vc
-vc
vc
+
_
+vA
-
+vB
-
Vdc
-vc
vA
Vdc
0
vB
Vdc
0
vAB
Vdc
0
14 August 2009B Chitti Babu, EE NIT Rourkela
53
Power Electronic Converters in ED SystemsDC DRIVESAC-DC-DCAC-DC-DC
Bipolar switching scheme
0.04 0.0405 0.041 0.0415 0.042 0.0425 0.043 0.0435 0.044 0.0445 0.045
-200
-150
-100
-50
0
50
100
150
200
Unipolar switching scheme
0.04 0.0405 0.041 0.0415 0.042 0.0425 0.043 0.0435 0.044 0.0445 0.045
-200
-150
-100
-50
0
50
100
150
200
• Current ripple in unipolar is smaller• Output frequency in unipolar is effectively doubled
Vdc
Vdc
Vdc
DC-DC: Four-quadrant Converter
Armature current
Armature current
14 August 2009B Chitti Babu, EE NIT Rourkela
54
Power Electronic Converters in ED SystemsAC DRIVESAC-DC-ACAC-DC-AC
control
The common PWM technique: CB-SPWM with ZSS
SVPWM
14 August 2009B Chitti Babu, EE NIT Rourkela
55
Modeling and Control of Electrical Drives
• Control the torque, speed or position
• Cascade control structure
Motor
Example of current control in cascade control structure
converterspeed
controllerposition
controller
−
+ω*
1/s
+ +
− −current
controller
T*θ*
ω
θ
kT
14 August 2009B Chitti Babu, EE NIT Rourkela
56
Modeling and Control of Electrical Drives
Current controlled converters in DC Drives - Hysteresis-based
iref
+
Vdc
−
ia
iref
va
ierr
ierr
q+_
+
Va
−
q
• High bandwidth, simple implementation, insensitive to parameter variations
• Variable switching frequency – depending on operating conditions
14 August 2009B Chitti Babu, EE NIT Rourkela
57
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - Hysteresis-based
3-phase�AC Motor
+
+
+
i*a
i*b
i*c
Converter
• For isolated neutral load, ia + ib + ic = 0 ∴control is not totally independent
• Instantaneous error for isolated neutral load can reach double the band
14 August 2009B Chitti Babu, EE NIT Rourkela
58
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - Hysteresis-based
id
iq
is
ΔhΔh ΔhΔh
• For isolated neutral load, ia + ib + ic = 0 ∴control is not totally independent
• Instantaneous error for isolated neutral load can reach double the band
14 August 2009B Chitti Babu, EE NIT Rourkela
59
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - Hysteresis-based
powergui
Continuous
Universal Bridge 1
g
A
B
C
+
-
To Workspace1
iaref
Subsystem
c1
c2
c3
ina
inb
inc
p1
p2
p3
p4
p5
p6
Sine Wave 2
Sine Wave 1
Sine Wave
Series RLC Branch 3
Series RLC Branch 2
Series RLC Branch 1
Scope
DC Voltage Source Current Measurement 3
i+ -
Current Measurement 2
i+ -
Current Measurement 1
i+ -
• Δh = 0.3 A• Sinusoidal reference current, 30Hz
• Vdc = 600V• 10Ω, 50mH load
14 August 2009B Chitti Babu, EE NIT Rourkela
60
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - Hysteresis-based
0.005 0.01 0.015 0.02 0.025 0.03
-10
-5
0
5
10
Actual and reference currents Current error
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
4 6 8 10 12 14 16
x 10-3
4
5
6
7
8
9
10
14 August 2009B Chitti Babu, EE NIT Rourkela
61
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - Hysteresis-based
-10 -5 0 5 10
-10
-5
0
5
10
Actual current locus
0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06
-0.5
0
0.5
0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06
-0.5
0
0.5
0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06
-0.5
0
0.5
0.6A
0.6A
0.6A
Current error
14 August 2009B Chitti Babu, EE NIT Rourkela
62
vtri
Vdc
qvc
q
Vdc
Pulse widthmodulator
vc
Vdc
Pulse widthmodulator
vciref
PI+
− q
Modeling and Control of Electrical Drives
Current controlled converters in DC Drives - PI-based
14 August 2009B Chitti Babu, EE NIT Rourkela
63
Motor
+
+
+
i*a
i*b
i*c
Converter
PWM
PWM
PWM
PWM
PWM
PWM
• Sinusoidal PWM
PI
PI
PI
• Interactions between phases → only require 2 controllers• Tracking error
Modeling and Control of Electrical Drives
Current controlled converters in DC Drives - PI-based
14 August 2009B Chitti Babu, EE NIT Rourkela
64
• Interactions between phases → only require 2 controllers• Tracking error
• Perform the control in synchronous frame- the current will appear as DC
• Perform the 3-phase to 2-phase transformation- only two controllers (instead of 3) are used
Modeling and Control of Electrical Drives
Current controlled converters in DC Drives - PI-based
14 August 2009B Chitti Babu, EE NIT Rourkela
65
Motor
i*a
i*b
i*c
Converter
PWM
+
+
+
PWM
PWM
PI
PI
PI
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - PI-based
14 August 2009B Chitti Babu, EE NIT Rourkela
66
Motor
i*a
i*b
i*c
Converter
3-2
3-2SVM2-3
PI
PI
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - PI-based
14 August 2009B Chitti Babu, EE NIT Rourkela
67
id*
iq*PI
controller
dq→abc
abc→dq
SVM or SPWM
VSIIM
va*
vb*
vc*
id
iq
+
+
−
−
PIcontroller
Synch speed estimator
ωs
ωs
Modeling and Control of Electrical Drives
Current controlled converters in AC Drives - PI-based
14 August 2009B Chitti Babu, EE NIT Rourkela
68
Modeling and Control of Electrical Drives
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01-4
-2
0
2
4
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01-4
-2
0
2
4
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020
1
2
3
4
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020
1
2
3
4
Stationary - ia Stationary - id
Rotating - ia Rotating - id
Current controlled converters in AC Drives - PI-based
14 August 2009B Chitti Babu, EE NIT Rourkela
69
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with Controlled rectifier
firingcircuit
controlled rectifier
α
+
Va
–
vc
va(s)vc(s)DC motor
The relation between vc and va is determined by the firing circuit
?
It is desirable to have a linear relation between vc and va
14 August 2009B Chitti Babu, EE NIT Rourkela
70
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with Controlled rectifierCosine-wave crossing control
Vm
vsvc
0 π 2π 3π 4π
Input voltage
Cosine wave compared with vc
Results of comparison trigger SCRs
Output voltage
14 August 2009B Chitti Babu, EE NIT Rourkela
71
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with Controlled rectifierCosine-wave crossing control
Vm
vsvc
0 π 2π 3π 4π
α
α
Vscos(ωt)Vscos(α) = vc
⎟⎟⎠
⎞⎜⎜⎝
⎛=α −
s
c1
vvcos
( )απ
= cosV2V ma ⎟
⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛π
= −
s
c1ma v
vcoscosV2Vs
cma v
vV2Vπ
=
A linear relation between vc and Va
14 August 2009B Chitti Babu, EE NIT Rourkela
72
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 DrivesModeling of the Power Converters: DC drives with Controlled rectifier
14 August 2009B Chitti Babu, EE NIT Rourkela
73
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 DrivesModeling of the Power Converters: DC drives with Controlled rectifier
14 August 2009B Chitti Babu, EE NIT Rourkela
74
s2T
H Ke)s(G−
=
vc(s) Va(s)
s
m
VV2K
π=
Single phase, 50Hz
T=10ms
s
m,LL
VV3
Kπ
= −
Three phase, 50Hz
T=3.33ms
Simplified if control bandwidth is reduced to much lower than the sampling frequency
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with Controlled rectifier
14 August 2009B Chitti Babu, EE NIT Rourkela
75
firingcircuit
currentcontroller
controlled rectifier
α+
Va
–
vciref
• 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 DrivesModeling of the Power Converters: DC drives with Controlled rectifier
14 August 2009B Chitti Babu, EE NIT Rourkela
76
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with Controlled rectifier
powergui
ContinuousVoltage Measurement4
v+-
Voltage Measurement3
v+-
Voltage Measurement2
v+-
Voltage Measurement1
v+-
Voltage Measurement
v+-
Universal Bridge
g
A
B
C
+
-
acos
To Workspace2
ir
To Workspace1
ia
To Workspace
v
Synchronized6-Pulse Generator
alpha_deg
AB
BCCA
Block
pulses
Step
SignalGenerator
Series RLC Branch
Scope3
Scope2
Scope1
Scope
SaturationPID Controller 1
PID
ux
Mu
-K-
Current Measurement1
i+ -
Current Measurement
i +-
Controlled Voltage Source
s
-+
Constant1
7
AC Voltage Source2
AC Voltage Source1
AC Voltage Source
• Input 3-phase, 240V, 50Hz • Closed loop current control with PI controller
14 August 2009B Chitti Babu, EE NIT Rourkela
77
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with Controlled rectifier
• Input 3-phase, 240V, 50Hz • Closed loop current control with PI controller
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-500
0
500
1000
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
5
10
15
Voltage
Current
0.22 0.23 0.24 0.25 0.26 0.27 0.28-500
0
500
1000
0.22 0.23 0.24 0.25 0.26 0.27 0.280
5
10
15
14 August 2009B Chitti Babu, EE NIT Rourkela
78
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
14 August 2009B Chitti Babu, EE NIT Rourkela
79
vc
+
Va
−
vtri
Vdc
q
Switching signals obtained by comparing control signal with triangular wave
Va(s)vc(s)DC motor
We want to establish a relation between vc and Va
?
AVERAGE voltage
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
14 August 2009B Chitti Babu, EE NIT Rourkela
80
dtqT1d triTt
ttri∫
+=
tri
on
Tt
=
Vdc
0
Ttri
ton
0
1
⎩⎨⎧
=01
qVc > Vtri
Vc < Vtrivc
dcdT
0 dctri
a dVdtVT1V tri == ∫
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
14 August 2009B Chitti Babu, EE NIT Rourkela
81
-Vtri
Vtri
-Vtri
vc
d
vc
0.5
Modeling of the Power Converters: DC drives with SM Converters
For vc = -Vtri → d = 0
Modeling and Control of Electrical Drives
14 August 2009B Chitti Babu, EE NIT Rourkela
82
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
0.5
Vtri
Vtri
vc
d
vc
-Vtri-Vtri
For vc = -Vtri → d = 0For vc = 0 → d = 0.5
For vc = Vtri → d = 1
14 August 2009B Chitti Babu, EE NIT Rourkela
83
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
0.5
vc
d
-Vtri-Vtri
ctri
vV215.0d +=
Vtri
Vtri
vc
For vc = -Vtri → d = 0For vc = 0 → d = 0.5
For vc = Vtri → d = 1
14 August 2009B Chitti Babu, EE NIT Rourkela
84
Thus relation between vc and Va is obtained as:
ctri
dcdca v
V2VV5.0V +=
Introducing perturbation in vc and Va and separating DC and AC components:
ctri
dcdca v
V2VV5.0V +=
ctri
dca v~
V2Vv~ =
DC:
AC:
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
14 August 2009B Chitti Babu, EE NIT Rourkela
85
Taking Laplace Transform on the AC, the transfer function is obtained as:
tri
dc
c
a
V2V
)s(v)s(v
=
va(s)vc(s)DC motor
tri
dc
V2V
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
14 August 2009B Chitti Babu, EE NIT Rourkela
86
2vtrivc
vc
vtri +
Vdc
−
q-Vdc
q
Vdc
+ VAB −
vAB
Vdc
-Vdc
ctri
dcABBA v
VVVVV ==−
tri
cAB V2
v5.0d1d −=−=
ctri
dcdcB v
V2VV5.0V −=
vB
Vdc
0
tri
cA V2
v5.0d +=
ctri
dcdcA v
V2VV5.0V +=
vA
Vdc
0
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
Bipolar switching scheme
14 August 2009B Chitti Babu, EE NIT Rourkela
87
tri
dc
c
a
VV
)s(v)s(v
=
va(s)vc(s)DC motor
tri
dc
VV
Bipolar switching scheme
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
14 August 2009B Chitti Babu, EE NIT Rourkela
88
+
Vdc
−vc
vtri
qa
Vdc
-vc
vtri
qb
Leg a
Leg b
The same average value we’ve seen for bipolar !
Vtri
vc
-vc
tri
cA V2
v5.0d +=
ctri
dcdcA v
V2VV5.0V +=
vA
tri
cB V2
v5.0d −+=
ctri
dcdcB v
V2VV5.0V −=
vB
ctri
dcABBA v
VVVVV ==−
vAB
Unipolar switching scheme
Modeling of the Power Converters: DC drives with SM Converters
Modeling and Control of Electrical Drives
14 August 2009B Chitti Babu, EE NIT Rourkela
89
tri
dc
c
a
VV
)s(v)s(v
=
va(s)vc(s)DC motor
tri
dc
VV
Unipolar switching scheme
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
14 August 2009B Chitti Babu, EE NIT Rourkela
90
DC motor – separately excited or permanent magnet
Extract the dc and ac components by introducing small perturbations in Vt, ia, ea, Te, TL and ωm
aa
aaat edtdi
LRiv ++=
Te = kt ia ee = kt ω
dtdJTT m
leω
+=
aa
aaat e~dti~d
LRi~v~ ++=
)i~(kT~ aEe =
)~(ke~ Ee ω=
dt)~(dJ~BT~T~ Le
ω+ω+=
ac components
aaat ERIV +=
aEe IkT =
ω= Ee kE
)(BTT Le ω+=
dc components
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
14 August 2009B Chitti Babu, EE NIT Rourkela
91
Perform Laplace Transformation on ac components
aa
aaat e~dti~d
LRi~v~ ++=
)i~(kT~ aEe =
)~(ke~ Ee ω=
dt)~(dJ~BT~T~ Le
ω+ω+=
Vt(s) = Ia(s)Ra + LasIa + Ea(s)
Te(s) = kEIa(s)
Ea(s) = kEω(s)
Te(s) = TL(s) + Bω(s) + sJω(s)
DC motor – separately excited or permanent magnet
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
14 August 2009B Chitti Babu, EE NIT Rourkela
92
Tkaa sLR
1+
)s(Tl
)s(Te
sJB1+
Ek
)s(Ia )s(ω)s(Va+
-
-
+
DC motor – separately excited or permanent magnet
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
14 August 2009B Chitti Babu, EE NIT Rourkela
93
Tc
vtri
+
Vdc
−
q
q
+
–
kt
Torque controller
Tkaa sLR
1+
)s(Tl
)s(Te
sJB1+
Ek
)s(Ia )s(ω)s(Va
+-
-
+Torquecontroller
Converter
peak,tri
dc
VV)s(Te
-+
DC motor
Modeling of the Power Converters: DC drives with SM Converters
Modeling and Control of Electrical Drives
14 August 2009B Chitti Babu, EE NIT Rourkela
94
Design procedure in cascade control structure
• Inner loop (current or torque loop) the fastest –largest bandwidth
• The outer most loop (position loop) the slowest –smallest bandwidth
• Design starts from torque loop proceed towards outer loops
Closed-loop speed control – an example
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
14 August 2009B Chitti Babu, EE NIT Rourkela
95
OBJECTIVES:
• Fast response – large bandwidth• Minimum overshoot
good phase margin (>65o)• Zero steady state error – very large DC gain
BODE PLOTS
Closed-loop speed control – an example
• Obtain linear small signal modelMETHOD
• Design controllers based on linear small signal model
• Perform large signal simulation for controllers verification
Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters
14 August 2009B Chitti Babu, EE NIT Rourkela
96
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
INDUCTION MOTOR DRIVES
Scalar ControlScalar Control Vector ControlVector Control
Const. V/HzConst. V/Hz is=f(ωr)is=f(ωr) FOCFOC DTCDTC
Rotor FluxRotor Flux Stator FluxStator FluxCircularFlux
CircularFlux
HexagonFlux
HexagonFlux
DTCSVMDTCSVM
14 August 2009B Chitti Babu, EE NIT Rourkela
97
Control of induction machine based on steady-state model (per phase SS equivalent circuit):
Rr’/s
+
Vs
–
RsLls Llr’
+
Eag
–
Is Ir’
Im
Lm
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
14 August 2009B Chitti Babu, EE NIT Rourkela
98
ωrωss
Trated
Pull out Torque(Tmax)
Te
sm ωratedωrotor
TL
Te
Intersection point (Te=TL) detersteady –state speed
mines the
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
14 August 2009B Chitti Babu, EE NIT Rourkela
99
Given a load T–ω characteristic, the steady-state speed can be changed by altering the T–ω of the motor:
Pole changing Synchronous speed change with no. of polesDiscrete step change in speed
Pole changing Synchronous speed change with no. of polesDiscrete step change in speed
Variable voltage (amplitude), frequency fixedE.g. using transformer or triacSlip becomes high as voltage reduced – low
Variable voltage (amplitude), frequency fixedE.g. using transformer or triacSlip becomes high as voltage reduced – low
Variable voltage (amplitude), variable frequency (Constant V/Hz)Using power electronics converter Operated at low slip frequency
Variable voltage (amplitude), variable frequency (Constant V/Hz)Using power electronics converter Operated at low slip frequency
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
14 August 2009B Chitti Babu, EE NIT Rourkela
100
Variable voltage, fixed frequency
0 20 40 60 80 100 120 140 1600
100
200
300
400
500
600
Torq
ue
w (rad/s)
Lower speed → slip higherLow efficiency at low speed
e.g. 3–phase squirrel cage IM
V = 460 V Rs= 0.25 Ω
Rr=0.2 Ω Lr = Ls = 0.5/(2*pi*50)
Lm=30/(2*pi*50)
f = 50Hz p = 4
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
14 August 2009B Chitti Babu, EE NIT Rourkela
101
Constant V/Hz
Approximates constant air-gap flux when Eag is large
Eag = k f φag
fV
fEag ≈=agφ = constant
Speed is adjusted by varying f - maintaining V/f constant to avoid flux saturation
To maintain V/Hz constant
+V_
+Eag
_
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
14 August 2009B Chitti Babu, EE NIT Rourkela
1020 20 40 60 80 100 120 140 160
0
100
200
300
400
500
600
700
800
900
Torq
ue
50Hz
30Hz
10Hz
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
Constant V/Hz
14 August 2009B Chitti Babu, EE NIT Rourkela
103
Vrated
frated
Vs
f
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
Constant V/Hz
14 August 2009B Chitti Babu, EE NIT Rourkela
104
VSIRectifier
3-phase supply IM
Pulse Width
Modulatorωs*+
Rampf
C
V
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
Constant V/Hz
14 August 2009B Chitti Babu, EE NIT Rourkela
105
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
To Workspace1
speed
To Workspace
torque
Subsystem
In1Out1
Step SliderGain1
0.41147Scope
Rate Limiter
Induction Machine
Va
Vb
Vc
isd
isq
ird
speed
Vd
irq
Vq
TeConstant V/Hz
In1
Out1
Out2
Out3
Constant V/Hz
Simulink blocks for Constant V/Hz Control
14 August 2009B Chitti Babu, EE NIT Rourkela
106
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100
0
100
200
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-200
0
200
400
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100
0
100
200
Constant V/Hz
Torque
Stator phase current
Speed
14 August 2009B Chitti Babu, EE NIT Rourkela
107
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 speed2. Maintain Im constant – constant Φag
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
14 August 2009B Chitti Babu, EE NIT Rourkela
108
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
0 20 40 60 80 100 120 140 1600
100
200
300
400
500
600
700
Torq
ue
50Hz
30Hz
10Hz
A low speed, flux falls below the rated value
14 August 2009B Chitti Babu, EE NIT Rourkela
109
With compensation (Is,ratedRs)
0 20 40 60 80 100 120 140 1600
100
200
300
400
500
600
700
Torq
ue
• Torque deteriorate at low frequency – hence compensation commonly performed at low frequency
• In order to truly compensate need to measure stator current –seldom performed
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
14 August 2009B Chitti Babu, EE NIT Rourkela
110
With voltage boost at low frequency
Vrated
frated
Linear offset
Non-linear offset – varies with IsBoost
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
14 August 2009B Chitti Babu, EE NIT Rourkela
111
Poor speed regulation
Solution:1. Compensate slip2. Closed-loop control
Problems with open-loop constant V/f
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
14 August 2009B Chitti Babu, EE NIT Rourkela
112
VSIRectifier
3-phase supply IM
Pulse Width
Modulator
VboostSlip speed calculator
ωs*++
++ V
Vdc Idc
Rampf
C
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
14 August 2009B Chitti Babu, EE NIT Rourkela
113
A better solution : maintain Φag constant. How?
Φag, constant → Eag/f , constant → Im, constant (rated)
maintain at rated
Controlled to maintain Im at rated
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
Rr’/s
+
Vs
–
RsLls Llr’
+
Eag
–
Is Ir’
Im
Lm
14 August 2009B Chitti Babu, EE NIT Rourkela
114
0 20 40 60 80 100 120 140 1600
100
200
300
400
500
600
700
800
900To
rque
50Hz
30Hz
10Hz
Constant air-gap flux
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
14 August 2009B Chitti Babu, EE NIT Rourkela
115
sr
mlr
rlr
m I
sR)LL(j
sRLj
I++ω
+ω=
,I1T
1j
1TjI
I
sRL
1j
sRLj
I
s
rr
rslip
rslipm
sr
rr
r
rr
m
+⎟⎟⎠
⎞⎜⎜⎝
⎛σ+
σω
+ω=
+⎟⎟⎠
⎞⎜⎜⎝
⎛σ+
σω
+ω=
,I1Tj
1T1
jI m
rslip
rr
rslip
s +ω
+⎟⎟⎠
⎞⎜⎜⎝
⎛σ+
σω
=
• Current is controlled using current-controlled VSI
• Dependent on rotor parameters –sensitive to parameter variation
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
Constant air-gap flux
14 August 2009B Chitti Babu, EE NIT Rourkela
116
VSIRectifier
3-phase supply IM
ω*
+
+ |Is|ωslip
C
Current controller
ωs
PI
+
ωr
-
Modeling and Control of Electrical DrivesModeling of the Power Converters: IM drives
Constant air-gap flux
14 August 2009B Chitti Babu, EE NIT Rourkela
117
THANK YOUTHANK YOU
14 August 2009B Chitti Babu, EE NIT Rourkela
118
Simulation of SPWM 1Φ-Voltage Source Inverter
• Objectives:• Control of Inverter Output Voltage• Reduction of Lower order Harmonics
• Limitations:• Increase of Switching Loss due to switching Frequency.
• Reduction of Available Voltage• EMI problems due to higher order harmonics
14 August 2009B Chitti Babu, EE NIT Rourkela
119
1Φ-Voltage Source Inverter
14 August 2009B Chitti Babu, EE NIT Rourkela
120
SPWM Technique