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


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


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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


4

Implementation of problem-oriented andproject-organised education

Literature Lectures Groupstudies

Experiments/Fieldwork/Tutorials

Problemanalysis

Problemsolving Report

PrototypingSimulation


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


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.


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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.


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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


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


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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


LoadLoad

Controller

Controller

Output- AC- DC

InputSource- AC- DC- unregulated

Reference

POWER ELECTRONIC CONVERTERS – the heart of power a power electronics system

sensors


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Why Power Electronics ?

Power semiconductor devices Power switches

+ vsw −= 0

ON or OFF

isw

+ vsw −

isw = 0

Ploss = vsw× isw = 0

Losses ideally ZERO !


12




−

Vak

+ia

G

K

A

−

Vak

+ia

K

A

−

Vak

+ia

G

K

A


13




D

S

G

+

VDS

−

iD

G

C

E

+

VCE

−

ic


14



Passive elements High frequencytransformer

+

V

1

−

+

V2

−

Inductor

+ VL−

i

L

+ VC−

i

C


15

Passive Elements In Power Electronics

• Resistors• Capacitors• Inductors• Transformers• Filters• Integrated Magnetics


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.


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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


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


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sensors

LoadLoad

Controller

Controller

Output- AC- DC

InputSource- AC- DC- unregulated

Reference

IDEALLY LOSSLESS !IDEALLY

LOSSLESS !


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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)


21


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)


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


23


Classic Electrical Drive for Variable Speed Application :

• Bulky

• Inefficient

• inflexible


24


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


25

Modern Electrical Drive SystemsExample on VSD application

motor pump

valve

Supply

Constant speed Variable Speed Drives

PowerIn

Power lossMainly in valve

Power out


26

Modern Electrical Drive SystemsExample on VSD application

PowerIn


Power out

motor pump

valve

SupplymotorPEC pump

Supply


PowerIn

Power loss

Power out


27


PowerIn


Power out

PowerIn

Power loss

Power out

motor pump

valve

SupplymotorPEC pump

Supply


Example on VSD application


28


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


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


Overview of AC and DC drives


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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




31


Courtesy: Electrical Drives by Ion Boldea ,CRC Press



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


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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


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+

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


35


+

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


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


37


Q1Q2

Q3 Q4

ω

T

3-phasesupply

3-phasesupply

+

Vt

−


38


Q1Q2

Q3 Q4

ω

T

F1

F2

R1

R2+ Va -

3-phasesupply


39


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

_


40

Power Electronic Converters in ED SystemsDC DRIVESAC-DC-DCAC-DC-DC

controlUncontrolled rectifier

Switch Mode DC-DC1-Quadrant2-Quadrant4-Quadrant


41


control


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



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




44

Q1Q2

Va

Ia

T1

T2

D1

+

Va

-

D2

ia

+

Vdc

−

D1 conducts → va = Vdc




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




46


+vc

2vtrivc

+vA

-

Vdc

0



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


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



49



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

−



50



Positive current

va = -Vdc when Q3 and Q4 are ONva = Vdc when D1 and D2 are ON


Negative current

leg A leg B

+ Va −Q1

Q4

Q3

Q2

D1 D3

D2D4

+

Vdc

−



51


vAB

Vdc

-Vdc

Vdc

0vB

vAVdc

0

2vtrivc

vc

+

_

Vdc+vA

-

+vB

-

Bipolar switching scheme – output swings between VDC and -VDC


52


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


53


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


54

Power Electronic Converters in ED SystemsAC DRIVESAC-DC-ACAC-DC-AC

control

The common PWM technique: CB-SPWM with ZSS

SVPWM


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


56


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


57


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


58



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


59



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


60



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


61



-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


62

vtri

Vdc

qvc

q

Vdc

Pulse widthmodulator

vc

Vdc

Pulse widthmodulator

vciref

PI+

− q


Current controlled converters in DC Drives - PI-based


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




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




65

Motor

i*a

i*b

i*c

Converter

PWM

+

+

+

PWM

PWM

PI

PI

PI


Current controlled converters in AC Drives - PI-based


66

Motor

i*a

i*b

i*c

Converter

3-2

3-2SVM2-3

PI

PI




67

id*

iq*PI

controller

dq→abc

abc→dq

SVM or SPWM

VSIIM

va*

vb*

vc*

id

iq

+

+

−

−

PIcontroller

Synch speed estimator

ωs

ωs




68


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



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


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


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


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



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



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



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)



76


powergui

ContinuousVoltage Measurement4

v+-

Voltage Measurement3

v+-


v+-


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


77


• 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


78

Modeling and Control of Electrical DrivesModeling of the Power Converters: DC drives with SM Converters


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



80

dtqT1d triTt

ttri∫

+=

tri

on

Tt

=

Vdc

0

Ttri

ton

0

1

⎩⎨⎧

=01

qVc > Vtri

Vc < Vtrivc

dcdT

0 dctri

a dVdtVT1V tri == ∫



81

-Vtri

Vtri

-Vtri

vc

d

vc

0.5

Modeling of the Power Converters: DC drives with SM Converters

For vc = -Vtri → d = 0



82


0.5

Vtri

Vtri

vc

d

vc

-Vtri-Vtri

For vc = -Vtri → d = 0For vc = 0 → d = 0.5

For vc = Vtri → d = 1


83


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


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:



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



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




87

tri

dc

c

a

VV

)s(v)s(v

=

va(s)vc(s)DC motor

tri

dc

VV




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





89

tri

dc

c

a

VV

)s(v)s(v

=

va(s)vc(s)DC motor

tri

dc

VV




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



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)




92

Tkaa sLR

1+

)s(Tl

)s(Te

sJB1+

Ek

)s(Ia )s(ω)s(Va+

-

-

+




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




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



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



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


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



98

ωrωss

Trated

Pull out Torque(Tmax)

Te

sm ωratedωrotor

TL

Te

Intersection point (Te=TL) detersteady –state speed

mines the



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



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



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

_



1020 20 40 60 80 100 120 140 160

0

100

200

300

400

500

600

700

800

900

Torq

ue

50Hz

30Hz

10Hz


Constant V/Hz


103

Vrated

frated

Vs

f


Constant V/Hz


104

VSIRectifier

3-phase supply IM

Pulse Width

Modulatorωs*+

Rampf

C

V


Constant V/Hz


105


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


106


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


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



108


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


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



110

With voltage boost at low frequency

Vrated

frated

Linear offset

Non-linear offset – varies with IsBoost



111

Poor speed regulation

Solution:1. Compensate slip2. Closed-loop control

Problems with open-loop constant V/f



112

VSIRectifier

3-phase supply IM

Pulse Width

Modulator

VboostSlip speed calculator

ωs*++

++ V

Vdc Idc

Rampf

C



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


Rr’/s

+

Vs

–

RsLls Llr’

+

Eag

–

Is Ir’

Im

Lm


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



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




116

VSIRectifier

3-phase supply IM

ω*

+

+ |Is|ωslip

C

Current controller

ωs

PI

+

ωr

-




117

THANK YOUTHANK YOU


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


119

1Φ-Voltage Source Inverter


120

SPWM Technique