power electronics epe 550 circuits, devices, and applications electrical drives:

POWER ELECTRONICSPOWER ELECTRONICSEPE 550

CIRCUITS, DEVICES, AND APPLICATIONS

ELECTRICAL DRIVES: ELECTRICAL DRIVES: An Application of Power Electronics

Eng.Mohammed AlsumadyEng.Mohammed Alsumady

CONTENTSCONTENTS

Power Electronic SystemsPower Electronic Systems

Modern Electrical Drive Systems Modern Electrical Drive 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 Modeling and Control of Electrical DrivesDrives:: Current controlled Converters:: Current controlled Converters

:: Modeling of Power Converters:: Modeling of Power Converters :: Scalar control of IM:: Scalar control of IM


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

ControllerController

Output- AC- DC

InputSource- AC- DC- unregulated

Reference

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

sensors


Why Power Electronics ?

Power semiconductor devices Power switches

ON or OFF+ vsw − = 0

isw

+ vsw −

isw = 0

Ploss = vsw× isw = 0

Losses ideally ZERO !




Vak

+ia

G

K

A

Vak

+ia

K

A

Vak

+ia

G

K

A




D

S

G

+

VDS

iD

G

C

E

+

VCE

ic



Passive elements High frequencytransformer

+

V1

+

V2

Inductor

+ VL

iL

+ VC

iC





sensors

LoadLoad

ControllerController

Output- AC- DC

InputSource- AC- DC- unregulated

Reference

IDEALLY LOSSLESS !IDEALLY LOSSLESS !



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)

Advancement in semiconductor fabrication• A field-programmable gate array (FPGA) is an integrated circuit designed to be configured by the

customer or designer after manufacturing—hence "field-programmable". The FPGA configuration is generally specified using a hardware description language (HDL), similar to that used for an application-specific integrated circuit (ASIC) circuit diagrams were previously used to specify the configuration, as they were for ASICs, but this is increasingly rare). FPGAs can be used to implement any logical function that an ASIC could perform. The ability to update the functionality after shipping, partial re-configuration of the portion of the design and the low non-recurring engineering costs relative to an ASIC design (notwithstanding the generally higher unit cost), offer advantages for many applications.

• FPGAs contain programmable logic components called "logic blocks", and a hierarchy of reconfigurable interconnects that allow the blocks to be "wired together"—somewhat like many (changeable) logic gates that can be inter-wired in (many) different configurations. Logic blocks can be configured to perform complex combinational functions, or merely simple logic gates like AND and XOR. In most FPGAs, the logic blocks also include memory elements, which may be simple flip-flops or more complete blocks of memory.

• In addition to digital functions, some FPGAs have analog features. The most common analog feature is programmable slew rate and drive strength on each output pin, allowing the engineer to set slow rates on lightly loaded pins that would otherwise ring unacceptably, and to set stronger, faster rates on heavily loaded pins on high-speed channels that would otherwise run too slow. Another relatively common analog feature is differential comparators on input pins designed to be connected to differential signaling channels.

A field-programmable gate array (FPGA)

• The FPGA industry sprouted from programmable read-only memory (PROM) and programmable logic devices (PLDs). PROMs and PLDs both had the option of being programmed in batches in a factory or in the field (field programmable), however programmable logic was hard-wired between logic gates.

• A recent trend has been to take the coarse-grained architectural approach a step further by combining the logic blocks and interconnects of traditional FPGAs with embedded microprocessors and related peripherals to form a complete "system on a programmable chip“.

A field-programmable gate array (FPGA)


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)

Modern Electrical Drive SystemsModern 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

• IM: Induction Motor• PMSM: Permanent Magnet Synchronous Motor• SRM: Switched Reluctance Motor• BLDC: Brushless DC Motor

AC motors - IM- PMSM

DC motors (brushed)

SRMBLDC

Permanent Magnet Synchronous MotorPermanent Magnet Synchronous Motor The Permanent Magnet Synchronous motor is a rotating electric machine

where the stator is a classic three phase stator like that of an induction motor and the rotor has permanent magnets. In this respect, the PM Synchronous motor is equivalent to an induction motor, except the rotor magnetic field in case of PMSM is produced by permanent magnets. The use of a permanent magnet to generate a substantial air gap magnetic flux makes it possible to design highly efficient PM motors. Medium construction complexity, multiple fields, delicate magnets

• High reliability (no brush wear), even at very high achievable speeds

• High efficiency

• Low EMI

• Driven by multi-phase Inverter controllers

• Sensorless speed control possible

• Higher total system cost than for DC motors

• Smooth rotation - without torque ripple

• Appropriate for position control

Permanent Magnet Synchronous MotorPermanent Magnet Synchronous Motor

Switched Reluctance (SR) MotorSwitched Reluctance (SR) Motor

Switched reluctance (SR) motor is a brushless AC motor. It has simple mechanical construction and does not require permanent magnet for its operation. The stator and rotor in a SR motor have salient poles. The number of poles presence on the stator depends on the number of phases the motor is designed to operate in. Normally, two stator poles at opposite ends are configured to form one phase. In this configuration, a 3-phase SR motor has 6 stator poles. The number of rotor poles are chosen to be different to the number of stator poles. A 3-phase SR motor with 6 stator poles and 4 rotor poles is also known as a 6/4 3-Phase SR motor.

SR motor has the phase winding on its stator only. Concentrated windings are used. The windings are inserted onto the stator poles and connected in series to form one phase of the motor. In a 3-Phase SR motor, there are 3 pairs of concentrated windings and each pair of the winding is connected in series to form each phase respectively.

Future Electric Motors Build will be SR MotorsFuture Electric Motors Build will be SR Motors• The small-size SR motor was developed by Akira Chiba, professor at the

Department of Electrical Engineering, Faculty of Science & Technology, Tokyo University of Science.

• The prototyped SR motor has the same size as the 50kW synchronous motor equipped in the second-generation Toyota Prius. Currently all produced Electric cars are equipped with a synchronous motor whose rotor is embedded with a permanent magnet.

• But as the permanent magnets are getting more and more pricey (the price has doubled or tripled) because of higher demand, the future of SR Motors is now imminent.

• A four-phase 8/6 switched-reluctance motor is shown in cross section. In order to produce continuous shaft rotation, each of the four stator phases is energized and then de-energized in succession at specific positions of the rotor as illustrated.

Future electric motors build will be SR Motors.Future electric motors build will be SR Motors.

Brushless DC MotorBrushless DC Motor

• A BLDC motor has permanent magnets which rotate, and a fixed armature, eliminating the problems of connecting current to the moving armature. An electronic controller replaces the brush commutator assembly of the brushed DC motor, which continually switches the phase to the windings to keep the motor turning. The controller performs similar timed power distribution by using a solid-state circuit rather than the brush commutator system.

• BLDC motors offer several advantages over brushed DC motors, including more torque per weight, more torque per watt (increased efficiency), increased reliability, reduced noise, longer lifetime (no brush and commutator erosion), elimination of ionizing sparks from the commutator, and overall reduction of electromagnetic interference (EMI). With no windings on the rotor, they are not subjected to centrifugal forces, and because the windings are supported by the housing, they can be cooled by conduction, requiring no airflow inside the motor for cooling. This in turn means that the motor's internals can be entirely enclosed and protected from dirt or other foreign matter.

BLDC: Brushless DC Motor


Classic Electrical Drive for Variable Speed Application :

• Bulky

• Inefficient

• inflexible


PowerElectronicConverters

PowerElectronicConverters

LoadLoadMotor

Motor

ControllerControllerReference

POWER IN

feedback

Typical Modern Electric Drive Systems

Power Electronic Converters

Electric Energy- Unregulated -

Electric Energy- Regulated -

Electric MotorElectric Energy

Mechanical Energy

Modern Electrical Drive SystemsModern Electrical Drive SystemsExample on Variable Speed Drives (VSD) application

motor pump

valve

Supply

Constant speed Variable Speed Drives

PowerIn

Power lossMainly in valve

Power out

Modern Electrical Drive SystemsModern Electrical Drive SystemsExample on Variable Speed Drives (VSD) application

PowerIn


Power out

motor pump

valve

SupplymotorPEC pump

Supply


PowerIn

Power loss

Power out


PowerIn


Power out

PowerIn

Power loss

Power out

motor pump

valve

SupplymotorPEC pump

Supply


Example on VSD application


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 large impact 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

DC drives: Electrical drives that use DC motors as the prime mover

Regular maintenance, heavy, expensive, speed limit

AC drives: Electrical drives that use AC motors as the prime mover

Less maintenance, light, less expensive, high speed


Overview of AC and DC drives

Easy control, decouple control of torque and flux

Coupling between torque and flux – variable spatial angle between rotor and stator flux

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



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




Extracted from Boldea & Nasar


Power Electronic Converters in Electrical Drive SystemsPower Electronic Converters in Electrical Drive Systems

Converters for Motor Drives(some possible configurations)

DC Drives AC Drives

DC SourceAC Source

AC-DC-DCAC-DC-DCAC-DCAC-DC

AC Source

Const. DC

Variable DC

AC-DC-ACAC-DC-AC AC-ACAC-AC

NCC FCC

DC Source

DC-ACDC-AC DC-DC-ACDC-DC-AC

DC-DCDC-DCDC-AC-DCDC-AC-DC

Power Electronic Converters in ED SystemsPower Electronic Converters in ED Systems

Converters for Motor Drives

Configurations of Power Electronic Converters depend on:

Sources available

Type of Motors

Drive Performance - applications

- Braking

- Response

- Ratings

Power Electronic Converters in ED SystemsPower Electronic Converters in ED SystemsDC DRIVES

Available AC source to control DC motor (brushed)

AC-DC-DCAC-DC-DCAC-DCAC-DC

Controlled Rectifier Single-phase Three-phase

Uncontrolled Rectifier Single-phase Three-phase

DC-DC Switched mode 1-quadrant, 2-quadrant 4-quadrant

Control Control


+

Vo

+

Vo

cosV2

V mo

cosV3

V m,LLo

Average voltage over 10ms

Average voltage over 3.33 ms

50Hz1-phase

50Hz3-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


+

Vo

+

Vo

cosV2

V mo

90o 180o

mV2

mV2

90o

m,LLV3

m,LLV3

cosV3

V m,LLo

Average voltage over 10ms

Average voltage over 3.33 ms

50Hz1-phase

50Hz3-phase

180o

AC-DCAC-DC


AC-DCAC-DC

Ia

Q1Q2

Q3 Q4

Vt

3-phasesupply

+

Vt

ia

- Operation in quadrant 1 and 4 only


AC-DCAC-DC

Q1Q2

Q3 Q4

T

3-phasesupply

3-phasesupply

+

Vt


AC-DCAC-DC

Q1Q2

Q3 Q4

T

F1

F2

R1

R2+ Va -

3-phasesupply


AC-DCAC-DC

Cascade control structure with armature reversal (4-quadrant):

Speedcontroller

Speedcontroller

CurrentController

CurrentController

FiringCircuitFiringCircuit

Armature reversal

Armature reversal

iD

iD,ref

iD,ref

iD,

ref + +

__


AC-DC-DCAC-DC-DC

controlUncontrolled rectifier

Switch Mode DC-DC1-Quadrant2-Quadrant4-Quadrant


AC-DC-DCAC-DC-DC

control

T1 conducts va = Vdc

Q1Q2

Va

Ia

T1

T2

D1

+

Va

-

D2

ia

+

Vdc

DC DRIVES

AC-DC-DCAC-DC-DC DC-DC: Two-quadrant Converter


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 DRIVES



Q1Q2

Va

Ia

T1

T2

D1

+

Va

-

D2

ia

+

Vdc

D1 conducts va = Vdc

DC DRIVES



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 DRIVES



DC DRIVES


+vc

2vtri

vc

+vA

-

Vdc

0


leg A leg B

+ Va Q1

Q4

Q3

Q2

D1 D3

D2D4

+

Vdc

va = Vdc when Q1 and Q2 are ON

Positive current


AC-DC-DCAC-DC-DC DC-DC: Four-quadrant Converter

leg A leg B

+ Va Q1

Q4

Q3

Q2

D1 D3

D2D4

+

Vdc

va = -Vdc when D3 and D4 are ON


va = 0 when current freewheels through Q and D

Positive current






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






Positive current

va = -Vdc when Q3 and Q4 are ON

va = Vdc when D1 and D2 are ON


Negative current

leg A leg B

+ Va Q1

Q4

Q3

Q2

D1 D3

D2D4

+

Vdc




AC-DC-DCAC-DC-DC

vAB

Vdc

-Vdc

Vdc

0vB

vAVdc

0

2vtri

vc

vc

+

_

Vdc+vA

-

+vB

-

Bipolar switching scheme – output swings between VDC and -VDC


AC-DC-DCAC-DC-DCUnipolar switching scheme – output swings between Vdc and -Vdc

Vtri

vc

-vc

vc

+

_

Vdc+vA

-

+vB

-

-vc

vA

Vdc

0

vB

Vdc

0

vAB

Vdc

0


AC-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


AC DRIVES

AC-DC-ACAC-DC-AC

control

The common PWM technique: CB-SPWM with ZSS

SVPWM

Modeling and Control of Electrical DrivesModeling 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

+*

1/s

+ +

current

controller

T**

kT


Current controlled converters in DC Drives - Hysteresis-based

iref

+

Vdc

−

ia

iref

va

+

Va

ierr

ierr

q

q

• High bandwidth, simple implementation, insensitive to parameter variations

• Variable switching frequency – depending on operating conditions

+

_


Current controlled converters in AC Drives - Hysteresis-based

3-phaseAC 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



id

iq

is

hh hh

• For isolated neutral load, ia + ib + ic = 0 control is not totally independent

• Instantaneous error for isolated neutral load can reach double the band



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+ -


i+ -

• h = 0.3 A• Sinusoidal reference current, 30Hz

• Vdc = 600V• mH load



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



-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

vtri

Vdc

qvc

q

Vdc

Pulse widthmodulator

vc

Vdc

Pulse widthmodulator

vciref

PI+

q


Current controlled converters in DC Drives - PI-based

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 Modeling and Control of Electrical DrivesDrives


•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



Motor

i*a

i*b

i*c

Converter

PWM

+

+

+

PWM

PWM

PI

PI

PI


Current controlled converters in AC Drives - PI-based

Motor

i*a

i*b

i*c

Converter

3-2

3-2

SVM2-3

PI

PI



id*

iq*

PIcontroller

dqabc

abcdq

SVM or SPWM

VSIIM

va*

vb*

vc*

id

iq

+

+

PIcontroller

Synch speed estimator

s

s



Modeling and Control of Electrical Modeling and Control of Electrical DrivesDrives

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 - iaStationary - id

Rotating - ia Rotating - id


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

firingcircuit

controlled rectifier

+

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


Cosine-wave crossing control

Vm

vsvc

0 2 3 4

Input voltage

Cosine wave compared with vc

Results of comparison trigger SCRs

Output voltage


Cosine-wave crossing control

Vm

vsvc

0 2 3 4

Vscos(t)Vscos() = vc

s

c1

vv

cos

cosV2

V ma

s

c1ma v

vcoscos

V2V

s

cma v

vV2V

A linear relation between vc and Va

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


s2

T

H Ke)s(G

vc(s) Va(s)

s

m

V

V2K

Single phase, 50Hz

T=10ms

s

m,LL

V

V3K

Three phase, 50Hz

T=3.33ms

Simplified if control bandwidth is reduced to much lower than the sampling frequency


firingcircuit

currentcontroller

controlled rectifier

+

Va

–

vciref

• To control the current – current-controlled converter• Torque can be controlled• Only operates in Q1 and Q4 (single converter topology)



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

BC

CA

Block

pulses

Step

SignalGenerator

Series RLC Branch

Scope3

Scope2

Scope1

Scope

SaturationPID Controller 1

PID

Mux

Mux

-K-


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


• 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

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

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


dtqT1

dtriTt

ttri

tri

on

Tt

Vdc

0

Ttri

ton

0

1

01

qVc > Vtri

Vc < Vtrivc

dc

dT

0 dctri

a dVdtVT1

Vtri


-Vtri

Vtri

-Vtri

vc

d

vc

0.5

For vc = -Vtri d = 0



0.5

Vtri

Vtri

vc

d

vc

-Vtri-Vtri


For vc = 0 d = 0.5

For vc = Vtri d = 1


0.5

vc

d

-Vtri-Vtri

ctri

vV21

5.0d

Vtri

Vtri

vc


For vc = 0 d = 0.5

For vc = Vtri d = 1

Thus relation between vc and Va is obtained as:

ctri

dcdca v

V2V

V5.0V

Introducing perturbation in vc and Va and separating DC and AC components:

ctri

dcdca v

V2V

V5.0V

ctri

dca v~

V2V

v~

DC:

AC:


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


2vtri

vc

vc

vtri+

Vdc

−

q-Vdc

q

Vdc

+ VAB

vAB

Vdc

-Vdc

ctri

dcABBA v

VV

VVV

tri

cAB V2

v5.0d1d

ctri

dcdcB v

V2V

V5.0V

vB

Vdc

0

tri

cA V2

v5.0d

ctri

dcdcA v

V2V

V5.0V

vA

Vdc

0



tri

dc

c

a

VV

)s(v)s(v

va(s)vc(s)DC motor

tri

dc

VV



+

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

V2V

V5.0V

vA

tri

cB V2

v5.0d

ctri

dcdcB v

V2V

V5.0V

vB

ctri

dcABBA v

VV

VVV

vAB



tri

dc

c

a

VV

)s(v)s(v

va(s)vc(s)DC motor

tri

dc

VV



DC motor – separately excited or permanent magnet

Extract the dc and ac components by introducing small perturbations in Vt, ia, ea, Te, TL and m

aa

aaat edtdi

LRiv

Te = kt ia ee = kt

dtd

JTT mle

aa

aaat e~dti~

dLRi

~v~

)i~(kT

~aEe

)~(ke~ Ee

dt)~(d

J~BT~

T~

Le

ac components

aaat ERIV

aEe IkT

Ee kE

)(BTT Le

dc components


Perform Laplace Transformation on ac components

aa

aaat e~dti~

dLRi

~v~

)i~(kT

~aEe

)~(ke~ Ee

dt)~(d

J~BT~

T~

Le

Vt(s) = Ia(s)Ra + LasIa + Ea(s)

Te(s) = kEIa(s)

Ea(s) = kE(s)

Te(s) = TL(s) + B(s) + sJ(s)



Tkaa sLR

1

)s(Tl

)s(Te

sJB1

Ek

)s(Ia )s()s(Va

+-

-

+



Tc

vtri

+

Vdc

−

q

q

+

–

kt

Torque controller

Tkaa sLR

1

)s(Tl

)s(Te

sJB1

Ek

)s(Ia )s()s(Va

+-

-

+

Torquecontroller

Converter

peak,tri

dc

VV)s(Te

-+

DC motor


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


OBJECTIVES:• Fast response – large bandwidth

• Minimum overshoot good phase margin (>65o)

• Zero steady state error – very large DC gain

BODE PLOTS

• Obtain linear small signal model

METHOD

• Design controllers based on linear small signal model

• Perform large signal simulation for controllers verification



Ra = 2 La = 5.2 mH

J = 152 x 10–6 kg.m2B = 1 x10–4 kg.m2/sec

kt = 0.1 Nm/Ake = 0.1 V/(rad/s)

Vd = 60 V Vtri = 5 V

fs = 33 kHz


• PI controllers • Switching signals from comparison of vc and triangular waveform


Bode Diagram

Frequency (rad/sec)

-50

0

50

100

150From: Input Point To: Output Point

Mag

nitu

de (

dB)

10-2

10-1

100

101

102

103

104

105

-90

-45

0

45

90

Pha

se (

deg)

compensated

compensated

kpT= 90

kiT= 18000


Torque controller design Open-loop gain

Speed controller design

1Speedcontroller sJB

1

* T* T

–

+

Torque loop


Bode Diagram

Frequency (Hz)

-50

0

50

100

150From: Input Point To: Output Point

Mag

nitu

de (

dB)

10-2

10-1

100

101

102

103

104

-180

-135

-90

-45

0

Pha

se (

deg)

Open-loop gain

compensated

kps= 0.2

kis= 0.14

compensated

Speed controller design


Large Signal Simulation results

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45-40

-20

0

20

40

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45-2

-1

0

1

2

Speed

Torque


Modeling and Control of Electrical DrivesModeling 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(r)is=f(r) FOCFOC DTCDTC

Rotor FluxRotor Flux Stator FluxStator Flux CircularFlux

CircularFlux

HexagonFlux

HexagonFlux

DTCSVMDTCSVM

Control of induction machine based on steady-state model (per phase SS equivalent circuit):

Rr’/s

+

Vs

–

RsLls Llr’

+

Eag

–

Is Ir’

Im

Lm


rs

Trated

Pull out Torque(Tmax)

Te

ssm ratedrotor

TL

Te

Intersection point (Te=TL) determines the steady –state speed


Given a load T– characteristic, the steady-state speed can be changed by altering the T– of the motor:

Pole changing Synchronous speed change with no. of 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 efficiency

Variable voltage (amplitude), frequency fixedE.g. using transformer or triacSlip becomes high as voltage reduced – low efficiency

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


Variable voltage, fixed frequency

0 20 40 60 80 100 120 140 1600

100

200

300

400

500

600

Tor

que

w (rad/s)

Lower speed slip higher

Low efficiency at low speed

e.g. 3–phase squirrel cage IM

V = 460 V Rs= 0.25

Rr=0.2 Lr = Ls = 0.5/(2*pi*50)

Lm=30/(2*pi*50)

f = 50Hz p = 4


Constant V/Hz

Approximates constant air-gap flux when Eag is large

Eag = k f ag

f

V

f

Eag ag = constant

Speed is adjusted by varying f - maintaining V/f constant to avoid flux saturation

To maintain V/Hz constant

+V

_

+Eag

_


0 20 40 60 80 100 120 140 1600

100

200

300

400

500

600

700

800

900

Tor

que

50Hz

30Hz

10Hz


Modeling of the Power Converters: IM drives

Constant V/Hz

Vrated

frated

Vs

f


Constant V/Hz

VSIRectifier

3-phase supply IM

Pulse Width

Modulators*+

Rampf

C

V


Constant V/Hz


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


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

Speed

Torque

Stator phase current

1Problems 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 ag



0 20 40 60 80 100 120 140 1600

100

200

300

400

500

600

700

Tor

que

50Hz

30Hz

10Hz

A low speed, flux falls below the rated value

With compensation (Is,ratedRs)

0 20 40 60 80 100 120 140 1600

100

200

300

400

500

600

700

Tor

que

• Torque deteriorate at low frequency – hence compensation commonly performed at low frequency

• In order to truly compensate need to measure stator current – seldom performed


With voltage boost at low frequency

Vrated

frated

Linear offset

Non-linear offset – varies with IsBoost


Poor speed regulation

Solution:1. Compesate slip2. Closed-loop control

Problems with open-loop constant V/f

2Modeling and Control of Electrical DrivesModeling and Control of Electrical Drives

Modeling of the Power Converters: IM drives

VSIRectifier

3-phase supply IM

Pulse Width

Modulator

VboostSlip speed calculator

s*++

++ V

Vdc Idc

Rampf

C


A better solution : maintain ag constant. How?

ag, 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

0 20 40 60 80 100 120 140 1600

100

200

300

400

500

600

700

800

900

Tor

que

50Hz

30Hz

10Hz


Constant air-gap flux

sr

mlr

rlr

m I

sR

)LL(j

sR

LjI

,I

1T1

j

1TjI

I

sR

L1

j

sR

LjI

s

rr

rslip

rslipm

s

rr

r

r

rr

m

,I1Tj

1T1

j

I mrslip

rr

rslip

s

• Current is controlled using current-controlled VSI

• Dependent on rotor parameters – sensitive to parameter variation



VSIRectifier

3-phase supply IM

*

+

+ |Is|slip

C

Current controller

s

PI

+

r

-



THANK YOUTHANK YOU

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