Power Electronics 01

7/31/2019 Power Electronics 01

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EEE 4213 Industrial ElectronicsSection: B and D-

ourse eac er: Dr. Mohammad Abdul Mannan


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ev ew ome equ rea er a s e a e o


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Voltage and Current Relation in a Resistive Element

Instantaneous voltage across a resistor:

vR = RiRInstantaneous current flows through a resistor:

iR = vR/R


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Voltage and Current Relation in an Inductive Element

Instantaneous voltage across an inductor:

Ldi

Lv =

Instantaneous current flows through an inductor:t

)0( =+= t

L

idt

L

v

LL

i


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Voltage and Current Relation in a Capacitive Element

)0(1 =+= tC

vdtiCv

Instantaneous current flows through a capacitor:

dt

CCCi =


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RL Circuit

Svdi

LRiLvRv =+=+

= tLReRSvti )/(1)(

== tLReSvRiRv )/(1

tLReSv

diLLv

)/(==

=


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RC Circuit

SvtCvidtCRi ==++ )0(

eR

ti )( =

tRC/1

= tRCevv )/1(1

=


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LC Circuit

SvtCvidtCdt

diL ==++ )0(

1

toC

Svti sin)( =

o1

=

=

tvtv cos1)( =


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Accordin to KVL:

RLC Series Circuit

Sv

Cv

Lv

Rv =++

SvtCvidtCdtLRi ==+++ )0(

dt

Sdv

dt

tC

dvi

Cdt

diR

dt

idL =

=+++

)0(1

2

20

1

2

2=++ i

Cdt

diR

idL

The roots of the previous equation are given by:

R 1 02,1 =s L2= LCo = o==

is called damping factor of circuit

o is called natural (or oscillation or resonance) frequency of circuit

or is called damping ratio of circuit


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Case 1: If = o or = = 1, the roots are equal and

real, s1 = s2, and the system is called critically damped.

tsetAAti 1)21()( +=The solution will be:

The constant A1 and A2 can be determined from the

A critically damped system converges to zero faster

.

than any other, and without oscillating. The systemreturns to equilibrium as quickly as possible without

osc at ng.


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Case 2: If > o or = > 1, the roots are unequal but

real, s1 s2, and the system is called overdamped.

tseA

tseAti 22

11)( +=The solution will be:

The system returns (exponentially decays) to

equ r um w ou osc a ng. arger va ues o edamping ratio return to equilibrium slower.


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Case 3: If < o or = < 1, the roots are unequal and

comp ex, s1 s2, an e sys em s ca e un er ampe .

rjs =2,1The roots are: 22 = or

r is called ringing (or damped resonance) frequency

The solution will be: )sin2cos1()( trAtrAt

eti +=

The system oscillates (with a slightly different

fre uenc than the undam ed case) with the

amplitude gradually decreasing to zero.


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Accordin to KCL:

RLC Parallel Circuit

SitLivdtLdt

dvC

R

v==+++ )0(

1

0112

=++ vdvvd

Ct

The roots of the revious e uation are iven b :

22 =s 1=1

=

==RC2 LC o

11

224 CR

LCr =


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Fourier AnalysisFourier Theorem: A periodic function v

o(t) can be described by a constant

term plus an infinite number of sine and cosine terms of frequency n , where

n is an integer.

++= 0 sincos)( nno tnbtnaa

tv = ,..2,1n

)2sin2cos()sincos()( 22110 ++++= tbtatbta

atvo

.......)4sin4cos()3sin3cos( 4433 +++++ tbtatbta

.......++++ HramonicFourthHramonicThirdHramonicSecondo


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===

20000

)()(1

)(2

)(

2/

1tdtvdttv

T

dttv

T

a oT

oT

o

===

2000

)(cos)(1

cos)(2

cos)()2/(

1tdtntvdttntv

Tdttntv

Ta o

To

Ton

===

2000

)(sin)(1

sin)(2

sin)(1

tdtntvdttntvdttntvb oT

oT

on

22 a1

nnnn

nnn nn ban=

++= 0 sin tnC

atv

= ,..2,12 n


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=

++= 0 )sin(2

)( nno tnCa

tv

.....4sin3sin2sin

)sin()( 11

+++++++

++=

tVtVtV

tVVtv mdco

,..,

;707.0;707.0;707.02

332211

1 mmmm VVVVV

VV ====

;.....707.0;707.0;707.0 665544 mmm VVVVVV ===

sin2 ++= tVVtv

.....)4sin(2)3sin(2)2sin(2 443322 +++++++ tVtVtV

==+++++=

4,3,2

22625242322 ...

n

nh VVVVVVV

221

226

25

24

23

22

21

2 ...hdcdco

VVVVVVVVVVV ++=+++++++=


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Types of Symmetry

EvenFunctionSymmetry

) )tftf =NosinecomponentspresentinFourierSeries

OddFunction

Symmetry tt =

NocosinecomponentspresentinFourierSeries


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Fourier Series For Waveform with Half-Wave Symmetry

T

2oooo

In a waveform with half-wave symmetry, the negative half-wave is

- ,

T/2 s (or rad).In that case the average value and an are zero and odd harmonics

are not presented.

a0 = an = 0 and bn = 0 for n = 2, 4, 6, 8,


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Fourier Series For Waveform with Quarter-Wave Symmetry

)2

()()4

()(

+=+= tvtvT

tvtv oooo

In that case the average value and bn are zero and odd harmonics

.

a0 = bn = 0 and an = 0 for n = 2, 4, 6, 8,


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=T

sdc dtti

T

I

0

)(1

=

2

0)()(

2

1tdtiI sdc

=T

dttiI21

T 0

=

2

2 )()(1

tdtiI ss

=

++=

.......21

)sincos()(

n

nndcs tnbtnaIti

+= )sin(2)( nsns tnIti

.......,,

.waveshapeaboveforandofexpressiontheFind nsnI


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Industrial Electronics

(analog or digital) electronic, power electronic, meters, sensors, analyzers,

automatic test equipment, multimeters, data recorders, relays, resistors,

wave uides, sco es, am lifiers, radio fre uenc (RF) circuit boards, timers,

counters, etc.

It covers all of the methods and facts of: control systems, instrumentation,

mechanism and diagnosis, signal processing and automation of various

industrial applications.

The scope of industrial electronics ranges from the design and maintenance of

simple electrical fuses to complicated programmable logic controllers (PLCs),so -s a e ev ces an mo or r ves.

Some of the specialty equipment used in industrial electronics includes:

variable frequency converter and inverter drives, human machine interfaces,

.

Industrial electronics are also used extensively in: chemical processing plants,

oil/gas/petroleum plants, mining and metal processing units, electronics and

semiconductor manufacturin .

The core area of industrial electronics is power electronics.


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Power ElectronicsDefinition of Power Electronics: Power electronics defined as the applications of

solid-state electronics for the control and conversion of electrical power.

Power Electronics combine power, electronics and control.

ower ea s w e s a c an ro a ng power equ pmen s or e genera on,

transmission and distribution of electrical energy.

Electronics deals with the solid-state devices and circuits for signal processing to

meet the desired control objectives.

Control deals with the steady-state and dynamic characteristics of closed-loop

s stems for ener conversion to meet the desired of electrical load.


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Elements of Power Electronics

Power electronics incorporates concepts from

e o ow ng e s:

1. Analog circuits

. ec ron c ev ces

3. Control systems

. owe ys ems

5. Magnets

. m n7. Numerical Simulation

.


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Classification of Power Semiconductor Switching

ev ces:Power semiconductor devices are classified as follows:

.

2. Power Transistors3. Th ristors

Power diodes are classified as follows:

1. Standard or General-Pur ose diodes

2. Fast-recovery or High-speed diodes

3. Schottky diodes


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Standard or General-Purpose Diodes

Operating Frequency: Up to 1 kHz

Current Rating: Less than 1 A to several thousands of amperes

o tage at ng: to aroun

Fast-Recovery or High Speed DiodesSwitching Time: Less than 5 to 10 s


Current Ratin : Less than 1 A to hundreds of am eresVoltage Rating: 50 V to around 6 kV

Switching Time: 0.2 s


Current Rating: Less than 1 A to 400 A

Voltage Rating: up 150 V


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Classification of Power Transistors:

1. Bipolar Junction Transistors (BJTs)

2. Metal-Oxide-Semiconductor Field Effect Transistors

(MOSFETs)

3. Static Induction Transistors (SITs)

4. Insulated Gate Bipolar Transistors (IGBTs)

5. COOLMOS Transistors


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Classification of Thyristors:

yr s ors are c ass e as o ows:1. Phase-controlled thyristors [or Silicon-controlled

rectifiers (SCRs)]

2. Fast switching thyristors (or SCRs)

3. Gate-turn off thyristors (GTOs)

5. Reverse-conduction thyristors (RCTs)

6. Static induction thyristors (SITHs). - -

8. FET-controlled thyristors (FET-CTHs)

9. MOS-controlled Thyristors (MCTs)

10. MOS turn-off thyristors (MTOs)11. Bidirectional phase-controlled thyristors (BCTs)

12. Emiter turn off control th ristors ETOs

13. Integrated gate-commutated thyristors (IGCTs)


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Classification of power semiconductor switching

The power semiconductor switching devices can be classified on the

basis of:

. ncon ro e urn on an o e.g. o e

2. Controlled turn on and uncontrolled turn off (e.g. SCR)3. Controlled turn on and off characteristics (e.g. BJT,

MOSFET, GTO, SITH, IGBT, SIT, MCT)

4. Continuous gate signal requirement (e.g. BJT, MOSFET,

IGBT, SIT)5. Pulse gate requirement (e.g. SCR, GTO, MCT)

6. Bipolar voltage withstanding capability (e.g. BJT, MOSFET,

GTO, IGBT, MCT)

7. Unipolar voltage withstanding capability (e.g. BJT,MOSFET, GTO, IGBT, MCT)

8. Bidirectional current capability (e.g. TRIAC, RCT)

9. Unidirectional current capability (e.g. SCR, GTO, BJT,

MOSFET, MCT, IGBT, SITH, SIT, diode)


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Power Electronics Circuits:

The power electronic circuits can be classified into sixtypes:

1. Diode rectifiers (uncontrolled ac-dc converter)

2. AC-DC converters (controlled rectifier)

. -

4. DC-DC converters (dc choppers)

5. DC-AC converters inverters

6. Static switch


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ACtoDCConverter

nver er

utput


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opper u pu

ACtoACConverter

ACSupply

o tage

ACOutput

Power Electronics 01

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