Dr. Adel Gastliape.gastli.info/Chapter5/APE_CH5.pdf · r m m t r m t re t e t t dt di 1 m m tan 1 1 0 cos sin Dr. Adel Gastli Resonant Pulse Inverters 10 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ =

ADVANCED POWER ELECTRONICSADVANCED POWER ELECTRONICS

RESONANT PULSE INVERTERSRESONANT PULSE INVERTERS

Dr. Adel GastliEmail: [email protected]

http://adel.gastli.net

Dr. Adel Gastli Resonant Pulse Inverters 2

Learning ObjectivesLearning Objectives

To learn the switching techniques for resonant inverters and their types.

To study the operation and frequency characteristics of resonant inverters.

To understand the performance parameters of resonant inverters.

To learn the techniques for analyzing and designing of some resonant inverters.


CONTENTSCONTENTSCONTENTS

1. Introduction

2. Series Resonant Inverter

3. Parallel Resonant Inverter

4. Summary

(Textbook: Sections 8.1(Textbook: Sections 8.1--8.4)8.4)


IntroductionIntroduction

High di/dt & dv/dt➭stress on devicesHigh High di/dtdi/dt & & dv/dtdv/dt➭➭stress on devicesstress on devices

Psw_loss➚ fswPPsw_losssw_loss ➚➚ ffswsw

Turn on-off losses could be significant portion of total power loss

Turn onTurn on--off losses could off losses could be significant portion of be significant portion of total power losstotal power loss

EMI is also produced due to high di/dt and dv/dt in the converter waveforms

EMI is also produced due EMI is also produced due to high to high di/dtdi/dt and and dv/dtdv/dt in in the converter waveformsthe converter waveforms

PWM ControlPWM PWM

ControlControl


Introduction (ContIntroduction (Cont’’d)d)

Disadvantages of PWM control can be eliminated or minimized by

Disadvantages of PWM control can Disadvantages of PWM control can be eliminated or minimized bybe eliminated or minimized by

Turning on and off when isw or vsw

becomes zero

Turning Turning onon and and off off when when iiswsw or or vvswsw

becomes zerobecomes zero

Force zero-crossing by an LC-resonant circuit

Force zeroForce zero--crossing by crossing by an LCan LC--resonant circuitresonant circuit

Resonant Pulse Inverter

Resonant Pulse Resonant Pulse InverterInverter


Series Resonant InverterSeries Resonant Inverter

Unidirectional Switch Type– Basic Circuit

– Coupled Inductor Circuit

– Half-Bridge Circuit

– Full-Bridge Circuit

– Examples


Basic Series Resonant InverterBasic Series Resonant Inverter

2 4LR

C<

Load

Assume:

Unidirectional switches T1 on

T1 and T2 off

T2 on

Basic circuit

Underdamped


Mode 2

Mode 3

Mode 1

WaveformsWaveforms

m1 m2 m3 m2 m1


Mode 1: Series Resonant InverterMode 1: Series Resonant Inverter1

1 1 1 1

1( 0) ( 0)C S C c

diL Ri i dt v t V v t V

dt C+ + + = = = = −∫

2

2

211

4

1

sin)(

L

R

LC

teAti

r

r

tL

R

−=

=−

ω

ω

L

R

L

VV

dt

diA

r

cs

t

2

0

11

=

+==

=

α

ω teL

VVti r

t

r

cs ωω

α sin)(1−+

=

Underdamped

Resonant frequency

⎟⎠⎞

⎜⎝⎛=⇒−== −−−

αω

ωωαωω αα r

rmmr

tmr

tr ttete

dt

dimm 11 tan

1 sincos0


⎟⎠⎞

⎜⎝⎛= −

αω

ωr

rmt

1tan1

c

t

c VdttiC

tv −= ∫0 11 )(1

)(( ) ( ) srrr

t

r

csc Vtte

VVtv ++

+−= − ωωωα

ωα cossin)(1

1 1( ) 0mi t t= =

1 1 1

/

( )

( ) r

C m c

S c S

v t t V

V V e Vαπ ω−

= =

= + +

rmt ω

π=1


Mode 2: Series Resonant InverterMode 2: Series Resonant Inverter

2

2 1

2 2 2 1

( ) 0

( )

( )C C

C m C C

i t

v t V

v t t V V

==

= = =


Mode 3: Series Resonant InverterMode 3: Series Resonant Inverter

teL

Vti r

t

r

c ωω

α sin)( 13

−=

0)0(1

30 333 ==+++ ∫ tvdti

CRi

dt

diL c

t

123 )0( ccc VVtv ===


rmt

ωπ

=3

reV

V

Vttv

tti

c

c

cmc

m

ωαπ

−

−=

−=====

1

333

33

)(

0)(

10 33 )(1

)( c

t

c VdttiC

tv −= ∫ ( ) srrrt

r

cc Vtte

Vtv ++

−= − ωωωα

ωα cossin)( 1

3

teL

Vti r

t

r

c ωω

α sin)( 13

−−=


reVVVttv

tti

cccmc

m

ωαπ

−

====

==

1333

33

)(

0)(1 1 1

/

( )

( ) r

C m c

S c S

v t t V

V V e Vαπ ω−

= =

= + +

( )[ ]( )

( ) ( )zs

zzc

sz

csz

c

zs

zcs

zccc

eVeeV

VeVVeV

eVeVVeVVV

−−

−

−−−

+=−⇒

++=⇒

++===

1

13

zz

z

sc ee

eVV −

−

−+

=1

1

11 −

=−+

= − z

z

szz

z

sc e

eV

ee

eVV

r

zωαπ

=

ParametersParameters


Parameters (ContParameters (Cont’’d)d)

1−=

zs

c e

VV

11 −=

z

z

sc e

eVV

csc VVV +=1

In steady-state conditions, the peak values of positive and negative current through the load are the same.

In steady-state conditions, the peak values of positive and negative current through the load are the same.


Parameters (ContParameters (Cont’’d)d)

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=≤

>=−

rq

qoffr

t

ff

tt

ωπ

ωπ

ωπ

2

1(max)00

0

Output voltage frequency

toff : dead zone

Switch turn off time

Switch T1 should turn off before T2 turns on to avoid short-circuit Output frequency is limited


Coupled Inductor Series Resonant Coupled Inductor Series Resonant

When T1 turns on and i1(t) starts risingWhen T1 turns on and i1(t) starts rising

Voltage across L1is positiveVoltage across L1is positive

Voltage across L2is added to Vc in reverse biasing T2

Voltage across L2is added to Vc in reverse biasing T2

T2 is forced to turn offT2 is forced to turn off

Improved circuit


HalfHalf--Bridge Series Resonant InverterBridge Series Resonant Inverter

2121 & CCLL ==

Power is drawn from the dc source during both half-cycles of output voltage.

One half of the load current is supplied by capacitor C1 or C2 and other half by the source


FullFull--Bridge Series Resonant Inverter Bridge Series Resonant Inverter

High power output power.

When T1 and T2 are fired, a positive resonant current flows through the load; and when T3 and T4are fired, a negative load current flows.

The supply current is continuous, but pulsating Improvement


Remarks

Resonant frequency and available dead-zone depend on the load and for this reason, resonant inverters are most suitable for fixed-load applications.

The inverter load (or resistor) could also be connected in parallel with the capacitor.


Example 8.1Example 8.12

(max)2

2, 50 , 6 , 7 , 220 , 2 43,982 / , 10

1 154,160 / 13.42 7352

4 2( )

o s o o q

r off oo r

qr

R L H C F f kHz V V f rad s t s

Rrad s t s f Hz

LC L t

μ μ ω π μ

π πω μ πω ωω

= = = = = = = =

= − = = − = = =+

/

11

1

/ 2 2 2( )

/ 2

( )

20,000 100.42 1

1320.4 tan 22.47

( ) sin 70.82

2 ( ) 4.41 3889

17.68 ( ) 17.68

r

sc

rc c s m

r

tS cm p r m

r

T

o rms o o o oo

To

s A average o ooS

p

VRV V

L e

V V V V t s

V Vi t t I e t A

L

I f i t dt A P RI W

PI A I f i t dt A

V

I

απ ω

α

α

ω μω α

ωω

−

−

= = = =−

= + = = =

+= = = =

= = = =

= = = =

∫

∫

( ) 70.82 31.182o

k thyristor p R

II A I A= = = =


Example 8.1Example 8.1


PSIM SIMULATIONPSIM SIMULATION


Dead-time


Example 8.2Example 8.22, 50 , 3 , 7 , 220 , 2 43,982 / , 10o s o o qR L H C F f kHz V V f rad s t sμ μ ω π μ= = = = = = = =


Example 8.2Example 8.21 2

2

2 2 22 2

1 2 (max)

2, 50 , 3 , 7 , 220 , 2 43, 982 / , 10

1 1( 0) 0 ( 0) 54,160 /

2 2 4

16 , 13.42 7352

2( )

o s o o q

oo o C S C c r

e off oo r

qr

R L H C C C F f kHz V V f rad s t s

di RL Ri i dt v t V v t V rad s

dt C LC L

C C C F t s f Hzt

μ μ ω π μ

ω

π πμ μ πω ωω

= = = = = = = = = =

+ + + = − = = = − = − =

= + = = − = = =+

∫

/

11

1

/ 2 2 2( )

/ 2

( )

20,000 100.42 1

1320.4 tan 22.47

( ) sin 70.82

2 ( ) 4.41 3889

17.68 ( ) 17.68

r

sc

rc c s m

r

tS cm p r m

r

T

o rms o o o oo

To

s A average o ooS

p

VRV V

L e

V V V V t s

V Vi t t I e t A

L

I f i t dt A P RI W

PI A I f i t dt A

V

I

απ ω

α

α

ω μω α

ωω

−

−

= = = =−

= + = = =

+= = = =

= = = =

= = = =

∫

∫

( ) 70.82 31.182o

k thyristor p R

II A I A= = = =


PSIM SIMULATIONPSIM SIMULATION



Parallel Resonant InverterParallel Resonant Inverter

Parallel Resonant Circuit

Parallel Resonant Inverter


Parallel Resonant CircuitParallel Resonant Circuit

( )R

jZ

I

V

RI

RV

I

IjG

iii

R ωω ==== 00 1/)(

⎟⎠⎞

⎜⎝⎛ −−

=

++==

CRL

Rj

CjRLj

RjRYjG

ωω

ωω

ωω

1

1

1

1

)(

1)(

Current gainCurrent gain

iR


2

1

1)(

⎟⎠⎞

⎜⎝⎛ −+

=

CRL

RjG

ωω

ω

L

CR

L

RCRQp ===

00 ω

ω

2

0

0

21

1)(

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

=

ωω

ωω

ω

pQ

jG

22

0

11

1)(

,1

1

1)(

⎟⎠⎞

⎜⎝⎛ −+

=

=⎟⎠⎞

⎜⎝⎛ −+

=

uuQ

jG

u

uujQ

jG

p

p

ω

ωωω

Gain is maximum when:

000

=− CRL

R ωω

LCLC

11 0

20 =⇒= ωω


Note that maximum gain is obtained for u=1.

Output power (current) can be controlled by frequency control (adjusting u=ω/ω0).

See example 8.3 for typical application.

220 1

1

1)(,

⎟⎠⎞

⎜⎝⎛ −+

==

uuQ

jGu

p

ωωω


s

t

sLRC

IvdtLR

v

dt

dvC

Iiii

=++

=++

∫01

teC

Itv r

t

r

s ωω

α sin)( −=


t

rωπ

rωπ2

RC2

1=α

224

11

CRLCr −=ω Damping resonant frequency

r

r

rmt ω

παω

ω≅⎟

⎠⎞

⎜⎝⎛= −1tan

1 Time at which voltage vbecomes maximum

teC

Itv r

t

r

s ωω

α sin)( −=


iLiC

is iR

v


Parallel Resonant InverterParallel Resonant Inverter




Some ApplicationsSome Applications

High-voltage supplies such as this multiple-output model use more efficient and higher-performance components and power conversion techniques to reduce weight and improve performance.

Compared with line frequency operation, high frequencies offer the following advantages in regulated high voltage power supplies:

Smaller size and weight; Faster response time; Lower stored energy;

Higher efficiency;


Applications (ContApplications (Cont’’d)d)

The series resonant inverter can be used in a dielectric barrier discharge cells (DBDCs) application (generation of cold plasmas for the degradation of toxic organic compounds ), showing its effectiveness in the generation of the electron discharge by means of a charge/voltage figure of merit. Resonant Inverters can be used in resonant power supply which produces a controllable high-frequency high-voltage sinusoidal alternating-current output.


Applications (ContApplications (Cont’’d)d)

Electronic ballasts for high pressure discharge lamps.

Induction-Heating Appliances.


SummarySummary

A resonant pulse inverter can convert a fixed dc voltage to a fixed or variable ac voltage at a fixed frequency.

The output frequency which is the same as the resonant frequency remains almost fixed.

The parallel resonant inverter is most suitable for applications with variable load parameters.

Documents

Dr. Adel Gastliape.gastli.info/Chapter5/APE_CH5.pdf · r m m t r m t re t e t t dt di 1 m m tan 1 1 0 cos sin Dr. Adel Gastli Resonant Pulse Inverters 10 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ =