2

Chapter 2 AC to DC Converters

Outline2.1 Single-phase controlled rectifier2.2 Three-phase controlled rectifier2.3 Effect of transformer leakage inductance on rectifier circuits2.4 Capacitor-filtered uncontrolled rectifier2.5 Harmonics and power factor of rectifier circuits2.6 High power controlled rectifier2.7 Inverter mode operation of rectifier circuit2.8 Thyristor-DC motor system2.9 Realization of phase-control in rectifier

2.1 Single- phase controlled (controllable) rectifier

2.1.1 Single-phase half-wave controlled rectifier

Resistive load

T VT

R

a )

u 1 u 2

u VT u d

i d

0 t 1

2

t

u 2

u g

u d

u VT

0

b )

c )

d )

e )

0

0

t

t

t

2

cos145.0)cos1(

2

2)(sin2

2

12

22d U

UttdUU

（ 2-1）

Inductive (resistor-inductor) load

a )

u 1

T

VT

R

L

u 2

u VT u d

i d

u 2

0 t 1 2

t

u g

0

u d

0

i d

0 u VT

0

b )

c )

d )

e )

f )

+ +

t

t

t

t

Basic thought process of time-domain analysis for power electronic circuits

The time- domain behavior of a power electronic circuit is actually the combination of consecutive transients of the different linear circuits when the power semiconductor devices are in different states.

a ) b )

VT

R

L

VT

R

L u 2 u 2

tURit

iL sin2

d

d2d

d

ω t = a ， i d = 0

)sin(2

)sin(2 2

)(2

d

tZ

Ue

Z

Ui

tL

R

（ 2 - 2 ）

（ 2 - 3 ）

Single- phase half- wave controlled rectifier with freewheeling diode

load (L is large enough) Inductive

a ) L

T VT

R u 1

u 2

u VT u d

VD R

i d i VD

u 2

u d

i d

u VT

i VT I d

I d

t O

O

O

O

O

O

- +

b )

i VD R

t

t

t

t

t

g )

c )

e )

f )

d )

T1

Maximum forward voltage, maximum reverse voltage

Disadvantages:

–Only single pulse in one line cycle

–DC component in the transformer current

ddVT 2II

d2dVT 2

)(2

1ItdII

d

2 2dVD 2

)(2

1R

ItdII

ddVD 2RII

（ 2 -5）

（ 2 -6）

（ 2 -7）

（ 2 -8）

2.1.2 Single- phase bridge fully-controlled rectifier

• Resistive load

t

0

0

0

i 2

u d i d

b )

c )

d )

u d ( i d )

R

T

u 1 u 2

a )

i 2 a

b

VT3

u d

i d

u VT 1 , 4

t

t

VT4

VT1

VT2

Average output (rectified) voltage:

Average output current:

For thyristor:

For transformer:

2

cos19.0

2

cos122)(dsin2

12

22d U

UttUU （ 2-9）

（2-10）

2

cos19.0

2

cos122 22dd

R

U

R

U

R

UI

（ 2 - 1 1 ） 2

cos145.0

2

1 2ddVT

R

UII

2sin

2

1

2)(d)sin

2(

2

1 222VT

R

Utt

R

UI （ 2 - 1 2 ）

2sin

2

1)()sin

2(

1 2222 R

Utdt

R

UII (2-13)

• Inductive load (L is large enough)

t

t

t

t

t

t

t

u2

ud

id

Id

Id

Id

Id

Id

iVT1,4

iVT2,3

uVT1,4

i2

,

b )

R

T

u 1 u 2

a )

i 2 a

b

VT3

u d

i d

VT4

VT1

VT2

• Electro- motive-force (EMF) load With resistor

cos9.0cos

22)(dsin2

1222d UUttUU （2-15）

a ) b )

R

E

i d

u d i d

O

E

u d

t

I d

O t

• With resistor and inductor

When L is large enough, the output voltage and current waveforms are the same as ordinary inductive load.

When L is at a critical value

O

u d

0

E

i d

t

t

=

dmin

23

dmin

2 1087.222

I

U

I

UL （2-17）

2.1.3 Single- phase full- wave controlled rectifier

a ) b )

u 1

T

R

u 2

u 2

i 1 VT 1

VT 2 u d

u d

i 1

O

O

t

t

2.1.4 Single- phase bridge half-controlled rectifier

a)

T a

b R

L

Ob)

u2

i2

ud

idVT

1

VT

2

VD

3

VD

4

VD

R

u2

O

ud

id Id

O

O

O

O

Oi2

Id

Id

Id

Id

Id

t

t

t

t

t

t

t

iVT1iVD4

iVT2iVD

3

iVDR

• Another single- phase bridge half-controlled rectifier

Comparison with previous circuit:

–No need for additional freewheeling diode

–Isolation is necessary between the drive circuits of the two thyristors

load

T

u 2

VT2 VT4

VT1 VT3

Summary of some important points in analysis

When analyzing a thyristor circuit, start from a diode circuit with the same topology. The behavior of the diode circuit is exactly the same as the thyristor circuit when firing angle is 0.

A power electronic circuit can be considered as different linear circuits when the power semiconductor devices are in different states. The time- domain behavior of the power electronic circuit is actually the combination of consecutive transients of the different linear circuits.

Take different principle when dealing with different load– For resistive load: current waveform of a resistor is the same as the

voltage waveform–For inductive load with a large inductor: the inductor current canbe considered constant

2.2 Three- phase controlled (controllable) rectifier

2.2.1 Three- phase half- wave controlled rectifier

Resistive load, α= 0º

a

b

c

T

R

u d

i d

VT 2

VT 1

VT 3

u 2

O

O

O

u ab u ac

O

i VT 1

u VT 1

t

t

t

t

t

u a u b u c

u G

u d

t1 t2 t3

Common-cathode connection

Natural commutation point

Resistive load, α= 30º

u 2 u a u b u c

O

O

O t

O t

O t

u G

u d

u ab u ac

t 1 i VT 1

u VT 1 u ac

t

t

a

b

c

T

R

u d

i d

VT 2

VT 1

VT 3

Resistive load, α= 60º

t

u 2 u a u b u c

O

O

O

O

u G

u d

i VT 1

t

t

t

a

b

c

T

R

u d

i d

VT 2

VT 1

VT 3

Resistive load, quantitative analysis

When α≤ 30º , load current id is continuous.

When α > 30º , load current id is discontinuous.

Average load current

Thyristor voltages

cos17.1cos

2

63)(sin2

321

226

5

6

2d UUttdUU

（2-18）

)

6cos(1675.0)

6cos(1

2

23)(sin2

321

26

2d

UttdUU (2-19)

R

UI dd （2-20）

0 30 60 90 120 150

0 . 4

0 . 8

1 . 2 1 . 17

3 2

1

/( ° )

Ud/U2

• Inductive load, L is large enough

T

R

L

u d

e L i d

VT 3

u d

i a

u a u b u c

i b

i c

i d

u ac u ab

u ac O

O

O

O

O

O t

u VT 1

t

t

t

t

t

a

b

c

VT 2

Thyristor voltage and currents, transformer current :

cos17.1cos

2

63)(sin2

321

226

5

62d UUttdUU

（2-18）

ddVT2 577.03

1IIII d

VTVT(AV) 368.0

57.1I

II

2RMFM 45.2 UUU

（2-23）

（2-25）

（2-24）

2.2.2 Three- phase bridge fully-controlled rectifier

Circuit diagram

Common- cathode group and common- anode group of thyristors

Numbering of the 6 thyristors indicates the trigger sequence.

b

a

c

T

n load

i a

i d

u d

VT 1 VT 3 VT 5

VT 4 VT 6 VT 2 d 2

d 1

Resistive load, α= 0º

b

a

c

T

n load

i a

i d

u d

VT 1 VT 3 VT 5

VT 4 VT 6 VT 2 d 2

d 1

u 2 u d 1

u d 2

u 2 L u d

u ab u ac

u ab u ac u bc u ba u ca u cb u ab u ac

u ab u ac u bc u ba u ca u cb u ab u ac I II III IV V VI

u a u c u b

t 1 O t

O t

O t

O t

= 0 °

i VT 1

u VT 1

Resistive load, α= 30º

b

a

c

T

n load

i a

i d

u d

VT 1 VT 3 VT 5

VT 4 VT 6 VT 2 d 2

d 1

u d 1

u d 2

= 30 ¡

ã

i a

O

O

O

O t

u d

u ab u ac

u a u b u c

t 1

u ab u ac u bc u ba u ca u cb u ab u ac І II III IV V VI

u ab u ac u bc u ba u ca u cb u ab u ac u VT 1

t

t

t

Resistive load, α= 60º

b

a

c

T

n load

i a

i d

u d

VT 1 VT 3 VT 5

VT 4 VT 6 VT 2 d 2

d 1

= 60 º u

d 1

u d 2

u d

u ac u

ac

u ab

u ab u ac u

bc u ba u

ca u cb u

ab u ac

u a

I II III IV V VI

u b u c

O

t 1

O t

O

u VT

1

t

t

Resistive load, α= 90º

b

a

c

T

n load

i a

i d

u d

VT 1 VT 3 VT 5

VT 4 VT 6 VT 2 d 2

d 1

u d 1

u d 2

u d

u a u b u c u a u b

t

O

O

O

O

O

i a

i d

u ab u ac u bc u ba u ca u cb u ab u ac u bc u ba

i VT 1

t

t

t

t

Inductive load, α= 0º

b

a

c

T

n load

i a

i d

u d

VT 1 VT 3 VT 5

VT 4 VT 6 VT 2 d 2

d 1

u d 1 u 2

u d 2 u 2 L u d

i d

O

O

O

t O

u a = 0 u b u c

t 1

u ab u ac u bc u ba u ca u cb u ab u ac I II III IV V VI

i VT 1

t

t

t

º

Inductive load, α= 30º

b

a

c

T

n load

i a

i d

u d

VT 1 VT 3 VT 5

VT 4 VT 6 VT 2 d 2

d 1

u d 1

= 30

u d 2

u d u ab u ac u bc u ba u ca u cb u ab u ac I II III IV V VI

t O

t O

t O

t O

i d

i a

t 1

u a u b u c °

Inductive load, α= 90º

b

a

c

T

n load

i a

i d

u d

VT 1 VT 3 VT 5

VT 4 VT 6 VT 2 d 2

d 1

= 90 ° u d 1

u d 2 u ac u bc u ba u ca u cb u ab u ac u ab I II III IV V VI

u d

u ac

u ab

u ac

t O

t O

t O

u b u c u a

t 1

u VT 1

Quantitative analysis

Average output voltage:

For resistive load, When a > 60º, load current id is discontinuous.

everage output current (load current):

Transformer current:

cos34.2)(sin6

3

12

3

2

3

2d UttdUU

（2-26）

（2-27）

)

3cos(134.2)(sin6

32

32d

UttdUU

R

UI dd （2-20）

dddd IIIII 816.03

2

3

2)(

3

2

2

1 222

（2-28）

2.3 Effect of transformer leakage inductance on rectifier circuits

In practical, the transformer leakage inductance has to be taken into account.Commutation between thyristors, thus can not happen instantly,but with a

commutation process.

a

b

c

T

L u d i c i b i a L B

L B

L B

i k VT1 VT2

VT3 R

i d O

i c i a i b i c i a I d

u d

t

u a u b u c

t

O

Commutation process analysis

Circulating current ik during commutation

Output voltage during commutation

ik: 0 Id

ub-ua = 2·LB·dia/dt

ia = Id-ik : Id

ib = ik : 0 Id

0

2d

d

d

d bakBb

kBad

uu

t

iLu

t

iLuu

（2-30）

Quantitative calculation

Reduction of average output voltage due to the commutation process

Calculation of commutation angle

– Id ↑,γ↑

– XB↑, γ↑

– For α ≤ 90 ۫ , α↓, γ↑

dB0

B6

5

6

5 B

6

5

6

5 Bbb6

5

6

5 dbd

2

3d

2

3)(d

d

d

2

3

)(d)]d

d([

2

3)(d)(

3/2

1

IXiLtt

iL

tt

iLuutuuU

I

d

kk

k

（2-31）

2

dB

6

2)cos(cos

U

IX （2-36）

Summary of the effect on rectifier circuits

Circuits Single- phase

Full wave

Single- phase bridge

Three- phase

half wave

Three- phase bridge

m-pulse recfifier

dUd

B IX

dB2

IX

dB

2

3I

X

dB3I

X

dB

2I

mX

)cos(cos 2

Bd

2U

XI

2

Bd

2

2

U

XI

2

dB

6

2

U

IX

2

dB

6

2

U

IX

mU

XI

sin2 2

Bd

• Conclusions

–Commutation process actually provides additional working states of the circuit.

–di/dt of the thyristor current is reduced.

–The average output voltage is reduced.

–Positive du/dt

– Notching in the AC side voltag

2.4 Capacitor- filtered uncontrolled (uncontrollable) rectifier

2.4.1 Capacitor- filtered single- phase uncontrolled rectifierSingle-phase bridge, RC load:

a )

+ R C u 1 u 2

i 2 VD 1 VD 3

VD 2 VD 4

i d

i C i R

u d

b )

0

i

u d

2 t

i , u d

Single-phase bridge, RLC load

a ) b )

-

+

R C

L +

u 1 u 2

i 2

u d

u L i d

i C i R

VD 2 VD 4

VD 1 VD 3

u 2 u d

i 2

0 t

i 2 , u 2 , u d

2.4.2 Capacitor- filtered three- phase uncontrolled rectifier

Three-phase bridge, RC load

a)

+ a

b c

T i a

R C u d

i d

i C i R

VD 2

b)

O

i a

u d

i d

u d u ab u ac

0 3

t VD 6 VD 4

VD 1 VD 3 VD 5

t

Three- phase bridge, RC load Waveform when ωRC≤1.732

a ) b )

t t

t t

i a

i d

i a

i d

O

O

O

O

a）RC= •

b）RC<

3 3

Three- phase bridge, RLC load

a )

b )

c )

+ a

b

c

T i a

R C u d

i d i C i R

VD 4 VD 6

VD 1 VD 3 VD 5

VD 2

i a

i a

O

O t

t

2.5 Harmonics and power factor of rectifier circuits

2.5.1 Basic concepts of harmonics and reactive power

For pure sinusoidal waveform

For periodic non-sinusoidal waveform

where

• Harmonics-related specifications

Take current harmonics as examples

Content of nth harmonics

In is the effective (RMS) value of nth harmonics.

I1 is the effective (RMS) value of fundamental component.

Total harmonic distortion

Ih is the total effective (RMS) value of all the harmonic components.

%1001

I

IHRI n

n （2-57）

%1001

I

ITHDhi （2-58）

• Definition of power and power factor for sinusoidal circuits

Active power

Reactive power

Apparent power

Power factor

2

0cos)(

2

1UItuidP （2-59）

Q=U I sin （2-61）

S=UI （2-60） 222 QPS （2-63）

S

P （2-62）

=cos （2-64）

• Definition of power and power factor For non- sinusoidal circuit

Active power:

Power factor:

Distortion factor (fundamental- component factor):

Displacement factor (power factor of fundamental component):

Definition of reactive power is still in dispute

P=U I1 cos1 （2-65）

（2-66） 11111 coscos

cos I

I

UI

UI

S

P

=I1 / I

=cos

• Review of the reactive power concept

The reactive power Q does not lead to net transmission of energy between the source and load. When Q ≠ 0, the rms current and apparent power are greater than the minimum amount necessary to transmit the average power P.

Inductor: current lags voltage by 90°, hence displacement factor is zero. The alternate storing and releasing of energy in an inductor leads to current flow and nonzero apparent power, but P = 0. Just as resistors consume real (average) power P, inductors can be viewed as consumers of reactive power Q.

Capacitor: current leads voltage by 90°, hence displacement factor is zero. Capacitors supply reactive power Q. They are often placed in the utility power distribution system near inductive loads. If Q supplied by capacitor is equal to Q consumed by inductor, then the net current (flowing from the source into the capacitor- inductive- load combination) is in phase with the voltage, leading to unity power factor and minimum rms current magnitude.

2.5.2 AC side harmonics and power factor of controlled rectifiers with inductive load

• Single- phase bridge fully-controlled rectifier

R

T

u 1 u 2

a )

i 2 a

b

VT3

u d

i d

VT4

VT1

VT2

t

t

t

t

t

t

t

u2

ud

id

Id

Id

Id

Id

Id

iVT1,4

iVT2,3

uVT1,4

i2

,

b )

AC side current harmonics of single- phase bridge fully-controlled rectifier with inductive load

Where

Conclusions

–Only odd order harmonics exist

– In∝1/n

– In / I1 = 1/n

,5,3,1,5,3,1d

d2

sin2sin14

)5sin5

13sin

3

1(sin

4

nn

n

tnItnn

I

tttIi

（2-72）

nI

Ind22 n=1,3,5,… （2-73）

• A typical gate triggering control circuit

220 V 36V

+

B TP

+ 15 V

A VS

+ 15 V

- 15 V - 15 V X Y Disable

R Q

u ts

VD 1 VD 2

C 1 R 2

R 4 T S

V 2 R 5 R 8

R 6

R 7

R 3

R 9

R 10

R 11 R 12

R 13

R 14

R 16

R 15

R 18

R 17

RP 1

u co

u p

C 2 C 3

C 3

C 5

C 6 C 7

R 1

RP 2

V 1

I 1c V 3

V 4

V 6

V 5

V 7

V 8

VD 4

VD 10 VD 5

VD 6

VD 7

VD 9

VD 8

VD 15

VD 11 ~VD 14

• Three- phase bridge fully-controlled rectifier

b

a

c

T

n load

i a

i d

u d

VT 1 VT 3 VT 5

VT 4 VT 6 VT 2 d 2

d 1

u d 1

= 30

u d 2

u d u ab u ac u bc u ba u ca u cb u ab u ac I II III IV V VI

t O

t O

t O

t O

i d

i a

t 1

u a u b u c °

• AC side current harmonics of three- phase bridge fully- controlled rectifier with inductive load

where

3,2,116

1

3,2,116

dd

da

sin2)1(sin2sin1

)1(32

sin32

]13sin13

111sin

11

17sin

7

15sin

5

1[sin

32

kkn

nk

kkn

k tnItItnn

ItI

tttttIi

（2-79）

（2-80）

,3,2,1,16,6

6

d

d1

kknIn

I

II

n

2.5.3 AC side harmonics and power factor of capacitor- filtered uncontrolled rectifiers

Situation is a little complicated than rectifiers with inductive load.

Some conclusions that are easy to remember: –Only odd order harmonics exist in single- phase circuit, and only 6k±1 (k is

positive integer) order harmonics exist in three- phase circuit. –Magnitude of harmonics decreases as harmonic order increases. –Harmonics increases and power factor decreases as capacitor increases. –Harmonics decreases and power factor increases as inductor increases.

2.5.4 Harmonic analysis of output voltage and current

tnn

kUtnbUu

mknmknn cos

1

cos21cos

2d0d0d0 （2-85）

（2-86） m

mUU

sin2 2d0

d02 1

cos2U

n

kbn

（2-87）

u d

t O m

m

2 m

U 2 2

Output voltage of m- pulse

rectifier when α = 0º

Ripple factor in the output voltage

Output voltage ripple factor

where UR is the total RMS value of all the harmonic components in the output voltage

and U is the total RMS value of the output voltage

d0

R

U

Uu （2-88）

（2-89） 2d0

22R UUUU

mknn

• Harmonics in the output current

where

)cos(dd nmkn

n tndIi

（2-92）

（2-93） R

EUI

d0

d

22 )( LnR

b

z

bd n

n

nn

R

Lnn

arctan

（2-94）

（2-95）

Conclusions for α = 0ºOnly mk (k is positive integer) order harmonics exist in the output voltage and

current of m- pulse rectifiersMagnitude of harmonics decreases as harmonic order increases when m is

constant.The order number of the lowest harmonics increases as m increases. The

corresponding magnitude of the lowest harmonics decreases accordingly. For α ≠ 0ºQuantitative harmonic analysis of output voltage and current is verycomplicated for α ≠ 0º.As an example,for 3- phase bridge fully- controlled rectifie

2.6 High power controlled rectifier

2.6.1 Double- star controlled rectifier

Circuit Waveforms When α= 0º

T a b c

L

R

n i P L P

u d

i d VT5

c a ' b '

n 1 n 2

' VT4 VT6 VT2 VT3 VT1

u d 1 u a u b u c

i a

u d 2

i a '

u c ' u a ' u b ' u c '

O t

O t

O t

O t

I d

1 2

I d

1 6

I d

1 2

I d

1 6

• Effect of interphase reactor(inductor, transformer)

n

L

R

+ - + -

u d 1

L P

u b '

u d 2 u

d

n 2 n

1 i P

u a

VT 1 VT

6

u P

1 2

u p

u d 1 , u d 2

O

O

60

360

t 1 t

t b )

a )

u a u b u c u c ' u a ' u b ' u b '

d1d2p uuu

)(2

1

2

1

2

1d2d1pd1pd2d uuUuuuu

（ 2-97）

（ 2-98）

Quantitative analysis when α = 0º

]9cos40

16cos

35

23cos

4

11[

2

63 2d1 ttt

Uu

]9cos40

16cos

35

23cos

4

11[

2

63

])60(9cos40

1)60(6cos

35

2)60(3cos

4

11[

2

63

2

2d2

tttU

tttU

u

]9cos20

13cos

2

1[

2

63 2p tt

Uu

]6cos35

21[

2

63 2d t

Uu

（ 2 - 9 9 ）

（ 2 - 1 0 0 ）

（ 2 - 1 0 1 ）

（ 2 - 1 0 2 ）

Waveforms when α > 0º

Ud=1.17 U2 cos

90

60

30 u d

u d

u d

t O

t O

t O

u a u b u c u c ' u a ' u b '

u b u c u c ' u a ' u b '

u b u c u c ' u a ' u b '

2.6.2 Connection of multiple rectifiers

Connection of multiple rectifiers

To increase the output capacity

To improve the AC side current waveform and DC side voltage waveform

Larger output voltage: series connection

Larger output current: parallel connection

• Phase-shift connection of multiple rectifiers

Parallel connection

M

L T VT

1 2

c 1

b 1

a 1

c 2

b 2

a 2

L P

12- pulse rectifier realized by paralleled 3- phase bridge rectifiers

Series connection

C ?

L

R B

A

1

* ?

?

*

*

0

30 °

3

i A c 1

b 1

a 1

1

c 2

b 2

a 2 i ab 2

u a 2 b 2

u a 1 b 1

i a 1 i d

u d

I

II

I

III

0a)

b)

c)

d)

ia1

Id

ia2

iab2'

iA

Idiab2

t

t

t

t

0

0

0

Id23

33Id

33Id

Id32 3

(1+ )Id32 3

(1+ )Id33

Id13

12- pulse rectifier realized by series 3- phase bridge rectifiers

• Sequential control of multiple series-connected rectifiers

L i

a)

l oad

Ⅰ

Ⅱ

Ⅲ

u 2

u 2

u 2

I d VT11

u d b)

c)

i I d

2 I d

u d O + VT12

VT13 VT14

VT21 VT22

VT23 VT24

VT31 VT32

VT33 VT34

Circuit and waveforms of series- connected three single-phase bridge rectifiers

2.7 Inverter mode operationof rectifiers

• Review of DC generator- motor system

c)b)a)

MG MG MGE G E M

Id

R ¡ÆE G E M

Id

R ¡Æ

E G

E M

Id

R ¡Æ

I d =

E G E M

R Σ

- I d =

E M E G

R Σ

- s h o u l d b e a v o i d e d

• Inverter mode operation of rectifiers

Rectifier and inverter mode operation of single- phase full- wave converter

a ) b )

R

+

-

engry M

1 0

2

u 10

u 20

u d i d

L VT 1

VT 2

u 10 u d u 20 u 10

O

O t

t

I d i d

U d > E M

E M

engry M

R

+

-

1

0

2

u d i d

L VT 1

VT 2

u 10 u d

u 20 u 10

O

O t

t

I d i d

U d < E

M

E M

i VT 1

i VT 2

i VT

1

i VT

2

i VT 1

i VT 2

i VT 2

i d = + i VT 1 i VT 2

i VT 1

i VT 2

i VT 1

i d = + i VT 1 i VT 2

Id =

Ud EG

RΣ

- Id =

Ud EM

RΣ

-

Necessary conditions for the inverter mode operation of controlled rectifiers

There must be DC EMF in the load and the direction of the DC EMF must be enabling current flow in

thyristors. (In other word EM must be negative if taking the ordinary output voltage direction as positive.)

α > 90º so that the output voltage Ud is also negative.

• Inverter mode operation of 3- phase bridge rectifier

u ab u ac u bc u ba u ca u cb u ab u ac u bc u ba u ca u cb u ab u ac u bc u ba u ca u cb u ab u ac u bc

u a u b u c u a u b u c u a u b u c u a u b u 2

u d

t O

t O

= 4

= 3

= 6

= 4

= 3

= 6

t 1 t 3 t 2

Inversion angle (extinction angle) βα+ β=180º

Inversion failure and minimum inversion angle Possible reasons of inversion failures –Malfunction of triggering circuit –Failure in thyristors –Sudden dropout of AC source voltage –Insufficient margin for commutation of thyristors

Minimum inversion angle (extinction angle)βmin= δ + γ+ θ′ （ 2-109）

L a

b

c

+

- M u d

i d

E M

L B

L B

L B

VT 1

VT 2

VT 3

o

u d

O

O

i d

t

t

u a u b u c u a u b

p

i VT 1 i VT 2

i VT 3

i VT 1 i VT 2

i VT 3 i VT 1

i VT 3

L B

L B

2.8 Thyristor- DC motor system

2.8.1 Rectifier mode of operation

Waveforms and equations

U I R E U d M d (2-112)

where R R M

R B

3XB 2π

(for 3- phase half-wave)

u d

O

i d

t

u a u b u c

u d

O

i a i b i c i c

t

E U d

i d R

(Waveforms of 3- phase half- wave rectifier with DC motor load

• Speed- torque (mechanic) characteristic when load current is continuous

n E M C e （2-113）

For 3- phase half-wave

U I E M cos 1.17 2 U R d

E M cos 1.17 2 U

e d

e C

U I R

C

U n

cos 1.17 2

（2-114）

For 3-phase bridge

e d

e C

I R

C

U n

cos 2.34 2

（2-115）

（2-116）

O

n

a1<a2<a3

a3

a2

a1

Id

(RB+RM+ )Id

Ce

3XB

2

For 3- phase half-wave

• Speed- torque (mechanic) characteristic when load current is discontinuous

EMF at no load (taking 3- phase half-wave as example)

F o r α ≤ 6 0 º

22 UE o =

F o r α > 6 0 º

)3cos(2 2 UE o =

d i s c o n t i n u o u t s

m o d e

c o n t i n u o u s m o d e

E

E 0

E 0 '

O

I d m i n

I d

( 0 . 5 8 5 U 2 )

( U 2 ) 2

F o r 3 - p h a s e h a l f - w a v e

2.8.2 Inverter mode of operation

Equations

–are just the same as in the rectifier mode of operation except that Ud, EM and n become negative. E.g., in 3- phase half- wave

U I E M cos 1.17 2 U R d

e d

e C

U I R

C

U n

cos 1.17 2

（2-114）

（2-115） – Or in another form

（2-123）

I) 0 cos + ( R I U E d d M = - （2-122）

e C n

R I U d d cos 0

rectifier mode

n

3

2

1

I d

4

2

3

4

1

= = 2

inverter mode

α increasing

β increasing

Speed-torque characteristic of a DC motor fed by a thyristor rectifier circuit

2.8.3 Reversible DC motor drive system(4-quadrant operation)

L

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

AC

source

converter 2 converter 1

converter 2

+ T - T

converter 1 rectifying

converter 2 rectifying

converter 2 inverting

converter 1 inverting

forward motoring

reverse motoring

forward braking(regenerating)

reverse braking(regenerating)

converter 1

converter 2

E M M

a b c

a b c

+ n I d I d

U d

M E M

I d

M E M M E M

I d

Energy

M E M

- n

U d

U d U d

O

AC

source

converter 1

Energy

Energy

Energy

converter 2 converter 2 converter 1

converter 1

AC

source

AC

source

Back-to-back connection of two 3- phase bridge circuits

converter 1

converter 2

n

3

2

1

I d

4

2

3

4

1

= = 2

' = ' = 2

' 3

' 2

' 1

' 4

' 2

' 3

' 4

' 1

1 = ' 1 ; ' 1 = 1

2 = ' 2 ; ' 2 = 2

α increasing

β increasing

β increasing

α increasing

2.9 Gate triggering control circuit for thyristor rectifiers

A typical gate triggering control circuit

220 V 36V

+

B TP

+ 15 V

A VS

+ 15 V

- 15 V - 15 V X Y Disable

R Q

u ts

VD 1 VD 2

C 1 R 2

R 4 T S

V 2 R 5 R 8

R 6

R 7

R 3

R 9

R 10

R 11 R 12

R 13

R 14

R 16

R 15

R 18

R 17

RP 1

u co

u p

C 2 C 3

C 3

C 5

C 6 C 7

R 1

RP 2

V 1

I 1c V 3

V 4

V 6

V 5

V 7

V 8

VD 4

VD 10 VD 5

VD 6

VD 7

VD 9

VD 8

VD 15

VD 11 ~VD 14