AC to DC converters

Chapter 2 AC to DC ConvertersOutline 2.1 Single-phase controlled rectifier 2.2 Three-phase controlled rectifier 2.3 Effect of transformer leakage inductance on rectifier circuits 2.4 Cap

Chapter 2 AC to DC Converters

Outline

2.1 Single-phase controlled rectifier

2.2 Three-phase controlled rectifier

2.3 Effect of transformer leakage inductance on rectifier circuits 2.4 Capacitor-filtered uncontrolled rectifier

2.5 Harmonics and power factor of rectifier circuits

2.6 High power controlled rectifier

2.7 Inverter mode operation of rectifier circuit

2.8 Thyristor-DC motor system

2.9 Realization of phase-control in rectifier

2.1 Single- phase controlled (controllable) rectifier

2.1.1 Single-phase half-wave controlled rectifier

π ω

ω

cos 1

45 0 ) cos 1

( 2

2 )

( sin 2

2

1

2

2 2

U

（2-1）

Inductive (resistor-inductor) load

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.

VT

R L

Ri t

ω t= a ，id=0

) sin(

2 )

Single- phase half- wave controlled rectifier with freewheeling diode load (L is large enough) Inductive

Maximum forward voltage, maximum reverse voltage

Disadvantages:

–Only single pulse in one line cycle

–DC component in the transformer current

d dVT

2

)

( 2

1

I t

d I I

π

α π ω

π

π α

2

)

(2

π

α π π

+

=

d dVD

2.1.2 Single- phase bridge fully-controlled rectifier

 Resistive load

0 0 0

Average output (rectified) voltage:

Average output current:

ω

ω

cos1

9

02

cos1

22)(dsin2

1

2

2 2

9

02

cos1

2

d d

α

α π

U R

U I

（2-11） 2

cos 1

45

0 2

d dVT

α +

=

=

R

U I

I

π

α π α π

ω ω

π

π α

− +

=

2

1 2

) ( d ) sin

2 ( 2

VT

R

U t

t R

U

π

α π α π

ω

ω π

π α

− +

( ) sin

2 (

2

R

U t

d

t R

U I

 Inductive load (L is large enough)

 Electro- motive-force (EMF) load With resistor= ∫π+α = =

1

2 2

 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

U

2.1.3 Single- phase full- wave controlled rectifier

2.1.4 Single- phase bridge half-controlled rectifier

Id Id

 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

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 can

be 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

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

α

α π

ω ω π

α π α

2

63)(sin

23

2

1

2 2

6 5

) 6

cos(

1 2

2 3 ) ( sin 2

3

2

1

2 6

2

π

ω ω π

π α

α /( ° )

U d/ U 2

 Inductive load, L is large enough

VT 2

Thyristor voltage and currents, transformer current :

α

α π

ω

ω π

α π α

2

6

3 ) ( sin 2

3

2

1

2 2

6 5

I

57

I

2 RM

2.2.2 Three- phase bridge fully-controlled rectifier

ud1 α = 30

ud2

ud uIab IIuac IIIubc uIVba uVca uVIcb uab uac

ωt O

ωt O

ωt O

ωt O

Quantitative analysis

Average output voltage:

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

everage output current (load current):

Transformer current:

αω

ωπ

α π α

3

1

2 3

6

3

2 3

2

π

π α

2 )

( 3

2 2

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.

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

2 d

d d

B b

k B a

d

u u

t

i L u

t

i L u

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↑

d B

6 5

6

6 5

6

6 5

2

3)(

dd

d2

3

)(d

)]

d

d(

[2

3)(d)

(3

/21

I X i

L

t t

i L

t t

i L u u t

u u U

I

π

ωπ

ωπ

ωπ

ωπ

π γ α π α

π γ α π α

π γ α π α

+ + +

+ + +

d

k k

k

（2-31）

2

d B

6

2 ) cos(

cos

U

I X

= +

− α γ

Summary of the effect on rectifier circuits

Circuits Single- phase

Full wave

Single- phase bridge

Three- phase half wave

Three- phase bridge

cos(

cos α − α + γ

2

B d

2U

X I

2

B d 2

2

U

X I

2

d B

6

2

U

I X

2

d B 6

2

U

I X

m U

 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 rectifier

Single-phase bridge, RC load:

a )

+

R C

i,ud

Single-phase bridge, RLC load

-+

R C

L +

2.4.2 Capacitor- filtered three- phase uncontrolled rectifier

Three-phase bridge, RC load

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

Three- phase bridge, RLC load

R C

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.

% 100

 Definition of power and power factor for sinusoidal circuits

 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 cosϕ1 （2-65）

（2-66）

1 1

1 1

1cosϕ cos ϕ ν cos ϕ

I

I UI

UI S

P

ν =I1 / I

λ 1 =cos ϕ 1

 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

b )

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

5 , 3 , 1 d

d 2

sin2

sin14

)5

sin5

13

sin3

1(sin

4

n

n n

t n I

t

n n

I

t t

t I

i

ω

ω π

ω ω

ω π

 A typical gate triggering control circuit

 Three- phase bridge fully-controlled rectifier

ud1 α = 30

ud2

ud uIab IIuac uIIIbc uIVba uVca uVIcb uab uac

ωt O

ωt O

ωt O

ωt O

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

=

− +

=

− +

16 1

1 3

, 2 ,

16 1

d d

d a

sin 2 ) 1 ( sin

2 sin

1 ) 1 ( 3

2 sin

3 2

] 13

sin 13

1 11

sin 11

1 7

sin 7

1 5

sin 5

1 [sin

3 2

k k n

n k

k k n

n I

t I

t t

t t

t I

i

ω ω

ω π

ω π

ω ω

ω ω

6

6

d

d 1

k k n I

n I

I I

n

π π

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.

2.5.4 Harmonic analysis of output voltage and current

k U

t n b

U

u

mk n mk

n

1

cos 2 1

π sin

2 2d0 =

d0

2 1

cos 2

U n

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

2 2

U

mk n

n = −

= ∑∞

=

 Harmonics in the output current

where

)cos(

d

mk n

n n t d

b

n

n n

ω +

Conclusions

for α = 0º

Magnitude of harmonics decreases as harmonic order increases when

The order number of the lowest harmonics increases as m increases The corresponding magnitude of the lowest harmonics decreases accordingly.

2.6 High power controlled rectifier

2.6.1 Double- star controlled rectifier

Circuit Waveforms When α= 0º

Id

1 6

Id

1 2

Id

1 6

 Effect of interphase reactor(inductor, transformer)

u = −

)

( 2

1 2

1 2

1

d2 d1

p d1

p d2

（2-97）

（2-98）

Quantitative analysis when α = 0º

] 9

cos 40

1 6

cos 35

2 3

cos 4

1 1

[ 2

cos 40

1 6

cos 35

2 3

cos 4

1 1

[ 2

6 3

] ) 60 (

9

cos 40

1 ) 60 (

6

cos 35

2 ) 60 (

3

cos 4

1 1

[ 2

6 3

2

2 d2

=

t t

t U

t t

t

U u

ω ω

ω π

ω ω

ω π

]9

cos20

13

cos2

1[2

cos 35

2 1

[ 2

ωt O

ωt O

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

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

 Sequential control of multiple series-connected rectifiers

L i

2.7 Inverter mode operationof rectifiers

 Review of DC generator- motor system

c)b)

 Inverter mode operation of rectifiers

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

R

+ -

engry

M

1 0

1 0

-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.)

 Inverter mode operation of 3- phase bridge rectifier

Inversion angle (extinction angle) β

α+ 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)

a b c

+

M

2.8 Thyristor- DC motor system

2.8.1 Rectifier mode of operation

Waveforms and equations

 Speed- torque (mechanic) characteristic when load current is

R C

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

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

2U2 α −π

E o =

discontinuouts mode

For 3- phase half-wave

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

R C

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

converter 2 converter 1 converter 2

converter 1

Energ y

Energ y

Energ y

converter 1

converter 1

AC source

AC source

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

2.9 Gate triggering control circuit for thyristor rectifiers

A typical gate triggering control circuit