Transcript
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
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