Presiding Officer Training module 2024 lok sabha elections
2.ppt
1. 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. 2.1 Single- phase controlled (controllable) rectifier
2.1.1 Single-phase half-wave controlled rectifier
Resistive load
T
VT
R
a)
u1
u2
uVT
ud
id
0 t1 2
t
u2
ug
ud
uVT
0
b)
c)
d)
e)
0
0
t
t
t
2
cos
1
45
.
0
)
cos
1
(
2
2
)
(
sin
2
2
1
2
2
2
d U
U
t
td
U
U
(2-1)
4. 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
u2 u2
t
U
Ri
t
i
L
sin
2
d
d
2
d
d
ωt= a ,id=0
)
sin(
2
)
sin(
2 2
)
(
2
d
t
Z
U
e
Z
U
i
t
L
R
(2-2)
(2-3)
5. Single- phase half- wave controlled rectifier with freewheeling diode
load (L is large enough) Inductive
a)
L
T VT
R
u1
u2
uVT
ud
VDR
id
iVD
u2
ud
id
uVT
iVT
Id
Id
t
O
O
O
O
O
O
- +
b)
iVDR
t
t
t
t
t
g)
c)
e)
f)
d)
T1
6. Maximum forward voltage, maximum reverse voltage
Disadvantages:
–Only single pulse in one line cycle
–DC component in the transformer current
d
dVT
2
I
I
d
2
d
VT
2
)
(
2
1
I
t
d
I
I
d
2
2
d
VD
2
)
(
2
1
R
I
t
d
I
I
d
dVD
2
R
I
I
(2-5)
(2-6)
(2-7)
(2-8)
7. 2.1.2 Single- phase bridge fully-controlled rectifier
Resistive load
t
0
0
0
i2
ud
id
b)
c)
d)
ud
(id
)
R
T
u1 u2
a)
i2
a
b
VT3
ud
i
d
uVT
1,4
t
t
VT4
VT1
VT2
8. Average output (rectified) voltage:
Average output current:
For thyristor:
For transformer:
2
cos
1
9
.
0
2
cos
1
2
2
)
(
d
sin
2
1
2
2
2
d U
U
t
t
U
U (2-9)
(2-10)
2
cos
1
9
.
0
2
cos
1
2
2 2
2
d
d
R
U
R
U
R
U
I
(2-11)
2
cos
1
45
.
0
2
1 2
d
dVT
R
U
I
I
2
sin
2
1
2
)
(
d
)
sin
2
(
2
1 2
2
2
VT
R
U
t
t
R
U
I (2-12)
2
sin
2
1
)
(
)
sin
2
(
1 2
2
2
2
R
U
t
d
t
R
U
I
I (2-13)
9. 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
u1 u2
a)
i2
a
b
VT3
ud
i
d
VT4
VT1
VT2
10. Electro- motive-force (EMF) load With resistor
cos
9
.
0
cos
2
2
)
(
d
sin
2
1
2
2
2
d U
U
t
t
U
U (2-15)
a) b)
R
E
id
ud id
O
E
ud
t
Id
O t
11. 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
ud
0
E
id
t
t
=
dmin
2
3
dmin
2
10
87
.
2
2
2
I
U
I
U
L
(2-17)
12. 2.1.3 Single- phase full- wave controlled rectifier
a) b)
u1
T
R
u2
u2
i1 VT1
VT2 ud
ud
i1
O
O
t
t
13. 2.1.4 Single- phase bridge half-controlled rectifier
a)
T a
b R
L
O
b)
u2
i2
ud
id
VT
1
VT
2
VD
3
VD
4
VD
R
u2
O
ud
id Id
O
O
O
O
O
i2
Id
Id
Id
Id
Id
t
t
t
t
t
t
t
iVT
1
iVD
4
iVT
2
iVD
3
iVD
R
14. 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
u2
VT2 VT4
VT1 VT3
15. 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
16. 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
ud
id
VT2
VT1
VT3
u2
O
O
O
uab uac
O
iVT1
uVT
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
17. Resistive load, α= 30º
u2
ua ub uc
O
O
O t
O
t
O
t
uG
ud
uab uac
t1
iVT
1
uVT1 uac
t
t
a
b
c
T
R
ud
id
VT2
VT1
VT3
18. Resistive load, α= 60º
t
u2 ua ub uc
O
O
O
O
uG
ud
iVT
1
t
t
t
a
b
c
T
R
ud
id
VT2
VT1
VT3
19. 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
cos
17
.
1
cos
2
6
3
)
(
sin
2
3
2
1
2
2
6
5
6
2
d U
U
t
td
U
U
(2-18)
)
6
cos(
1
675
.
0
)
6
cos(
1
2
2
3
)
(
sin
2
3
2
1
2
6
2
d
U
t
td
U
U (2-19)
R
U
I d
d (2-20)
0 30 60 90 120 150
0.4
0.8
1.2
1.17
3
2
1
/(°)
Ud/U2
21. Thyristor voltage and currents, transformer current :
cos
17
.
1
cos
2
6
3
)
(
sin
2
3
2
1
2
2
6
5
6
2
d U
U
t
td
U
U
(2-18)
d
d
VT
2 577
.
0
3
1
I
I
I
I
d
VT
VT(AV) 368
.
0
57
.
1
I
I
I
2
RM
FM 45
.
2 U
U
U
(2-23)
(2-25)
(2-24)
22. 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
ia
id
ud
VT1 VT3 VT5
VT4 VT6 VT2 d2
d1
23. Resistive load, α= 0º
b
a
c
T
n
load
ia
id
ud
VT1 VT3 VT5
VT4 VT6 VT2 d2
d1
24. u2
ud1
ud2
u2L
ud
uab uac
uab uac ubc uba uca ucb uab uac
uab uac ubc uba uca ucb uab uac
I II III IV V VI
ua uc
ub
t1
O t
O t
O t
O t
= 0°
iVT
1
uVT
1
25. Resistive load, α= 30º
b
a
c
T
n
load
ia
id
ud
VT1 VT3 VT5
VT4 VT6 VT2 d2
d1
26. ud1
ud2
=30
¡
ã
ia
O
O
O
O t
ud
uab uac
ua ub
uc
t1
uab uac ubc uba uca ucb uab uac
І II III IV V VI
uab u ac ubc uba u ca ucb u ab u ac
uVT
1
t
t
t
27. Resistive load, α= 60º
b
a
c
T
n
load
ia
id
ud
VT1 VT3 VT5
VT4 VT6 VT2 d2
d1
35. Inductive load, α= 90º
b
a
c
T
n
load
ia
id
ud
VT1 VT3 VT5
VT4 VT6 VT2 d2
d1
36.
37. Quantitative analysis
Average output voltage:
For resistive load, When a > 60º, load current id is discontinuous.
everage output current (load current):
Transformer current:
cos
34
.
2
)
(
sin
6
3
1
2
3
2
3
2
d U
t
td
U
U
(2-26)
(2-27)
)
3
cos(
1
34
.
2
)
(
sin
6
3
2
3
2
d
U
t
td
U
U
R
U
I d
d (2-20)
d
d
d
d I
I
I
I
I 816
.
0
3
2
3
2
)
(
3
2
2
1 2
2
2
(2-28)
38. 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
ud
ic
ib
ia
LB
LB
LB
ik VT1
VT2
VT3
R
id
O
ic ia ib ic ia Id
ud
t
ua ub uc
t
O
39. 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
d b
a
k
B
b
k
B
a
d
u
u
t
i
L
u
t
i
L
u
u
(2-30)
40. Quantitative calculation
Reduction of average output voltage due to the commutation process
Calculation of commutation angle
– Id ↑,γ↑
– XB↑, γ↑
– For α ≤ 90۫ , α↓, γ↑
d
B
0
B
6
5
6
5 B
6
5
6
5 B
b
b
6
5
6
5 d
b
d
2
3
d
2
3
)
(
d
d
d
2
3
)
(
d
)]
d
d
(
[
2
3
)
(
d
)
(
3
/
2
1
I
X
i
L
t
t
i
L
t
t
i
L
u
u
t
u
u
U
I
d
k
k
k
(2-31)
2
d
B
6
2
)
cos(
cos
U
I
X
(2-36)
41. 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
d
U
d
B
I
X
d
B
2
I
X
d
B
2
3
I
X
d
B
3
I
X
d
B
2
I
mX
)
cos(
cos
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
X
I
sin
2 2
B
d
42. 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
43. 2.4 Capacitor- filtered uncontrolled (uncontrollable) rectifier
2.4.1 Capacitor- filtered single- phase uncontrolled rectifier
Single-phase bridge, RC load:
a)
+
R
C
u1 u2
i2
VD1 VD3
VD2 VD4
id
iC
iR
ud
b)
0
i
ud
2 t
i,ud
44. Single-phase bridge, RLC load
a) b)
-
+
R
C
L
+
u1 u2
i2
ud
uL
id
iC iR
VD2 VD4
VD1
VD3
u2 ud
i2
0
t
i2,u2,ud
45. 2.4.2 Capacitor- filtered three- phase uncontrolled rectifier
Three-phase bridge, RC load
a)
+
a
b
c
T
ia
R
C
ud
id
iC
iR
VD2
b)
O
ia
ud
id
ud
u
ab u
ac
0
3
t
VD6
VD4
VD1VD3VD5
t
46. Three- phase bridge, RC load Waveform when ωRC≤1.732
a) b)
t t
t
t
ia
id
ia
id
O
O
O
O
a)RC=
•
b)RC<
3 3
47. Three- phase bridge, RLC load
a)
b)
c)
+
a
b
c
T ia
R
C
ud
id
iC
iR
VD4
VD6
VD1
VD3
VD5
VD2
ia
ia
O
O t
t
48. 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
49. 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
1
I
I
HRI n
n (2-57)
%
100
1
I
I
THD h
i (2-58)
50. Definition of power and power factor for sinusoidal circuits
Active power
Reactive power
Apparent power
Power factor
2
0
cos
)
(
2
1
UI
t
uid
P (2-59)
Q=U I sin (2-61)
S=UI (2-60)
2
2
2
Q
P
S
(2-63)
S
P
(2-62)
=cos (2-64)
51. 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)
1
1
1
1
1
cos
cos
cos
I
I
UI
UI
S
P
=I1 / I
=cos
52. 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.
53. 2.5.2 AC side harmonics and power factor of controlled rectifiers with
inductive load
Single- phase bridge fully-controlled rectifier
R
T
u1 u2
a)
i2
a
b
VT3
ud
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)
54. 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
,
1
d
d
2
sin
2
sin
1
4
)
5
sin
5
1
3
sin
3
1
(sin
4
n
n
n
t
n
I
t
n
n
I
t
t
t
I
i
(2-72)
n
I
In
d
2
2
n=1,3,5,… (2-73)
55. A typical gate triggering control circuit
220V 36V
+
B
TP
+15V
A
VS
+15V
-15V -15V
X Y
Disable
R
Q
uts
VD1
VD2
C1 R2
R4
TS
V2 R5
R8
R6
R7
R3
R9
R10
R11
R12
R13
R
14
R16
R15
R18
R17
RP1
uco
up
C2
C3
C3
C5
C6
C7
R1
RP2
V1
I1c
V3
V4
V6
V5
V7
V8
VD4
VD
10 VD5
VD6
VD7
VD9
VD8
VD15
VD11
~VD
14
56. Three- phase bridge fully-controlled rectifier
b
a
c
T
n
load
ia
id
ud
VT1 VT3 VT5
VT4 VT6 VT2 d2
d1
58. AC side current harmonics of three- phase bridge fully- controlled
rectifier with inductive load
where
3
,
2
,
1
1
6
1
3
,
2
,
1
1
6
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
k
t
n
I
t
I
t
n
n
I
t
I
t
t
t
t
t
I
i
(2-79)
(2-80)
,
3
,
2
,
1
,
1
6
,
6
6
d
d
1
k
k
n
I
n
I
I
I
n
59. 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.
60. 2.5.4 Harmonic analysis of output voltage and current
t
n
n
k
U
t
n
b
U
u
mk
n
mk
n
n
cos
1
cos
2
1
cos 2
d0
d0
d0 (2-85)
(2-86)
m
m
U
U
sin
2 2
d0
d0
2
1
cos
2
U
n
k
bn
(2-87)
u
d
t
O
m
m
2
m
U
2
2
Output voltage of m- pulse
rectifier when α = 0º
61. 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
U
u
(2-88)
(2-89)
2
d0
2
2
R U
U
U
U
mk
n
n
62. Harmonics in the output current
where
)
cos(
d
d n
mk
n
n t
n
d
I
i
(2-92)
(2-93)
R
E
U
I
d0
d
2
2
)
( L
n
R
b
z
b
d n
n
n
n
R
L
n
n
arctan
(2-94)
(2-95)
63. Conclusions
for α = 0º
Only mk (k is positive integer) order harmonics exist in the output voltage
and current of m- pulse rectifiers
Magnitude 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 ≠ 0º
Quantitative harmonic analysis of output voltage and current is very
complicated for α ≠ 0º.
As an example,for 3- phase bridge fully- controlled rectifie
64. 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
iP
LP
ud
id
VT5
c
a'
b'
n1
n2
'
VT4 VT6 VT2
VT3 VT1
ud1
ua ub uc
ia
ud2
ia
'
uc
' ua
' ub
' uc
'
O t
O t
O t
O t
Id
1
2
Id
1
6
Id
1
2
Id
1
6
65. Effect of interphase reactor(inductor, transformer)
n
L
R
+
- +
-
ud1
LP
ub
'
ud2
ud
n2
n1
iP
ua
VT1 VT6
uP
1
2
up
ud1
,ud2
O
O
60
360
t1 t
t
b)
a)
ua ub uc
uc
' ua
'
ub
' ub
'
d1
d2
p u
u
u
)
(
2
1
2
1
2
1
d2
d1
p
d1
p
d2
d u
u
U
u
u
u
u
(2-97)
(2-98)
66. Quantitative analysis when α = 0º
]
9
cos
40
1
6
cos
35
2
3
cos
4
1
1
[
2
6
3 2
d1
t
t
t
U
u
]
9
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
]
9
cos
20
1
3
cos
2
1
[
2
6
3 2
p
t
t
U
u
]
6
cos
35
2
1
[
2
6
3 2
d
t
U
u
(2-99)
(2-100)
(2-101)
(2-102)
67. Waveforms when α > 0º
Ud=1.17 U2 cos
90
60
30
ud
ud
ud
t
O
t
O
t
O
ua ub uc
uc
' ua
' ub
'
ub
uc
uc
' ua
' ub
'
ub
uc
uc
' ua
' ub
'
68. 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
69. Phase-shift connection of multiple rectifiers
Parallel connection
M
L
T
VT
1 2
c1
b1
a1
c2
b2
a2
LP
12- pulse rectifier realized by
paralleled 3- phase bridge rectifiers
71. Sequential control of multiple series-connected rectifiers
L
i
a)
load
Ⅰ
Ⅱ
Ⅲ
u
2
u
2
u
2
Id
VT11
u d
b)
c)
i Id
2 Id
ud
O +
VT12
VT13
VT14
VT21
VT22
VT23
VT24
VT31
VT32
VT33
VT34
Circuit and waveforms of series- connected
three single-phase bridge rectifiers
72. 2.7 Inverter mode operationof rectifiers
Review of DC generator- motor system
c)
b)
a)
M
G M
G M
G
EG EM
Id
R¡Æ
EG EM
Id
R¡Æ
EG
EM
Id
R¡Æ
Id =
EG EM
RΣ
-
Id =
EM EG
RΣ
- should be avoided
73. Inverter mode operation of rectifiers
Rectifier and inverter mode operation of single- phase full- wave
converter
74. 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.
75. Inverter mode operation of 3- phase bridge rectifier
uab uac ubc uba uca ucb uab uac ubc uba uca ucb uab uac ubc uba uca ucb uab uac ubc
ua ub uc ua ub uc ua ub uc ua ub
u2
ud
t
O
t
O
=
4
=
3
=
6
=
4
=
3
=
6
t1 t3
t2
76. 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)
βmin= δ + γ+ θ′(2-109)
77.
78. 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 RM RB
3XB
2π
(for 3- phase half-wave)
u
d
O
id
t
ua ub uc
ud
O
ia ib ic
ic
t
E
Ud
idR
(Waveforms of 3- phase half- wave
rectifier with DC motor load
79. Speed- torque (mechanic) characteristic when load current is
continuous
n
EM
Ce (2-113)
For 3- phase half-wave
U
I
EM
cos
1.17 2
U
R d
EM 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
80. Speed- torque (mechanic) characteristic when load current is
discontinuous
EMF at no load (taking 3- phase half-wave as example)
For α≤ 60º
2
2U
Eo=
For α>60º
)
3
cos(
2 2
U
Eo=
discontinuouts
mode
continuous mode
E
E0
E0'
O
Idmin
Id
(0.585U2)
( U2)
2
For 3- phase half-wave
81. 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
EM
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)
0cos +
(
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
Id
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
82. 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
EM
M
a
b
c
a
b
c
+n
Id Id
Ud
M EM
Id
M EM
M
EM
Id
Energ
y
M
EM
- n
Ud
Ud Ud
O
AC
source
converter 1
Energ
y
Energ
y
Energ
y
converter 2 converter 2
converter 1
converter 1
AC
source
AC
source
Back-to-back
connection of two 3-
phase bridge circuits