– DC component in the transformer current
7
3.1.2 Single-phase bridge fully-controlled rectifier
Resistive load
ud ud(id) id
b)
T
i2 a
VT 1 VT 3
id
0
t
uVT1,4
u1
Inductive (resistor-inductor) load
u2
T
VT
id
a) u1
uVT
u2
ud
b)
0 t1
ug
c) 0
ud
+
d) 0 id
e)
0
uVT
f) 0
2
t
t +
t
t
t
5
Basic thought process of time-domain analysis for power electronic circuits
3
Power
3.1.1 Single-phase half-wave controlled rectifier
Resistive load
u2
b) 0 t1 ug
2
t
T
VT
c) 0
t
uVT
id
ud
u1
u2
ud R
d) 0
t
uVT
e)
a)
0
t
Power
1
Ud 2
2U2 sin td(t)
2
Power
3.1 Single-phase controlled (controllable) rectifier
3.1.1 Single-phase half-wave controlled rectifier 3.1.2 Single-phase bridge fully-controlled rectifier 3.1.3 Single-phase full-wave controlled rectifier 3.1.4 Single-phase bridge half-controlled rectifier
T
u2
load
VT2 VD4
Power
Comparison with previous circuit: – No need for additional freewheeling diode – Isolation is necessary between the drive circuits
of the two thyristors
2 d
d
(t
)
2 Id
(3-7)
O uVT
t
g)
IVDR
1 2
2
Id2d (t)
2
Id
(3-8)
O
t
Maximum forward voltage, maximum reverse voltage
Disadvantages:
– Only single pulse in one line cycle
Id
Ud R
2
2U 2
R
1 cos
2
0.9 U 2 R
1 cos
2
For thyristor
I dVT
1 2
Id
0.45U 2 R
1 cos
2
IVT
1
(
2U2 sint)2 d(t) U2
2 R
2R
1 sin 2
2
For transformer
(3-10)
(3-11) (3-12)
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.
Id
t
O i2
Id
t
O
t
fully-controlled rectifier
Additional freewheeling diode
14
Another single-phase bridge half-controlled rectifier
VT1 VD3
3.2.2 Three-phase bridge fully-controlled rectifier (the most widely used circuit among three-phase rectifiers)
17
Power
Power
3.2.1 Three-phase half-wave controlled rectifier
Power
Inductive load (L is large enough)
u2
T
VT
id
u VT
iVDR
L
b)
O ud
t1
c)
t
a) u 1
u2
ud
O
t
id
VDR
R
d)
Id
O
t
IdVT
2
Id
IdVDR 2 Id
iVT
Id
(3-5)
e)
(3-6)
O iVDR
-
+
t
f)
I VT
1
2
I
Power
I I2
1
(
2U2 sin t)2 d (t) U2
R
R
1 sin 2
2
(3-13)
9
3.1.2 Single-phase bridge fully-controlled rectifier
Inductive load
u2
(L is large enough)
O
t
id
ud
Transformer current
10
Power
Electro-motive-force (EMF) load
With resistor
id
ud
R O
ud
id
E
O
a)
b)
Discontinuous current id
E t Id t
11
Electro-motive-force (EMF) load
rectifier circuits 3.4 Capacitor-filtered uncontrolled rectifier 3.5 Harmonics and power factor of rectifier circuits 3.6 High power controlled rectifier 3.7 Inverter mode operation of rectifier circuit 3.8 Realization of phase-control in rectifier circuits
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
VT3
VT1
Power
T i2 a
u1
u2
b
L ud
R
O
id
iVT1O,4 iVT2O,3
O i2 O uVT1,4
Id Id
Id Id
VT4
VT2
U d
1
O
a)
b)
2U 2
sintd(t)
22
U2
cos
0.9U 2
cos
t Id
t t t t
t
(3-15)
Commutation
Thyristor voltages and currents
ud
=
E
0
t
Power
id
O
t
L 2 2U2 2.87 103 U2 (3-17)
Idmin
I dm in
12
3.1.3 Single-phase full-wave controlled rectifier