Three Phase Rectifers.pdf
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2
sLLLLLL
aveo VVVVV 3,235.1
223
., ===π
)3
2(2)(
)3
2(2)(
)(2)(
πω
πω
ω
+=
−=
=
tSinVtv
tSinVtv
tSinVtv
sC
sB
sA
Three-Phase, Half-Wave, Uncontrolled Rectifier
3
Three-Phase, Half-Wave, Controlled Rectifier
sLL
LLLL
aveo
VV
CosVCosVV
3235.1
223
.,
=
== ααπ
4
AC
AC
AC
Cd Rloadvd
Lsa
b
c
n
ia
id
D1 D3 D5
D4 D6 D2
Three-Phase, Full-Wave, Uncontrolled Rectifier
5
AC
AC
AC
D1
D4
D3 D5
D6 D2
Idvd
ia
n
a
b
c
AC
AC
AC
ia
n
a
b
c
Id
Id
n
D1
D3
D5
D2
D6
D4
vd
vPn
vNn
P
N
Full-Bridge Rectifier
NnPnd vvv −=
6
AC
AC
AC
ia
n
a
b
c
Id
Id
n
D1
D3
D5
D2
D6
D4
vd
vPn
vNn
P
N
7
⎪⎩
⎪⎨
⎧−=0
d
d
a II
iwhen D1 is conducting
when D4 is conductingwhen neither D1 or D4 is conducting
LLLLLLdo
LLabd
VVtdtCosVV
ttCosVvv
35.123)()(23/
166
),(2
6/
6/
===
<<−==
∫− π
ωωπ
πωπω
π
π
LLVA 2=
1
1
1
78.061
816.032
ssh
dds
dds
Ih
I
III
III
=
==
==
π
line current
8
π3&0.1 == PFDPF
18
Comparison of Single-Phase and Three-Phase Rectifiers
Line current in a 1-phase rectifier contains significantly more distortion.
Much poorer power factor in a 1-phase rectifier compared to a 3-phase rectifier.
Ripple in the DC current is smaller in a 3-phase rectifier.
The filter required may be much smaller in a 3-phase rectifier.
Lower output DC voltage ripple in a 3-phase rectifier.
Regulation in the DC voltage from a no-load to a full-load condition for a 3-phase rectifier is much smaller than a 1-phase rectifier.
19
AC
AC
AC
Loadvdn
LdLs
a
van
id
Three-Phase, Full-Wave, Controlled Rectifier
20
AC
AC
AC
Idn
a
b
c
1
3
5
4
6
2
vd
ia
ib
ic
P
N
AC
AC
AC
n
a
b
c
1 3 5
4 6 2
Idvd
ia
ib
ic
P
N
Full-Bridge Rectifier
NnPnd vvv −=
21
22
α
αααπ
απππ
π
αωω
ω
α
α
αα
α
α
CosIVIVP
CosVCosVCosVV
CosVVAVV
VVV
CosVtdtSinVA
tSinVv
dLLdd
doLLLLd
LLLLdod
LLLLdo
LLLL
LLac
35.1
35.123
)1(23233/
35.123
)1(2)()(2
)(2
0
==
===
−−=−=
==
−==
=
∫
23
Two-Quadrant Operation
24
Two-Quadrant Operation
38
12-Pulse AC/DC Rectifiers
39
⎟⎠⎞
⎜⎝⎛ +−=+=
⎟⎠⎞
⎜⎝⎛ −+−+=
⎟⎠⎞
⎜⎝⎛ +−+−=
L
L
L
θθθπ
θθθθθπ
θθθθθπ
1313111
11132
1313111
1117
715
51
232
1313111
1117
715
51
232
21
2
1
CosCosCosIN
iii
CosCosCosCosCosIN
i
CosCosCosCosCosIN
i
daaa
da
da
),3,2,1(112L=
±=m
mh
ds
LL
ddd
ILCosV
VVV
πωα
π323
221
−=
==
41
High Voltage DC (HVDC) Transmission Systems