Three – Phase Power System
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Three – Phase Power System
Three-Phase Power
Definitions
• 4 wires– 3 “active” phases, A, B, C– 1 “ground”, or “neutral”
• Color Code– Phase A Red– Phase B Black– Phase C Blue– Neutral White or Gray
Balanced Three – Phase System
0 cba VVV
Phasor DiagramPositive Phase Sequence abc
120
120
0
mc
mb
ma
VV
VV
VV
Phasor Diagram Negative Phase Sequence acb
120
120
0
mc
mb
ma
VV
VV
VV
Delta-Connected Sources
Vline = V
Line Voltages Vline
Vab Vbc Vca
Phase Voltages VΦ
Va Vb Vc
Currents for the Delta Connection
Line Current Iline Phase Current IΦ
Iline = √3IΦ
Y-Connected Sources
Line Voltages Vline
Vab Vbc Vca
Phase Voltages VΦ
Va Vb Vc
Vline = √3VΦ
Currents for the Y - Connection
Line Current IlinePhase Current IΦ
Line Current = Phase Current ---- Iline = IΦ
Power in a Balanced Three – Phase System
Total Power is equal to 3 times the power per phase!
cos3
3
cos
IVP
PPPPP
PPPP
IVP
T
CBAT
CBA
Power in a Balanced Three – Phase System
(Continued)
For a Balanced Y – Connected System
cos3
cos3
3
3
cos3
linelineT
lineline
T
line
line
T
IVP
IV
P
II
VV
IVP
For a Balanced Δ – Connected System,
cos3
cos3
3
3
cos3
linelineT
linelineT
line
line
T
IVP
IVP
II
VV
IVP
Three-Phase Bridge Rectifier
Conduction Sequence
Average Output Voltage, Vdc
0
6
0
1( )
23 cos ( )
26
3 31.654
T
dc
dc m
dc m m
V f t dtT
V V td t
V V V
rms Output Voltage1
2
62 2
0
1
2
23 cos ( )
26
3 9 3
2 4
1.6554
rms m
rms m
rms m
V V td t
V V
V V
Diode Currents
1
26
2 2
0
3
4cos ( )
2
0.5518
mm
r m
r m
VI peak
R
I I td t
I I
Transformer Secondary Current1
26
2 2
0
1
2
8cos ( )
2
2 1 2sin
6 2 6
0.7804
s m
s m
s m
I I td t
I I
I I
Instantaneous Output Voltage
0
2 2( ) 0.9549 (1 cos(6 ) cos(12 ) ...
35 143mv t V t t