Download Three-Phase Bridge Rectifier

Three – Phase Power System
Three-Phase Power
Definitions
• 4 wires
– 3 “active” phases, A, B, C
– 1 “ground”, or “neutral”
• Color Code
– Phase A
– Phase B
– Phase C
– Neutral
Red
Black
Blue
White or Gray
Balanced Three – Phase System
Va  Vb  Vc  0
Phasor Diagram
Positive Phase Sequence abc
Va  Vm 0
Vb  Vm   120
Vc  Vm   120
Phasor Diagram
Negative Phase Sequence acb
Va  Vm 0
Vb  Vm   120
Vc  Vm   120
Delta-Connected Sources
Line Voltages Vline
Vab
Vbc
Vca
Phase Voltages VΦ
Va
Vb
Vc
Vline = V
Currents for the Delta Connection
Phase Current IΦ
Line Current Iline
Iline = √3IΦ
Y-Connected Sources
Line Voltages
Vline
Vab
Vbc
Vca
Phase Voltages VΦ
Vline = √3VΦ
Va
Vb
Vc
Currents for the Y - Connection
Phase Current
IΦ
Line Current
Line Current = Phase Current ---- Iline = IΦ
Iline
Power in a
Balanced Three – Phase System
P  V I cos 
PA  PB  PC  P
PT  PA  PB  PC  3P
PT  3V I cos 
Total Power is equal to 3 times the power per phase!
Power in a
Balanced Three – Phase System
(Continued)
For a Balanced Y – Connected System
PT  3V I cos 
Vline
V 
3
I  I line
Vline
PT  3
I line cos 
3
PT  3VlineI line cos 
For a Balanced Δ – Connected System,
PT  3V I cos 
V  Vline
I line
I 
3
I line
PT  3Vline
cos 
3
PT  3VlineI line cos 
Three-Phase Bridge Rectifier
Conduction Sequence
Average Output Voltage, Vdc
T
1
Vdc   f (t )dt
T 0

2 6
Vdc 
3Vm cos td (t )

2 0
6
3 3
Vdc 
Vm  1.654Vm

rms Output Voltage
Vrms

 2

2

 6

6

2
2
0 3Vm cos td (t ) 



1
2
Vrms
Vrms
3 9 3
  
 Vm
 2 4 
 1.6554Vm
1
2
Diode Currents
3Vm
 peak
Im 
R



6

 4
2
2
I m cos td (t ) 
Ir  

2 0


I r  0.5518I m
1
2
Transformer Secondary Current

 8
Is  
2



6

2
2
I
cos

td
(

t
)
m
0


2  1
2
I s  I m    sin
6
  6 2
I s  0.7804 I m



1
2
1
2
Instantaneous Output Voltage
2
2
v0 (t )  0.9549Vm (1  cos(6t ) 
cos(12t )  ...
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