Polyphase

1. POLYPHASE CIRCUITS
LEARNING GOALS
Three Phase Circuits
Advantages of polyphase circuits
Three Phase Connections
Basic configurations for three phase circuits
Source/Load Connections
Delta-Y connections
Power Relationships
Study power delivered by three phase circuits
Power Factor Correction
Improving power factor for three phase circuits

2. THREE PHASE CIRCUITS
)
)(
240
cos(
)
(
)
)(
120
cos(
)
(
)
)(
cos(
)
(
V
t
V
t
v
V
t
V
t
v
V
t
V
t
v
m
c
m
bn
m
an










Voltages
Phase
ous
Instantane
2
120

m
V
Vcn
Vbn
Van
0 120 240
3 phase
voltage

3. _
_
_
+
+
+
n
a
b
c
c
b
a
V0
V-120
V-240
Wye Connected
Source

4. a
b
c
a
b
c
+
+
+
_
_
_
Delta
Source
Delta Source
Vab = | Vab |  0
Vbc = Vab  -120
Vca = Vab  -240

5. Zl
Zl
Zl
ZL
ZL ZL
a
n
b
c
A
B C
N
Wye – Wye System

6. Zl
Zl
Zl
a
b
c
A
B C
ZL
Z
L
Z
L
+
+
+
_
_
_
Delta – Delta System

7. Zl
Zl
Zl
a
b
c
A
B C
+
+
+
_
_
_
ZL
ZL
ZL
Delta – Wye System

8. _
_
_
+
+
+
n
a
b
c
c
b
a
V0
V-120
V-240
A
B C
Z Z
Z
IaA ICA
IBC
IAB

9. Van
Vbn
Vcn
- Vbn
Vab
Vab = Van - Vbn
Vab = 3 Van 30o
30o

10.  

























30
|
|
3
2
3
2
1
|
|
|
|
)
120
sin
120
(cos
1
|
|
120
|
|
0
|
|
p
p
p
p
p
p
bn
an
ab
V
j
V
V
j
V
V
V
V
V
V








210
|
|
3
90
|
|
3
p
ca
p
bc
V
V
V
V
Voltage
Line

 |
|
3 p
L V
V

11. IAB
IBC
ICA
- ICA
IaA
IaA = 3 IAB -30o

12. )
240
cos(
)
(
)
120
cos(
)
(
)
cos(
)
(
















t
I
t
i
t
I
t
i
t
I
t
i
m
c
m
b
m
a
Currents
Phase
Balanced
)
(
)
(
)
(
)
(
)
(
)
(
)
( t
i
t
v
t
i
t
v
t
i
t
v
t
p c
cn
b
bn
a
an 


power
ous
Instantane
Theorem
For a balanced three phase circuit the instantaneous power is constant
)
(
cos
2
3
)
( W
I
V
t
p m
m


)
)(
240
cos(
)
(
)
)(
120
cos(
)
(
)
)(
cos(
)
(
V
t
V
t
v
V
t
V
t
v
V
t
V
t
v
m
c
m
bn
m
an










Voltages
Phase
ous
Instantane
INSTANTANEOUS POWER

13. Y
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
c
b
a











3
2
1
1
3
3
2
1
3
2
3
2
1
2
1











Y
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
a
a
c
c
b
b
a
c
a
c
c
b
b
a
b
a
c
c
b
b
a
3
2
1
tions
Transforma
Y
OF
REVIEW



14. Y




Y
b
a
ab R
R
R 

)
(
|| 3
1
2 R
R
R
Rab 

3
2
1
3
1
2 )
(
R
R
R
R
R
R
R
R b
a





3
2
1
2
1
3 )
(
R
R
R
R
R
R
R
R c
b





3
2
1
3
2
1 )
(
R
R
R
R
R
R
R
R a
c





SUBTRACT THE FIRST TWO THEN ADD
TO THE THIRD TO GET Ra
a
b
b
a
R
R
R
R
R
R
R
R 1
3
3
1



c
b
c
b
R
R
R
R
R
R
R
R 1
2
1
2



REPLACE IN THE THIRD AND SOLVE FOR R1
Y
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
c
b
a











3
2
1
1
3
3
2
1
3
2
3
2
1
2
1











Y
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
a
a
c
c
b
b
a
c
a
c
c
b
b
a
b
a
c
c
b
b
a
3
2
1
tions
Transforma
Y
OF
REVIEW



15. POWER FACTOR CORRECTION
Balanced
load
Low pf
lagging
Similar to single phase case.
Use capacitors to increase the
power factor
Keep clear about total/phase
power, line/phase voltages
added
be
to
Power
Reactive
old
new Q
Q
Q 


To use capacitors this value
should be negative
2
1
sin
cos pf
pf f
f 


 

2
1
tan
pf
pf
f



0

 Q
lagging
f
P
Q 
tan


16. LEARNING EXAMPLE
leading
pf
rms
kV
V
Hz
f line 94
.
0
.
5
.
34
|
|
,
60 

 :
Required
626
.
0
1
sin
cos 2




 pf
pf f
f 

MW
P
MVA
Q
old
old
72
.
18
02
.
15
|
|


2
1
tan
pf
pf
f



0

 old
Q
lagging
f
f
f
pf
S
Q
S
P
jQ
P
S



cos
sin
|
|
cos
|
|





f
P
Q 
tan

MVA
Q
leading
pf
MW
P
new
new
old
8
.
6
94
.
0
72
.
18








MVA
Q
MVA
Q
273
.
7
82
.
21
02
.
15
8
.
6








capacitor
per
rms
kV
V
Y
3
5
.
34


 capacitor
connection
2
3
6
3
10
5
.
34
60
2
10
273
.
7 






 






 C

F
C 
6
.
48


17. LEARNING BY DESIGN
Proposed new store
rms
A
170
at
rated
wire
#4ACSR
kVA
j
S
420
560
9
.
36
700
1





kVA
j
kVA
S
866
500
60
1000
2





kVA
j
kVA
S
349
720
8
.
25
800
3





kVA
kVA
j
Stotal 



 57
.
42
2417
1635
1780
rms
A
V
S
I
line
total
line 1
.
101
10
8
.
13
3
10
417
.
2
3
|
|
|
| 3
6






 Wire is OK
new
new
old
Q
pf
P




old
new Q
Q
Q 


)
(
tan new
f
P 
 kVA
28
.
758

kVA
72
.
876


2
capacitor
per
|
| CV
Q 
  
  3
/
10
8
.
13
60
2
3
/
10
72
.
876
2
3
3






C F

2
.
12
