1. THREE PHASE CIRCUIT ANALYSIS:
Unbalanced loads

2. ELE101/102 Dept of E&E,MIT Manipal 2
Unbalanced delta connected load
240
;
120
;
0











ph
BR
ph
YB
ph
RY
V
V
V
V
V
V
BR
BR
BR
YB
YB
YB
RY
RY
RY
Z
V
I
;
Z
V
I
;
Z
V
I 


YB
BR
B
RY
YB
Y
BR
RY
R I
I
I
;
I
I
I
;
I
I
I 














BR
BR
BR
YB
YB
YB
RY
RY
RY
Z
Z
Z
Z
Z
Z



ˆ
ˆ
ˆ

3. ELE101/102 Dept of E&E,MIT Manipal 3
Unbalanced 4 wire star connected load









B
B
B
Y
Y
Y
R
R
R
Z
Ẑ
Z
Ẑ
Z
Ẑ



The line voltages are symmetrical
and balanced
O
N
R
Y
B
RN
V
YN
V
BN
V
B
I
Y
I
R
I
RO
V R
Ẑ
y
Ẑ
B
Ẑ
B
BN
B
Y
YN
Y
R
RN
R
Z
V
I
;
Z
V
I
;
Z
V
I 


B
Y
R
N I
I
I
I







Neutral current

4. ELE101/102 Dept of E&E,MIT Manipal 4
Unbalanced 3 wire star connected load









B
B
B
Y
Y
Y
R
R
R
Z
Ẑ
Z
Ẑ
Z
Ẑ



240
;
120
;
0











ph
BN
ph
YN
ph
RN
V
V
V
V
V
V
The line voltages are symmetrical
and balanced
O
N
R
Y
B
RN
V
YN
V
BN
V
B
I
Y
I
R
I
RO
V R
Ẑ
y
Ẑ
B
Ẑ

5. ELE101/102 Dept of E&E,MIT Manipal 5
Method (1) Conversion of star connected load to delta
A
Z
B
Z
C
Z
AB
Z
BC
Z
CA
Z
B
A
C
A
C
CA
A
C
B
C
B
BC
C
B
A
B
A
AB
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
.
.
.









Application of analysis of unbalanced delta connected load

6. ELE101/102 Dept of E&E,MIT Manipal 6
Illustration:
45
10
Z
30
12
Z
0
12
Z C
B
A 








120
V
V
,
0
V
V
,
120
V
V L
CA
L
BC
L
AB 













are connected in star across a 3Φ, 3 wire, 416 volt supply system,
the voltages being
Three impedances
Find line currents IA, IB and IC by star delta transformation
method
A
84
.
2
35
.
15
IB 



A
5
.
63
26
A
21
.
116
46
.
26
IC 






;
A
99
3
.
23
IA 


Ans: