1. ELE101/102 Dept of E&E,MIT Manipal 1
Method (2) LOOP CURRENT ANALYSIS
RI
∧
1Z
3Z2Z
R
Y
B
YI
∧
BI
∧
1I
∧
2I
∧
O
Mesh equations are given by








=
















+−
+
∧
∧
∧
∧
YB
RY
2
1
322
221
)Z
Z)ZZ(
V
V
I
I
ZZ(
-
)(21 BRYBR IIIIIII
∧∧∧∧∧∧∧
+−=−==

2. ELE101/102 Dept of E&E,MIT Manipal 2
Illustration:
°∠=°∠=°∠= 4510Z3012Z012Z CBA
°∠=°∠=°−∠=
∧∧∧
120VV0VV120VV LCALBCLAB
Determine all the line currents and the voltage of common point
of load impedances with respect to neutral of supply system
are connected in star across a 3Φ, 3 wire, 416 Volt supply system.
The voltages being
Three impedances
Ans:
38.9V87.55V
A42.11626.5A57.635.26I
A7.242.15I
A91.983.23I
ON
C
B
A
∠=
∠=−∠−=
−∠=
−∠=
∧
∧
∧

3. ELE101/102 Dept of E&E,MIT Manipal 3
BONBNB
YONYNY
RONRNR
Yˆ)VV(I
Yˆ)VV(I
Yˆ)VV(I
−=
−=
−=
Star point voltage with respect to the neutral
Method (3) : Neutral displacement method
ONV
O
N
R
Y
B
RNV
YNVBNV
BIYI
RI
RZˆ
yZˆ
BZˆ
ROV
VVV
VVV
VVV
ONBNBO
ONYNYO
ONRNRO
−=
−=
−=
B
BO
B
Y
YO
Y
R
RO
R
Zˆ
V
I
Zˆ
V
I
Zˆ
V
I ===
Line current = phase current

4. ELE101/102 Dept of E&E,MIT Manipal 4
ONVDisplacement Neutral Voltage ( )
Three wire unbalanced star connected load
0=++ BYR III
BYR
BBNYYNRRN
ON
YYY
YVYVYV
V
ˆˆˆ
ˆˆˆ
++
++
=
0ˆ)(ˆ)(ˆ)( =−+−+− BONBNYONYNRONRN YVVYVVYVV
BONYONRONBBNYYNRRN YVYVYVYVYVYV ˆˆˆˆˆˆ ++=++
)ˆˆˆ(ˆˆˆ
BYRONBBNYYNRRN YYYVYVYVYV ++=++

5. ELE101/102 Dept of E&E,MIT Manipal 5
Illustration
6010Z;4510Z;305Z BYR °∠=°∠=°∠=
An unbalanced star connected load is supplied from a
symmetrical, 3 Φ, 440 V, 3 wire system. Determine the
voltage of common point of load impedances with respect to
neutral of supply system and all the line currents. The branch
impedances of the load are
V9.2321.86V
:Ans
ON ∠=
;A16.4143.35 −∠=RI
=YI ;A17.17479.32 −∠
A..IB 1578827 ∠=

6. ELE101/102 Dept of E&E,MIT Manipal 5
Illustration
6010Z;4510Z;305Z BYR °∠=°∠=°∠=
An unbalanced star connected load is supplied from a
symmetrical, 3 Φ, 440 V, 3 wire system. Determine the
voltage of common point of load impedances with respect to
neutral of supply system and all the line currents. The branch
impedances of the load are
V9.2321.86V
:Ans
ON ∠=
;A16.4143.35 −∠=RI
=YI ;A17.17479.32 −∠
A..IB 1578827 ∠=