266
Practical MATLAB
® Applications for Engineers
Then, I 1 = I 12 − I 31
I 1 12
90
12 30
12 3
120
ϭ
Ϫ ЊϪ
Њϭ
Ϫ Њ
∠
∠
∠
A
and I 2 = I 23 − I 12
I 2 12 150
12
90
12 3 120
ϭ
ЊϪ
Ϫ Њϭ
Њ
∠
∠
∠
A
and I 3 = I 31 − I 23 = 12 ∠30° − 12 ∠150° A
I 3 = 12 √
__
3 ∠0° A
Part b
The system for part b is shown in Figure 3.48.
Transforming the Y load into a ∆ confi guration, and making use of the symmetry of
the system, the equivalent impedances are evaluated.
Z
Z Z
Z Z
Z Z
Z
12
1 2
2 3
3 1
3
ϭ
ϩ
ϩ
and since Z 1 = Z 2 = Z 3 = j10, then
Z
Z
Z
Z
j
j
12
1
2
1
1
3
3
3 10
30
ϭ
ϭ
ϭ
ϭ
( )
Ω
Z
Z Z
Z Z
Z Z
Z
23
1 2
2 3
3 1
1
ϭ
ϩ
ϩ
Z 23 = 30j Ω
Z
Z Z
Z Z
Z Z
Z
31
1 2
2 3
3 1
2
ϭ
ϩ
ϩ
and
Z 31 = 30j Ω
FIGURE 3.48
3 Φ system connected to a Y load with Z 1 = Z 2 = Z 3 = 10j.
+
−
V 23
V 31
V 12
Z 2
Z 3
Z 1
I 1
I 2
2
+
−
−
+
1
•
•
•
•
N
CRC_47760_CH003.indd 266
CRC_47760_CH003.indd 266
7/23/2008 1:27:42 PM
7/23/2008 1:27:42 PM
Practical MATLAB
® Applications for Engineers
Then, I 1 = I 12 − I 31
I 1 12
90
12 30
12 3
120
ϭ
Ϫ ЊϪ
Њϭ
Ϫ Њ
∠
∠
∠
A
and I 2 = I 23 − I 12
I 2 12 150
12
90
12 3 120
ϭ
ЊϪ
Ϫ Њϭ
Њ
∠
∠
∠
A
and I 3 = I 31 − I 23 = 12 ∠30° − 12 ∠150° A
I 3 = 12 √
__
3 ∠0° A
Part b
The system for part b is shown in Figure 3.48.
Transforming the Y load into a ∆ confi guration, and making use of the symmetry of
the system, the equivalent impedances are evaluated.
Z
Z Z
Z Z
Z Z
Z
12
1 2
2 3
3 1
3
ϭ
ϩ
ϩ
and since Z 1 = Z 2 = Z 3 = j10, then
Z
Z
Z
Z
j
j
12
1
2
1
1
3
3
3 10
30
ϭ
ϭ
ϭ
ϭ
( )
Ω
Z
Z Z
Z Z
Z Z
Z
23
1 2
2 3
3 1
1
ϭ
ϩ
ϩ
Z 23 = 30j Ω
Z
Z Z
Z Z
Z Z
Z
31
1 2
2 3
3 1
2
ϭ
ϩ
ϩ
and
Z 31 = 30j Ω
FIGURE 3.48
3 Φ system connected to a Y load with Z 1 = Z 2 = Z 3 = 10j.
+
−
V 23
V 31
V 12
Z 2
Z 3
Z 1
I 1
I 2
2
+
−
−
+
1
•
•
•
•
N
CRC_47760_CH003.indd 266
CRC_47760_CH003.indd 266
7/23/2008 1:27:42 PM
7/23/2008 1:27:42 PM