- Home
Documents
- Electrical Power and Machines- Lec04_Single Phase Circuit
Electrical Power and Machines- Lec04_Single Phase Circuit
Embed Size (px)
Citation preview
-
8/9/2019 Electrical Power and Machines- Lec04_Single Phase
Circuit
1/10
U
n i t 2
S
i n g l e - P h
a s e C i r
c u i t s
-
8/9/2019 Electrical Power and Machines- Lec04_Single Phase
Circuit
2/10
N o d
a l A n a l y s i s
M e s h A n a l y s i s
L e c t u
r e O u t l i n e
-
8/9/2019 Electrical Power and Machines- Lec04_Single Phase
Circuit
3/10
I 1
I
I 2
I 1
I 3
N o d a
l A n a l y s i s
K i r c h h o f f ’ s C u r r e
n t L a w
I 4
I 2
0
4
3
2
1
=
+
+
+
I
I
I
I
3
2
1
I
I
I
+
=
-
8/9/2019 Electrical Power and Machines- Lec04_Single Phase
Circuit
4/10
V 1
V 2
V 3
Z
1
Z 3
I 1
I 3
I 2
O f
t e n , t h e c u r r e n
t v a l u e s
a r e n o t a v a i l a b l e
b u t K C L
c a n b e a p p l i e d i f
t h e
N o d a
l A n a l y s i s
K i r c h h o f f ’ s C u r r e
n t L a w
V 0
Z 2
3
2
1
I
I
I
+
=
2
0
2
3
3
2
1
2
1
Z V
V
Z
V
V
Z
V
V
−
+
−
=
−
l e v e l s a r e p r o v i d
e d .
-
8/9/2019 Electrical Power and Machines- Lec04_Single Phase
Circuit
5/10
F i n d i x i n t h e c i r c u i t u s i n g n o d a l a n a l y s i s
N o d a
l A n a l y s i s : E x a m
p l e 1
°
∠
=
⇒ °
0
2 0
)
4
c o
s (
2 0
V
t
Ω
=
×
⇒
2
5 . 0
4
H 5 . 0
j
j
Ω
−
=
×
⇒
5 . 2
1 . 0
4 1
F
. 1 0
j
j
Ω
=
×
⇒
4
1
4
H 1
j
j
-
8/9/2019 Electrical Power and Machines- Lec04_Single Phase
Circuit
6/10
N o d a l A n a l y s i s : E x a m p l e 1 ( c o
n t . )
4
5 . 2
1 0
2 0
2
1
1
1
j
j
V
V
V
V
−
+
−
=
−
2
0
5 . 2
) 5 . 1
1 (
2
1
=
+
+
V
V
j
j
2
4
2
2
2
1
X
j
j
V
V
V
I
=
−
+
2
4
5 . 2
2
2
2
1
1
j
j
j
V
V
V
V
=
−
+
−
0
1 5
1 1
2
1
=
+
V
V
5 . 2 1
X
j
− =
V
I
-
8/9/2019 Electrical Power and Machines- Lec04_Single Phase
Circuit
7/10
0
1 5
1 1
2
1
=
+
V
V
S o l v e t h e e q u a t i o n s
N o d a l A n a l y s i s : E x a m p l e 1 ( c o
n t . )
2 0
5 . 2
) 5 . 1
1 (
2
1
=
+
+
V
V
j
j
1
2
1
5
1
1 V
V
− =
2 0
)
1 5 1 1
( 5 . 2
)
5 . 1
1 (
1
1
=
−
+
+
V
V
j
j
2 0
)
8 3 .
1
5 . 1
1 (
1
=
−
+
V
j
j
°
−
∠
°
∠
=
− =
4 .
1 8
0 5 3
. 1
0
2 0
3 3 .
0
1
2 0
1
j
V
°
−
∠
°
∠
=
− =
9 0
5 . 2
4 .
1 8
9 7 .
1 8
5 . 2 1
X
j V
I
°
∠
=
4 .
1 8
9 7 .
1 8
1
V
°
∠
=
4 .
1 0 8
5 9 .
7
) 4 .
1 0 8
4
c o s (
5 9 .
7
)
(
°
+
=
t
t i x
-
8/9/2019 Electrical Power and Machines- Lec04_Single Phase
Circuit
8/10
+ V 1 -
+ Z 1 -
+ Z
3 -
+ Z 2
+ Z
I 1
I 2
M e s h
A n a l y s i s
K i r c h h o
f f ’ s V o l t a g
e L a w
-
-
M e s h 1 :
V 1 = I 1 Z 1 + ( I 1 - I 2 ) Z 2
M e s h 2 :
( I 2 - I 1 ) Z 2 = I 2 Z
3 + I 2 Z 4
M e s h 1
M e s h 2
-
8/9/2019 Electrical Power and Machines- Lec04_Single Phase
Circuit
9/10
I 1
I 2
D e t e r m i n e
I o
a n d V
o
M e s h
A n a l y s i s :
E x a m p l e 1 ( Q 1 0 . 3 2
)
M e s h 1
M e s h 2
0
3
4
)
3 0
- 4
( 2
1
1
=
+
+ °
∠ −
o
j
V
I
I M e s h 1 :
)
3 0 -
4 (
2
1
o
I
V
− °
∠
=
0 )
3 0 -
4 ( 6
3 0 -
8
) 4 j
2 (
1
1
=
− °
∠
+ °
∠
−
+
I
I
1
) j
1 (
3 0 -
4
I
−
= °
∠
°
∠
=
1 5
8 4 . 2
1 I
0
3 0 -
2
4
3 0 -
8
) 6 4
2 (
1
= °
∠
+ °
∠ −
−
+
I
j
0
3 0 -
1 6
) 4
4 (
1
= °
∠
+
+ −
I j
1
4 5
4
1
. 1
3 0 -
4
I °
− ∠
= °
∠
-
8/9/2019 Electrical Power and Machines- Lec04_Single Phase
Circuit
10/10
I 1
I o
D e t e r m i n e
I o
a n d V
o
M e s h
A n a l y s i s :
E x a m p l e 1 ( c o n t . )
M e s h 1
M e s h 2
M e s h 1 :
)
3 0 -
4 ) ( 2 (
2 - 3
2
- 3
1 I
V
I
− °
∠
=
=
j
j o
o
)
1 5
8 4 .
2
3 0 -
4 ( 3
°
∠
− °
∠
= j
o I
° ∠
=
1 5
4 8 .
8
o I
M e s h 2 :
°
− ∠
=
=
7 5
6 6 . 5
3 2
-
o
o
j
I
V
°
∠
=
1 5
8 4 .
2
1 I
