λ
λ
λ
λ
Δ
λ
(J1)1 (J1)2 (J1)3
(IC)1 = 30A
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
=15
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
=15
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 3
= 30
ISARE
(IC)2 = 90A (IC)3 = 60A
(IC)1= 30A
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
=15
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
=15⇒ n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
=n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
(IC)2= 90A (IC)2 = 3(IC)1
(IC)3= 60A (IC)3 = 2(IC)1
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 3
= 30⇒ n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 3
= 2 ⋅ n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
(V13)1
(V1)2 = (V13)3
30o
λ
λ
(J1)1
(IC)1 = 30A
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
=15
30 60 90 120 150 180 210 240 270 300 330 360
(VL)1
(Is1)1
(V13)1 (V23)1 (V21)1 (V31)1 (V32)1 (V12)1
(J1)1 = (Ip1)1
(IC)1
-‐(IC)1
€
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⋅ IC( )1 = x
€
−n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⋅ IC( )1 = −x
(V32)1
30 60 90 120 150 180 210 240 270 300 330 360
(VL)2
(Is1)2
(V2)2 (V3)2 (V1)2
(J1)2 = (Ip1)2
(IC)2
€
23⎛
⎝ ⎜ ⎞
⎠ ⎟ ⋅
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
⋅ IC( )2 =23⎛
⎝ ⎜ ⎞
⎠ ⎟ ⋅
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⎡
⎣ ⎢
⎤
⎦ ⎥ ⋅ 3 ⋅ IC( )1[ ] = 2 ⋅ n2
n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⋅ IC( )1⎡
⎣ ⎢
⎤
⎦ ⎥ = 2x
€
−13⎛
⎝ ⎜ ⎞
⎠ ⎟ ⋅
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
⋅ IC( )2 = −13⎛
⎝ ⎜ ⎞
⎠ ⎟ ⋅
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⎡
⎣ ⎢
⎤
⎦ ⎥ ⋅ 3 ⋅ IC( )1[ ] = −
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⋅ IC( )1 = −xλ
λ
(J1)2
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
=15
(IC)2 = 90A
30 60 90 120 150 180 210 240 270 300 330 360
(VL)3
(Is1)3
(V13)3 (V23)3 (V21)3 (V31)3 (V32)3 (V12)3
(IC)3
-‐(IC)3
€
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 3
⋅ IC( )3 =12⋅n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⎡
⎣ ⎢
⎤
⎦ ⎥ ⋅ 2 ⋅ IC( )1[ ] =
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⋅ IC( )1 = x
€
−n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 3
⋅ IC( )3 = −xΔ
λ
(J1)3
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 3
= 30
(IC)3 = 60A
(Ip1)3
30 60 90 120 150 180 210 240 270 300 330 360
(VL)3
(Is3)3
(V13)3 (V23)3 (V21)3 (V31)3 (V32)3 (V12)3
(IC)3
-‐(IC)3
€
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 3
⋅ IC( )3 = x
€
−n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 3
⋅ IC( )3 = −xΔ
λ
(J1)3
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 3
= 30
(IC)3 = 60A
(Ip3)3
€
x
€
−x
Δ
λ
(J1)3
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 3
= 30
(IC)3 = 60A
(Ip3)3
€
x
€
−x
(Ip1)3
(J1)3 = (Ip1)3 -‐ (Ip3)3
€
x€
2x
€
−x
€
−2x
30 60 90 120 150 180 210 240 270 300 330 360
(J1)3
€
x€
2x
€
−x
€
−2x30 60 90 120 150 180 210 240 270 300 330 360
(J1)2
€
2x
€
−x
(J1)1
€
x
€
−x
€
J1( )1 =12π
⋅ 2 ⋅ 2π3⋅ x 2
⎡
⎣ ⎢ ⎤
⎦ ⎥ = x ⋅ 2
3
J1( )1 = x ⋅ 23
=n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⋅ IC( )1⎡
⎣ ⎢
⎤
⎦ ⎥ ⋅
23
=115
⋅ 30⎡
⎣ ⎢ ⎤
⎦ ⎥ ⋅23
=1.63A
€
J1( )2 =12π
⋅ 1⋅ 2π3⋅ 2x( )2 +1⋅ 4π
3⋅ x( )2
⎡
⎣ ⎢ ⎤
⎦ ⎥ = x ⋅ 1
2⋅23⋅ 4 +
43
⎡
⎣ ⎢ ⎤
⎦ ⎥ = x ⋅ 1
2⋅123
⎡
⎣ ⎢ ⎤
⎦ ⎥
J1( )2 = x ⋅ 2 =n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⋅ IC( )1⎡
⎣ ⎢
⎤
⎦ ⎥ ⋅ 2 =
115
⋅ 30⎡
⎣ ⎢ ⎤
⎦ ⎥ ⋅ 2 = 2.83A
€
J1( )3 =12π
⋅ 2 ⋅ π3⋅ 2x( )2 + 4 ⋅ π
3⋅ x( )2
⎡
⎣ ⎢ ⎤
⎦ ⎥ = x ⋅ 1
2⋅ 2 ⋅ 1
3⋅ 4 + 4 ⋅ 1
3⎡
⎣ ⎢ ⎤
⎦ ⎥ = x ⋅ 1
2⋅123
⎡
⎣ ⎢ ⎤
⎦ ⎥
J1( )3 = x ⋅ 2 =n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⋅ IC( )1⎡
⎣ ⎢
⎤
⎦ ⎥ ⋅ 2 =
115
⋅ 30⎡
⎣ ⎢ ⎤
⎦ ⎥ ⋅ 2 = 2.83A
(J1)3
€
x€
2x
€
−x
€
−2x30 60 90 120 150 180 210 240 270 300 330 360
(J1)2
€
2x
€
−x
(J1)1
€
x
€
−x
ISARE
30 60 90 120 150 180 210 240 270 300 330 360
€
−2x
€
−3x
€
5x
€
−4x
€
4x
€
ISARE =12π
⋅ 4 ⋅ π6⋅ 4x( )2 + 2 ⋅ π
6⋅ 5x( )2 + 2 ⋅ π
6⋅ 2x( )2 + 2 ⋅ π
6⋅ 3x( )2
⎡
⎣ ⎢ ⎤
⎦ ⎥
= x ⋅ 12π
⋅ 4 ⋅ π6⋅16 + 2 ⋅ π
6⋅ 25 + 2 ⋅ π
6⋅ 4 + 2 ⋅ π
6⋅ 9
⎡
⎣ ⎢ ⎤
⎦ ⎥
= x ⋅ 12⋅646
+506
+86
+186
⎡
⎣ ⎢ ⎤
⎦ ⎥ = x ⋅ 1
2⋅1406
⎡
⎣ ⎢ ⎤
⎦ ⎥ = x ⋅ 70
6
ISARE = x ⋅ 353
=n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⋅ IC( )1⎡
⎣ ⎢
⎤
⎦ ⎥ ⋅
353
=115
⋅ 30⎡
⎣ ⎢ ⎤
⎦ ⎥ ⋅353
= 6.83A