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λ λ λ
(J1)1 (J1)2 (J1)3
(IC)1= 30A
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
=15
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
= 30
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 3
= 30
ISARE
(IC)2= 90A (IC)3= 60A
Δ Δ λ
€
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
=115
€
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
=130
⇒n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
=12⋅n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
€
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 3
=130
⇒n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 3
=12⋅n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
(V13)1
(V13)3 30o
(V1)2
(IC)1= 30A
(IC)2= 90A (IC)2 = 3(IC)1
(IC)3= 60A (IC)3 = 2(IC)1
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
(Ip1)2
(IC)2
€
23⎛
⎝ ⎜ ⎞
⎠ ⎟ ⋅
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
⋅ IC( )2 =23⎛
⎝ ⎜ ⎞
⎠ ⎟ ⋅12n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⎡
⎣ ⎢
⎤
⎦ ⎥ ⋅ 3 ⋅ IC( )1[ ] =
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⋅ IC( )1⎡
⎣ ⎢
⎤
⎦ ⎥ = x
€
−13⎛
⎝ ⎜ ⎞
⎠ ⎟ ⋅
n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
⋅ IC( )2 = −13⎛
⎝ ⎜ ⎞
⎠ ⎟ ⋅12n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⎡
⎣ ⎢
⎤
⎦ ⎥ ⋅ 3 ⋅ IC( )1[ ] = −
12⋅n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⋅ IC( )1 = −12x
λ
(J1)2
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
= 30
(IC)2 = 90A
Δ
30 60 90 120 150 180 210 240 270 300 330 360
(VL)2
(Is3)2
(V2)2 (V3)2 (V1)2
(Ip3)2
(IC)2
€
x
€
−12x
λ
(J1)2
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
= 30
(IC)2 = 90A
Δ
Δ
λ
(J1)2
€
n1n2
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
= 30
(Ip3)2
(Ip1)2
(J1)2 = (Ip1)2 - (Ip3)2
30 60 90 120 150 180 210 240 270 300 330 360 €
−12x
€
x
€
−12x
€
x
€
−32x
€
32x
(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 (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
(V13)3 (V23)3 (V21)3 (V31)3 (V32)3 (V12)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
(J1)1
€
x
€
−x
ISARE
30 60 90 120 150 180 210 240 270 300 330 360
€
−2x
€
−3x
€
5x
€
−4x
€
4x
€
ISARE =12π
⋅ 2 ⋅ π6⋅52x
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
+ 2 ⋅ π6⋅72x
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
+ 2 ⋅ π3⋅92x
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
+ 2 ⋅ π6⋅ 2x( )2 + 2 ⋅ π
6⋅ x( )2
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
= x ⋅ 12π
⋅ 2 ⋅ π6⋅254
+ 2 ⋅ π6⋅494
+ 2 ⋅ π3⋅814
+ 2 ⋅ π6⋅ 4 + 2 ⋅ π
6⎡
⎣ ⎢ ⎤
⎦ ⎥
= x ⋅ 12⋅5024
+9824
+16212
+86
+26
⎡
⎣ ⎢ ⎤
⎦ ⎥ = x ⋅ 1
2⋅51224
⎡
⎣ ⎢ ⎤
⎦ ⎥ = x ⋅ 32
3
ISARE = x ⋅ 323
=n2n1
⎛
⎝ ⎜
⎞
⎠ ⎟ 1
⋅ IC( )1⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥ ⋅323
=115⋅ 30
⎡
⎣ ⎢ ⎤
⎦ ⎥ ⋅353
= 6.53A
€
−32x
€
32x
€
−x
€
3x
€
2x
€
x
€
−5x
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