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