λ 

(J1)1  (J1)2 

(IC)1 = 270A 

€

U1

U2

1

=6300370

€

U1

U2

2

=6300370

ISARE, (I1)SARE FSARE 

Δ  λ 

(IC)2 = 270A 

λ 

Ψ1=0o  Ψ2=30o 

€

U1

U2

1

=6300370

⇒n1n2

1

=U1

U2

=6300370

3=17 3

U1

U2

2

=6300370

⇒n1n2

2

=

U13

U23

=6300

3370

3=17

λ 

Δ 

λ 

λ 

€

⇒n2n1

2

= 3 ⋅ n2n1

1

(V13)1

(V13)2

30o

30o

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

(Ip1)1

IC

-IC

€

n2n1

1

⋅ IC( )1 = x

€

−n2n1

1

⋅ IC( )1 = −x

(V32)1

(J1)1 

(IC)1 = 270A 

Δ 

λ 

Ψ1=0o 

30 60 90 120 150 180 210 240 270 300 330 360

(VL)1

(Is3)1

(V13)1 (V23)1 (V21)1 (V31)1 (V32)1 (V12)1

(Ip3)1

IC

-IC

€

−n2n1

1

⋅ IC = −x

(V32)1

€

n2n1

1

⋅ IC = x

(J1)1 

(IC)1 = 270A 

Δ 

λ 

Ψ1=0o 

(J1)1 

(IC)1 = 270A 

Δ 

λ 

Ψ1=0o  (Ip3)3

(Ip1)3

(J1)3 = (Ip1)3 - (Ip3)3

€

x€

2x

€

−x

€

−2x

30 60 90 120 150 180 210 240 270 300 330 360

€

n2n1

1

⋅ IC = x

€

−n2n1

1

⋅ IC = −x

€

−n2n1

1

⋅ IC = −x

€

n2n1

1

⋅ IC = x

30 60 90 120 150 180 210 240 270 300 330 360

(VL)2

(Is1)2

(V13)2 (V23)2 (V21)2 (V31)2 (V12)2

IC

-IC

€

n2n1

2

⋅ IC( )2 = 3 ⋅ n2n1

1

⋅ IC( )1 = 3 ⋅ x

(V32)2

(J1)2 

(IC)2 = 270A 

λ 

Ψ2=30o 

λ 

(J1)2 = (Ip1)2

€

−n2n1

2

⋅ IC( )2 = − 3 ⋅ n2n1

1

⋅ IC( )1 = − 3 ⋅ x

ISARE

30 60 90 120 150 180 210 240 270 300 330 360

(J1)2

(J1)1

€

x =n2n1

1

⋅ IC( )1 =1

17 3⋅ 270 = 9.17A

1+ 3( ) ⋅ x = 1+ 3( ) ⋅ 9.17 = 25A

2 + 3( ) ⋅ x = 2 + 3( ) ⋅ 9.17 = 34.22A

ISARE =12π

⋅ 2 ⋅ π3⋅ 9.172 + 2 ⋅ π

3⋅ 252 + 2 ⋅ π

3⋅ 34.222

=9.172 + 252 + 34.222

3

ISARE = 25A

€

x€

2x

€

−x

€

−2x

€

3 ⋅ x

€

− 3 ⋅ x

€

−x

€

x

€

− 1+ 3( ) ⋅ x

€

2 + 3( ) ⋅ x

€

1+ 3( ) ⋅ x

€

− 2 + 3( ) ⋅ x

€

VLC( )1 = VLC 0( )1 − ΔVX( )1 = 500 − 60 = 440V

VLC 0( )1 =VLC 0 PD3 =3 3VO PD3

π=

3 3 370 23

π= 500v

VO PD3 = 2 ⋅ U23

= 370 2

3

λ 

Δ 

λ 

€

VLC( )2 = VLC '( )2 = VLC 0 '( )2 − ΔVX( )2 = 433− 60 = 373V

VLC 0 '( )2 = VLC 0( )2 ⋅ cosψ2 = 500 ⋅ cos30º= 433V

VLC 0( )2 =VLC 0 PD3=3 3VO PD3

π=

3 ⋅ 3 ⋅ 370 23

π= 500v

VO PD3 = 2 ⋅ U23

= 370 2

3

λ 

€

FSARE =PLC( )1 + PLC( )23 ⋅U1 ⋅ ISARE

=VLC( )1 ⋅ (IC )1[ ] + VLC( )2 ⋅ (IC )2[ ]

3 ⋅U1 ⋅ ISARE=440 ⋅ 270[ ] + 373 ⋅ 270[ ]

3 ⋅ 6300 ⋅ 25= 0.80

€

cos ϕ1( )1 =1− ΔVX

VLC 0

1

cos ϕ1( )1 =1− 0.12 = 0.88

ϕ1( )1 = arccos 0.88( ) = 28.35º

cos ϕ1( )2 = cosψ2 −ΔVX

VLC 0

2

cos ϕ1( )2 = cos30º− 60500

= 0.74

ϕ1( )2 = arccos 0.74( ) = 41.75º

VR

(I1)1 (I1)2

€

ϕ1( )1 ≠ ϕ1( )2

€

(I1)SARE = (I1)SARE ,X2 + (I1)SARE ,Y

2 = 20.112 +14.112 = 24.56A

(I1)SARE ,X = (I1)1,X + (I1)2,X =10.88 + 9.23 = 20.11A

(I1)1,X = (I1)1 ⋅ cos ϕ1( )1 =12.37 ⋅ cos28.35 =10.88A

(I1)2,X = (I1)2 ⋅ cos ϕ1( )2 =12.37 ⋅ cos41.75 = 9.23A

(I1)SARE ,Y = (I1)1,Y + (I1)2,Y = 5.87 + 8.24 =14.11A

(I1)1,Y = (I1)1 ⋅ sin ϕ1( )1 =12.37 ⋅ sin28.35 = 5.87A

(I1)2,Y = (I1)2 ⋅ sin ϕ1( )2 =12.37 ⋅ sin41.75 = 8.24A

(I1)1 (I1)2

€

I1( )1 =VLC 0( )1 ⋅ (IC )1

3 ⋅U1

=500 ⋅ 2703 ⋅ 6300

=12.37A

I1( )2 =VLC 0( )2 ⋅ (IC )2

3 ⋅U1

=500 ⋅ 2703 ⋅ 6300

=12.37A

(I1)2,X (I1)1,X

(I1)1,Y (I1)2,Y