eep konstr.zadatak upute

TEHNIČKO VELEUČILIŠTE U ZAGREBU

ELEKTROTEHNIČKI ODJEL

Upute za izradu konstrukcijskog zadatka iz Elektroenergetskih postrojenja

Pripremio: Mr. sc. Dubravko Žigman

Zagreb 2004/2005.

SADRŽAJ

PRIMJER PROGRAMSKOG ZADATKA IZ EEP POSTROJENJA........................................ 3 1 PRORAČUN ....................................................................................................................... 4

1.1 VODOVA.................................................................................................................... 4 1.2 GENERATORA.......................................................................................................... 4 1.3 TRANSFORMATORA............................................................................................... 5

2 EKVIVALENTNE SHEME ............................................................................................... 5 2.1 DIREKTNI SUSTAV ................................................................................................. 5 2.2 INVERZNI SUSTAV ............................................................................................... 10 2.3 NULTI SUSTAV ...................................................................................................... 15

3 PRORAČUN STRUJA KRATKOG SPOJA .................................................................... 20 3.1 JEDNOPOLNI KRATKI SPOJ ................................................................................ 20 3.2 DVOPOLNI KRATKI SPOJ .................................................................................... 20 3.3 DVOPOLNI KRATKI SPOJ SA ZEMLJOSPOJEM ............................................... 20 3.4 TROPOLNI KRATKI SPOJ ..................................................................................... 21

4 RASPODJELA STRUJA U EKVIVALENTNIM SHEMAMA ZA ZADANO MJESTO KS I MJERODAVNI KS .......................................................................................................... 21 5 STRUJE FAZA R, S i T.................................................................................................... 24

JEDNOPOLNI KS ................................................................................................................ 24 TROPOLNI KS..................................................................................................................... 24 5.1 STRUJE FAZE R...................................................................................................... 24

5.1.1 Struje vodova..................................................................................................... 24 5.1.2 Struje transformator – sabirnica ........................................................................ 25

5.2 STRUJE FAZE S ...................................................................................................... 25 5.2.1 Struje vodova..................................................................................................... 25 5.2.2 Struje transformator – sabirnica ........................................................................ 25

5.3 STRUJE FAZE T ...................................................................................................... 25 5.3.1 Struje vodova..................................................................................................... 25 5.3.2 Struje transformator – sabirnica ........................................................................ 25

6 STRUJE GENERATORA ODNOSNO PRIMARA TRANSFORMATORA.................. 26 6.1 JEDNOPOLNI KS .................................................................................................... 26 6.2 TROPOLNI KS......................................................................................................... 26

6.2.1 Struje generatora G1 .......................................................................................... 26 6.2.2 Struje generatora G2 .......................................................................................... 26 6.2.3 Struje generatora G3 .......................................................................................... 26 6.2.4 Struje generatora G4 .......................................................................................... 26

7 TROPOLNA SHEMA – RASPODJELA STRUJA U MREŽI ZA VRIJEME TROPOLNOG KRATKOG SPOJA ......................................................................................... 27

Literatura: Hrvoje Požar: Visokonaponska Rasklopna Postrojenja, Tehnička

knjiga, Zagreb, 1963.

2

PRIMJER PROGRAMSKOG ZADATKA IZ EEP POSTROJENJA

(PRORAČUN STRUJA KRATKOG SPOJA) ZADATAK: Proračunati struje kratkog spoja na zadanim sabirnicama

i odrediti struje u pojedinim granama za najnepovoljniji slučaj kratkog spoja u mreži prema slici.

Ostali podaci: Za reaktancije vodova uzeti 0,4 Ω/km.

G1

G4

G3

T1

T4

T2

T3

G2

E

B

D

C

A LAD

LDE

LBD

LAC LBC

Element Veličina Jedinica Primjer 0 S MVA 25

G1, G2 U kV 10 X’d % 17 Xi % 4,5 S MVA 70

G3 U kV 10 X’d % 28 Xi % 15 S MVA 35

G4 U kV 10 X’d % 38 Xi % 8 S MVA 25

T1, T2 U1/U2 kV/kV 10/110 Xk % 10 S MVA 70

T3 U1/U2 kV/kV 10/110 Xk % 11 S MVA 35

T4 U1/U2 kV/kV 10/110 Xk % 9 lAD km 60 lAC km 110

Vodovi lBC km 85 lBD km 70 lDE km 70

MJESTO KRATKOG SPOJA D

1 PRORAČUN

1.1 VODOVA

VAD Xd = Xi = l * Xv = 60 km * 0,4 Ω/km = 24 Ω

X0 = 3 Xd = 3 * 24 Ω = 72 Ω

VAC Xd = Xi = l * Xv = 110 km * 0,4 Ω/km = 44 Ω

X0 = 3 Xd = 3 * 44 Ω = 132 Ω

VBC Xd = Xi = l * Xv = 85 km * 0,4 Ω/km = 34 Ω

X0 = 3 Xd = 3 * 34 Ω = 102 Ω

VBD Xd = Xi = l * Xv = 70 km * 0,4 Ω/km = 28 Ω

X0 = 3 Xd = 3 * 28 Ω = 84 Ω

VDE Xd = Xi = l * Xv = 70 km * 0,4 Ω/km = 28 Ω

X0 = 3 Xd = 3 * 28 Ω = 84 Ω

1.2 GENERATORA

G1 Ω=⋅⋅

⋅=⋅= ÷ 28,821025

)10110(10017

100 6

2232

VAV

SUX

X dd

Ω=⋅⋅

⋅=⋅= ÷ 78,211025

)10110(100

5,4100 6

2232

VAV

SUX

X ii

G2 Ω=⋅⋅

⋅=⋅= ÷ 28,821025

)10110(10017

100 6

2232

VAV

SUX

X dd

Ω=⋅⋅

⋅=⋅= ÷ 78,211025

)10110(100

5,4100 6

2232

VAV

SUX

X ii

G3 Ω=⋅⋅

⋅=⋅= ÷ 4,481070

)10110(10028

100 6

2232

VAV

SUX

X dd

Ω=⋅⋅

⋅=⋅= ÷ 92,251070

)10110(10015

100 6

2232

VAV

SUX

X ii

G4 Ω=⋅⋅

⋅=⋅= ÷ 37,1311035

)10110(10038

100 6

2232

VAV

SUX

X dd

Ω=⋅⋅

⋅=⋅= ÷ 65,271035

)10110(100

8100 6

2232

VAV

SUX

X ii

4

1.3 TRANSFORMATORA

T1 Ω=⋅⋅

⋅=⋅=== ÷ 4,481025

)10110(10010

100 6

2232

0 VAV

SUX

XXX kid

T2 Ω=⋅⋅

⋅=⋅=== ÷ 4,481025

)10110(10010

100 6

2232

0 VAV

SUX

XXX kid

T3 Ω=⋅⋅

⋅=⋅=== ÷ 01,191070

)10110(10011

100 6

2232

0 VAV

SUX

XXX kid

T4 Ω=⋅⋅

⋅=⋅=== ÷ 11,311035

)10110(100

9100 6

2232

0 VAV

SUX

XXX kid

2 EKVIVALENTNE SHEME

2.1 DIREKTNI SUSTAV

A B

C

D E

G G G G

XG1

XG2

XG3

XG4 XT4

XT3

XT2

XT1 XAD

XAC

XDE

XDB

XCB

Slika 2.1: Ekvivalentna shema direktnog sustava

A B

C

D E

G G G G

XG1

XG2

XG3

XG4 XT4

XT3

XT2

XT1 XAD

XAC

XDE

XDB

XCB

Slika 2.2 a): Ekvivalentna shema direktnog sustava s reaktancijama

82,28 Ω 48,4 Ω

82,28 Ω 48,4 Ω

48,4 Ω 19,01 Ω

44 Ω 34 Ω

28 Ω 24 Ω

28 Ω

31,11 Ω 131,37 Ω

5

X1 = XG1 + XT1 = 82,28 Ω + 48,4 Ω = 130,68 Ω

X2 = XG2 + XT2 = 82,28 Ω + 48,4 Ω = 130,68 Ω

X3 = XG3 + XT3 = 48,4 Ω + 19,01 Ω = 67,41 Ω

X4 = XG4 + XT4 = 31,11 Ω + 131,37 Ω = 162,48 Ω

A

B

C D

G G G

X4

X3

X2

X1 XAD

XAC

XDB

XCB

Slika 2.2 b)

130,68 Ω

130,68 Ω

67,41 Ω

44 Ω 34 Ω

28 Ω 24 Ω

162,48 Ω

G

Ω=+⋅

=+⋅

= 34,6568,13068,13068,13068,130

21

2112 XX

XXX

A B

C

D

G G

X4

X3

X12

XAD

XAC

XDB

XCB

Slika 2.2 c)

65,34 Ω

67,41 Ω

44 Ω 34 Ω

28 Ω 24 Ω

162,48 Ω

G

XAC3 XCB3

XAB

1

323223

2

313113

3

212112

XXX

XXX

XXX

XXX

XXXXXX

⋅++=

⋅++=

⋅++=

6

Ω=⋅

++=

⋅+⋅+⋅=

⋅++=

Ω=⋅

++=

⋅+⋅+⋅=

⋅++=

Ω=⋅+⋅+⋅

=

⋅+⋅+⋅=

⋅++=

19,10041,6734443444

49,15344

41,673441,6734

64,19834

41,67443441,673444

3

33

3

3

33333

3

33333

AB

CBACCBACCBACCBACAB

CB

AC

CBACACCB

AC

CBCBCB

AC

CB

ACCBCBAC

CB

ACACAC

X

XXXXXXX

XXX

XXX

X

XXXXXXX

XXX

XXX

X

XXXXXXX

XXX

XXX

A

B D

G G

X4 X12

XAD

XAB

XDB

Slika 2.2 d)

65,34 Ω

100,19 Ω

198,64 Ω 153,49 Ω

28 Ω 24 Ω

162,48 Ω

G

XAC3 XCB3

Ω=+⋅

=+⋅

= 16,4964,19834,6564,19834,65

312

3121

AC

ACA XX

XXX

Ω=+⋅

=+⋅

= 92,7849,15348,16249,15348,162

34

344

CB

CBB XX

XXX

231312

23133

231312

23122

231312

13121

XXXXX

X

XXXXX

X

XXXXX

X

++⋅

=

++⋅

=

++⋅

=

7

A B

D XAD

XAB

XDB

100,19 Ω

49,16 Ω 78,92 Ω

28 Ω 24 Ω

Slika 2.2 e)

G

X1A X4B

XB XA

XC

P

Ω=++

⋅=

++⋅

=

Ω=++

⋅=

++⋅

=

Ω=++

⋅=

++⋅

=

83,1692,7819,10016,49

92,7816,49

63,3492,7819,10016,49

19,10092,78

57,2192,7819,10016,49

19,10016,49

41

41

41

4

41

1

C

BABA

BAC

B

BABA

ABBB

A

BABA

ABAA

X

XXXXXX

X

XXXXXX

X

XXXXXX

A

B D

XAD XDB

21,57 Ω

16,83 Ω

28 Ω 24 Ω

XA

34,63 Ω

XB

Slika 2.2 f)

G

P

XC

8

XA’ = XAD + XA = 24 Ω + 21,57 Ω = 45,57 Ω

XB’ = XDB + XB = 28 Ω + 34,63 Ω = 62,63 Ω

D

16,83 Ω

62,63 Ω 45,57 Ω

Slika 2.2 g)

G

P

XC

XB'XA

'

Ω=+⋅

=+⋅

= 37,2663,6257,4563,6257,45

''

'''

BA

BAAB XX

XXX

Xd = XAB’ + XC = 26,37 Ω + 16,83 Ω = 43,2 Ω

Zd = j 43,2 Ω

D

16,83 Ω

Slika 2.2 h)

G

P

XC

26,37 Ω XAB' k 43,2 Ω

Slika 2.2 i)

P 3

110V

Xd

G

9

2.2 INVERZNI SUSTAV

A B

C

D E

XG1

XG2

XG3

XG4 XT4

XT3

XT2

XT1 XAD

XAC

XDE

XDB

XCB

Slika 2.3: Ekvivalentna shema inverznog sustava

P

A B

C

D E

X1 = XG1 + XT1 = 21,78 Ω + 48,4 Ω = 70,18 Ω

X2 = XG2 + XT2 = 21,78 Ω + 48,4 Ω = 70,18 Ω

X3 = XG3 + XT3 = 25,92 Ω + 19,01 Ω = 44,93 Ω

X4 = XG4 + XT4 = 27,65 Ω + 31,11 Ω = 58,76 Ω

XG1

XG2

XG3

XG4 XT4

XT3

XT2

XT1 XAD

XAC

XDE

XDB

XCB

Slika 2.3 a): Ekvivalentna shema inverznog sustava s reaktancijama

21,78Ω 48,4 Ω

21,78 Ω 48,4 Ω

25,92 Ω 19,01 Ω

44 Ω 34 Ω

28 Ω 24

28 Ω

31,11 Ω 27,65 Ω

Ω

10

A

B

C D

P

X4

X3

X2

X1 XAD

XAC

XDB

XCB

Slika 2.3 b)

70,18 Ω

70,18 Ω

44,93 Ω

44 Ω 34 Ω

28 Ω 24 Ω

58,76 Ω

Ω=+⋅

=+⋅

= 09,3518,7018,7018,7018,70

21

2112 XX

XXX

A B

C

D

P

X4

X3

X12

XAD

XAC

XDB

XCB

Slika 2.3 c)

35,09 Ω

44,93 Ω

44 Ω 34 Ω

28 Ω 24 Ω

58,76 Ω

XAC3 XCB3

XAB

1

323223

2

313113

3

212112

XXX

XXX

XXX

XXX

XXXXXX

⋅++=

⋅++=

⋅++=

11

Ω=⋅

++=

⋅+⋅+⋅=

⋅++=

Ω=⋅

++=

⋅+⋅+⋅=

⋅++=

Ω=⋅

++=

⋅+⋅+⋅=

⋅++=

3,11193,4434443444

68,11344

93,443493,4434

07,14734

93,444493,4444

3

33

3

3

33333

3

33333

AB

CBACCBACCBACCBACAB

CB

AC

CBACACCB

AC

CBCBCB

AC

CB

ACCBCBAC

CB

ACACAC

X

XXXXXXX

XXX

XXX

X

XXXXXXX

XXX

XXX

X

XXXXXXX

XXX

XXX

A

B D

P

X4 X12

XAD

XAB

XDB

Slika 2.3 d)

35,09 Ω

111,3 Ω

147,07 Ω 113,68 Ω

28 Ω 24 Ω

58,76 Ω

XAC3 XCB3

Ω=+⋅

=+⋅

= 33,2807,14709,3507,14709,35

312

3121

AC

ACA XX

XXX

Ω=+⋅

=+⋅

= 73,3868,11376,5868,11376,58

34

344

CB

CBB XX

XXX

231312

23133

231312

23122

231312

13121

XXXXX

X

XXXXX

X

XXXXX

X

++⋅

=

++⋅

=

++⋅

=

12

A B

D XAD

XAB

XDB

111,3Ω

28,33 Ω 38,73 Ω

28 Ω 24 Ω

Slika 2.3 e)

X1A X4B

XB XA

XC

P

Ω=++

⋅=

++⋅

=

Ω=++

⋅=

++⋅

=

Ω=++

⋅=

++⋅

=

15,673,383,1113,28

73,383,28

16,2473,383,1113,28

3,11173,38

67,1773,383,1113,28

73,383,28

41

41

41

4

41

1

C

BABA

BAC

B

BABA

ABBB

A

BABA

ABAA

X

XXXXXX

X

XXXXX

X

X

XXXXX

X

A

B D

XAD XDB

17,67 Ω

6,15Ω

28 Ω 24 Ω

XA

24,16 Ω

XB

Slika 2.3 f)

P

XC

13

XA’ = XAD + XA = 24 Ω + 17,67 Ω = 41,67 Ω

XB’ = XDB + XB = 28 Ω + 24,16 Ω = 52,16 Ω

D

6,15Ω

52,16Ω 41,67Ω

Slika 2.3 g)

P

XC

XB'XA

'

Ω=+⋅

=+⋅

= 16,2316,5267,4116,5267,41

''

'''

BA

BAAB XX

XXX

Xi = XAB’ + XC = Ω + 6,15 Ω = 29,31 Ω 16,23

Zi = j 29,31 Ω

D

6,15 Ω

Slika 2.3 h)

P

XC

23,16 Ω XAB' k 29,31 Ω

Slika 2.3 i)

P

Xi

14

2.3 NULTI SUSTAV

A B

C

D E

∞ XT4

XT3

XT1 XAD

XAC

XDE

XDB

XCB

Slika 2.4: Ekvivalentna shema nultog sustava

P

∞ ∞

∞

∞

A B

C

D E

∞ XT4

XT3

XT1 XAD

XAC

XDE

XDB

XCB

Slika 2.4 a): Ekvivalentna shema nultog sustava s reaktancijama

P

∞ ∞

∞

∞

48,4 Ω 72 Ω

84 Ω

84 Ω

31,11 Ω

102 Ω 132 Ω

19,01 Ω

A B

C

D

P

X4

X3

X1

XAD

XAC

XDB

XCB

48,4 Ω

19,01

15Slika 2.4 b)

Ω

132 Ω 102 Ω

84 Ω 72 Ω

31,11 Ω

XAC3 XCB3

XAB

1

323223

2

313113

3

212112

XXX

XXX

XXX

XXX

XXXXXX

⋅++=

⋅++=

⋅++=

Ω=⋅

++=

⋅+⋅+⋅=

⋅++=

Ω=⋅

++=

⋅+⋅+⋅=

⋅++=

Ω=⋅

++=

⋅+⋅+⋅=

⋅++=

25,94201,19102132102132

7,135132

01,1910201,19102

61,175102

01,1913201,19132

3

33

3

3

33333

3

33333

AB

CBACCBACCBACCBACAB

CB

AC

CBACACCB

AC

CBCBCB

AC

CB

ACCBCBAC

CB

ACACAC

X

XXXXXXX

XXX

XXX

X

XXXXXXX

XXX

XXX

X

XXXXXXX

XXX

XXX

A

B D

P

X4 X1

XAD

XAB

XDB

Slika 2.4 c)

48,4Ω

942,25Ω

175,61Ω 135,7Ω

84 Ω 72 Ω

31,11Ω

XAC3 XCB3

Ω=+⋅

=+⋅

= 94,3761,1754,4861,1754,48

31

311

AC

ACA XX

XXX

Ω=+⋅

=+⋅

= 3,257,13511,317,13511,31

34

344

CB

CBB XX

XXX

16

A B

D XAD

XAB

XDB

942,25Ω

37,94Ω 25,3Ω

84 Ω 72 Ω

Slika 2.4 d)

X1A X4B

XB XA

XC

P

231312

23133

231312

23122

231312

13121

XXXXX

X

XXXXX

X

XXXXX

X

++⋅

=

++⋅

=

++⋅

=

Ω=++

⋅=

++⋅

=

Ω=++

⋅=

++⋅

=

=++

⋅=

++

Ω

⋅=

95,03,2525,94294,37

3,2594,37

7,233,2525,94294,37

25,9423,25

53,353,2525,94294,37

25,94294,37

41

41

41

4

41

1

C

BABA

BAC

B

BABA

ABBB

A

BABA

ABAA

X

XXXXXX

X

XXXXX

X

X

XXXXX

X

A

B D

XAD XDB

35,53Ω

0,95Ω

84 Ω 72 Ω

XA

23,7Ω

XB

Slika 2.4 e)

P

XC

17

XA’ = XAD + XA = 72 Ω + 35,53 Ω = 107,53 Ω

XB’ = XDB + XB = 84 Ω + 23,7 Ω = 107,7 Ω

D

0,95Ω

107,7Ω 107,53Ω

Slika 2.4 f)

P

XC

XB'XA

'

Ω=+⋅

=+⋅

= 8,537,10753,1077,10753,107

''

'''

BA

BAAB XX

XXX

X0 = XAB’ + XC = 53,8Ω + 0,95 Ω = 54,75 Ω

Z0 = j 54,75 Ω

D

0,95Ω

Slika 2.4 g)

P

XC

53,8 Ω XAB'

k 54,75Ω

Slika 2.4 h)

P

X0

153,075,5431,29

0

<==XX i ⇒ mjerodavan je tropolni kratki spoj

18

Slika 2.5: Područja omjera α = Zi/Zd i β = Zi/Z0 u kojima se pojavljuju najveće struje za različite vrste kratkog spoja

19

3 PRORAČUN STRUJA KRATKOG SPOJA

3.1 JEDNOPOLNI KRATKI SPOJ

00

0

31

0

497,126,127

52,19075,5431,292,43

31103

3

ZZZEIIII

II

kAjjjjjZZZ

EI

id

dRid

TS

id

dR

&&&

&&&&&

&&

&&&

&&

++====

==

−==++

⋅=

++=

3.2 DVOPOLNI KRATKI SPOJ

( ) ( )0;

517,151,72

11031,292,43

31103

3

00

0

22

=+

=−=

−=−=

−==+

⋅=

+=−=

=+=

IZZ

EII

aaIIaaII

kAjjjjZZ

EII

III

id

did

dTdS

id

dTS

TSR

&&&

&&&

&&&&

&&

&&&

&&&

3.3 DVOPOLNI KRATKI SPOJ SA ZEMLJOSPOJEM

( ) ( )

( ) ( )

( )

000

00

0

00

0

0

00

0

00

0

0

07,2054,1

53,045,111,5236

13,279248,76342,236572,160419,1266

426,24093,87754,31

75,542,4375,5431,2931,292,4375,54231,29331,293

32110233

21

07,2054,1

53,045,111,5236

13,279248,76342,236572,160419,1266

426,24093,87754,31

75,542,4375,5431,2931,292,4375,54231,29331,293

32110233

21

0

ZZZZZZZE

IZZZZZZ

ZEI

ZZZZZZZZE

I

IIII

kAI

jjjI

jjjjjjjjjj

ZZZZZZZZjZ

EI

kAI

jjjI

jjjjjjjjjj

ZZZZZZZZjZ

EI

I

diid

id

diid

di

diid

idd

idR

T

T

diid

iidT

S

S

diid

iidS

R

&&&&&&

&&&

&&&&&&

&&&

&&&&&&

&&&&

&&&&

&

&

&&&&&&

&&&&&

&

&

&&&&&&

&&&&&

&

o

o

⋅+⋅+⋅⋅

−=⋅+⋅+⋅

⋅−=

⋅+⋅+⋅+⋅

=

=++=

∠=

=+=−

−−=

−−−+

⋅−=

=⋅+⋅+⋅

⋅+−⋅⋅

⋅−

=⋅+⋅+⋅

⋅+−⋅⋅−=

−∠=

=+−=−

−=

−−−−

⋅−=

=⋅+⋅+⋅

⋅++⋅⋅

⋅−

=⋅+⋅+⋅

⋅++⋅⋅−=

=

20

3.4 TROPOLNI KRATKI SPOJ

( ) 0310

03047,112019047,1

15047,124019047,1

9047,147,12,43

3110

0

2

=++====

=++

∠=∠⋅−∠=⋅=

∠=∠⋅−∠=⋅=

−∠=−===

TSRid

dRd

TSR

RT

RS

d

dR

IIIIIZE

II

IIIkAaII

kAaII

kAjjZ

EI

&&&&&&

&&&

&&&

&&

&&

&

&&

ooo

ooo

o

4 RASPODJELA STRUJA U EKVIVALENTNIM SHEMAMA ZA ZADANO MJESTO KS I MJERODAVNI KS

Mjesto kratkog spoja(KS) je sabirnica D, a mjerodavni KS je tropolni kratki spoj.

D

j16,83 Ω

Slika 4.2

G

P

j26,37 Ω İd = -j1,47kA

İd = -j1,47kA

k

Slika 4.1 P

3110

V

Żd

G İd = -j1,47kA

j43,2Ω

Za tropolni KS vrijedi:

( ) 0310

47,1

0

3047,112019047,1

15047,124019047,1

9047,147,12,43

3110

0

2

=++==

−===

=++

∠=∠⋅−∠=⋅=

∠=∠⋅−∠=⋅=

−∠=−===

TSRi

d

dRd

TSR

RT

RS

d

dR

IIIII

kAjZEII

III

kAaII

kAaII

kAjjZ

EI

&&&&&

&

&&&

&&&

&&

&&

&

&&

ooo

ooo

o

21

kAjj

kVZ

UI

kAjj

kVZ

UI

kVjjZIUili

kAjjjIII

kAjjj

jII

strujedvijedrugesedobijudjelilomstrujnimSakAjI

B

AD

A

AD

ADAD

62,063,62

76,38

85,057,45

76,3876,3837,2647,1

62,085,047,1

85,063,6257,45

63,62:

47,1

'3

'2

1

213

12

1

−=Ω

==

−=Ω

==

=⋅−=⋅=

−=+−=−=

−=+

⋅=

−=

&

&

&&

&&&

&&

&

D

j16,83 Ω

j62,63 Ω j45,57 Ω

Slika 4.2 a)

G

P

İ1

İ2 İ3

( )

( )

( ) ( )

kAjj

kVZUI

kAjj

kVZUI

kAjj

kVZUI

kVUjjjjU

ZIZIUkVU

jjjjUZIZIU

kVUjjjjU

ZIZIU

AB

AB

B

B

A

A

AB

AB

BAAB

B

B

BCB

A

A

ACA

031,019,100

136,3

586,092,78

21,46

876,016,49

075,43

136,347,2133,1863,3462,057,2147,1

21,4647,2174,2463,3462,083,1647,1

075,4333,1874,2457,2185,083,1647,1

4

4

46

1

15

32

4

4

314

1

1

211

−=Ω

==

−=Ω

==

−=Ω

==

=+−=⋅−+⋅−−=

⋅+⋅−=

=+=⋅−+⋅−=

⋅+⋅=

=+=⋅−+⋅−=

⋅+⋅=

&&

&&

&&

&&&&

&&&&

&&&&

kAjjjIII

kAjjjIII

kAjjjIII

rezultatadobivenihovjera

85,003,088,0

62,059,003,0

47,159,088,0

:Pr

245

364

165

−=+−=−

−=−−=+

−=−−=+

&&&

&&&

&&&

A

İ1

D ŻAD

ŻAB

ŻDB

j100,19 Ω

j49,16 Ω j78,92 Ω

j28 Ω j24 Ω

Slika 4.2 b)

G

Ż1A Ż4B

ŻB ŻA

ŻC

P

j21,57Ω j34,63Ω

j16,83 Ω

İ2 İ3

İ4

İ5 İ6

B

1

A D ŻAD

ŻAB

ŻDB

j100,19 Ω

j49,16 Ω j78,92 Ω

j28 Ω j24 Ω

Slika 4.2 c)

G

Ż1A Ż4B

P

İ4

İ5 İ6

B

1

İ2 İ3

İ1

22

A B

D

G G

Ż4 Ż12

ŻAD

ŻAB

ŻDB

Slika 4.2 d)

j65,34 Ω

j100,19 Ω

j198,64 Ω j153,49 Ω

j28 Ω j24 Ω

j162,48 Ω

G

ŻAC3 ŻCB3

İ2

İ61

İ62

İ51

İ52

İ3

İ4

( )

( ) kAjkAjkAjIIjj

jII

kAjkAjjj

jII

kAjkAjkAjIIjj

jII

kAjkAjjj

jII

659,0217,0876,064,19834,65

64,198

217,0247,0876,064,19834,65

34,65

285,0301,0586,048,16249,153

49,153

301,0514,0586,048,16249,153

48,162

515552

551

616662

661

−=−−−=−=+

⋅=

−=⋅−=+

⋅=

−=−−−=−=+

⋅=

−=⋅−=+

⋅=

&&&&

&&

&&&&

&&

A B

C

D

G G

Ż4

ŻAD

ŻAC

ŻDB

ŻCB

Slika 4.2 e)

Ż1

j130,68 Ω

j44 Ω j34 Ω

j28 Ω j24 Ω

j162,48 Ω

ŻAC3 ŻCB3

ŻAB

( )( )( )

kAjkAjIII

kAjkAjII

kAjkAjkAjIII

kAjkAjkAjIII

kAjkAjkAjIII

GG

G

C

B

A

329,02659,0

2

329,02659,0

2

332,0301,0217,0

332,0031,0301,0

186,0031,0217,0

5212

521

6151

461

451

−=−

===

−=−

==

−=−+−=+=

−=−+−=+=

−=−−−=−=

&&&

&&

&&&

&&&

&&&

İ61İ51

İA

j67,41 ΩŻ3

G

İB

İC

İ4 Ż2

j130,68 Ω

İG1 İG2

İ62

İ3 İ2 İ1

G

23

A B

C

D E

Slika 4.3: Jednopolna shema sustava

P

İ1 = -j1,47 kA

İ3 = -j0,62 kA İ2 = -j0,85 kA

İA = -j0,19 kA İB = -j0,33 kA

İ62 = -j0,29 kA

İC = -j0,52 kA

İG2 = -j0,33 kA

İG1 = -j0,33 kA

Provjera rezultata:

kAjkAjkAjIII

kAjkAjkAjkAjkAjIIIII CGG

47,162,085,0

47,129,052,033,033,0

321

62211

−=−−=+=

−=−−−−=+++=&&&

&&&&&

5 STRUJE FAZA R, S i T

JEDNOPOLNI KS

0

3

==

⋅=

TS

dR

II

II&&

&&

TROPOLNI KS

aII

aII

II

RT

RS

dR

⋅=

⋅=

=

&&

&&

&&

2

5.1 STRUJE FAZE R

5.1.1 Struje vodova

kAkAjIIkAkAjII

kAkAjII

kAkAjII

DB

DA

BCB

ACA

o

o

o

o

&&

&&

&&

&&

9062,062,09085,085,0

9033,033,0

9019,019,0

3

2

−∠=−==

−∠=−==

−∠=−==

−∠=−==

−

−

−

−

24

5.1.2 Struje transformator – sabirnica

kAkAjII

kAkAjII

kAkAjII

kAkAjII

BT

CCT

GAT

GAT

o

o

o

o

&&

&&

&&

&&

9029,029,0

9052,052,0

9033,033,0

9033,033,0

624

3

22

11

−∠=−==

−∠=−==

−∠=−==

−∠=−==

−

−

−

−

5.2 STRUJE FAZE S

5.2.1 Struje vodova

kAkAIaI

kAkAIaI

kAkAIaI

kAkAIaI

RDB

RDA

RCB

RCA

ooo

ooo

ooo

ooo

&&

&&

&&

&&

15062,09062,02401

15085,09085,02401

15033,09033,02401

15019,09019,02401

2

2

2

2

∠=−∠⋅∠=⋅=

∠=−∠⋅∠=⋅=

∠=−∠⋅∠=⋅=

∠=−∠⋅∠=⋅=

−

−

−

−


kAkAIaI

kAkAIaIkAkAIaI

kAkAIaI

RBT

RCT

RAT

RAT

ooo

ooo

ooo

ooo

&&

&&

&&

&&

15029,09029,02401

15052,09052,0240115033,09033,02401

15033,09033,02401

24

23

22

21

∠=−∠⋅∠=⋅=

∠=−∠⋅∠=⋅=

∠=−∠⋅∠=⋅=

∠=−∠⋅∠=⋅=

−

−

−

−

5.3 STRUJE FAZE T

5.3.1 Struje vodova

kAkAIaI

kAkAIaI

kAkAIaI

kAkAIaI

RDB

RDA

RCB

RCA

ooo

ooo

ooo

ooo

&&

&&

&&

&&

3062,09062,01201

3085,09085,01201

3033,09033,01201

3019,09019,01201

∠=−∠⋅∠=⋅=

∠=−∠⋅∠=⋅=

∠=−∠⋅∠=⋅=

∠=−∠⋅∠=⋅=

−

−

−

−


kAkAIaI

kAkAIaIkAkAIaI

kAkAIaI

RBT

RCT

RAT

RAT

ooo

ooo

ooo

ooo

&&

&&

&&

&&

3029,09029,01201

3052,09052,012013033,09033,01201

3033,09033,01201

4

3

2

1

∠=−∠⋅∠=⋅=

∠=−∠⋅∠=⋅=

∠=−∠⋅∠=⋅=

∠=−∠⋅∠=⋅=

−

−

−

−

25

26

6 STRUJE GENERATORA ODNOSNO PRIMARA TRANSFORMATORA

6.1 JEDNOPOLNI KS

0315,0886,0

''''

''

==

⋅=+−=

TS

RdddR

II

IIIjII

&&

&&&&&

dT

ddS

RdddR

IjI

IjII

IIIjII

&&

&&&

&&&&&

−=

+=

=+−=

''

''

''

5,0886,0

5,0886,0

( )

6.2 TROPOLNI KS

6.2.1 Struje generatora G1 ( )

( ) ( )( ) kAjjI

kAjjjjjI

kAjjjjjI

GT

GS

GR

33,033,0

286,0165,0165,0286,033,05,033,0886,0

286,0165,0165,0286,033,05,033,0886,0

''1

''1

''1

−=−−=

−=+−=−⋅+−⋅=

+=+=−⋅+−⋅−=

−

−

−

&

&

&

( )


( )( )( ) kAjjI

jjjjjI

jjjjjI

GT

GS

GR

33,033,0

0286,033,05,033,0886,0

286,0286,033,05,033,0886,0

''2

''2

''2

−=−−=

−+−=−⋅+−⋅=

++=−⋅+−⋅−=

−

−

−

&

&

&

)

kA

kA

286,165,0165,0

165,0165,0

=

=

6.2.3 Struje generatora G3 ( ( )

( )kAjj

kAjjjjj

kAjjjjj

52,052,0

45,026,026,045,052,05,052,0886

45,026,026,045,052,05,052,0886,0

−=−

−=+−=−⋅+−⋅

+=+=−⋅+−⋅

( )

( )( )I

I

I

GT

GS

GR

,0''

3

''3

''3

−=

=

−=

−

−

−

&

&

&


( ) ( )( ) kAjjI

kAjjjjjI

kAjjjjjI

GT

GS

GR

29,029,0

25,0145,0145,025,029,05,029,0886,0

25,0145,0145,025,029,05,029,0886,0

''4

''4

''4

−=−−=

−=+−=−⋅+−⋅=

+=+=−⋅+−⋅−=

−

−

−

&

&

&

Red.br. KS Zd(Ω) Zi(Ω) Z0(Ω) Zi /Z0 - vrsta

KS Id (kA) 1pKS

(IR-kA) 2pKS

(IS-kA) 2pzKS (IS-kA)

3pKS (IR-kA)

0 D j 43,2 j 29,31 j 54,75 0,53 - 3pks -j 1,47 -j 1,497 -j 1,517 1,45+j0,53 -j 1,47

Za struje sabirnica mora vrijediti I K.Z.:

01

=∑=

n

iiI&

7 TROPOLNA SHEMA – RASPODJELA STRUJA U MREŽI ZA VRIJEME TROPOLNOG KRATKOG SPOJA

0,165+j0,286 0,165-j0,286

0,165+j0,286 0,165-j0,286

0,145+j0,25

0,26+j0,45 0,26-j0,45

-j0,33 -j0,85 -j0,62

0,145+j0,25

-j0,33 -j0,19 -j0,33

-j0,52

A B

C

D

-0,33

-0,52

0,145-j0,25 -0,29

-0,33

-1,03 +j1,05 -j1,47 0,23 +j1,45

-0,23+j0,24

-0,23+j0,24

0,03+j0,19

0,03+j0,19

-0,36+j0,37

0,05+j0,33

0,08+j0,51

-0,23+j0,24

-0,2+j0,21 0,04+j0,29

-0,59+j0,61

0,13+j0,84

-0,43+j0,44

0,10+j0,61

-0,13+j0,14 0,03+j0,19

Slika 7.1: Tropolna shema struja u mreži za vrijeme tropolnog KS

27

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