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energetski transformatori

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elektrotehnika

Text of energetski transformatori

, 2004.

1: : Sn=31,5 MVA; mt =121/10 kV/kV; Pcu=200 kW ( ); Pfe = 86 kW ( ); uk=10,5%; io=2,7%. , . : ) ; b) . : Ip Ztp Iop Up Ytp Usp Up Isp Ip Iop Ytp Usp Ztp Isp

*) Ip Zp Iop Up Ytp Usp Zsp Isp

**) Ztp- , Ytp- , Zp- , Zsp- . ***)

: *) , **) , ***) . ( ) . : , :

1

Y t = G Fe jB =Yt jX RFe

1 1 j ; RFe X2 100 U n . I o (%) S n

RFe =

2 Un , PFe

X =

Zt , ( ) .Zt Rt U Rt = Pcu n S n , 2

jXt

Z t = Rt + jX t ;

2 u (%) U n ; Zt = k 100 S n

X t = Z t2 Rt2 .

(Un=Unp) . (Un=Uns) . ( ). , , : Z p Z sp = Z tp 2 , Z s Z ps =Z ts . 2

e . .

Un (kV) a) 121 10 b)

RFe () 170244 1162,8

GFe (S) 5,87410-6 8,610-4

X () 17214,6 117,58

B (S) 5,8110-5 8,510-3

Rt () 2,95 0,0201

Xt () 48,8 0,333

2

2: Sn =1 MVA; mt =10/0,4 (kV/kV); i0 =1,4 %; uk =5,5 % :) ; ) ; ) 50% .

: . (a) . , ( ). . . , . . , .

Ip

j Xt

Isp

Xt - ( + ), Rt - , X - ,

j X Up Iop

RfeUsp

Rfe - ( ). , , .

) (Isp=0) (Q0) ( ).2 I (%) I Un 1,4 = 3U n I 0 = 3U n I n 0 = S n I o (r. j ) = S n 0 = 1 = 0,014 Mvar. 100 In 100 X

Q0 =

3

b) , (Q0), (Q) , Xt . (Qpn) :2 Q pn = 3 X t I n = 3 X t 2 2 I nU n

U

2 n

= Xt

2 Sn

U

2 n

= Xt

Sn U2 n

Sn =

Xt x (%) S n = X t (r. j.) S n = t Sn . 100 Z baz

(xt(%)) (uk(%)) :u k (%) = Uk 100 = Un 3Z k I n Z S Z 100 = k 2 n 100 = k 100 = z k (%) = Rt (%) 2 + X t (%) 2 X t (%) Un Z baz Un

(Qpn) .Q pn = u k (%) 5,5 = 0,055 Mvar . S n = 1 100 100

(Qn) :

Qn = Q0 + Q pn = 0,014 + 0,055 = 0,069 Mvar .

c) , (Qp) :

Qp = 3X t I 2 = 3X t (

u (%) I 2 I n ) 2 = 3 X t 2 I n = 2 Q pn = 2 k Sn , 100 InI ). In

I ( = S =0,5Sn (Q50%) :Q 50% = Q o + Q p 50% = S n

i 0 (%) u (%) 5,5 1,4 + 2Sn k = 1 + 0,5 2 = 0,02775 Mvar. 100 100 100 100

50% - 40,22% .

4

400 (kV / kV ) , 220 xt = 10% , S n = 400 MVA , x . =320 MW - I II . I U1 = 400 kV. P=320 MW U =? U1= 400 kV 2 U2 II I II - I, Q2=0. Q2=? .

3:

: mt =

: x , . . .

P1=P Q1=Q U1

jXt

P2=P Q2=0 U2p=U2p 0 0

U2p II .

Q

- (, ) , . , . U1 U2p , , I Xt ( II ). , U1 U2p I II. :

S 1 = P1 + jQ1 = 3U 1 I ; P1 = P,

*

Q1 = Q = 3 X t I 2 .P3 U2p2 1

S 2 = P2 = P = 3 U 2 p I I = I =

.

S1 S 1 = P + Q = 3 U 1 I2 2

P2 P2 U = P2 + X t 2 2 U U2p 2p

2

5

:4 2 U 2 p U 12U 2 p + X t2 P 2 = 0.

. : Ubaz=U1=400 kV Sbaz=Snt=400 MVA. :4 2 u 2 p 1 u 2 p + 0,12 0,8 2 = 0

4 2 u 2 p u 2 p + 0,0064 = 0.

: u 2 p = 0,99356 r. j. , :U 2 p = u 2 p U baz = 0,99356 400 = 397,42 kV .

II :

U2 =

U2p mt

=

397,42 220 = 218,58 kV . 400

U2 220 kV> U2> 218,58 kV, () II, I. U2 U2=220 kV I II.

6

4: , , B, ( ). Yd5, (Uab, Ubc, Uca) A c . UA UB B a : Yd5; Sn = 4 MVA; mt = 35/10,5 (kV/kV); Io(%) = 1%; UC C b Xt(%) = 8%. . : , 300 , . 5, 5300=1500. , Yd5 . . UA

UbcUb

Uc 150o Ua

Uca

mt Uca 3 m UB = t Uab 3 m UC = t Ubc 3UA =

Uab UC

UB

, , ( D , y ). . ( ) , Yd5. Yd5.

7

AUA UB

c a b

B C

UC

( ) B. , () ( ) . :

UB =A

35 3

kV 0 0

B

C

uB = N p

c

/2

a

b

/2

d d ( / 2) ; u A = uC = N P . dt dt d d ( / 2) uab = N s ; uca = ubc = N s . dt dt u u B N p mt ; u bc = u ca = ab . = = 2 u ab N s 33 UB = mt 3 10,5 35 = 10,5 kV 35 3

U ab =

U ca = U bc =

U ab 10,5 = = 5,25kV . 2 2

, , .

8

5: , Sn=4 MVA; mt=35/10(kV/kV); Io(%)=1%; Xt(%)=10%; Yd9 , . () : ) ; b) () (); c) (). .UA UC UB PA PB PC B A C c b a

: ) , :I 0 A = I 0 B = I 0C = I 0 = I 0 (%) I (%) S n 1 4000 In = 0 = = 0,67 A . 100 100 3U n 100 3 35

b) , . . U b B C , I A0 A , I b A0 , Ua, :c

A = N p = N p

N pI e

b A0

= Np

N pI3 2

b A0

=

2N I 3

2 p

b A0

b

/2

a

/2

. : N p - ,

, - ( ). 2 Np , L =

9

b (I0) ( I A0 ). :

UA =

Un3

= A =

2 N p I0

= L I 0 .

:2 b 2 N p I A0 2 b UA = = A = = L I A 0 . 3 3 3

Un

b , I A0 I0, . :

b I a0 =

3 I 0 = 1,5 0,67 = 1A . 2

c) , . . UC U A B C c c I 0C I 0A .I n 0 = I 0 A + I 0Cc c

c

A

b

A+C

a

C

( ).A UA C UC 1 N p I 0C 2 N p c 1 c ( I 0 A I 0C ) = AA AC = 3 = 3 2 2 3 2 2 2 2 Np c 1 c 2 1 c c ( I 0 A I 0C ) = j L ( I 0 A I 0C ) = j N p A = j 3 2 3 2 c c N p I 0C 1 N p I 0 A 2 N p c 1 c ( I 0C I 0 A ) = CC CA = 3 = 3 2 2 3 2 2 2 2 Np c 1 c 2 1 c c ( I 0C I 0 A ) = j L ( I 0C I 0 A ) = j N p C = j 3 2 3 2 N p I 0Ac c

10

UA UC :

I 0A = j

c

2U A + U C

L

=j

U A U B

L

=j

U AB

L ;

I 0C = jc

U U B 2U C + U A U =j C = j BC ; L L L

:

I 0 n = I oA + I oC = 3

c

c

U A +U C U = j3 B . j L L

B C :

I 0 A = I 0C =c c

Un = 3 I 0 = 3 0,67 = 1,16 A L

:

I 0n = 3

U nf

L

= 3 I 0 = 3 0,67 = 2,01 A

.

UA

I0n I 0C I 0Ac c

UC

U

11

6: Dy, Sn=100 MVA, mt=110/10 (kV/kV) io= 0,5%. A UA UB B Dy11, U C C , .

:A 1 Dy11. . , , ( ). 2.

a UCAUa

UA

UAB330o Ub

UC

b cUc UB

C UBC 1

B

A UA UC UB B C

b c

2

3 , , 3.I0 A

I0 B I0 C

3

12

4 5: A

B

110kV I0BC

C

A IA I0AB B UBC C IB IC=IA

IB IA

B

IA=IC

4 a b 5 5 ( B): c n

B = BB + BA + BC , - IB , : N pIB3 2

BB =

, :

N p - , - ( ). , . , (), , :

BA = BC =

1 N pIA . 2 3 2

:

13

2 2 2 Np Np 1 N pIA B = N p B = 3 +2 = ( I A + I B ) 3 = I 0 BC 3 . 2 3 2 2 2 2

2 N pIB

Un, :

U n = B =

2 Np 3 2

I 0 BC I 0 BC =

Un

2 Np 3 2

( 3) : I0 = I o (%) I (%) S n 0,5 100 10 3 In = o = = 2,624 A , 100 100 3U n 100 3110

( ) :

I0

2 Np Un Un 3U n = = L = = . 2 I 0 Np 3 L

:I 0 BC = Un = Un 2 3U n 3 I 0 = 3 2 3 I 0 = 0,866 I 0 = 0,866 2,624 = 2,27 A .

N3 2

2 p

14

7: : Dy, 630 kVA, mt=10/0,4 (kV/kV) . : sprega ; Un=0,4 kV; Pn=160 kW. 0,4 kV, , , . . A UA UC UB B C b cR R R

: , ( ):2 2 3U n 3 0,4 2 Un R= = = 3 . Pn = 3 0,16 R Pn

10 kV 0,4 kV :Ia = Ib = Ic = Pn 160 10 3 = = 230 , 94 A ; 3U n 3 400

I A = I B = IC =

I c 0,4 = 230,94 = 9,238 A . mt 10

a , b c ( ), , , Ubc, :N IA=I A UA UC UB IB=I B IC=2I C 0 I I I I N Ia=0 b Ib=I c Ic=I Ubc R R R

I 2R R, :

15

Re =

2R R 63 = = 2 . 2R + R 6 + 3

b c , b c:

I"=

U bc 400 = = 200 A, I b = I c = I " = 200 A, I a = 0 A. Re 2

, , .: N ' I ' = N " I " . , . , :

I'=

1 N" 1 0,4 I"= I"= 200 = 4,619 A . N' 3 mt 3 10

. , , 10 kV , 0,4 kV :

I A = I ' = 4,619 A,

I B = I ' = 4,619 A I C = 2 I ' = 2 4,619 = 9,238 A .

, , .

16

8: . 35 X c IA , ako je U= kV , X=1 . C 3 b : B X Snt=4 MVA; mt=35/10 (kV/kV); xt=10% . A X IA=? U : . .IC=0 C IB=0 B A U IA=? Ic=0 Ic=0 Ia Ia

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