Proteção de Sistemas Elétricos - Notas de Aula

7/24/2019 Proteo de Sistemas Eltricos - Notas de Aula

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Universidade Federal de Campina Grande

Centro de Engenharia Eltrica e Informtica

Departamento de Engenharia Eltrica

Proteo de Sistemas Eltricos

Notas de Aula

Francisco das Chagas Fernandes Guerra

Campina Grande - PB


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Universidade Federal de Campina GrandeCentro de Engenharia Eltrica e InformticaDepartamento de Engenharia EltricaCoordenadoria de Graduao em Engenharia Eltrica

DISCIPLINA: Proteo de Sistemas EltricosPERODO: 10.2PROFESSOR: Francisco das Chagas Fernandes Guerra

Plano de Curso

1 DADOS PRELIMINARES:

Pr-requisito:Anlise de Sistemas Eltricos Carga Horria:60 N de crditos:04 Ementa:Clculo de parmetros de linha, Transitrios eletromag-

nticos: ondas viajantes em linhas de transmisso, sobretensesatmosfricas e de manobras, sobretenses sustentadas ecomputao digital de transitrios eletromagnticos. Proteo desistemas eltricos: filosofia, proteo de linhas de transmisso, detransformadores e de geradores. Fundamentos da transmisso emcorrente contnua.

2 OBJETIVOS

Ensinar ao aluno, de maneira sistemtica, os conceitosfundamentais relacionados aos distrbios nos sistemas eltricos decorrente alternada e as respectivas tcnicas de proteo, bem comonoes do funcionamento de sistemas de transmisso em correntecontnua.

3 PROGRAMA:

1 UNIDADE FILOSOFIA DA PROTEO1 - Conceitos gerais sobre proteo dos sistemas eltricos.

2 - Requisitos bsicos de um sistema de proteo.3 - Classificao de distrbios em sistemas eltricos.

2 UNIDADE INSTRUMENTAL DA PROTEO1 - Transformadores de corrente.2 - Transformadores de potencial eletromagnticos e capacitivos.3 - Rels Classificao geral.4 - Pra-raios.

3 UNIDADE TRANSITRIOS ELETROMAGNTICOS

1 - Parmetros de linhas de transmisso.2 - Ondas viajantes.


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2

3 - Sobretenses atmosfricas.4 - Sobretenses de manobra.5 - Sobretenses sustentadas..6 - Introduo coordenao de isolamento.

4 UNIDADE PROTEO DE SISTEMAS ELTRICOS POR RELS1 - Proteo de mquinas eltricas.

1.1 - Proteo contra defeitos no estator.1.2 - Proteo contra defeitos no rotor.1.3 - Protees adicionais Anti-motorizao, perda de excitao,

sobretenses.1.4 - Proteo de motores.

2 - Proteo de transformadores.2.1 - Proteo de sobrecorrente.2.2 - Proteo diferencial.

2.3 - Protees adicionais. Sobrepresso, sobretemperatura nosenrolamentos e no leo.3 - Proteo de linhas de transmisso.

3.1 - Proteo de sobrecorrente no direcional e direcional.3.2 - Proteo de distncia.3.3 - Proteo diferencial.3.4 - Teleproteo.

4 - Proteo de barras.5 - Introduo proteo digital..

5.1 - Rels e sistemas digitais de proteo.

5.2 - Fundamentos matemticos de algoritmos de proteo digital.

5 UNIDADE TRANSMISSO EM CORRENTE CONTNUA1 - Comparao com a transmisso em corrente alternada.2 - Pontes conversoras.3 - Tipos de linhas de CCAT.4 - Controles na transmisso em corrente contnua.

4 METODOLOGIA E TCNICAS DE ENSINO

Aulas expositivas da teoria e das tcnicas de anlise, sempreacompanhadas da resoluo de problemas, procurando-se, sempreque possvel, desenvolver a criatividade do aluno.

Listas de exerccios, propostas para os alunos resolver em casa.

5 RECURSOS DIDTICOS

Quadro branco, lpis marcador, retroprojetor, data-show.

6 AVALIAO

Trs provas escritas, alm de prova de reposio e de exame final.


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3

7 BIBLIOGRAFIA

GUERRA, F. C. F. Notas de Aula, DEE/CEEI/UFCG, 2011.KINDERMANN, G. - Proteo de Sistemas Eltricos de Potncia,

Vols. 1. 2 e 3, UFSC / EEL / LabPlan, 2008.

MASON, C. R. - The Art and Science of Protective Relaying, Wiley,1956.

ANDERSON, P. M. - Power System Protection, IEEE Press / McGrawHill, 1998.

8 RESULTADOS ESPERADOS

Prover o aluno dos conceitos fundamentais relacionados aosdistrbios nos sistemas eltricos de corrente alternada e asrespectivas tcnicas de proteo, bem como noes do

funcionamento de sistemas de transmisso em corrente contnua.

9 ATENDIMENTO INDIVIDUAL AO ALUNO

LOCAL: Sala do professor (Bloco CG)HORRIO: A definir com os alunos em funo do(s) horrio(s)definidos para a disciplina.

Campina Grande, 25 de novembro de 2010

Francisco das Chagas Fernandes Guerra- Professor -


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7/344

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8/344

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9/344

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1.

U F. 1, t = 0. A , (U ) (I ) . P , .

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P t> 0, x .L C . A . C UxCQ= , :

dt

dxUC

dt

dQ= (1)

S v , I:

vUCI= (2)

O :

IxL= (3)

dtdxIL

dtd = (4)


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C DEE / UFCG

2

C U = d/ dt, :vILU= (5)

S (2) (5), :

CLv /1= (6)A , v, , . D ,

L C , 2:

( )rDlnL /2

0

= (7)

( )rDlnC //2 0= (8)A r D .S (7) (8) (6):

812-6

00 1031085,81026,1/1/1 xxxxv ===

m/s (9)

E . N , v . N ,

, v . D (2) (6), :

CLUCI /= (10)

D (10), :

CLIUZ //0 == (11)

S (7) (8) (11):

=r

DlnZ

0

00

2

1 (12)

Z0 . Z0 . , . E, , . A T 1 ,

. P , , Z0 30 80.


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3

T 1. Z0 .

CONDUTORES POR FASE IMPEDNCIA DE SURTO,Z0()1 4002 320

3 2804 240

2.

U F. 2, :

R , / . L , H / .

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P , :

),(),(

),(),( txxixRt

txxixLtxutxxu ++

=+ (13)

ttxuxCtxuxGtxitxxi =+ ),(),(),(),( (14)

E i(x + x, t) T, :

...),(

),(),( +++ x

x

txitxitxxi (15)

...),(),(),(

2

+

+

+x

xt

txi

t

txi

t

txxi (16)

D (x)n n > 1 (15) (16) (13):


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C DEE / UFCG

4

t

txixRtxixR

xt

txixL

t

txixLtxutxxu

=+

),(),(

),(),(),(),(

2

22

(17)

T x0:

),(),(),(),(),(

lim 0 txiRt

txiL

x

txu

x

txutxxux

=

=

+= (18)

C (14), :

t

txuCtxuG

x

txi

x

txitxxix

=

=

+

=),(

),(),(),(),(

lim 0 (19)

A, u = u(x,t) i = i(x,t), :

t

iLiR

x

u

+=

(20)

t

uCuG

x

i

+=

(21)

D (20) (21) x:

tx

iL

x

iR

x

u

+=

2

2

2

(22)

txuC

xuG

xi

+

=

2

2

2

(23)

S (21) (22) (20) (23), :

2

2

2

2

)(t

uCL

t

uGLCRuGR

x

u

+

++=

(24)

2

2

2

2

)(t

iCL

t

iGLCRiGR

x

i

+

++=

(25)

D ,Zc, :

CjG

LjRZc +

+= (26)

SR= G= 0, Zc= Z0= (L/C)1/2,

, . A, .A (24) (25) ,

.


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C DEE / UFCG

5

E, , (24) (25) . P , , .

3.

FR= G= 0 (24) (25), :

2

2

2

2

t

uCL

x

u

=

(27)

2

2

2

2

t

iCL

x

i

=

(28)

P L. A, U (x,s)= L [u(x, t)]I (x,s) = L [i(x, t)],

:

),(),( 2

2

2

sxUCLsdx

sxUd= (29)

),(),( 2

2

2

sxICLsdx

sxId= (30)

D (6),LC= 1 / v2. S (29), :

),(),(2

2

2

2

sxUv

s

dx

sxUd = (31)

vsxvsx esFesFsxU /2

/1 )()(),( += (32)

P :

)()(])([ 11

atfatusFe sa =L (33)

a u1 .

T (32) , :)/()/()/()/(),( 1211 vxtuvxtfvxtuvxtftxu +++= (34)

P , R= 0 (20); , :

t

txiL

x

txu

=

),(),( (35)

U L:

),(),(

sxILsdx

sxdU= (36)

A (32) (36):


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C DEE / UFCG

6

[ ]vsxvsx esFesFLv

sxI /2/

1 )()(1

),( = (37)

[ ]vsxvsx esFesFZ

sxI /2/

1

0

)()(1

),( = (38)

Z0 , . A Z0= v L C (6) (11). N :

[ ])/()/()/()/(1

),( 12110

vxtuvxtfvxtuvxtfZ

txi ++= (39)

A, (34) (39), :

)/()/(),( 21 vxtgvxtgtxu ++= (40)

[ ] 021 /)/()/(),( Zvxtgvxtgtxi += (41)N (40), t = 0,g1( tx / v )

g1( x/v ). Ex= a, g1(a / v ). E , g1(x / v), g1( a / v) x = a + v . I g1 x. D , g2 .O

. N , x , F. 3.

F. 3. S u i.

O : F. 3. A, x ,

, .


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C DEE / UFCG

7

A , (40) (41) :

ri uuu += (42)

riri iiZuZui +== 00 // (43)O i , . O r , .

4.

Q ( ), . A

, . A , .

4.1 .

S F. 4, . A Z1 Z2. P, .

F. 4. M .


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C DEE / UFCG

8

A, (42) (43), :

ii= ui/Z1, ir= - ur/Z1, i= u /Z2 (44)

S (44) (43):

112 Z

u

Z

u

Z

uri = (45)

C (45) (42), :

irir uKuZZ

ZZu =+=

21

12 (46)

ii uKuZZ

Zu =+=

21

22 (47)

D :

21

12

ZZ

ZZKr +

= (48)

21

22

ZZ

ZK+= (49)

C (44) (46) (47):

irir iKiZZ

ZZi =+=

21

21

(50)

ii iKiZZ

Zi =+=

21

12 (51)

SZ1=Z2, Kr= 0,K= 1, ur= 0, u= ui , ir= 0, i= ii. D , . A , .

N (47) (51), Z1> Z2. A , . O Z1< Z2, F. 4.

4.2

N ,Z2= 0. D (46), (47), (50) (51), :

ur= - ui, u= 0, ir= ii, i= 2 ii (52)

A F. 5 .


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9

F. 5. L .

4.3

D (46), (47), (50) (51) Z2= ,:

ur= ui, u= 2 ui, ir= - ii, i= 0 (53)

U .I F. 6.

F. 6. L .

4.4

F. 7 . N , :


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C DEE / UFCG

10

dt

duCi= (54)

F. 7. L .

A L, :

)()( sUCssI = (55)

D :CssIsUsZ /1)(/)()( == (56)

A ui = U0 u1(t), u1(t) . A L ui:

sUsui /)( 0= (57)S (57) (46), Z1=Z0eZ2= 1 /s C, :

+

=

+

=

sZC

sZC

s

U

ZCs

ZCs

s

UsUr

0

00

0

00

/1

/1

/1

/1)( (58)

C , Z0 . A,CZ0 . P, :

0/1 ZC= (59)

L, (58) :

++

=

sssUsUr

1

)()( 0 (60)

:

( )tr eUu = 210 (61)


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C DEE / UFCG

11

D (42), :

( )tri eUtuUuuu +=+= 21)( 010 (62)P t0, :

( )t

eUu

= 12 0 (63)A F. 7 . , , , . A i .

4.

F. 8 .

N , :

dt

diLu= (64)

F. 8. L .

A L:

)()( sILssU = (65)A :

LssIsUsZ == )(/)()( (66)

C ui= U0u1(t), (46), :

+

=

+

=

LZs

LZs

s

U

ZLs

ZLs

s

UsUr

/

/)(

0

00

0

00 (67)


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C DEE / UFCG

12

A L /Z0 , :

0//1 ZL= (68)

A:

++= )(

1)( 0

sss

UsUr (69)

N :

( )tr eUu = 210 (70)( )tri eUtuUuuu =+= 21)( 010 (71)

P t0, :teUu = 02 (72)

A F. 8 . P , , , . A i .

4.

Q , . U Z1 F. 9,

n 1 Z2,Z3, ...,Zn.

F. 9. J .

C ,

. A, :


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C DEE / UFCG

13

ii= ui/Z1, i2= u/Z2, i3= u/Z3, in= u/Zn (73)

1

1Z

uuiiZuuuu irriri==+= (74)

nri iiiii +++=+ ...32 (75)

S (73) (74) (75), :

n

ii

Z

u

Z

u

Z

u

Z

uu

Z

u+++=

+ ...

3211

(76)

i

n

uZZZZ

Zu

/1.../1/1/1

/2

321

1

++++= (77)

A (77) . SZ1=Z2=Z3= ... =Zn ui= r (t), :

)(

2

trnu = (78) , u. A, .

.

A

. N , , . N , .E 1930, L. . B , , . F. 10 Z0. N

R u= U0u1( t).I : , . , , . O , , , t= d/ v, d

v (v= 300 m/s).


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C DEE / UFCG

14

F. 10. D .

N , . S

x( ), + 1/v. S x () 1 / v.D (48), :

RZ

RZ

ZR

ZRKr

/1

/1

0

0

0

0

+=+= (79)

, , . L, (48), Kre= - 1.

N . N t= 0, (x = 0) , , t= 2 d/ v. I , .P , , , , .D F. 10, x :


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C DEE / UFCG

15

...]/)4([

]/)4([]/)2([

]/)2([)/(),(

10

2

10

2

10

1010

+++

+

+=

vxdtuUK

vxdtuUKvxdtuUK

vxdtuUKvxtuUtxu

r

rr

r

(80)

S ,R= . D (79),Kr= 1. Px= dx= d/ 2 , :

...)/5(2)/3(2)/(2),(

111

0

++= vdtuvdtuvdtuU

tdu (81)

...)/5,4()/5,3(

)/5,2()/5,1()/5,0(),2/(

11

111

0

++

+=

vdtuvdtu

vdtuvdtuvdtuU

tdu

(82)

S F. 11 x= dx= d/ 2.

F. 11. E .

.

.1

A . D . E :


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C DEE / UFCG

16

, , .

A :

, , , , , .

A :

, ( , .),

.A :

, , .

A , .

.2 U , u, F. 12.

F. 12. O .

L Z0= u / i = (L/C )1/2

, dx :


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C DEE / UFCG

17

dxuCdxiLdxuCw 222

2

1

2

1=+= (83)

A v, , v= dx/dt. Cu x t, :

t

u

x

uv

t

u

dt

dxu

dt

du

+=

+

= (84)

L:

+

==t

u

x

uvdxuC

dt

dudxuC

dt

dw22 (85)

C (u) , dx:

dxudt

dw)(= (86)

I ; , :

+

=t

u

x

uvuCu 2)( (87)

N F. 12, y=D, y= v tx, u/x ; , :

tuuCu=

2)( (88)

A u= U0 t = 0.S L, C, R e G,

( u):

22222)( uL

LGCRuGu

L

CRuGiRu +

=+=+= (89)

C (88) (89):

tuuCu

LLGCR

=+ 22 (90)

2

u

C

G

L

R

t

u

+=

(91)

tt

C

G

L

R

eUeUu

+

== 02

1

0 (92)

+= C

G

L

R

2

1 (93)


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C DEE / UFCG

18

A :

ueUdt

du t == 0 (94)

A F. 13 .

F. 13. A .

.3

O , . I F. 14, , C1, C2, ..., Cn.

F. 14. A .

A :

kk CLv /1= (95)

k . C C1< C2< ...< Cn, v1> v2> ...> vn. I , F. 14.

F. 15 d1< d2< d3< d4.


27/344

C DEE / UFCG

19

F. 15. A d1< d2< d3< d4.

1.

B, L. . ,

. .; DP, 1963.

2.F, R. D. , LTC/EFEI,1977.

3. G, A. , /I,1971.

4. H, D. E. , ELETROBRS/UFSM,1978.

5. N, S. R. , E.G, 1985.

6. , M. , E. P, 1973.


28/344

C DEE / FCG

1

.

, .

D , L

.

.

D . H

,

. A 30 /, . H 15

50 , . O ,

.

, , ,

.

.

N, . C 80%

2 20% 3 5. H

40 . F,

.


29/344

C DEE / FCG

2

.

I 200 A,

1 10 .

. C

: ( ) 6 ,

90% . E

, .

E ,

,

,

. N ,

,

, .N , ,

, .

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: N

.

C : L () . A, B .


30/344

C DEE / FCG

3


31/344

C DEE / FCG

4

.

A ABN NB 6936:1992 (

)

.

S , .

R , .

M , .

Up , .

Tn I .

Ts 30% 90% .

Ts D , 1,67Ts.

Td 50 % , .

O 1,2 50 .

A

().

A ABN NB 6939:2000 (C

) () .


32/344

C DEE / FCG

5

.

()

NBI ( )

(1,2 50 )

. A . O

,

.

TENSO NOMINALDO SISTEMA (kV, RMS)

NBIPADRO

(kV, PICO)

NBIREDUZIDO

(kV, PICO)

15 110

34,5 20069 350

138 650 550

230 1050 825-900

345 1550 1175-1300

500 1300-1800

.

A

:

H ( F).

G F.

C ( ).

D ().

E .


33/344

C DEE / FCG

1

1.

O

,

/ ( ,

, , .).

2.

,

H, ,

4 . A 345 ,

.

. ()

.1

( H),

.

.2

, (

) .

L I .

C C (, C,

). E 60 H, C .


34/344

C DEE / FCG

2

C : A . N

, ,

. A

( ).

F : O . C .

H LC (0= 1/LC).

E

tUudt

diL

mC =+ cos ,

dt

duCi

C=

tLC

U

LC

u

dt

udmCC =+ cos

2

2

, 0)0( Cu

S

( )ttUtumC 022

0

2

0 coscos)(

=

( ) 1Hz60,kHz220

2

000

>>

( )ttUtumC 0coscos)( =

S i =0 uC= Um( ), 60 H ( 1).

( )tUtumC 0cos1)( =

: ( ) mmaxCC Uuu 2,0 ==/

S 0 , , , .


35/344

C DEE / FCG

3

.

E

S ( ).

A .

H ,

(

).

O (,

, ),

.

O .

D

, .

E

S . P, .

P , : A .P , : A ().

S > . S , ,

. S

, .

: C

. D : 2 4 .

D : 8 .


36/344

C DEE / FCG

4

.

C, , , . P :

. F :

. F (): (.

. ()

A

. H ()

, () , .

.

ABN NBR IEC 62271100:2006 (E P 100:

D ).

.

C: D .

P

( ).

Lm I .

C C .


37/344

C DEE / FCG

5

P : P .

P : P

(. ., ).


38/344

C DEE / FCG

6

H

, :

CLm

/1=0 , H.

D , ,

:

2

0

2

0 ILUCW mT2

1+

2

1=

O uC

C, , , :

2

0

2

0

2ILUCUCW

mCmCm

21+

21=

21=

2

0

2

0 IC

LUU m

Cm +=

C ,

, . C

, . A,

.

A ,

,

.


39/344

C DEE / FCG

7

E: P 1 MA, 13,8 ,

3,5%, :

)(A5,1

8,133

1000

100

5,3RMS

x

xIm

=

HxI

UL

m 14

5,1377

3/138000

==

)pico(A5,20 =I ( ).

C 5 F ( : 1 7 F).

S :

6,1322875,2105140 2922020 +=+= xx

IC

LUU mCm

N , , ,

,

, .

N id> 0.

N id< 0.

C I0: OBB: E

.

BBC: E

.


40/344

C DEE / FCG

8

.

C: D

.

A ,

, uD= 2Um.

LCdt

duCitUu

dt

diL

C

mC

1,,cos 0 ===+

tUudt

udmC

C =+ 2020 cos2

2

mC

CUu

dt

ud 20

20 +2

2

J: O (0 >> ). A , Um, t0 0.


41/344

C DEE / FCG

9

C : mC Uu =)0(

0/)0()0(' == CiuC

S: ( )tUtu mC 0= cos21)(

O ,

.

.

P , :

D ().

R :

. D

, , 6 10 ,

.


42/344

C DEE / FCG

10

.

A H. N

6, MH

( ).

E: O L C 6

,

. , 6 2,5

. D 3 5 (

), 10 . I

(, , C, P,

, ).A , ( )

,

.


43/344

C DEE / UFCG

1

1.

A :

C .

P .

E F.

R .

F.

2.

O ,

, 1,5 .

O ; ,

. O

, .

3.

P ,

: ,

.

3.1

R : A

(

). O .


44/344

C DEE / UFCG

2

D : H

, 3. D

, .

F ( ).

(A) O . A ,

( ,

).

(B) O Uan .

A, I= 0. A

, .(C) A ,

180. N , 0 2

, . A,

.

D , + 2Uan

2Uan, 20 100 60 H. O

,

.


45/344

C DEE / UFCG

3

3.2

A . N ,

. O

, .

C .

T . A,

.

A ,

.


46/344

C DEE / UFCG

4

3.3

P T , :

021 ZZZZ ++=

,

=

Z

UI 0a

UZ

ZZU

+= 021a

UZ

ZIZU

== 2022 aa

UZ

ZIZU

== 2000 aa

O F: a=1 ej120

021

021

aaac

aaab

UUaUaU

UUaUaU

2 ++=

++= 2

CZ1Z2. C :

UZZ

ZZaU

10

10

/2/1

+

+= 2b

UZZ

ZZaU10

10

/2/1

++=c

S: 221100 XjXjXj Z,Z,Z

M Ub Uc, U:

10

10

/2/1XX

XXU pub, +

+= 2a

10

10/2 /1 XX XXU puc, ++=

a


47/344

C DEE / UFCG

5

11

0 =X

X , Ub,pu = Uc,pu= 1 N .

N

21

0 >>XX , Ub,pu = Uc,pu 3 S .

3.4

C : R, ,

,

.

S : X0/X1 3 , R0/X1 1

C : .

Tambm podem estar includos sistemas onde h resistncias ou reatnciasentre neutro e terra.

E ,

80% ( < 80%). O pra-raios podem ser especificados para 85% . A orrentes de defeito fase-terra tm valores apreciveis, sensibilizando a

proteo de sobrecorrente. As correntes de defeito fase-terra prximos aos pontos de aterramento podem

atingir valores superiores s correntes de defeito trifsico.

Em um sistema efetivamente aterrado, para um defeito fase a - terra:

0,8

Tomando como base a tenso fase-neutro nominal do sistema:


48/344

C DEE / UFCG

6

pux 4,138,0

Assim, a sobretenso nas fases ss no ultrapassa 40%.

S : X0/X1> 3, R0/X1> 1.

C : .

A orrente fase-terra so menores que as de defeito trifsico. medida que R0/X1 X0/X1 ,

. O .

O 100%. O pra-raios devem ser especificados para mais de 100%

.

3.

P , h grficos que fornecem os coeficiente deaterramento para sistemas com neutro aterrado por impedncia.

R1=R2= 0

H R1=R2= 0,1X1,R1=R2= 0,2X1, .

3.

N ,

. O , ,

P.


49/344

C DEE / UFCG

7

O

.

E , . E (2,4 15 V),

.

4.

Q ( ),

. I :

A , (

, ). I

, .

A ,

. A,

.

I . C

.

A ,

. O

, . A,

, .

E , 10%, 1.

E , 40%, 3 4 . I

.


50/344

C DEE / UFCG

8

.

E LT. A

,

. I . N (, )

,

( ).

E :

cldx

d 2=2

2U

F .l I .

c C .S: )()()( xasenZjxacosx += R0R IUU

clZ /=0 I .

cl= C .

C :

)()( xacosUxU = R N , x =0:

acosUU RS

= ,acos

xacosUxU

)(

)(

= S

A (=

x). U 2 , :

f/c

=

==

222


51/344

C DEE / UFCG

9

V : c300000 km /s. Pf= 60 Hz:

kmrad/x

/00126,060103

25

=

=

E LT 230 kV 1100 kV, (0,00127 a 0,00130 rad/km).

[ ]( )acos

xacos

U

xU

0,00126)(0,00126

)( =

S

O 600

. A 37,4% ( ).

L ( / ).

O 60 H :

kmfc 500060/300000/ ===

U LT a= /4 = 1250 km . E: a= 1246 km:

[ ]( ) )!(7,119512460,00126

)12461246(0,00126 puxcoscos

U

U

=

=S

R

0.00 200.00 400.00 600.00Distncia ao Emissor, x ( km )

0.90

1.00

1.10

1.20

1.30

1.40

Te

nso,U

(pudeU

)s


52/344

C DEE / UFCG

10

A ,

. C

(UR) .

( ) S L UR US.

( ) S R UR>> US.


53/344

C DEE / UFCG

11

.

H

, 0 = 1/LC (L C ).

I ,

0 H, 60 H.

E ,

. F

,

. A .

A AT EAT

,

. Q

, .

O

.

.

.1

A

. H

,

.

F: CL UUU +=


54/344

C DEE / UFCG

12

P :

IC

UUUU CL +=+=

1

C : P1(

f UL). O (>).

C U C, P1

. C P1

, 1. A,

P3, 3.

C:

O ,

(, UC> UL).

A I I1I3.


55/344

C DEE / UFCG

13

A UL UC , .

O UL ,

, .

C ,

.

.2

F T P

A

, .


56/344

C DEE / UFCG

14

A

. A ,

,

,

, .

F T P

P

(TPI), .

A ,

TPI . P

TPI.

O .


57/344

C DEE / UFCG

15

O AT ,

. P

, (

). A, TPI,

B.

O

.

Cd C .

Cb C .

R R TPI.

L I TPI.

Rd R TPI.Lm I TPI.

.3

RLC ,

,

. O :

N , . P : 3 kVA. T /: 77 / 127 V. N /: 48 /88. : 44,4x10-4m2. C : 0,57 m. F : 0,95. V :R= 0,5 , C = 0,2mF.

T : 77 V.


58/344

C DEE / UFCG

16

O JA.

O .

S

, :

V9,108772, == xU MAXL

A36,177

3000100

5,3= xIRMS

IMAX2x1,36 = 2,72 A

MAX = UL, MAX/ = 108,9 / 377 = 0,29 V.s

A

:

UL, MAX =183,3 V

IMAX = 149,9 A

MAX = 0,43 V.s

-8000.00 -4000.00 0.00 4000.00 8000.00

Campo Magntico, ( A / m )

-4.00

-2.00

0.00

2.00

4.00

Induo,

(T)

H

B


59/344

C DEE / UFCG

17

0.00 0.04 0.08 0.12 0.16 0.20Tempo ( s )

-400.00

-200.00

0.00

200.00

400.00

TensonoTransformador,u

(V

)

L

0.00 0.04 0.08 0.12 0.16 0.20Tempo ( s )

-400.00

-200.00

0.00

200.00

400.00

TensonoC

apacitor,u

(V)

C


60/344

C DEE / UFCG

18

0.00 0.04 0.08 0.12 0.16 0.20Tempo ( s )

-200.00

-100.00

0.00

100.00

200.00

Corrente,i(A)

0.00 0.04 0.08 0.12 0.16 0.20Tempo ( s )

-0.80

-0.40

0.00

0.40

0.80

FluxodeE

nlace,

(V.s)


61/344

C DEE / UFCG

19

.4

M : C

. U , ,

, . , . S ,

. S

, .

M : U F

,

.

.

M . O

,

, T. O ,

, f 1/T , 2f, 3f,

.O .

M . O . O

(nT, n),

, n ( 1/n). O

. O .

0.12 0.16 0.20 0.24

Tempo ( s )

-2.00

-1.00

0.00

1.00

2.00

Tenso

(p.u.

)

-2.00 -1.00 0.00 1.00 2.00

Fluxo de Enlace ( p.u. )

-2.00

-1.00

0.00

1.00

2.00

Tenso

(p.u.

)


62/344

C DEE / UFCG

20

M . O .E . T .

N

,

, .

.

A

,

. A,

. E

, ,

.

0.12 0.16 0.20 0.24 0.28 0.32

Tempo ( s )

-4.00

-2.00

0.00

2.00

4.00

Tenso(p.u.

)

-2.00 -1.00 0.00 1.00 2.00


-4.00

-2.00

0.00

2.00

4.00

Tenso(p.u.

)

0.00 0.04 0.08 0.12 0.16 0.20

Tempo ( s )

-4.00

-2.00

0.00

2.00

4.00

Tenso(p.u.

)

-2.00 -1.00 0.00 1.00 2.00


-4.00

-2.00

0.00

2.00

4.00

Tenso(p.u.

)


63/344

C DEE / UFCG

1

Sobrecorrentes

A ,

,

, ().

O

. C: J

, .

A ,

,

. I

. A, .


64/344

C DEE / UFCG

2

C: C

( , , , ).

F : C CA 60 H

CC . A

X/R (/ ).

C

E ,

. T

, .

E ,

.

P

,

(,

, ). E ,

( FP 0,92). P .

0.00 0.05 0.10 0.15 0.20

Tempo ( s )

-40.00

-20.00

0.00

20.00

40.00

60.00

Corrente

(kA)


65/344

C DEE / UFCG

3

O

N

. E: ,

30 . P, ,

,

( ). C :

; ;

,

. O

, .

U n

, .

021

021

021

cccc

bbbb

aaaa

IIII

IIII

IIII

++=

++=

++=

021

021

021

aaac

aaab

aaaa

IIaIaI

IIaIaI

IIII

2 ++=

++=

++=2

( )

( )( ) 3/

3/

3/

2

1

0

cbaa

cbaa

cbaa

IaIaII

IaIaII

IIII

2 ++=

++=

++=2

C S

E T T .

Z1,Z2,Z0 I T , , .


66/344

C DEE / UFCG

4

D T: F a b c.

11

,Z

EIIII cbaFF ===== 33

Z

EI

D M: F a .

0021,0,0 IIIIUII ====== aaaacb

10

1

01021

01/2

3

2

333

ZZ

Z/E

ZZ

E

ZZZ

EIII

+=

+

++=== aF

FF 3

10

1/2

3I

ZZI

+=

SZ0=Z1 I1F=I3F

SZ0I3F,

.

SZ0>Z1 I1F


67/344

C DEE / UFCG

5

D B: F b F c.

21021 ,0,,0, aaaaacbacb III,UUIIIUU ======

( ) FjjajaaabF eee 32/1

2/

1

2/

12122

3

233 I

Z

EIIaaIaIaII

===+== 22

FFF III 332 866,02

3=

A,I2F


68/344

C DEE / UFCG

6

13

11

01

011

02

021

1Z

K

IKKZI

ZZ

ZZI

ZZ

ZZIU

+==

+

+= Faaa

K

IK

Z

U

Z

UI

+

==1

3

12

2F

a

0

13

0

01 Z

Z

K

IK

Z

UI

+= Fa

021 aaab IIaIaI ++= 2

+

+=

+==

01

123

0

1232

11 ZZ

ZKaa

K

I

Z

ZKKaa

K

III FFbFT

Z0=Z1 , K = 1/2 , :

( ) ( ) FFFT 32232 5,05,03/2 IaaaII ==

FFT II 32 =

Z00 , K 0 , :

( ) FjFbFT e 36/5232 31 IaIII ===

FFT II 32 3=

C: E ,

.

P , :

L : 50%

C : 9%

T 10%

G: 7%

D: 12%

E , TP TC: 12%

N , :

F : 85%

F : 8%

F : 5%

F : 2%


69/344

C DEE / UFCG

7

()

D F

Q ,

(H). N , :

A .

A , U0.

O .

C H (>> 60 H),

, , u Um.

mC Utudt

tdiL + )()( , +=

t

C dttiC

Utu0

0 )(1

)(

m

t

UdttiC

Udt

tdiL =++ 00 )(

1)( , 0)0( i

S

C

LZ

LC

tsen

Z

UUti m ==

= 000

0

0 ,1

,)(

0 F .Z0 I .

V : P 15

(). A

.

D: A . O

.


70/344

C DEE / UFCG

8

E 1: S

30 MVA, 69 V. C: 4074,5 A (); = 528,8 H.

E , :

A350693

300002==

x

xINP

A, 12 .

E 2: U 40 MVA

230 V, 60 H, 20 A.

C .

S: A

mH17,6203773230/

3/

xIUL

CC

N ===

A

F2230377

40

22 ===

xU

QC

N

A

Hz3,8482

5330

,rad/s5330102106,17

1

0630 ==== fxxx


71/344

C DEE / UFCG

9

( ) ( ) === 8,93102/106,17/ 630 xxCLZ

A , , ,

. A 50V.S , U0= 0. A, :

kA28,93

3/2302

0

=== x

Z

UI mMAX

E , :

A1422303

400002==

x

xINP

A, 14

.

E

Q ,

( ),

, ,

L2, ,L1.

C L1>> L2,

, .

A, ().

()

()


72/344

C DEE / UFCG

10

uC1(0) = Um uC2(0) = 0; :

0)()()(

21 =++ tutudt

tdiL CC

=+= t

Ct

mC dttiC

tudttiC

Utu0

2

20

1

1 )(1)(,)(1)(

C L, :

21

21

2

00

2

,1

,/

)(CC

CCC

CLtsen

CL

Uti m

+==

=

C L2 ,

, 20

250 .N

100 .

F : U

, ,

, .

E 3: S

30 MVA 69 V, 30 MVA . C = 9431,8 A (); = 2341,9 H.


73/344

C DEE / UFCG

11

E , 350 A (

). A,

27 .

D F

E ,

0,5% 2% . P,

, :

V 30

, , (, 6 10). D .

A , .

E . S :

A .

A ( ).

S

, . S

, CCAT.

A :

V .

M .

R .

I . C .

V .

I .

V .

O

.


74/344

C DEE / UFCG

12

O im=f (). S . A ,

:

tsenUiRdt

dmm =+

A im=f() . L, . P,

,

. I im=

f() = / Lm, Lm ,

- im.A, :

tsenUL

R

dt

dm

m

=+

S (0) 0 (); , :

+

+

+

= tcostsen

L

R

LR

ULe

LR

ULt

mm

mmtLR

m

mm m

22

2)/(

22

2

)()()(

CR


75/344

C DEE / UFCG

13

O

. N

, u = Um sen t, u(0) = 0.P, u(0) 0.

A, u = Umsen (t+ ). A, u(0) = Umsen , ( ), .

S , . FR= 0, :

)( += tsenUdt

dm

C (0) = R m= Um/ , :

[ ])++= tcoscosmR ( A t=

k( k= 1, 3,.5,...) = 0. N ,

. A, R+ 2 m.

P , R= 0

= /2. A Um t= 0. E , ,

.

D ,

. P

, , (). I .

N, i

( ), .


76/344

C DEE / UFCG

14

A R,

. N , im

. O m ,

, .

S

, ,

. S , .

D ,

. N ,

, .

E: O , ()

3 VA, 70/127 V, 70 V, (0)= 0 = 0. ( ).

P , .


77/344

C DEE / UFCG

15

0.00 0.10 0.20 0.30

Tempo ( s )

-40.00

0.00

40.00

80.00

120.00

Corrente

(A)

0.00 0.01 0.02 0.03

Tempo ( s )

-200.00

-100.00

0.00

100.00

200.00

Tens

o(V)


78/344

C DEE / UFCG

16

P

(T2) (T1).

S T2 1. A

1

(

,

). I

, ,

T2 . P,

T1

. A, . O

.


79/344

C DEE / UFCG

17

N ,

, ,

, . I .

O

,

.

C A

A

. P ,

.

O

. U

, .

C .

HARMNICA% EM RELAO FUNDAMENTAL

2 63,0

3 26,8

4 5,15 4,16 3,7

7 2,4


80/344

C DEE / UFCG

18

Q ,

,

.

P ,

,

.

A, .

F M

A

: U .

C ( ),

.

E ,

. I

,

, .

Q (, , ,

, , .),

, ,

. A

,

. A ,

.

A 4 10

.

S

,

.


81/344

C DEE / UFCG

19

F M

N , :

C .

C .

.

C .

R . P .

O

. O

.

O

M

E, I E E P.


82/344

C DEE / UFCG

20

C

, ,

. I , .

A, ,

,

.

E

, /

.


83/344

C DEE / UFCG

1

Distores de Ondas

1.

1.1

U f (t) T

=

++=1

0 )()(k

kk tksenFFtf

Tf ==22 k= 1, 2, 3,... F0 CC ( ).

A

1 .

1.2

O f(t) :

dttfT

F T

= 0 )(1

=F

Sf(- t) =f(t)( ), F .

Sf(-t) = -f(t) ( ) f(t) = -f(t+ T/2) (

), F= 0.

O i(t),

T, , Ie,

R

i(t), T, :

dttiRTIR T

e = 022 )( dtti

TI

T

e = 02 )(

1

D i(t) F, :


84/344

C DEE / UFCG

2

=

=

+=+=1

22

0

1

22

0 2k

ekk

ke IIIII

Ik k.

Iek=Ik/ 2 .

E

, :

1

2

22

0

e

kek

I

II

TD

=

+

=

E ,

.

1

2

2

e

kek

I

I

TDH

==

1.3

A , (W),

,p(t), :

dttituT

dttpT

P TT

== 00 )()(1

)(1

E u(t) i(t) F, :

( )

=

++=1

0)(k

kk tksenUUtu

( )

=

++=1

0)(k

kk tksenIIti

D i(t) i(t) F,

kkkkekekk

cosIUIUP =+=

=

,1

00


85/344

C DEE / UFCG

3

D , (VA),

, :

+

+==

=

= 1

22

0

1

22

0

kek

kekee IIUUIUS

D

,P, , S, :

S

P

APARENTEPOTNCIA

ATIVAPOTNCIAFP ==

C 1: u(t) i(t).

cosIU

cosIUFP

ee

ee ==

O 0 1. O

, . N

( ),

0,92. E

, . A

,

, .

C 2: u(t) i(t) .

+

+

+==

=

=

=

1

22

0

1

22

0

1

000

)()(1

kek

kek

kekekk

ee

T

IIUU

cosIUIU

IU

dttituTFP

O: S

, ,

. T

.


86/344

C DEE / UFCG

4

C 3: C .

N , ,

e

e

kek

e

keke

ee

I

Icos

II

cosI

IIU

cosIUFP 1

1

1

22

0

11

1

22

01

111

=

+

=

+

=

=

=

O : A

. P, ,

.

P, , :

=

= ==2

222

1

1

12

2

keke

e

kek

ITDHII

ITDH

SI12 :

( )2

12

1

222

1

1

11

TDHI

IIITDHI

e

ee

keke

+===+

=

S :

DISDESFPFPTDH

cosFP =+

=2

1

1

1

O FPDES= cos1 .

O FPDES=1/(1+TDH2) .

O: O

. A

FPDES, FPDIS. T ,

.

S u(t) = 2 Ucost i (t)= 2Icos(t+ ),

:

( ) ( ) tsenQtcosPtsenUItcoscosUItp 221221)( +=+=


87/344

C DEE / UFCG

5

A Q= UIsen ,

(VA). E

,

.

E, Q

. R, .

E , .

1.

A

. P,

, .

A , ,

, . A,

.

E ,

, f (t+T/2)= f (t).

F, .

P k a, b c :

uka= Uksen(kt+ k)

ukb= Uksen(kt 120 k+ k)

ukc= Uksen (kt 240 k + k)= Uksen (kt + 120 k + k)

I :

P k= 1, 7, 13, ..., k ub 120

ua k uc 120 ua.

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88/344

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89/344

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90/344

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91/344

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92/344

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98/344

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99/344

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100/344

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102/344

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104/344

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107/344

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108/344

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110/344

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114/344

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115/344

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116/344

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117/344

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118/344

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119/344

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120/344

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124/344

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125/344

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126/344


127/344

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129/344


130/344

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133/344

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136/344

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137/344

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138/344

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139/344

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140/344

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141/344


142/344

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143/344

C DEE / UFCG

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144/344

C DEE / UFCG

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145/344

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146/344

C DEE / UFCG

11

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147/344

C DEE / UFCG

12

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148/344

C DEE / UFCG

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149/344


150/344

C DEE / UFCG

15

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151/344

C DEE / UFCG

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152/344

C DEE / UFCG

17

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153/344

C DEE / UFCG

18

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154/344


155/344

C DEE / UFCG

20

T 1. C TC

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156/344

C DEE / UFCG

21

TC , , . N,

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157/344

C DEE / UFCG

22

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158/344

C DEE / UFCG

23

A TC , ; , :Z= 0,1 + 2x(0,55 + 0,14 +j0,07) = 1,48 +j0,14 = 1,49 e

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159/344

C DEE / UFCG

24

F. 27 TC 72,5 kV, 31,5 kA.

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160/344

C DEE / UFCG

25

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2

===xxxxAfN

UB eNmS

P A, H:

A.esp/m4,250,5

05,0218022 ==xx

l

INH eNmS .

V B - H Fe-Si GO:BmS= 1,5 THmS= 40 A.esp/m.() A :

=++= 3,25,0)0,225,0( 22Z .A :

2,10900/80053,2 == xxUe V.A :

Bm= (10,2 / 105)x1,2 = 0,12 T.V , , TC B - H.

A F. 28 TC 500 5 A

( ) 0,5 . C , , .

()2,50 +j0,10 , 500 A( ).()

2,50 +j0,10 , 1200 A( ).()11,5 +j0,10 , 500 A( ).()

11,5 +j0,10 , 1200 A( ).


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C DEE / UFCG

26

F. 28. C TC E 6.

S D F. 28, :

ee IU 100= , 0,0 Ie0,550)5,0(6,8 += ee IU , 0,5 Ie4,0

80)0,4(2 += ee IU , 4,0 Ie9,0

()

A =+=++= 9,131,031,05,25,0 jejjZ . P, , Ie I1

( F. 3.12 ); , TC.

)/( 12 eNe IKIZIZU = = )100/500(3 eI ee IU 315=

TC ( Ue - Ie) ; , :

ee II 315100 = 14,0103/15 ==eI A.I2=I1/KN-Ie= 500 / 100 - 0,14 = 4,86 A.

O :%9,286,4/14,0100/100 2% === xIIe .

() )100/1200(3 ee IU = ee IU 336= .

O TC Ue-Ie.

ee II 336100 = 35,0103/36 ==eI AI2= 1200 / 100 - 0,35 = 11,6 A.

%0,36,11/35,0100% == x .

() A :=+=++= 5,0121,0121,05,115,0 jejjZ .

)100/500(12 ee IU = ee IU 1260= .O TC Ue-

Ie.


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C DEE / UFCG

27

ee II 126050)5,0(6,8 =+ 69,06,20/3,14 ==eI A.I2= 500 / 100 - 0,69 = 4,3 A.

%163,4/69,0100/100 2% === xIIe .

())100/1200(12

eeIU =

eeIU 12144=

.O TC Ue-Ie.

ee II 1214480)4(2 =+ 1,514/72 ==eI A.I2= 1200 / 100 5,1 = 6,9 A.

%9,739,6/1,5100% == x .E TC. N (),

, (3 ) , TC (10%). J (), , TC , .U : TC 8 A, , (). I , .

A , .D . A , , . U .

1. ABNT (1992) NBR 6821. T C M E.

2. ABNT (1992) NBR 6856. T C E.3. G, J. D. ; S, M. S. (2001). ,

. 1, 3. ., B / C, P G, USA.4. IEC S. 600441 (1996). I T P I: C

T.5. IEEE S. C57.13 (1993). IEEE S R I

T.


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C DEE / UFCG

28

6. IEEE S. C37.110 (1996). IEEE G A CT U P R P.

7. L, T. (2001). D 100 H

, , 3: 4754.

8. M F, S. (1980). 2. ., E.U UFPE / E, R PE, B.


164/344

C DEE / UFCG

1

S

F. 1, u(t)= Umsen (t + ). P t= 0, u(0)= Umsen ; O , .

F. 1. R .

A :

1= jeZ11Z (1)

( )212

11 LRZ += (2)

LS RRR +=1 (3)

LS LLL +=1 (4)

= 1

1

11

R

Ltan (5)

A , T1, :

1

11

R

LT = (6)

A, :

( )+=+ tsenUiRdt

diL mF

F11

11 (7)

S F. 1 t= 0

i1F(0) =I0, (7) :

( ) ( )1/

11

011

1

Ttmm

F esenZ

U

ItsenZ

U

i

++=

(8)


165/344

C DEE / UFCG

2

A i1F : , ,

, , F. 2.

F. 2. C .

S 1= /2 i1 .E ,

1 90

0

. C

( )

u(t) .

P , I0= 0 1= / 2 (8). SI1F i1F, :

( ) ( )tcoseItcoseZ

Ui

Tt

F

TtmF ==

11 /1

/

1

1 2 (9)

S ,

. A F. 3 .

() ()

F. 3. ( ) T ; ( ) .

O

N1 N2, ; R2 L2 , ,

; Lm

.

O

, F. 4.


166/344

C DEE / UFCG

3

F. 4 C .

E F. 3(), (F. 4), :

dt

diLiR

dt

d 2222 +=

(10)

S H , l , B

, A , :

N1 i1F-N2i2 =H l (11)

AN

BH

2

=

= (12)

S (12) (11):

=

AN

li

N

Ni F 2

2

1

2

12 (13)

A :

l

ANLm

2

2= (14)

FKN=N2/N1, (13) (14):

= mNF

LK

i

i

112 (15)

D (15) (10), :

dt

d

L

L

dt

di

KL

L

R

K

iR

dt

d

m

F

NmN

F += 2122121

(16)

A L (9) (16):

+

+=

22

11

1/1

1)(

s

s

TsZ

UsI mF (17)

)()( 12222

sIK

LsR

sL

R

sL

LLF

Nmm

m +=+

+

(18)


167/344


168/344

C DEE / UFCG

5

( ) ( )

= 2

2

+

tsencos

eeTT

TT

K

RI TtTt

N

F 1212 //

12

2121 (32)

A (32) F. 5,

,

i1F, . A, TC

. O

i1F :

. N

, ,

T1 T2 .

F. 5. F TC .

N F. 6, TC N1=N2.

F. 6. F 1, 2 .


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