Notas - Protecciones - Fallas

8/10/2019 Notas - Protecciones - Fallas

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e (t) =Ri + Ldidt

R= Rg+ RL L= Lg+ LL

i (t) =KeRLt + ist(t)

ist(t) K

K = i (0) ist(0)

e (t) =

2Esin (t + )

i (t)

i (t) =

i0

2Iccsin ( )

eRLt +

2Iccsin (t + )

Icc = E

R2 + (L)2

tg () =L

R =

X

R

i (0) =

2I0sin ( 0)

I0= E

(R+ Rc)2 + (L+ Xc)

2

tg (0) =L+ Xc

R+ Rc

Rc+jXc= 1

Y =Z


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t > 5L

Rs

R L

I0 Icc

i (t) t = 0 [i (0)]

i (t) =

2Iccsin ( ) eRL t +

2Iccsin (t + )

i (t)

2

2Icc R = 0

=

90

L > R

i (t) = 0 t = , 3, 5, . . .

= 0

[imax(t)]

imax(t) =i (0) eRLt +

2Iccsin ()

1 + e

RLt

i (0)

imax(t) = 2Iccsin ()

1 + eRXt


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Icc

imax(t)

2 I(t)

imax(t) =

2Iccsin (eq)

1 + e

ReqXeq

t

Req Xeq eq

imax(t)

t = , t = 10ms

Ipeak=

2Iccsin ()

1 + eRX

= 0 t =

Imin=

2Icc

Ipeak

2Icc

1.02 + 0.98e

3RX

R/X


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Ipeak 1.8

2Icc

Ipeak 1.15

2Icc

1.02 + 0.98e

3RX

Ipeak 2

2Icc

R X

Ipeak

2Icc

1.02 + 0.98e3RX

R/X R/X= 20Rc/50Xc Rc Xc

I0

Icc


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In

t= 0 t= tc

imax=

2Iccsin ()

1 + eRLt


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tc

Ic=

2Iccsin ()1 + eRLtc

Ia

Ia =

2IcceRLtc

I=

I

2

a + I

2

cc

Sb =

3UnI Un

SC C =

3UnIcc Un

Icc

Imin=

2Icc

imax(t) Ipeak

Ic Ia

Icc

Imin


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abc2sc

sc2abc


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I2a =I2a0 =I

2a

I2b =I2a120 =aI

2a

I2c =I2a240 =a

2I2a

I0a =I0b =I

0c

Ia Ib Ic

Ia = I0a + I

1a + I

2a

Ib= I0b + I

1b + I

2b

Ic = I0c + I

1c + I

2c


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Ia = I0a + I

1a + I

2a

Ib= I0a + a

2I1a+ aI2a

Ic= I0a + aI

1a+ a

2I2a

Ia

Ib

Ic

=

1 1 1

1 a2 a

1 a a2

I0aI1aI2a

Iabc

= AI012

a

A


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Iabc I012a

A =

1 1 1

1 a2 a1 a a2

I012

a = A

1Iabc

A

A1 =

1

3A

A1

I0aI1aI2a

=1

3

1 1 1

1 a a2

1 a2 a

Ia

Ib

Ic

I0a = 13(Ia+ Ib+ Ic)

I1a = 13(Ia+ aIb+ a

2Ic)

I2a = 13(Ia+ a2Ib+ aIc)


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Va= V0a + V

1a + V

2a

Vb= V0a + a

2V1a + aV2a

Vc= V0a + aV1a + a2V2a

Vabc

= AV012

a

V012

a = A

1V

abc

S(3)= VabcT

Iabc

S(3)=AV

012a

TAI

012a

= V012

T

a ATA

I012

a

AT

=A A

TA

= 3

S(3) = 3V

012TI012

= 3V0aI

0

a + 3V1aI

1

a + 3V2aI

2

a

ATA

= 3

I0 I1 I2


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Ia= 1.625

Ib= 1180

Ic= 0.9132

V0a = 0.690

V1a = 130

V2a = 0.8 30

Va= 300 120Vb= 20090

Vc = 100 30

I0a = 3 30I1a = 590

I2a = 430

(1+a)(1+a2)

= 1120

(1a)2(1+a)2

= 3 180 (a a2) (a2 a) = 30

V1an= 13V1bc90

V2an= 13

V2bc 90


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Va

Vb

Vc

= Zs+ Zn Zm+ Zn Zm+ Zn

Zm+ Zn Zs+ Zn Zm+ Zn

Zm+ Zn Zm+ Zn Zs+ Zn

Ia

Ib

Ic

Vabc = ZabcIabc

Z

abc

=

Zs+ Zn Zm+ Zn Zm+ Zn

Zm+ Zn Zs+ Zn Zm+ ZnZm+ Zn Zm+ Zn Zs+ Zn

Vabc

Iabc

AV012a = Z

abcAI

012a

A1

V012a = A

1Z

abcAI

012a

= Z012I012a

Z012 = A1ZabcA

Z012

=

1

3

1 1 1

1 a a2

1 a2 a

Zs+ Zn Zm+ Zn Zm+ Zn

Zm+ Zn Zs+ Zn Zm+ ZnZm+ Zn Zm+ Zn Zs+ Zn

1 1 1

1 a2

a1 a a2


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Z012

=

Zs+ 3Zn+ 2Zm 0 0

0 Zs Zm 00 0 Zs Zm

Zm= 0

Z012 =

Zs+ 3Zn 0 0

0 Zs 0

0 0 Zs

Z1 =Z2

Z0

Z1 Z2 Z0

Dn


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I0a + I0b + I

0c + In= 0

I0a =I0b =I

0c

In= 3I0a

a0 = 2 107

I0aln1

r+ I0b ln

1

D+ I0c ln

1

D+ Inln

1

Dn

I0b I0c In I

0a

a0 = 2 107I0a

ln 1r

+ ln 1D

+ ln 1D 3 ln 1

Dn

= 2 107I0aln D

3n

rD2Wb/m

L0= a0/I0a


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L0 = 0.2 ln D3nrD2

= 0.2 ln DD3n

rD3

= 0.2 ln Dr + 3

0.2 ln DnD

mH/Km

X0 =X1 + 3Xn

Xn= 2f

0.2 ln

DnD

m/Km

Xd Xd Xd

X2 Xd


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X0 =Xl

Z0 =Z1 =Z2 =Zl

Y Y

YY


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YY

Y

Y

Zn In = 3I0

3Zn I0

Y

Zs= j12 Zm= j4


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Y

ZsIa+ ZmIb ZsIb ZmIa= Va Vb= |VL|

6ZsIb+ ZmIc ZsIc ZmIb= Vb Vc= |VL| 2

Ia+ Ib+ Ic= 0

Zs Zm (Zs Zm) 0

0 Zs Zm (Zs Zm)1 1 1

Ia

Ib

Ic

=

|VL|6|VL| 2

0

ZmeshIabc = Vmesh

Iabc = Z1meshVmesh

Ia

Ib

Ic

= 12.5 90

12.5150

12.530


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V012 = Z012I012

V012 =

0

Va

0

Z012 =

Zs+ 2Zm 0 0

0 Zs Zm 00 0 Zs Zm

I012 =

Z

0121

V012

Ia

Ib

Ic

=

12.5 9012.5150

12.5

30

Vabc =

10010

300 5040140

Zs=

12+j12 Zm= j12

Z012


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In= Ia+ Ib+ Ic

Va

VbVc

= Ea

EbEc

Zs+ Zn Zn Zn

Zn Zs+ Zn ZnZn Zn Zs+ Zn

Ia

IbIc

Vabc = Eabc ZabcIabc

Vabc

Iabc

AV012a = AE

012a

Z

abcAI

012a

A1

V012a = E

012a A1ZabcAI012a

= E012a Z012I012a

Z012 =

1

3

1 1 1

1 a a2

1 a2 a

Zs+ Zn Zn Zn

Zn Zs+ Zn Zn

Zn Zn Zs+ Zn

1 1 1

1 a2 a

1 a a2

Z012 =

Zs+ 3Zn 0 0

0 Zs 0

0 0 Zs

=

Z0 0 0

0 Z1 0

0 0 Z2


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3Zn


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Zf = 0.16

Zf

V3(0)

I3(F) = V3(0)

Z33+ Zf


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abc2sc

sc2abc


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