Transient Angle

7/26/2019 Transient Angle

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1539pk

TRANSIENT (ANGLE)TRANSIENT (ANGLE)

STABILITYSTABILITY

Copyright P. Kundur

This material should not be used without the author's consent


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Transient Angle StabilityTransient Angle Stability

Description of Transient Stability

An elementary ie! of TS

"et#o$s of TS analysis

Time%$omain sim&lation

Str&ct&re of po!er system mo$el

Representation fa&lts

'erformance of protectie relaying

oncept of electrical centre*

ase st&$ies

"et#o$s of TS en#ancement

"a+or blac,o&ts ca&se$ by Transient Instability

Noember -. /-01 Nort#east 2S. 3ntario

blac,o&t

"arc# //. /--- Bra4il blac,o&t

3&tline


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5#at is Transient (Angle) Stability65#at is Transient (Angle) Stability6

T#e ability of t#e po!er system to maintain

sync#rono&s operation !#en s&b+ecte$ to a seere

transient $ist&rbance

fa&lts on transmission circ&its. transformers.

b&ses

loss of generation

loss of loa$s

Response inoles large e7c&rsions of generator

rotor angles8 infl&ence$ by nonlinear po!er%angle

relations#ip

Stability $epen$s on bot# t#e initial operating stateof t#e system an$ t#e seerity of t#e $ist&rbance

'ost%$ist&rbance stea$y%state operating con$itions

&s&ally $iffer from pre%$ist&rbance con$itions


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In large po!er systems. transient instability may notal!ays occ&r as 9first s!ing9 instability

co&l$ be as a res&lt of s&perposition of seeral

s!ing mo$es ca&sing large e7c&rsions of rotor

angle beyon$ t#e first s!ing

St&$y perio$ of interest in transient stability st&$ies

is &s&ally limite$ to : to 1 secon$s follo!ing t#e$ist&rbance;

may e7ten$ &p to abo&t /< secon$s for ery large

systems !it# $ominant inter%area s!ing mo$es

'o!er system $esigne$ an$ operate$ to be stable for

specifie$ set of contingencies referre$ to as 9normal

$esign contingencies9

selecte$ on t#e basis t#at t#ey #ae a reasonable

probability of occ&rrence

In t#e f&t&re. probabilistic or ris,%base$ approac#

may be &se$


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/= An Elementary >ie! of Transient/= An Elementary >ie! of Transient

StabilityStability

Demonstrate t#e p#enomenon &sing a ery simple

system an$ simple mo$els

System s#o!n in ?ig= /:=/

All resistances are neglecte$

Generator is represente$ by t#e classical mo$el

?ig= /:=/ Single mac#ine % infinite b&s system


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T#e generator@s electrical po!er o&tp&t is

5it# t#e stator resistance neglecte$. Perepresents t#e

air%gap po!er as !ell as t#e terminal po!er

?ig= /:= System representation !it# generator

represente$ by classical mo$el

=

= sinsinma7

P#

$$P

T

%

e


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'o!er%Angle Relations#ip'o!er%Angle Relations#ip

Bot# transmission circ&its in%serice8 &re /

operate at point 9a9 (Pe= Pm)

3ne circ&it o&t%of%serice8 &re

lo!er Pmax

operate at point 9b9

#ig#er reactance #ig#er to transmit same

po!er

?ig= /:=: 'o!er%angle relations#ip


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T#e oscillation of is s&perimpose$ on t#e

sync#rono&s spee$ D conerters. ?ATs $eices. etc=

At present. t#e most practical aailable met#o$ of

transient stability analysis is time $omain sim&lation8 sol&tion of nonlinear $ifferential e&ations an$

algebraic e&ations

step%by%step n&merical integration tec#ni&es

complimente$ by efficient tec#ni&es for soling

non%linear #ig#ly sparse algebraic e&ations


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= N&merical Integration "et#o$s= N&merical Integration "et#o$s

Differential e&ations to be sole$ are nonlinear

or$inary $ifferential e&ations !it# ,no!n initial

al&es8

x is t#e state ector of n $epen$ent ariables.

tis t#e in$epen$ent ariable (time)

Objectie! sole x as a f&nction of t. !it# t#e initial

al&es of x an$ te&al to x0an$ t0. respectiely=

"ethods! E&ler@s "et#o$

"o$ifie$ E&ler@s "et#o$

R&nge%H&tta (R%H) "et#o$s

Trape4oi$al R&le

( )txfdt

dx+=


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N&merical stabilityN&merical stability

Depen$s on propagation of error

N&merically stable if early errors ca&se no significant

errors later

N&merically &nstable ot#er!ise

Important to consi$er n&merical stability in t#e

application of n&merical integration met#o$s


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Stiffness of Differential E&ationsStiffness of Differential E&ations

Ratio of largest to smallest time constants or. more

precisely. eigenal&es

Increases !it# mo$elling $etail

Affects n&merical stability

Sol&tion &sing e7plicit integration met#o$s may

9blo! &p9 !it# stiff systems &nless ery small time

step is &se$=


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N&merical Stability of E7plicit IntegrationN&merical Stability of E7plicit Integration

"et#o$s"et#o$s

E7plicit "et#o$s

E&ler@s. 're$ictor%orrector. an$ R%H met#o$s

Depen$ent ariables 7 at any al&e of t is comp&te$ from

a ,no!le$ge of t#e al&es of 7 from t#e preio&s timesteps

7n/for (n/)t#step is calc&late$ e7plicitly by

eal&ating f(7.t) !it# ,no!n 7

Easy to implement for t#e sol&tion of a comple7 set of

system state e&ations

Disa$antage

Not n&merically A%stable

step si4e limite$ by small time constants or

eigenal&es


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Implicit Integration "et#o$sImplicit Integration "et#o$s

onsi$er t#e $ifferential e&ation

T#e sol&tion forx at t=t1=t0# t may be e7presse$ int#e integral form as

Implicit met#o$s &se interpolation f&nctions for t#e

e7pression &n$er t#e integral Interpolation implies t#at t#e f&nctions m&st pass

t#ro&g# t#e yet &n,no!n points at time t/

$ra%e&oidal '(leis simplest met#o$

( ) += dxfxx t

t+)

**)

( ) **+ ttatxxwithtxfdt

dx===


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Trape4oi$al R&leTrape4oi$al R&le

Simplest implicit met#o$; &ses linear interpolation

Integral appro7imate$ by trape4oi$s

f(x,t)

f(x0,t0)f(x1,t1)

t0 t1t

t

?ig= /:=J


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Trape4oi$al r&le is gien by

A general form&la giing t#e al&e of 7 at t=tn#1is

KnI/appears on bot# si$es of E&ation

implies t#at t#e ariable 7 is comp&te$ as a f&nction

of its al&e at t#e preio&s time step as !ell as t#e

c&rrent al&e (!#ic# is &n,no!n)

an implicit e&ation m&st be sole$

N&merically A%stable 8 stiffness affects acc&racy not

stability

Trape4oi$al r&le is a secon$ or$er met#o$

ig#er or$er met#o$s $iffic&lt to program an$ less

rob&st

]

110001 t,xft,xf2

txx

]1n1nnnn1n t,xft,xf2

txx


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:= Sim&lation of 'o!er System Dynamic:= Sim&lation of 'o!er System Dynamic

ResponseResponse

Str&ct&re of t#e 'o!er System "o$el8

omponents8

Sync#rono&s generators. an$ t#e associate$ e7citationsystems an$ prime moers

Interconnecting transmission net!or, incl&$ing static

loa$s

In$&ction an$ sync#rono&s motor loa$s

3t#er $eices s&c# as >D conerters an$ S>s

"onitore$ Information8

Basic stability information

B&s oltages

Line flo!s

'erformance of protectie relaying. partic&larly

transmission line protection


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?ig= /:= Str&ct&re of t#e complete po!er system mo$el

for transient stability analysis


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"o$els &se$ m&st be appropriate for transient

stability analysis

transmission net!or, an$ mac#ine stator

transients are neglecte$

$ynamics of mac#ine rotors an$ rotor circ&its.

e7citation systems. prime moers an$ ot#er

$eices s&c# as >D conerters are represente$

E&ations m&st be organi4e$ in a form s&itable for

n&merical integration

Large set of or$inary $ifferential e&ations an$ largesparse algebraic e&ations

$ifferential%algebraic initial al&e problem


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3erall System E&ations3erall System E&ations

E&ations for eac# $ynamic $eice8

!#ere

7$ C state ector of in$ii$&al $eice

I$ C 'an$) components of c&rrent in+ection from

t#e $eice into t#e net!or,

>$ C 'an$ )components of b&s oltage

Net!or, e&ation8

!#ere

YN C net!or, mo$e a$mittance matri7I C no$e c&rrent ector

> C no$e oltage ector

( )

( )dddd

dddd

VxgI

Vxfx

+

+

=

=

VYIN

=


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3erall system e&ations8

comprises a set of first or$er $ifferentials

an$ a set of algebraic e&ations

!#ere

7 C state ector of t#e system

> C b&s oltage ector

I C c&rrent in+ection ector

Time t$oes not appear e7plicitly in t#e aboe

e&ations

"any approac#es for soling t#ese e&ations

c#aracteri4e$ by8

a) T#e manner of interface bet!een t#e $ifferential an$

algebraic e&ations8 partitione$ or sim&ltaneo&s

b) Integration met#o$ &se$

c) "et#o$ &se$ for soling t#e algebraic e&ations8

- Ga&ss%Sei$al met#o$ base$ on a$mittance matri7

- $irect sol&tion &sing sparsity oriente$ triang&larfactori4ation

- iteratie sol&tion &sing Ne!ton%Rap#son met#o$

( )Vxfx +=

( ) VYVxI N=+


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Analy4e transient stability incl&$ing t#e effects of

rotor circ&it $ynamics an$ e7citation control of t#e

follo!ing po!er plant !it# fo&r 111 ">A &nits8

Dist&rbance8 T#ree p#ase fa&lt on circ&it M at ?.

cleare$ by tripping t#e circ&it

E7ample /:=E7ample /:=

?ig= E/:=0


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*enerator %arameters!

T#e fo&r generators of t#e plant are represente$ by an e&ialent

generator !#ose parameters in per &nit on < ">A base are as

follo!s8

T#e aboe parameters are &nsat&rate$ al&es= T#e effect of

sat&ration is to be represente$ ass&ming t#e d% an$ +axes#ae

similar sat&ration c#aracteristics base$ on 3

Excitation system %arameters!

T#e generators are e&ippe$ !it# t#yristor e7citers !it# A>R an$

'SS as s#o!n in ?ig= /:=/. !it# parameters as follo!s8

T#e e7citer is ass&me$ to be alternator s&pplie$; t#erefore E?ma7 an$

E?minare in$epen$ent of Et

Prefa(lt system condition in %( on 2220 "-A, 2. /- base!

PC


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3b+ectie

E7amine t#e stability of t#e system !it# t#e follo!ing

alternatie forms of e7citation control8

(i) "an&al control. i=e=. constant Efd

(ii) A>R !it# no 'SS

(iii) A>R !it# 'SS

onsi$er t#e follo!ing alternatie fa&lt clearing

times8

a)


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omp&te$ &sing t#e Gill@s ersion of fo&rt# or$er R%H

integration met#o$ !it# a time step of


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?ig= E/:=J(a) Rotor angle response !it# fa&lt

cleare$ in


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?ig= E/:=J(c) Terminal oltage response !it# fa&lt

cleare$ in


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Responses of rotor angle

!it# t#e t#ree alternatie

forms of e7citation control are comp&te$

5it# constant Ef$. t#e generator is first s!ing

&nstable

5it# a fast acting e7citer an$ A>R. t#e generator

maintains first s!ing stability. b&t loses sync#ronism

$&ring t#e secon$ s!ing

T#e a$$ition of 'SS contrib&tes to t#e $amping of

secon$ an$ s&bse&ent s!ings

2se of a fast e7citer #aing a #ig# ceiling

oltage an$ e&ippe$ !it# a 'SS contrib&tes

significantly to t#e en#ancement of t#e oerall

system stabilityO

ase (b)8 Transient response !it# t#e fa&lt clearing

time tc e&al to


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?ig= E/:= Rotor angle response !it# fa&lt cleare$

in


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1= Representation of ?a&lts in Stability1= Representation of ?a&lts in Stability

St&$iesSt&$ies

'ositie%se&ence net!or, is represente$ in $etail

Negatie% an$ 4ero%se&ence oltages an$ c&rrents

t#ro&g#o&t t#e system are &s&ally not of interest in

stability st&$ies

&nnecessary to sim&late t#e complete negatie% an$4ero%se&ence net!or,s in system stability

sim&lations

effects represente$ by e&ialent impe$ances (P

an$ P


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0= 'erformance of 'rotectie Relaying0= 'erformance of 'rotectie Relaying

"onitor. $etect abnormal con$itions. select brea,ers

to be opene$. an$ energi4e trip circ&its

T#ree re&irements8 selectiity. spee$. an$ reliability

$isting&is# bet!een stable s!ings an$ o&t%of%step

operate !#en nee$e$ an$ only !#en nee$e$

operate s&fficiently fast

coor$inate !it# ot#er relays

?&nction of certain relays essential to ens&re

transient stability

Special relaying may be &se$ to separate systems

"ostly intereste$ in transmission line protection


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Transmission Line 'rotectionTransmission Line 'rotection

?actors

Type of circ&it8 single line; parallel line. m&lti%

terminal. magnit&$e of fa&lt c&rrent infee$s. etc=

?&nction of line. its effect on serice contin&ity.spee$ !it# !#ic# fa&lt #as to be cleare$

oor$ination an$ matc#ing re&irements

T#ree basic types8

a) oerc&rrent relaying

b) $istance relaying. an$

c) pilot relaying


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(a) 3erc&rrent Relaying(a) 3erc&rrent Relaying

Simplest an$ c#eapest form of line protection

T!o basic forms8 instantaneo&s oerc&rrent relay an$

time oerc&rrent relay

Diffic&lt to apply !#ere coor$ination. selectiity. an$

spee$ are important c#anges to t#eir settings are &s&ally re&ire$ as

system config&ration c#anges

cannot $iscriminate bet!een loa$ an$ fa&lt c&rrents;

t#erefore. !#en &se$ for p#ase%fa&lt protection. t#ey

are applicable only !#en t#e minim&m fa&lt c&rrent

e7cee$s t#e f&ll loa$ c&rrent

2se$ principally on s&btransmission systems. an$

ra$ial $istrib&tion systems

fa&lts #ere &s&ally $o not affect system stability so

#ig#%spee$ protection is not re&ire$


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(b) Distance Relaying(b) Distance Relaying

Respon$s to a ratio of meas&re$ oltage to meas&re$

c&rrent

Impe$ance is a meas&re of $istance along t#e line

Relatiely better $iscrimination an$ selectiity. bylimiting relay operation to a certain range of t#e

impe$ance

Types

impe$ance relay

reactance relay

m#o relay

mo$ifie$ m#o an$ impe$ance relays. an$ #ybri$s

"ost !i$ely &se$ form for protection of transmission

lines

Triggering c#aracteristics s#o!n coneniently onR%K plane


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?ig= /:= Distance relay c#aracteristics $isplaye$ on a

coor$inate system !it# resistance (') as t#e abscissa.

an$ reactance () as t#e or$inate


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T#ree 4one approac#8

Pone / primary protection for protecte$ line


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(c) 'ilot Relaying Sc#emes(c) 'ilot Relaying Sc#emes

2se comm&nication c#annels (pilots) bet!een t#e

terminals of t#e line t#at t#ey protect

Determine !#et#er t#e fa&lt is internal or e7ternal to

t#e protecte$ line. an$ t#is information is transmitte$

?or an internal fa&lt. circ&it brea,ers at all terminals

of t#e protecte$ line are trippe$; for an e7ternal fa&lt

t#e tripping is bloc,e$

>omm(nication medi(mmay be pilot !ire (metallic

!ires). po!er%line carrier. micro!ae. or fibre optic


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Eac# terminal station of t#e line #as8

?nderreachin@ &one 1p#ase an$ gro&n$ $irectional$istance relays coering abo&t J1%


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?ig= /:=:/ ,elay characteristic at station

?ig= /:=:/ ault locations )+ 2and 3


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?a&lt learing Times?a&lt learing Times

ompose$ of relay time an$ brea,er operating time

E> relays8 /% cycles

irc&it brea,ers8 % cycles

Brea,er fail&re bac,&p protection proi$e$ for eac#

brea,er on all critical circ&its

if a brea,er fails to operate at a local station. trip

signals sent to a$+acent 4one brea,ers an$ remote

en$ brea,ers


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Notes8

(i) ?or p&rposes of ill&stration. cycle brea,ers #ae been ass&me$ at

A an$ : cycle brea,ers at B

(ii) omm&nication time $epen$s on c#annel me$i&m &se$= 5it# po!er

line carrier. t#e time may be longer

Local (B&s A) brea,ers /an$

Remote (B&s B) brea,ers :an$

'rimary relay time

(?a&lt $etection)

1 ms 1 ms

A&7iliary relay(s) time : ms - ms

omm&nication time % /J ms (micro!ae)

Brea,er trip mo$&le : ms : ms

Brea,er clearing time :: ms ( cycles) 1< ms (: cycles)

Total Time 0 ms /


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Notes8

Brea,er fail&re timer setting #as been ass&me$ to be -< ms for t#e cycle brea,er =

T#is co&l$ ary from one application to anot#er= ?or a : cycle oil brea,er a typical

al&e is /1< ms

?ig= /:=: Typical fa&lt clearing times for a st&c, brea,er

fa&lt

LocalBrea,er 1

Remotebrea,ers0 an$ J

Local bac,&pbrea,er :

Remote bac,&pbrea,ers/ an$

'rimary relay time (atb&s B) 1 ms 1 ms 1 ms 1 ms

A&7iliary relay(s) time : ms - ms 0 ms / ms

omm&nicationc#annel time

% /J ms % /J ms

Brea,er fail&re timersetting

% % -< ms -< ms

Brea,er tripping

mo$&le time

: ms : ms : ms : ms

Brea,er time :: ms 1< ms :: ms :: ms

Total time 0 ms /


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Relaying &antities D&ring S!ingsRelaying &antities D&ring S!ings

T#e performance of protectie relaying $&ring electro%

mec#anical oscillations an$ o&t%o&t%step con$itions

ill&strate$ by consi$ering t#e follo!ing system8

(a) Sc#ematic $iagram

(b) E&ialent circ&it

?ig= /:=:0 Two machine system

T#e c&rrent )is gien by

T#e oltage at b&s is

T

BA

Z

EEI

*/ =

IZEE AAC///

=


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T#e apparent impe$ance seen by an impe$ance relay at

loo,ing to!ar$s t#e line is gien by

If EACEBC/=< p&

0EE

E

)

)

E

)

E

BA

A$A

AA>>

=

2cot2

j2

sin2

cos1j

2

1

sinj2

sinjcos1

101101

101

101

$

A

$

$A

$A

$A

$A>


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D&ring a s!ing. t#e angle c#anges= ?ig= /:=:J s#o!s

t#e loc&s of >as a f&nction of

on an '$iagram.!#en EACEB

Note8 3rigin is ass&me$ to be at . !#ere t#e relay is locate$=

?ig= /:=:J Loc&s of >as a f&nction of . !it# EA=EB


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5#en EAan$ EBare e&al. t#e loc&s of >is seen to be a

straig#t line !#ic# is t#e perpen$ic&lar bisector of t#e

total system impe$ance bet!een A an$ B. i=e=. of t#e

impe$ance PT

t#e angle forme$ by lines from A an$ B to any

point on t#e loc&s is e&al to t#e correspon$ing

angle

5#en

Cis infinite

5#en

C/


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?ig= /:=: Loci of P!it# $ifferent al&es of EAEB


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?or generators connecte$ to t#e main system t#ro&g# a

Dea/ transmission system(#ig# e7ternal impe$ance). t#e

electrical centre may appear on t#e transmission line

5#en a generator is connecte$ to t#e main system

t#ro&g# a stron@ transmission system. t#e electrical

centre !ill be in t#e step &p transformer or possibly

!it#in t#e generator itself

Electrical centres in effect are not fi7e$ points8 effectie

mac#ine reactance an$ t#e magnit&$es of internal

oltages ary $&ring $ynamic con$itions=

>oltage at t#e electrical centre $rops to 4ero as

increases to /


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'reention of Transmission Line Tripping'reention of Transmission Line Tripping

D&ring Transient on$itionsD&ring Transient on$itions

Re&irements for preention of tripping $&ring s!ing

con$itions fall into t!o categories8

'reention of tripping $&ring stable s!ings. !#ile

allo!ing tripping for &nstable transients=

'reention of tripping $&ring &nstable transients. an$

forcing separation at anot#er point=

'reention of tripping $&ring stable transients

Um#oV $istance relay c#aracteristic may be too large

an$ #ae regions into !#ic# stable s!ings may enter

In or$er to minimi4e t#e possibility of tripping $&ring

stable s!ings8

&se of o#m &nits (blin$ers)

composite relays

s#ape$ relay (lens. pean&t. etc=)


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Tripping can occ&r

only for impe$ance

bet!een 3/an$ 3.

an$ !it#in "

?ig= /:=: Re$&ction of m#o relay ang&lar range

?ig= /:= S#ape$ Relay


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3&t%of%Step Bloc,ing an$ Tripping Relays3&t%of%Step Bloc,ing an$ Tripping Relays

In some cases. it may be $esirable to preent tripping of lines

at t#e nat&ral separation point. an$ c#oose t#e separation

point so t#at8

a) loa$ an$ generation are better balance$ on bot# si$es.

or

b) a critical loa$ is protecte$. or

c) t#e separation is at a corporate bo&n$ary=

In certain instances. it may be $esirable to trip faster in or$er

to preent oltage $eclining too far=

Princi%le of o(tofste% relayin@!

"oement of t#e apparent impe$ance &n$er o&t%of%step

con$itions is slo! compare$ to its moement !#en a line

fa&lt occ&rs

transient s!ing con$ition can be $etecte$ &sing t!o

relays #aing ertical or circ&lar c#aracteristics on an

'plane

if time re&ire$ to cross t#e t!o c#aracteristics

(33S. 33S/) e7cee$s a specifie$ al&e. t#e o&t%of%

step f&nction is initiate$


58/102

1539pkTS - !

?ig= /:=1 0ut-o1-step relaying schemes


59/102

1539pkTS - !(

In an o(tofste% tri%%in@ scheme. local brea,ers

!o&l$ be trippe$= s&c# a sc#eme co&l$ be &se$ to

spee$ &p tripping to oltage $ecline

ens&re tripping of a selecte$ line. instea$ of ot#er

more critical circ&its

In an o(tofste% bloc/in@ scheme.

relays are preente$ from initiating tripping of t#e

line monitore$. an$ transfer trip signals are sent to

open circ&its of a remote location

ob+ectie is to ca&se system separation at a more

preferable location


60/102

1539pkTS - "*

J= ase St&$y % Transient StabilityJ= ase St&$y % Transient Stability

T#e ob+ect

$emonstrate transient instability an$ actions of

protectie relaying

s#o! met#o$s of maintaining stability

T#e system

J- b&ses. 0J generators. an$ 01/ branc#es

t#e foc&s is on a plant !it# n&clear &nits. !it# a

total capacity of J


61/102

1539pkTS - ")

?ig= /:=1 Diagram of system in t#e icinity of a J


62/102

1539pkTS - "2

T#e ontingency8

Do&ble line%to%gro&n$ (LLG) fa&lt occ&rs on t#e 1$o&ble circ&it line at W&nction K

Time (ms) Eent

< No $ist&rbance

/


63/102

1539pkTS - "3

Sim&lation8

A 1 secon$ sim&lation !as performe$

G: is seen to lose sync#ronism an$ becomes

monotonically &nstable

similar be#aio&r for t#e ot#er J &nits of t#e n&clear

plant

As G/ to G become &nstable. t#e rest of t#e system

becomes generation $eficient

absol&te angles of all mac#ines in t#e system $rift

slig#tly

?ig= /:=1: Rotor angle time response


64/102

1539pkTS - "

Analysis8

o! $oes t#e system come apart as a res&lt of instability6

3&t%of%step protection $oes not operate on G:

?ig= /:=1 2nit G: o&t%of%step protection


65/102

1539pkTS - "!

?ig= /:=11 Line protection (circ&it :) at b&s /

?ig= /:=10 Line protection (circ&it :) at b&s J


66/102

1539pkTS - ""

Line 'rotection8

"#o $istance relays #ae 4one / coerage of abo&t J1Q of

line lengt#. an$ 4one oer%reac# of abo&t /1Q of line

lengt#

Apparent impe$ance enters t#e 4one relays at b&s / an$

enters 4one / an$ 4one relays at b&s J

4one / relay at b&s J !o&l$ trip circ&it : at b&s J an$

sen$ a transfer trip signal to brea,ers at b&s / !#ic#

!o&l$ t#en trip circ&it : at b&s /

tr&e for t#e companion 1 circ&it (M) !#ic# !o&l$

be trippe$ in an i$entical manner

?ollo!ing t#e loss of t#e 1 circ&its (at appro7imately circ&its !o&l$ become

e7tremely oer%loa$e$ an$ !o&l$ be lost t#ro&g# protection

actions. t#ereby completely isolating t#e &nstable plant from

t#e system Impe$ance plot s#o!s t#e impe$ance s!ing crosses t#e

circ&it at a point abo&t Q of t#e line lengt# from b&s /

represents t#e electrical centre follo!ing t#e

$ist&rbance. an$ is t#eoretically !#ere separation

occ&rs


67/102

1539pkTS - "&

B&s >oltages8

?ig= /:=1J >oltages at b&ses /. J an$ t#e electrical

centre


68/102

1539pkTS - "

"et#o$s of "aintaining Stability8

Re$&ction of t#e pre%contingency o&tp&t of t#e plant costly to bottle energy in t#e plant

Tripping of generating &nits (generation re+ection)

follo!ing t#e $ist&rbance

?ig= /:=1 2nit G: rotor angle response !it# an$

!it#o&t generation re+ection


69/102

1539pkTS - "(

= Transient Stability En#ancement= Transient Stability En#ancement

3b+ecties8

Re$&ce t#e $ist&rbing infl&ence by minimi4ing t#e

fa&lt seerity an$ $&ration

Increase t#e restoring sync#roni4ing forces

Re$&ce accelerating tor&e t#ro&g# control of prime%

moer mec#anical po!er

Re$&ce accelerating tor&e by applying artificial loa$


70/102

1539pkTS - &*

ig#%Spee$ ?a&lt learingig#%Spee$ ?a&lt learing

Amo&nt of ,inetic energy gaine$ by t#e generators

$&ring a fa&lt is $irectly proportional to t#e fa&lt $&ration

&ic,er t#e fa&lt is cleare$. t#e less $ist&rbance it

ca&ses

T!o%cycle brea,ers. toget#er !it# #ig# spee$ relays an$comm&nication. are no! !i$ely &se$ in locations !#ere

rapi$ fa&lt clearing is importance

In special circ&mstances. een faster clearing may be

$esirable

$eelopment an$ application of a / cycle circ&it

brea,er by Bonneille 'o!er A$ministration (B'A)

combine$ !it# a rapi$ response oerc&rrent type

sensor. !#ic# anticipates fa&lt magnit&$e. nearly

one%cycle total fa&lt $&ration is attaine$

&ltra #ig# spee$ relaying system for E> lines base$

on traeling !ae $etection

not in !i$esprea$ &se


71/102

1539pkTS - &)

Re$&ction of Transmission SystemRe$&ction of Transmission System

ReactanceReactance

Series in$&ctie reactances of transmission net!or,s

are primary $eterminants of stability limits

re$&ction of reactances of ario&s elements of t#e

transmission net!or, improes transient stability

by increasing post%fa&lt sync#roni4ing po!ertransfers

"ost $irect !ay of ac#ieing t#is is by re$&cing t#e

reactances of transmission circ&its

oltage rating. line an$ con$&ctor config&rations.

an$ n&mber of parallel circ&its $etermine t#e

reactances of transmission lines

A$$itional met#o$s of re$&cing t#e net!or,

reactances8

&se of transformers !it# lo!er lea,age reactances

series capacitor compensation of transmission

lines


72/102

1539pkTS - &2

Typically. t#e per &nit transformer lea,age reactance

ranges bet!een


73/102

1539pkTS - &3

3ne problem !it# series capacitor compensation is t#e

possibility of s&bsync#rono&s resonance !it# t#e

nearby t&rbo alternators

m&st be analy4e$ caref&lly an$ appropriate

preentie meas&res ta,en

Series capacitors #ae been &se$ to compensate ery

long oer#ea$ lines

recently. t#ere #as been an increasing recognition oft#e a$antages of compensating s#orter. b&t #eaily

loa$e$. lines &sing series capacitors

?or transient stability applications. t#e &se of s!itc#e$

series capacitors offers some a$antages

can be s!itc#e$ in &pon $etection of a fa&lt or po!er

s!ing. an$ t#en remoe$ abo&t #alf secon$ later

can be locate$ in a s&bstation !#ere it can sere

seeral lines

protectie relaying is ma$e more comple7 !#en

series compensation is &se$. an$ more so if t#e

series capacitors are s!itc#e$


74/102

1539pkTS - &

Reg&late$ S#&nt ompensationReg&late$ S#&nt ompensation

an improe system stability by increasing t#e flo!

of sync#roni4ing po!er among interconnecte$

generators (oltage profile control)

Static >AR compensators can be &se$ for t#is

p&rpose

?ig= //=0< 'erformance of a 0S

reg&lating mi$point oltage


75/102

1539pkTS - &!

Reg&late$ S#&nt ompensationReg&late$ S#&nt ompensation(cont@$)(cont@$)

?ig= //=0 'o!er%angle relations#ips !it# reg&late$

compensation at $iscrete interals $ii$ing line

into nin$epen$ent sections

n Xn ($egrees)

/ =J< /=


76/102

1539pkTS - &"

Dynamic Bra,ingDynamic Bra,ing

2ses t#e concept of applying an artificial electrical

loa$ $&ring a transient $ist&rbance to increase t#e

electrical po!er o&tp&t of generators an$ t#ereby

re$&ce rotor acceleration

3ne form of $ynamic bra,ing inoles s!itc#ing ins#&nt resistors for abo&t


77/102

1539pkTS - &&

To $ate. bra,ing resistors #ae been applie$ only to

#y$ra&lic generating stations remote from loa$ centres #y$ra&lic &nits. in comparison to t#ermal &nits. are

&ite r&gge$; t#ey can. t#erefore. !it#stan$ t#e

s&$$en s#oc, of s!itc#ing in resistors !it#o&t any

a$erse effect on t#e &nits

If bra,ing resistors are applie$ to t#ermal &nits. t#e

effect on s#aft fatig&e life m&st be caref&lly e7amine$

If t#e s!itc#ing $&ty is fo&n$ &nacceptable. t#e

resistors may #ae to be s!itc#e$ in t#ree or fo&r steps

sprea$ oer one f&ll cycle of t#e lo!est torsional mo$e

Bra,ing resistors &se$ to $ate are all s#&nt $eices

series resistors may be &se$ to proi$e t#e bra,ingeffect

t#e energy $issipate$ is proportional to t#e generator

c&rrent rat#er t#an oltage

!ay of inserting t#e resistors in series is to install a

star%connecte$ t#ree%p#ase resistor arrangement !it#

a bypass s!itc# in t#e ne&tral of t#e generator% step%&p transformer to re$&ce resistor ins&lation an$

s!itc# re&irements

resistor is inserte$ $&ring a transient $ist&rbance by

opening t#e bypass s!itc#


78/102

1539pkTS - &

Anot#er form of bra,ing resistor application. !#ic#

en#ances system stability for only &nbalance$gro&n$ fa&lts. consists of a resistor connecte$

permanently bet!een gro&n$ an$ t#e ne&tral of t#e Y

connecte$ #ig# oltage !in$ing of t#e generator

step%&p transformer

&n$er balance$ con$itions no c&rrent flo!s

t#ro&g# t#e ne&tral resistor

!#en line%to%gro&n$ or $o&ble line%to%gro&n$

fa&lts occ&r. c&rrent flo!s t#ro&g# t#e ne&tral

connection an$ t#e resistie losses act as a

$ynamic bra,e

5it# s!itc#e$ form of bra,ing resistors. t#es!itc#ing times s#o&l$ be base$ on $etaile$

sim&lations

if t#e resistors remain connecte$ too long. t#ere is

a possibility of instability on t#e 9bac,s!ing9


79/102

1539pkTS - &(

Reactor S!itc#ingReactor S!itc#ing

S#&nt reactors near generators proi$e a simple an$

conenient means of improing transient stability

Reactor normally remains connecte$ to t#e net!or,

Res&lting reactie loa$ increases t#e generator

internal oltage an$ re$&ces internal rotor angle

?ollo!ing a fa&lt. t#e reactor is s!itc#e$ o&t !#ic#

f&rt#er improes stability


80/102

1539pkTS - *

Steam T&rbine ?ast >alingSteam T&rbine ?ast >aling

Applicable to t#ermal &nits to assist in maintaining

po!er system transient stability

Inoles rapi$ closing an$ opening of steam ales in

a prescribe$ manner to re$&ce t#e generator

accelerating po!er. follo!ing t#e recognition of aseere transmission system fa&lt

2se recogni4e$ in t#e early /-:


81/102

1539pkTS - )

?ast >aling 'roce$&res?ast >aling 'roce$&res

T#e main inlet control ales (>) an$ t#e re#eat intercept

ales (I>) proi$e a conenient means of controlling t#e

t&rbine mec#anical po!er

>ariety of possibilities e7ist for t#e implementation of fast

aling sc#emes

ommon sc#eme8 only t#e intercept ales are rapi$lyclose$ an$ t#en f&lly reopene$ after a s#ort time $elay

since t#e intercept ales control nearly J


82/102

1539pkTS - 2

Generator TrippingGenerator Tripping

Selectie tripping of generating &nits for seere transmission

system contingencies #as been &se$ as a met#o$ of

improing system stability for many years

Re+ection of generation at an appropriate location in t#e

system re$&ces po!er to be transferre$ oer t#e critical

transmission interfaces

2nits can be trippe$ rapi$ly so t#is is a ery effectie means

of improing transient stability

istorically. t#e application confine$ to #y$ro plants; no!

&se$ on fossil an$ n&clear plants

"any &tilities $esign t#ermal &nits so t#at. after tripping. t#ey

contin&e to r&n. s&pplying &nit a&7iliaries; permits t#e &nitsto re resync#roni4e$ to t#e system an$ restore$ to f&ll loa$

in abo&t /1 to :< min&tes

"a+or t&rbine%generator concerns8

t#e oerspee$ res&lting from tripping t#e generator

t#ermal stresses $&e to t#e rapi$ loa$ c#anges

#ig# leels of s#aft tor&es $&e to s&ccessie

$ist&rbances


83/102

1539pkTS - 3

ontrolle$ System Separation an$ Loa$ontrolle$ System Separation an$ Loa$

S#e$$ingS#e$$ing

"ay be &se$ to preent a ma+or $ist&rbance in one part of an

interconnecte$ system from propagating into t#e rest of t#e

system an$ ca&sing a seere system brea,&p

Seere $ist&rbance &s&ally c#aracteri4e$ by s&$$en

c#anges in tie line po!er

if $etecte$ in time an$ t#e information is &se$ toinitiate correctie actions. seere system &psets can

be aerte$

Impen$ing instability $etecte$ by monitoring one or more of

t#e follo!ing8 s&$$en c#ange in po!er flo! t#ro&g# specific

transmission circ&its. c#ange of b&s oltage angle. rate of

po!er c#ange. an$ circ&it brea,er a&7iliary contacts

2pon $etection of t#e impe$ing instability. controlle$ system

separation is initiate$ by opening t#e appropriate tie lines

before casca$ing o&tages can occ&r

In some instances it may be necessary to s#e$ selecte$

loa$s to balance generation an$ loa$ in t#e separate$

systems

E7amples8

P

relay on t#e tie lines bet!een 3ntarioy$ro an$ "anitoba y$ro


84/102

1539pkTS -

ig#%Spee$ E7citation Systemsig#%Spee$ E7citation Systems

Significant improements in transient stability can be

ac#iee$ t#ro&g# rapi$ temporary increase of generator

e7citation

Increase of generator fiel$ oltage $&ring a transient

$ist&rbance #as t#e effect of increasing t#e internal oltage

of t#e mac#ine. !#ic# in t&rn increases sync#roni4ing po!er

ig# initial response e7citation systems !it# #ig# ceiling

oltages are most effectie in t#is regar$

ceiling oltages limite$ by generator rotor ins&lation

consi$erations

for t#ermal &nits. limite$ to abo&t =1 to :=< times rate$%

loa$ fiel$ oltage

?ast e7citation response to terminal oltage ariations.re&ire$ for improement of transient stability. often lea$s to

$egra$ing t#e $amping of local plant mo$e oscillations

S&pplementary e7citation control. commonly referre$ to as

po!er system stabili4er ('SS) proi$es a conenient means

of $amping system oscillations

2se of #ig# initial response e7citation systems s&pplemente$!it# 'SS is by far t#e most effectie an$ economical met#o$

of en#ancing t#e oerall system stability


85/102

1539pkTS - !

Discontin&o&s E7citation ontrolDiscontin&o&s E7citation ontrol

'roperly applie$ 'SS proi$es $amping to bot# local an$ inter%

area mo$es of oscillations

2n$er large signal or transient con$itions. t#e stabili4er

generally contrib&tes positiely to first s!ing stability

In t#e presence of bot# local an$ inter%area s!ing mo$es.

#o!eer. t#e normal stabili4er response can allo! t#e e7citationto be re$&ce$ after t#e pea, of t#e first local%mo$e s!ing an$

before t#e #ig#est composite pea, of t#e s!ing is reac#e$

A$$itional improements in transient stability can be reali4e$ by

,eeping t#e e7citation at ceiling. !it#in terminal oltage

constraints. &ntil t#e #ig#est point of t#e s!ing is reac#e$

Discontin&o&s e7citation control sc#eme referre$ to as

Transient Stability E7citation ontrol (TSE) #as been$eelope$ by 3ntario y$ro to ac#iee t#e aboe

improes transient stability by controlling t#e generator

e7citation so t#at t#e terminal oltage is maintaine$ near

t#e ma7im&m permissible al&e of abo&t /=/ to /=/1 p&

oer t#e entire positie s!ing of t#e rotor angle


86/102

1539pkTS - "

&ses a signal proportional to c#ange in angle of

t#e generator rotor. in a$$ition to t#e terminal

oltage an$ rotor spee$ signals

angle signal is &se$ only $&ring t#e transient

perio$ of abo&t secon$s follo!ing a seere

$ist&rbance. since it res&lts in oscillatory

instability if &se$ contin&o&sly

angle signal preents premat&re reersal of fiel$

oltage an$ #ence maintains t#e terminal oltageat a #ig# leel $&ring t#e positie s!ing of t#e

rotor angle

e7cessie terminal oltage is preente$ by t#e

terminal oltage limiter

5#en TSE &se$ on seeral generating stations in an

area;

system oltage leel in t#e entire area is raise$

increases po!er cons&me$ by loa$s in t#e entire

area. contrib&ting to f&rt#er improement in TS


87/102

1539pkTS - &

?ig= /J=J Bloc, $iagram of TSE sc#eme

?ig= /J= Effect of TSE on transient stability


88/102

1539pkTS -

Integrating >D 'arallel Lin,sIntegrating >D 'arallel Lin,s

>D lin,s are #ig#ly controllable= 'ossible to ta,e

a$antage of t#is &ni&e c#aracteristic of t#e >D lin,

to a&gment t#e transient stability of t#e ac system

'arallel application !it# ac transmission can be

effectiely &se$ to bypass ac net!or, congestion 3ften. proi$es t#e best option for &sing limite$ rig#t of

!ay

'roi$es a fire!all against casca$ing o&tages $&ring

ma+or system $ist&rbances

?or e7ample. $&ring t#e A&g&st D conerters so as to proi$e

reactie po!er an$ oltage s&pport=


89/102

1539pkTS - (

E7amples of >D 'arallel Lin,sE7amples of >D 'arallel Lin,s

'acific >D Inter%tie in t#e 2S !est

/ bipolar >D oer#ea$ line from

ol&mbia Rier in 3regon to Los Angeles. alifornia

B&ilt in t#e early /-JD Lin, in Bra4il

D oer#ea$ line

from ?o4 $& Ig&ac& #y$ro po!er plant to t#e loa$

centre in t#e city of Sao 'a&lo

:./1< "5 >D lin, b&ilt in t#e mi$ /- A transmission net!or,

&ebec% Ne! Englan$ m&lti%terminal >D system

/1


90/102

1539pkTS - (*

>S%Base$ >D Tec#nology>S%Base$ >D Tec#nology

>D transmission systems b&ilt oer t#e years &se

conerter bri$ge circ&its t#at rely on nat&ral oltage

of t#e ac system for comm&tation8 line%comm&tate$

conerter tec#nology*

Res&lts in generation of lo!er%or$er #armonics

an$ cons&mption of reactie po!er. !#ic# in t&rn

call for co&nter meas&res

In recent years. self%comm&tate$ oltage%so&rce$

conerter (>S) tec#nology* #as been $eelope$ an$

a$ance$ for >D transmission application !it# t#e

follo!ing tec#nical benefits8

Actie an$ reactie po!er can be controlle$in$epen$ently

E7cellent $ynamic response

an be connecte$ to ery !ea, ac net!or,

armonic filter re&irements are significantly less

Goo$ blac,%start* capability

Lo!er oerall footprint* re&irements

>S%base$ >D conerters are more e7pensie an$

#ae #ig#er losses

Depen$ing on t#e nat&re of t#e application. t#ese

may not be significant iss&es


91/102

1539pk

Noember -. /-01 Blac,o&t ofNoember -. /-01 Blac,o&t of

Nort#east 2S an$ 3ntarioNort#east 2S an$ 3ntario


92/102

1539pkTS - (2

Noember -. /-01 % Blac,o&t ofNoember -. /-01 % Blac,o&t of

Nort#east 2S an$ ana$aNort#east 2S an$ ana$a

lear $ay !it# mil$ !eat#er;

Loa$ leels in t#e regional normal

'roblem began at 18/0 p=m=

5it#in a fe! min&tes. t#ere !as a complete s#&t

$o!n of electric serice to

irt&ally all of t#e states of Ne! Yor,.

onnectic&t. R#o$e Islan$. "assac#&setts.

>ermont

parts of Ne! amps#ire. Ne! Wersey an$

'ennsylania

most of 3ntario. ana$a

Nearly :< million people !ere !it#o&t po!er for

abo&t /: #o&rs

'resi$ent Wo#nson or$ere$ #airman of ?e$eral

'o!er ommission to con$&ct an imme$iate

inestigation

Deelopments t#at follo!e$ #a$ a ma+or impact on

t#e in$&stryO


93/102

1539pkTS - (3

Nort# American Eastern Interconnecte$Nort# American Eastern Interconnecte$

SystemSystem


94/102

1539pkTS - (

Eents t#at a&se$ t#e /-01 Blac,o&tEents t#at a&se$ t#e /-01 Blac,o&t

T#e initial eent !as t#e operation of a bac,&p relay

(Pone :) at Bec, GS in 3ntario near Niagara ?alls

opene$ circ&it -BD. one of fie :< ,>

circ&its connecting Bec, GS to loa$ centers in

Toronto an$ amilton

'rior to opening of -BD. t#e fie circ&its !ere

carrying

/;

T#e relay setting correspon$e$ to :J1 "5


95/102

1539pkTS - (!

Eents t#at a&se$ t#e /-01 Blac,o&tEents t#at a&se$ t#e /-01 Blac,o&t(cont@$)(cont@$)

Bec,


96/102

1539pkTS - ("

Eents t#at a&se$ t#e /-01 Blac,o&tEents t#at a&se$ t#e /-01 Blac,o&t(cont@$)(cont@$)

3pening of -BD res&lte$ in se&ential tripping of

t#e remaining fo&r parallel circ&its

'o!er flo! reerse$ to Ne! Yor,

total c#ange of /J


97/102

1539pkTS - (&

Special 'rotections Implemente$ after t#eSpecial 'rotections Implemente$ after t#e

/-01 Blac,o&t/-01 Blac,o&t

' Relays on Niagara Ties

trip Niagara ties to NY;

cross%trip St= La!rence ties to NY

in place &ntil mi$ /-


98/102

1539pkTS - (

?ormation of Reliability o&ncils?ormation of Reliability o&ncils

Nort#east 'o!er oor$inating o&ncil (N')

forme$ in Wan&ary /-00

to improe coor$ination in planning an$ operation

among &tilities in t#e region t#at !as blac,e$ o&t

first Regional Reliability o&ncil (RR) in Nort#

America

3t#er eig#t RRs forme$ in t#e follo!ing mont#s

NationalNort# American Electric Reliability o&ncil

(NER) establis#e$ in /-0


99/102

1539pkTS - ((

Reliability En#ancement after t#e /-01Reliability En#ancement after t#e /-01

Blac,o&tBlac,o&t

All &tilities in Nort# America began to reie!

reliability relate$ policies. practices an$ proce$&res

oor$ination of actiities an$ information e7c#ange

bet!een neig#bo&ring &tilities became a priority

Eac# Regional o&ncil establis#e$ $etaile$ Reliability

criteria an$ g&i$elines for member systems

'o!er system stability st&$ies became an important

part of operating st&$ies

le$ to t#e $eelopment of improe$ Transient

Stability programs

e7c#ange of $ata bet!een &tilities

"any of t#ese $eelopments #as #a$ an infl&ence on

&tility practices !orl$!i$e


100/102

1539pk

"arc# //. /---"arc# //. /---

Bra4il Blac,o&tBra4il Blac,o&t


101/102

1539pkTS - )*)

"arc# //. /--- Bra4il Blac,o&t"arc# //. /--- Bra4il Blac,o&t

Time8 8/08


102/102

"arc# //. /--- Bra4il Blac,o&t"arc# //. /--- Bra4il Blac,o&t (cont@$)(cont@$)

"eas&res to improe system sec&rity8

Woint 5or,ing Gro&p comprising ELETR3BRAS.

E'EL an$ 3NS staff forme$

3rgani4e$ actiities into Tas, ?orces

?o&r international e7perts as a$isors

Reme$ial Actions8

'o!er system $ii$e$ into 1 sec&rity 4ones8

regions !it# ma+or generation an$ transmission

system protecte$ or emergency controls

All ma+or E> s&bstations classifie$ into #ig#.

me$i&m. lo! ris, categories base$ on

impact leel to system sec&rity of b&s fa&lts

intrinsic reliability leel of s&bstation (layo&t.

e&ipment c#anges) to re$&ce ris, leel

Transient Angle

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