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1. Bus Bar Protection

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(1)

Discussion on Bus

Discussion on Bus

Discussion on

Bus-Discussion on Bus-

-bar protection for

-bar protection for

bar protection for

bar protection for

different Bus bar arrangement of

different Bus bar arrangement of

different Bus bar arrangement of

different Bus bar arrangement of

Sub

Sub

Sub-Sub-

-station. Different types of problem &

-station. Different types of problem &

station. Different types of problem &

station. Different types of problem &

its remedy.

its remedy.

its remedy.

its remedy.

calculation, per unit and % impedance.

calculation, per unit and % impedance.

calculation, per unit and % impedance.

calculation, per unit and % impedance.

Engr.

Engr.

Engr. Morshed

Engr. MorshedMorMorshedshedlllalaamammm!h!h!han!hananan

E"ecutive Engineer

E"ecutive Engineer

E"ecutive Engineer

E"ecutive Engineer

#rid Maintenance Division Dha$a

#rid Maintenance Division Dha$a

#rid Maintenance Division

(2)

A

A

Bus arrangements

Bus arrangements

A

A

Bus components

Bus components

A

A

Bus protection techni2ues

Bus protection techni2ues

A

A

') Saturation

') Saturation

A

A

pplication 'onsiderations(

pplication 'onsiderations(



+

+ii h

h iim

m e

ed

da

an

ncce

e b

bu

us

s d

diiffffe

erre

en

nttiia

al

l rre

ella

a iin

n



4o impedance bus differential relaying

4o impedance bus differential relaying

At a glance:

(3)

Bus Bar syst

Bus Bar syst

em in

em in

Electrical sub

Electrical sub

Bus Bar syst

Bus Bar syst

em in

em in

Electrical sub-

Electrical sub-

-station

-station

station

station

••

Single Bus-bar

Single Bus-bar arrangem

arrangement

ent

••

Double Main Bus-bar scheme

Double Main Bus-bar scheme

••

Main and Transfer bus-bar scheme

Main and Transfer bus-bar scheme

••

(4)

Single Bus

Single Bus

Single

Bus-Single Bus-

-bar scheme

-bar scheme

bar scheme

bar scheme

This is the

This is the simplest bus bar scheme simplest bus bar scheme avavailable which consists ofailable which consists of single set of bus bars connected to the generators, transformers single set of bus bars connected to the generators, transformers and load feeders !ll the feeders are connected b" circuit breaker and load feeders !ll the feeders are connected b" circuit breaker and set

and set of isolators This arrangement helps to remove theof isolators This arrangement helps to remove the ,

, ,,

maintenance b" opening the

maintenance b" opening the circuit breakcircuit breaker contacts and furtherer contacts and further opening the

(5)
(6)

dvantages(

dvantages(

••

This bus bar arrangemen

This bus bar

arrangement en&o"s less cost of

t en&o"s less cost of installation

installation

••

'ess maintenance

'ess maintenance

••

simple operation

simple operation

Disadvantages(

Disadvantages(

••

w

wh

he

en

n B

Bu

us

s b

ba

ar i

r is u

s un

nd

de

er

r m

ma

aiin

ntte

en

na

an

ncce

e tto

otta

al s

l su

u

l

l a

an

nd a

d allll

feeder

feeders should be

s should be disconnected

disconnected

••

'east fle(ibilit" and

'east fle(ibilit"

and reliabilit"

reliabilit"

••

)ault

)ault on

on the

the bus

bus bar

bar all

all the

the feeder

feeders

s connected

connected to

to the

the

bus bars should be disconnected

bus bars should be disconnected

(7)

Double Main Bus bar Scheme

Double Main Bus bar Scheme

Double Main Bus bar Scheme

Double Main Bus bar Scheme

*ormall" in double main bus-bar scheme each circuit is

*ormall" in double main bus-bar scheme each circuit is

connected t

connected to both the buses +n some cases half of

o both the buses +n some cases half of the

the

circuits can be connected and operated on each bus,

circuits can be connected and operated on each bus, in

in

these cases bus or

these cases bus or circuit break

circuit breaker failure would cause loss

er failure would cause loss

to half of the

to half of the circuits +n double main bus-bar arrangement

circuits +n double main bus-bar arrangement

one or

one or two breaker

two breakers can be

s can be provided f

provided for each

or each circuit

circuit

Double main bus-bar

Double main bus-bar and double breaker scheme provides

and double breaker scheme provides

high reliabilit" in the case of fault or outage of one of the

high reliabilit" in the case of fault or outage of one of the

breaker

(8)
(9)

dvantages(

dvantages(

••

!n" circuit can be taken out

!n" circuit can be tak

en out of circuit for maintenance

of circuit for maintenance

••

)le(ibilit" in connecting the feeder circuit to either of

)le(ibilit" in connecting the feeder circuit to either of

the bus-bars

the bus-bars

Disadvantages(

Disadvantages(



••

'oose circuits connected to bus-bar when

'oose circuits connected to bus-bar when fault occurs

fault occurs

on the bus-bar

on the bus-bar

(10)

Main and )ransfer Bus-bar Scheme

Main and )ransfer Bus-bar Scheme

Main and Transfer bus-bar scheme is similar to single bus-bar Main and Transfer bus-bar scheme is similar to single bus-bar arrang

arrangement with additional ement with additional transftransfer bus er bus connected Tie connected Tie circuitcircuit breaker is provided to tie both the main and transfer bus

breaker is provided to tie both the main and transfer bus During normal operation all the circuits are connected to the During normal operation all the circuits are connected to the main bus hen

main bus hen circuit breakcircuit breaker connected to er connected to the circuitthe circuit ,, circuit break

circuit breaker connecting the er connecting the main and transfer bus is closedmain and transfer bus is closed The rela" protection for the circuits connected to the transfer The rela" protection for the circuits connected to the transfer bus is taken care b" the tie circuit breaker

(11)
(12)

dvantages(

dvantages(

••

'ow initial cost

'ow initial cost

••

!n" breaker can be taken of circuit for maintenance

!n" breaker can be taken of circuit for maintenance

Disadvantages(

Disadvantages(

••

Reuires one e(tra breaker for bus tie

Reuires one e(tra breaker for bus tie

••

S

Sw

wiittcc iin

ng

g iis

s sso

om

me

ew

w a

at

t cco

om

mp

p iicca

atte

e w

w e

en

n rre

ea

a e

er

r iiss

under maintenance

under maintenance

(13)

*ne and

*ne and

+alf brea$

+alf brea$

er Bus-bar scheme

er Bus-bar scheme

+n One and

+n One and half breakhalf breaker scheme, two cer scheme, two circuits arircuits are connectede connected between the three

between the three circuit breakcircuit breakers .ence One ers .ence One and .alfand .alf break

breaker name was coined er name was coined for this t"pe for this t"pe of arrangement /nderof arrangement /nder normal operating conditions all the breaker

normal operating conditions all the breakers are closed s are closed andand both the bus-bars are energi0ed !n" 1ircuit fault will trip two both the bus-bars are energi0ed !n" 1ircuit fault will trip two circuit breakers and no other circuit will be affected in this circuit breakers and no other circuit will be affected in this arrang

arrangement hen a ement hen a bus-bar fault occur bus-bar fault occur onl" breakeronl" breakerss

ad&acent to bus-bars trips and no circuit will loose power Two ad&acent to bus-bars trips and no circuit will loose power Two bus-bars can also be taken out of ser

bus-bars can also be taken out of service with out vice with out affaffectingecting the power flow if the

the power flow if the power source circuit # alternatopower source circuit # alternator circuit%r circuit% and receiving circuit #transmission line% availa

and receiving circuit #transmission line% available in ble in the samethe same ba"

(14)
(15)

dvantages(

dvantages(

••

Most fle(ible operation possible

Most fle(ible operation possible

••

.igh

.igh reliabilit"

reliabilit"

••

Bus failure will not remove an" circuit from service

Bus failure will not remove an" circuit from service

Disadvantages(

Disadvantages(

••

g

g cco

oss 

••

Rela"ing is somewhat complicated since the

Rela"ing is somewhat complicated since the

middle breaker must responsible for both the

middle breaker must responsible for both the

circuits on either direction and should

(16)

ing bus bar scheme

ing bus bar scheme

+n this ring

+n this ring main bus bar main bus bar scheme arrangement, breakscheme arrangement, breakers areers are connected in ring and circuits are connected between the connected in ring and circuits are connected between the break

breakers There will be same number ers There will be same number of circuits as theof circuits as the number of

number of breakbreakers in the ers in the arrangarrangement During normalement During normal

operation all the breakers are closed During circuit fault two operation all the breakers are closed During circuit fault two br

breaeakkerers s ccononnnecectitin n ththe e cicirrcucuit it trtrii s s DuDuririn n brbreaeakkerer maintenance the ring is broken but all the lines

maintenance the ring is broken but all the lines remain inremain in service

(17)
(18)

dvantages(

dvantages(

••

'ow cost

'ow cost

••

)le(ible operation for breaker maintenance

)le(ible operation for breaker maintenance

••

!n" break

!n" breaker can be

er can be tak

taken out

en out of ser

of service without

vice without

interrupting load

interrupting load

••

2ow

2ower can be

er can be fed from both the direction

fed from both the direction

s

s

a

a

v

v

a

a

n

n

a

a

g

g

e

e

s

s

(

(

••

)ault occur during maintenance will break the ring

)ault occur during maintenance will break the ring

••

Rela"ing is comple(

Rela"ing is comple(

(19)

Fandamentals

Fandamentals

of

of

Bus bar protection

Bus bar protection

(20)

+n

+n earl" da"

earl" da"s

s onl" con

onl" conventional over

ventional over current

current rela"s

rela"s

were used for

were used for

bus-bar protection

bus-bar protection

 But

 But it is desired that

it is desired that

fault in an" feeder or transformer connected to the

fault in an" feeder or transformer connected to the

bus bar should not

bus bar should not disturb bus bar s"st

disturb bus bar s"stem +n viewing

em +n viewing

of this time setting of bus bar protection rela"s are

of this time setting of bus bar protection rela"s are

made length" So when faults occurs on bus bar itself,

made length" So when faults occurs on bus bar itself,

it takes much time to isolate the bus from source

it takes much time to isolate the bus from source

which ma" came much damage in the bus s"stem

which ma" came much damage in the bus s"stem

(21)

Basic rotec

Basic rotec

tion

tion

Scheme

Scheme

Basic rotec

(22)

•• +n recent da"s, the second 0one distance protection rela"s on incoming+n recent da"s, the second 0one distance protection rela"s on incoming

feeder, with operating time of 34 to 35 seconds have been applied for feeder, with operating time of 34 to 35 seconds have been applied for bus-bar p

bus-bar proterotectionction

•• But this scheme has also a main disadvantage This scheme of protectionBut this scheme has also a main disadvantage This scheme of protection

can not discriminate the fault" section of the bus-bar can not discriminate the fault" section of the bus-bar

•• *ow da"s, 2ower s"stem dea*ow da"s, 2ower s"stem deals with ls with huge amount ohuge amount of powerf power .ence  .ence an"an"

interruption in total bus s"stem causes big loss to the compan" So it interruption in total bus s"stem causes big loss to the compan" So it becomes essential to isolate onl" fault" section of bus-bar during bus becomes essential to isolate onl" fault" section of bus-bar during bus



•• !nother drawback of second 0one distance protection scheme is that,!nother drawback of second 0one distance protection scheme is that,

sometime the clearing time is not short enough to ensure the s"stem sometime the clearing time is not short enough to ensure the s"stem stabilit"

stabilit"

•• )o overcome the above mentioned difficulties,)o overcome the above mentioned difficulties, differedifferential bntial bus-barus-bar

protection scheme

protection scheme ith an operating time less than /.0 sec., iith an operating time less than /.0 sec., iss commonly applied to many b

(23)

Differential Bus

Differential Bus

Differential

Bus-Differential Bus-

-bar rotection

-bar rotection

bar rotection

bar rotection

••

'urrent Differential rotection

'urrent Differential rotection

••

1

1oltage Differential 

oltage Differential rotection

rotection

(24)

'urrent Differential rotection

'urrent Differential rotection

•• The scheme of bus-bar protectionThe scheme of bus-bar protection, inv, involvolves, 6irches, 6irchoff7off7ss currcurrentent

law, which states that, total current entering an electrical law, which states that, total current entering an electrical node is e(actl" eual to total current leaving the node node is e(actl" eual to total current leaving the node

•• .ence, total current entering int.ence, total current entering into a bus o a bus section is eual section is eual toto

total curren

total current leaving the t leaving the bus sectionbus section

•• The principle of diffThe principle of differential bus-bar protection is ver" simpleerential bus-bar protection is ver" simple

.ere, secondar"8s of 1Ts are connected parallel That means, .ere, secondar"8s of 1Ts are connected parallel That means, S

S99 terminals of all 1Ts connected together and forms a busterminals of all 1Ts connected together and forms a bus wire Similarl" S

wire Similarl" S:: terminals of all 1Ts connected together toterminals of all 1Ts connected together to form another bus wire

form another bus wire

(25)

S

Soo,, iitt iiss cclleeaarr tthhaatt uunnddeerr nnoorrmmaall ccoonnddiittiioonn tthheerree iiss nnoo ccuurrrreenntt fflloowwss tthhrroouugghh the

the busbus-bar-bar prprototectectionion ttririppppiingng rreelala"" ThThiiss rreelala"" iiss ggenenereraallll"" rreeffeerrrreded aass RRelelaa"" ;<

;< E

Esssseennttiiaallllyy aallll tthhee ''))ss uusseedd ffoorr ddiiffffeerreennttiiaall bbuuss--bbaarr pprrootteeccttiioonn aarree ooff ssaammee

cur

currerentntrratatio.io.

+

(26)

E"te

E"te

rnal

rnal

fault condition

fault condition

E"te

E"te

rnal

rnal

fault condition

fault condition

*ow, sa" fault is occurred at an" of the feeders, outside the protected 0one +n *ow, sa" fault is occurred at an" of the feeders, outside the protected 0one +n that case, the fault" current will pass through primar" of the 1T of that feeder that case, the fault" current will pass through primar" of the 1T of that feeder This fault current

This fault current is contributed b" is contributed b" all other feeders all other feeders connected to the connected to the bus So,bus So, contributed part of

contributed part of fault current fault current flows through flows through the corresponding 1T the corresponding 1T ofof

respective feeder .ence at that fault" condition, if we appl" 61' at node 6, we respective feeder .ence at that fault" condition, if we appl" 61' at node 6, we will still get, i

(27)

o consider a situation

o consider a situation hen fault is ohen fault is occurred on the bus itselfccurred on the bus itself..

o consider a situation

o consider a situation hen fault is ohen fault is occurred on the bus itselfccurred on the bus itself..

!t this condition, also the fault" current is contributed b" all feeders connected to the !t this condition, also the fault" current is contributed b" all feeders connected to the bus .ence, at this condition,

bus .ence, at this condition, sum of all contributed fault current is eual sum of all contributed fault current is eual to totalto total fault" current

fault" current

*ow, at fault" path there is no 1T *ow, at fault" path there is no 1T

(28)

•• The sum of all secondar" The sum of all secondar" currents is no longer 0ercurrents is no longer 0ero +t is eualo +t is eual

to secondar" euivalent of

to secondar" euivalent of fault" currentfault" current

*ow, if we appl" 61' at the nodes, we will get a non 0ero *ow, if we appl" 61' at the nodes, we will get a non 0ero value of i

value of iRR

•• So at this So at this condition current starts flowing through ;< rela"condition current starts flowing through ;< rela"

and it makes trip the

and it makes trip the circuit breakcircuit breaker corresponding to all er corresponding to all thethe feeders connected to this section of the bus-bar !s all the feeders connected to this section of the bus-bar !s all the incoming and outgoing feeders

incoming and outgoing feeders, connected to this , connected to this section ofsection of bus are tripped, the bus be

bus are tripped, the bus becomes deadcomes dead

•• This differential bus-bar protection scheme This differential bus-bar protection scheme is also is also refreferred aserred as

current differential protection of bus-bar current differential protection of bus-bar

(29)

Differential rotection of Sectionali3ed Bus

Differential rotection of Sectionali3ed Bus

.ere, bus section ! or 0one ! is bounded b" 1T

.ere, bus section ! or 0one ! is bounded b" 1T99, 1T, 1T:: and 1Tand 1T44 where 1Twhere 1T99andand 1T

1T::are feeder 1Ts and 1Tare feeder 1Ts and 1T44 is bus 1Tis bus 1T

Similarl" bus section B or 0one B is bounded b" 1T

Similarl" bus section B or 0one B is bounded b" 1T>>, 1T, 1T55 and 1Tand 1T??where 1Twhere 1T>> isis bus 1T, 1T

(30)

•• Therefore, 0one ! and B are overlapped to ensure that,Therefore, 0one ! and B are overlapped to ensure that,

there is no 0one left behind this

there is no 0one left behind this

bus-bar

bus-bar prot

protection

ection

scheme scheme

!S+ terminals of 1T

!S+ terminals of 1T99, : , : and 4 are and 4 are connected togeconnected together tother to form secondar" bus !S+

form secondar" bus !S+

•• BS+ terminals of 1TBS+ terminals of 1T

>

>, 5 , 5 and ? are and ? are connectconnected together toed together to



•• SS

:

: terminals of all 1Ts are connected together to form aterminals of all 1Ts are connected together to form a

common bus S common bus S::

*ow, bus-bar protection rela" ;<! for 0one ! is connected *ow, bus-bar protection rela" ;<! for 0one ! is connected across bus !S+ and S

across bus !S+ and S::

•• Rela" ;<B for 0one B is connected across bus BS+ and SRela" ;<B for 0one B is connected across bus BS+ and S

: :

(31)

••

This section

This section

bus-bar differential protection scheme

bus-bar differential protection scheme

operat

operates in

es in some manner

some manner simple current differential

simple current differential

protecti

protection of

on of bus-bar

bus-bar

••

That is, an" fault in 0one !, with trip onl"

That is, an" fault in 0one !, with trip onl" 1B

1B

9

9

, 1B

, 1B

::

and

and

bus 1

bus 1

BB



••

!n" f

!n" fault in 0one B, will trip

ault in 0one B, will trip onl" 1B

onl" 1B

5

5

, 1B

, 1B

??

and bus 1B

and bus 1B

••

.ence, fault in an" section of bus will

.ence, fault in an" section of bus will isolate onl" that

isolate onl" that

portion from live s"stem

portion from live s"stem

+n current differential protection of bus-bar, if 1T

+n current differential protection of bus-bar, if 1T

secondar" circuits, or bus wires is open

secondar" circuits, or bus wires is open the rela" ma" be

the rela" ma" be

operat

operated to isolate the

ed to isolate the bus from live s"stem But this is

bus from live s"stem But this is

not desirable

(32)

1oltage Differential rotection of Bus-bar

1oltage Differential rotection of Bus-bar

+n voltage diff

+n voltage differential bus-bar protection the erential bus-bar protection the 1T1Ts of s of all incoming andall incoming and outgoing feeders are connected in series instead of connecting

outgoing feeders are connected in series instead of connecting them in parallel

them in parallel The secondar"8s

The secondar"8s of all 1of all 1TTs and differential rela" form a closed s and differential rela" form a closed looploop +f polarit" of a

+f polarit" of all 1Tll 1Ts are properl" matched, the sum s are properl" matched, the sum of voltage acrossof voltage across all 1T secondar"8s

all 1T secondar"8s is 0ero .ence there would be no resultantis 0ero .ence there would be no resultant voltage appears across the

voltage appears across the differdifferential rela"ential rela" hen a  hen a buss faultbuss fault occurs, sum

occurs, sum of the all of the all 1T secondar" voltag1T secondar" voltage e is no longis no longer 0erer 0eroo resultant volt

resultant voltage !s this loop current also fage !s this loop current also flows through thelows through the differ

differential rela"ential rela", the , the rela" is operated to trrela" is operated to trip all the ip all the circuit breakercircuit breaker associated with protected bus 0one @(cept when ground fault

associated with protected bus 0one @(cept when ground fault

current is severall" limited b" neutral impedance there is usuall" no current is severall" limited b" neutral impedance there is usuall" no selectivit" problem hen such a problem e(ists, it is solved b" use selectivit" problem hen such a problem e(ists, it is solved b" use of an additional more sensitive rela"ing euipment including a

of an additional more sensitive rela"ing euipment including a supervising

(33)

1oltage Differential rotection scheme

1oltage Differential rotection scheme

1oltage Differential rotection scheme

(34)

•• The current differential scheme is sensitive onl" when the 1Ts do not getThe current differential scheme is sensitive onl" when the 1Ts do not get

saturated and maintain same current ratio, phase angle error under saturated and maintain same current ratio, phase angle error under

ma(imum fault" condition This is usuall" not perfect, particularl", in the ma(imum fault" condition This is usuall" not perfect, particularl", in the case of an e(ternal fault on one of the feeders The 1T on the fault" feeder case of an e(ternal fault on one of the feeders The 1T on the fault" feeder ma" be saturated b" total current and conseuentl" it will have ver" large ma" be saturated b" total current and conseuentl" it will have ver" large errors Due t

errors Due to this large erro this large erroror, the summation of secondar" current , the summation of secondar" current of allof all 1Ts in a particular 0one ma" not be 0ero So there ma" be a high chance of 1Ts in a particular 0one ma" not be 0ero So there ma" be a high chance of tripping of all circuit breakers associated with this protection 0one even in tripping of all circuit breakers associated with this protection 0one even in the case of an e(ternal large fault To prevent this mal-operation of current the case of an e(ternal large fault To prevent this mal-operation of current

ecessity of 1oltage Differential Schemes

ecessity of 1oltage Differential Schemes

ecessity of 1oltage Differential Schemes

ecessity of 1oltage Differential Schemes

e

erreenn a a uuss-- aar r pprroo eecc oonn, , e e rree aa""s s aarre e pprroovv e w e w g p ccg p up

up current current and enough and enough time dela"time dela"

•• The greatest trouble some cause of 1T saturation is the transient dcThe greatest trouble some cause of 1T saturation is the transient dc

component of the short circuit current component of the short circuit current

•• This difficulties can be overcome b" using air core 1Ts This 1T is alsoThis difficulties can be overcome b" using air core 1Ts This 1T is also

called

called linear couplerlinear coupler !s the core of the 1T does not use iron the secondar" !s the core of the 1T does not use iron the secondar" characteristic of these 1Ts, is straight line

(35)

Bus

Bus component

componentss

4

(36)

Disconnect sitches & au"iliar

Disconnect sitches & au"iliar

y contacts

y contacts

BUS 2 BUS 2 BUS 1 BUS 1

ISO 1

ISO 1 ISO 2ISO 2

--+ + F1a F1a F1c F1c

Contact Input F1a On Contact Input F1a On Contact Input F1c On Contact Input F1c On F1b F1b    I    I    S    S    O    O    L    L    A    A    T    T    O    O    R    R    1    1 ISOLATO

ISOLATOR 1 OPER 1 OPE NN

7 7BB 77AA BUS 1 BUS 1 CB 1 CB 1 ISO 3 ISO 3 BYPASS BYPASS --+ + F1a F1a F1c F1c

Contact Input F1a On Contact Input F1a On Contact Input F1c On Contact Input F1c On F1b F1b    I    I    S    S    O    O    L    L    A    A    T    T    O    O    R    R    1    1 ISOLATO

ISOLATOR 1 R 1 CLOSEDCLOSED

7

7BB 77AA BUS 1

(37)

BUS 2 BUS 2 BUS 1 BUS 1

ISO 1

ISO 1 ISO 2ISO 2

'urrent

'urrent

)

)

r

r

ansfo

ansfo

rmers

rmers

CB 1 CB 1 ISO 3 ISO 3 BYPASS BYPASS *il insulated

*il insulated current transformercurrent transformer

567$1 up to 8//$19

567$1 up to 8//$19

#as 5S:9 insulated current

#as 5S:9 insulated current

transformer

transformer

Bushing

Bushing type type 5medium5medium

voltage sitchgear9

(38)

rotection e2uirements

rotection e2uirements

rotection e2uirements

rotection e2uirements

+igh bus fault currents due to large number of ci+igh bus fault currents due to large number of circuitsrcuits

connected(

connected(

 – 

 –  ') saturation often becomes a problem as ')s ma') saturation often becomes a problem as ')s may not by not be sufficientlye sufficiently

rated for orst fault condition case rated for orst fault condition case

 – 

 –  large dynamic forces associated ith bus large dynamic forces associated ith bus faults re2uire fast clearingfaults re2uire fast clearing

times in order to reduce e2uip

times in order to reduce e2uipment damagement damage

alse trip by bus alse trip by bus protection may creatprotection may create serious e serious problems(problems(

 – 

 –  service interruption to a large number of circuits 5distribution and sub-service interruption to a large number of circuits 5distribution and

sub-transmission voltage levels9 transmission voltage levels9

 – 

 –  systsystem-ide stability em-ide stability problems 5transmission voltage levels9problems 5transmission voltage levels9

;ith both dependability a;ith both dependability and security important, prefnd security important, preference iserence is

alays given to security

(39)

Bus rotection )echni2ues

Bus rotection )echni2ues

Bus rotection )echni2ues

Bus rotection )echni2ues

<nte

<nterloc$ing

rloc$ing schemes

schemes

*ver current 5=unrestrained> or =unbiased>9

*ver current 5=unrestrained> or =unbiased>9

differential.

differential.

*ver current percent 5=restrained> or =biased>9

*ver current percent 5=restrained> or =biased>9

4inear couplers

4inear couplers

+igh-impedance bus differ

+igh-impedance bus

differential schemes

ential schemes

(40)

<nter

<nter

loc$ing

loc$ing

Schemes

Schemes

A

A Bloc$ing scheme typicallyBloc$ing scheme typically used

used A

A Short coordination timeShort coordination time re2uired

re2uired A

A 'are must be ta$en ith'are must be ta$en ith

possible saturation of feeder possible saturation of feeder

50 50      L      L      O      O      C      C      K      K A

A Bloc$ing signal could be sentBloc$ing signal could be sent over communications ports. over communications ports. A

A )his techni2ue is limited to)his techni2ue is limited to simple one-incomer simple one-incomer distribution buses distribution buses 5 500 5500 5500 5500 5500

(41)

•• ! simpl! simple prote protection fection for distribution or distribution busbarsbusbars can becan be

accomplished as an interlocking scheme Over

accomplished as an interlocking scheme Over current #O1%current #O1% rela

rela"s are placed on an "s are placed on an incoming circuit and at all outgoingincoming circuit and at all outgoing feeder

feeders The feeder O1s s The feeder O1s are set to sense are set to sense the fault currentsthe fault currents on the feeders The O1 on the incoming circuit is set to trip on the feeders The O1 on the incoming circuit is set to trip the busbar

the busbar unless blockunless blocked b" aned b" an" of the f" of the feeder O1 relaeeder O1 rela"s !"s ! short coordination timer is t"picall" reuired to avoid race short coordination timer is t"picall" reuired to avoid race conditions

conditions

•• Modern rela"s provide for fast peer-to-peer communicationsModern rela"s provide for fast peer-to-peer communications

using protocol

using protocols such as s such as the /1! with the the /1! with the $OOS@$OOS@

mechanism This allows eliminating wiring and sending the mechanism This allows eliminating wiring and sending the blocking signals over the

blocking signals over the communicacommunicationstions

•• The scheme although eas" to appl" and eThe scheme although eas" to appl" and economical conomical isis

limi

(42)

*ver current

*ver current

*ver current 5unrestrained9 Differential

*ver current 5unrestrained9 Differential

5unrestrained9 Differential

5unrestrained9 Differential

A

A DifferDifferential signal ential signal formeformed d byby summation of all

summation of all currents feedingcurrents feeding the bus

the bus A

A ') ratio matching may be') ratio matching may be re2uired

re2uired A

A *n e"ternal faults, saturated ')s*n e"ternal faults, saturated ')s

51

51

A

A )ime delay used to cope ith '))ime delay used to cope ith ') saturation

saturation A

A <nstantaneous differ<nstantaneous differential ential *'*' function useful

function useful on integraton integrateded microprocessor-based relays microprocessor-based relays

(43)

•• T"picall" a differential current is created e(ternall" to a currentT"picall" a differential current is created e(ternall" to a current

sensor b"

sensor b" summation of all the summation of all the circuit currents 2recircuit currents 2referferabl" theabl" the 1Ts should be of the same ratio +f the" are not, a matching 1T 1Ts should be of the same ratio +f the" are not, a matching 1T #or several 1Ts% is needed This in turn ma" increase the

#or several 1Ts% is needed This in turn ma" increase the burden for the main 1Ts and make the saturation problem burden for the main 1Ts and make the saturation problem even more serious

even more serious

•• .istoricall", means to deal with the 1T saturation problem.istoricall", means to deal with the 1T saturation problem

include definite time or

include definite time or invinverse-time over currenterse-time over current characteristics

characteristics

•• !lthough economical and applicable to distribution bus bars,!lthough economical and applicable to distribution bus bars,

this solution does

this solution does not match performance of more advancednot match performance of more advanced schemes and should not be

schemes and should not be applied to transmissioapplied to transmission-level busn-level bus bars

(44)

4inear 'ouplers

4inear 'ouplers

?

?''@ A@ A ΩΩΩΩΩΩΩΩ   A/A/ ΩΩΩΩΩΩΩΩ-- typicatypical col coil imil impedanpedancece

59 59 p peer r mmpps s @@C C . . 33 <f @ 8///  <f @ 8///  4 400VV 1100VV 1100VV 00VV 2200VV A///  A///  2000 A2000 A / /  /// ///  0 V 0 V E"ternal E"ternal ault ault

(45)

4inear 'ouplers

4inear 'ouplers

4inear 'ouplers

4inear 'ouplers

E

Esecsec@ <@ <primprimFGFGmm -- secondary voltagsecondary voltage on e on relay relay terminalsterminals <<@@ ΣΣΣΣΣΣΣΣ<<primprimFGFGmmH5?H5?IIΣΣΣΣΣΣΣΣ??''99  mimininimumum opem operratatining curg currerentnt

here, here,

<<primprim   primary current in each circuitprimary current in each circuit G

Gmm   liner coupler mutual reactance 57liner coupler mutual reactance 571 per 0///mps @C /.//71 per 0///mps @C /.//7ΩΩΩΩΩΩΩΩ :/+3 9 :/+3 9 ?

?   relay tap imrelay tap impedancepedance Σ Σ Σ Σ Σ Σ Σ

Σ??''   sum of all linear coupler self impedancessum of all linear coupler self impedances

59 59 <f @ 8///  <f @ 8///  /  /  0 0 VV 1100VV 1100VV 00VV 2200VV 40 V 40 V A A///// /  AA///// /  / /  ///// /  <nternal Bus <nternal Bus ault ault

(46)

4inear 'ouplers

4inear 'ouplers

4inear 'ouplers

4inear 'ouplers

A

A ))aasstt, , sseeccuurre e aannd d pprroovveenn A

A ReReuuirire de dededicicatated ed aiair gr gap ap 1T1Ts, ws, whihich ch mama" n" not bot be use used fed foror an" other protection

an" other protection A

A 1a1annnnot ot be be eaeasisil" l" apapplplieied td to ro rececononfifigugurrabable le bubusesess A

A ThThe sce scheheme me ususes es a sa siimpmplle ve vololttagage de deettececttor or  it it ddoeoes ns noott

! linear coupler #air core mutual reactor% produces its output

! linear coupler #air core mutual reactor% produces its output

voltag

voltage proportional to the e proportional to the derivativderivative of e of the input the input currentcurrent

Because the" are using air

Because the" are using air cores, linear couplers do notcores, linear couplers do not

saturate

saturate

provide benefits of

provide benefits of a microprocessor-based relaa microprocessor-based rela" #eg" #eg oscillograph", breaker failure protection, other functions% oscillograph", breaker failure protection, other functions%

(47)

! scheme of bus protection offering advantages in simplicit", speed, and ! scheme of bus protection offering advantages in simplicit", speed, and si0e uses linear couplers #air-core mutual reactances% in place of current si0e uses linear couplers #air-core mutual reactances% in place of current transformers This solves the troublesome problem of saturation and transformers This solves the troublesome problem of saturation and provides a

provides a linear relationship beteen secondary voltage and primarylinear relationship beteen secondary voltage and primary current.

current. The coupler secThe coupler secondariesondaries for a givfor a given bus are cen bus are connected onnected in a seriesin a series loop with the rela" hen the currents entering and leaving the bus are loop with the rela" hen the currents entering and leaving the bus are eual, the net induced voltage in the rela" loop is 0ero )or a fault on the eual, the net induced voltage in the rela" loop is 0ero )or a fault on the bus, however, the net induced voltage, proportional to the fault current, bus, however, the net induced voltage, proportional to the fault current,

 

available energ" : To build couplers of sufficientl" eual mutual available energ" : To build couplers of sufficientl" eual mutual reactance and unaffected b" stra" fields

reactance and unaffected b" stra" fields ! toroi

! toroidaldal coil solved the latcoil solved the latter problem Thrter problem Through tests havough tests have shown thate shown that the performance is strictl" linear with respect to primar" current,

the performance is strictl" linear with respect to primar" current, practicall" unaffected b" the primar" d-c transient, and thus can be practicall" unaffected b" the primar" d-c transient, and thus can be calculated accuratel" and simpl"

(48)

+igh <mpedance

+igh <mpedance

Differ

Differ

ential

ential

+igh <mpedance

+igh <mpedance

Differ

Differ

ential

ential

 – 

 –  *perating signal created by*perating signal created by

connect

connecting all ') ing all ') secondaryJs insecondaryJs in parallel

parallel

')')s must as must all have the sall have the same ratiome ratio

Must have dedicated ')sMust have dedicated ')s

 – 

 –  *vervoltage element operates*vervoltage element operates

on voltage developed across on voltage developed across resistor connected in secondary resistor connected in secondary circuit

circuit

ee uiuireres s vvararisistotorsrs or or ''

59 59

shorting relays to limit energy shorting relays to limit energy during faults

during faults

 – 

 –  ccuracy dependent onccuracy dependent on

secondary circuit resistance secondary circuit resistance

Ksually re2uires larger ') cablesKsually re2uires larger ') cables

to reduce errors

to reduce errors⇒⇒⇒⇒⇒⇒⇒⇒higher costhigher cost

'annot easily be

'annot easily be applied to reconfigurable buses and offers noapplied to reconfigurable buses and offers no

advanced functionality.

(49)

ault 4evel 'alculation

ault 4evel 'alculation

ault 4evel 'alculation

ault 4evel 'alculation

hen a short

hen a short circuit occurs in an electric s"stem, heacircuit occurs in an electric s"stem, heav"v" current flow

current flows through all the s through all the sections of the sections of the s"ss"stem whichtem which are in the path between the power source and the

are in the path between the power source and the

euipment The short circuit current is limited onl" b" euipment The short circuit current is limited onl" b" thethe impedance of the

impedance of the s"ss"stemtem

This heav" current can damage the components of This heav" current can damage the components of thethe electric s"st

electric s"stem if em if the" are not the" are not properl" ratproperl" rated +f ced +f circuitircuit break

breakers are not able ers are not able to interrupt the high to interrupt the high short circuitshort circuit currents in a s"stem, arcing and e(plosions ma" occur currents in a s"stem, arcing and e(plosions ma" occur

(50)

ault 4evel 'alculation

ault 4evel 'alculation

ault 4evel 'alculation

ault 4evel 'alculation

•• The Rating of the components is done based The Rating of the components is done based on the ma(imumon the ma(imum

short circuit current The short

short circuit current The short circuit currencircuit current is t is calculated frcalculated fromom the fault le

the fault level 6vel 6! of the S"s! of the S"stemtem The )ault The )ault 'evel in a'evel in a dis

distributtribution ion s"s"stem stem is a vis a ver" imper" importaortant pnt pararametameterer The kThe k!! atat the instant of a )ault should be correctl" calculated and the the instant of a )ault should be correctl" calculated and the components of the distribution s"st

components of the distribution s"stem such as em such as bus bars, circuitbus bars, circuit breakers, isolators, etc should be properl" si0ed

breakers, isolators, etc should be properl" si0ed

•• To calculate the fault current in a s"stem it is first necessar" toTo calculate the fault current in a s"stem it is first necessar" to

calculate the M! during a fault calculate the M! during a fault

(51)

ault 4evel 'alculation

ault 4evel 'alculation

ault 4evel 'alculation

ault 4evel 'alculation

)rom this, the ma(imum current during the fault can be

)rom this, the ma(imum current during the fault can be

deduced as

deduced as

!ll the euipments should be rated to withstand this

!ll the euipments should be rated to withstand this

curr

current

ent The f

The fault

ault leve

level sho

l should b

uld be ca

e calcula

lculated

ted ever

ever" fiv

" five

e

"ears and after an" modification to the s"stem such as

"ears and after an" modification to the s"stem such as

the addition of an" load or the installation of further

the addition of an" load or the installation of further

sources of power such as transformers and alternators

sources of power such as transformers and alternators

(52)

2er unit fault calculations is a method whereb" s"stem 2er unit fault calculations is a method whereb" s"stem impedances and

impedances and uantities are normali0ed across differenuantities are normali0ed across differentt vol

voltagtage leve levels tels to a co a commoommon basen base B" rB" removiemoving the ing the impact mpact ofof var"ing voltag

var"ing voltages, the es, the necessar" calculations are simplifiednecessar" calculations are simplified

er unit fault calculations

er unit fault calculations

er unit fault calculations

er unit fault calculations

n

n aapppp "" nng g e e ppeer r uun n mmee oo , , e e rrs ss s eep p s o s o ssee eec ac ann arbitrar" voltage #

(53)

<mportant otations

<mportant otations

<mportant otations

<mportant otations

CC peper r ununit it memeththod od cucurrrrenent bt basasee

CC peper ur uninit mt meeththod od popowwer er bbasasee CC peper ur uninit met meththod od vvololttagage be basasee CC peper ur uninit mt metethohod ad admdmititttanance ce babasese CC peper ur uninit mt metethohod id impmpededanance ce babasese

-2ercen

-2ercentage tage +mpedance+mpedance -- 2e2er unit +r unit +mpedmpedancancee -- !ct!ctual +ual +mpempedandancece

-2er unit base +mpedance -2er unit base +mpedance

(54)

er Knit Method

er Knit Method

er Knit

Method-er Knit Method-

-<mportant ormulas

-<mportant ormulas

<mportant ormulas

<mportant ormulas

•• .aving selected a base power and voltage, the base per unit values of.aving selected a base power and voltage, the base per unit values of

impedance, admittance and current can be calculated fromC impedance, admittance and current can be calculated fromC

2

2eer r //nniitt TThhrreee e 22hhaassee

•• Dividing a s"stem element b" it7s per-unit base value gives the per-unitDividing a s"stem element b" it7s per-unit base value gives the per-unit

value of the element value of the element

•• Some times per-unit values are available for a given base k, but theSome times per-unit values are available for a given base k, but the

problem

problem being solbeing solved is ved is using a diusing a diffefferent rent basebase +n this ins+n this instance it tance it is possibleis possible to convert the unit

(55)

)aul

)ault calculation problems t"picall" deal t calculation problems t"picall" deal wit power wit power sources,sources, gener

generatatorsors, tran, transfsformerormers and s"ss and s"stem impetem impedancesdances 2e2er-unir-unitt values for these elements can be

values for these elements can be uickl" derived from Cuickl" derived from C

E

Elleemmeenntt PPeer r UUnniit t VVaalluuee

Source +mpedance Source +mpedance $enerator $enerator Transformer Transformer +mpedance +mpedance where  is in k where  is in k

(56)

E"ample

E"ample

E"ample

-E"ample -

-

-

calculating per unit values

calculating per unit values

ca

ca

lcu

lcu

lat

lat

ing p

ing p

er u

er u

nit v

nit v

alu

alu

es

es

1onsider a s"stem of source impedance >>; E connected to a 1onsider a s"stem of source impedance >>; E connected to a :3 M

:3 M! tr! transfansformer #9ormer #99F39F3> k% a> k% at ?G impt ?G impedanceedance e wane wantt to find the fault level at the transformer secondar"

to find the fault level at the transformer secondar"

Selecting

Selecting as as :3 :3 MM! ! and and as as 99 99 k k and and using using the the aboveabove euations

(57)

ault 5singl

ault 5singl

e phase9'alculation.

e phase9'alculation.

ault 5singl

ault 5singl

e phase9'alculation.

e phase9'alculation.

and and

the 'ine-*eutral voltage on the secondar" of the transformer is 3>FH4 = 3:43 k, givingC the 'ine-*eutral voltage on the secondar" of the transformer is 3>FH4 = 3:43 k, givingC

#3<> I33? =3;% #3<> I33? =3;%

(58)

)hree hase ault E"ample

)hree hase ault E"ample

)hree hase ault E"ample

)hree hase ault E"ample

2er unit anal"sis can be used to calculate s"stem three phase fault levels and the current 2er unit anal"sis can be used to calculate s"stem three phase fault levels and the current distributions

distributions TTo gain a beo gain a better understter understanding, it is tanding, it is worth running through the worth running through the t"pical stt"pical stepseps reuired to solve a

reuired to solve a fault calculation problemfault calculation problem

$iven the s"stem single line diagram, construct and simplif" the per uni

$iven the s"stem single line diagram, construct and simplif" the per uni t impedance diagramt impedance diagram

here Jpu, is the total impedance between the source and the here Jpu, is the total impedance between the source and the faultfault )ault flow through parallel branches is given b"

)ault flow through parallel branches is given b" the ratio of impedances !s the ratio of impedances !s illustratillustrated this ed this can enablecan enable fault flows to be found through each

(59)

.aving calculat

.aving calculated the fault flow ed the fault flow in each branch, it is in each branch, it is then relativel" simple to find thethen relativel" simple to find the current distribution using C

current distribution using C

where where

(60)

Seuence *

Seuence *

etw

etw

ork

ork

Seuence *

Seuence *

etw

etw

ork

ork

@lectrical power and voltage are generall" taken as base uantities +n @lectrical power and voltage are generall" taken as base uantities +n three phase s"stem, three phase power

three phase s"stem, three phase power in Min M! or 6! or 6! is tak! is taken as baseen as base power and line to line voltage in 6 is taken as base voltage The base power and line to line voltage in 6 is taken as base voltage The base impedance of the s"stem can be calculated from these base power and impedance of the s"stem can be calculated from these base power and base voltage, as follows,

base voltage, as follows,

er unit

er unit is an impedance value of an" s"stem is nothing but the radio ofis an impedance value of an" s"stem is nothing but the radio of actual impedance of the s"stem to the base impedance value

actual impedance of the s"stem to the base impedance value

ercentage impedance

ercentage impedance value can be calculated b" multipl"ing 933 withvalue can be calculated b" multipl"ing 933 with per unit

(61)

!gain it is sometimes reuired to convert

!gain it is sometimes reuired to convert per unit values referred to newper unitvalues referred to new base values for simplif"ing different

base values for simplif"ing different electrical fault calculationelectrical fault calculations +n thats +n that case,

case,

s"stem

s"stem $enerall" base $enerall" base voltage of voltage of a s"sa s"stem is so tem is so chosen that it rchosen that it reuireseuires minimum number of transfers

minimum number of transfers

Suppose, one s"stem as a large number of 94: 6 over head lines, few Suppose, one s"stem as a large number of 94: 6 over head lines, few numbers of 44 6 lines and ver" few number of 99 6 lines The base numbers of 44 6 lines and ver" few number of 99 6 lines The base voltage

voltage of the s"stem can be of the s"stem can be chosen either as 94chosen either as 94: 6 or 44 6 or : 6 or 44 6 or 99 699 6,, but here the best base voltages 94: 6, because it reuires minimum but here the best base voltages 94: 6, because it reuires minimum number of transfer during

(62)

The above fault calculation is made on assumption o

The above fault calculation is made on assumption of threef three phase balanced s"stem The calculation is made for one phase phase balanced s"stem The calculation is made for one phase onl" as the curr

onl" as the current ent and voltand voltage conditiage conditions are same ons are same in all thrin all threeee phases hen actual faults occur in

phases hen actual faults occur in electrical power s"selectrical power s"stem,tem, such as phase to earth fault, phase to phase

such as phase to earth fault, phase to phase fault and doublefault and double phase to earth fault, the

phase to earth fault, the s"ss"stem becomes unbalanced means,tem becomes unbalanced means, the

the condconditionitions s of of volvoltata es es and and currcurrents ents in in all all hases hases are are nono longer s"mmetrical Such faults are solved b"

longer s"mmetrical Such faults are solved b" symmetricalsymmetrical component analysis

component analysis  $enerall" $enerall" three three phase phase vector vector diagram diagram ma"ma" be replaced b" three sets of balanced vectors One has opposite be replaced b" three sets of balanced vectors One has opposite or negative phase rotation, second has positive

or negative phase rotation, second has positive phase rotationphase rotation and last one is

and last one is co-phasal That means these vectors sets areco-phasal That means these vectors sets are described as negative, positive and 0ero seuence, respectivel" described as negative, positive and 0ero seuence, respectivel"

(63)
(64)

Se2uence <mpedance

Se2uence <mpedance

Se2uence <mpedance

Se2uence <mpedance

ositive Se2uence <mpedance ositive Se2uence <mpedance

The impedance offered b" the s"stem to the flow of positive seuence The impedance offered b" the s"stem to the flow of positive seuence current is called

current is called positive se2uence impedancepositive se2uence impedance  egativ

egative Se2uence e Se2uence <mpedance<mpedance

The impedance offered b" the s"stem to the flow of negative seuence The impedance offered b" the s"stem to the flow of negative seuence current is called

current is called negativnegative se2uence e se2uence impedanceimpedance 

The impedance offered b" the s"stem to the flow of 0ero seuence current The impedance offered b" the s"stem to the flow of 0ero seuence current is known as

is known as 3er3ero se2uo se2uence impedanceence impedance  +n previous fault calculation, J

+n previous fault calculation, J99, J, J:: and Jand J33 are positive, negative and 0eroare positive, negative and 0ero seuence impedance respectivel" The

seuence impedance respectivel" The se2uence impedance varies withse2uence impedance varies with the t"pe of power s"stem components under consideration

(65)

•• +n static and balanced power s"stem components like transfo+n static and balanced power s"stem components like transformer and lines, rmer and lines, thethe

se2uence impedance

se2uence impedance offered boffered b" the s"stem are the same " the s"stem are the same for positive and negativefor positive and negative seuence currents +n other words, the

seuence currents +n other words, the positive se2uence impedancepositive se2uence impedance andand

negative se2uence impedance

negative se2uence impedance are same for transformers and power linesare same for transformers and power lines

•• But in case of rotating machines theBut in case of rotating machines the positive and negative se2uence impedancepositive and negative se2uence impedance

are different are different

•• The assignment ofThe assignment of 3ero se2uence impedance3ero se2uence impedance values is a more comple( one This isvalues is a more comple( one This is

because the three 0ero seuence

because the three 0ero seuence current at an" point in a current at an" point in a electrical power s"stem,electrical power s"stem, being in phase, do

being in phase, do not sum to 0ero but must return through the neutral and Fornot sum to 0ero but must return through the neutral and For earth +n three phase transformer and machine flu(es due to 0ero seuence earth +n three phase transformer and machine flu(es due to 0ero seuence components do not sum to 0ero in the "oke or field s"stem The impedance ver" components do not sum to 0ero in the "oke or field s"stem The impedance ver" w

w ee " " eeppeenn nng g uuppoon n e e pp ""ss cca a aarrrraannggeemmeen o n o e e mmaaggnnee c c cc rrccuu s s aann winding

winding

 – 

 –  The reactance of transmission lines of 0ero seuence currents can be about 4 to 5 times theThe reactance of transmission lines of 0ero seuence currents can be about 4 to 5 times the

positive seuence current, the lighter value being for lines without earth

positive seuence current, the lighter value being for lines without earth wires This is becausewires This is because the spacing between the go and return#ie neutral andFor earth% is so much greater than for the spacing between the go and return#ie neutral andFor earth% is so much greater than for positive and negative seuence currents which return #balance% within the three phase positive and negative seuence currents which return #balance% within the three phase conductor groups

conductor groups

 – 

 –  The 0ero seuence reactance of a machine is compounded of leakage and winding reactance,The 0ero seuence reactance of a machine is compounded of leakage and winding reactance,

and a small component due to winding balance

and a small component due to winding balance #depends on winding tritch%#depends on winding tritch%

 – 

 –  The 0ero seuence reactance of transformers depends both on winding connections and uponThe 0ero seuence reactance of transformers depends both on winding connections and upon

construction of core construction of core

(66)

ercentage

ercentage

ercentage <

ercentage <

<mpedance

<mpedance

mpedance

mpedance

The percentage impedanc

The percentage impedance of a e of a transformer is the volt drop ontransformer is the volt drop on  full load due to the

 full load due to the winding resistwinding resistance and leakance and leakage reactanceage reactance expressed as a percentage of the ra

expressed as a percentage of the rated voltage.ted voltage.

+t is also the

+t is also the percentag+t is also the percentage of te of the normal terminal voltage reuirhe normal terminal voltage reuireded +t is also the percentagpercentage of te of the normal terminal voltage reuirhe normal terminal voltage reuireded to circulate full

to circulate fullto circulate

full-to circulate full--load current under short -load current under short circuit conditionsload current under short load current under short circuit conditionscircuit conditionscircuit conditions The impedance is measured b" means of

The impedance is measured b" means of a short circuita short circuit tes

testt ith oith one windne winding shoing shorted, a rted, a volvoltagtage at the e at the rarated frted freuenc"euenc" is applied to the

is applied to the other winding sufficient to circulate full loadother winding sufficient to circulate full load current

(67)

The percentage impedance can then be

The percentage impedance can then be calculatcalculated as follows Ced as follows C

ated 1oltage ated 1oltage

References

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