Experiment Experimen t No:-
Date:-
SEQUENCE IMPEDANCES IMPEDANC ES OF O F ALTERNA ALTERNATOR TOR Aim: To Determine Positive, Negative and Zero Sequence Impedances of an Alternator. Alternator. Apparatus Reuire!: S. No !.
+. /.
). *.
A pparatus R"eostats
Type Type #ire $ound
Range %&&'(!A
uantity !
)&&'(!A
! ! !
oltmeters
-I
*+'(*A &*&&
Ammeters
-I -I
&+*& &!&A
! !
-I
&!A
!
-0 Digital Digital(Analog
&!A
! ! !
-ultimeter Tac"ometer
&!&&&&RP-
T"eor#: 1or a po$er system during un2alanced operation, unsymmetrical faults suc" as single p"ase to grou ground nd faul fault, t, p"as p"asee to p"as p"asee faul fault, t, dou2 dou2le le p"as p"asee to grou ground nd faul fault, t, simp simple le p"as p"asee representations leads to complicated calculations. T"e met"od of symmetrical components is used for t"e analysis of un2alanced system. T"e principle of symmetrical components is as follo$s. A set of n un2alanced p"asors are resolved into n sets of 2alanced p"asors, eac" of $"ic" consists of n 2alanced vectors. T"ese 2alanced vectors are called symmetrical components of t"e original system p"asors.
S#mmetri$a% $omponents o& '-p"ase s#stem:An un2alanced systems of t"ree vectors 3 a,2, a,2, c or Ia, I2, Ic4 can 2e resolved into t"ree 2alanced systems of vectors , t"e vectors of t"e resolved system are 5 !. Positive sequence components5 6a!, 2!, c! or Ia!,I2!,Ic!7 comprising t"ree 2alanced systems of vectors of t"e displaced mutually 2y !+&& and "aving t"e same p"ase sequence as t"at of a original system.
+.Negative sequence components5 6a+,2+,c+ or Ia+,I2+,Ic+7 comprising t"ree 2alanced systems of vectors of equal magnitude displaced mutually 2y !+& & and "aving t"e opposite p"ase sequence as t"at of a original system of vectors. /. Zero sequence components5 6a&, 2 &, c & or Ia&, I2 &, Ic &7 comprising t"ree equal vectors "aving 8ero p"ase displacement i.e., "aving same p"ase. Sym2olically, Su2script ! is for t"e positive sequence entities. Su2script + is for t"e negative sequence entities and su2script & is used for t"e 8ero sequence entities. a, a, 2, c or Ia, I2, Ic
9riginal system components
a!, 2!, c! or Ia!, I2!, Ic!
Positive sequence components
a+, 2+, c+ or Ia+, I2+, Ic+
Negative sequence components
a&, 2&, c& or Ia&, I2&, Ic&
Zero sequence components
Si(ni&i$an$e o& t"e operator )a*: :etter ;a< is commonly used to designate t"e operator t"at causes a countercloc=$ise rotation of !+& &. It "as unit magnitude and an angle of !+& &. T"e vector operator ;a< is defined as a >!e ?+@(/ >0os3+@(/4?Sin3+@(/4 > &.* ?&.BCC a+>!e ?)@(/ >0os3)@(/4?Sin3)@(/4 > &.* ?&.BCC a/>!e ?+@> !?& and !aa+ > &. T"e original un2alanced system of vectors can 2e resolved into t"eir symmetrical components or t"e respective symmetrical components can 2e added to get t"e original system of vectors. T"us
and
a> a&a!a+
6!7
2> 2&2!2+
6+7
c > c&c!c+
6/7
6)7
Ia> Ia&Ia!Ia+
I2>I2&I2!I2+
6*7
Ic >Ic&Ic!Ic+
6C7
1rom t"e equations, $e can get symmetrical components of un2alanced systems of vectors. Summari8ing
Va Va Va
&
!
+
! = ! ! / !
a a
!
+
a a
Va Vb Vc
!
+
Va ! Vb = ! Vc !
a a
!
a
!
+
+
a
Va Vb Vc
&
&
&
In similar $ay,
Ia Ia Ia
&
!
+
=
! /
! ! !
!
a a
+
a a !
+
Ia Ib Ic
Ia ! Ib = ! Ic !
!
a
+
a
a a !
+
Ia Ib Ic
&
&
&
+ero seuen$e $urrents:In t"e t"ree p"ase syst system ems, s, $"en t"ere is a neut eutral ral pat" for for curre rrents , t"en I N>IaI2Ic #e get T"erefore
IaI2Ic >/EIao Iao>I N(/
T"erefore in t"e delta connected load, t"e line currents do not find return pat". Fence line currents do not "ave 8ero sequence components. 1rom 2alanced vector to symmetrical components5 Positive sequence
Negative sequence
Zero sequence
a!
a+
a&
2!>a+ a!
2+>a a!
2&>a&
c!>a a!
c+>a+ a+
c&>a&
1rom t"e sets of t"e equations, a > a&a!a+ 2 > a&a+a!aa+ c > a&aa!a+a+
In star connected system $it"out neutral pat" or neutral grounding, 8ero sequence currents are 8ero.
Seuen$e impe!an$es:T"e impedance offered 2y a rotating mac"ine to positive sequence component of current, differ from t"ose offered to negative sequence components of currents. T"e impedance offered 2y a circuit to positive sequence component current is called positive sequence impedance of t"at circuit 3Z!4.T"e impedance offered 2y a circuit to negative sequence sequence component component current is called negative negative sequence sequence impedance impedance of t"at circuit 3Z +4. T"e impedance offered 2y a circuit to 8ero sequence component current is called 8ero sequence impedance of t"at circuit 3Z&4.
Seuen$e Impe!an$es an! net,ors o& t"e a%ternator:T"e positive positive sequence sequence net$or= of /p"ase /p"ase alternator consists consists of an e.m.f source Ga in series $it" positive positive sequence sequence impedance3Z impedance3Z!4. Ga is t"e induced e.m.f of one p"ase, Z ! is positive sequence impedance a!>GaIa!Z!. T"e negative sequence net$or= of a generator consists of simply negative sequence impedance Z + as t"ere are no negative sequence e.m.f Ia+ Z+ Zero sequence sequence net$or= net$or= of an alternator alternator consists consists of t"e 8ero sequence sequence alternat alternator or per p"ase
impedance impedance of
plus plus t"ree t"ree times t"e impedanc impedancee in neutral neutral to ground ground circuit circuit i.e., i.e.,
Z&>Zgo/EZn oltage dropa& > Ia & Z&
.o%ta(e .o%ta(e euations: #e o2serve o2serve t"at t"e curren currents ts of a particu particular lar sequen sequence ce produc produces es voltage drop of line sequence. T"e equations are
a!> GaIa!EZ! a+> Ia+EZ+ a&> Ia&EZ& Z&> Zgo/EZn Pro$e!ure:Measurement o& Positi/e Seuen$e Impe!an$e:-
!. 0onnec 0onnectt t"e circu circuit it as per t"e t"e circui circuitt diagram diagram!. !. +. S$itc" on t"e t"e supply supply circuit after c"ec=ing c"ec=ing connec connections. tions. /. Hring t"e t"e motor motor to rated speed speed 2y using motor motor field regulat regulator. or. ). Hy varying varying t"e field field regulator regulator of t"e t"e alternator alternator t"e open open circuit circuit voltage voltage varies. varies. *. ary t"e open circuit circuit voltage voltage until until t"e rated voltage voltage of t"e alternato alternatorr is reac"ed. C. Ta2ulat 2ulatee t"e valu values. es. %. Reduce t"e field current to a minimum value. B. No$ close close t"e TPST TPST s$itc", s$itc", to to ma=e t"e t"e armature armature terminals terminals s"ort circuite circuited. d. . ary t"e s"ort s"ort circuit current current until until t"e rated current current alternator alternator current current is reac"ed. reac"ed. !&. Ta2ulate Ta2ulate t"e values and Dra$ Dra$ t"e open circuit and s"ort circuit c"aracteristics. !!. !!. At any field current, measure open circuit circuit voltage and s"ort circuit current from grap". !+. T"e ratio of open open circuit circuit voltage voltage to s"ortcir s"ortcircui cuitt current current gives gives t"e value value of t"e positive impedance of t"e alternator. !/. ∴Positive sequence impedance
3Z!4 >9pen circuit voltage ( S"ort circuit current
- easurement o& Ne(ati/e Seuen$e Impe!an$e:!. 0onnec 0onnectt t"e circu circuit it as per t"e t"e circui circuitt diagram diagram+. +. +. S$itc" on t"e t"e D0 supply to circuit circuit after after c"ec=ing c"ec=ing connections. connections. /. Hring t"e t"e motor motor to t"e speed speed 2y using using field field regulator regulator of motor. motor. ). Apply Apply voltag voltagee to t"e t"e alterna alternator tor 2y using using ! ! Φ variac till t"e ammeter reads t"e rated current. *. Note Note do$n do$n t"e readin readings gs of voltme voltmeter ter and and ammeter ammeter.. C. Negativ Negativee seque sequence nce impedan impedance ce is is give given n 2y 2y Z+>(3√/I4 ' Measurement o& +ero Seuen$e Impe!an$e:-
!. 0onnec 0onnectt t"e circu circuit it as per t"e t"e circui circuitt diagram diagram/. /.
+. Jeep t"e field field terminals terminals of of t"e alternator alternator open open circuited. circuited. /. Apply reduced voltage voltage to alternator alternator t"rou t"roug" g" t"e t"e ! Φ variac. ). Note Note do$n do$n t"e value valuess of voltag voltagee 34 and and current current 3I4. 3I4. *. Zero Zero sequ sequenc encee impe impedan dance ce is given given 2y Z&>(3/ I4 Pre$autions:-
!. :oose :oose conne connecti ctions ons must must 2e avoide avoided. d. +. TPST s$itc" contact contact s"ould s"ould come come to touc" touc" in a simultaneo simultaneous us manner. manner. /. T"e sin single gle p"as p"asee vari variac ac s"ou s"ould ld 2e at minim inimum um posi positi tio on 2efo efore star starti tin ng t"e t"e eKperiment. ). -otor field regulator regulator must must 2e at minimum minimum resistance resistance position position.. *. 0onnection 0onnectionss must 2e 2e c"ec=ed c"ec=ed t"oroug" t"oroug"ly ly 2efore 2efore giving giving supply supply..
O0ser/ations:Positi/e seuen$e impe!an$e:a1Open $ir$uit test
S.no
1ield current If Amps Amps
01 S"ort $ir$uit test
Terminal voltage volts
S. no
1ield current If Amps Amps
S"ort circuit current Isc in Amps
Ne(ati/e seuen$e impe!an$e:-
S.no
oltage in olts
0urrent I in Amps
Z+ >
√/ I
Average Average Z+> LLL '
+ero seuen$e impe!an$e:-
S.no
oltage in olts
0urrent I in Amps
Z& > /I Average Z&> LLL '
Resu%t:Positive, Negative and Zero sequence impedances of alternator are measured. Z !>LLLL', LLLLLpu Z+>LLLL', LLLLLpu Z &>LLLL', LLLLLpu
Dis$ussions: !. +. /. ). *. C.
#"at is is meant meant 2y positive, positive, negativ negative, e, 8ero sequence sequence currentsM currentsM Define symmetrical symmetrical components components transformatio transformation n matriK. matriK. #"at is is meant meant 2y positive positive negative, negative, 8ero sequen sequence ce impedance impedancesM sM #"at #"at are t"e t"e adva advanta ntages ges of of pu quan quantit titiesM iesM :ist out out t"e assumpti assumptions ons made made in fault fault studies studies of po$er system net$or=. net$or=. Dra$ t"e t"e interconnecti interconnection on of sequence sequence net$or= net$or=ss for all s"unt s"unt faults faults on po$er po$er system system
net$or=. %. Dra$ 8ero 8ero sequence sequence net$or= net$or= of O( transform transformer. er. B. #"at is t"e order order of sequence sequence impedances impedances of 3a4 Tur2o Tur2o alternat alternator or 324 Fydro Fydro alternator. alternator. . #"at #"at is is s"ort s"ort circui circuitt - -AM
