Power System Analysis

Loadflows
Short Circuit Analysis
BUs Impedane matrix
Power System Stability are well explained.

1. POWER
SYSTEM
ANALYSIS
III B.TechII Semester
Course Teacher:
Dr. MAHABOOB SHAREEF SYED

2. Students should able to

Necessityofpowerflowstudies.

Derivationofstaticpowerflowequations.

Powerflowsolutionusing

Gauss-SeidelMethod

NewtonRaphsonMethod
(Rectangularandpolarcoordinatesform)

Decoupled

FastDecoupledmethods
Power Flow Studies

3. Students should able to
Power flow studies are undertaken for various reasons, some of
which are the following:
1.The line flows
2. The bus voltages and system voltage profile
3. The effect of change in configuration and incorporating new
circuits on system loading
4. The effect of temporary loss of transmission capacity and/or
generation on system loading and accompanied effects
5. The effect of in-phase and quadrativeboost voltages on system
loading
6. Economic system operation
7. System loss minimization
8. Transformer tap setting for economic operation
9.Possibleimprovementstoanexistingsystembychangeof
conductorsizesandsystemvoltages.
NECESSITY OF POWER
FLOW STUDIES

4. Students should able to

Loadflowstudiesareoneofthemostimportant
aspectsofpowersystemplanningandoperation.

Theloadflowgivesusthesinusoidalsteadystateofthe
entiresystem-voltages,realandreactivepower
generatedandabsorbedandlinelosses.

Sincetheloadisastaticquantityanditisthepower
thatflowsthroughtransmissionlines,itispreferto
callthisPowerFlowstudiesratherthanloadflow
studies.
NECESSITY OF POWER
FLOW STUDIES

5. Students should able to

Throughtheloadflowstudiesitcanbeobtainedthevoltage
magnitudesandanglesateachbusinthesteadystate.

itisrequiredtoheldthebusvoltageswithinaspecified
limits.

Oncethebusvoltagemagnitudesandtheiranglesare
computedusingtheloadflow,therealandreactivepower
flowthrougheachlinecanbecomputed.

Alsobasedonthedifferencebetweenpowerflowinthe
sendingandreceivingends,thelossesinaparticularline
canalsobecomputed.

Furthermore,fromthelineflowwecanalsodeterminethe
overandunderloadconditions.
NECESSITY OF POWER
FLOW STUDIES

6. Students should able to
Thepowersystemnetworkisasuchalargeinterconnected
network,wherevariousbusesareconnectedthrougha
transmissionlines.
Atanybus,complexpowerisinjectedintothebusbythe
generatorsandcomplexpowerisdrawnbytheloads.
ThecomplexpowerS
iatanybusiisgivenby,
WhereV
iisvoltageatbusiwithangleδ
i.
V
i=|V
i|∟δ
i=|V
i|(cosδ
i+jsinδ
i)
Y
ik=G
ik+jB
ik
POWER FLOW
EQUATIONS

7. Students should able to
POWER FLOW
EQUATIONS

8. Students should able to
POWER FLOW
EQUATIONS

9. Students should able to
Thegeneralpracticeinpower-flowstudiesisto
identifytypesofbusesinthenetwork.
Theloadflowproblemconsistsofdeterminingthe
magnitudesandphaseanglesofVoltagesateach
busandactiveandreactivepowerflowineachline.
Whilesolvingpowerflowproblem,thesystemis
assumedtobeoperatingunderbalancedcondition.
Thequantitiesassociatedwitheachbusare:δ
i,
|V
i|,P
iandQ
i.
TYPES OF BUSES

10. Students should able to
Dependinguponwhichtwovariablesare
specifiedapriori,thebusesareclassifiedinto
threecategories.
Loadbus:Anongeneratorbusiscalledload
bus.Atthisbus,therealpowerdemandand
reactivepowerdemands arespecified.The
parametersistobedeterminedareδ
iand|V
i|.A
loadbusisoftencalledasP-Qbus.
TYPES OF BUSES

11. Students should able to
VoltagecontrolledBus:Anybusofthesystem
atwhichthevoltagemagnitudeiskeptconstant
issaidtobevoltagecontrolled.
Ateachbustowhichthereisagenerator
connected,themegawattgenerationcanbe
controlledbyadjustingtheprimemover,andthe
voltagemagnitudecanbecontrolledbyadjusting
thegeneratorexcitation.
Thesebusesarethegeneratorbuses.
TYPES OF BUSES

12. Students should able to
Atthesebuses,therealpowergenerationand
voltagemagnitudesarespecified.Theothertwo
parametersδ
iandreactivepowershastobe
determined.
ThesebusesarealsocalledP-Vbus.
Someloadbuseswithcontinuousreactive
powervariationcapabilityarealsocalled
voltagecontrolledbusatwhichtherealpower
generationissimplyzero.
TYPES OF BUSES

13. Students should able to
SlackBus:Thisbusisalsocalledslackbusorswing
bus,whichistakenasreferencetotheentiresystem.
Thevoltageangleoftheslackbusservesas
referencefortheanglesofallotherbusvoltages.
Therealandreactivepowersarenotspecifiedat
thisbus.
GenerallyBus1isconsideredtobeaslackbus.
Thevoltagemagnitudeandphaseanglesare
specifiedatthisbus.
TYPES OF BUSES

14. Students should able to
Inanyloadflowstudy,thelossesinthesystem
cannotbeknownapriori,withoutthesolutionof
voltagesatallthebuses.
Theslackbussuppliesthedifferencebetweenthe
totalsystemloadpluslossesandthesumofthe
complexpowersattheremainingbuses.
Slackbusisageneratorbusasitneedstosupply
thelosses.
Thebusconnectedtothelargestgeneratingstation
isnormallyselectedasslackbus.
TYPES OF BUSES

15. Students should able to
TYPES OF BUSES

16. Students should able to
TheGSmethodismostpopulariterative
algorithmforsolvingnonlinearalgebraic
equations.
Ateverysubsequentiteration,thesolutionis
updatedtillconvergenceisreached.
Itisappliedtopowerflowproblemasdescribed
insubsequentsections.
GAUSS-SEIDEL
(GS) METHOD

17. Students should able to
GS METHOD

18. Students should able to
Startingfromaninitialestimateofallthebus
voltages,themostrecentvaluesofthebusvoltages
aresubstituted.
Oneiterationofthemethodinvolvescomputation
ofallbusvoltages.
Thevaluesoftheupdatedvoltagesareusedinthe
computationofsubsequentvoltagesinthesame
iteration.
Iterationsarecarriedouttillthemagnitudesofall
busvoltagesdonotchangemorethanthe
tolerancevalue.
GS METHOD

19. Students should able to
InGSmethod,numberofiterationsincreases
withincreaseofsizeofthesystem.
Itcanbereduced,ifthecorrectionsinvoltage
ateachbusisaccelerated.
Therefore,amultiplicationfactorcalled
accelerationfactor(α)isintroduced.
Generally,αistakenbetween1.6to2.0.
Awrongvalueofαmayleadtodivergence.
GS METHOD

20. Students should able to Problem
GS METHOD

21. Students should able to
InthefirststepformulateY
bus
Problem
GS METHOD

22. Students should able to Problem
GS METHOD

23. Students should able to Problem
GS METHOD

24. Students should able to Problem
GS METHOD

25. Students should able to Problem
GS METHOD

26. Students should able to Problem
GS METHOD

27. Students should able to
Case(ii):
IncaseofanyPVBusinasystem:
1.CalculateQatthatbus.
2.CalculateVbyusingaboveQvalue.
3.Since,itisaPVbus|V|=Vspecified,
butangleonlyhastobeupdated.
GS METHOD

28. Students should able to
Case(iii):
IncaseQlimitsspecifiedatPVBusinasystem:
1.CalculateQatthatbus.
2.CheckforQlimits,Ifthelimitsarenotsatisfied,
treatthatPVbusasPQbuswithQasfollows:
GS METHOD

29. Students should able to
Themostwidelyusedmethodforsolving
simultaneousnonlinearalgebraicequations.
NEWTON –RAPHSON
METHOD

30. Students should able to
NEWTON –RAPHSON
METHOD

31. Students should able to
NEWTON –RAPHSON
METHOD (Polar Co-ordinates)

32. Students should able to
NEWTON –RAPHSON
METHOD (Polar Co-ordinates)

33. Students should able to
Intheaboveequation,bus1isassumedtobe
slackbus.TheJacobianmatrixgivesthe
linearizedrelationbetweensmallchangesin
withsmallchangesinrealand
reactivepower Elementsofjacobian
matrixarethepartialderivativesofpowerflow
equations.Itcanbewrittenas:
NEWTON –RAPHSON
METHOD (Polar Co-ordinates)

34. Students should able to
NEWTON –RAPHSON
METHOD (Polar Co-ordinates)

35. Students should able to
NEWTON –RAPHSON
METHOD (Polar Co-ordinates)

36. Students should able to NEWTON –RAPHSON
METHOD (Rectangular Co -
ordinates)

37. Students should able to NEWTON –RAPHSON
METHOD (Rectangular Co -
ordinates)

38. Students should able to NEWTON –RAPHSON
METHOD (Rectangular Co -
ordinates)

39. Students should able to NEWTON –RAPHSON
METHOD (Rectangular Co -
ordinates)

40. Students should able to NEWTON –RAPHSON
METHOD (Rectangular Co -
ordinates)

41. Students should able to NEWTON –RAPHSON
METHOD (Rectangular Co -
ordinates)

42. Students should able to NEWTON –RAPHSON
METHOD (Rectangular Co -
ordinates)

43. Students should able to Problem
NR METHOD

44. Students should able to Problem
NR METHOD

45. Students should able to Problem
NR METHOD

46. Students should able to Problem
NR METHOD

47. Students should able to Problem
NR METHOD

48. Students should able to Problem
NR METHOD

49. Students should able to Problem
NR METHOD

50. Students should able to
Whensolvinglargescalepowersystem,analternativestrategyfor
improvingcomputationalefficiencyandreducingcomputer
storageisintroducedcalledDecoupledpowerflowmethod.
ThismakesuseofanapproximateversionofNRmethod.
Thebasicprincipleunderlyingthedecoupledapproachisbased
ontwoobservations:
Changeinthevoltageangleδatabusprimarilyaffectstheflowof
realpowerPinthetransmissionlinesandleavestheflowof
reactivepowerQrelativelyunchanged.
ChangeinthevoltagemagnitudeIVIatabusprimarilyaffectsthe
flowofreactivepowerQinthetransmissionlinesandleavesthe
flowofrealpowerPrelativelyunchanged.
Decoupled Load
flow

51. Students should able to
Thefirstobservationstatesessentiallythatis
dP/dδmuchlargerthandQ/dδ,whichwenow
considertobeapproximatelyzero.
ThesecondobservationstatesthatdQ/d|v|is
muchlargerthandP/d|V|,whichisalso
consideredtobeapproximatelyzero.
Incorporationoftheseapproximationsintothe
jacobian:
J
2=0andalsoJ
3=0;
Decoupled Load
flow

52. Students should able to Decoupled Load
flow

53. Students should able to
Theseequationsaredecoupledinthesensethatthe
voltage-anglecorrections∆δarecalculatedusingonly
realpowermismatches∆P,whilethevoltage-magnitude
correctionsarecalculatedusingonly∆Qmismatches.
However,thesetwointerdependent.
Butthisschemewouldstillrequireevaluationand
factoringofthetwocoefficientmatricesateach
iteration.
Toavoidsuchcomputations,weintroducefurther
simplifications,whicharejustifiedbythephysicsof
transmissionlinepowerflow.
Decoupled Load
flow

54. Students should able to
Inawell-designedandproperlyoperatedpower
transmissionsystem:
Theangulardifferences(δ
i-δ
j)betweentypical
busesofthesystemareusuallysosmallthat
Cos(δ
i-δ
j)=1;Sin(δ
i-δ
j)=(δ
i-δ
j);
The line susceptancesB
ijare many times larger
than the line conductances, G
ij so that,
G
ijSin(δ
i-δ
j) << B
ijCos(δ
i-δ
j) << B
ij
Fast Decoupled
Load flow

55. Students should able to Fast Decoupled
Load flow

56. Students should able to Fast Decoupled
Load flow

57. Students should able to Fast Decoupled
Load flow

58. Students should able to Fast Decoupled
Load flow -Problem

59. Students should able to Fast Decoupled
Load flow -Problem

60. Students should able to Fast Decoupled
Load flow -Problem

61. Students should able to Fast Decoupled
Load flow -Problem

62. Students should able to Limitations of GS
method

63. Students should able to Limitations & Merits
of NR method

64. Students should able to
TheBusimpedancematrix(Z
BUS)canbe
formulatedbytwomethods.
1.FormulatingY
BUSandtakingtheinverse.
2.Basedonalgorithm.
Byusingsystemparametersandcodedbus
numbers.
Constructionofthenetworkiscarriedoutby
addingoneelementatatime.
Z–BUS FORMULATION

65. Students should able to
Considerthefollowingpartialnetworkwith
‘m’no.ofbusesand‘0’asthereference
node.
Algorithm for
Z–BUS FORMULATION
Theperformanceequationinthe
busframeofreference:
E
BUS=Z
BUSI
BUS
E
BUSisthevectorofbusvoltagesofsize
mx1measuredw.r.toreferencenode.
I
BUSisthevectorofbuscurrentsofsize
mx1.

66. Students should able to
The voltage equations can be written as:
E
1= Z
11I
1+Z
12I
2+…..+Z
1kI
k+….+Z
1mI
m
.
.
E
k= Z
k1I
1+Z
k2I
2+…..+Z
kkI
k+….+Z
kmI
m
.
.
E
m= Z
m1I
1+Z
m2I
2+…..+Z
mkI
k+….+Z
mmI
m
ByinjectingthecurrentsatK
th
bus,bykeepingall
otherbuscurrentinjectionsas‘0’.
I
i = 0 , i≠k
Algorithm for
Z–BUS FORMULATION

67. Students should able to
E
k= Z
kkI
k
E
i= Z
ikI
k
Now I
k= 1.0 pu
E
k= Z
kk
E
i= Z
ik
The Z
Busformulation can be carried out in
two aspects.
Whenanelementp-qisaddedtothepartial
network,itmaybebranchoralinkas
showninfigures.
Algorithm for
Z–BUS FORMULATION

68. Students should able to
Algorithm for
Z–BUS FORMULATION
Pisanexistingbusin
apartialnetworkand
qisanewbus,this
results into p-q
branch.
Bothpandqare
existinginthepartial
networkinthiscase
p-qisalink.

69. Students should able to
Letusassume,theaddedbranchp-qismutually
coupledwithsomeelementsofthepartialnetwork.
Theperformanceequationwiththeaddedbranch
is:
Addition of a
Branch

70. Students should able to
Iftheelementsofthenetworkarebilateralpassive
elements:Z
qi=Z
iq
Addition of a
Branch
Where,Z
qiisthevoltage
atq
th
busbyinjecting
1.0pucurrentati
th
bus.
Thevoltageacrossthe
addedelementis:
V
pq=E
p-E
q

71. Students should able to
Thecurrentthroughtheelementpqis:
I
pq:Currentthroughtheelementpq
I
rs:Currentthroughtheelementsofpartialnetwork.
V
pq:Voltageacrosstheelementpq
V
rs:Voltageacrosstheelementsofpartialnetwork.
Y
pqpq=Selfadmittanceofaddedelement.
Y
pqrs=Vectorofmutualadmittancebetweenpq-rsof
partialnetworks.
Y
rsrs=Primitiveadmittanceofpartialnetwork
Y
rspq=[Y
pqrs]
T
Addition of a
Branch

72. Students should able to
Since pqis a branch, i
pq= 0 but V
pq≠ 0. V
rs= E
r–E
s
Addition of a
Branch

73. Students should able to
ToobtainZ
qq,inject1p.ucurrentatq
th
nodeandat
remaining‘0’
Addition of a
Branch

74. Students should able to Addition of a
Branch

75. Students should able to
Thelinkisanelementaddedinbetweentwo
existingbuses.
Addition of a
Link
Firstly,anvoltage
source ‘e
l’ is
connectedinseries
withtheadded
element.
This creates a
fictitiousnode'l'.
Thee
lisselected
suchthatI
pq=0.
Sothatthep-lis
treated as an
additionofbranch.

76. Students should able to
Theperformanceequationsaregivenby:
Addition of a
Link

77. Students should able to Addition of a
Link

78. Students should able to Addition of a
Link

79. Students should able to Addition of a
Link

80. Students should able to
Since,thenodelisaddedwhichisafictitious,itseffectisto
beeliminated.Mathematically,itcanbedonebyshort
circuitingtheseriesvoltagesource.
Addition of a
Link

81. Students should able to
FormZ
BUSforthenetworkshown.
Problem

82. Students should able to
Problem

83. Students should able to
Problem

84. Students should able to
Problem

85. Students should able to
Problem

86. Students should able to
Problem

87. Students should able to
Problem

88. Students should able to
Thechangeofbusimpedancematrixincludesinfollowing
cases:
Removalofelements:
ItcanbedonebymodifyingthealreadyexistingZbus.
Byaddinganelementinparallel,whoseimpedanceisequal
tonegativeoftheimpedanceoftheelementtoberemoved,if
theelementisnotmutuallycoupledtoanyoftheelementin
thepartialnetwork.
Thisisnothingbutadditionofalink.
Modification of Z-Bus

89. Students should able to
Changesintheimpedanceofelements:
BYaddinganlinkinparallelwiththeelementsuchthatthe
equivalentimpedanceofthetwoelementsisthedesired
value.
Modification of Z-Bus

90. Students should able to
•
Transients on a Transmission line-Short circuit
of synchronous machine(on no-load)
•
3–Phase short circuit currents and reactances
of synchronous machine
•
Short circuit MVA calculations
•
Series reactors and their Selection of reactors.
Symmetrical Fault
Analysis

91. Students should able to
•
Anumberofundesirablebutunavaoidable
incidentscantemporarilydisruptthis
condition.Suchincidentscanbesaidasa
fault.
•
Afaultinacircuitisanevent,whichcauses
adeviationfromthenormalflowofcurrent.
•
Thisdeviatesthepowersystembehavior.
Symmetrical Fault
Analysis

92. Students should able to
A fault may occur on a power system due to
number of reasons.
Some of them are listed below:
•
Insulationfailureofequipment
•
Flashoveroflinesinitiatedbylightning
stroke.
•
Fallingofatreealongaline.
•
Overloadingofundergroundcables.
•
WindandIceloadingonthetransmission
line.
•
Accidentalfaultyoperation.
Reasons for fault

93. Students should able to
•
Whenafaultoccursonasystem,thesystemgetshort
circuited.
•
Thecurrentflowingintothefaultdependsonthepath
metbythecurrent,ontheseverityandnearnessof
faulttothesourcesofpower.
•
Thesystemmustbeprotectedagainstflowofheavy
shortcircuitcurrents,otherwiseitleadstothedamage
ofelectricalequipment.
•
Thiscanbedonebyseparatingthefaultypartofthe
systemfromthehealthypartbyproperlyselecting
protectingdevice.
Faults

94. Students should able to
Basictwomaintypesoffaultsare:
Seriesfaults:Thefaultoccursthroughahighimpedance
inserieswiththeline.
Ex:Opencircuit,Thisoccurswhenacircuitbreakerora
lineisopened.
Shuntfaults:Inthistypealowimpedanceisconnected
betweenthelineandground.
Ex:Shortcircuitoflines.
Protectiverelaysareemployedtotripthecircuitbreaker
underfaultycondition.
Types of Faults

95. Students should able to
Theshuntfaultsareagainclassifiedinto:
1.Symmetricalfaults:
•
Inthisallthethreephasesareshortcircuitedto
eachotherandtotheearthalso.
•
Thesearebalancedandsymmetrical.
•
Thevoltagesandcurrentsremainsbalancedafter
theoccurrenceoffaultalso.
•
Itissufficienttoconsideronephaseforthefault
analysis.Ex:3-Phaseshortcircuitfaults.
Types of Faults

96. Students should able to
2.UnSymmetricalfaults:
Inthistypeonlyoneortwophasesonlyinvolvesin
afault.
Thevoltagesandcurrentsbecomesunbalanced
aftertheoccurrenceofthefault.
Eachphasehastobeanalyzedseparately,forthe
faultcurrentcalculations.
Ex:LinetoGround(LG),LinetoLine(LL/2L),
Doublelinetoground(LLG/2L-G).
Types of Faults

97. Students should able to
•
Thecomputation offaultcurrentsfor
unsymmetrical faultsinvolvesmethod of
symmetricalcomponents.
•
Frequencyoffaultsindecreasingseverity
Types of Faults
Type of fault Frequency of
occurrence
Three Phase faults 5 %
LLG 10 %
LL 15 %
LG 70 %

98. Students should able to
SYNCHRONOUS
MACHINE (ON NO LOAD)

99. Students should able to
SYNCHRONOUS
MACHINE (ON NO LOAD)

100. Students should able to
SYNCHRONOUS
MACHINE (ON NO LOAD)

101. Students should able to
SYNCHRONOUS
MACHINE (ON NO LOAD)

102. Students should able to
SYNCHRONOUS
MACHINE (ON NO LOAD)

103. Students should able to
SYNCHRONOUS
MACHINE (ON NO LOAD)

104. Students should able to
SYNCHRONOUS
MACHINE (ON NO LOAD)

105. Students should able to ShortCircuit
Capacity (SCC)

106. Students should able to ShortCircuit
Capacity (SCC)

107. Students should able to
Problems

108. Students should able to
Problems

109. Students should able to
Problems

110. Students should able to TRANSIENT ON A
TRANSMISSION LINE

111. Students should able to TRANSIENT ON A
TRANSMISSION LINE

112. Students should able to TRANSIENT ON A
TRANSMISSION LINE

113. Students should able to TRANSIENT ON A
TRANSMISSION LINE

114. Students should able to
Thecurrentlimitingreactorisaninductivecoilhavinga
largeinductivereactancesincomparisontotheir
resistanceandisusedfor

limitingshortcircuitcurrentsduringfaultconditions.

Reducethevoltagedisturbancesontherestofthe
system.
Itisinstalledinfeedersandties,ingeneratorsleads,and
betweenbussections,forreducingthemagnitudeof
shortcircuitcurrentsandtheeffectoftherespective
voltagedisturbance.
Current Limiting
Reactor

115. Students should able to
LocationofReactors

Reactorsarelocatedatdifferentlocationinapower
systemforreducingtheshortcircuitcurrent.These
reactorsmaybeconnectedinserieswiththe
generators,feedersorinbus-barsasexplainedbelow.
•
GeneratorsReactors
•
FeedersReactors
•
Bus-BarReactor
Current Limiting
Reactor

116. Students should able to
Generators Reactors
Generatorreactorsareinserted
betweenthegeneratorandthe
generatorbus.Such reactors
protectthemachinesindividually.
Inpowerstationgenerator,reactors
areinstalledalongwiththe
generators.Themagnitude of
reactorsisapproximatelyabout
0.05 perunit.The main
disadvantagesofsuchtypeof
reactorsarethatifthefaultoccurs
ononefeeder,thenthewholeofthe
systemwillbeadverselyaffectedby
it

117. Students should able to
Feeder Reactors
Reactors,whichisconnectedin
serieswiththefeederiscalled
feedersreactor.Whenthefault
occursonanyonefeeder,then
thevoltagedropsoccuronlyinits
reactorsandthebusbarisnot
affectedmuch.Hence the
machinescontinuetosupplythe
load.Theotheradvantageisthat
thefaultoccursonafeederwill
notaffecttheothersfeeders,and
thustheeffectsoffaultare
localized
Thedisadvantageofsuchtype
ofreactorsisthatitdoesnot
provideanyprotectiontothe
generatorsagainstshortcircuit
faultsoccursacrossthebus
bars.Also,thereisaconstant
voltagedropandconstant
powerlossinreactorsduring
normaloperatingconditions.

118. Students should able to
Bus-BarReactors(RingSystem)
Bus-barreactorsareusedtotietogetherthe
separatebussections.Inthissystemsections
aremadeofgeneratorsandfeedersandthese
sectionsareconnectedtoeachothertoa
commonbusbar.
Insuchtypeofsystemnormallyonefeederisfed
fromonegenerator.Innormaloperating
conditionsasmallamountofpowerflows
throughthereactors.Thereforevoltagedropand
thepowerlossinthereactorislow.Thebusbar
reactor,therefore,madewithhighohmic
resistancesothatthereisnotmuchvoltagedrop
acrossit.
Bus-Bar Reactors

119. Students should able to
Bus-Bar Reactors
Whenthefaultoccursonany
one feeders,onlyone
generatorfeedsthefaultwhile
thecurrentoftheother
generatorislimitedbecause
ofthepresenceofthebus-bar
reactors.
Theheavycurrentandvoltage
disturbancescausedbya
shortcircuitonabussection
arereducedandrestrictedto
thatfaultysectiononly.The
onlydrawbackofsuchtypeof
reactoristhatitdoesnot
protect the generators
connectedtothefaulty
sections.

120. Students should able to
Bus-bar Reactors (Tie-
Bus System)
Thisisthemodificationoftheabove
system.Intie-bussystem,the
generatorisconnectedtothe
common bus-barthroughthe
reactors,andthefeederisfedfrom
generatorside.
Theoperationofthesystemis
similartotheringsystem,butithas
gotadditionaladvantages.
Inthissystem,ifthenumberof
sectionsisincreased,thefault
currentwillnotexceedacertain
value,whichisfixedbythesizeof
theindividualreactors

121. POWER SYSTEM STABILITY

122. Stability
•Definition (IEEE / CIGRE):
Powersystemstabilityistheabilityofanelectric
powersystem,foragiveninitialoperatingcondition,
toregainastateofoperatingequilibriumafterbeing
subjectedtoaphysicaldisturbance,withmostsystem
variablesboundedsothatpracticallytheentire
systemremainsintact.
•Thedisturbancesmentionedinthedefinitioncouldbe
faults,loadchanges,generatoroutages,lineoutages,
voltagecollapseorsomecombinationofthese.

123. Classification of Power system
stability

124. •Thestudyofsteadystatestabilityisbasicallyconcernedwith
thedeterminationoftheupperlimitofmachineloadings
beforelosingsynchronism,providedtheloadingisincreased
gradually.
•Thesystemissaidtobedynamicallystableiftheoscillations
donotacquiremorethancertainamplitudeanddieout
quickly.
–Dynamicstabilitycanbesignificantlyimprovedthroughtheuseof
powersystemstabilizers.
•Foralargedisturbancesinangulardifferencesmaybeso
largeastocausethemachinestofallingoutofstep.This
typeofinstabilityisknownastransientinstabilityandisa
fastphenomenon.

125. Stability Classification

126. Dynamics of a synchronous Machines
•Inertiaconstant:Itisdefinedastheratioof
energystoredinmegajoulestotheratingofthe
machinesinMVA.
•Energystored=HxG
•Kineticenergystoredbytherotatingbodyis
givenby:

127. •On comparing above 2 expressions,

128. Swing Equation
•TheSwingEquationofa
generatordescribesthe
relativemotionbetween
therotoraxisandthe
synchronouslyrotatingstator
filedaxiswithrespecttotime.
•itdescribestherotordynamicsforasynchronousmachine.
•Itisasecond-orderdifferentialequation.
•Thisequationisveryhelpfulinanalyzingthestabilityof
connectedmachines.

131. It is called the swing equation.

132. Swing Equation for coherentMachines:

133. Swing Equation for Non -coherent
Machines:

135. Power –Angle Curve

140. Steady state stability –Small Disturbances

143. Transient Stability
•Itinvolvestofindwhetherthesystemretaineditssynchronism
aftermachinehasbeensubjectedtoseveredisturbances.
•Thedisturbancesmaybesuddenapplicationofload,lossof
generation,lossoflargeloadoroccurrenceoffaultona
system.
•Intheseinstantstheswingequationbecomeshighlynon
linearanddifficulttosolve.
•AmethodknownasEqualAreaCriterionisusedforaquickly
predictionofstability.
•Thismethodisapplicabletoonemachineconnectedtoinfinite
busortwomachinesystem.

144. Equal Area Criterion

145. Applications of Equal Area Criterion
TheEqualAreaCriterioncanbeimplyinthefollowing
casesandthetransientstabilityanalysiscanbe
performed.
•Suddenchangeinmechanicalinput.
•Suddenlossofoneoftheparallellines.
•Suddenshortcircuitononeoftheparallellines.
Shortcircuitatoneend
Shortcircuitawayfromthelineends

146. Sudden change in mechanical input
•Consider the following system SMIB.
•The electrical power transmitted is given by

149. Critical clearing time and Critical clearing angle
•ConsiderasystemoperatingwithmechanicalinputP
m
atsteadyangleofδ
0.
•Ifa3phasefaultoccursatpointpoftheoutgoing
radialline,theelectricaloutputofthegenerator
instantlyreducestozero.i.e.P
e=0.

161. Methods to improve Steady State Stability
1.Reductionoftransferreactance
•Apowersystemwhichhasalowervalueoftransferreactancecan
havebettersteady-statestabilitylimit.Thiscanbeachievedby:
i)useofparallellines
ii)useofseriescapacitors
•Ifthepowerhastobetransferredthroughlongdistance
transmissionlines,useofparallellinesreducetransferreactanceas
wellasimprovevoltageregulations.
•Similarlyseriescapacitorsaresometimesemployedinlinestoget
thesamefeatures.
2.IncreaseinthemagnitudesofEandV.
Higherandfastfieldexcitationsystemenhancessteady-state
powerlimits

162. Methods to improve Transient stability
•Transientstabilityofthesystemcanbeimprovedbyincreasingthesystemvoltage.
•IncreaseintheX/Rratiointhepowersystemincreasesthepowerlimitoftheline.Thus
helpstoimprovethestability.
•Highspeedcircuitbreakershelpstoclearthefaultasquickaspossible.Thequickerthe
breakeroperates,thefasterthefaultclearedandbetterthesystemrestorestonormal
operatingconditions.
•ByTurbinefastvalving:Oneofthemainreasonfortheinstabilityinthepowersystemis
duetotheexcessenergysuppliedbytheturbineduringthefaultperiod.FastValvinghelps
inreducingthemechanicalinputpowerwhenthegeneratorisunderaccelerationduring
thefaultandhenceimprovesthestabilityofthesystem.
•UseofAutoRe-closing:Majorityofthefaultsinthepowersystemwillbemomentaryand
canbeselfcleared.Hencecircuitbreakersemployedforfaultclearanceopensinsensing
thefaultwithtimedelayof2cyclesandre-closesafterparticulartimetodeterminewhether
the fault is cleared.
•Some oftheotherways toimprove thetransientstabilityareby
employinglightningarresters,highneutralgroundingimpedance,singlepoleswitching,
quickAutomaticVoltageRegulators.

163. Problems