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Power System Stability and

Control

1 – General Background

1

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2

Outline

•

Structure of a power system• Introduction of power system stability (basic concepts,

definitions and examples)

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3

1st 100 Years of Electric ndustry

• 1882: Pearl Street Station, te 1st !" system by #dison, operated in $%"

•

188&: "ommercially practical transformer and '" distribution systemdeeloped by Stanley• 1888: !eelopment of polypase '" by *esla started '" s+ !"

battle

• 188: 1st '" transmission line in te -S (1pase, 21.m at /.0 in

reon)• 183: 1st 3pase line (2+3.0, 12 .m by S"#) in $ort 'merica '" s+

!" battle ended wen '" was cosen at $iaara 4alls+• 112123: 1st 115.0 and 225.0 60'" oeread lines• 175s: 3/7.0/55.0 #60 '" lines by -S', ermany and Sweden

• 17/: 1st modern commercial 60!" transmission (&.m submarinecable) in Sweden+

• 1&5s: 9379&7.0 #60 '" in ussia, -S' and "anada

• 192: 1st tyristor based 60!" ;ac.*o;ac. system between

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Structure of an !C Power System

• Generation

–"ow #oltages $%&k' dueto insulation

re(uirements

• )ransmission system

– Backbone system

interconnecting ma*or

+ower +lants ,11-..k'/

and load center areas

– 1.%k' %%0k' .&k'

&00k'

23&k' etc4

• Sub5transmission system – )ransmitting +ower

to distribution

systems

– )y+ically ..633k'5

1.%k'• 7istribution system /

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P89POSE O: )9!;S4 S)!B4 S)87Y

*o predict ability of en+

*o recoer and remain connected to powersystem after a fault+

*o assess interaction of ens and oter rotatinplant (=*) connected to networ. after fault+

*o ensure minimum oltae disturbance due toloss of syncronism

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&

Bulk Power System ,Bulk Electric System/

• !efinition

– *e bul. electric system is a term commonly applied to te portionof an electric utility system tat interates sub transmission system connectin – +ower +lants

– ma*or substations and

– >' transmission lines

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9eliable Electric Power Su++ly

•e?uirements under bot normal andemerency conditions – 0oltae and fre?uency control around normal

alues witin close tolerances

@ enerators runnin syncronously wit ade?uatecapacity to meet te load demand

@ *e AinterityB of te bul. power networ.

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9eliability of Bulk Power Systems

•

4rom bot Plannin and perations perspecties: – Power systems sould be built and operated to aciee a reliableelectric power supply at te most economical cost

• eliability is defined usin two terms: @ 'de?uacy (plannin): *e ability of te electric systems to

supply te areate electrical demand and enery re?uirements ofteir customers at all times, taking into account sc=eduled andreasonably e?+ected unsc=eduled outaes of system elements+

@ Security (operation): *e ability of te electric systems towitstand sudden disturbances, i+e+ contingencies suc= aselectric s=ort circuits or unantici+ated loss of systemelements4

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>ow are reliability standards used@

•

In Plannin: @ eliability standards sould neer be

iolated in desinin te system+• In perations:

@ eliability standards sould neerbe intentionally iolated

@ Sometimes, iolations occur due to mis

operations or delayed awareness of te realtime situation

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9elated )erms57efinations

• O+erating (uantities: Pysical ?uantities (measuredor calculated) tat can be used to describe teoperatin conditions of a power system, e++

• real,• reactie and

• apparent powers,• CS alues>pasors of alternatin oltaes and• currents+

D Steadystate operatin condition of a power system: 'noperatin condition of a power system in wic all teoperatin ?uantities tat caracteriEe it can be consideredto be constant for t=e +ur+ose of analysis+

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D In desinin and operatin an interconnected powersystem, its dynamic performance subFected to canes(i+e+ continencies, small or lare) is considered

D It is important tat wen te canes are completed, tesystem settles to new operatin conditions witout

iolation of constraints+

D In oter words, not only sould te new operatin

conditions be acceptable (as reealed by steadystateanalysis) but also te system must surie te transitionto tose new conditions+ *is re?uires dynamic analysis+

11

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• 7isturbanceA a sudden c=ange or a se(uence of c=anges in one

or more +arameters or o+erating (uantities of t=e +ower system

i4e4 real,• reactie and

• apparent powers,• CS alues>pasors of alternatin oltaes and• currents

• Small and large disturbances

–a small disturbance if t=e e(uationsdescribing t=e dynamics of t=e system

may be linearied for t=e +ur+ose of

accurate analysis e4g4 a load c=ange

P

– a large disturbance if t=e e(uations t=atdescribe t=e dynamics of t=e system

cannot be linearied for t=e +ur+ose of

accurate analysis e4g4 a s=ort circuit

and loss of a generator or load4

δ

P (δ)

12

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9elated )erms ,contd/

• Sync=ronous o+erationA

– ! mac=ine is in sync=ronous o+eration wit= anot=er

mac=ine or a network to w=ic= it is connected if its a#erage

electrical s+eed ,D r P 6%/ is e(ual to t=e electric s+eed of t=e

ot=er mac=ine or t=e angular fre(uency of t=e ac network4

– ! +ower system is in sync=ronous o+eration if all its

connected sync=ronous mac=ines are in sync=ronous

o+eration wit= t=e ac network and wit= eac= ot=er4

• !sync=ronous o+erationA loss of sync=roniation orout of ste+

13

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Stability of linear dynamical systems canbe determined from +oles6eigen #alues+

"omplicated soundin terms li.e eienalues and determinant can be deriedfrom alebra alone+

Stability of nonlinear dynamical systemscan be locally ealuated usin eienalues+

Stability of linear dynamical systems

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15

7efinitions

Sync=ronous O+eration:Synchronous Operation of a Machine: A

machine is in synchronous operation with anetwork or another machine(s) to which it isconnected if its average electrical speed(product of its rotor angular velocity and the

number of pole pairs) equals the angularfrequency of the ac network or the electricalspeed of the other machine(s)Synchronous Operation of a !ower System: Apower system is in synchronous operation if allits connected synchronous machines are insynchronous operation with the ac networkand with each other

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16

7efinitions

!sync=ronous or nonsync=ronous o+eration:

Asynchronous Operation of a Machine: A machineis in asynchronous operation with a network or anothermachine to which it is connected if it is not insynchronous operation.

Asynchronous Operation of a !ower System: Apower system is in asynchronous operation if one ormore of its connected synchronous machines are inasynchronous operation.

>unting of a ac=ine: ' macine is untin if any of itsoperatin ?uantities experience sustained oscillations+

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What will your system do(according to eigenvalue

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"ponential increase (unsta#le$ncrease w% oscillation (unsta#le

&ta#le oscillation

'ecay w% oscillation (&ta#le!"ponential decay (&ta#le

What will your system do(according to eigenvalue

All λs are real andnegative%

ritically%overdamped

All λs are real and atleast one positive

All λs have negativereal parts) someimaginary parts

*nderdamped

At least one λ has positivereal parts) some

imaginary parts

All λs have +ero realparts and non+eroimaginary parts%*ndamped

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1

Power System Stability

• Power system stability is t=e ability of a +ower system for a gi#en

initial o+erating condition to regain an acce+table state of

o+erating e(uilibrium ,i4e4 t=e new condition/ after being sub*ected

to a disturbance

D Considering an interconnected +ower system as a w=ole

– )=e stability +roblem wit= a multi5mac=ine +ower system ismainly to maintain sync=ronous o+eration of t=e mac=ines

,generators or motors/

D Considering +arts of t=e system

@ ! +articular generator or grou+ of generators may losestability ,sync=ronism/ wit=out cascading instability of t=e

main system4

@ otors in +articular loads may lose stability ,run down andstall/ wit=out cascading instability of t=e main system4

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25

Stability Classification

• EEE6CG9E Foint )ask :orce on Stability )erms and 7efinitions

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Stability Classification

Pysical nature

!isturbance siEe

*ime span

21

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7E:;)O; O: S)!B")Y

S)E!7Y S)!)E S)!B")Y 'bility of Pow+ Sys+ to remain

stable after a small disturbance e+ load disturbance,switcin+)9!;SE;) S)!B")Y @ ability of Pow+ Sys+ to maintainsyncronism after a seere transient disturbance+ #++ Sort"ircuits, loss of load or en+

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S)!B")Y C>!""E;GES

"'-S#S

S6* "I"-I*S

GSS 4 *I# GI$#S I$ -*IGI*%

$#*=HGSS 4 #$#'*I$

S=I*"6I$ P#'*I$S 4 GI$#S,"'P'"I*S #*"+

S-!!#$ G'# S*#P "6'$# 4

#$#'*I$

"$S#

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,-

System 7ynamic PerformanceIn desinin and operatin te interconnected power networ.,system dynamic +erformance is ta.en into account because:

*e power system is subFected to canes (small and lare)+ It is important tat wen te canes are completed, tesystem settles to new operatin conditions suc tat noconstraints are #iolated4

$ot only sould te new operatin conditions be acceptable (asreealed by steadystate analysis) but also te system mustsur#i#e t=e transition to tese conditions+ *is re?uiresdynamic analysis+

)>E JEY S )>!) )>E GE;E9!)O9S CO;);8E )O OPE9!)E 9O;S O9 ;O) )O

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27

oltage &ta#ility

• $t refers to the a#ility of a powersystem to maintain steady

voltages at all #uses in the systemafter #eing su#/ected to adistur#ance.

• $nsta#ility may result in the form ofa progressive fall or rise ofvoltages of some #uses.

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2&

oltage &ta#ility ont0

• ossi#le outcomes of thisinsta#ility :

– 2oss of load in an area – 3ripping of lines and other elements

leading to cascading outages• 2oss of synchronism of some generators

may result from these outages or fromoperating condition that violate 4eldcurrent limit

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oltage &ta#ility ont..

• 'riving orce for oltage insta#ility(usually loads: – 3he power consumed #y the loads is

restored #y• 'istri#ution oltage regulators

• 3apchanging transformers

– A run down situation causing voltage

insta#ility occurs when the load dynamicsattempt to restore power consumption#eyond the capa#ility of the transmissionnetwork and the connected generation

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• $t involves: &mall and 2argedistur#ance as well as &hort 3erm

and 2ong 3erm time scales – &hort 3erm: $nvolves fast acting load

components : induction motors)!lectronically controlled loads ) 7'converters • &hort circuits near loads are important

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2


– 2ong 3erm:• "nvolves slow acting equipment:

–#ap changing transformers –#hermostatically controlled loads

eg heaters –$enerator current limiters

• "nstability is due to the loss of long%

term equilibrium• "n many cases static analysis can be

used• &or timing of control 'uasi%steady%

state time domain simulation isrecommended

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8o lights on9 Watts total(room is darkoltage is normal

ne light on1- Watts total(some light in roomoltage drops some

3wo lights on,9 Watts total(room gets #righteroltage drops more

3hree lights on,; Watts total(room gets #righteroltage drops more

our lights on,- Watts total(room gets #righteroltage drops more

ive lights on,5 Watts total(room gets #righteroltage drops more

&i" lights on,- Watts total (room gets darkeroltage drops more

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>omework L1• Gearn te I### paper A!efinition and "lassification of Power System StabilityB

• Select 1 Fournal paper publised by I### or any 6#" reconiEed Fournal since2515 tat introduces or addresses some stability problems on power systems

– Source: ttp:>>ieeexplore+ieee+or or ttp:>>scolar+oole+com – Heywords: e++ Apower systemB AstabilityB

• =rite a 12 paes essay : – *itle, autors, source of te paper – ;ac.round:

• =at stability problem is concernedJ (=ic I### cateoriesJ)• =y is te problem sinificantJ ('ny realworld storiesJ)• In wic aspect(s) was te problem not addressed well in earlier literatureJ

– 'pproac• =at new approac is proposedJ (utline of te procedure or steps)• 'ny .ey tecni?ues are applied by te approacJ• 6ow does te new approac performJ

– emar.• 'ny conclusions from te wor., or any room for furter wor.

• ie a 37 minutes tal. on your cosen paper and and in your essay ard copyin te class of Car 2& (Saturday)+ Please email me te paper title by Car 1

(=ed+) at Km+eFaE+asanLmail+comM

http://ieeexplore.ieee.org/http://scholar.google.com/http://scholar.google.com/http://ieeexplore.ieee.org/

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9otor !ngle Stability

• 9otor !ngle Stability refers to t=e ability of sync=ronous

mac=ines of an interconnected +ower system to remain insync=ronism after being sub*ected to a disturbance4

• P=enomenonA increasing angular swings of some generators

leading to t=eir loss of sync=ronism wit= ot=ers4

33

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9otor !ngle Stability ,contd/

• 9otor angle stability de+ends on t=e ability to maintain6restore

e(uilibrium between electromagnetic tor(ue ,)E/ and

mec=anical tor(ue ,)/ of eac= sync=ronous mac=ine in t=e

system4

• ! fundamental factor in t=is +roblem is t=e manner in w=ic= t=e

+ower out+uts of sync=ronous mac=ines #ary as t=eir rotor angles

c=ange ,Power #s4 9otor angle/

3/

SY;C>9O;O8S GE;E9!)O9S

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Power and )or(ue

A*+,"a-a ,./S "a

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Power and )or(ue

eal elect+ output power of syn+ en+in line to line 'oltage (uantities:

PoutNO3 0G IG cos in P=ase to ;eutral i4e4 Single +=ase 'oltage (uantities:

PoutN3 0Q I ' cos

reactie power output:

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Power and )or(ue

# 'N0Q FRS I '

PN3 0Q I ' cos*e ertical sement bc is # ' sin N RS I ' cos I ' cos N # ' sin > RSSubstitutin tis in e?uation of Pout

P N 30Q # ' sin > RS

A*+,"A-A ,./S "A


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Power and )or(ue

PeN3 0Q I ' cos*e ertical sement bc is # ' sin or RS I ' cos I ' cos N # ' sin > RSSubstitutin tis in e?uation of Pout Pe N 30Q # ' sin > RS

since resistances assumed ero losses not included in t=ise(uation ,M it is bot= Pcon# Pout/!bo#e e(uation s=ows +ower +roduced by a Syn4 Gen4de+ends on angle N ,between 'E!/ t=e tor(ue anglea?imum +ower t=at Gen4 can su++ly occurs w=en NDH04!t t=is angle sinND1

Pema?D.' E! 6 QS

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Power and )or(ueCaximum power in last e?uation called Astatic stability limit ofen+eal or practical en+ neer et close to tis limitIf 0Q assumed constant, real power output directly proportional toI ' cos and # ' sin*ese are useful for plottin pasor diaram of Syn+ en+ as loadcanes

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9otor !ngle Stability ,contd/ E ∠δ V ∠0

s

E V

X P 3

φ

sin

δ = 3

s

E V

X P max(3φ )= 3

e

ω ω X

s

P

T =3φ

E V

= 3 sin

δ

s

E V T

e,max

= 3

ω X

T e( P

3φ )

T m

Steadystate limit:

T a=T m-T eM5(accelerates)

T a=T m-T eK5(decelerates)

δ0

Unstable

Garedisturbance

/5

Smalldisturbance

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/1

Small signal stability

• Smalldisturbance anle stability or small sinal stabilityis te ability of a power system to maintain

syncronism under small disturbances+ – *e disturbances are considered to be sufficiently

small tat lineariEation of system e?uations ispermissible for purposes of analysis

– Small sinal stability depends on te initial operatinstate of te system (eienalues of te lineariEedsystem at te state)+

– In todayTs power systems, te smallsinal stabilityproblem is usually associated wit insufficient dampinof oscillations

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/2

Small signal stability ,contd/

• Small signal stability +roblems may be eit=er

local or global in nature4

– "ocal +lant mode oscillations ,at 042-%40>/A oscillations of a

small +art of t=e +ower system ,ty+ically a single +ower

+lant/ against t=e rest of t=e system

– nter5area mode oscillations ,at 041-042>/A oscillations of agrou+ of generators against t=e rest of t=e system

• )=e time frame of interest is 10 to %0 seconds

following a disturbance4 >owe#er oscillations maylast se#eral minutes

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/3

)ransient Stability

• Garedisturbance anle stability or transient stability is

concerned wit te ability of te power system to maintainsyncronism wen subFected to a seere disturbance, e++ asort circuit on a transmission line+

– *e resultin system response inoles lareexcursions of enerator rotor anles and is influenced byte nonlinear poweranle relationsip+

@ *ransient stability depends on bot te initial operatinstate of te system and te seerity of tedisturbance+

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//

)ransient Stability ,contd/

• *ransient instability is usually in te form of aperiodicanular separation, wic is often referred to as firstswin instability+

D 6oweer, in lare power systems, transient instability mayoccur after multiple swins as a result of, e++,

superposition of multiple oscillation modes+

D *e time frame of interest in transient stability studies isusually 3 to 7 seconds followin te disturbance+ It mayextend to 1525 seconds (to obsere a number of swins)for ery lare systems wit dominant interarea

oscillations+

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/7

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8o lights on9 Watts total(room is darkoltage is normal

ne light on1- Watts total(some light in roomoltage drops some

3wo lights on,9 Watts total(room gets #righteroltage drops more

3hree lights on,; Watts total(room gets #righteroltage drops more

our lights on,- Watts total(room gets #righteroltage drops more

ive lights on,5 Watts total(room gets #righteroltage drops more

&i" lights on,- Watts total (room gets darkeroltage drops more

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'oltage Stability• 'oltage stability refers to t=e ability of a +ower system to

maintain steady #oltages at all buses in t=e system after being

sub*ected to a disturbance from a gi#en initial o+eratingcondition4

– t de+ends on t=e ability to maintain6restore e(uilibrium

between load demand and su++ly

– n order words it de+ends on t=e ability to maintain bus

#oltages so t=at w=en t=e system nominal load at a bus isincreased t=e real +ower transferred to t=at load will

increase4

/9

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'oltage Stability ,contd/

• )=e term #oltage colla+se is also often used4 t is t=e

+rocess by w=ic= t=e se(uence of e#ents

accom+anying #oltage instability leads to a blackout or

abnormally low #oltages in a significant +art of t=e

+ower system4

/8

' l S bili , d/

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/


• Small5disturbance #oltage stability

– ability to maintain steady #oltages w=en sub*ected to

small +erturbations suc= as incremental c=anges in

system load4

– studies using linearied models for sensiti#ity

analysis

• "arge5disturbance #oltage stability

@ ability to maintain steady #oltages following largedisturbances suc= as system faults loss of generation or

circuit contingencies4

@ studied using nonlinear models on in#ol#ed de#ices e4g4motors transformer ta+ c=angers generator field5current

limiters etc4

' lt St bilit , td/

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75


• S=ort5term #oltage stability

–

in#ol#es dynamics of fast acting load com+onents e4g4induction motors electronically controlled loads and

>'7C con#ertors4

– )=e study +eriod of interest is in t=e order of se#eral

seconds

–re(uires solution of a++ro+riate system differentiale(uations

• "ong5term #oltage stability

@ in#ol#es slower acting e(ui+ment e4g4 ta+5c=angingtransformers t=ermostatically controlled loads and

generator current limiters4

@ t=e study +eriod of interest may e?tend to se#eral or manyminutes

@ re(uires long5term simulations

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;+ ao, et al, A*owards te deelopment of a systematic approac for oltae stability assessmentof larescale power systems, I### *rans+ Power Systems, 0ol+ 11 $o+ 3 'u+ 1&

71

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72

System O+eration

• Establis= most economical o+erating conditions under

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73

System Stability Studies)y+es !++roac= Pur+oses

Smallsinal

stability

• -sin linear system analysistools to study te modal system

response to a small disturbance+• !etails on te disturbance may

not be important

• btain safe operatin limits and uidelines

• Identify poorly damped modes of

oscillation• Settin of controls (e++, exciters, power

system stabiliEers)

*ransientstability

• -sin nonlinear system analysistools to study te system

response to a lare disturbance+

• *raditionally usin timedomainsimulation to Atrac.B te eolutionof system states and parametersdurin te transient period+

• #ery study is for a completelyspecified disturbance scenario

includin te predisturbancesystem condition anddisturbance se?uence (anycane re?uires a new study)

• $ew eneration studies (to meet reliabilitycriteria at te least cost)

• *ransmission plannin studies (to analyEeplans for future transmission expansion,and to meet reliability criteria)

• perations plannin studies (to cec. if aien system confiuration or operationsscedule meets reliability criteria)

• Special control to maintain stability (e++,

eneration trippin, load seddin, etc+)• Seere disturbance (extreme continency)

studies

• Special purpose studies (e++, systemblac.start or restoration plan, etc+)

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7/

)rends

• :ewer >' transmission lines built due to cost and

en#ironmental concerns

• >ea#ier use of some +ower +lants away from load centers

due to conser#ation of oil and natural gas

• >ea#ier loading of >' transmission due to growing electricity

markets under t=e '7C systems and solid state electronic de#ices

,e4g4 fle?ible ac transmission systems or :!C)S/

Structure of a Power System

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Structure of a Power System

and !ssociated Controls

2. Bkgrd SnC

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