1Georgia TechPSERC

Comprehensive Power System Reliability Assessment

A. P. Meliopoulos (GIT), D. Taylor (GIT), Fang Yang (GRA), George Stefopoulos (GRA), Chanan Singh (TAMU)

Comprehensive Power System Reliability Assessment

A. P. Meliopoulos (GIT), D. Taylor (GIT), Fang Yang (GRA), George Stefopoulos (GRA), Chanan Singh (TAMU)

2Georgia TechPSERC

• Objectives of Reliability Assessment

• Basic Observations

• Selective Enumeration Approach

• Important Advancements- Single Phase Quadratized Power Flow- Advanced Modeling Methods- Advanced Contingency Simulation Methods- Contingency Selection via Multiple Performance Indices- Remedial Actions

• Reliability Index Computations (Markov Models)

Outline

3Georgia TechPSERC

Reliability Assessment: Objectives

Identify Events that Will Results in Abnormal Conditions (Low Voltage, Congestion, etc.). Quantify the Frequency and Duration of Such Problems

Identify Sequence of Events/Outages That Will Result in Local Service Interruptions. Quantify the Number of Affected Customers, Lost Revenues, Frequency and Duration.

Identify Sequence of Events/Outages That Will Result in Wide Spread Service Interruptions/Blackouts. Quantify the Risk of Such Events.

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Basic ObservationsReliability Assessment ProblemsReliability Assessment ProblemsGeneration System ReliabilityGeneration System ReliabilityBulk System ReliabilityBulk System ReliabilityDistribution System ReliabilityDistribution System Reliability“Active” Distribution System Reliability“Active” Distribution System Reliability

m 0 1 2 3 4 5 6 ]P r[ mNG ≤ 2.0753e-7 3.4843e-6 2.9268e-5 1.6406e-4 6.9083e-4 0.0023 0.0065

]P r[ mNL ≤ 0.1352 0.4059 0.6767 0.8572 0.9474 0.9835 0.9955

m 0 1 2 3 4 5 6 ][# mNG ≤ 1 301 45,151 4.5e6 3.35e8 1.99e10 9.827e11 ][# mNL ≤ 1 2,001 2.0e6 1.3e9 6.66e11 2.66e14 8.85e16

Bulk System Reliability (NP Complete)Cumulative Probability and Number of States300 units (FOR=0.05), 2000 circuits (FOR=0.001)

ApproachesApproachesMonte Carlo SimulationMonte Carlo Simulation(Impractical for (Impractical for large systems)large systems)Selective EnumerationSelective Enumeration(Viable for (Viable for large systems)large systems)

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Reliability Assessment: Overall Computational Algorithm

Evaluated, Zero Contribution to Unreliability

Evaluated, Nonzero Contribution to Unreliability

Not Evaluated

Base Case

Wind-Chime SchemeAlgorithmStart

Base CasePeak Load

Option

Network SolutionApproach

System SimulationApproach

Remedial Actions

Effects Analysis

ContingencySelection/

EnumerationSLEVEL

Reliability Index Computation

Stop

Next Load Level

Next Contingency

StoreResults

A B

Define FeasibleContingencies

6Georgia TechPSERC

λij

λ jk

Sr

Syst

em L

oadi

ng S

tate

s

SystemTopology States

Evaluated Markov States Not Evaluated States

i

k j .),,(:

etcLOLVoltageEventS r

[ ]fST rPr=∑∑

∉∈∈

=rrr SkSjjk

Sjjpf

,

λ

Probability Index

Frequency Index Duration Index

Reliability Indices

[ ] ∑∈

=rSj

jr pSPr

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System Reliability IndicesA. Probability Indices

1. Service Failure Probability 2. Unsupplied Energy Probability

B. Expectation Indices 1. Service Failure Occurrences 2. Service Failure Duration 3. Expected Unsupplied Energy 4. Unserviced Customer Hours 5. Customer Interruptions

C. Bulk System Reliability Indices 1. Bulk Power Interruption Index 2. Bulk Power Energy Curtailment Index 3. Bulk Power Supply Average Curtailment Per Disturbance

D. Customer Interruption Indices 1. System Average Interruption Frequency Index 2. System Average Interruption Duration index 3. Customer Average Interruption Duration Index 4. Average Service Availability Index 5. Average Number of Customers Per Interruption

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Example Results: Selective EnumerationG G G G

+SEQ

G

+SEQ

+SEQ

+SEQ

+SE Q

+SE

Q+S

EQ

+SEQ

G1 G2 G4 G5

G3

S

S

S

BUS10 BUS80

BUS20 BUS70

BUS50

BUS60

BUS30

BUS90

BUS40

16.5(hrs/year)

102.2(hrs/year)

Service FailureDuration

16.6(per year)

76.2(per year)

Service FailureFrequency

0.03140.0614Service FailureProbability

Lower Bound

UpperBound

1,084Contingencies Screened as Noncritical

22Simulated Contingencies with Zero Contribution (probability of system failure)

30Simulated Contingencies with Nonzero Contribution (probability of system failure)

1,136Total Number of Considered Contingencies

9Georgia TechPSERC

Single Phase Quadratized Power Flow

g + j b u1 ( g + j b )

kkdk VjbguVjbgI ~)(~)(~1 +++=

dkPugugu −+= 21202

20 kVu −=

G

ykm

yskm yskmyk

Bus mBus k

IM ydk Sdk

OtherCircuits

Pgk + jQgk

Electric Load

FormulationKirchoff’s Current Law

Mostly Linear Equations

NonLinearNonLinear Component Example: Component Example: Constant Power LoadConstant Power Load

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ConnectivityConstraints

ConnectivityConstraints

Newton’sMethod

Newton’sMethod x(t)x(t)

Component Model

kkTk

kkTk

kkk

bxFx

xFx

xYi

−

+=

2

1

0

bxFx

xFx

Yx T

T

−

+=

2

1

00

SPQPF: Algorithm

1000

10

0.1

0.001

0.00001

0.00000010 1 2 3 4 5

Iteration Number

Mis

mat

ch A

fter I

tera

tion

205

0.08

7

0.00

94

0.00

0000

91

11Georgia TechPSERC

Electric Load Models

Load Types

Constant Impedance

Constant Power

Induction Motors

Load Control

Firm Load

Critical Load

Interruptible Load

CommentsCaptures CorrectSystem Response

CommentsProvide CapabilityTo Assess ImpactOf CustomerIncentives/LoadControl Programs

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Induction Motors Characteristics

CommentReactive Power Absorption VERY Sensitive to Motor Speed

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Contingency Simulation: Effects of Load ModelSteady State Operating Conditions

Constant Power LoadVmax=1.105, Vmin=0.955

50% Induction MotorsVmax=1.046, Vmin=0.908

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Contingency Simulation: Effects of Load DynamicsConditions Immediately After Fault Clearing

50% Induction Motors2% SlowDown During Fault

Vmax=1.01, Vmin=0.82

50% Induction MotorsVmax=1.046, Vmin=0.908

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Multiple Performance IndicesVoltage Security Index

∑

−=

j

n2

step,j

ave,jjjv V

VVWJ

∑

−=

j

n2

step,gj

ave,gjgjjq Q

QQWJ

∑∈

=)j(Km

jmgj QQ

Reactive Power Generation Index

Circuit-Loading Index

∑

=

km

n

km

kmkmC I

IWJ

2~

kmI Thermal limit of the transmission line km

( ) ( )22 ~Im~Re~kmkmkm III +=

( ) kikmsmikikmmrkrkmkm VbVVbVVgI −−−−= )()(~Re

( ) krkmsmrkrkmmikikmkm VbVVbVVgI +−+−= )()(~Im

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Reliability Assessment: Outage Model

Independent Outages

Common Mode Outages

Precise Modeling with the Introduction of

Outage Control Variable, u

Power System

i

.....

Pg1+s1Pgi(1-uc)ooPg2+s2Pgi(1-uc)oo

Pg3+s3Pgi(1-uc)oo Pg4+s4Pgi(1-uc)o

o

Pg5+s5Pgi(1-uc)o

o

Pgiuco

Pgk+skPgi(1-uc)oo k my1kmuc

y2kmuc

y1skmuc y1smkuc

y2smkucy2skmuc

(gkm + jbkm )uc

jbskmuc jbsmkuc

k m

17Georgia TechPSERC

Performance Index – Current Based More Realistic Ranking

))((~ ~~~

mkckmckmkckmskm VVujbugVujbI −++=

∑

=

km

n

km

kmkmC I

IWJ

2~

uc

(gkm + jbkm)uc

jbkms

BUS k BUS m

uc jbmks

= outaged iscomponent theif ,0.0

operationin iscomponent theif ,0.1u c

Contingency Selection – SPQPF Model

( )( )

( )( )

=

∂∂

0

~Im

~Re

0

~Im

~Re

0

mk

mk

km

km

c

II

II

uG

∂∂−

∂∂=

c

T

c

C

c

C

uGx

uJ

dudJ ˆ

n

km

kmkm

c

C

II

nWuJ

2~2

=

∂∂

1

ˆ−

∂∂

∂∂=

xG

xJx CT

ComputationalEfficiency

18Georgia TechPSERC

1

2

2-j10

(2-j8)uc

j0.1uc j0.1uc

Sd2

+−+−

−+−+

+++++−−−−−+++++

=

=

22

22

22

221

22

22

2

212

12221222

12221222

6

5

4

3

2

1

)105.0(

11083255.19.75.11225.19.75.11325

),(),(),(),(),(),(

),(

zVVzz

uVVuuu

uuVuVVuVuVVuuVuVVuVuVV

uxguxguxguxguxguxg

uxg

ir

ir

ciciircrr

ciciircrr

c

c

c

c

c

c

c

Traditional Power Flow

1zJ =

+−−−−+++−+−

=

=

5.1cos8sin2cos10sin2)109.7(3sin8cos2sin10cos24

),(),(

),(22222222

22

222222222

2

2

1

δδδδδδδδ

ccc

cc

c

cc uVuVVVVu

uVuVVVVuxguxg

uxg2

2

05.00.1

−= VJ

c

T

cc uuxgx

uJ

dudJ

∂∂−

∂∂= ),(ˆ

Quadratized Power Flow

Performance Index Based Ranking

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3P lot of Jv vs u

Control Variable u

Per

form

ance

Inde

x Jv

TP F and s imple QP F

QP F with one additional s ta te

QP F with twoadditional s ta tes

19Georgia TechPSERC

Contingency Selection – SPQPF Model

Test System Result of Ranking for the circuit loading index

Sun Wook Kang and A. P. Meliopoulos, “Contingency Selection via Quadratized Power Flow Sensitivity Analysis”, accepted for presentation and publication in the Proceedings of the IEEE/PES Summer Meeting, July 2002

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Remedial Actions

Control Options (u)Shunt Capacitor SwitchingShunt Reactor Switching Phase Shifter Adjustment MVAR GenerationGeneration Bus VoltageTransformer TapsFACTS ControlsLoad TransferMW Generation Area InterchangeInterruptible LoadFirm LoadCritical Load

∑∑∈∈

+=nonfreej

jjfreei

i ucuuxfMin )(),( µ

0),(: =uxGtosubject

0),( ≤uxh

maxmin uuu ≤≤

Special OPFLinearization via Co-StateLP SolutionVery Fast

Formulation

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Example Results: Effects of Load Model

+SEQ

G

S

+S E Q

+S E Q

G

S

+S E Q+S E Q

SS

G

+S E Q

G

S

S

+SEQ

S +S E Q

G

SS

+S E Q

+SEQ

S

S

+SEQ

S

+SEQ

S

S

+SEQ

S

G

S+SE Q

S

G

GG

G

G

G

G

+SE

Q

+SE Q

+SEQ

+S E Q

+SEQ

+SEQ

+SEQ

+SE Q+S

EQ

+SE

Q

+SEQ

+SEQ

+SEQ

+SEQ

+SEQ

+S E Q

+S E Q

+S E Q

+S E Q

G

GG

G

G

G

G

G

G

G

G

G G

GG

GG

G

GBUS170

BUS180 BUS210 BUS220

BUS160 BUS190 BUS200BUS230

BUS150 BUS140

BUS240

BUS30 BUS90

BUS10 BUS20

BUS40

BUS50

BUS100

BUS80

BUS60

BUS110

BUS130

BUS70

BUS120

Constant Power LoadSingle Contingencies

Probability of Voltage Problems: 0.031

50% Induction MotorsSingle Contingencies

Probability of Voltage Problems: 0.082

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Future Direction

Complete Prototype Program (Dec 2003)

Apply Method to a Realistic System

Apply Methodology to Identify System Vulnerabilities

(Risk Assessment,Sequence of Events that May Lead to Voltage Collapse,

Sequence of Events that may Lead to Blackout, etc.)

Extent Methodology to Probabilistic Congestion Management