Power System Vulnerability

FailureAnalysis

Information&

Sensing Vulnerability Assessment

Self Healing Strategies

StrategyDeployment

GPS

Sate

llite

LE

O

Sate

llite

Intr

anet

Inte

rnet

Power System Operating States

Early version by T. DyLiaccoThis version byL. Fink, K. Carlsen, IEEE Spectrum, March 1978 Slide by Areva T&D, 2006

Secure

System not intact System intact

System splitting and/or load lossIn extremis

Cut losses, Protect Equipment

Emergency

AlertRestorativeResynchronization Preventive Control

Heroic Action

Violation of inequality constraints

Reduction in reserve margins and/or increased probability of disturbance

E I

E I E I

E I

NormalLoad tracking, cost minimization, system coordination

E I

E = demand suppliedI = constraints met

Background� Electric power grid is considered a

national security matter� The reliable operation of the system is

of top priority to society.� Reliability concerns are amplified by the

utility’s deregulation, which increases the system’s openness while simultaneously decreasing the applied degree of control.

Vulnerability Assessment

� Is the assessment of power system’s ability to continue providing service in case of an unforeseen catastrophic contingency.

Sources of Vulnerability� Natural calamities� Component failures� Protection and control failures� Breaks in communication links� Faults� Human errors� Inadequate security margin� Gaming in the market� Sabotage or intrusion by external agents� Missing or uncertain information

Sources of Vulnerability

Intentional Human Acts

Network&

Protection

Market

Information & Decisions

CommunicationSystems

Sources of Vulnerability

Natural Calamities

InternalSources

ExternalSources

The system is insecure or vulnerableif any of these contingencies lead to a disruption of service to part(outages ) or all (blackouts ) of the system

Security Assessment Categories

� static security assessment� transient or dynamic security

assessment.

Static Security Assessment� deals with the post-disturbance period

after all transients have died down and the system reaches a new steady state operating condition

� A system is said to be statically secure if the new steady state operating condition does not violate any operating limits such as bus voltage or line current ratings.

Dynamic Security Assessment

� deals with each generator's ability to maintain synchronism with the rest of the system during the transient period immediately following the disturbance.

� The system is secured dynamically if the dynamics of the system is died out and the system operating point is viable

Example

� electrical short-circuit caused by the failure of an insulator on a high-voltage transmission line.

� Disturbances result in a sudden surge of current on the line severely disrupting all generators that are electrically close to the fault.

Example� Protective relays send a trip signal to

circuit breakers installed at each end of the line.

� The circuit breakers then open, removing the disturbance.

� The removal of the transmission line causes another disturbance to the power system.

Example� The tripping of the line may require

further corrective action. � This is called a cascading outage� These disturbances can lead to

severe consequences such as a blackout.

Few Example of Blackouts due to Lack of Dynamic Security

Date Location Affected Customers

Loss of Revenue

9-22-77 New York, USA

7.3 million $90 million

12-19-78 France 12 million $250 million

7-23-87 Tokyo, Japan

2.8 million $70 million

What Security Assessment Offers

� Fast, reliable security assessment techniques can reduce the risk of blackouts occurring by providing utilities with a means to quantify the relative risk at various operating strategies.

Challenges� Vulnerability assessment is a highly

nonlinear problem� Closed form detailed models do not exist� Power network is large and extensive� Operating conditions are wide Range� Topology is continuously changing� The list of contingencies is long� Some of the failures are single events

and some as a sequence of events.

Challenges� Vulnerability assessment is

computationally intensive process� Assessments need to be continually

repeated� On-line assessment is a challenge� Measurements and operating conditions

are noisy� Available knowledge is in historical

examples

Static Security Assessment

Definition� Ability of the system to reach a state

within the specified safety and supply quality following a contingency.

� The time period of consideration is such that the fast acting automatic control devices have restored the system load balance, but the slow acting controls and human decisions have not responded.

Contingency

� Is an abnormal event (such as a fault) which could be potentially damaging to the power system operation.

� Each contingency manifests itself differently, resulting in different types of outages.

� static security assessment (SSA).

Contingency

� The most common are the single/multiple line outages and generator outages.

Contingency� If a contingency causes a violation of

the security variables, the present power system state is insecuretowards that outage.

� The process of evaluating the steady state security of potentially damaging contingency of a power system is called static security assessment(SSA).

Security Variables

� Bus voltages � Line flows (thermal limits)

SSA Process

� Contingency definition (CD)� Contingency selection (CS)� Contingency evaluation (CE)

Contingency Definition (CD)

� CD is a process by which a list of contingencies whose – probability of occurrence is deemed

sufficiently high – are thought to be of vital interest to

system security.

Contingency Screening (CS)

� the process that shortens the original long list of contingencies by removing the vast majority of cases having no violations.

� fast and approximate method of selecting key contingencies for a more thorough evaluation.

Contingency Screening (CS)

� DC load flow (Active power contingency screening)

� Distribution Factor� Performance Index� Human expertise� Intelligent Techniques

Contingency Screening (CS): DC Load Flow

� Assumptions:– Only real power flow is used– All voltages have same magnitudes (1pu)– All voltage angles are small

1cossin

i

ii

Contingency Screening (CS): DC Load Flow

N

kikikikikkii BGVVP

1sincos

ikkiikikkiiikik VVBVVVGP sincos2

Contingency Screening (CS): DC Load Flow

ikkiikikkiiikik VVBVVVGP sincos2

N

kikikikikkii BGVVP

1sincos

N

kikikiki BGP

1

ikikik BP

Contingency Screening (CS): DC Load Flow

Step 1: Solve for

Step 2: Compute line flow

ikikik BP

N

kikikiki BGP

1

Contingency Screening (CS): DC Load Flow

Any contingency that causes

ikSMP ikik allfor

SMik =Magnitude of maximum apparent power flow of line ik

is eliminated from the list

Contingency Screening (CS): DC Load Flow

� Limitation of DC Load Flow

– Only real power is considered– Voltage violation is ignored

Contingency Screening (CS): Distribution Factor

� X(0): Predisturbance states

� : Contingency� X( ): Post disturbance states� Y: Change in system topology� XY: Sensitivity of system to change in topology

(Transfer matrix)

YXXX Y )()0()(

YXXY

Contingency Screening (CS): Distribution Factor

� Assumes linear relationship between pre and post contingency states

� Require the derivative XY

� Y could be hard to compute

Contingency Screening (CS): Performance Index (PI)

� Wi , Wik: weighting factors� Vi (ref): desired value of Vi� Sik (max): maximum rating of line ik

k i ik

ikik

iiii S

SWrefVVWPImax

)((

Contingency Evaluation (CE)

� A process by which a fast ac power-flow is used on successive individual cases in decreasing order of severity.

� The resulting security variables are checked for post contingency violations.

Contingency Evaluation (CE)� Assumes the system reaches a steady state� CE uses a full ac power-flow to calculate the

change in voltages and line flows after a contingency

� The system is insecure from static point of view if– any Voltage or power flow violations exists– substantial load is lost Operator View

System Display

Overloaded Line

Example Question

If any line trips, will another nearby line be overloaded?

Will a bus voltage be too low? Too high?

Must examine the entire system!

� Question: Given present operation, would any component outage cause an operating problem?

– What outages should be checked?� Difficult Question

– How do we check them?� System Power Flow Analysis

SSA: Issues� The objective of SSA is to detect

potential security violations before they actually occur.

� The detection– Warns operator of potential problems– gives operator sufficient time to steer

the system away from the insecure state.

SSA: Issues

� SSA is designed to performed periodically at the control center– based on the available computer

resources– the level of operational sophistication of

the particular utility

SSA: Issues

� For large scale power system, the task of security assessment is time consuming and computer intensive. – Large number of potential contingencies

that have to be analyzed– The different load levels– Changes in topologies– Changes in operational strategies

SSA: Issues

� Security assessment is a classificationproblem– the combination of system topologies,

states, and contingencies determine the security status of the system

� Hence, the concept of pattern recognition can be very effective

SSA: Issues� The concept of pattern recognition is to

capture common underlying characteristics between the pre and post-contingency status

� The captured knowledge can be generalized to classify independent test data originating from the same statistical source.

Advantages of Pattern Recognition

� Computational speed. – Classifiers can be developed off-line– Current and future operating states can

be quickly evaluated� classifying a new steady state power system

condition into a secure or insecure class is trivial and does not require the lengthy computations of an analytical solution.

� Pattern Recognition is discussed in Module 8

Dynamic Security Assessment  (DSA)

DSA

� Deals with the stability of the system following a contingency

� The system is dynamically secured if– Oscillations damped out and the system

reaches a new steady state condition– Oscillations are within acceptable range– The new steady state is statically

secured

Main Challenges to DSA� DSA is computationally intensive process:

– DSA is a highly nonlinear problem– Closed form detailed models do not exist– Power network is large and extensive– Operating conditions are wide Range– Topology is continuously changing– The list of contingencies is long– Some of the failures are single events and

some as a sequence of events.

Main Challenges to DSA� DSA need to be continually repeated� On-line assessment is a challenge� Measurements and operating conditions

are noisy� Available knowledge in historical

examples

DSA Methods

� Time domain simulations� Direct stability methods (Energy

function)� Small signal analysis (Eigenvalues)� Critical Clearing Angle (Time)� Classification and Pattern Recognition

Time Domain Methods

� Time domain methods seek to solve a set of differential equations describing the motion of the generators in the system. – Rotor dynamics (Swing Equation)– Electric power often reduced to the

power curve

Time Domain MethodsPm: mechanical power inputPmax: maximum electrical

power outputH: inertia constant, in

MWs/MVA: rotor angle, in electrical

radianst: time, in secondss: synchronous speed of

the rotor

sinsin maxPXEV

P fe

sin2max2

2

PPdtdH

ms

Time Domain Methods

� By solving the swing equation in the time domain, the stability of the system can be assessed. – If the rotor oscillations damp out, the

system is stable– If not, it is unstable.

Time Domain Methods: Stable

Time

Time Domain Methods: Unstable

Time

Time Domain Methods

� Many factors influence the stability of the system– Prefault system topology– Generator loading conditions– Duration of the disturbance– Severity of the disturbance– Rotor inertia– … …

Time Domain Methods: Challenges

� Time domain methods uses numerical simulation (e.g. Euler or Runge-Kutta)

� Methods could be time consuming– Rotor dynamics is nonlinear differential

equation– Interaction between machines impose

heavy computational burden

Direct Methods� By the Direct Methods, the transient

behavior of a power system can be predicted without complete time domain simulation

� Direct methods advantages:– Compromise between fast and reasonably

accurate assessment � could be used in an on-line environment or as a pre-

screening filter for time domain simulations– Able to rank the severity of a given contingency

in terms of its energy margin.

Direct Methods: Main Steps� Step1: Calculate the transient energy at the instant

the disturbance is cleared (e.g. accelerating energy Ea)

� Step2: Determine the critical energy for the current disturbance (maximum amount of damping energy that can be absorb by the power system Ed max)

� Step3: Calculate the difference (energy margin)Energy Margin= Ed max - Ea

Small Signal Analysis� The power system is linearize about

the current operating point. � The eigenvalues of the linearized

equations are calculated� The method is only accurate for small

disturbances

Critical Clearing Angle� It is another indication of the

balance between the accelerated Kinetic Energy due to a contingency versus the damping kinetic energy of the system.

Critical Clearing Angle

P

3 max

3-max

crCritical Clearing angle

2

Pm

1

Ad minAa max The critical

clearing angle (cr)is the maximum angle for a stable system, i.e. whenAa max = Ad min

Classification and Pattern Recognition (CPR)

� Several off-line simulations are made for several loading conditions assuming a class of contingencies

� The operating points identified with secure and insecure states are clustered in the input space

� The current operating condition is compared with the cantroids of the clusters– The minimum distance to the centroid of the clusters

determines the security status of the system.

Universe (X)

Subset A

Subset B

Subset C

1A1B

1C

0ACPR

Classification and Pattern Recognition (CPR)

� Merits:– Fast for on-line application– Can be made adaptive to system changes– Could use historical data in addition to simulations

� Challenges:– Input space can be very large– Features that determine the security status are hard to

obtain– Accuracy of clusters depends on the quality and quantity

of data

DSA Process

DSADSA Classification DSA Border

Features IdentificationFeatures Selection Features Extractions

System DataTopology States

Features Identification

Why Feature Identification?� Eliminates curse of dimensionality.� Enhances class separability.� Reduces pattern dimension � Maintains classification accuracy.� Reduce training time� Reduce computational time for other application

– Border Identification

Feature Selection

Sensors

Classifie

r

Feature

Selector

X1

Xn

X2

Xn

Most important features are selectedTechniques: Fisher Discriminate

Feature

Extractor

Feature Extraction

Sensors

Classifie

r

X1

Xn

Y2

Yk

All features are combined to form a new reduced set of featuresTechniques: Principal components, NN

Assessment

Challenges� All DSA methods assess given

operating conditions� Generalization is not possible unless

data is clustered– Data within clusters can be assessed

without querying power system models (Fast assessment)

– Data between clustered is unclassified

Security Assessment

Insecure

Secure

Region of Confusion

Border Identification

What is Border Identification

� A method to track the edge of the security region

� Allows users to identify security margins

Assessment with Border Identification

Insecure

Secure

Security Margin

Security Border

Operating Point 1

Margin of security

Challenges� Identifying a border point is

computationally intensive process� Identifying several points on the border

that are uniformly distributed is extremely difficult to achieve

� Identifying the border in high dimension space is extremely difficult and requires unrealistic computational power

Border Identification Techniques

� Border tracking– Gradient method– Projection technique

� Intelligent Techniques– Inverse intelligence– Border sectionalization

DSA Indices

Vulnerability Index� Reflect the level of system strength or

weakness relative to the occurrence of an undesired event

� The vulnerability of power system will change if :– The operating state change– Environmental conditions change– System equipment status change

� We need a quantitative measures

Common Vulnerability Index� Critical Clearing Time (CCT)

– Good accuracy, reliability, and modeling capability– Requires intensive computation time

� Energy Margin– Avoid the time-consuming computation– Modeling limitation, Less accurate than CCT

� Eigenvalues� Anticipated loss of load� ----------…………

Vulnerability Index based on Distance from Border

Vulnerability Border

Operating Point 1

Margin

Operating Point 2

Degree of Vulnerability

Vulnerability Border Visualization� After First Event

0 0.5 1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Qg 77

Qg 65

T PL

Pg 77

Pg 65

Qg 103

Qg 36

Pg 70

Pg 45

Pg 9

T QL

Pg 162

Qg 140

Pg 15

Pg 149

0 0.5 1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Qg 116

Qg 118

Pg 118

Qg 6

Qg 18

Qg 9

Pg 144

Pg 140

Qg 15

Qg 148

Qg 162

Qg 159

Pg 18

Qg 112

Qg 138

-1 0 1

1

Vulnerability Index

VI = -0.20057

Vulnerability Border Visualization� After Second Event

0 0.5 1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Qg 77

Qg 65

T PL

Pg 77

Pg 65

Qg 103

Qg 36

Pg 70

Pg 45

Pg 9

T QL

Pg 162

Qg 140

Pg 15

Pg 149

0 0.5 1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Qg 116

Qg 118

Pg 118

Qg 6

Qg 18

Qg 9

Pg 144

Pg 140

Qg 15

Qg 148

Qg 162

Qg 159

Pg 18

Qg 112

Qg 138

-1 0 1

1

Vulnerability Index

VI = 0.55317

Vulnerability Border Visualization� After Third Event

0 0.5 1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Qg 77

Qg 65

T PL

Pg 77

Pg 65

Qg 103

Qg 36

Pg 70

Pg 45

Pg 9

T QL

Pg 162

Qg 140

Pg 15

Pg 149

0 0.5 1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Qg 116

Qg 118

Pg 118

Qg 6

Qg 18

Qg 9

Pg 144

Pg 140

Qg 15

Qg 148

Qg 162

Qg 159

Pg 18

Qg 112

Qg 138

-1 0 1

1

Vulnerability Index

VI = 0.70661

Critical Clearing Time (CCT)

� : DSA Margin� CCT: Critical Clearing Time� CT: Actual Clearing Time

CTCCT

Critical Clearing Time (CCT)

� Advantages– Good accuracy– Reliability– Equal area criterion can be used (simple

modeling)

– Disadvantages– Requires intensive computation time

Energy Margin

EEref

� : DSA Margin� Eref : Allowable level of damping energy� E: Actual damping energy

Energy Margin

� Advantages– Faster than CCT

� Disadvantages– Less accurate than CCT

Eigenvalues

ref

� : DSA Margin� ref : Allowable real component of eigenvalues� : Actual real component of eigenvalues

Eigenvalues

� Advantages– Straight forward process

� Disadvantages– Doesn’t reflect the nonlinear nature of the

power system– Time consuming for large systems

Anticipated Loss of Load (ALL)

PPref

� : DSA Margin� Pref : Allowable amount of load to be shed� P : Actual load outage

Anticipated Loss of Load (ALL)� Advantages:

– This index is fully applicable in the case of cascading events

– Any control actions can be included (frequency shedding, …)

– Simple concept– Directly related to utility objectives (serving customers)

� Disadvantages– Computationally extensive

Anticipated Loss of Load (ALL)� For small System

– We can search all possible combinations of load reduction.� For realistic size system

– The exhaustive search is practically impossible.– For N loads, to shed each load from 0%-100% in 1% increment,

there are 100N possible combinations of load reductions

� Possible solution– Reduce N by selecting load to be shed from among the network

loads– Use intelligent technique to speed up the computation

Vulnerability Index (VI) based on anticipated loss of load

� It is proposed that the anticipated loss of load with respect to a sequence of events be used as a VI.

� This index is fully applicable in the case of cascading events.

� Any control actions can be considered.� This concept is simple but computationally

extensive.

Vulnerability Index (VI) based on anticipated loss of load (Cont’)

� Small System– We can search all possible combinations of load reduction.

� Realistic size system– The exhaustive search is practically impossible.– If we shed each load from 0% to 100% in 1% increment– N loads – 100N possible combinations of load reductions

� Fast search algorithms are needed for this technique to succeed.

Under Frequency Load Shedding

� Frequency decline, rate of frequency decline

59.5 Hz

59.3 Hz

58.8 Hz

58.6 Hz

58.3 Hz

Activated by frequency decline rate

20 % 5 % 4 % 4 %

Activated by frequency decline

10 % 15 %

Scenario 1

3332

31 30

35

80

78

74

7966

75

77

7672

8281

8683

84 85

156 157 161 162

vv

167165

158 159

15544

45 160

166

163

5 11

6

8

9

1817

43

7

14

12 13

138 139

147

15

19

16

112

114

115

118

119

103

107

108

110

102

104

109

142

376463

56153 145151

15213649

4847

146154

150149

143

4243

141140

50

57

230 kV345 kV500 kV The amount of Load Shedding

0

200

400

600

800

1000

1200

1400

1600

1800

119 117 101 113 112 116 118 105 106 TotalBus Number

Am

ount

of L

oad

Shed

ding

[MVA

]

Under Frequency Relay

PSO

The amount of Load Shedding

0

500

1000

1500

2000

2500

3000

3500

4000

119 117 101 113 112 116 118 105 106 TotalBus Number

Am

ount

of L

oad

Shed

ding

[MV

A]

Under Frequency RelayPSO with IslandingPSO without Islanding

� Scenario 2

77 82

86

83

vv

112

114

115

118

119

Three Phase Fault

at T = 0 ms

� Scenario 2 77 82

86

83

vv

112

114

115

118

119

Line Tripped

at T = 100 ms

� Scenario 2 77 82

86

83

vv

112

114

115

118

119

Additional Tripping due to Hidden Failure

at T = 100 ms

Load Shedding Control is Activated

at T = 400 ms

Under Frequency Relay– Cannot stabilize this event

The amount of Load Shedding

0

20

40

60

80

100

120

119 117 101 113 112 116 118 105 106 Total

Bus Number

Amou

nt o

f Loa

d S

hedd

ing

[MV

A]

Distribution of the Total Magnitude of Load Shedding for 1500 different operating conditions

� The amount of load shedding in MVA can be used directly. � This amount could be normalized between 0 and 1.� The load shedding percentage

the highest load shedding case : 3150 / 68398= 4.6 %

0 500 1000 1500 2000 2500 3000 35000

50

100

150

200

250

300

350

400

Total amount of Load Shedding[MVA]

Num

ber o

f Pat

tern

s