Cascading Failure and Self-Organized

Criticality in Electric Power System Blackouts

Ian DobsonECE, Univ. of Wisconsin

David NewmanPhysics, Univ. of Alaska

Ben Carreras, Vicky Lynch,Nate Sizemore

Oak Ridge National Lab

Funding from NSF & DOE isgratefully acknowledged ;also thanks to Cornell University

Outline

• Heavy tails in blackout data• A quick look at criticality: cascading

failure in a simple model• Self-Organized Criticality: power

system model, results• Analogy with sandpiles• Communication networks

Objective: overview of ideas and research themes; this is ongoing work in an emerging new topic:

Complex dynamics of a series of blackouts

BIG PICTURE

It is useful to look at causes of individual blackouts and

strengthen system accordingly

BUT

If series of blackouts show complex systems behavior in

stressed power systems

then we also need to understand this global behavior before we

can mitigate or control blackouts

Blackout data

• Record of major North American blackouts at NERC

• 15 years and 427 blackouts 1984-1998. (sparse data)

blackout and sandpile data

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

Sandpile avalanche

MWh lost

Probability

Event size

Blackout data

• Data shows heavy tails in pdf: there are more large blackouts than might be expected.

• Data suggests power tails.

• NON GAUSSIAN system! (e.g. it is not a linear system driven by Gaussian noise.)

• non finite variance; traditional risk analysis does not work.

Simple model of cascading failure

• Roughly models a transmission system with some path parallelism

• Multiple lines, each loaded.

• When a line overloads, it fails and transfers a fixed amount of load to other lines.

• Model represents weakening of system as cascade proceeds.

Cascading model

pdf at low loading

S = number of lines outaged

pdf at critical loading

S = number of lines outaged

• Simple cascading failure model

shows heavy tails at critical loading.

Now consider much more complex power system models:

• We are investigating critical behavior with respect to loading and other parameters in power system models.

Line outages and transitions as load increases in tree network

0 100 200 300

0

250

500

750

1000

Lines

Power demand

0.00 0.25 0.50 0.75 1.00

M

Why would power systems operate near criticality??

• Near criticality you get the maximum power served, but you increase the risk of outages.

0

5

10

15

20

25

30

1 104

1.2 104

1.4 104

1.6 104

1.2 104 1.4 104 1.6 104 1.8 104

outages

Power Served

<Number of line outages> Power Served

Power Demand

Self-Organized CriticalitySOC

• Criticality means a dynamic equilibrium in which events of all sizes occur ; power tails are present in pdf.

• Key idea: internal system dynamics move the system to operate near criticality.

• Paradigm (or definition) of SOC is a sandpile model.

Model ingredients

• Slow load growth (2% a year) makes blackouts more likely

• Blackouts (cascading outages) occur quickly but ...

• Engineering responses to blackouts occur slowly (days to years)

Summary of model:Fast dynamics of

blackout• Each day, look at peak loading.

Loading and initiating events are random.

• Overloaded lines outage with a certain probability and then generators are redispatched and (if needed) load is shed; this can cascade.

• Fast dynamics produces lines involved and blackout size.

Summary of model:Slow dynamics of load increase and responses

• Lines involved in blackout are improved by increasing loading limit; this strengthens system.

• Slow load increase weakens system.

• Hypothesis: these opposing forces cause dynamic equilibrium which can show SOC-like characteristics.

Model

Any overload lines?

yes, test for outage

Line outage?

no

no

If power shed,it is a blackout

LP redispatch

yes

Load increaseRandom load fluctuationUpgrade lines in blackoutPossible random outage

1 day loop

1 minute

loop

Is the total generation margin below critical?

no yes

Upgrade generatorafter n days

Blackout size PDF

SOC-like regime: reliable lines, low load fluctuation, high generator margin.

10-1

100

101

102

103

10-4 10-3 10-2 10-1 100

Probability distribution

Load shed/Power delivered

x-0.5

x-1.5

Blackout size PDF

10-1

100

101

102

10-4 10-3 10-2 10-1 100

PDF = 26.124 e-25.92(Ls/Pd)

Probability distribution

Load shed/Power delivered

Tree 190

Gaussian regime: unreliable lines, high load fluctuation, low generator margin.

Blackout size PDFs

10

-1

10

0

10

1

10

2

10

3

10

4

10

-3

10

-2

10

-1

10

0

PDF (Shifted)

Load Shed/Power Demand

P = 0.216 * (L/P

0

)

-1.133

P = 1.6 * (L/P

0

)

-1.157

P = 12.79 * (L/P

0

)

-1.157

Tree 190

Tree 94

Tree 46

self organization of generator capability also modeled

SOC in idealized sandpile

1 addition of sand builds up sandpile2 gravity pulls down sandpile in

cascade (avalanche)• Hence dynamic equilibrium at a

critical slope with avalanches of all sizes; power tails in pdf.

Analogy between power system and sandpile

powersystem

sand pile

system state line loading gradientprofile

drivingforce

load increase addition ofsand

relaxingforce

lineimprovement

gravity

event line limit oroutage

sand topples

cascade cascadinglines

avalanche

blackout and sandpile data

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

Sandpile avalanche

MWh lost

Probability

Event size

Communication Systems exhibit dynamics similar to power

transmission network

• Similar dynamics have been found in computer and communication networks

• Dynamic packet models can display similar characteristics (have fundamental difference from power network models…individual packets have a specific starting and ending point, electrons do not)

Real communication systems exhibit complex dynamicsOpen network; heavily stressed

50

100

150

200

250

300

0 5000 1 10

4

1.5 10

4

2 10

4

round trip time (ms)

time (sec)

100

200

300

400

500

600

700

0 5000 1 10

4

1.5 10

4

2 10

4

round trip time (ms)

time (sec)

Closed network; less stressed

0.1

1

10

100

1000

10

-4

10

-3

10

-2

10

-1

power spectrum for open internet route

power spectrum for ESnet route

Auto power (arb. units)

frequency (Hz)

~1/f

• Open network heavily stressed: large 1/f region

• Closed network less stressed: smaller 1/f region

Communications Model

• A dynamic communications model driven externally by a given demand was developed by T. Ohira and R. Sawatari. This model shows the existence of a critical point for a given value of package creation.

• We have taken this a step further by incorporating mechanisms of self-regulation that allows the system to operate in steady state.

• We have explored several congestion control mechanisms such as backpressure, choke packet, etc. and studied their relative efficiency.

Communications Model• These congestion control mechanisms

lead to operation close to the critical point.

• The PDF of the time taken for package to get to destination has an algebraic tail.

10-5

10-4

10-3

10-2

10-1

101 102 103

Probability

Delivery time

P = 0.97 * T-1.22

Conclusions

• Blackout data and desire to mitigate blackouts motivates study of complex dynamics of series of blackouts.

• Cascading failure model represents system weakening as cascade proceeds. Overly simple model, but analytic results, including heavy tail in pdf for critical loading

Conclusions• Power system models with

opposing forces of load growth and engineering responses to blackouts show rich and complicated behavior at dynamic equilibrium, including regimes with Gaussian and power law pdfs.

• Global complex dynamics of series of blackouts controls the frequency of large and small blackouts.

Future work

• Need fundamental and detailed understanding of cascading failure, criticality and self organization in power system models.

• Develop more realistic models and test networks.

• Implications for power system operation

• Communication networks and other large scale engineered systems.

REFERENCESavailable at

http://eceserv0.ece.wisc.edu/~dobson/home.html • B.A. Carreras, D.E. Newman, I. Dobson, A.B. Poole,

Initial evidence for self organized criticality in electric power system blackouts , Thirty-Third Hawaii International Conference on System Sciences, Maui, Hawaii, January 2000.

• B.A. Carreras, D.E. Newman, I. Dobson, A.B. Poole, Evidence for self organized criticality in electric power system blackouts , Thirty-Fourth Hawaii International Conference on System Sciences, Maui, Hawaii, January 2001

• I. Dobson, B.A. Carreras, V. Lynch, D.E. Newman, An initial model for complex dynamics in electric power system blackouts, ibid.

• B.A. Carreras, V.E. Lynch, M.L. Sachtjen, I. Dobson, D.E. Newman, Modeling blackouts dynamics in power transmission networks with simple structure, ibid.