Post on 28-Dec-2015
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.