initial evidence for self-organized criticality in blackouts ben carreras & bruce poole oak...
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Initial evidence for self-organized criticality
in blackouts
Ben Carreras & Bruce Poole Oak Ridge National Lab
David NewmanPhysics, U. of Alaska
Ian DobsonECE, U. of Wisconsin
Two approaches to blackouts:
1 Analyze specific causes and sequence of events for each blackout.
2 Try to understand global, complex system dynamics.
Gaussian model
Uncorrelated random disturbances (eg weather) drive a linear system to produce blackouts.
Then H 0.5 for large timespdf tails are exponential
Look at time series of blackout sizes
Hurst parameter H:H=1.0 deterministic H>0.5 + correlationH=0.5 uncorrelated
Analysis of NERC data
Then H = 0.7
pdf tails ~ (blackoutsize)^(-0.98)
Look at daily time series of blackout sizes1993-1998.
Analyze using SWV and R/S
H = 0.7 blackouts correlated with later blackouts
Consistent with SOC dynamics!
Ingredients of SOC in idealized sandpile
• system state = local max gradients • event = sand topples (cascade of
events is an avalanche)1 addition of sand builds up sandpile2 gravity pulls down sandpile• Hence dynamic equilibrium with
avalanches of all sizes and long time correlations
SOC dynamic equilibrium in power system transmission?
• system state = loading pattern• event = limiting or zeroing of flow
(events can cascade as flow redistributes)
• [cascadezero load] = blackout1 load demand drives loading up2 response to blackout relieves
loading specific to that blackout
Conclusions• NERC data shows long range time
correlations and power dependent pdf tails.
• Consistent with SOC hypothesis but SOC not yet established.
• Suggest qualitative description of opposing forces which could cause SOC: load demands vs. responses to blackouts.
• Study of global complex system dynamics could lead to insights and perhaps monitoring and mitigation of large blackouts
100
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0 500 1000 1500 2000
Energy unserved (MWh)
Time (day)
Figure 2. Blackout energy unserved time series.
0.1
1
10
1
10
100
10 100 1000
Time lag (days)
Number events H = 0.50
MWh unserved H = 0.70
σ
m
( )events
σm
( )MWh unserved
Scaled windowed variance analysis of the number of blackouts
10
-7
10
-6
10
-5
10
-4
10
1
10
2
10
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10
4
10
5
P= 0.00455 *(MWh)
-0.98
Probability
MWhour unserved
Probability distribution function of energy unserved
for North American blackouts 1993-1998.
Power system Sand pile
system state loading pattern gradient profile
driving force customer demand adding sand
relaxing force response to blackout gravity
event limit flow or trip sand topples
Analogy between power system and sand pile
Time series Hurst exponent H
Number of blackouts 0.52
Energy unserved (MWh) 0.70
Power lost (MW) 0.58
Number of customers 0.69
Restoration time 0.67
Hurst exponents of blackout numbers and sizes
0
1000
2000
3000
4000
5000
6000
0 500 1000 1500 2000
Power loss (MW)
Time (days)
Figure 1. Blackout power loss time series.