1. Initial evidence for self-organized criticality in blackouts Ben Carreras & Bruce Poole Oak Ridge National Lab David Newman Physics, U. of Alaska Ian Dobson ECE, U. of Wisconsin

2. Two approaches to blackouts: 1Analyze specific causes and sequence of events for each blackout. 2Try to understand global, complex system dynamics.

3. Gaussian model Uncorrelated random disturbances (eg weather) drive a linear system to produce blackouts. Then H  0.5 for large times pdf tails are exponential Look at time series of blackout sizes Hurst parameter H: H=1.0  deterministic H>0.5  + correlation H=0.5  uncorrelated

4. Analysis of NERC data Then H = 0.7 pdf tails ~ (blackoutsize)^(-0.98) Look at daily time series of blackout sizes 1993-1998. Analyze using SWV and R/S H = 0.7  blackouts correlated with later blackouts Consistent with SOC dynamics!

5. Ingredients of SOC in idealized sandpile system state = local max gradients event = sand topples (cascade of events is an avalanche) 1addition of sand builds up sandpile 2gravity pulls down sandpile Hence dynamic equilibrium with avalanches of all sizes and long time correlations

6. SOC dynamic equilibrium in power system transmission? system state = loading pattern event = limiting or zeroing of flow (events can cascade as flow redistributes) [cascade  zero load] = blackout 1load demand drives loading up 2response to blackout relieves loading specific to that blackout

7. 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

8. Figure 2. Blackout energy unserved time series.

9. Scaled windowed variance analysis of the number of blackouts

10. Probability distribution function of energy unserved for North American blackouts 1993-1998.

11. Analogy between power system and sand pile

12. Hurst exponents of blackout numbers and sizes

13. Figure 1. Blackout power loss time series.