Initial evidence for self-organized criticality in blackouts

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: • Analyze specific causes and sequence of events for each blackout. • Try to understand global, complex system dynamics.

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

4. Analysis of NERC data Look at daily time series of blackout sizes 1993-1998. Analyze using SWV and R/S Then H = 0.7 pdf tails ~ (blackoutsize)^(-0.98) 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) • addition of sand builds up sandpile • gravity 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 • load demand drives loading up • response 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.