Cascading Failure and Self-Organized Criticality in Electric Power System Blackouts Ian Dobson ECE, Univ. of Wisconsin David Newman Physics, Univ. of Alaska Ben Carreras, Vicky Lynch, Nate Sizemore Oak Ridge National Lab Funding from NSF & DOE is gratefully 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 (sparse data)

blackout and sandpile data

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

Why would power systems operate near criticality?? Near criticality you get the maximum power served, but you increase the risk of outages.

Self-Organized Criticality SOC 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 If power shed, it is a blackout LP redispatch yes Load increase Random load fluctuation Upgrade lines in blackout Possible random outage 1 day loop 1 minute loop Is the total generation margin below critical? noyes Upgrade generator after n days

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

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

Blackout size PDFs self organization of generator capability also modeled

SOC in idealized sandpile 1addition of sand builds up sandpile 2gravity 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

blackout and sandpile data

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 dynamics Open network; heavily stressed Closed network; less stressed

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.

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.

REFERENCES available at 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 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.