1. Criticality and Risk of Large Cascading Blackouts
Ian Dobson
PSerc, ECE Dept., University of Wisconsin
Benjamin A. Carreras
Oak Ridge National Laboratory, TN
in collaboration with
David E. Newman
University of Alaska, Fairbanks

2. Goal
Contribute to transmission system reliability by Understanding large, cascading failure blackouts and providing tools for analyzing and monitoring their risk.
In particular, the project will identify the threshold that leads to increased risk of cascading failure, express this threshold in terms of realistic power system parameters and develop monitoring tools and criteria to be applied in real power transmission systems.

3. Project History FY01-02 Team: ORNL and PSERC (Wisconsin,Cornell)
Budget: 100K per year
FY03-04
Team: ORNL and PSERC (Wisconsin)
Budget: 110K per year
Close collaboration between national lab and universities
LEVERAGE: Collaboration with University of Alaska
Collaboration with Christensen associates
Funding from NSF

4. TOPICS Challenges and costs of large blackouts
What is the risk of large blackouts?
Effect of overall loading on cascading failure
Criticality: Where is the ‘edge’ for cascading failure?
Monitoring closeness to criticality

5. Cascading failure; large blackouts
Rare, unanticipated, dependent events + huge number of possibilities and combinations = hard to analyze or simulate
Mechanisms include: hidden failures, overloads, oscillations, transients, control or operator error, ... but all depend on loading

6. Detailed postmortem analysis of a particular blackout
arduous (months of simulation and analysis) but very useful
a basis for strengthening weak parts of system
motivates good practice in reliability: “Blackouts cause reliability”

7. General approach
Instead of looking at the details of individual blackouts, look at statistics and risk of series of blackouts
Global top-down analysis; look at bulk system properties.
Complementary to detailed analysis

8. Who pays the blackout cost?
Public and business. Halts the economy + indirect costs + harms other infrastructures
Utilities. Reputational, legal, regulatory costs, cost of upgrade or personnel to avoid similar blackouts
Government. Political risk

9. Blackout risk as size increases
risk = probability x cost
Cost increases with blackout size. example: direct cost proportional to size
How does blackout probability decrease as size increases? … a crucial consideration for blackout risk!

10. power tails have huge impact
probability
(log scale) -1 S e -S
blackout size S (log scale)
power tails have huge impact
on large blackout risk.
risk = probability x cost

11. If probability of blackout decreases as a power law with exponent near -1, then risk of large blackouts is comparable to (or even exceeding) the risk of small blackouts.

12. NERC blackout data
Major North American transmission outages over 15 years
427 blackouts
Data includes MW shed, restoration time, number of customers
Can process data to obtain frequency of blackouts in various size ranges and hence estimate probability distribution of blackout size

13. NERC blackout data shows power tail
Large blackouts more likely than expected
Conventional risk analysis tools do not apply; new approaches needed
Consistent with complex system near criticality
Large blackouts are rare, but have high impact and significant risk

14. More NERC data
Number of blackouts with more than n customers affected plotted against n

15. Effect of Loading log log plots
probability
VERY LOW LOAD - failures independent - exponential tails
CRITICAL LOAD - power tails
VERY HIGH LOAD - total blackout likely
blackout size

16. not a fair representation of overall grid reliability.
does show some insight into blackout mechanism
example of reputational/political feedback

17. CASCADE: A probabilistic loading-dependent model of cascading failure --- captures system weakening as successive failures occur

18. CASCADE model
n identical components with random initial load uniform in [Lmin, Lmax]
initial disturbance D adds load to each component
component fails when its load exceeds threshold Lfail and then adds load P to every other component. Load transfer amount P measures component coupling, dependency
iterate until no further failures

19. 5 component example

20. CASCADE model Key output is number of failed components
There is an analytic formula for the probability distribution of number of failed components as a function of parameters.
Captures some salient features of cascading failure in a tractable model.

21. example of application: modeling load increase-
Lmax = Lfail = 1
increase average load L by increasing Lmin 1 L - -

22. <r>
average # failures <r>
versus average load L
P=D=0.005 and n=100
critical
load
average load L

23. probability distribution as average load L increases
number of failures

24. OPA blackout model summary
transmission system modeled with DC load flow and LP dispatch
random initial disturbances and probabilistic cascading line outages and overloads

25. Critical loading in OPA blackout model
Mean blackout size sharply increases at critical loading; increased risk of cascading failure.

26. OPA model can match NERC data
probability
(August 14 blackout is consistent with this power tail)
blackout size

27. Significance of criticality
At criticality there is a power tail, sharp increase in mean blackout size, and an increased risk of cascading failure.
Criticality gives a power system limit with respect to cascading failure.
How do we practically monitor or measure margin to criticality?

28. Ongoing research on margin to criticality
One approach is to increase loading in blackout simulation until average blackout size increases.
Another approach is to monitor or measure how much failures propagate (l) from real or simulated data.

29. CASCADE can be well approximated by a Galton-Watson Branching Process

30. Branching from one failure…
offspring failures
a failure
number of offspring ~ Poisson(l) mean number of failures = l

31. Branching Process stage 4
each failure independently has random number of offspring in next stage according to Poisson(l)
l = mean number failures per previous stage failure
l = mean number of failures in stage k
stage 3
stage 2 k
stage 1
stage 0

32. Branching Process Facts
l controls failure propagation
Subcritical case l<1: failures die out
Critical case l=1: probability distribution of total number of failures has power tail
Supercritical case l>1: failures can proceed to system size

33. Cumulative Line Trips from August 2003
Blackout Final Report

34. Implication for managing risk of cascading failure:
design and operate system so that
< lmax < 1
need to monitor l
can estimate risk of cascading failure from l

35. Current research
Measuring l from failure records (real or simulated). We are testing methods with OPA and also looking at real blackout data.
Relating abstract cascading models (branching/CASCADE) to OPA blackout model
Improving models to support above
Exploring and developing practical implications.

36. Context
We are suggesting adding an “increased risk of cascading failure” limit to usual power system operating limits such as thermal, voltage, transient stability etc.
Cascading failure limit measures overall system stress in terms of how failures propagate once started; complementary to measures to limit cascading failure by inhibiting start of cascade such as n-1, n-2 criterion.

37. KEY POINTS NERC data shows relatively high risk of large blackouts
Criticality is the “edge” for increasing risk of cascading failure
We are developing practical tools to quantify and monitor propagation of failures and margin to criticality.
For more information see papers at