![Page 1: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/1.jpg)
Beyond Contingency Analysis New Approaches to Cascading Failures Risk Analysis
Los Alamos Grid Science Conference Paul D.H. Hines University of Vermont (Engineering, Computer Science, Complex Systems) )
Credits Good ideas: P. Rezaei, M. Eppstein Funding: Dept. of Energy, Nat. Science Foundation Errors: Paul Hines
![Page 2: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/2.jpg)
Contingency analysis• N-1 security has been the core power systems
operating principle for >50 years
• While it has served us well, it also has limitations:
• Not all contingencies are equally likely.
• Not all limit violations are equally important—some produce blackouts, others don’t.
• Sometimes components fail in sets (e.g., storms) or in unexpected ways (Aug. 14 2003 blackout).
• Binary: Imperfect data (e.g., from neighboring areas) can change the apparent state of system from insecure to secure. (2011 SW blackout)
2
![Page 3: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/3.jpg)
Beyond contingency analysis
• Valuable insight comes from contingency analysis, so replacing it would be unwise.
• However, operators need additional indicators of risk.
• Lots of ongoing work: PMU angle difference analysis, statistical indicators (variance, autocorrelation), energy function/Lyaponav methods, …
• Focus: Given a state estimator or day-ahead planning model, quantify and explain the risk posed by all potential cascading blackouts.
3
![Page 4: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/4.jpg)
Beyond contingency analysis
• Focus: Given a state estimator or day-ahead planning model, quantify and explain the risk posed by all potential cascading blackouts.
• Why this is hard:
• All n-1 contingencies and most n-{2,3,4}s do not cause blackouts. Many samples needed to find one blackout.
• Power-law in blackout sizes means that we need many blackout simulations to describe the risk.
• Explaining why is always difficult (but probably the most important thing we can do)
4
102
103
104
10−2
10−1
100
Blackout size (S) in year−2000 MWP
rob. th
at x ≥
S for
a r
andom
ly c
hosen b
lackout w
ith s
ize x
Actual data
Weibull fit (100 < S ≤ 3000)
Power−law fit (S ≥ 1016)
![Page 5: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/5.jpg)
Illustration
5
Case 1 (noon tomorrow) High blackout risk
Case 2 (2 pm tomorrow) Low blackout risk
Both cases are secure. What makes the two cases different?
How can we make Case 1 more like Case 2?
![Page 6: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/6.jpg)
The Random Chemistry Method
Paul D.H. Hines University of Vermont (Engineering, Computer Science, Complex Systems) )
Credits Good ideas: P. Rezaei, M. Eppstein Funding: Dept. of Energy, Nat. Science Foundation Errors: Paul Hines
![Page 7: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/7.jpg)
7
1. Start with a grid model.
![Page 8: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/8.jpg)
2. Now find many of the outage combinations that cause blackouts (the malignancies)
8
![Page 9: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/9.jpg)
The Random Chemistry algorithm
9
40 outages
20 outages
10 outages
5 outages
2-3 outages
![Page 10: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/10.jpg)
3. Use the results to quantify blackout risk
10
The estimated number of malignancies of size k
The number of malignancies of size k found by RC
Blackout sizes
Probabilityof (multiple)contingency
![Page 11: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/11.jpg)
4. Estimating the number of blackout-‐causing contingencies by modeling the rate at which
unique malignancies are found
11
nba.com
![Page 12: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/12.jpg)
Comparing RC to Monte Carlo
12
![Page 13: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/13.jpg)
Now that we can estimate blackout risk, what insight can we gain?
13
![Page 14: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/14.jpg)
Risk vs. load, given SCOPF
14
Adding the SCOPF changes the results
substantially from prior work showing a phase
transition in risk vs. load
![Page 15: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/15.jpg)
Why?
• At high load levels SCOPF leaves larger margins on long inter-area tie lines (to allow for potential contingencies)
15
Total absolute flow on lines with large (>200MW) base case flow
![Page 16: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/16.jpg)
Finding the contribution of elements to risk
16
Differentiate the risk equation with respect to element outage probabilities
![Page 17: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/17.jpg)
Distribution of “risk sensitivity”
17
![Page 18: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/18.jpg)
18
Yet another power-law tail
![Page 19: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/19.jpg)
Can we use this insight to reduce risk?
• Take the 3 lines that contribute most to blackout risk
• Re-dispatch generators to leave more margin between the flow on these lines and the limit (cut the limit in half)
• Fuel costs increase by 1.6%
• Large (S>5%) blackout risk decreases by 61%
• Very large (S>40%) blackout risk decreases by 83%
• Perhaps we would be better off without these lines?
19
![Page 20: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/20.jpg)
Before and after
20
Base case 3 reduced capacities0
10
20
30
40
50
60Ri
sk (E
xpec
ted
blac
kout
size
, kW
)
5%<BO<10%10%<BO<20%20%<BO<30%30%<BO<40%40%<BO<50%BO>50%
![Page 21: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/21.jpg)
Do the blackout-‐causing n-‐2 contingencies change at different load levels?
21
![Page 22: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/22.jpg)
39 n-‐2 malignancies at 75% load
22
![Page 23: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/23.jpg)
540 n-‐2 malignancies at 100%
23
![Page 24: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/24.jpg)
378 n-‐2 malignancies at 115%
24
![Page 25: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/25.jpg)
Which components negatively interact with a given component at different load levels?
25
![Page 26: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/26.jpg)
Branches that negatively interact with * at 90% load
26
![Page 27: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/27.jpg)
Branches that negatively interact with * at 100% load
27
![Page 28: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/28.jpg)
Branches that negatively interact with * at 115% load
28
![Page 29: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/29.jpg)
Returning to the Illustration
29
Case 1 (noon tomorrow) High blackout risk
Case 2 (2 pm tomorrow) Low blackout risk
We now have a way to describe the differences in risk between these two cases and explain why the
two cases are different.
![Page 30: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/30.jpg)
Conclusions• It is possible to estimate cascading failure risk with a
reasonable amount of computation (e.g., overnight given tomorrow’s peak-load model). Random Chemistry approach is >100x faster than MC Does this hold up for correlated event probabilities?
• Doing so gives insight that can result in real risk reductions: More load is not always worse (8/14/2003, 9/8/2011) Adjusting the flow limits on critical lines Perhaps switching them out entirely?
• Providing visual feedback to operators may produce new isight and ideas for risk reduction
![Page 31: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/31.jpg)
Importantly, this method is completely model-‐agnostic. Describing risk in interdependent systems
31
Gen
Load
ControlArea A
Mea
sure
men
ts
Con
trol
Gen
Load
ControlArea B
Mea
sure
men
ts
Con
trol
Mar
ket i
nter
face
Inte
rnet
SCAD
APo
wer
Grid
Mar
ket i
nter
face
![Page 32: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/32.jpg)
Work in Progress: Influence Graphs
32
1 2 3
4 5 6
0
20
40
60
80
100
120
140
160
180
200
1−4
2−4
4−5
2−32−5
3−55−6
3−6
1−2
![Page 33: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/33.jpg)
A larger influence graph
33
graph showing links with a weight of 1000 or greater
![Page 34: Beyond’Contingency’Analysis NewApproachestoCascading Failures’Risk’Analysiscnls.lanl.gov/gridscience/media/Seminars/Hines.pdf · 2015-01-25 · Beyond’Contingency’Analysis](https://reader034.vdocuments.us/reader034/viewer/2022042201/5ea105936729ab316549bdd8/html5/thumbnails/34.jpg)
Beyond Contingency Analysis New Approaches to Cascading Failures Risk Analysis
For more information: Pooya Rezaei, Paul Hines and Margaret Eppstein, “Estimating Cascading Failure Risk with Random Chemistry,” IEEE Transactions on Power Systems (in press)http://arxiv.org/abs/1405.4213
Credits Good ideas: P. Rezaei, M. Eppstein Funding: Dept. of Energy, Nat. Science Foundation Errors: Paul Hines