1. METHODOLOGY FOR IDENTIFYING NEAR-OPTIMAL INTERDICTION STRATEGIES FOR A POWER TRANSMISSION SYSTEM
Vicki M. Bier, Eli Robert Gratz, Naraphorn J. Haphuriwat, and Wairimu Magua
Department of Industrial and Systems Engineering
University of Wisconsin-Madison
Kevin R. Wierzbicki
Department of Electrical and Computer Engineering

2. Objectives The objectives of the project are to:
Develop a simple, inexpensive, and practical method for identifying promising interdiction strategies
Compare our method and results with those of other proposed approaches for vulnerability assessment
Study the effectiveness of protecting transmission lines

3. System Topology We use the IEEE Reliability Test
System – 1996 (RTS-96):
Representative of typical systems
We base our analysis on decoupled
load (DC) flow with optimal dispatch

5. System Topology (continued)
We model the RTS-96 systems
as networks consisting of:
24 nodes and 38 arcs for the One Area RTS-96
48 nodes and 79 arcs for the Two Area RTS-96

6. (after a pre-determined
Schematic View of Process
Load-Flow Algorithm
(Determine optimal DC power dispatch)
Max Line Interdiction Algorithm
(Interdict the line with maximum flow,
and any lines in close geographical proximity)
Hardening Algorithm
(Make the first n sets of interdicted lines
from the Max Line algorithm invulnerable)
Terminate
(after a pre-determined
number of iterations)

7. Other Approaches
The method of Apostolakis and Lemon (2005) applies only to distribution networks (with one-directional flows)
Salmeron et al. (2004) use a non-linear nested optimization method that is difficult to solve

8. Results (One Area RTS-96)
Attacked:33%
Load shed: 56%
Attacked:11%
Load shed: 44%

9. Results (Two Area RTS-96)
45%
44%

10. Results cont’d…
The Max Line interdiction strategy reasonably approximates the load shed by Salmeron et al.
The transmission lines interdicted by Salmeron et al. differ from those interdicted by our strategy
MaxLine
Salmeron 64 30
19&21
78&78 23 41 52 11
74&73
34&35 21
21&19 22 24
27&28 30
38&39
61&59 62 69
72&79
77&78

11. Results (Random Interdiction)

12. Hardening We apply the hardening algorithm to
simulate an upgrade of the system
H0 represents the original interdiction
strategy
H1, H2, and H3 show the interdiction
strategies obtained after three iterations
of hardening

13. Results (One Area RTS-96)
Strategy H0 results in a loss of 56%
Strategy H3, hardening 39% of all lines, results in a loss of 42%

14. Results (Two Area RTS-96)
Strategy H0 results in a loss of 56%
Strategy H3, hardening 39% of all lines, results in a loss of 39%

15. Observations Our results cast doubt on the claim by Salmeron et al.:
“By considering the largest possible disruptions, our proposed plan will be appropriately conservative”
Hardening even a significant percentage of lines does not dramatically diminish the load shed by an attack
Hardening seems unlikely to be cost effective!

16. Conclusions
We developed a simple, inexpensive, and viable method of identifying promising attack strategies
Our results are comparable to those of Salmeron et al.
A single run of either method will not be sufficient to identify critical vulnerabilities
Hardening of transmission lines is unlikely to be cost effective

17. Directions for Future Research
In future research, this method could be extended to:
Address other components of transmission systems, such as transformers
Identify strategies that may trigger cascading power failures
Take into account the importance of different loads
Apply to other types of systems, such as structures, water, and transportation

18. Acknowledgement This material is based upon work supported in part by:
The U.S. Army Research Laboratory and the U.S. Army Research Office under grant number DAAD
The National Science Foundation under grant number ECS
The Department of Homeland Security under grant number EMW-004-GR-0112
Any opinions, findings, and conclusions or recommendations expressed
in this material are those of the authors and do not necessarily reflect
the views of the sponsors.
The authors would like to thank Prof. Ian Dobson of the University of
Wisconsin-Madison for his contributions to this study.