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

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

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

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

(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)

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

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

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

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

Results (Random Interdiction)

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

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%

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%

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!

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

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

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 DAAD19-01-1-0502 The National Science Foundation under grant number ECS-0214369 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.