1. Root Cause Localization on Power Networks Zhen Chen, ECEE, Arizona State University Joint work with Kai Zhu and Lei Ying

2. Locate Root Cause on Power Networks Questions we are interested: How to locate the root cause on power networks? Which information can be used to locate the root cause of cascading failures on power networks? Objective: develop high-performance algorithms to find the root cause of cascading failures on power networks.

3. Similarities to Information Source Detection Cascading failures on power networks: The failure of some transmission lines leads to the outage of other transmission lines in the power network. Similar to an information diffusion process. Related work: Information source detection (Shah&Zaman’10’11’12; Luo,Tay&Leng’12; Prakash, Vrekeen&Faloubsos’12; Zhu&Ying’12’13;…) Can we use existing information source detection algorithms to locate the root cause of cascading failures?

4. Propagation of Cascading Failures The spread of cascading failures: Ohm’s and Kirchhoff’s laws. Information does not necessarily diffuse according to physical topology of the power network. The power network topology does not capture the dependency of the transmission lines. Related work: Cascading failures in power networks (Chen,Throp&Dobson’05; Bernstein,Bienstock, Hay,etc’2014; Xiao&Yeh’11;…) Can not directly apply information source detection algorithms to power networks!

5. Correlation Network ( Zhang,Liu,Yao,etc’13) It models the influence of one transmission line to the others. : the change of power flow on line due to the outage of line. The correlation network: a weighted complete graph with each node representing a transmission line. Measure the correlation of failures between two transmission lines.

6. Diffusion on the Correlation Network a b c d e 4-bus power systemCorrelation network

7. Diffusion on the Correlation Network a b c d e

8. Greedy Algorithm a b c d e 2 3 4 Step 1: calculate the normalized average infection time: 0.5 0.6 0.5 1 0.6 0.9 0.5 0.8 0.7

9. Step 2: Include a node into the initial infection spreading tree. Step 3: Add the node with infection time observed to the infection spreading tree b c d e 2 3 4 0.5 1 0.6 0.9 0.5 0.8 0.7 5.25 Greedy Algorithm Step 4: Add other infected nodes to the infection spreading tree. Assign infection time. Step 5: Calculate the cost. a 0.75

10. Experiments Power systems: IEEE 300-bus system Electricity transmission network of Great Britain (2224 buses) Cascading failures traces: 1. Remove a transmission line randomly 2. Calculate the new power flow allocation 3. Remove overloaded transmission lines 4. Repeat Step 2 and Step 3 until no new overloaded transmission lines.

11. Experiments CR: Cost-based ranking TR: Tree-based ranking

12. Application to Other Networks The greedy algorithm can be used to detect source on weighted graphs. The network of air traffic volume between US airports (Dianati’15)

13. Conclusions 13 Combined the correlation network with information source detection Developed a cost-based approach and proposed a greedy algorithm to locate the root cause Evaluated performance on IEEE 300-bus power network and Great Britain power network.

14. Thank you! Q&A