## Probabilistic *N*- *k* failure-identification for power systems

## Abstract

This work considers a probabilistic generalization of the *N*- *k* failure-identification problem in power transmission networks, where the probability of failure of each component in the network is known a priori and the goal of the problem is to find a set of *k* components that maximizes disruption to the system loads weighted by the probability of simultaneous failure of the *k* components. The resulting problem is formulated as a bilevel mixed-integer nonlinear program. Convex relaxations, linear approximations, and heuristics are developed to obtain feasible solutions that are close to the optimum. A general cutting-plane algorithm is proposed to solve the convex relaxation and linear approximations of the *N*- *k* problem. Extensive numerical results corroborate the effectiveness of the proposed algorithms on small-, medium-, and large-scale test instances; the test instances include the IEEE 14-bus system, the IEEE single-area and three-area RTS96 systems, the IEEE 118-bus system, the WECC 240-bus test system, the 1354-bus PEGASE system, and the 2383-bus Polish winter-peak test system.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1463479

- Report Number(s):
- LA-UR-17-23601

Journal ID: ISSN 0028-3045

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Networks

- Additional Journal Information:
- Journal Volume: 71; Journal Issue: 3; Journal ID: ISSN 0028-3045

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION; 97 MATHEMATICS AND COMPUTING; Interdiction, convex optimization, N-k, component-failure probabilities; power network resilience; network interdiction; N-k vulnerability; nonlinear optimization; convex relaxation; cutting-plane algorithm; network flow; DC power flow; AC power flow

### Citation Formats

```
Sundar, Kaarthik, Coffrin, Carleton, Nagarajan, Harsha, and Bent, Russell. Probabilistic N-k failure-identification for power systems. United States: N. p., 2018.
Web. doi:10.1002/net.21806.
```

```
Sundar, Kaarthik, Coffrin, Carleton, Nagarajan, Harsha, & Bent, Russell. Probabilistic N-k failure-identification for power systems. United States. doi:10.1002/net.21806.
```

```
Sundar, Kaarthik, Coffrin, Carleton, Nagarajan, Harsha, and Bent, Russell. Mon .
"Probabilistic N-k failure-identification for power systems". United States. doi:10.1002/net.21806. https://www.osti.gov/servlets/purl/1463479.
```

```
@article{osti_1463479,
```

title = {Probabilistic N-k failure-identification for power systems},

author = {Sundar, Kaarthik and Coffrin, Carleton and Nagarajan, Harsha and Bent, Russell},

abstractNote = {This work considers a probabilistic generalization of the N-k failure-identification problem in power transmission networks, where the probability of failure of each component in the network is known a priori and the goal of the problem is to find a set of k components that maximizes disruption to the system loads weighted by the probability of simultaneous failure of the k components. The resulting problem is formulated as a bilevel mixed-integer nonlinear program. Convex relaxations, linear approximations, and heuristics are developed to obtain feasible solutions that are close to the optimum. A general cutting-plane algorithm is proposed to solve the convex relaxation and linear approximations of the N-k problem. Extensive numerical results corroborate the effectiveness of the proposed algorithms on small-, medium-, and large-scale test instances; the test instances include the IEEE 14-bus system, the IEEE single-area and three-area RTS96 systems, the IEEE 118-bus system, the WECC 240-bus test system, the 1354-bus PEGASE system, and the 2383-bus Polish winter-peak test system.},

doi = {10.1002/net.21806},

journal = {Networks},

number = 3,

volume = 71,

place = {United States},

year = {2018},

month = {1}

}

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