# Exact Convex Relaxation of Optimal Power Flow in Radial Networks

## Abstract

The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks.

- Authors:

- Publication Date:

- Sponsoring Org.:
- USDOE Advanced Research Projects Agency - Energy (ARPA-E)

- OSTI Identifier:
- 1211405

- DOE Contract Number:
- DE-AR0000226

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: IEEE Transactions on Automatic Control; Journal Volume: 60; Journal Issue: 1

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Gan, LW, Li, N, Topcu, U, and Low, SH.
```*Exact Convex Relaxation of Optimal Power Flow in Radial Networks*. United States: N. p., 2015.
Web. doi:10.1109/TAC.2014.2332712.

```
Gan, LW, Li, N, Topcu, U, & Low, SH.
```*Exact Convex Relaxation of Optimal Power Flow in Radial Networks*. United States. doi:10.1109/TAC.2014.2332712.

```
Gan, LW, Li, N, Topcu, U, and Low, SH. Thu .
"Exact Convex Relaxation of Optimal Power Flow in Radial Networks". United States.
doi:10.1109/TAC.2014.2332712.
```

```
@article{osti_1211405,
```

title = {Exact Convex Relaxation of Optimal Power Flow in Radial Networks},

author = {Gan, LW and Li, N and Topcu, U and Low, SH},

abstractNote = {The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks.},

doi = {10.1109/TAC.2014.2332712},

journal = {IEEE Transactions on Automatic Control},

number = 1,

volume = 60,

place = {United States},

year = {Thu Jan 01 00:00:00 EST 2015},

month = {Thu Jan 01 00:00:00 EST 2015}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.