# Identifying Redundant Flow Limits on Parallel Lines

## Abstract

Many power system optimization problems constrain line flows with limits specified in terms of the magnitudes of apparent power or current flows. The set of line-flow constraints may have redundancies (i.e., the feasible space may be unchanged upon removal of a subset of the line-flow constraints), which unnecessarily complicate optimization problems. This letter describes an algorithm for identifying redundant line-flow constraints corresponding to certain parallel lines. After formulating the constraints as ellipsoids in the voltage variables, redundancies are detected from the absence of intersections between pairs of ellipsoids corresponding to parallel lines. This algorithm is demonstrated using several large test cases.

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE)

- OSTI Identifier:
- 1461457

- DOE Contract Number:
- AC02-06CH11357

- Resource Type:
- Journal Article

- Journal Name:
- IEEE Transactions on Power Systems

- Additional Journal Information:
- Journal Volume: 33; Journal Issue: 3; Journal ID: ISSN 0885-8950

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Molzahn, Daniel K.
```*Identifying Redundant Flow Limits on Parallel Lines*. United States: N. p., 2018.
Web. doi:10.1109/TPWRS.2018.2816807.

```
Molzahn, Daniel K.
```*Identifying Redundant Flow Limits on Parallel Lines*. United States. doi:10.1109/TPWRS.2018.2816807.

```
Molzahn, Daniel K. Tue .
"Identifying Redundant Flow Limits on Parallel Lines". United States. doi:10.1109/TPWRS.2018.2816807.
```

```
@article{osti_1461457,
```

title = {Identifying Redundant Flow Limits on Parallel Lines},

author = {Molzahn, Daniel K.},

abstractNote = {Many power system optimization problems constrain line flows with limits specified in terms of the magnitudes of apparent power or current flows. The set of line-flow constraints may have redundancies (i.e., the feasible space may be unchanged upon removal of a subset of the line-flow constraints), which unnecessarily complicate optimization problems. This letter describes an algorithm for identifying redundant line-flow constraints corresponding to certain parallel lines. After formulating the constraints as ellipsoids in the voltage variables, redundancies are detected from the absence of intersections between pairs of ellipsoids corresponding to parallel lines. This algorithm is demonstrated using several large test cases.},

doi = {10.1109/TPWRS.2018.2816807},

journal = {IEEE Transactions on Power Systems},

issn = {0885-8950},

number = 3,

volume = 33,

place = {United States},

year = {2018},

month = {5}

}

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