# Identifying and Characterizing Non-Convexities in the Feasible Spaces of Optimal Power Flow Problems

## Abstract

Optimal power flow (OPF) is an important problem in the operation of electric power systems. The solution to an OPF problem provides a minimum cost operating point that satisfies constraints imposed by both the non-linear power flow equations and engineering limits. These constraints can yield non-convex feasible spaces that result in significant computational challenges. This brief proposes an algorithm that identifies and characterizes non-convexities in OPF feasible spaces. This algorithm searches for a pair of feasible points whose connecting line segment contains an infeasible point. Such points certify the existence of a non-convexity in the OPF feasible space. Moreover, the constraint violations at the infeasible point along the connecting line segment physically characterize a cause of the non-convexity. Numerical demonstrations include a small illustrative example as well as applications to various test cases.

- Authors:

- Publication Date:

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

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

- OSTI Identifier:
- 1460992

- DOE Contract Number:
- AC02-06CH11357

- Resource Type:
- Conference

- Resource Relation:
- Conference: 2018 IEEE International Symposium on Circuits and Systems, 05/27/18 - 05/30/18, Florence, IT

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Molzahn, Daniel K.
```*Identifying and Characterizing Non-Convexities in the Feasible Spaces of Optimal Power Flow Problems*. United States: N. p., 2018.
Web. doi:10.1109/TCSII.2018.2823712.

```
Molzahn, Daniel K.
```*Identifying and Characterizing Non-Convexities in the Feasible Spaces of Optimal Power Flow Problems*. United States. doi:10.1109/TCSII.2018.2823712.

```
Molzahn, Daniel K. Tue .
"Identifying and Characterizing Non-Convexities in the Feasible Spaces of Optimal Power Flow Problems". United States. doi:10.1109/TCSII.2018.2823712.
```

```
@article{osti_1460992,
```

title = {Identifying and Characterizing Non-Convexities in the Feasible Spaces of Optimal Power Flow Problems},

author = {Molzahn, Daniel K.},

abstractNote = {Optimal power flow (OPF) is an important problem in the operation of electric power systems. The solution to an OPF problem provides a minimum cost operating point that satisfies constraints imposed by both the non-linear power flow equations and engineering limits. These constraints can yield non-convex feasible spaces that result in significant computational challenges. This brief proposes an algorithm that identifies and characterizes non-convexities in OPF feasible spaces. This algorithm searches for a pair of feasible points whose connecting line segment contains an infeasible point. Such points certify the existence of a non-convexity in the OPF feasible space. Moreover, the constraint violations at the infeasible point along the connecting line segment physically characterize a cause of the non-convexity. Numerical demonstrations include a small illustrative example as well as applications to various test cases.},

doi = {10.1109/TCSII.2018.2823712},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {5}

}