## A multitree approach for global solution of ACOPF problems using piecewise outer approximations

## Abstract

Electricity markets rely on the rapid solution of the *optimal power flow* (OPF) problem to determine generator power levels and set nodal prices. Traditionally, the OPF problem has been formulated using linearized, approximate models, ignoring nonlinear alternating current (AC) physics. These approaches do not guarantee global optimality or even feasibility in the real ACOPF problem. We introduce an outer-approximation approach to solve the ACOPF problem to global optimality based on alternating solution of upper- and lower-bounding problems. The lower-bounding problem is a piecewise relaxation based on strong second-order cone relaxations of the ACOPF, and these piecewise relaxations are selectively refined at each major iteration through increased variable domain partitioning. Our approach is able to efficiently solve all but one of the test cases considered to an optimality gap below 0.1%. This approach opens the door for global solution of MINLP problems with AC power flow equations.

- Authors:

- Purdue Univ., West Lafayette, IN (United States). Davidson School of Chemical Engineering
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
- Purdue Univ., West Lafayette, IN (United States). Davidson School of Chemical Engineering; Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1570257

- Report Number(s):
- SAND2019-10860J

Journal ID: ISSN 0098-1354; 679386

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Computers and Chemical Engineering

- Additional Journal Information:
- Journal Volume: 114; Journal Issue: C; Journal ID: ISSN 0098-1354

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; optimal power flow; outer-approximation; piecewise relaxation; global optimization; second-order cone relaxation; ACOPF

### Citation Formats

```
Liu, Jianfeng, Bynum, Michael, Castillo, Anya, Watson, Jean-Paul, and Laird, Carl D. A multitree approach for global solution of ACOPF problems using piecewise outer approximations. United States: N. p., 2018.
Web. doi:10.1016/j.compchemeng.2017.10.018.
```

```
Liu, Jianfeng, Bynum, Michael, Castillo, Anya, Watson, Jean-Paul, & Laird, Carl D. A multitree approach for global solution of ACOPF problems using piecewise outer approximations. United States. doi:10.1016/j.compchemeng.2017.10.018.
```

```
Liu, Jianfeng, Bynum, Michael, Castillo, Anya, Watson, Jean-Paul, and Laird, Carl D. Sat .
"A multitree approach for global solution of ACOPF problems using piecewise outer approximations". United States. doi:10.1016/j.compchemeng.2017.10.018. https://www.osti.gov/servlets/purl/1570257.
```

```
@article{osti_1570257,
```

title = {A multitree approach for global solution of ACOPF problems using piecewise outer approximations},

author = {Liu, Jianfeng and Bynum, Michael and Castillo, Anya and Watson, Jean-Paul and Laird, Carl D.},

abstractNote = {Electricity markets rely on the rapid solution of the optimal power flow (OPF) problem to determine generator power levels and set nodal prices. Traditionally, the OPF problem has been formulated using linearized, approximate models, ignoring nonlinear alternating current (AC) physics. These approaches do not guarantee global optimality or even feasibility in the real ACOPF problem. We introduce an outer-approximation approach to solve the ACOPF problem to global optimality based on alternating solution of upper- and lower-bounding problems. The lower-bounding problem is a piecewise relaxation based on strong second-order cone relaxations of the ACOPF, and these piecewise relaxations are selectively refined at each major iteration through increased variable domain partitioning. Our approach is able to efficiently solve all but one of the test cases considered to an optimality gap below 0.1%. This approach opens the door for global solution of MINLP problems with AC power flow equations.},

doi = {10.1016/j.compchemeng.2017.10.018},

journal = {Computers and Chemical Engineering},

number = C,

volume = 114,

place = {United States},

year = {2018},

month = {6}

}