# Global Solution Strategies for the Network-Constrained Unit Commitment Problem with AC Transmission Constraints

## Abstract

Here, we propose a novel global solution algorithm for the network-constrained unit commitment problem that incorporates a nonlinear alternating current (AC) model of the transmission network, which is a nonconvex mixed-integer nonlinear programming (MINLP) problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. We exploit the mathematical structure of the unit commitment problem with AC power flow constraints (UC-AC) and leverage second-order cone relaxations, piecewise outer approximations, and optimization-based bounds tightening to guarantee a globally optimal solution at convergence. Numerical results on four benchmark problems illustrate the effectiveness of our algorithm, both in terms of convergence rate and solution quality.

- Authors:

- Purdue Univ., West Lafayette, IN (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Clemson Univ., Clemson, SC (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1485467

- Report Number(s):
- [SAND-2018-11995J]

[Journal ID: ISSN 0885-8950; 668931]

- Grant/Contract Number:
- [AC04-94AL85000]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- IEEE Transactions on Power Systems

- Additional Journal Information:
- [ Journal Volume: 34; Journal Issue: 2]; Journal ID: ISSN 0885-8950

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 24 POWER TRANSMISSION AND DISTRIBUTION; Optimal Power Flow; Unit Commitment; Optimization methods; Power system modeling

### Citation Formats

```
Liu, Jianfeng, Laird, Carl Damon, Scott, Joseph K., Watson, Jean -Paul, and Castillo, Anya. Global Solution Strategies for the Network-Constrained Unit Commitment Problem with AC Transmission Constraints. United States: N. p., 2018.
Web. doi:10.1109/TPWRS.2018.2876127.
```

```
Liu, Jianfeng, Laird, Carl Damon, Scott, Joseph K., Watson, Jean -Paul, & Castillo, Anya. Global Solution Strategies for the Network-Constrained Unit Commitment Problem with AC Transmission Constraints. United States. doi:10.1109/TPWRS.2018.2876127.
```

```
Liu, Jianfeng, Laird, Carl Damon, Scott, Joseph K., Watson, Jean -Paul, and Castillo, Anya. Wed .
"Global Solution Strategies for the Network-Constrained Unit Commitment Problem with AC Transmission Constraints". United States. doi:10.1109/TPWRS.2018.2876127. https://www.osti.gov/servlets/purl/1485467.
```

```
@article{osti_1485467,
```

title = {Global Solution Strategies for the Network-Constrained Unit Commitment Problem with AC Transmission Constraints},

author = {Liu, Jianfeng and Laird, Carl Damon and Scott, Joseph K. and Watson, Jean -Paul and Castillo, Anya},

abstractNote = {Here, we propose a novel global solution algorithm for the network-constrained unit commitment problem that incorporates a nonlinear alternating current (AC) model of the transmission network, which is a nonconvex mixed-integer nonlinear programming (MINLP) problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. We exploit the mathematical structure of the unit commitment problem with AC power flow constraints (UC-AC) and leverage second-order cone relaxations, piecewise outer approximations, and optimization-based bounds tightening to guarantee a globally optimal solution at convergence. Numerical results on four benchmark problems illustrate the effectiveness of our algorithm, both in terms of convergence rate and solution quality.},

doi = {10.1109/TPWRS.2018.2876127},

journal = {IEEE Transactions on Power Systems},

number = [2],

volume = [34],

place = {United States},

year = {2018},

month = {10}

}

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#### Figures / Tables:

Works referencing / citing this record:

##
A joint energy and reserve scheduling framework based on network reliability using smart grids applications

journal, July 2019

- Ansari, Javad; Malekshah, Soheil
- International Transactions on Electrical Energy Systems, Vol. 29, Issue 11

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*