# Two-stage minimax stochastic unit commitment

## Abstract

The study proposes a stochastic optimisation approach based on discrete scenarios and the minimax criterion to deal with demand uncertainty in the two-stage unit commitment problem. To avoid making an over-conservative decision, the approach is designed to assign a probability-based weight to each demand scenario and provide a unit commitment schedule that minimises the maximum possible-weighted generation cost. Unit commitment is determined in the first stage and the economic dispatch under the scenario that corresponds to the maximum possible-weighted generation cost is determined in the second stage. The problem is formulated as a type of min-max-min mixed integer programming model. By introducing an auxiliary variable, the model is further transformed into a minimisation problem. A Benders decomposition algorithm is developed to solve the problem. The Benders master problem determines the unit commitment decision, while the Benders subproblem determines the dispatch decision. Multiple Benders feasibility cuts are constructed when the Benders subproblem is infeasible. Valid inequalities are derived to improve the lower bound provided by the Benders master problem. Numerical results show the performance of the algorithm.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- National Key Research and Development Program of China; National Natural Science Foundation of China (NNSFC); USDOE Office of Electricity Delivery and Energy Reliability

- OSTI Identifier:
- 1466391

- DOE Contract Number:
- AC02-06CH11357

- Resource Type:
- Journal Article

- Journal Name:
- IET Generation, Transmission, & Distribution

- Additional Journal Information:
- Journal Volume: 12; Journal Issue: 4; Journal ID: ISSN 1751-8687

- Publisher:
- Institution of Engineering and Technology

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Che, Ping, Tang, Lixin, and Wang, Jianhui.
```*Two-stage minimax stochastic unit commitment*. United States: N. p., 2018.
Web. doi:10.1049/iet-gtd.2017.1467.

```
Che, Ping, Tang, Lixin, & Wang, Jianhui.
```*Two-stage minimax stochastic unit commitment*. United States. doi:10.1049/iet-gtd.2017.1467.

```
Che, Ping, Tang, Lixin, and Wang, Jianhui. Tue .
"Two-stage minimax stochastic unit commitment". United States. doi:10.1049/iet-gtd.2017.1467.
```

```
@article{osti_1466391,
```

title = {Two-stage minimax stochastic unit commitment},

author = {Che, Ping and Tang, Lixin and Wang, Jianhui},

abstractNote = {The study proposes a stochastic optimisation approach based on discrete scenarios and the minimax criterion to deal with demand uncertainty in the two-stage unit commitment problem. To avoid making an over-conservative decision, the approach is designed to assign a probability-based weight to each demand scenario and provide a unit commitment schedule that minimises the maximum possible-weighted generation cost. Unit commitment is determined in the first stage and the economic dispatch under the scenario that corresponds to the maximum possible-weighted generation cost is determined in the second stage. The problem is formulated as a type of min-max-min mixed integer programming model. By introducing an auxiliary variable, the model is further transformed into a minimisation problem. A Benders decomposition algorithm is developed to solve the problem. The Benders master problem determines the unit commitment decision, while the Benders subproblem determines the dispatch decision. Multiple Benders feasibility cuts are constructed when the Benders subproblem is infeasible. Valid inequalities are derived to improve the lower bound provided by the Benders master problem. Numerical results show the performance of the algorithm.},

doi = {10.1049/iet-gtd.2017.1467},

journal = {IET Generation, Transmission, & Distribution},

issn = {1751-8687},

number = 4,

volume = 12,

place = {United States},

year = {2018},

month = {2}

}