### Abstract

The unit commitment problem consists of determining the schedules for power generating units and the generating level of each unit. The decisions concern which units to commit during each time period and at what level to generate power to meet the electricity demand. The problem is a typical scheduling problem in an electric power system. The electric power industry is undergoing restructuring and deregulation. This article developes a stochastic programming model which incorporates power trading. The uncertainty of electric power demand or electricity price are incorporated into the unit commitment problem. It is assumed that demand and price uncertainty can be represented by a scenario tree. A stochastic integer programming model is proposed in which the objective is to maximize expected profits. In this model, on/off decisions for each generator are made in the first stage. The approach to solving the problem is based on Lagrangian relaxation and dynamic programming.

Original language | English |
---|---|

Pages (from-to) | 705-719 |

Number of pages | 15 |

Journal | Engineering Optimization |

Volume | 36 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2004 Dec |

Externally published | Yes |

### Fingerprint

### Keywords

- Electric power
- Lagrangian relaxation
- Stochastic programming
- Unit commitment

### ASJC Scopus subject areas

- Management Science and Operations Research
- Engineering (miscellaneous)

### Cite this

*Engineering Optimization*,

*36*(6), 705-719. https://doi.org/10.1080/0305215042000274933

**Lagrangian relaxation method for price-based unit commitment problem.** / Shiina, Takayuki; Watanabe, Isamu.

Research output: Contribution to journal › Article

*Engineering Optimization*, vol. 36, no. 6, pp. 705-719. https://doi.org/10.1080/0305215042000274933

}

TY - JOUR

T1 - Lagrangian relaxation method for price-based unit commitment problem

AU - Shiina, Takayuki

AU - Watanabe, Isamu

PY - 2004/12

Y1 - 2004/12

N2 - The unit commitment problem consists of determining the schedules for power generating units and the generating level of each unit. The decisions concern which units to commit during each time period and at what level to generate power to meet the electricity demand. The problem is a typical scheduling problem in an electric power system. The electric power industry is undergoing restructuring and deregulation. This article developes a stochastic programming model which incorporates power trading. The uncertainty of electric power demand or electricity price are incorporated into the unit commitment problem. It is assumed that demand and price uncertainty can be represented by a scenario tree. A stochastic integer programming model is proposed in which the objective is to maximize expected profits. In this model, on/off decisions for each generator are made in the first stage. The approach to solving the problem is based on Lagrangian relaxation and dynamic programming.

AB - The unit commitment problem consists of determining the schedules for power generating units and the generating level of each unit. The decisions concern which units to commit during each time period and at what level to generate power to meet the electricity demand. The problem is a typical scheduling problem in an electric power system. The electric power industry is undergoing restructuring and deregulation. This article developes a stochastic programming model which incorporates power trading. The uncertainty of electric power demand or electricity price are incorporated into the unit commitment problem. It is assumed that demand and price uncertainty can be represented by a scenario tree. A stochastic integer programming model is proposed in which the objective is to maximize expected profits. In this model, on/off decisions for each generator are made in the first stage. The approach to solving the problem is based on Lagrangian relaxation and dynamic programming.

KW - Electric power

KW - Lagrangian relaxation

KW - Stochastic programming

KW - Unit commitment

UR - http://www.scopus.com/inward/record.url?scp=6344283164&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=6344283164&partnerID=8YFLogxK

U2 - 10.1080/0305215042000274933

DO - 10.1080/0305215042000274933

M3 - Article

AN - SCOPUS:6344283164

VL - 36

SP - 705

EP - 719

JO - Engineering Optimization

JF - Engineering Optimization

SN - 0305-215X

IS - 6

ER -