### Abstract

We propose a new algorithm for the stochastic unit commitment problem which is based on the Lagrangian relaxation and the column generation approach. This problem is formulated as a multi-stage nonlinear integer programming problem because the fuel cost function is assumed to be a convex quadratic function. The algorithm consists of two phases. After solving the problem by Lagrangian relaxation, the algorithm continues adding schedules from the dual solution of the restricted linear master program until the algorithm cannot generate new schedules. The schedule generation problem is solved by the calculation of dynamic programming on the scenario tree. We applied the Lagrangian relaxation-column generation approach to a test problem based on the system of a certain Japanese electric power company. Numerical results indicate a significant improvement in the quality of the solution.

Original language | English |
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Title of host publication | Proceedings of the 2008 International Conference on Scientific Computing, CSC 2008 |

Pages | 64-70 |

Number of pages | 7 |

Publication status | Published - 2008 |

Externally published | Yes |

Event | 2008 International Conference on Scientific Computing, CSC 2008 - Las Vegas, NV, United States Duration: 2008 Jul 14 → 2008 Jul 17 |

### Other

Other | 2008 International Conference on Scientific Computing, CSC 2008 |
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Country | United States |

City | Las Vegas, NV |

Period | 08/7/14 → 08/7/17 |

### Fingerprint

### Keywords

- Column generation
- Lagrangian relaxation
- Stochastic programming
- Unit commitment

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Science Applications
- Software

### Cite this

*Proceedings of the 2008 International Conference on Scientific Computing, CSC 2008*(pp. 64-70)

**Column generation method for unit commitment.** / Shiina, Takayuki; Imaizumi, Jun.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 2008 International Conference on Scientific Computing, CSC 2008.*pp. 64-70, 2008 International Conference on Scientific Computing, CSC 2008, Las Vegas, NV, United States, 08/7/14.

}

TY - GEN

T1 - Column generation method for unit commitment

AU - Shiina, Takayuki

AU - Imaizumi, Jun

PY - 2008

Y1 - 2008

N2 - We propose a new algorithm for the stochastic unit commitment problem which is based on the Lagrangian relaxation and the column generation approach. This problem is formulated as a multi-stage nonlinear integer programming problem because the fuel cost function is assumed to be a convex quadratic function. The algorithm consists of two phases. After solving the problem by Lagrangian relaxation, the algorithm continues adding schedules from the dual solution of the restricted linear master program until the algorithm cannot generate new schedules. The schedule generation problem is solved by the calculation of dynamic programming on the scenario tree. We applied the Lagrangian relaxation-column generation approach to a test problem based on the system of a certain Japanese electric power company. Numerical results indicate a significant improvement in the quality of the solution.

AB - We propose a new algorithm for the stochastic unit commitment problem which is based on the Lagrangian relaxation and the column generation approach. This problem is formulated as a multi-stage nonlinear integer programming problem because the fuel cost function is assumed to be a convex quadratic function. The algorithm consists of two phases. After solving the problem by Lagrangian relaxation, the algorithm continues adding schedules from the dual solution of the restricted linear master program until the algorithm cannot generate new schedules. The schedule generation problem is solved by the calculation of dynamic programming on the scenario tree. We applied the Lagrangian relaxation-column generation approach to a test problem based on the system of a certain Japanese electric power company. Numerical results indicate a significant improvement in the quality of the solution.

KW - Column generation

KW - Lagrangian relaxation

KW - Stochastic programming

KW - Unit commitment

UR - http://www.scopus.com/inward/record.url?scp=62649087577&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62649087577&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:62649087577

SN - 1601320590

SN - 9781601320599

SP - 64

EP - 70

BT - Proceedings of the 2008 International Conference on Scientific Computing, CSC 2008

ER -