TY - GEN

T1 - Column generation method for unit commitment

AU - Shiina, Takayuki

AU - Imaizumi, Jun

PY - 2008/12/1

Y1 - 2008/12/1

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

T3 - Proceedings of the 2008 International Conference on Scientific Computing, CSC 2008

SP - 64

EP - 70

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

T2 - 2008 International Conference on Scientific Computing, CSC 2008

Y2 - 14 July 2008 through 17 July 2008

ER -