Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 368024, 13 pages
Research Article

A Comparative Study of Three Different Mathematical Methods for Solving the Unit Commitment Problem

Department of Electrical and Electronics Engineering, Anadolu University, 26470 Eskişehir, Turkey

Received 23 December 2008; Revised 10 March 2009; Accepted 10 March 2009

Academic Editor: Joaquim J. Júdice

Copyright © 2009 Mehmet Kurban and Ümmühan Başaran Filik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The unit commitment (UC) problem which is an important subject in power system engineering is solved by using Lagragian relaxation (LR), penalty function (PF), and augmented Lagrangian penalty function (ALPF) methods due to their higher solution quality and faster computational time than metaheuristic approaches. This problem is considered to be a nonlinear programming-(NP-) hard problem because it is nonlinear, mixed-integer, and nonconvex. These three methods used for solving the problem are based on dual optimization techniques. ALPF method which combines the algorithmic aspects of both LR and PF methods is firstly used for solving the UC problem. These methods are compared to each other based on feasible schedule for each stage, feasible cost, dual cost, duality gap, duration time, and number of iterations. The numerical results show that the ALPF method gives the best duality gap, feasible and dual cost instead of worse duration time and the number of iterations. The four-unit Tuncbilek thermal plant which is located in Kutahya region in Turkey is chosen as a test system in this study. The programs used for all the analyses are coded and implemented using general algebraic modeling system (GAMS).