Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 497014, 17 pages
Research Article

Robust Optimization-Based Generation Self-Scheduling under Uncertain Price

1Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
2College of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410004, China
3Department of Mathematics, Hengyang Normal University, Hengyang 421002, China

Received 19 September 2010; Revised 20 November 2010; Accepted 24 January 2011

Academic Editor: J. Rodellar

Copyright © 2011 Xiao Luo et al. 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.


This paper considers generation self-scheduling in electricity markets under uncertain price. Based on the robust optimization (denoted as RO) methodology, a new self-scheduling model, which has a complicated max-min optimization structure, is set up. By using optimal dual theory, the proposed model is reformulated to an ordinary quadratic and quadratic cone programming problems in the cases of box and ellipsoidal uncertainty, respectively. IEEE 30-bus system is used to test the new model. Some comparisons with other methods are done, and the sensitivity with respect to the uncertain set is analyzed. Comparing with the existed uncertain self-scheduling approaches, the new method has twofold characteristics. First, it does not need a prediction of distribution of random variables and just requires an estimated value and the uncertain set of power price. Second, the counterpart of RO corresponding to the self-scheduling is a simple quadratic or quadratic cone programming. This indicates that the reformulated problem can be solved by many ordinary optimization algorithms.