Modified cuckoo search algorithm for short-term hydrothermal scheduling Thang Trung Nguyen a , Dieu Ngoc Vo b,⇑ a Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, 19 Nguyen Huu Tho str., 7th dist., Ho Chi Minh city, Viet Nam b Department of Power Systems, Ho Chi Minh City University of Technology, 268 Ly Thuong Kiet str., 10th dist., Ho Chi Minh city, Viet Nam article info Article history: Received 8 March 2014 Received in revised form 11 June 2014 Accepted 10 October 2014 Keywords: Lévy flight Modified cuckoo search algorithm Non-convex fuel cost function Short-term hydrothermal scheduling Water availability constraint abstract This paper proposes a modified cuckoo search algorithm (MCSA) for solving short-term hydrothermal scheduling (HTS) problem. The considered HTS problem in this paper is to minimize total cost of thermal generators with valve point loading effects satisfying power balance constraint, water availability, and generator operating limits. The MCSA method is based on the conventional CSA method with modifica- tions to enhance its search ability. In the MCSA, the eggs are first sorted in the descending order of their fitness function value and then classified in two groups where the eggs with low fitness function value are put in the top egg group and the other ones are put in the abandoned one. The abandoned group, the step size of the Lévy flight in CSA will change with the number of iterations to promote more localized searching when the eggs are getting closer to the optimal solution. On the other hand, there will be an information exchange between two eggs in the top egg group to speed up the search process of the eggs. The proposed MCSA method has been tested on different systems and the obtained results are compared to those from other methods available in the literature. The result comparison has indicated that the pro- posed method can obtain higher quality solutions than many other methods. Therefore, the proposed MCSA can be a new efficient method for solving short-term fixed-head hydrothermal scheduling problems. Ó 2014 Elsevier Ltd. All rights reserved. Introduction A modern power system consists of a large number of thermal and hydro plants connected at various load centers through a transmission network. An important objective in the operation of such a power system is to generate and transmit power to meet the system load demand at minimum fuel cost by an optimal mix of various types of plants. However, the hydro resources being limited, thus the worth of water is greatly increased [1]. Therefore, an optimal operation of a hydrothermal system will lead to a huge saving in fuel cost of thermal power plants. The objective of the hydrothermal scheduling problem is to find the optimum alloca- tion of hydro energy so that the annual operating cost of a mixed hydrothermal system is minimized [1]. Several conventional methods have been implemented for solving the hydrothermal scheduling problem such as gradient search techniques (GS) [2], lambda-gamma iteration method, dynamic programming (DP) [2], Lagrange relaxation (LR) [3], decomposition and coordination method [4], mixed integer programming (MIP) [5], and Newton’s method [6]. The GS method has been applied to the problem where the hydro generation models were represented as piecewise linear functions or polynomial approximation with a monotonically increasing nature. However, such an approximation may be too rough and seems impractical. In the lambda-gamma method, the gamma values associated with different hydro plants are initially chosen and then the lambda iterations are invoked for the given power demand at each interval of the schedule time horizon. The DP method is another popular optimization method implemented for solving the hydrothermal scheduling problems. However, com- putational and dimensional requirements in the DP method will drastically increase for large-scale systems [7]. On the contrary to the DP method, the LR method is more reliable and efficient for dealing with large-scale problems. However, the LR method may suffer to the duality gap oscillation during the convergence process due to the dual problem formulation, leading to divergence for some problems with non-convexity of incremental heat rate curves of thermal generators. In the decomposition and coordination method, the problem is decomposed into thermal and hydro sub- problems and they are solved by network flow programming and http://dx.doi.org/10.1016/j.ijepes.2014.10.004 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author at: Department of Power Systems, Ho Chi Minh City University of Technology, 268 Ly Thuong Kiet str., 10th dist., Ho Chi Minh city, Viet Nam. Tel.: +84 8 3864 7256x5730. E-mail address: vndieu@gmail.com (D.N. Vo). Electrical Power and Energy Systems 65 (2015) 271–281 Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes