Grey wolf optimization applied to economic load dispatch problems Moumita Pradhan a,⇑ , Provas Kumar Roy b , Tandra Pal c a Department of Computer Science and Engineering, Dr. B C Roy Engineering College, Durgapur, West Bengal, India b Department of Electrical Engineering, Jalpaiguri Government Engineering College, Jalpaiguri, West Bengal, India c Department of Computer Science and Engineering, National Institute of Technology, Durgapur, West Bengal, India article info Article history: Received 17 January 2015 Received in revised form 7 April 2016 Accepted 11 April 2016 Keywords: Grey wolf optimization Evolutionary algorithm Economic load dispatch Valve point loading Prohibited zone abstract This article presents a new evolutionary optimization approach named grey wolf optimization (GWO), which is based on the behaviour of grey wolves, for the optimal operating strategy of economic load dis- patch (ELD). Nonlinear characteristics of generators like ramp rate limits, valve point discontinuities and prohibited operating zones are considered in the problem. GWO method does not require any informa- tion about the gradient of the objective function, while searching for an optimum solution. The GWO algorithm concept, appears to be a robust and reliable optimization algorithm is applied to the nonlinear ELD problems. The proposed algorithm is implemented and tested on four test systems having 10, 40, 80 and 140 units. The results confirm the potential and effectiveness of the proposed algorithm compared to various other methods available in the literature. The outcome is very encouraging and proves that the GWO is a very effective optimization technique for solving various ELD problems. Ó 2016 Elsevier Ltd. All rights reserved. Introduction Nowadays, the electrical power market becomes highly com- petitive and more liberal for increasing energy demand. Economic load dispatch (ELD) is one of the useful tools in the modern energy management system of operation and planning. ELD plays a vital role in maintaining the economy of the power system. Reduction of the production cost and growth in the system reliability maxi- mize the energy capability of thermal units through a good load dispatch. The main goal of ELD process is to schedule the power system control variables for sharing the total load to achieve high- est economy of operation while satisfying all equality and inequal- ity constraints. To achieve optimal solution of a practical ELD problem, the realistic operation of the ELD problem should con- sider valve point effects, ramp rate and multiple fuels. Several derivative based approaches such as the classical optimization methods based on Lagrangian relaxation [1], quadratic program- ming (QP) [2], branch and bound method [3], lambda iteration method (LIM) [4], gradient method [5], linear programming (LP) [6], co-ordination equation [7], dynamic programming (DP) [8] assuming monotonically increasing piecewise linear cost function, have successfully been applied to solve ELD. However, the classical optimization techniques are highly sensitive to staring points and often converge to local optimum or diverge altogether. Solutions of ELD problem applying DP may cause the dimensions extremely large, which requires enormous computational efforts. Due to the presence of nonlinear characteristics such as ramp rate limits, dis- continuous prohibited operating zones and non-smooth cost func- tions of practical ELD problem, these methods are infeasible in practical systems and are unable to locate the global optima solu- tion. To solve non smooth and non convex ELD problem, Yang et al. [9] presented an analytical method named quadratically con- strained programming (QCP). Due to a large number of constraints and highly nonlinear characteristics of the ELD problem, the classi- cal calculus based methods cannot perform satisfactorily and are trapped to local optimum. Hence, it becomes essential to overcome these drawbacks and handle such difficulties through developing a robust, improved and reliable technique. In the recent years, com- plex constrained optimization problems are solved by many artifi- cial intelligent methods such as Hopfield neural network (HNN) [10,11] and adaptive HNN [12]. These techniques have successfully been applied in recent years to solve non-convex, non-smooth and non-differentiable ELD problems. However, due to excessive numerical iterations of these methods, more reliable and fast methods are needed. With the development of computer technology, the population based modern intelligent heuristic and stochastic optimization methods such as evolutionary programming (EP) [13], hybrid evo- lutionary programming (HEP) [14], differential evolution (DE) [15], genetic algorithm (GA) [16], adaptive real coded GA (ARCGA) [17], http://dx.doi.org/10.1016/j.ijepes.2016.04.034 0142-0615/Ó 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author at: Dr. B C Roy Engineering College, Fuljhore, Jemua Road, Durgapur 713206, West Bengal, India. Tel.: +91 9433486517; fax: 91 3432503424. E-mail address: pradhanmoumita17@gmail.com (M. Pradhan). Electrical Power and Energy Systems 83 (2016) 325–334 Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes