Improved differential evolution for economic dispatch

Abstract This paper presents an improved differential evolution to solve economic dispatch problem of thermal generating units with non-smooth/non-convex cost functions due to valve-point loading taking into account transmission losses and nonlinear generator constraints such as prohibited operating zones. Differential evolution exploits the differences of randomly sampled pairs of objective vectors for its mutation process. Consequently the variation between vectors will outfit the objective function toward the optimization process and therefore provides efficient global optimization capability. However, although DE is shown to be precise, fast as well as robust, its search efficiency will be impaired during solution process with fast descending diversity of population. This paper proposes Gaussian random variable instead of scaling factor which improves search efficiency. The proposed method has been applied to four different non-convex economic dispatch problems with valve-point effects, prohibited operating zones with transmission losses, multiple fuels with valve point effects and the large-scale Korean power system with valve-point effects and prohibited operating zones. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed improved differential evolution based approach is able to provide better solution.

[1]  A. Srinivasa Reddy,et al.  Shuffled differential evolution for large scale economic dispatch , 2013 .

[2]  Z.-X. Liang,et al.  A zoom feature for a dynamic programming solution to economic dispatch including transmission losses , 1992 .

[3]  Chih-Wen Liu,et al.  Non-smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm , 2007 .

[4]  A. Selvakumar,et al.  A New Particle Swarm Optimization Solution to Nonconvex Economic Dispatch Problems , 2007, IEEE Transactions on Power Systems.

[5]  P. K. Chattopadhyay,et al.  Biogeography-Based Optimization for Different Economic Load Dispatch Problems , 2010, IEEE Transactions on Power Systems.

[6]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[7]  Y. W. Wong,et al.  Genetic and genetic/simulated-annealing approaches to economic dispatch , 1994 .

[8]  Ching-Tzong Su,et al.  New approach with a Hopfield modeling framework to economic dispatch , 2000 .

[9]  Chao-Lung Chiang,et al.  Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels , 2005 .

[10]  Malcolm Irving,et al.  Economic dispatch of generators with prohibited operating zones: a genetic algorithm approach , 1996 .

[11]  Hong-Tzer Yang,et al.  Evolutionary programming based economic dispatch for units with non-smooth fuel cost functions , 1996 .

[12]  Chun Che Fung,et al.  Simulated annealing based economic dispatch algorithm , 1993 .

[13]  Bijaya Ketan Panigrahi,et al.  Bacterial foraging optimisation: Nelder-Mead hybrid algorithm for economic load dispatch , 2008 .

[14]  Rainer Storn,et al.  Minimizing the real functions of the ICEC'96 contest by differential evolution , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[15]  Leandro dos Santos Coelho,et al.  Differential evolution based on truncated Lévy-type flights and population diversity measure to solve economic load dispatch problems , 2014 .

[16]  Jong-Bae Park,et al.  An Improved Particle Swarm Optimization for Nonconvex Economic Dispatch Problems , 2010 .

[17]  Yunhe Hou,et al.  Generalized ant colony optimization for economic dispatch of power systems , 2002, Proceedings. International Conference on Power System Technology.

[18]  Joong-Rin Shin,et al.  A particle swarm optimization for economic dispatch with nonsmooth cost functions , 2005, IEEE Transactions on Power Systems.

[19]  Whei-Min Lin,et al.  An Improved Tabu Search for Economic Dispatch with Multiple Minima , 2002, IEEE Power Engineering Review.

[20]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[21]  Abbas Rabiee,et al.  Continuous quick group search optimizer for solving non-convex economic dispatch problems , 2012 .

[22]  G. Sheblé,et al.  Genetic algorithm solution of economic dispatch with valve point loading , 1993 .

[23]  Sanjoy Mandal,et al.  Economic load dispatch using krill herd algorithm , 2014 .

[24]  Zwe-Lee Gaing,et al.  Particle swarm optimization to solving the economic dispatch considering the generator constraints , 2003 .

[25]  P. K. Chattopadhyay,et al.  Evolutionary programming techniques for economic load dispatch , 2003, IEEE Trans. Evol. Comput..

[26]  Aniruddha Bhattacharya,et al.  Oppositional Real Coded Chemical Reaction Optimization for different economic dispatch problems , 2014 .

[27]  Hong-Chan Chang,et al.  Large-scale economic dispatch by genetic algorithm , 1995 .

[28]  Yunhe Hou,et al.  Application of generalized ant colony optimizaiton algorithm integrated with particle swarm optimization algorithm in economic dispatch of power system , 2004 .

[29]  Osvaldo R. Saavedra,et al.  EFFICIENT EVOLUTIONARY STRATEGY OPTIMISATION PROCEDURE TO SOLVE THE NONCONVEX ECONOMIC DISPATCH PROBLEM WITH GENERATOR CONSTRAINTS , 2005 .

[30]  Manoj Kumar Tiwari,et al.  A clonal algorithm to solve economic load dispatch , 2007 .

[31]  M. Pandit,et al.  Self-Organizing Hierarchical Particle Swarm Optimization for Nonconvex Economic Dispatch , 2008, IEEE Transactions on Power Systems.

[32]  Y. W. Wong,et al.  Thermal generator scheduling using hybrid genetic/simulated-annealing approach , 1995 .

[33]  H. Iba,et al.  Differential evolution for economic load dispatch problems , 2008 .