A Hybrid With Cross-Entropy Method and Sequential Quadratic Programming to Solve Economic Load Dispatch Problem

This paper presents a new hybrid approach integrating the cross-entropy (CE) algorithm and the sequential quadratic programming (SQP) technique to solve the economic load dispatch (ELD) problem related to electrical power generating units. Due to the introduction of the valve-point effect in the ELD objective function, the optimization task requires tools appropriate for a nonconvex optimization landscape. In this respect, we employ the CE approach, which constructs a random sequence of solutions probabilistically converging to a near-optimal solution and, thus, facilitating the exploration capability. Additionally, to fine-tune the solution in promising basins of attraction, the SQP algorithm is invoked, which performs a local search. Despite its reliance on a global heuristic scheme, CE-SQP is vested with fast convergence capability, which may entail its use for online power dispatch. The effectiveness and the robustness of the proposed method in comparison with several state-of-the-art approaches have been demonstrated with four standard test systems that are widely reported in the ELD literature.

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

[2]  P. Subbaraj,et al.  Enhancement of Self-adaptive real-coded genetic algorithm using Taguchi method for Economic dispatch problem , 2011, Appl. Soft Comput..

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

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

[5]  A. Ebenezer Jeyakumar,et al.  A modified hybrid EP–SQP approach for dynamic dispatch with valve-point effect , 2005 .

[6]  Fuli Wang,et al.  Hybrid genetic algorithm for economic dispatch with valve-point effect , 2008 .

[7]  Ieee Report,et al.  Present Practices in the Economic Operation of Power Systems , 1971 .

[8]  June Ho Park,et al.  Adaptive Hopfield neural networks for economic load dispatch , 1998 .

[9]  P. Subbaraj,et al.  Parallel particle swarm optimization with modified stochastic acceleration factors for solving large scale economic dispatch problem , 2010 .

[10]  Lan Zhang,et al.  Real-time economic dispatch with line flow and emission constraints using quadratic programming , 1998 .

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

[12]  Paul T. Boggs,et al.  Sequential Quadratic Programming , 1995, Acta Numerica.

[13]  Allen J. Wood,et al.  Power Generation, Operation, and Control , 1984 .

[14]  Z. Dong,et al.  Quantum-Inspired Particle Swarm Optimization for Valve-Point Economic Load Dispatch , 2010, IEEE Transactions on Power Systems.

[15]  Dirk P. Kroese,et al.  The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning , 2004 .

[16]  Amir Hossein Gandomi,et al.  Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect , 2012, Appl. Soft Comput..

[17]  Waree Kongprawechnon,et al.  Ant colony optimisation for economic dispatch problem with non-smooth cost functions , 2010 .

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

[19]  A. Immanuel Selvakumar,et al.  Enhanced cross-entropy method for dynamic economic dispatch with valve-point effects , 2011 .

[20]  Jonathan F. Bard,et al.  Short-Term Scheduling of Thermal-Electric Generators Using Lagrangian Relaxation , 1988, Oper. Res..

[21]  Lixiang Li,et al.  A hybrid FCASO-SQP method for solving the economic dispatch problems with valve-point effects , 2012 .

[22]  Whei-Min Lin,et al.  A novel stochastic search method for the solution of economic dispatch problems with non-convex fuel cost functions , 2011 .

[23]  Sishaj P. Simon,et al.  Artificial Bee Colony Algorithm for Economic Load Dispatch Problem with Non-smooth Cost Functions , 2010 .

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

[25]  S. Sivasubramani,et al.  Hybrid SOA–SQP algorithm for dynamic economic dispatch with valve-point effects , 2010 .

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

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

[28]  Jan K. Sykulski,et al.  Application of pattern search method to power system valve-point economic load dispatch , 2007 .

[29]  Tomonobu Senjyu,et al.  Solving economic load dispatch problem with valve-point effects using a hybrid quantum mechanics inspired particle swarm optimisation , 2011 .

[30]  D. Ernst,et al.  The cross-entropy method for power system combinatorial optimization problems , 2007, 2007 IEEE Lausanne Power Tech.

[31]  Leandro dos Santos Coelho,et al.  An efficient cultural self-organizing migrating strategy for economic dispatch optimization with valve-point effect , 2010 .

[32]  Malabika Basu,et al.  Hybridization of bee colony optimization and sequential quadratic programming for dynamic economic dispatch , 2013 .

[33]  P. K. Chattopadhyay,et al.  Hybrid Differential Evolution With Biogeography-Based Optimization for Solution of Economic Load Dispatch , 2010, IEEE Transactions on Power Systems.

[34]  A. Immanuel Selvakumar,et al.  Anti-predatory particle swarm optimization : Solution to nonconvex economic dispatch problems , 2008 .

[35]  Nima Amjady,et al.  Solution of non-convex economic dispatch problem considering valve loading effect by a new Modified Differential Evolution algorithm , 2010 .

[36]  L. Coelho,et al.  Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect , 2006, IEEE Transactions on Power Systems.

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

[38]  Tharam S. Dillon,et al.  Experimental study of a new hybrid PSO with mutation for economic dispatch with non-smooth cost function , 2010 .

[39]  Hak-Keung Lam,et al.  Hybrid Particle Swarm Optimization With Wavelet Mutation and Its Industrial Applications , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[40]  Chao-Lung Chiang,et al.  Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels , 2005, IEEE Transactions on Power Systems.

[41]  S. Khamsawang,et al.  DSPSO–TSA for economic dispatch problem with nonsmooth and noncontinuous cost functions , 2010 .

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

[43]  A. Srinivasa Reddy,et al.  Shuffled differential evolution for economic dispatch with valve point loading effects , 2013 .

[44]  Leandro dos Santos Coelho,et al.  An improved harmony search algorithm for power economic load dispatch , 2009 .

[45]  P. K. Chattopadhyay,et al.  Solving complex economic load dispatch problems using biogeography-based optimization , 2010, Expert Syst. Appl..

[46]  Haipeng Peng,et al.  Chaotic ant swarm optimization to economic dispatch , 2007 .

[47]  J.G. Vlachogiannis,et al.  Economic Load Dispatch—A Comparative Study on Heuristic Optimization Techniques With an Improved Coordinated Aggregation-Based PSO , 2009, IEEE Transactions on Power Systems.

[48]  A. Immanuel Selvakumar,et al.  Optimization using civilized swarm: Solution to economic dispatch with multiple minima , 2009 .

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

[50]  Zhang Zhisheng.  Short Communication: Quantum-behaved particle swarm optimization algorithm for economic load dispatch of power system , 2010 .

[51]  Chern-Lin Chen,et al.  Branch-and-bound scheduling for thermal generating units , 1993 .

[52]  Dirk P. Kroese,et al.  Optimal generation expansion planning via the Cross-Entropy method , 2009, Proceedings of the 2009 Winter Simulation Conference (WSC).

[53]  Taher Niknam,et al.  A new fuzzy adaptive hybrid particle swarm optimization algorithm for non-linear, non-smooth and non-convex economic dispatch problem , 2010 .

[54]  B. J. Cory,et al.  A homogeneous linear programming algorithm for the security constrained economic dispatch problem , 2000 .

[55]  Lixiang Li,et al.  An Optimization Method Inspired by "chaotic" Ant Behavior , 2006, Int. J. Bifurc. Chaos.

[56]  Taher Niknam,et al.  Probabilistic multiobjective wind-thermal economic emission dispatch based on point estimated method , 2012 .

[57]  Zhisheng Zhang,et al.  Quantum-behaved particle swarm optimization algorithm for economic load dispatch of power system , 2010, Expert Syst. Appl..

[58]  Samir Sayah,et al.  A hybrid differential evolution algorithm based on particle swarm optimization for nonconvex economic dispatch problems , 2013, Appl. Soft Comput..

[59]  Leandro dos Santos Coelho,et al.  Improved differential evolution approach based on cultural algorithm and diversity measure applied to solve economic load dispatch problems , 2009, Math. Comput. Simul..

[60]  Abbas Rabiee,et al.  Iteration PSO with time varying acceleration coefficients for solving non-convex economic dispatch problems , 2012 .

[61]  Lixiang Li,et al.  A hybrid CPSO–SQP method for economic dispatch considering the valve-point effects , 2012 .

[62]  J. Nanda,et al.  Economic emission load dispatch with line flow constraints using a classical technique , 1994 .

[63]  Lixiang Li,et al.  Fuzzy system identification via chaotic ant swarm , 2009 .

[64]  Bijaya K. Panigrahi,et al.  Neighborhood Search-Driven Accelerated Biogeography-Based Optimization for Optimal Load Dispatch , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

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

[66]  C.-L. Chiang,et al.  Genetic-based algorithm for power economic load dispatch , 2007 .

[67]  Whei-Min Lin,et al.  Combining of Direct Search and Signal-to-Noise Ratio for economic dispatch optimization , 2011 .

[68]  Dirk P. Kroese,et al.  The Cross-Entropy Method for Continuous Multi-Extremal Optimization , 2006 .

[69]  K.S. Swarup,et al.  Particle swarm optimization for security constrained economic dispatch , 2004, International Conference on Intelligent Sensing and Information Processing, 2004. Proceedings of.

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

[71]  Fuli Wang,et al.  A hybrid genetic algorithm approach based on differential evolution for economic dispatch with valve-point effect , 2008 .

[72]  Jan K. Sykulski,et al.  A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems , 2010 .

[73]  Sai-Ho Ling,et al.  An Improved Genetic Algorithm with Average-bound Crossover and Wavelet Mutation Operations , 2007, Soft Comput..

[74]  Ying Cai,et al.  Taguchi method for solving the economic dispatch problem with nonsmooth cost functions , 2005 .

[75]  Abhinav Sadu,et al.  A hybrid multi-agent based particle swarm optimization algorithm for economic power dispatch , 2011 .

[76]  P. Martin,et al.  An optimal formulation and solution of short-range operating problems for a power system with flow constraints , 1972 .

[77]  Shie Mannor,et al.  A Tutorial on the Cross-Entropy Method , 2005, Ann. Oper. Res..

[78]  Eric S. Fraga,et al.  On the modelling of valve point loadings for power electricity dispatch , 2012 .

[79]  Lixiang Li,et al.  CHAOTIC PARTICLE SWARM OPTIMIZATION FOR ECONOMIC DISPATCH CONSIDERING THE GENERATOR CONSTRAINTS , 2007 .

[80]  A. Ebenezer Jeyakumar,et al.  Hybrid PSO–SQP for economic dispatch with valve-point effect , 2004 .