An enhanced moth-flame optimizer for solving non-smooth economic dispatch problems with emissions

Abstract This paper proposes an Enhanced Moth-Flame Optimization (EMFO) algorithm for solving the non-convex economic dispatch (ED) problem with valve point effects and emissions. It determines the optimal generation schedule of generating units by minimizing both fuel cost and emission simultaneously while the system constraints are achieved. The moth-flame optimization (MFO) is a recent nature-inspired method, which is based on the navigation mechanism called transverse orientation of Moths in space. The EMFO combines the merits of the traditional MFO and levy flight by concentration the search space. The usage of L e vy-flight has the prominent properties to increase the diversity of population. The effectiveness of the proposed EMFO method is proven on using 10 benchmark functions and 3 standard test systems consisting of 6, 40 and a large scale 80 generating units with non-convex fuel cost functions. The capability of the proposed algorithm is verified also for single and multi-objective studied cases and its results are compared with several well-known previous techniques. The results confirm the high performance of the proposed EMFO method for finding the optimal economic generation scheduling at acceptable low emission levels.

[1]  A.A. Abou Ela,et al.  Different transmission loss allocation schemes in deregulated power markets , 2007, 2007 42nd International Universities Power Engineering Conference.

[2]  Seyed Mohammad Mirjalili,et al.  Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm , 2015, Knowl. Based Syst..

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

[4]  Hany M. Hasanien,et al.  Optimal power flow solution in power systems using a novel Sine-Cosine algorithm , 2018, International Journal of Electrical Power & Energy Systems.

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

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

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

[8]  Indrajit N. Trivedi,et al.  Optimal power flow with voltage stability improvement and loss reduction in power system using Moth-Flame Optimizer , 2016, Neural Computing and Applications.

[9]  J. P. Zhan,et al.  Dynamic economic emission dispatch based on group search optimizer with multiple producers , 2012 .

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

[11]  J. M. Grau,et al.  The Exact Solution of the Environmental/Economic Dispatch Problem , 2012, IEEE Transactions on Power Systems.

[12]  Narayana Prasad Padhy,et al.  Comparison and application of evolutionary programming techniques to combined economic emission dispatch with line flow constraints , 2003 .

[13]  Yasser G. Hegazy,et al.  A review on accuracy issues related to solving the non-convex economic dispatch problem , 2016 .

[14]  Bachir Bentouati,et al.  Optimal Power Flow using the Moth Flam Optimizer: A case study of the Algerian power system , 2016 .

[15]  Nima Amjady,et al.  Solution of nonconvex and nonsmooth economic dispatch by a new Adaptive Real Coded Genetic Algorithm , 2010, Expert Syst. Appl..

[16]  Ragab A. El-Sehiemy,et al.  Multiobjective Real-Coded Genetic Algorithm for Economic/Environmental Dispatch Problem, , 2013 .

[17]  Yasser G. Hegazy,et al.  Modified social spider algorithm for solving the economic dispatch problem , 2016 .

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

[19]  Taher Niknam,et al.  Non-smooth economic dispatch computation by fuzzy and self adaptive particle swarm optimization , 2011, Appl. Soft Comput..

[20]  Hossam Faris,et al.  Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems , 2017, Adv. Eng. Softw..

[21]  A. Chowdhury,et al.  Cuckoo search algorithm for economic dispatch , 2013 .

[22]  Mohammed Azmi Al-Betar,et al.  Tournament-based harmony search algorithm for non-convex economic load dispatch problem , 2016, Appl. Soft Comput..

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

[24]  Xin‐She Yang,et al.  Appendix A: Test Problems in Optimization , 2010 .

[25]  H. Shayeghi,et al.  A modified artificial bee colony based on chaos theory for solving non-convex emission/economic dispatch , 2014 .

[26]  Hamdan Daniyal,et al.  Optimal reactive power dispatch solution by loss minimization using moth-flame optimization technique , 2017, Appl. Soft Comput..

[27]  David C. Yu,et al.  An Economic Dispatch Model Incorporating Wind Power , 2008, IEEE Transactions on Energy Conversion.

[28]  M. Fesanghary,et al.  A novel meta-heuristic optimization methodology for solving various types of economic dispatch problem , 2009 .

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

[30]  Hossein Nezamabadi-pour,et al.  GSA: A Gravitational Search Algorithm , 2009, Inf. Sci..

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

[32]  Ugur Güvenc,et al.  Combined economic and emission dispatch solution using gravitational search algorithm , 2012, Sci. Iran..

[33]  I. Pavlyukevich.  Cooling down Lévy flights , 2007, cond-mat/0701651.

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

[35]  Dong Yue,et al.  Multi-elite guide hybrid differential evolution with simulated annealing technique for dynamic economic emission dispatch , 2015, Appl. Soft Comput..

[36]  Eid Emary,et al.  Feature selection approach based on moth-flame optimization algorithm , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[37]  Lalit Chandra Saikia,et al.  Automatic generation control in competitive market conditions with moth-flame optimization based cascade controller , 2016, 2016 IEEE Region 10 Conference (TENCON).

[38]  Indrajit N. Trivedi,et al.  Optimal active and Reactive Power dispatch problem solution using Moth-Flame Optimizer algorithm , 2016, 2016 International Conference on Energy Efficient Technologies for Sustainability (ICEETS).

[39]  Cunbin Li,et al.  A least squares support vector machine model optimized by moth-flame optimization algorithm for annual power load forecasting , 2016, Applied Intelligence.

[40]  Whei-Min Lin,et al.  Quantum genetic algorithm for dynamic economic dispatch with valve-point effects and including wind power system , 2011 .

[41]  Malabika Basu,et al.  Dynamic economic emission dispatch using nondominated sorting genetic algorithm-II , 2008 .

[42]  Clifford T. Brown,et al.  Lévy Flights in Dobe Ju/’hoansi Foraging Patterns , 2007 .

[43]  Ji Xiang,et al.  Distributed Consensus Based Supply–Demand Balance Algorithm for Economic Dispatch Problem in a Smart Grid With Switching Graph , 2017, IEEE Transactions on Industrial Electronics.

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

[45]  Mimoun Younes,et al.  Multi-objective economic emission dispatch solution using hybrid FFA (firefly algorithm) and considering wind power penetration , 2014 .

[46]  Ragab A. El-Sehiemy,et al.  A novel parallel hurricane optimization algorithm for secure emission/economic load dispatch solution , 2018, Appl. Soft Comput..

[47]  Waree Kongprawechnon,et al.  Application of multiple tabu search algorithm to solve dynamic economic dispatch considering generator constraints , 2008 .

[48]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[49]  W. T. Elsayed,et al.  A Fully Decentralized Approach for Solving the Economic Dispatch Problem , 2015, IEEE Transactions on Power Systems.

[50]  Mahmood Joorabian,et al.  An improved cuckoo search algorithm for power economic load dispatch , 2015 .

[51]  Marte A. Ramírez-Ortegón,et al.  An optimization algorithm inspired by the States of Matter that improves the balance between exploration and exploitation , 2013, Applied Intelligence.

[52]  Sakti Prasad Ghoshal,et al.  A novel opposition-based gravitational search algorithm for combined economic and emission dispatch problems of power systems , 2012 .

[53]  Xiaoxin Zhou,et al.  Economic Dispatch With Non-Smooth Objectives—Part I: Local Minimum Analysis , 2015, IEEE Transactions on Power Systems.

[54]  Almoataz Y. Abdelaziz,et al.  Flower pollination algorithm to solve combined economic and emission dispatch problems , 2016 .

[55]  Ilya Pavlyukevich.  Lévy flights, non-local search and simulated annealing , 2007, J. Comput. Phys..

[56]  Indrajit N. Trivedi,et al.  Moth flame optimization to solve optimal power flow with non-parametric statistical evaluation validation , 2017 .

[57]  Pradeep Jangir,et al.  Economic Load Dispatch problem with ramp rate limits and prohibited operating zones solve using Levy flight Moth-Flame optimizer , 2016, 2016 International Conference on Energy Efficient Technologies for Sustainability (ICEETS).

[58]  Gang Chen,et al.  Distributed Finite-Time Economic Dispatch of a Network of Energy Resources , 2017, IEEE Transactions on Smart Grid.

[59]  Kazem Zare,et al.  Solving non-convex economic dispatch problem with valve point effects using modified group search optimizer method , 2012 .

[60]  Mostafa Modiri-Delshad,et al.  Backtracking search algorithm for solving economic dispatch problems with valve-point effects and multiple fuel options , 2016 .

[61]  Malabika Basu,et al.  Modified particle swarm optimization for nonconvex economic dispatch problems , 2015 .

[62]  Jian Xie,et al.  A Novel Bat Algorithm Based on Differential Operator and Lévy Flights Trajectory , 2013, Comput. Intell. Neurosci..