The formulation and solution of the Dynamic Economic Dispatch (DED) problem is one of the key disciplines in modern power system operation, planning, operation and control. Past researches have considered DED on Quadratic Cost Functions (QCF), with only few works considering higher order cost functions which are more accurate. The Static Economic Dispatch (SED) has been widely tackled in past researches, however, it is the DED problem that represents a real life power system. There is need to review this problem and establish a more practical formulation of the same taking into consideration all the objectives and constraints possible. The methods used in the solution of DED problem have evolved from the traditional deterministic ones, to the pure heuristic, and finally to the state of the heart hybrids. The hybrids methods have been developed to exalt the strengths and improve the weaknesses of the base method. Such optimisation methods need to be reviewed and classified. This paper will do an in depth review of the DED problem on both quadratic and cubic cost functions. Further it will provide a detailed classification of the methods used to solve the problem as its complexity increases. Consequently, three method Hybrids is the way go as far as the solution of the cubic Multi Objective DED (MODED) with five objectives is concerned.
| DOI | 10.11648/j.ijepe.20150403.14 |
| Published in | International Journal of Energy and Power Engineering (Volume 4, Issue 3, June 2015) |
| Page(s) | 153-167 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Cubic Cost Functions (CCF), Dynamic Economic Dispatch (DED), Hybrid Methods, Multi Objective DED (MODED)
| [1] | Jizhong Zhu (2009) Optimization of Power System Operation, New Jersey &Canada: John Wiley and Sons. |
| [2] | N.P. Padhy,"Unit Commitment-a Bibliographical Survey," Power Systems, IEEE Transactions on, Vol. 19, No. 2, pp. 1196-1205, 2004. |
| [3] | http://www.sciencedirect.com/science,April 2015. |
| [4] | J.A. Momoh, M.E. El-Hawary and R. Adapa,"A Review of Selected Optimal Power Flow Literature to 1993. II. Newton, Linear Programming and Interior Point Methods," Power Systems, IEEE Transactions on, Vol. 14, No. 1, pp. 105-111, 1999. |
| [5] | M.R. AlRashidi and M.E. El-Hawary, "Applications of Computational Intelligence Techniques for Solving the Revived Optimal Power Flow Problem, “Electrical. Power Syst. Res., Vol. 79, No. 4, pp. 694-702, 2009. |
| [6] | A. Mahor, V. Prasad and S. Rangnekar,"Economic Dispatch using Particle Swarm Optimization: A Review," Renewable and Sustainable Energy Reviews, Vol. 13, No. 8, pp. 2134-2141, 2009. |
| [7] | H. Altun and T. Yalcinoz,"Implementing Soft Computing Techniques to Solve Economic Dispatch Problem in Power Systems," Expert Systems Applications, Vol. 35, No.4, pp. 1668-1678, 2008. |
| [8] | T.E. Bechert and H.G. Kwatny, "On the Optimal Dynamic Dispatch of Real Power," Power Apparatus and Systems, IEEE Transactions on, Vol. PAS-91, no.3, pp. 889-898, 1972. |
| [9] | T.E. Bechert and Nanming Chen,"Area Automatic Generation Control by Multi-Pass Dynamic Programming," Power Apparatus and Systems, IEEE Transactions on, Vol. 96, no. 5, pp. 1460-1469, 1977. |
| [10] | X. Xia and A.M. Elaiw,"Optimal Dynamic Economic Dispatch of Generation: A Review," Electrical Power Systems Res., Vol. In Press, Corrected Proof, 2010. |
| [11] | Faisal A. Mohamed et al “Environmental/Economic Power Dispatch of Micro Grid Using Multiobjective Optimization“ International Conference on Renewable Energies and Power Quality (ICREPQ’09) Valencia (Spain), 15th to 17th April, 2009. |
| [12] | M.A. Abido and J.M. Bakhashwain “ A Novel Multiobjective Evolutionary Algorithm for Optimal Reactive Power Dispatch Problem” in Proceedings of the 2003 10th IEEE International Conference on Electronics, Circuits and Systems, 2003 (ICECS 2003), IEEE, Vol. 3, pp.1054--1057, December 2003. |
| [13] | Zhao Bo and Cao Yi-Jia “Multiple objective particle swarm optimization technique for economic load dispatch” Journal of Zhejiang University of Science and Technology Vol.6 No.5 pp.420-427 2005. |
| [14] | M.A. Abido.” Multiobjective Optimal VAR Dispatch Using Strength Pareto Evolutionary Algorithm” in 2006 IEEE Congress on Evolutionary Computation (CEC'2006), pp. 2745--2751, IEEE, Vancouver, BC, Canada, July 2006. |
| [15] | M. Basu, "Particle Swarm Optimization Based Goal-Attainment Method for Dynamic Economic Emission Dispatch," Electric Power Components and Systems, Vol. 34, No. 9, pp. 1015-1025, 2006. |
| [16] | Amitah Mahor et al “Economic dispatch using particle swarm optimization: A review” Renewable and Sustainable Energy Reviews, Vol 11, pp. 2134-2141,2009. |
| [17] | M. Basu, "Dynamic Economic Emission Dispatch using Evolutionary Programming and Fuzzy Satisfying Method," International Journal of Emerging Electric Power Systems, Vol. 8, No. 4, pp. 1-15, 2007. |
| [18] | C.-. Chen, "Simulated Annealing-Based Optimal Wind-Thermal Coordination Scheduling," Generation, Transmission & Distribution, IET, Vol. 1, no. 3, pp. 447-455, 2007. |
| [19] | M. Basu, "Dynamic Economic Emission Dispatch using Non dominated Sorting Genetic Algorithm-II," International Journal of Electrical Power & Energy Systems, Vol. 30, No. 2, pp. 140-149, 2008. |
| [20] | R.P. Brent, Algorithms for Minimization without Derivatives, N.J.: Prentice-Hall,Englewood Cliffs, 1973. |
| [21] | Zwe-Lee Gaing and Ting-Chia Ou, "Dynamic Economic Dispatch Solution using Fast Evolutionary Programming with Swarm Direction," Industrial Electronics and Applications, 2009. ICIEA 2009. 4th IEEE Conference on, pp. 1538-1544, 2009. |
| [22] | J.S. Alsumait, M. Qasem, J.K. Sykulski and A.K. Al-Othman, "An Improved Pattern Search Based Algorithm to Solve the Dynamic Economic Dispatch Problem with Valve-Point Effect," Energy Conversion and Management, Vol. 51, No. 10, pp. 2062-2067, 2010. |
| [23] | S Subramanian and S Ganesan. “A Simple Approach for Emission Constrained Economic Dispatch Problems” International Journal of Computer Applications Vol. 8, No. 11 pp39–45, October 2010. |
| [24] | Chunghun Kim; Yonghao Gui; Chung Choo Chung; Yong-Cheol Kang, "Model predictive control in dynamic economic dispatch using Weibull distribution," Power and Energy Society General Meeting (PES), 2013 IEEE , Vol.10, pp.1,5, 21-25 July 2013. |
| [25] | Haiwang Zhong; Qing Xia; Yang Wang; Chongqing Kang, "Dynamic Economic Dispatch Considering Transmission Losses Using Quadratically Constrained Quadratic Program Method," Power Systems, IEEE Transactions on , Vol.28, No.3, pp.2232-2241, Aug. 2013. |
| [26] | Azza a. Eldesouky,”Security and stochastic economic dispatch of power system including wind and solar resources with environmental consideration” International journal of renewable energy research Vol.3, No.4 pp. 951-958, 2013.7. |
| [27] | Bakirtzis, E.A; Ntomaris, AV.; Kardakos, E.G.; Simoglou, C.K.; Biskas, P.N.; Bakirtzis, AG., "A unified unit commitment — Economic dispatch model for short-term power system scheduling under high wind energy penetration," European Energy Market (EEM), 2014 11th International Conference on the , Vol.4, pp.1,6, 28-30 May 2014. |
| [28] | Soubache ID and Sudhakara Reddy “solution Combined Economic and Emission Dispatch” American Journal of Engineering Science and Research Vol 1, No 1, pp 1-5 2014. |
| [29] | Z.X Liang and J.D Glover “Improved cost functions for Economic Dispatch compensations “Power Systems IEEE Transactions on Vol 6.pp 821-829,1991. |
| [30] | Z.X Liang and J.D Glover “A zoom feature for a Dynamic Programming Solution to Economic Dispatch including transmission Loses” Power Systems IEEE Transactions on Vol 7.pp 544-550, 1992. |
| [31] | A.jiang and S.Ertem “Economic Dispatch with non-monotonically increasing incremental cost units and transmission system losses” Power Systems IEEE Transactions on Vol 10. pp 891-897, 1995. |
| [32] | Bharathkumar.S et al “Multi Objective Economic Load Dispatch using Hybrid Fuzzy, Bacterial Foraging –Nelder-Mead Algorithm “International Journal of Electrical Engineering and Technology, Vol 4, Issue 3 pp. 43-52, May June 2013. |
| [33] | Hari Mohan D.et al “A Fuzzy field improved hybrid PSO-GSA for Environmental /Economic power dispatch “International Journal of Engineering Science and Technology, Vol.6, No.4,pp.11-23,2014. |
| [34] | Deepak Mishra et al “OR-Neuron Based Hopfield Neural Network for Solving Economic Load Dispatch Problem “Letter and Reviews for Neural Information Processing ,Vol.10,No.11 pp249-259,November 2006. |
| [35] | N.A Amoli et al “Solving Economic Dispatch Problem with Cubic Fuel Cost Function by Firefly Algorithm” Proceedings of the 8th International Conference on Technical and Physical Problems of Power Engineering,ostfold University College Fredrikstad,Norway.pp 1-5,5-7th September 2012. |
| [36] | Krishnamurthy, S.; Tzoneva, R., "Impact of price penalty factors on the solution of the combined economic emission dispatch problem using cubic criterion functions," Power and Energy Society General Meeting, 2012 IEEE , vol., no., pp.1,9, 22-26 July 2012. |
| [37] | Yusuf Sonmez “Estimation of Fuel cost curve parameters for thermal power plants using the ABC Algorithm“ ,Turkish Journal Of Electrical Engineering and Computer Science ,Vol .21 pp. 1827-1841,2013. |
| [38] | T.Adhinarayanan and M.Sydulu “ Fast and effective Algorithm for Economic Dispatch of Cubic Fuel Cost based thermal units “ First international conference on industrial and information systems ,ICIIS ,2006 ,Sirlanka ,8th -11th August 2006. |
| [39] | T.Adhinarayanan and M.Sydulu “An effective non-iterative λ-Logic Based algorithm for Economic Dispatch of generators with cubic fuel cost function” Electrical power and energy systems ,vol 32,pp 539-542,2010. |
| [40] | E.B Elanchezhian et al “Economic Dispatch with cubic cost models using Teaching learning Algorithm “ IET Generation,Transmission and Distribution ,vol 8 issue 7 ,pp 1187-1202,2014. |
| [41] | John Hetzer et al “An Economic Dispatch Model Incorporating Wind Power”IEEE Transactions on Energy Conversion, Vol .23, No.2 June 2008. |
| [42] | Bo Zhao, Chuangxin Guo and Yijia Cao, "Dynamic Economic Dispatch in Electricity Market using Particle Swarm Optimization Algorithm," Intelligent Control and Automation, 2004. WCICA 2004. Fifth World Congress on, Vol. 6, pp. 5050-5054, 2004. |
| [43] | M. Basu, "Particle Swarm Optimization Based Goal-Attainment Method for Dynamic Economic Emission Dispatch," Electric Power Components and Systems, Vol. 34, No. 9, pp. 1015-1025, 2006. |
| [44] | Bandi ramesh et al “Application of BAT algorithm for Combined Economic Load and Emission Dispatch” IJEETC Vol 2 No1.pp 2512-2523, 2013. |
| [45] | Zhao Bo and Cao Yi-Jia “Multiple objective particle swarm optimization technique for economic load dispatch” Journal of Zhejiang University of Science and Technology Vol.6 No.5 pp.420-427 2005. |
| [46] | Amitah Mahor et al “Economic dispatch using particle swarm optimization: A review” Renewable and Sustainable Energy Reviews, Vol 11, pp. 2134-2141,2009. |
| [47] | A. A. Mousa et al “A Hybrid Optimization Technique Coupling an Evolutionary and a Local Search Algorithm for Economic Emission Load Dispatch Problem “Journal of Applied Mathematics, Vol.2, pp. 90-898 ,2011. |
| [48] | Ahmed Ahmed El-Sawy et al, “Reference Point Based TR-PSO for Multi-Objective Environmental/Economic Dispatch “Journal Applied Mathematics, 2013, Vol 4,pp 803-813 ,2013. |
| [49] | Streiffert, D., "Multi-area economic dispatch with tie line constraints," Power Systems, IEEE Transactions on, Vol.10, No.4, pp.1946, 1951, Nov. 1995. |
| [50] | T. Jayabarathi, G. Sadasivam and V. Ramachandran , “Evolutionary Programming-Based Multiarea Economic Dispatch with Tie Line Constraints”, Electric Machines & Power Systems, pp 1165-1176,2000. |
| [51] | P. s. manoharan et al , 2009, “A Novel EP Approach for Multi-area Economic Dispatch with Multiple Fuel Options “Turk J Electrical Engineering & Computer Science Vol.17, No.1, PP1-19, 2009. |
| [52] | Prasanna.T.S and Somasundaram. P “Multi-Area Security Constrained Economic Dispatch by Fuzzy- Stochastic Algorithms” Journal of Theoretical and Applied Information Technology, pp 88-94, 2009. |
| [53] | S.Chitra Selvi et al “Hybrid Evolutionary Programming Approach to Multi-Area Unit Commitment with Import and Export Constraints” International Journal of Recent Trends in Engineering, Vol.1,No. 3, 223-228, May 2009. |
| [54] | Manisha Sharma et al, “Multi-area economic dispatch with tie-line constraints employing evolutionary approach” International Journal of Engineering, Science and Technology Vol. 2, No. 3, pp. 132-149, 2010. |
| [55] | Manisha Sharma et al “Reserve Constrained Multi-Area Economic Dispatch Employing Evolutionary Approach “International Journal of Applied Evolutionary Computation Vol .1 Issue 3 pp. 49-69 July 2010. |
| [56] | Sudhakar A.V.V et al ”Multi Area Economic Dispatch using Secant Method” Journal of Electrical Engineering Technology Vol. 8, No. 4: 744-751,2013. |
| [57] | Huynh This and Thanh Binh “Hybrid Particle Swarm Optimization for Solving Multi-Area Economic Dispatch Problem” International Journal on Soft Computing (IJSC) Vol.4, No.2, pp. 17-27 May 2013. |
| [58] | M.Basu“Artificial bee colony optimization for multi-area economic dispatch “International Vol. 49, July 2013, pp. 181–187, 2013. |
| [59] | De,Shankha Suvr et al “Artificial Immune System for Multi-Area Economic Dispatch” International Journal of Emerging Electric Power Systems Vol. 14, Issue 6, pp.581-590, Dec 2013. |
| [60] | Lee, K.Y.; Park, Y.M.; Ortiz, J. L., "A United Approach to Optimal Real and Reactive Power Dispatch," Power Apparatus and Systems, IEEE Transactions on , Vol.PAS-104, No.5, pp.1147,1153, May 1985. |
| [61] | Q.H. Wu, Y.J. Cao, J.Y. Wen”Optimal reactive power dispatch using an adaptive genetic algorithm” International Journal of Electrical power and energy systems Vol.20, Issue 8, Pages 563–569, November 1998. |
| [62] | Serrano, B. R.; Vargas, A., "Active-reactive power economic dispatch of very short term in competitive electric markets," Power Technology Proceedings, 2001 IEEE Porto, Vol.1, No.10 pp.6-8, 2001. |
| [63] | Worawat Nakawiro et al “A Novel Optimization Algorithm for Optimal Reactive Power Dispatch: A Comparative Study” IEEE Transactions on Power Systems, Vol.1 pp. 1155-1161, 2011. |
| [64] | R. Mallipeddi et al “Efficient constraint handling for optimal reactive power dispatch problems” Swarm and Evolutionary Computation Vol. 5, Pages 28-36, August 2012. |
| [65] | Lopez, J.C.; Munoz, J.I.; Contreras, J.; Mantovani, J. R S, "Optimal reactive power dispatch using stochastic chance-constrained programming," Transmission and Distribution: Latin America Conference and Exposition (T&D-LA), 2012 Sixth IEEE/PES , Vol.3, pp.1-7, 3-5 Sept. 2012. |
| [66] | A. M. Elaiw, X. Xia,and A. M. Shehata “Dynamic Economic Dispatch Using Hybrid DE-SQP for Generating Units with Valve-Point Effects” Hindawi Publishing Corporation Mathematical Problems in Engineering Vol. 20,pp 1-10,2012. |
| [67] | Kyoung-Shin Kim; Leen-Hark Jung; Lee, K.Y.; Un-Chul Moon, "Security Constrained Economic Dispatch Using Interior Point Method," Power System Technology, 2006. PowerCon 2006. International Conference on, Vol.12, pp.1-6, 22-26 Oct. 2006. |
| [68] | Prasanna. T.S, Somasundaram. P “Multi-Area Security Constrained Economic Dispatch by Fuzzy- Stochastic Algorithms “Journal of Theoretical and Applied Information Technology pp. 88-94, 2009. |
| [69] | Lizhi Wang and Nan Kong “Security Constrained Economic Dispatch: A Markov Decision Process Approach with Embedded Stochastic Programming” Industrial and Manufacturing Systems Engineering Iowa State University 3016 Black Engineering, Ames, IA 50014, USA PP 1-14,2010. |
| [70] | Cvijic, S.; Jinjun Xiong, "Security constrained unit commitment and economic dispatch through benders decomposition: A comparative study," Power and Energy Society General Meeting, 2011 IEEE, Vol.10, pp.1-8, 24-29 July 2011. |
| [71] | K.Vaisakh, P. Praveena, S. Rama Mohana Rao, Kala Meah, “Solving dynamic economic dispatch problem with security constraints using bacterial foraging PSO-DE algorithm” International Journal of Electrical Power & Energy Systems, Vol. 39, Issue 1, Pages 56-67, July 2012. |
| [72] | W.G. Wood, "Spinning Reserve Constrained Static and Dynamic Economic Dispatch," Power Apparatus and Systems, IEEE Transactions on, Vol. PAS-101,no.2, pp. 381-388, 1982. |
| [73] | W.R. Barcelo and P. Rastgoufard,"Dynamic Economic Dispatch using the Extended Security Constrained Economic Dispatch Algorithm," Power Systems, IEEE Transactions on, Vol. 12, no. 2, pp. 961-967, 1997. |
| [74] | S. Hemamalini and S.P. Simon, "Dynamic Economic Dispatch using Maclaurin Series Based Lagrangian Method," Energy Conversion and Management, Vol. 51, no. 11, pp. 2212-2219, 2010. |
| [75] | Ahmed Farag et al, “Economic load dispatch multiobjective optimization Procedures using linear programming techniques” IEEE Transactions on Power Systems, Vol. 10, No. 2, pp 731-738 May 1995. |
| [76] | Y.H. Song and I. Yu,"Dynamic Load Dispatch with Voltage Security and Environmental Constraints," Electrical Power Systems. Res., Vol. 43, no. 1, pp. 53-60, 1997. |
| [77] | P.P.J. van den Bosch,"Optimal Dynamic Dispatch Owing to Spinning-Reserve and Power-Rate Limits," Power Apparatus and Systems, IEEE Transactions on, Vol. PAS-104, no. 12, pp. 3395-3401, 1985. |
| [78] | K. Chandram, N. Subrahmanyam and M. Sydulu,"Dynamic Economic Dispatch by Equal Embedded Algorithm," Electrical and Computer Engineering, 2006.ICECE '06. International Conference on, pp. 21-24, 2006. |
| [79] | K. Chandram, N. Subrahmanyam and M. Sydulu,"Brent Method for Dynamic Economic Dispatch with Transmission Losses," Transmission and Distribution Conference and Exposition, 2008. T&D. IEEE/PES, pp. 1-5, 2008. |
| [80] | Xiaohua Xia, Jiangfeng Zhang and A. Elaiw, "A Model Predictive Control Approach to Dynamic Economic Dispatch Problem," Power Tech, 2009 IEEE Bucharest, pp. 1-7, 2009. |
| [81] | X. Xia, J. Zhang and A. Elaiw, "An Application of Model Predictive Control to the Dynamic Economic Dispatch of Power Generation," Control Eng. Pract. Vol.19, no. 6, pp. 638-648, 2011. |
| [82] | Ruey-Hsum Liang, "A Neural-Based Dispatch Approach to Dynamic Generation Allocation," Power Systems, IEEE Transactions on, Vol. 14, No. 4, pp.1388-1393, 1999 |
| [83] | A.Y. Abdelaziz, M.Z. Kamh, S.F. Mekhamer and M.A.L. Badr, "A Hybrid HNNQP Approach for Dynamic Economic Dispatch Problem," Electrical Power Systems. Res. Vol. 78, No. 10, pp. 1784-1788, 2008. |
| [84] | A.Y. Abdelaziz, S.F. Mekhamer, M.Z. Kamh and M.A.L. Badr, "A Hybrid Hopfield Neural Network-Quadratic Programming Approach for Dynamic Economic Dispatch Problem," Power System Conference, 2008. MEPCON 2008.12th International Middle-East, pp. 565-570, 2008. |
| [85] | Ahmed Ahmed El-Sawy et al, “Reference Point Based TR-PSO for Multi-Objective Environmental/Economic Dispatch “Journal Applied Mathematics, 2013, Vol 4,pp 803-813 ,2013. |
| [86] | Wenxia Liu, Yuying Zhang, Bo Zeng Shuya Niu, Jianhua Zhang, and Yong Xiao “An Environmental-Economic Dispatch Method for Smart Microgrids Using VSS_QGA” Hindawi Publishing Corporation Journal of Applied Mathematics Vol.24, pp. 1-11 2014. |
| [87] | F. Li, R. Morgan and D. Williams, "Towards More Cost Saving Under Stricter Ramping Rate Constraints of Dynamic Economic Dispatch Problems-a Genetic Based Approach," Genetic Algorithms in Engineering Systems: Innovations and Applications, 1997. GALESIA 97. Second International Conference on (Conf.Publ. no. 446), pp. 221-225, 1997. |
| [88] | W. Ongsakul and J. Tippayachai, "Parallel Micro Genetic Algorithm Based on Merit Order Loading Solutions for Constrained Dynamic Economic Dispatch," Electrical Power Systems. Res., Vol. 61, no. 2, pp. 77-88, 2002. |
| [89] | W. Ongsakul and J. Tippayachai, "Parallel Micro Genetic Algorithm Based on Merit Order Loading Solutions for Constrained Dynamic Economic Dispatch," Electrical Power Systems. Res., Vol. 61, no. 2, pp. 77-88, 2002. |
| [90] | Robert T. F. Ah King et al “Evolutionary Multi-Objective Environmental/Economic Dispatch: Stochastic vs. Deterministic Approach” Department of Electrical and Electronic Engineering, Faculty of Engineering, University of Mauritius, Reduit, Mauritius, pp. 1-15,2004. |
| [91] | K. Shailti Swamp and A. Natarajan, "Constrained Optimization using Evolutionary Programming for Dynamic Economic Dispatch, “Intelligent Sensing and Information Processing, 2005. Proceedings of 2005 International Conference on, pp. 314-319, 2005. |
| [92] | A.M.A.A. Joned, I. Musirin and Titik Khawa Abdul Rahman, "Solving Dynamic Economic Dispatch using Evolutionary Programming," Power and Energy Conference, 2006. PECon '06. IEEE International, pp. 144-149, 2006. |
| [93] | G.S.S. Babu, D.B. Das and C. Patvardhan, "Dynamic Economic Dispatch Solution using an Enhanced Real-Quantum Evolutionary Algorithm," Power System Technology and IEEE Power India Conference, 2008. POWERCON 2008. Joint International Conference on, pp. 1-6, 2008. |
| [94] | K. Deb, "An Efficient Constraint Handling Method for Genetic Algorithms, “Computer Methods Applications in Mechanical Engineering, Vol. 186, no. 2-4, pp. 311-338, 2000. |
| [95] | J. Chiou, "A Variable Scaling Hybrid Differential Evolution for Solving Large-Scale Power Dispatch Problems," Generation, Transmission & Distribution, IET, Vol. 3, No. 2, pp. 154-163, 2009. |
| [96] | Noman, N.; Iba, H.,"Solving dynamic economic dispatch problems using cellular differential evolution," Evolutionary Computation (CEC), 2011 IEEE Congress on, Vol.14. pp.2633,2640, 5-8 June 2011. |
| [97] | Zwe-Lee Gaing, "Constrained Dynamic Economic Dispatch Solution using Particle Swarm Optimization," Power Engineering Society General Meeting, 2004. IEEE, pp. 153-158 Vol.1, 2004. |
| [98] | Hardiansyah, Junaidi, and Yohannes MS“Solving Economic Load Dispatch Problem Using Particle Swarm Optimization Technique” I.J. Intelligent Systems and Applications, pp 12-18,2012. |
| [99] | Niknam, T.; Golestane, F.; Bahmanifirouzi, B., "Modified adaptive PSO algorithm to solve dynamic economic dispatch," Power Engineering and Automation Conference (PEAM), 2011 IEEE , Vol.1, No.10, pp.108,111, 8-9 Sept. 2011. |
| [100] | Divya Mathur “New Methodology for Solving Different Economic Dispatch Problems” International Journal of Engineering Science and Innovative Technology (IJESIT) Vol.2, No.1, pp.494-498 January 2013. |
| [101] | C.K. Panigrahi, P.K. Chattopadhyay, R.N. Chakrabarti and M. Basu, "Simulated Annealing Technique for Dynamic Economic Dispatch," Electric Power Components and Systems, Vol. 34, No. 5, pp. 577-587, 2006. |
| [102] | X.S. Han, H.B. Gooi and D.S. Kirschen, "Dynamic Economic Dispatch: Feasible and Optimal Solutions," Power Engineering Society Summer Meeting, 2001.IEEE, Vol.3, pp. 1704-1710, 2001. |
| [103] | W. Ongsakul and J. Tippayachai, "Parallel Micro Genetic Algorithm Based on Merit Order Loading Solutions for Constrained Dynamic Economic Dispatch," Electrical Power Systems. Res., Vol. 61, no. 2, pp. 77-88, 2002. |
| [104] | X. Yuan, L. Wang, Y. Zhang and Y. Yuan, "A Hybrid Differential Evolution Method for Dynamic Economic Dispatch with Valve-Point Effects," Expert Systems. Application, Vol. 36, no. 2, Part 2, pp. 4042-4048, 2009. |
| [105] | M. Basu, "Artificial Immune System for Dynamic Economic Dispatch," International Journal of Electrical Power & Energy Systems, Vol. 33, No. 1, pp. 131-136, 2011. |
| [106] | S. Hemamalini and S.P. Simon, "Dynamic Economic Dispatch using Artificial Immune System for Units with Valve-Point Effect,"International Journal of Electrical Power & Energy Systems, Vol. In Press, Corrected Proof, pp. 1-7,2011. |
| [107] | Niknam, T.; Azizipanah-Abarghooee, R.; Aghaei, J., "A new modified teaching-learning algorithm for reserve constrained dynamic economic dispatch," Power Systems, IEEE Transactions on, Vol.28, No.2, pp.749, 763, May 2013. |
| [108] | Rabiee, A; Mohammadi-Ivatloo, B.; Moradi-Dalvand, M., "Fast Dynamic Economic Power Dispatch Problems Solution Via Optimality Condition Decomposition," Power Systems, IEEE Transactions on , Vol.29, No.2, pp.982,983, March 2014. |
| [109] | C.B. Somuah and N. Khunaizi, "Application of Linear Programming Dispatch Technique to Dynamic Generation Allocation," Power Systems, IEEE Transactions on, Vol. 5, No. 1, pp. 20-26, 1990. |
| [110] | X.S. Han, H.B. Gooi and D.S. Kirschen, "Dynamic Economic Dispatch: Feasible and Optimal Solutions," Power Engineering Society Summer Meeting, 2001.IEEE, Vol.3, pp. 1704-1710, 2001. |
| [111] | W. Lin and S. Chen, "Bid-Based Dynamic Economic Dispatch with an Efficient Interior Point Algorithm," International Journal of Electrical Power & Energy Systems, Vol. 24, No. 1, pp. 51-57, 2002. |
| [112] | W. Ongsakul and N. Ruangpayoongsak, "Constrained Dynamic Economic Dispatch by Simulated annealing/genetic Algorithms,"Power Industry Computer Applications, 2001. PICA 2001. Innovative Computing for Power – Electric Energy Meets the Market. 22nd IEEE Power Engineering Society International Conference on, pp. 207-212, 2001. |
| [113] | T.A.A. Victoire and A.E. Jeyakumar, "Reserve Constrained Dynamic Dispatch of Units with Valve-Point Effects," Power Systems, IEEE Transactions on, Vol. 20, No. 3, pp. 1273-1282, 2005. |
| [114] | T.A.A. Victoire and A.E. Jeyakumar, "A Modified Hybrid EP–SQP Approach for Dynamic Dispatch with Valve-Point Effect," International Journal of Electrical Power & Energy Systems, Vol. 27, No. 8, pp. 594-601, 2005. |
| [115] | T.A.A. Victoire and A.E. Jeyakumar, "Deterministically Guided PSO for Dynamic Dispatch Considering Valve-Point Effect," Electrical Power Systems. Res., Vol. 73, No. 3, pp. 313-322, 2005. |
| [116] | F. Li, R. Morgan and D. Williams, "Hybrid Genetic Approaches to Ramping Rate Constrained Dynamic Economic Dispatch," Electrical. Power Systems. Res., Vol. 43, No.2, pp. 97-103, 1997. |
| [117] | F. Li and R.K. Aggarwal, "Fast and Accurate Power Dispatch using a Relaxed Genetic Algorithm and a Local Gradient Technique," Expert Systems Application, Vol. 19,No. 3, pp. 159-165, 2000. |
| [118] | P. Attaviriyanupap, H. Kita, E. Tanaka and J. Hasegawa, "A Hybrid EP and SQP for Dynamic Economic Dispatch with Non smooth Fuel Cost Function," Power Systems, IEEE Transactions on, Vol. 17, No. 2, pp. 411-416, 2002. |
| [119] | Zwe-Lee Gaing and Ting-Chia Ou, "Dynamic Economic Dispatch Solution using Fast Evolutionary Programming with Swarm Direction," Industrial Electronics and Applications, 2009. ICIEA 2009. 4th IEEE Conference on, pp. 1538-1544, 2009. |
| [120] | Y. Lu, J. Zhou, H. Qin, Y. Li and Y. Zhang, "An Adaptive Hybrid Differential Evolution Algorithm for Dynamic Economic Dispatch with Valve-Point Effects, "Expert Systems. Application, Vol. In Press, Accepted Manuscript, 2009. |
| [121] | F. Kappel and A.V. Kuntsevich, "An Implementation of Shor's r-Algorithm,"Computational Optimization and Applications, Vol. 15, no. 2, pp. 193-205, 2000. |
| [122] | V. Ravi Kumar Pandi and B.K. Panigrahi, "Dynamic Economic Load Dispatch using Hybrid Swarm Intelligence Based Harmony Search Algorithm," Expert Systems Applications, Vol. In Press, Corrected Proof, pp. 1-6, 2011. |
| [123] | S. Sivasubramani and K.S. Swarup, "Hybrid SOA–SQP Algorithm for Dynamic Economic Dispatch with Valve-Point Effects," IEEE Transactions on Energy Conversion, Vol. 35, No. 12, pp. 5031-5036, 2010. |
| [124] | A. M. Elaiw, X. Xia,and A. M. Shehata “Dynamic Economic Dispatch Using Hybrid DE-SQP for Generating Units with Valve-Point Effects” Hindawi Publishing Corporation Mathematical Problems in Engineering Vol. 20,pp 1-10,2012. |
| [125] | Guoli Zhang, Hai Yan Lu, Gengyin Li and Hong Xie, "A New Hybrid Real-Coded Genetic Algorithm and Application in Dynamic Economic Dispatch, "Intelligent Control and Automation, 2006. WCICA 2006. The Sixth World Congess on, Vol.1, pp. 3627-3632, 2006. |
| [126] | Dun-wei Gong et al “Environmental/economic power dispatch using a hybrid multi-objective optimization algorithm” IEEE Electrical Power and Energy Systems Vol. 32 pp 607-614,2013. |
| [127] | Niknam, T.; Azizipanah-Abarghooee, R.; Roosta, A, "Reserve Constrained Dynamic Economic Dispatch: A New Fast Self-Adaptive Modified Firefly Algorithm," Systems Journal, IEEE, Vol.6, No.4, pp.635, 646, Dec. 2012. |
| [128] | H. Shayeghi and A. Ghasemi “Application of MOPSO for Economic Load Dispatch Solution with Transmission Losses” International Journal on Technical and Physical Problems of Engineering (IJTPE), Vol 4 No.1, Issue 10 pp. 27-34, 2012. |
| [129] | Hardiansyah “Solving Economic Dispatch Problem with Valve-Point Effect using a Modified ABC Algorithm” International Journal of Electrical and Computer Engineering (IJECE) Vol. 3, No. 3, pp. 377-385 June 2013. |
| [130] | V.Karthikeyan S.Senthilkumar and V.J.Vijayalakshmi “A New Approach to the Solution of Economic Dispatch using Particle Swarm Optimization with Simulated Annealing” International Journal on Computational Sciences & Applications (IJCSA) Vol.3, No.3,pp 37-49 June 2013. |
| [131] | P. Attaviriyanupap, H. Kita, E. Tanaka and J. Hasegawa, "A Fuzzy-Optimization Approach to Dynamic Economic Dispatch Considering Uncertainties, "Power Systems, IEEE Transactions on, Vol. 19, No. 3, pp. 1299-1307, 2004. |
| [132] | Y. Lu, J. Zhou, H. Qin, Y. Wang and Y. Zhang, "Chaotic Differential Evolution Methods for Dynamic Economic Dispatch with Valve-Point Effects," Engineering Application of Artificial Intelligence , Vol. 24, No. 2, pp. 378-387, 2011. |
| [133] | S. Titus and A.E. Jeyakumar, "A Hybrid EP-PSO-SQP Algorithm for Dynamic Dispatch Considering Prohibited Operating Zones," Electric Power Components and Systems, Vol. 36, No. 5, pp. 449-467, 2008. |
| [134] | P. Praveena, K. Vaisakh and S. Rama Mohana Rao, "A Bacterial Foraging PSODE Algorithm for Solving Dynamic Economic Dispatch Problem with Security Constraints," in Power Electronics, Drives and Energy Systems (PEDES) & 2010 Power India, 2010 Joint International Conference on, pp. 1-7, 2010. |
| [135] | A. A. Mousa et al “A Hybrid Optimization Technique Coupling an Evolutionary and a Local Search Algorithm for Economic Emission Load Dispatch Problem “Journal of Applied Mathematics, Vol.2, pp. 90-898 ,2011. |
| [136] | Wang, M.Q.; Gooi, H.B.; Chen, S.X.; Lu, S., "A Mixed Integer Quadratic Programming for Dynamic Economic Dispatch With Valve Point Effect," Power Systems, IEEE Transactions on , Vol.29, No.5, pp.2097,2106, Sept. 2014. |
APA Style
Moses Peter Musau, Nicodemus Odero Abungu, Cyrus Wabuge Wekesa. (2015). Multi Objective Dynamic Economic Dispatch with Cubic Cost Functions. International Journal of Energy and Power Engineering, 4(3), 153-167. https://doi.org/10.11648/j.ijepe.20150403.14
ACS Style
Moses Peter Musau; Nicodemus Odero Abungu; Cyrus Wabuge Wekesa. Multi Objective Dynamic Economic Dispatch with Cubic Cost Functions. Int. J. Energy Power Eng. 2015, 4(3), 153-167. doi: 10.11648/j.ijepe.20150403.14
AMA Style
Moses Peter Musau, Nicodemus Odero Abungu, Cyrus Wabuge Wekesa. Multi Objective Dynamic Economic Dispatch with Cubic Cost Functions. Int J Energy Power Eng. 2015;4(3):153-167. doi: 10.11648/j.ijepe.20150403.14
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Download@article{10.11648/j.ijepe.20150403.14,
author = {Moses Peter Musau and Nicodemus Odero Abungu and Cyrus Wabuge Wekesa},
title = {Multi Objective Dynamic Economic Dispatch with Cubic Cost Functions},
journal = {International Journal of Energy and Power Engineering},
volume = {4},
number = {3},
pages = {153-167},
doi = {10.11648/j.ijepe.20150403.14},
url = {https://doi.org/10.11648/j.ijepe.20150403.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijepe.20150403.14},
abstract = {The formulation and solution of the Dynamic Economic Dispatch (DED) problem is one of the key disciplines in modern power system operation, planning, operation and control. Past researches have considered DED on Quadratic Cost Functions (QCF), with only few works considering higher order cost functions which are more accurate. The Static Economic Dispatch (SED) has been widely tackled in past researches, however, it is the DED problem that represents a real life power system. There is need to review this problem and establish a more practical formulation of the same taking into consideration all the objectives and constraints possible. The methods used in the solution of DED problem have evolved from the traditional deterministic ones, to the pure heuristic, and finally to the state of the heart hybrids. The hybrids methods have been developed to exalt the strengths and improve the weaknesses of the base method. Such optimisation methods need to be reviewed and classified. This paper will do an in depth review of the DED problem on both quadratic and cubic cost functions. Further it will provide a detailed classification of the methods used to solve the problem as its complexity increases. Consequently, three method Hybrids is the way go as far as the solution of the cubic Multi Objective DED (MODED) with five objectives is concerned.},
year = {2015}
}
TY - JOUR T1 - Multi Objective Dynamic Economic Dispatch with Cubic Cost Functions AU - Moses Peter Musau AU - Nicodemus Odero Abungu AU - Cyrus Wabuge Wekesa Y1 - 2015/05/15 PY - 2015 N1 - https://doi.org/10.11648/j.ijepe.20150403.14 DO - 10.11648/j.ijepe.20150403.14 T2 - International Journal of Energy and Power Engineering JF - International Journal of Energy and Power Engineering JO - International Journal of Energy and Power Engineering SP - 153 EP - 167 PB - Science Publishing Group SN - 2326-960X UR - https://doi.org/10.11648/j.ijepe.20150403.14 AB - The formulation and solution of the Dynamic Economic Dispatch (DED) problem is one of the key disciplines in modern power system operation, planning, operation and control. Past researches have considered DED on Quadratic Cost Functions (QCF), with only few works considering higher order cost functions which are more accurate. The Static Economic Dispatch (SED) has been widely tackled in past researches, however, it is the DED problem that represents a real life power system. There is need to review this problem and establish a more practical formulation of the same taking into consideration all the objectives and constraints possible. The methods used in the solution of DED problem have evolved from the traditional deterministic ones, to the pure heuristic, and finally to the state of the heart hybrids. The hybrids methods have been developed to exalt the strengths and improve the weaknesses of the base method. Such optimisation methods need to be reviewed and classified. This paper will do an in depth review of the DED problem on both quadratic and cubic cost functions. Further it will provide a detailed classification of the methods used to solve the problem as its complexity increases. Consequently, three method Hybrids is the way go as far as the solution of the cubic Multi Objective DED (MODED) with five objectives is concerned. VL - 4 IS - 3 ER -
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