Water Science and Engineering 2014, 7(4) 420-432 DOI:   10.3882/j.issn.1674-2370.2014.04.007  ISSN: 1674-2370 CN: 32-1785/TV

Current Issue | Archive | Search                                                            [Print]   [Close]
Information and Service
This Article
Supporting info
Service and feedback
Email this article to a colleague
Add to Bookshelf
Add to Citation Manager
Cite This Article
Email Alert
hydro unit
economic load dispatch
dynamic programming
genetic algorithm
numerical experiment
Bin XU
Ping-an ZHONG
Yun-fa ZHAO
Yu-zuo ZHU
Gao-qi ZHANG
Article by Bin XU
Article by Ping-an ZHONG
Article by Yun-fa ZHAO
Article by Yu-zuo ZHU
Article by Gao-qi ZHANG

Comparison between dynamic programming and genetic algorithm for hydro unit economic load dispatch

Bin XU1, Ping-an ZHONG*1, 2, Yun-fa ZHAO3, Yu-zuo ZHU4, Gao-qi ZHANG5

1. College of Hydrology and Water Resources, Hohai University, Nanjing 210098, P. R. China
2. National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety, Hohai University, Nanjing 210098, P. R. China
3. China Three Gorges Corporation, Beijing100038, P. R. China
4. Datang Yantan Hydropower Corporation, Nanning 530022, P. R. China
5. Yellow River Engineering Consulting Co., Ltd., Zhengzhou 450003, P. R. China


The hydro unit economic load dispatch (ELD) is of great importance in energy conservation and emission reduction. Dynamic programming (DP) and genetic algorithm (GA) are two representative algorithms for solving ELD problems. The goal of this study was to examine the performance of DP and GA while they were applied to ELD. We established numerical experiments to conduct performance comparisons between DP and GA with two given schemes. The schemes included comparing the CPU time of the algorithms when they had the same solution quality, and comparing the solution quality when they had the same CPU time. The numerical experiments were applied to the Three Gorges Reservoir in China, which is equipped with 26 hydro generation units. We found the relation between the performance of algorithms and the number of units through experiments. Results show that GA is adept at searching for optimal solutions in low-dimensional cases. In some cases, such as with a number of units of less than 10, GA’s performance is superior to that of a coarse-grid DP. However, GA loses its superiority in high-dimensional cases. DP is powerful in obtaining stable and high-quality solutions. Its performance can be maintained even while searching over a large solution space. Nevertheless, due to its exhaustive enumerating nature, it costs excess time in low-dimensional cases.

Keywords hydro unit   economic load dispatch   dynamic programming   genetic algorithm   numerical experiment  
Received 2013-03-05 Revised 2014-05-10 Online: 2014-10-27 
DOI: 10.3882/j.issn.1674-2370.2014.04.007

This work was supported by the National Basic Research Program of China (973 Program, Grant No. 2013CB036406), the National Natural Science Foundation of China (Grant No. 51179044), and the Research Innovation Program for College Graduates in Jiangsu Province of China (Grant No. CXZZ12-0242).

Corresponding Authors: Ping-an ZHONG
Email: pazhong@hhu.edu.cn
About author:


Bahmanifirouzi, B., Farjah, E., and Niknam, T. 2012. Multi-objective stochastic dynamic economic emission dispatch enhancement by fuzzy adaptive modified theta particle swarm optimization. Journal of Renewable and Sustainable Energy, 4(2), 0231052. [doi:10.1063/1.3690959]
Bakirtzis, A., Petridis, V., and Kazarlis, S. 1994. Genetic algorithm solution to the economic dispatch problem. IEE Proceedings: Generation, Transmission and Distribution, 141(4), 377-382.
Baskar, S., Subbaraj, P., and Rao, M. V. C. 2003. Hybrid real coded genetic algorithm solution to economic dispatch problem. Computers and Electrical Engineering, 29(3), 407-419. [doi:10.1016/S0045- 7906(01)00039-8]
Benhamida, F., and Abdelbar, B. 2010. Enhanced Lagrangian relaxation solution to the generation scheduling problem. International Journal of Electrical Power and Energy Systems, 32(10), 1099-1105. [doi:10.1016/j.ijepes.2010.06.007]
Cheng, C. T., Liao, S. L., Tang, Z. T., and Zhao, M. Y. 2009. Comparison of particle swarm optimization and dynamic programming for large scale hydro unit load dispatch. Energy Conversion and Management, 50(12), 3007-3014. [doi:10.1016/j.enconman.2009.07.020]
Chiang, C. L. 2007. Genetic-based algorithm for power economic load dispatch. IET Generation, Transmission and Distribution, 1(2), 261-269. [doi:10.1049/iet-gtd:20060130]
Coelho, L. D. S., and Mariani, V. C. 2009. An improved harmony search algorithm for power economic load dispatch. Energy Conversion and Management, 50(10), 2522-2526. [doi:10.1016/j.enconman. 2009.05.034]
Hemamalini, S., and Simon, S. P. 2011. Dynamic economic dispatch using artificial bee colony algorithm for units with valve-point effect. European Transactions on Electrical Power, 21(1), 70-81. [doi:10.1002/etep.413]
Holland, J. H. 1975. Adaptation in Nature and Artificial System. The University of Michigan Press:      Ann Arbor.
Howard, R. A. 1960. Dynamic Programming and Markov Process. Cambridge: Technology Press of Massachusetts Institute of Technology and John Wiley and Sons, Inc.
Hrstka, O., and Kucerova, A. 2004. Improvements of real coded genetic algorithms based on differential  operators preventing premature convergence. Advances in Engineering Software, 35(3-4), 237-246. [doi: 10.1016/S0965-9978(03)00113-3]
Kumar, S., and Naresh, R. 2009. Nonconvex economic load dispatch using an efficient real-coded genetic algorithm. Applied Soft Computing, 9(1), 321-329. [doi:10.1016/j.asoc.2008.04.009]
Li, F., Morgan, R., and Williams, D. 1997. Hybrid genetic approaches to ramping rate constrained dynamic economic dispatch. Electric Power Systems Research, 43(2), 97-103. [doi:10.1016/S0378-7796 (97)01165-6]
Liang, Z. X., and Glover, J. D. 1992. A zoom feature for a dynamic programming solution to economic dispatch including transmission losses. IEEE Transactions on Power Systems, 7(2), 544 - 550. [doi: 10.1109/59.141757]
Michalewicz, Z., Janikow, C. Z. 1996. GENOCOP: A genetic algorithm for numerical optimization problem with linear constraints. Communications of the ACM, 39(12), 175-201. [doi:10.1145/272682.272711]  
Ngundam, J. M., Kenfack, F., and Tatietse, T. T. 2000. Optimal scheduling of large-scale hydrothermal power systems using the Lagrangian relaxation technique. International Journal of Electrical Power and Energy Systems, 22(4), 237-245. [doi:10.1016/S0142-0615(99)00054-X]
Ongsakul, W., and Petcharaks, N. 2004. Unit commitment by enhanced adaptive Lagrangian relaxation. IEEE Transactions on Power Systems, 19(1), 620-628. [doi:10.1109/TPWRS.2003.820707]
Ongsakul, W., and Ruangpayoongsak, N. 2001. Constrained dynamic economic dispatch by simulated annealing/genetic algorithms. Proceedings of the 22nd IEEE Power Engineering Society International Conference on Power Electric Energy, 207-212. [doi:10.1109/PICA.2001.932349]
Orero, S. O., and Irving, M. R. 1996. Economic dispatch of generators with prohibited operating zones: A genetic algorithm approach. IEE Proceedings: Generation, Transmission and Distribution, 143(6), 529-534. [doi:10.1049/ip-gtd:19960626]
Panigrahi, B. K., Pandi, V. R., and Das, S. 2008. Adaptive particle swarm optimization approach for static and dynamic economic load dispatch. Energy Conversion and Management, 49(6), 1407-1415. [doi:10.1016/ j.enconman.2007.12.023]
Sinha, N., Chakrabarti, R., and Chattopadhyay, P. K. 2003. Evolutionary programming techniques for economic load dispatch. IEEE Transactions on Evolutionary Computation, 7(1), 83-94. [doi:10.1109/ TEVC.2002.806788]
Somasundaram, P., Kuppusamy, K., and Kumudini Devi, R. 2006. Fast computation evolutionary programming algorithm for the economic dispatch problem. European Transactions on Electrical Power, 16(1), 35-47. [doi:10.1002/etep.63]
Yamin, H. Y. 2004. Review on methods of generation scheduling in electric power systems. Electric Power Systems Research, 69(2-3), 227-248. [doi:10.1016/j.epsr.2003.10.002]
Yang, K. 1995. Multiple dynamic model used in economic operation of large hydroelectric station. Journal of Hohai University, 23(4), 85-90. [doi:10.3321/j.issn:1000-1980.1995.04.014 ] (in Chinese)
Zheng, J., Yang, K., and Lu, X. Y. 2013. Limited adaptive genetic algorithm for inner-plant economical operation of hydropower station. Hydrology Research, 44(4), 583-599. [doi:10.2166/nh.2012.198]
Zhong, P. A., and Tang, L. 2010. Sensitive analysis on the parameters of genetic algorithm applied in optimal operation of reservoir. Water Power, 36(11), 13-16. (in Chinese)

Similar articles
1.Reza BARATI, Sajjad RAHIMI, Gholam Hossein AKBARI.Analysis of dynamic wave model for flood routing in natural rivers[J]. Water Science and Engineering, 2012,5(3): 243-258

Copyright by Water Science and Engineering