# Solving Dynamic Economic Emission Dispatch Problem by Random Drift Particle Swarm Optimization

### Abstract

The objective of dynamic economic emission dispatch (DEED) problem is scheduling of the optimal power outputs of the online generating units over a time horizon by minimizing the fuel cost and emission level simultaneously while satisfying the generators and system constraints such as power balance constraint, ramp-rate, and generation limits. In this paper for a more practical and comprehensive study, in addition to the above constraints, the valve-point effect and spinning reserve constraints have been taken into account too. With considering the above conditions, DEED becomes a complex multi-objective optimization problem with non-convex and non-smooth objective function that traditional methods are not able to solve it. So, in this paper random drift particle swarm optimization (RDPSO) has been used to solve the above problem. In addition, a ten unit test system has been studied to demonstrate the effectiveness of the mentioned algorithm and the results are compared with the other algorithms.

### References

[2] A.M. Elaiw, X. Xia, A.M. Shehata, “Hybrid DE-SQP and hybrid PSO-SQP methods for solving dynamic economic emission dispatch problem with valve-point effects,” Electric Power Systems Research, Vol. 103, pp. 192-200, 2013.

[3] A. M. Elaiwa, X. Xia, A. M. Shehata, “Solving dynamic economic emission dispatch problem with valve-point effects using hybrid DE-SQP,” 9-13 July 2012. DOI: 10.1109/PowerAfrica.2012.6498646.

[4] K. Chandram and N. Subrahmanyam, “Brent method for Economic Load Dispatch with Transmission Losses,” The International Conference on Computer as a Tool, pp. 1601–1607, 2007.

[5] R. N. Dhar and P. K. Mukherjee, “Reduced-gradient method for economic dispatch,” Electrical Engineers, Proceedings of the Institution of, Vol. 120, No. 5, pp. 608–610, May 1973.

[6] C. E. Lin, S. T. Chen, and C.-L. Huang, “A direct Newton-Raphson economic dispatch,” Power Systems, IEEE Transactions on, Vol. 7, No. 3, pp. 1149–1154, Aug. 1992.

[7] Z.-X. Liang and J. D. Glover, “A zoom feature for a dynamic programming solution to economic dispatch including transmission losses,” Power Systems, IEEE Transactions on, Vol. 7, No. 2, pp. 544–550, May 1992.

[8] K. S. Hindi and M. R. A. Ghani, “Dynamic economic dispatch for large scale power systems: a Lagrangian relaxation approach,” International Journal of Electrical Power & Energy Systems, Vol. 13, No. 1, pp. 51–56, 1991.

[9] Behnam Mohammadi-ivatloo, Abbas Rabiee, Alireza Soroudi, Mehdi Ehsan, “Imperialist competitive algorithm for solving non-convex dynamic economic power dispatch,” Energy, Vol. 44, pp. 228-240, 2012.

[10] Taher Niknam, Faranak Golestaneh, “Enhanced Bee Swarm Optimization Algorithm for Dynamic Economic Dispatch,” IEEE Systems Journal, Vol. 7, No. 4, pp. 754-762, 2013.

[11] Behnam Mohammadi-Ivatloo, Abbas Rabiee, Alireza Soroudi, “Nonconvex Dynamic Economic Power Dispatch Problems Solution Using Hybrid Immune-Genetic Algorithm,” IEEE Systems Journal, Vol. 7, No. 4, pp. 777-785, 2013.

[12] S. Sivasubramani, K.S. Swarup, “Environmental/economic dispatch using multi-objective harmony search algorithm,”Electric Power Systems Research, Vol. 81, pp. 1778-1785, 2011.

[13] Ruey-Hsun Liang, Jia-Ching Wang, Yie-Tone Chen, Wan-Tsun Tseng, “An enhanced firefly algorithm to multi-objective optimal active/reactive power dispatch with uncertainties consideration,” Electrical Power and Energy Systems, Vol. 64, pp. 1088-1097, 2015.

[14] K.K. Mandal , S. Mandal , B. Bhattacharya, N. Chakraborty, “Non-convex emission constrained economic dispatch using a new self-adaptive particle swarm optimization technique,” Applied Soft Computing, Vol. 28, pp. 188-195, 2015.

[15] M. Basu, “Dynamic economic emission dispatch using nondominated sorting genetic algorithm-II,” Electrical Power and Energy Systems, Vol. 30, pp. 140-149, 2008.

[16] C.X. Guo, J.P. Zhan, Q.H. Wu, “Dynamic economic emission dispatch based on group search optimizer with multiple producers,” Electric Power Systems Research, Vol. 86, pp. 8-16, 2012.

[17] Taher Niknam, Hasan Doagou Mojarrad, Bahman Bahmani Firouzi,“A new optimization algorithm for multi-objective Economic/Emission Dispatch,” Electrical Power and Energy Systems, Vol. 46, pp. 283-293, 2013.

[18] Xingwen Jiang, Jianzhong Zhou, Hao Wangc, Yongchuan Zhang,“ Dynamic environmental economic dispatch using multiobjective differential evolution algorithm with expanded double selection and adaptive random restart,” Electrical Power and Energy Systems, Vol. 49, pp. 399-407, 2013.

[19] Taher Niknam, Rasoul Azizipanah-Abarghooee, Mohsen Zare, Bahman Bahmani-Firouzi, “Reserve Constrained Dynamic Environmental/Economic Dispatch: A New Multiobjective Self- Adaptive Learning Bat Algorithm,” IEEE Systems Journal, pp. 763-776, 2013.

[20] Nicole Pandit, Anshul Tripathi, Shashikala Tapaswi, Manjaree Pandit,“An improved bacterial foraging algorithm for combined static/dynamic environmental economic dispatch,” Applied Soft Computing, Vol. 12, pp. 3500-3513, 2012.

[21] Jun Sun, Vasile Palade, Xiao-Jun Wu, Wei Fang, Zhenyu Wang, “Solving the Power Economic Dispatch Problem With Generator Constraints by Random Drift Particle Swarm Optimization,” IEEE Transactions On Industrial Informatics, Vol. 10, no. 1, pp. 222-232, 2014.

[22] D. C.Walters and G. B. Sheble, “Genetic algorithm solution of economic dispatch with valve point loading,” IEEE Trans. Power Syst., Vol. 8, pp. 1325–1332, Aug. 1993.

[23] Z.-L. Gaing, “Particle swarm optimization to solving the economic dispatch considering the generator constraints,” IEEE Trans. Power Syst., Vol. 18, No. 3, pp. 1187–1195, Aug. 2003.

[24] Nnamdi I. Nwulu, Xiaohua Xia, “Multi-objective dynamic economic emission dispatch of electric power generation integrated with game theory based demand response programs,” Energy Conversion and Management, Vol. 89, pp. 963-974