# Improved Artificial Cooperative Search Algorithm for Solving Non-convex Economic Dispatch Problems with Valve-point Effects

### Abstract

This paper presents Improved Artificial Cooperative Search (IACS) algorithm for solving economic dispatch problems considering the valve point effects, ramp rate limits, transmission losses and prohibited operation zones. In order to improve the solution quality and increase the search efficiency, a novel perturbation scheme called “Global best guided chaotic local search” is proposed and incorporated into ACS algorithm. The effectiveness of the proposed IACS algorithm has been benchmarked with twelve widely known optimization test problems. In order to assess the performance of the proposed algorithm on non-convex optimization problems, four case studies related to highly nonlinear economic dispatch problems have been solved . Results retrieved from IACS algorithm have been compared with literature approaches in terms of minimum, maximum and average generation cost values. Comparison results indicate that IACS produces more economical power load than those of other optimizers available in the literature### Downloads

### References

S. Pothiya, I. Ngamroo, W. Kongprawechnon, “Ant colony optimization for economic dispatch problem with non-smooth cost functions,” Int. J. Elec. Power., vol.32, pp.478-87, 2010.

J.C. Dodu, P. Martin, A. Merlin, J. Pouget, “An optimal formulation and solution of short-range operating problems for a power system with flow constraints,” In: Proceedings of the IEEE, vol. 60, pp. 53-54, 1972

R.A. Jabr, A.H. Coonick, B.J. Cory, “A homogeneous linear programming algorithm for the security constrained economic dispatch problem,” IEEE T. Power. Syst., vol.15, pp. 930-937, 2000.

C.L. Chen, S.C. Wang, “Branch-and-bound scheduling for thermal generating units,” IEEE T. Energy. Conver., vol. 8, pp. 184-86, 1993.

L.d.S. Coelho, V.C. Mariani, “Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect,” IEEE T. Power Syst., vol.21, pp.989-96, 2006.

J. Nanda, L. Hari, M.L. Kothari, “Economic emission load dispatch with line flow constraints using a classical technique,” IEEE Proc. Generat. Transm. Distrib., vol.141, pp.1-10, 1994.

A.A. El-Keib, H. Ma, J.L. Hart, “Environmentally constrained

economic dispatch using the lagrangian relaxation method,” IEEE T. Power. Syst., vol.9, pp.1723-1727, 1994.

G. Xiong, D. Shi, X. Duan, “Multi-strategy ensemble biogeography-based optimization for economic dispatch problems,” Appl. Energy, vol. 111, pp. 801–811, 2013.

Z.X. Liang, J.D. Glover, “A zoom feature for a dynamic programming solution to economic dispatch including transmission losses,” IEEE T. Power. Syst., vol.7, pp.544-550, 1992.

J.S. Al-Sumait, A.K. AL-Othman, J.K. Sykulski, “Application of pattern search method to power system valve-point economic load dispatch,” Int. J. Elec. Power., vol.11, pp. 720-30, 2007.

J.O. Kim, D.J. Shin, J.N. Park, C. Singh, “Atavistic genetic algorithm for economic dispatch with valve point effect,” Int. J. Elec. Power., vol. 62, pp.201-207, 2002.

C.L. Chiang, “Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels,” IEEE T. Power. Syst., vol.20, pp. 1690-1699, 2005.

S. Baskar, P, Subbaraj, M.V.C. Rao, “Hybrid real coded genetic algorithm solution to economic dispatch problem,” Comput. Electr. Eng., vol. 29, pp.407-419, 2003.

R.K. Swain, N.C. Sahu, P.K. Hota, “Gravitational search algorithm for optimal economic dispatch,” Procedia Technol., vol.6, pp.411-19, 2012.

S. Duman, A.B. Arsoy, N. Yörükeren, “Solution of economic dispatch problem using gravitational search algorithm,” In: 7th International Conference on Electrical and Electronics Engineering, Bursa, Turkey, pp.54-59, 2011.

K.P. Wong, C.C. Fong, “Simulated annealing based economic dispatch algorithm.,” IEEE Conference Proceedings, vol.140, pp.509-515, 1993.

K.K. Vishwakarma, H.M. Dubey, M. Pandit, B.K. Panigrahi, “Simulated annealing approach for solving economic load dispatch problems with valve point loading effects,” Int. J. Eng. Sci. Technol., vol. 4, pp. 60-72, 2012

C.K. Panigrahi, P.K. Chattopadhyay, R.N. Chakrabarti, M. Basu, “Simulated annealing technique for dynamic economic dispatch,” Electr. Pow. Compo. Sys, vol.34, pp. 577-586, 2006.

D.N. Jeyakumar, T. Jayabarathi, T. Raghunathan, “Particle swarm optimization for various types of economic dispatch problems,” Int. J. Elec. Power., vol . 28, pp. 36-42, 2006.

C.K. Panigrahi, V.R. Pandi, S. Das, “Adaptive particle swarm optimization approach for static and dynamic economic load dispatch,” Energy. Convers. Manage., vol. 49, pp.1407-1415, 2008.

J.B. Park, “A particle swarm optimization for economic dispatch with non-smooth cost functions,” IEEE T. Power. Syst. vol.20, pp.34-42, 2005.

V. Mahidhar, G. S. Reddy, “Economic load dispatch with valve point effects and ramp rates using new approach in PSO,” IJERT, vol.1, pp.1-6, 2012.

S.K. Wang, J.P. Chiou, C.W. Liu, “Non-smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm,” IET Gener. Transm. Dis., vol.1, pp.793-803, 2007.

L.d.S. Coelho, A.D.V. Almeida, V.C. Mariani. “Cultural differential evolution approach to optimize the economic dispatch of electrical energy using thermal generators,” In: Proc. 13th IEEE International Conference on Emerging Technologies and Factory Automation (ETFA), Hamburg, Germany, pp.1378–83, 2008.

L.d.S Coelho, V.C. Mariani, “Improved differential evolution algorithms for handling economic dispatch optimization with generator constraints,” Energy Convers. Manage., vol. 48, pp.1631–39, 2007.

L.d.S. Coelho, T.C. Bora, V.C. Mariani, “Differential evolution based on truncated Levy-type flights and population diversity measure to solve economic load dispatch problems,” Electr. Pow. Compo. Sys, vol.57, pp.178-188, 2014.

L.d.S. Coelho, V.C. Mariani, “An improved harmony search algorithm for power economic load dispatch,” Energy Convers. Manage., vol.50, pp. 2522– 2526, 2009.

P. Chakraborty, G.G. Roy, B.K. Panigrahi, R.C. Bansal, A. Mohapatra, “Dynamic economic dispatch using harmony search algorithm with modified differential mutation operator,” Electr. Eng., vol.94, pp.197-205, 2012.

S. Hemamalini, S.P. Simon, “Artificial bee colony algorithm for economic load dispatch problem with non-smooth cost functions,” Electr. Pow. Compo. Sys., vol.38, pp.786-803, 2010.

M. Basu, “Artificial bee colony optimization for multi-area economic dispatch,” Int. J. Elec. Power. 2013, vol.49, pp.181–87.

X.S. Yang, S.S.S. Hosseini, A.H. Gandomi, “Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect,” Appl. Soft. Comput., vol.12, pp.1180–1186, 2012.

M.H. Sulaiman, M.W. Mustafa, Z.N. Zakaria, O. Aliman, S.R. Abdul Rahim, “Firefly algorithm technique for solving economic dispatch problem,” IEEE International Power Engineering and Optimization Conference (PEOCO2012), Melaka, Malaysia, pp.90-95, 2012.

M.H. Sulaiman, H. Daniyal, M.W. Mustafa, “Modified firefly algorithm in solving economic dispatch problems with practical constraints.,” IEEE International Conference on Power and Energy (PECon), Kota Kinabalu Sabah, Malaysia, pp.157-61, 2012.

A. Rathinam, R. Phukan, “Solution to economic load dispatch problem based on firefly algorithm and its comparison with BFO,CBFO-S and CBFO-Hybrid,” Swarm, Evolutionary, and Memetic Computing Lecture Notes in Computer Science 7677, 57-65, 2012.

T. Nikham, R. Azizipanah-Abarghooee, A. Roosta, “Reserved constrained dynamic economic dispatch: A new fast self-adaptive modified firefly algorithm.” IEEE Syst. J. vol.6, pp.635-46, 2012.

B.S. Ganesh, A.S. Reddy, “Teaching learning based optimization for economic dispatch problem with valve point loading effect,” IJEAR, vol.4, pp. 9-15, 2014.

T. Nikham, R. Azizipanah-Abarghooee, J. Aghaei, “A new modified teaching-learning algorithm for reserve constrained dynamic economic dispatch,” IEEE T. Power Syst., vol.28, pp.749-63, 2013.

M. Basu, A. Chowdhury, “Cuckoo search algorithm for economic dispatch,” Energy, vol. 60, pp. 99-108, 2013.

D.N. Vo, P. Schegner, W. Ongsakul, “Cuckoo search algorithm for non-convex economic dispatch,” IET Gener. Transm. Dis., vol.7, pp. 645–54, 2013.

P.K. Roy, S.P. Ghoshal, S.S. Thakur, “Biogeography-based optimization for economic load dispatch problems,” Electr. Pow. Compo. Sys. vol.38, pp.166-181, 2009.

B, Khokhar, K.P. Singh Parmar, .S Dahiya, “Application of biogeography-based optimization for economic dispatch problems,” IJCA, vol.47, pp.25-30, 2012.

S. Aravind, R. Scaria, “Biogeography-based optimization for the solution of the combined heat and power economic dispatch problem,” IJEIT vol.3, pp.429-32, 2013.

A. Bhattacharya, P.K..Chattopadhyay, “Solution of economic power dispatch problems using oppositional biogeography-based optimization,” Electr. Pow. Compo. Sys., vol.38, pp.1139-60, 2010.

P, Civicioglu, “Artificial cooperative search algorithm for numerical optimization problems,” Inform. Sciences., vol.229, pp. 58–76, 2013.

E.S. Fraga, L. Yang, L.G. Papageorgiou, “On the modelling of valve point loadings for power electricity dispatch,” Appl. Energy., vol. 9, pp.301-303, 2012.

P.H. Chen, H.C. Chang, “Large-scale economic dispatch by genetic algorithm,” IEEE T. Power. Syst., vol.10, pp.1919–1926, 1995.

J.B. Park, Y.W. Jeong, J.R. Shin, K.Y. Lee. “An improved particle swarm optimization for non-convex economic dispatch problems,” IEEE T. Power. Syst. vol.25, pp.156-166, 2010.

I. Fister Jr, X.S. Yang, I. Fister, J. Brest, D. Fister, “A brief review of nature-inspired algorithms for optimization,” Elektroteh. Vestn., vol.80, pp.1-7, 2013.

R. Storn, K. Price, “Differential evolution: a simple evolution strategy for fast optimization,” Dr Dobbs. J. vol.22, pp.18–24, 1997.

D. Karaboga, “An idea based on honey bee swarm for numerical optimization,” Technical Report-Tr06t, Erciyes University, Engineering faculty, Computer Engineering Department, Turkey, 2005.

R.M. May, “Simple mathematical models with very complicated dynamics,” Nature, vol.261, pp.59-67, 1976.

A.H. Gandomi, X.S. Yang, “Evolutionary boundary constraint handling scheme,” Neural. Comput. Appl. vol.21, pp.1449-1462, 2012.

J. Sun, B. Feng, W. Xu, “Particle Swarm Optimization with particles having quantum behavior,” In: Proceedings of congress on evolutionary computation, Portland, OR, USA, pp.325-331, 2004.

J. Sun, W. Xu, B. Feng, “Adaptive parameter control for quantum behaved particle swarm optimization on individual level,” In: Proceedings of IEEE International Conference on Systems, Man and Cybernetics, Big Island, HI, USA, pp.3049-54, 2005.

P. Yadav, R. Kumar, S.K. Panda, C.S. Chang, “An intelligent tuned harmony search algorithm for optimization.” Inform. Sciences, vol.196, pp.47-72, 2012.

P. Civicioglu, “Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm,” Comput. Geosci. vol. 46, pp.229-247, 2012.

A. Askerzadeh, “Bird Mating Optimizer: an optimization algorithm inspired by bird mating strategies,” Commun. Nonlinear. Sci. Numer. Simul., vol.19, pp.1213-1228, 2014.

X.S. Yang, “A new metaheuristic bat-inspired algorithm,”In: Nature Inspired Cooperative Strategies for Optimization (NISCO 2010) (Eds. J. R. Gonzales et.al.), Studies in Computational Intelligence, Springer, Berlin, 284, pp. 65-74, 2010.

N. Sinha, R. Chakrabarti, P.K. Chattopadhyay, “Evolutionary programming techniques for economic load dispatch,” IEEE Trans. Evol. Comput., vol.7, pp.83-94, 2003.

D. He, F. Wang, Z. Mao, “A hybrid genetic algorithm approach based on diﬀerential evolution for economic dispatch with valve-point eﬀect,” Int. J. Elec. Power. vol.30, pp.31-38, 2008.

C.K. Panigrahi, V.R. Pandi, “Bacterial foraging optimization:

Nelder–Mead hybrid algorithm for economic load dispatch,” IET Gener. Transm. Dis., vol.2, pp.556–65, 2008.

N. Amjady, H. Sharifzadeh, “Solution of non-convex economic dispatch problem considering valve loading effect by a new Modiﬁed Differential Evolution algorithm,” Int. J. Elec. Power., vol.32, pp.893-903, 2010.

B. Mohammadi-Ivatlooa, A. Rabiee, A. Soroud, M. Ehsana, “Iteration PSO with time varying acceleration coefﬁcients for solving non-convex economic dispatch problems,” Int. J. Elec. Power., vol.42, pp.508-516, 2012.

S.A. Reddy, K. Vaisakh, “Shufﬂed differential evolution for large scale economic dispatch,” Electr. Pow. Syst. Res., vol.96, pp. 237-24, 2013.

T. Nikham, H.D. Mojarrad, M. Nayeripour, “A new fuzzy adaptive particle swarm optimization for non-smooth economic dispatch,” Energy, vol.35, pp.1764-78, 2010.

M. Fesanghary, M.M. Ardehali, “A novel meta-heuristic optimization methodology for solving various types of economic dispatch problem,” Energy, vol.34, pp.757-766, 2009.

J.G. Vlachogiannis, K.Y. Lee, “Economic load dispatch – a comparative study on heuristic optimization techniques with an improved coordinated aggregation based PSO,” IEEE T. Power. Syst. vol.24, pp.991-1001, 2009.

A. Bhattacharya, P.K. Chattopadhyay, “Hybrid differential evolution with biogeography - based optimization for solution of economic load dispatch,” IEEE T. Power. Syst., vol.25, pp.1955–1964, 2010.

K.T. Chaturvedi, M. Pandit, L. Srivastava, “Particle swarm optimization with time varying acceleration coefficients for non-convex economic power dispatch,” Int. J. Elec. Power., vol.31, pp.249-257, 2009.

K.T. Chaturvedi, M. Pandit, “Self-organizing hierarchical particle swarm optimization for non-convex economic dispatch,” IEEE T. Power. Syst., vol. 23, pp.1079–1087, 2008.

M.M. Dalvand, B.M. Ivatloo, A. Najaﬁ, A. Rabiee, “Continuous quick group search optimizer for solving non-convex economic dispatch problems,” Electr. Pow. Syst. Res., vol.93, pp. 93–105, 2012.

K. Meng, H.G. Wang, Z.Y. Dong, K.P. Wong , “Quantum-inspired particle swarm optimization for valve-point economic load dispatch,” IEEE T. Power. Syst. vol. 25, pp.215-222, 2010.

A.I. Selvakumar, K. Thanushkodi, “Anti-predatory particle swarm optimization solution to non-convex economic dispatch problems,” Electr. Pow. Syst. Res., vol.78, pp.2–10, 2008.

H.Lu, P. Sriyanyong, Y.H. Song, T. Dillon, “Experimental study of a new Hybrid PSO with mutation for economic dispatch with non-smooth cost function,” Int. J. Elec. Power, vol.32, pp.921–935, 2010.

A.I. Selvakumar, K. Thanushkodi, “A new particle swarm

optimization solution to non-convex economic dispatch problem,” IEEE T. Power. Syst., vol.22, pp.42-51, 2007.

A. Bhattacharya, P.K. Chattopadhyay, “Solving complex economic load dispatch problems using biogeography-based optimization,” Expert. Syst. Appl., vol.37, pp.3605-3615, 2010.

LdS Coelho, V.C. Mariani. “Use of chaotic sequences in a biologically inspired algorithm for engineering design optimization.,” Expert. Syst. Appl., vol.34,pp. 1905-1913. 2008.

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