A Proposed Improved Hybrid Hill Climbing Algorithm with the Capability of Local Search for Solving the Nonlinear Economic Load Dispatch Problem

Document Type : Original Article

Authors

1 Electrical Engineering Department, Engineering Faculty, Razi University, Kermanshah, Iran

2 Electrical Engineering Department, Engineering Faculty, Ilam University, Ilam, Iran

Abstract

This paper introduces a new hybrid hill-climbing algorithm (HHC) for solving the Economic Dispatch (ED) problem. This algorithm solves the ED problems with a systematic search structure with a global search. It improves the results obtained from an evolutionary algorithm with local search and converges to the best possible solution that grabs the accuracy of the problem. The most important goal of economic load dispatch is the optimal allocation of each generator's contribution to provide the load and reduce the costs of active units in the power system. This is generally due to presence of the nonlinear factors and limitations, such as the effect of the steam inlet valve (valve point effect (VPE)), the balance between the power generation and power demand of the system, the prohibited operating zones (POZS), power generation limits, ramp rate limits, and transmission losses. This algorithm is implemented on three 13-unit, 15-unit and 40-unit test systems with different operating conditions, and also for the same three test systems in combination with the evolutionary PSO algorithm. The simulation results show the efficiency of the proposed algorithm in solving ED problems.

Keywords


 
1. Azizipanah-Abarghooee, R., Niknam, T., Gharibzadeh, M. and
Golestaneh, F., “Robust, fast and optimal solution of practical
economic dispatch by a new enhanced gradient-based simplified
swarm optimisation algorithm”, IET Generation, Transmission
& Distribution, Vol. 7, No. 6, (2013), 620–635.  
2. Pradhan, M., Roy, P.K. and Pal, T., “Grey wolf optimization
applied to economic load dispatch problems”, International
Journal of Electrical Power & Energy Systems, Vol. 83, (2016),
325–334.  
 
3. Pancholi, R.K. and Swarup, K. S., “Particle swarm optimization
for security constrained economic dispatch”, In International
Conference on Intelligent Sensing and Information Processing,
IEEE, (2004), 7–12.  
4. Abaci, K. and Yamacli, V., “Differential search algorithm for
solving multi-objective optimal power flow problem”,
International Journal of Electrical Power & Energy Systems,
Vol. 79, (2016), 1–10.  
5. Adaryani, M.R. and Karami, A., “Artificial bee colony algorithm
for solving multi-objective optimal power flow problem”,
International Journal of Electrical Power & Energy Systems,
Vol. 53, (2013), 219–230.  
6. Cai, H.R., Chung, C.Y. and Wong, K. P., “Application of
differential evolution algorithm for transient stability constrained
optimal power flow”, IEEE Transactions on Power Systems,
Vol. 23, No. 2, (2008), 719–728.  
7. Wu, Z.L., Ding, J.Y., Wu, Q.H., Jing, Z.X. and Zhou, X. X.,
“Two-phase mixed integer programming for non-convex
economic dispatch problem with spinning reserve constraints”,
Electric Power Systems Research, Vol. 140, (2016), 653–662.  
8. Daryani, N., Hagh, M.T. and Teimourzadeh, S., “Adaptive group
search optimization algorithm for multi-objective optimal power
flow problem”, Applied Soft Computing, Vol. 38, (2016), 1012–
1024.  
9. Neto, J.X.V., Reynoso-Meza, G., Ruppel, T.H., Mariani, V.C. and
dos Santos Coelho, L., “Solving non-smooth economic dispatch
by a new combination of continuous GRASP algorithm and
differential evolution”, International Journal of Electrical
Power & Energy Systems, Vol. 84, (2017), 13–24.  
10. Bouchekara, H. R. E. H., “Optimal power flow using black-holebased
optimization
approach”,
Applied
Soft
Computing,
Vol.
24,
(2014),
879–888.

11. Abatari, H.D., Abad, M.S.S. and Seifi, H., “Application of bat
optimization algorithm in optimal power flow”, In 2016 24th
Iranian Conference on Electrical Engineering (ICEE), IEEE,
(2016), 793–798.  
12. Fathima, A.H. and Palanisamy, K., “Optimization in microgrids
with hybrid energy systems–A review”, Renewable and
Sustainable Energy Reviews, Vol. 45, (2015), 431–446.  
13. Bhowmik, A.R. and Chakraborty, A. K., “Solution of optimal
power flow using non dominated sorting multi objective
opposition based gravitational search algorithm”, International
Journal of Electrical Power & Energy Systems, (2015), 1237–
1250.  
14. Elsayed, W.T., Hegazy, Y.G., Bendary, F.M. and El-Bages, M.
S., “A review on accuracy issues related to solving the nonconvex
economic dispatch problem”, Electric Power Systems
Research, Vol. 141, (2016), 325–332.  
15. Pereira-Neto, A., Unsihuay, C. and Saavedra, O. R., “Efficient
evolutionary strategy optimisation procedure to solve the
nonconvex economic dispatch problem with generator
constraints”, IEE Proceedings-Generation, Transmission and
Distribution, Vol. 152, No. 5, (2005), 653–660.  
16. Russell, S. and Norvig, P., Artificial intelligence: a modern
approach, Prentice Hall, Englewood Cliffs, New Jersey, (2003). 
17. Reinefeld, A. and Marsland, T. A., “Enhanced iterativedeepening
search”,
IEEE
Transactions
on
Pattern
Analysis
and
Machine
Intelligence,
Vol.
16,
No.
7,
(1994),
701–710.
 

18. Burke, E.K. and Bykov, Y., “The late acceptance hill-climbing
heuristic”, European Journal of Operational Research, Vol.
285, No. 1, (2017), 70–78.  
19. Civicioglu, P., “Backtracking search optimization algorithm for
numerical optimization problems”, Applied Mathematics and
Computation, Vol. 219, No. 15, (2013), 8121–8144.  
20. Sinha, N., Chakrabarti, R. and Chattopadhyay, P. K.,
“Evolutionary programming techniques for economic load
dispatch”, IEEE Transactions on Evolutionary Computation,
Vol. 7, No. 1, (2003), 83–94.  
21. Victoire, T.A.A. and Jeyakumar, A. E., “Hybrid PSO–SQP for
economic dispatch with valve-point effect”, Electric Power
Systems Research, Vol. 71, No. 1, (2004), 51–59.  
22. Dos Santos Coelho, L. and Mariani, V. C., “An improved
harmony search algorithm for power economic load dispatch”,
Energy Conversion and Management, Vol. 50, No. 10, (2009),
2522–2526.  
23. Alsumait, J.S., Sykulski, J.K. and Al-Othman, A. K., “A hybrid
GA–PS–SQP method to solve power system valve-point
economic dispatch problems”, Applied Energy, Vol. 87, No. 5,
(2010), 1773–1781.  
24. Wang, S.K., Chiou, J.P. and Liu, C. W., “Non-smooth/nonconvex
economic dispatch by a novel hybrid differential
evolution algorithm”, IET Generation, Transmission &
Distribution, Vol. 1, No. 5, (2007), 793–803.  
25. Yang, X.S., Hosseini, S.S.S. and Gandomi, A. H., “Firefly
algorithm for solving non-convex economic dispatch problems
with valve loading effect”, Applied Soft Computing, Vol. 12, No.
3, (2012), 1180–1186.  
26. Gaing, Z. L., “Particle swarm optimization to solving the
economic dispatch considering the generator constraints”, IEEE
Transactions on Power Systems, Vol. 18, No. 3, (2003), 1187–
1195.  
27. Niknam, T., Mojarrad, H.D. and Meymand, H. Z., “Non-smooth
economic dispatch computation by fuzzy and self adaptive
particle swarm optimization”, Applied Soft Computing, Vol. 11,
No. 2, (2011), 2805–2817.  
28. Noman, N. and Iba, H., “Differential evolution for economic load
dispatch problems”, Electric Power Systems Research, Vol. 78,
No. 8, (2008), 1322–1331.  
29. Chaturvedi, K.T., Pandit, M. and Srivastava, L., “Self-organizing
hierarchical particle swarm optimization for nonconvex economic
dispatch”, IEEE Transactions on Power Systems, Vol. 23, No.
3, (2008), 1079–1087.  
30. Selvakumar, A.I. and Thanushkodi, K., “Optimization using
civilized swarm: solution to economic dispatch with multiple
minima”, Electric Power Systems Research, Vol. 79, No. 1,
(2009), 8–16.  
31. Panigrahi, B.K., Pandi, V.R. and Das, S., “Adaptive particle
swarm optimization approach for static and dynamic economic
load dispatch”, Energy Conversion and Management, Vol. 49,
No. 6, (2008), 1407–1415.  
32. Zakian, P. and Kaveh, A., “Economic dispatch of power systems
using an adaptive charged system search algorithm”, Applied Soft
Computing, Vol. 73, (2018), 607–622.