An Intelligent Water Drop Algorithm for Solving Economic Load Dispatch Problem
Economic Load Dispatch (ELD) is a method of determining
the most efficient, low-cost and reliable operation of a power
system by dispatching available electricity generation resources to
supply load on the system. The primary objective of economic
dispatch is to minimize total cost of generation while honoring
operational constraints of available generation resources. In this paper
an intelligent water drop (IWD) algorithm has been proposed to
solve ELD problem with an objective of minimizing the total cost of
generation. Intelligent water drop algorithm is a swarm-based natureinspired
optimization algorithm, which has been inspired from natural
rivers. A natural river often finds good paths among lots of possible
paths in its ways from source to destination and finally find almost
optimal path to their destination. These ideas are embedded into
the proposed algorithm for solving economic load dispatch problem.
The main advantage of the proposed technique is easy is implement
and capable of finding feasible near global optimal solution with
less computational effort. In order to illustrate the effectiveness of
the proposed method, it has been tested on 6-unit and 20-unit test
systems with incremental fuel cost functions taking into account the
valve point-point loading effects. Numerical results shows that the
proposed method has good convergence property and better in quality
of solution than other algorithms reported in recent literature.
[1] A. J. Wood and B. F. Wollenberg, "Power generation operation and
control", John Wiley and Sons, New York, 1984
[2] J. B. Park, K. S. Lee, J. R. Shin and K. Y. Lee, "A particle swarm
optimization for economic dispatch with non smooth cost functions",
IEEE Trans. on Power Systems, Vol. 8, No. 3, pp. 1325-1332, Aug. 1993.
[3] H. T. Yang, P. C. Yang and C. L. Huang, "Evolutionary Programming
Based Economic Dispatch For Units With Non-smooth Fuel Cost Functions",
IEEE Transactions on Power Systems, Vol. 11, No. 1, pp. 112-118,
1996.
[4] T. Jayabarathi, G. Sadasivam and V. Ramachandran, "Evolutionary
programming based economic dispatch of generators with prohibited
operating zones", Electric Power Systems Research, Vol. 52, No. 3, pp.
261-266, 1999.
[5] Z. X. Liang and J. D. Glover, "A zoom feature for a dynamic programming
solution to economic dispatch including transmission losses, IEEE
Trans. on Power Systems, Vol. 7, No. 2, pp. 544-550, May 1992.
[6] El-Sharkawy, M., and Nieebur, D., "Artificial neural networks with
application to power systems", IEEE Power Engineering Society, A
Tutorial Course, 1996.
[7] Yalcinoz, T., and Short, M. J., "Neural networks approach for solving economic
dispatch problem with transmission capacity constraints", IEEE
Trans. on Power Systems, Vol. 13, pp. 307-313, 1998.
[8] K.Y. Lee, A. Sode-Yome, J.H. Park, "Adaptive hopfield neural networks
for economic load dispatch", IEEE Trans. on Power Systems, Vol.13,
No. 2, pp. 519526, 1998.
[9] J.H. Park,Y.S. Kim, I.K. Eom, K.Y. Lee, "Economic load dispatch for
piecewise quadratic cost function using Hop field neural network", IEEE
Trans. on Power Systems, Vol. 8, No. 3, pp. 10301038, 1993.
[10] Pancholi, R. K., and Swarup, K. S., "Particle swarm optimization for
security constrained economic dispatch", International Conference on
Intelligent Sensing and Information Processing, Chennai, India, pp. 712,
2004.
[11] Youssef, H. K., and El-Naggar, K. M., "Genetic based algorithm for
security constrained power system economic dispatch", Electric Power
Systems Research, Vol. 53, pp. 4751, 2000.
[12] S.O. Orero, M.R. Irving, "Economic dispatch of generators with prohibited
operating zones: a genetic algorithm approach", IEE Proc. Gen.
Transm. Distrib., Vol. 143, No. 6, pp. 529534, 1996.
[13] D. C. Walters and G. B. Sheble, "Genetic algorithm solution of economic
dispatch with the valve-point loading", IEEE Trans. on Power Systems,
Vol. 8, No. 3, pp. 1325-1332, Aug. 1993.
[14] Nasimul Nomana, Hitoshi Iba, "Differential evolution for economic
load dispatch problems", Electric Power Systems Research, Vol. 78, pp.
13221331, 2008.
[15] W. M. Lin, F. S. Cheng and M. T. Tsay, "An improved Tabu search
for economic dispatch with multiple minima", IEEE Trans. on Power
Systems, Vol. 17, No. 1, pp.108-112, Feb. 2002.
[16] Aniruddha Bhattacharya, P.K. Chattopadhyay, "Solving complex economic
load dispatch problems using biogeography-based optimization",
Expert Systems with Applications, Vol. 37, pp. 36053615, 2010.
[17] Hamed Shah-Hosseini, "The intelligent water drops algorithm: a natureinspired
swarm-based optimization algorithm", International Journal of
Bio-Inspired Computation, Vol. 1, Nos. 1 and 2, pp. 71-79, 2009.
[18] Shah-Hosseini. H, "Optimization with the Nature- Inspired Intelligent
Water Drops Algorithm", Int. Journal of Intelligent Computing and
Cybernetics, Vol. 1, No. 2, pp. 193-212, 2008.
[19] [25] Z. Michalewicz, M. Schoenauer, "Evolutionary algorithms for
constrained parameter optimization problems", Evol. Comput. vol. 4, no.
1, pp. 1-32, 1996.
[20] Gaing ZL, "Particle swarm optimization to solving the economic dispatch
considering the generator constraints", IEEE Trans. on Power
Systems, Vol. 18, No. 3, pp. 118795, 2003.
[21] Su CT, Lin CT, "New approach with a Hop field modeling framework
to economic dispatch", IEEE Trans. on Power Systems, Vol. 15, No. 2,
pp. 541545, 2000.
[1] A. J. Wood and B. F. Wollenberg, "Power generation operation and
control", John Wiley and Sons, New York, 1984
[2] J. B. Park, K. S. Lee, J. R. Shin and K. Y. Lee, "A particle swarm
optimization for economic dispatch with non smooth cost functions",
IEEE Trans. on Power Systems, Vol. 8, No. 3, pp. 1325-1332, Aug. 1993.
[3] H. T. Yang, P. C. Yang and C. L. Huang, "Evolutionary Programming
Based Economic Dispatch For Units With Non-smooth Fuel Cost Functions",
IEEE Transactions on Power Systems, Vol. 11, No. 1, pp. 112-118,
1996.
[4] T. Jayabarathi, G. Sadasivam and V. Ramachandran, "Evolutionary
programming based economic dispatch of generators with prohibited
operating zones", Electric Power Systems Research, Vol. 52, No. 3, pp.
261-266, 1999.
[5] Z. X. Liang and J. D. Glover, "A zoom feature for a dynamic programming
solution to economic dispatch including transmission losses, IEEE
Trans. on Power Systems, Vol. 7, No. 2, pp. 544-550, May 1992.
[6] El-Sharkawy, M., and Nieebur, D., "Artificial neural networks with
application to power systems", IEEE Power Engineering Society, A
Tutorial Course, 1996.
[7] Yalcinoz, T., and Short, M. J., "Neural networks approach for solving economic
dispatch problem with transmission capacity constraints", IEEE
Trans. on Power Systems, Vol. 13, pp. 307-313, 1998.
[8] K.Y. Lee, A. Sode-Yome, J.H. Park, "Adaptive hopfield neural networks
for economic load dispatch", IEEE Trans. on Power Systems, Vol.13,
No. 2, pp. 519526, 1998.
[9] J.H. Park,Y.S. Kim, I.K. Eom, K.Y. Lee, "Economic load dispatch for
piecewise quadratic cost function using Hop field neural network", IEEE
Trans. on Power Systems, Vol. 8, No. 3, pp. 10301038, 1993.
[10] Pancholi, R. K., and Swarup, K. S., "Particle swarm optimization for
security constrained economic dispatch", International Conference on
Intelligent Sensing and Information Processing, Chennai, India, pp. 712,
2004.
[11] Youssef, H. K., and El-Naggar, K. M., "Genetic based algorithm for
security constrained power system economic dispatch", Electric Power
Systems Research, Vol. 53, pp. 4751, 2000.
[12] S.O. Orero, M.R. Irving, "Economic dispatch of generators with prohibited
operating zones: a genetic algorithm approach", IEE Proc. Gen.
Transm. Distrib., Vol. 143, No. 6, pp. 529534, 1996.
[13] D. C. Walters and G. B. Sheble, "Genetic algorithm solution of economic
dispatch with the valve-point loading", IEEE Trans. on Power Systems,
Vol. 8, No. 3, pp. 1325-1332, Aug. 1993.
[14] Nasimul Nomana, Hitoshi Iba, "Differential evolution for economic
load dispatch problems", Electric Power Systems Research, Vol. 78, pp.
13221331, 2008.
[15] W. M. Lin, F. S. Cheng and M. T. Tsay, "An improved Tabu search
for economic dispatch with multiple minima", IEEE Trans. on Power
Systems, Vol. 17, No. 1, pp.108-112, Feb. 2002.
[16] Aniruddha Bhattacharya, P.K. Chattopadhyay, "Solving complex economic
load dispatch problems using biogeography-based optimization",
Expert Systems with Applications, Vol. 37, pp. 36053615, 2010.
[17] Hamed Shah-Hosseini, "The intelligent water drops algorithm: a natureinspired
swarm-based optimization algorithm", International Journal of
Bio-Inspired Computation, Vol. 1, Nos. 1 and 2, pp. 71-79, 2009.
[18] Shah-Hosseini. H, "Optimization with the Nature- Inspired Intelligent
Water Drops Algorithm", Int. Journal of Intelligent Computing and
Cybernetics, Vol. 1, No. 2, pp. 193-212, 2008.
[19] [25] Z. Michalewicz, M. Schoenauer, "Evolutionary algorithms for
constrained parameter optimization problems", Evol. Comput. vol. 4, no.
1, pp. 1-32, 1996.
[20] Gaing ZL, "Particle swarm optimization to solving the economic dispatch
considering the generator constraints", IEEE Trans. on Power
Systems, Vol. 18, No. 3, pp. 118795, 2003.
[21] Su CT, Lin CT, "New approach with a Hop field modeling framework
to economic dispatch", IEEE Trans. on Power Systems, Vol. 15, No. 2,
pp. 541545, 2000.
@article{"International Journal of Electrical, Electronic and Communication Sciences:60436", author = "S. Rao Rayapudi", title = "An Intelligent Water Drop Algorithm for Solving Economic Load Dispatch Problem", abstract = "Economic Load Dispatch (ELD) is a method of determining
the most efficient, low-cost and reliable operation of a power
system by dispatching available electricity generation resources to
supply load on the system. The primary objective of economic
dispatch is to minimize total cost of generation while honoring
operational constraints of available generation resources. In this paper
an intelligent water drop (IWD) algorithm has been proposed to
solve ELD problem with an objective of minimizing the total cost of
generation. Intelligent water drop algorithm is a swarm-based natureinspired
optimization algorithm, which has been inspired from natural
rivers. A natural river often finds good paths among lots of possible
paths in its ways from source to destination and finally find almost
optimal path to their destination. These ideas are embedded into
the proposed algorithm for solving economic load dispatch problem.
The main advantage of the proposed technique is easy is implement
and capable of finding feasible near global optimal solution with
less computational effort. In order to illustrate the effectiveness of
the proposed method, it has been tested on 6-unit and 20-unit test
systems with incremental fuel cost functions taking into account the
valve point-point loading effects. Numerical results shows that the
proposed method has good convergence property and better in quality
of solution than other algorithms reported in recent literature.", keywords = "Economic load dispatch, Transmission loss, Optimization,
Valve point loading, Intelligent Water Drop Algorithm.", volume = "5", number = "10", pages = "1372-7", }