Multi-Objective Short-Term Fixed Head Hydrothermal Scheduling Using Augmented Lagrange Hopfield Network

  • Nguyen, Thang Trung ;
  • Vo, Dieu Ngoc
  • Received : 2013.03.04
  • Accepted : 2014.07.24
  • Published : 2014.11.01


This paper proposes an augmented Lagrange Hopfield network (ALHN) based method for solving multi-objective short term fixed head hydrothermal scheduling problem. The main objective of the problem is to minimize both total power generation cost and emissions of $NO_x$, $SO_2$, and $CO_2$ over a scheduling period of one day while satisfying power balance, hydraulic, and generator operating limits constraints. The ALHN method is a combination of augmented Lagrange relaxation and continuous Hopfield neural network where the augmented Lagrange function is directly used as the energy function of the network. For implementation of the ALHN based method for solving the problem, ALHN is implemented for obtaining non-dominated solutions and fuzzy set theory is applied for obtaining the best compromise solution. The proposed method has been tested on different systems with different analyses and the obtained results have been compared to those from other methods available in the literature. The result comparisons have indicated that the proposed method is very efficient for solving the problem with good optimal solution and fast computational time. Therefore, the proposed ALHN can be a very favorable method for solving the multi-objective short term fixed head hydrothermal scheduling problems.


Augmented lagrange hopfield network;Fixed head;Fuzzy set theory;Hydrothermal scheduling;Multi-objective


  1. I. A. Farhat and M. E. El-Hawary, "Multi-objective short-term hydro-thermal scheduling using bacterial foraging algorithm", 2011 IEEE Electrical Power and Energy Conference, 176-181.
  2. A. H. A. Rashid and K. M. Nor, "An efficient method for optimal scheduling of fixed head hydro and thermal plants", IEEE Trans. Power Systems, vol. 6, no. 2, pp. 632-636, May 1991.
  3. J. Sasikala. M. Ramaswamy, "PSO based economic emission dispatch for fixed head hydrothermal systems", Electr. Eng., vol. 94, no. 12, pp. 233-239, Dec. 2012
  4. A. J. Wood and B. F. Wollenberg, Power generation, operation and control, 2nd edn, New York: John Wiley & Sons, 1996.
  5. G.G. Oliveira and S. Soares, "A second-order network flow algorithm for hydrothermal scheduling," IEEE Trans. Power Systems, vol. 10, no. 3, pp. 1635-1641, Aug. 1995.
  6. Md.S. Salam, K.M. Nor, and A.R, Hamdan, "Hydrothermal scheduling based Lagrangian relaxation approach to hydrothermal coordination," IEEE Trans. Power Systems, vol. 13, no. 1, pp. 226-235, Feb. 1998.
  7. W.S. Sifuentes and A. Vargas, "Hydrothermal scheduling using benders decomposition: accelerating techniques," IEEE Trans. Power Systems, vol. 23, no. 3, pp. 1351-1359, Aug. 2007.
  8. K.P. Wong and Y.W. Wong, "Short-term hydrothermal scheduling - Part II: parallel simulated annealing approach," IEE Proc.-Gener. Transm. Distrib., vol. 141, no. 5, pp. 502-506, Sept. 1994.
  9. P.-C. Yang, H.-T. Yang, and C.-L. Huang, "Scheduling short-term hydrothermal generation using evolutionary programming techniques," IEE Proc.- Gener. Transnm. Distrib., vol. 143, no. 4, 371-376, Jul. 1996.
  10. E. Gil, J. Bustos, and H. Rudnick, "Short-term hydrothermal generation scheduling model using a genetic algorithm," IEEE Trans. Power Systems, vol. 18, no. 4, 1256-1264, Nov. 2003.
  11. L. Lakshminarasimman and S. Subramanian, "Shortterm scheduling of hydrothermal power system with cascaded reservoirs by using modified differential evolution," IEE Proc.-Gener. Transm. Distrib., vol. 153, no. 6, 693-700, Nov. 2006.
  12. J.Polprasert and W.Ongsakul, "Augmented Lagrange Hopfield network for economic dispatch," Australasian Universities Power Engineering Conference, AUPEC 2007, Dec. 2007, Perth, Australia.
  13. J. Zhang, J. Wang, and C. Yue, "Small populationbased particle swarm optimization for short-term hydrothermal scheduling," IEEE Trans. Power Systems, vol. 27, no. 1, 142-152, Feb. 2012.
  14. R. Naresh and J. Sharma, "Two-phase neural network based solution technique for short term hydrothermal scheduling," IEE Proc-Gener. Transm. Distrib., vol. 146, no. 6, 657-663, Nov. 1999.
  15. V. N. Dieu and W. Ongsakul, "Hopfield Lagrange for short-term hydrothermal scheduling," IEEE Power Tech 2005, June 2005, St. Petersburg, Russia.
  16. V. N. Dieu and W. Ongsakul, "Enhanced merit order and augmented Lagrange Hopfield network for hydrothermal scheduling," Int. J. Electrical Power & Energy Systems, vol. 30, no. 2, pp. 93-101, Feb. 2008.
  17. V. N. Dieu and W. Ongsakul, "Improved merit order and augmented Lagrange Hopfield network for short term hydrothermal scheduling," Energy Conversion and Management, vol. 50, no. 12, pp. 3015-3023, Dec. 2009.
  18. M. Sakawa, H. Yano, and T. Yumine, "An interactive fuzzy satisfying method for multi-objective linear programming problems and its applications," IEEE Trans. Systems, Man, and Cybernetics, vol. SMC-17, no. 4, pp. 654-661, Jul./Aug. 1987.
  19. C.G. Tapia and B.A. Murtagh, "Interactive fuzzy programming with preference criteria in multi-objective decision making," Computers & Operations Research, vol. 18, no. 3, pp. 307-316, 1991.
  20. J.S. Dhillon, S.C. Parti and D.P. Kothari, "Fuzzy decision-making in stochastic multiobjective shortterm hydrothermal scheduling," IEE Proc. Gener., Transm. Distrib., vol. 149, pp. 191-200, 2002.

Cited by

  1. An efficient cuckoo bird inspired meta-heuristic algorithm for short-term combined economic emission hydrothermal scheduling 2016,