Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon free Dynamic formulation and approximation methods to solve economic dispatch problems

  • Author(s): Mohammed I. Abouheaf 1 ; Wei-Jen Lee 2 ; Frank L. Lewis 1
    • View affiliations
    • Affiliations: 1: The University of Texas at Arlington Research Institute, Electrical Engineering, University of Texas at Arlington, 7300 Jack Newell Blvd. S., Fort Worth, Texas, TX 76118, USA;
      2: University of Texas at Arlington, Electrical Engineering, Energy Systems Research Center, UTA Box 19048, Arlington, Texas 76019, USA
  • Source: Volume 7, Issue 8, August 2013, p. 866 – 873
    DOI:  10.1049/iet-gtd.2012.0397 , Print ISSN 1751-8687, Online ISSN 1751-8695
© The Institution of Engineering and Technology
Received 15/07/2012, Accepted 10/03/2013, Revised 17/02/2013, Published

Economic dispatch (ED) is an optimisation tool that is used to allocate active load demands to the generating units through optimising the fuel generation cost function subject to the different operational constraints. The high non-linearity of the power system imposes mathematical challenges in formulating the generation cost function models, which makes the ED problem hard to solve. This study introduces two ideas to solve issues related to the ED problem. First, a dynamic formulation technique is developed to optimally allocate the change in the total active load demand to the generating units. This technique is shown to be insensitive to the optimality of the initial active load distribution unlike the base point and participation factor method. Moreover, it guarantees an optimal distribution among the generating units due the change in the active load demand. Second, a novel approximation of the non-convex generation cost function is developed to solve non-convex ED problem with the transmission losses. This approximation enables the use of gradient and Newton techniques to solve the non-convex ED problem with valve point loading effect and transmission losses in an analytic approach. This approximation is compared with some heuristic optimisation techniques.

Inspec keywords: power generation dispatch; concave programming; Newton method; gradient methods; costing; power generation economics

Other keywords: active load distribution optimality; dynamic formulation-approximation methods; optimal distribution; nonconvex ED problem; economic dispatch problems; fuel generation cost function optimization; transmission loss; active load demand; nonconvex generation cost function; gradient technique; Newton technique; base point method; generating units; power system nonlinearity; optimisation tool; participation factor method; valve point loading effect; active load demand allocation; operational constraints; generation cost function models

Subjects: Power system management, operation and economics; Interpolation and function approximation (numerical analysis); Optimisation techniques

References

    1. 1)
      • 9. Granelli, G.P., Montagna, M.: ‘Security-constrained economic dispatch using dual quadratic programming’, Electr. Power Syst. Res., 2000, 56, (1), pp. 71–80 (doi: 10.1016/S0378-7796(00)00097-3).
    2. 2)
      • 6. Amjady, N., Nasiri-Rad, H.: ‘Solution of non-convex and non smooth economic dispatch by a new adaptive real coded genetic algorithm’, Exp. Syst. Appl., 2010, 37, (7), pp. 5237–5245 (doi: 10.1016/j.eswa.2009.12.084).
    3. 3)
      • 15. Chinag, C.L.: ‘Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels’, IEEE Trans. Power Syst., 2005, 20, (4), pp. 1690–1699 (doi: 10.1109/TPWRS.2005.857924).
    4. 4)
      • 16. Coelho, L.S., Mariani, V.C.: ‘Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect’, IEEE Trans. Power Syst., 2006, 21, (2), pp. 989–96 (doi: 10.1109/TPWRS.2006.873410).
    5. 5)
      • 2. Raol, C.S., Nagaraju, S.S., Raju, P.S., Reddy, M.R.: ‘Optimized integral controller for economic dispatch in a two area system based on Hooke-Jeeves algorithm’, J. Eng. Appl. Sci., 2007, 2, (6), pp. 49–56.
    6. 6)
      • 24. Guvenc, U., Duman, S., Saracoglu, B., Özturk, A.: ‘A hybrid GA-PSO approach based on similarity for various types of economic dispatch problems’, Electronics and Electrical Engineering Journal2011, 2, (108), pp. 109–114.
    7. 7)
      • 3. Niknam, T., Mojarrad, H.D., Meymand, H.Z., Firouzi, B.B.: ‘A new honey bee mating optimization algorithm for non-smooth economic dispatch’, Energy, 2011, 36, (2), pp. 896–908 (doi: 10.1016/j.energy.2010.12.021).
    8. 8)
      • 20. Vanitha, M., Thanushkodi, K.: ‘An efficient technique for solving the economic dispatch problem using biogeography algorithm’, Eur. J. Sci. Res., 2011, 50, (2), pp. 165–172.
    9. 9)
      • 4. Duman, S., Guvenc, U., Yorukeren, N.: ‘Gravitational search algorithm for economic dispatch with valve point effects’, Int. Rev. Electr. Eng., 2010, 5, (6), pp. 2890–2895.
    10. 10)
      • 12. Chen, C.L., Wang, C.L.: ‘Branch-and-bound scheduling for thermal generating units’, IEEE Trans. Energy Convers., 1993, 8, (2), pp. 184–189 (doi: 10.1109/60.222703).
    11. 11)
      • 17. Chaturvedi, K.T., Pandit, M., Srivastava, L.: ‘Particle swarm optimization with crazy particles for nonconvex economic dispatch’, Appl. Soft Comput., 2009, 9, (3), pp. 962–969 (doi: 10.1016/j.asoc.2008.11.012).
    12. 12)
      • 21. Ciornei, I., Kyriakides, E.: ‘A GA – API solution for the economic dispatch of generation in power system operation’, IEEE Trans. Power Syst., 2011, 27, (1), pp. 1–9.
    13. 13)
      • 23. Gaing, Z.L.: ‘Particle swarm optimization to solving the economic dispatch considering the generator constraints’, IEEE Trans. Power Syst., 2003, 18, (3), pp. 1187–1195 (doi: 10.1109/TPWRS.2003.814889).
    14. 14)
      • 7. Lukman, D., Walshe, K., Blackburn, T.R.: ‘Loss minimisation in industrial power system operation’. Australasian Universities Power Engineering Conf. (AUPEC2000), Brisbane, Australia, 2000, pp. 15–20.
    15. 15)
      • 13. Yang, H.T., Yang, P.C., Huang, C.L.: ‘Evolutionary programming based economic dispatch for units with non-smooth fuel cost functions’, IEEE Trans. Power Syst., 1996, 11, (1), pp. 112–118 (doi: 10.1109/59.485992).
    16. 16)
      • 8. Lin, W.M., Chen, S.J.: ‘Bid-based dynamic economic dispatch with an efficient interior point algorithm’, Electr. Power Energy Syst., 2002, (24), pp. 51–57 (doi: 10.1016/S0142-0615(01)00007-2).
    17. 17)
      • 1. Wood, A.J., Wollenberg, B.F.: ‘Power generation, operation and control’ (Wiley, New York, 1996, 1984, 2nd edn.).
    18. 18)
      • 14. Walters, D.C., Sheble, G.B.: ‘Genetic algorithm solution of economic dispatch with valve point loading’, IEEE Trans. Power Syst., 1993, 8, (3), pp. 1325–1331 (doi: 10.1109/59.260861).
    19. 19)
      • 22. Min, K., Lee, S., Moon, Y.: ‘An economic dispatch algorithm as combinatorial optimization problems’, Int. J. Con. Aut. and Sys., 2008, 6, (4), pp. 468–476.
    20. 20)
      • 10. Lin, C.E., Viviani, G.L.: ‘Hierarchical economic dispatch for piecewise quadratic cost functions’, IEEE Trans. Power Appl. Syst., 1984, PAS-103, (6), pp. 1170–1175 (doi: 10.1109/TPAS.1984.318445).
    21. 21)
      • 5. Amjady, N., Nasiri-Rad, H.: ‘Economic dispatch using an efficient real-coded genetic algorithm’, IET Gener. Trans. Distrib., 2009, 3, (3), pp. 266–278 (doi: 10.1049/iet-gtd:20080469).
    22. 22)
      • 11. Yang, H.T., Chen, S.L.: ‘Incorporating a multi-criteria decision procedure into the combined dynamic programming/production simulation algorithm for generation expansion planning’, IEEE Trans. Power Syst., 1989, 4, (1), pp. 165–175 (doi: 10.1109/59.32474).
    23. 23)
      • 18. Wong, K.P., Fung, C.C.: ‘Simulated annealing based economic dispatch algorithm’, IEE Proc. C, 1993, 140, (6), pp. 509–515.
    24. 24)
      • 19. Lin, W.M., Cheng, F.S., Tsay, M.T.: ‘An improved Tabu search for economic dispatch with multiple minima’, IEEE Trans. Power Syst., 2002, 17, (1), pp. 108–112 (doi: 10.1109/59.982200).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-gtd.2012.0397
Loading

Related content

content/journals/10.1049/iet-gtd.2012.0397
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
Print this page
This is a required field
Please enter a valid email address