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Pseudo-Gradient Based Particle Swarm Optimization Method for Nonconvex Economic Dispatch

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Power, Control and Optimization

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 239))

Abstract

This chapter proposes a pseudo-gradient based particle swarm optimization (PGPSO) method for solving nonconvex economic dispatch (ED) including valve point effects, multiple fuels, and prohibited operating zones. The proposed PGPSO is based on the self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients (HPSO-TVAC) with position of particles guided by a pseudo-gradient. The pseudo-gradient here is to determine an appropriate direction for the particles during their movement so that they can quickly move to an optimal solution. The proposed method has been tested on several systems and the obtained results are compared to those from many other methods available in the literature. The test results have indicated that the proposed method can obtain less expensive total costs than many others in a faster computing manner, especially for the large-scale systems. Therefore, the proposed PGPSO is favorable for online implementation in the practical ED problems.

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Abbreviations

a i , b i , c i :

fuel cost coefficients of unit i

e i , f i :

fuel cost coefficients of unit i reflecting valve-point effects

a ij , b ij , c ij :

fuel cost coefficients for fuel type j of unit i

e ij , f ij :

fuel cost coefficients for fuel type j of unit i reflecting valve-point effects

B ij , B 0i , B 00 :

B-matrix coefficients for transmission power loss

c1i , c1f :

initial and final values of cognitive acceleration factor, respectively

c2i , c2f :

initial and final values of social acceleration factor, respectively

c1, c2:

cognitive and social acceleration coefficients, respectively

DR i :

ramp down rate limit of unit i

\( g_{p} \left( {x_{id}^{(k)} } \right) \) :

pseudo-gradient at point k for particle d of element i

N :

total number of generating units

n i :

number of prohibited operating zones of unit i

N p :

number of particles

P D :

total system load demand

P i :

power output of unit i

P i,high :

highest possible power output of generator i

P i,low :

lowest possible power output of generator i

P i,max :

maximum power output of generator i

P i,min :

minimum power output of generator i

P ij,min :

minimum power output for fuel j of generator i

P L :

total transmission loss

\( P_{ik}^{l} \) :

lower bound for prohibited zone k of generator i

\( P_{ik}^{u} \) :

upper bound for prohibited zone k of generator i

UR i :

ramp up rate limit of unit i

v id :

velocity of particle d for element i

x id :

position of particle d for element i

Ω:

set of units with prohibited operating zones

\( \delta \left( {x_{{id}} } \right) \) :

direction indicator for position of element i in particle d

References

  1. Chowdhury, E.H., Rahrnan, S.: A review of recent advances in economic dispatch. IEEE Trans. Power Syst. 5, 1248–1259 (1990)

    Article  Google Scholar 

  2. Xia, X., Elaiw, A.M.: Optimal dynamic economic dispatch of generation: a review. Electr. Power Syst. Res. 80, 975–986 (2010)

    Article  Google Scholar 

  3. Wood, A.J., Wollenberg, B.F.: Power Generation, Operation, and Control, 2nd edn. Wiley, New York (1996)

    Google Scholar 

  4. Fink, L.H., Kwatny, H.G., Mcdonald, J.P.: Economic dispatch of generation via valve-point loading. IEEE Trans. Power Appar. Syst. 88, 805–811 (1969)

    Article  Google Scholar 

  5. Lin, C.E., Viviani, G.L.: Hierarchical economic dispatch for piecewise quadratic cost functions. IEEE Trans. Power Appar. Syst. 103, 1170–1175 (1984)

    Article  Google Scholar 

  6. Lee, F.N., Breipohl, A.M.: Reserve constrained economic dispatch with prohibited operating zones. IEEE Trans. Power Syst. 8, 246–254 (1993)

    Article  Google Scholar 

  7. Fan, J.Y., McDonald, J.D.: A practical approach to real time economic dispatch considering unit’s prohibited operating zones. IEEE Trans. Power Syst. 9, 1737–1743 (1994)

    Article  Google Scholar 

  8. Hemamalini, S., Simon, S.P.: Maclaurin series-based Lagrangian method for economic dispatch with valve-point effect. IET Gener. Transm. Distrib. 3, 859–871 (2009)

    Article  Google Scholar 

  9. Lin, W.-M., Gowa, H.-J., Tsai, M.-T.: Combining of direct search and signal-to-noise ratio for economic dispatch optimization. Energy Conver. Manag. 52, 487–493 (2011)

    Article  Google Scholar 

  10. Park, J.H., Kim, Y.S., Eom, I.K., Lee, K.Y.: Economic load dispatch for piecewise quadratic cost function using Hopfield neural network. IEEE Trans. Power Syst. 8, 1030–1038 (1993)

    Article  Google Scholar 

  11. Lee, K.Y., Sode-Yome, A., Park, J.H.: Adaptive Hopfield neural networks for economic load dispatch. IEEE Trans. Power Syst. 13, 519–526 (1998)

    Article  Google Scholar 

  12. Chiang, C.-L.: Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels. IEEE Trans. Power Syst. 20, 1690–1699 (2005)

    Article  Google Scholar 

  13. Sinha, N., Chakrabarti, R., Chattopadhyay, P.K.: Evolutionary programming techniques for economic load dispatch. IEEE Trans. Evol. Comput. 7, 83–94 (2003)

    Article  Google Scholar 

  14. Pereira-Neto, A., Unsihuay, C., Saavedra, O.R.: Efficient evolutionary strategy optimization procedure to solve the nonconvex economic dispatch problem with generator constraints. IEE Proc. Gener. Transm. Distrib. 152, 653–660 (2005)

    Article  Google Scholar 

  15. Manoharan, P.S., Kannan, P.S., Baskar, S., Iruthayarajan, M.W.: Penalty parameter-less constraint handling scheme based evolutionary algorithm solutions to economic dispatch. IET Gener. Transm. Distrib. 2, 478–490 (2008)

    Article  Google Scholar 

  16. Noman, N., Iba, H.: Differential evolution for economic load dispatch problems. Elec. Power Syst. Res. 78, 1322–1331 (2008)

    Article  Google Scholar 

  17. Hemamalini, S., Simon, S.P.: Artificial bee colony algorithm for economic load dispatch problem with non-smooth cost functions. Elec. Power Comp. Syst. 38, 786–803 (2010)

    Article  Google Scholar 

  18. Panigrahi, B.K., Yadav, S.R., Agrawal, S., Tiwari, M.K.: A clonal algorithm to solve economic load dispatch. Elec. Power Syst. Res. 77, 1381–1389 (2007)

    Article  Google Scholar 

  19. Bhattacharya, A., Chattopadhyay, P.K.: Biogeography-based optimization for different economic load dispatch problems. IEEE Trans. Power Syst. 25, 1064–1077 (2010)

    Article  Google Scholar 

  20. Gaing, Z.L.: Particle swarm optimization to solving the economic dispatch considering the generator constraints. IEEE Trans. Power Syst. 18, 1187–1195 (2003)

    Article  Google Scholar 

  21. Mahor, A., Prasad, V., Rangnekar, S.: Economic dispatch using particle swarm optimization: a review. Renew. Sustain. Energy Rev. 13, 2134–2141 (2009)

    Article  Google Scholar 

  22. Meng, K., Wang, H.G., Dong, Z.Y., Wong, K.P.: Quantum-inspired particle swarm optimization for valve-point economic load dispatch. IEEE Trans. Power Syst. 25, 215–222 (2010)

    Article  Google Scholar 

  23. Chaturvedi, K.T., Pandit, M., Srivastava, L.: Self-organizing hierarchical particle swarm optimization for nonconvex economic dispatch. IEEE Trans. Power Syst. 23, 1079–1087 (2008)

    Article  Google Scholar 

  24. Park, J.-B., Lee, K.-S., Shin, J.-R., Lee, K.Y.: A particle swarm optimization for economic dispatch with nonsmooth cost functions. IEEE Trans. Power Syst. 20, 34–42 (2005)

    Article  Google Scholar 

  25. Neyestani, M., Farsangi, M.M., Nezamabadi-pour, H.: A modified particle swarm optimization for economic dispatch with non-smooth cost functions. Eng. Apps. AI 23, 1121–1126 (2010)

    Article  Google Scholar 

  26. Subbaraj, P., Rengaraj, R., Salivahanan, S., Senthilkumar, T.R.: Parallel particle swarm optimization with modified stochastic acceleration factors for solving large scale economic dispatch problem. Electr. Power Energy Syst. 32, 1014–1023 (2010)

    Article  Google Scholar 

  27. Selvakumar, A.I., Thanushkodi, K.: A new particle swarm optimization solution to nonconvex economic dispatch problems. IEEE Trans. Power Syst. 22, 42–51 (2007)

    Article  Google Scholar 

  28. Kuo, C.-C.: A novel coding scheme for practical economic dispatch by modified particle swarm approach. IEEE Trans. Power Syst. 23, 1825–1835 (2008)

    Article  Google Scholar 

  29. He, D.-K., Wang, F.-L., Mao, Z.-Z.: Hybrid genetic algorithm for economic dispatch with valve-point effect. Elec. Power Syst. Res. 78, 626–633 (2008)

    Article  Google Scholar 

  30. dos Santos Coelho, L., Mariani, V.C.: Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect. IEEE Trans. Power Syst. 21, 989–996 (2006)

    Article  Google Scholar 

  31. dos Santos Coelho, L., Mariani, V.C.: Correction to Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect. IEEE Trans. Power Syst. 21, 1465 (2006)

    Article  Google Scholar 

  32. Wang, S.-K., Chiou, J.-P., Liu, C.-W.: Non-smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm. IET Gener. Transm. Distrib. 1, 793–803 (2007)

    Article  Google Scholar 

  33. Niknam, T.: A new fuzzy adaptive hybrid particle swarm optimization algorithm for non-linear, non-smooth and non-convex economic dispatch problem. Appl. Energy 87, 327–339 (2010)

    Article  Google Scholar 

  34. Ratnaweera, A., Halgamuge, S.K., Watson, H.C.: Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans. Evol. Comput. 8, 240–255 (2004)

    Article  Google Scholar 

  35. Wen, J.Y., Wu, Q.H., Jiang, L., Cheng, S.J.: Pseudo-gradient based evolutionary programming. Electron. Lett. 39, 631–632 (2003)

    Article  Google Scholar 

  36. Walter, D.C., Sheble, G.B.: Genetic algorithm solution of economic load dispatch with valve point loading. IEEE Trans. Power Syst. 8, 1325–1332 (1993)

    Article  Google Scholar 

  37. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of the IEEE Conference Neural Networks (ICNN’95), vol. 4, pp. 1942–1948 (1995)

    Google Scholar 

  38. Pham, D.T., Jin, G.: Genetic algorithm using gradient-like reproduction operator. Electron. Lett. 31, 1558–1559 (1995)

    Article  Google Scholar 

  39. Vlachogiannis, J.G., Lee, K.Y.: Economic load dispatch: a comparative study on heuristic optimization techniques with an improved coordinated aggregation-based PSO. IEEE Trans. Power Syst. 24, 991–1001 (2009)

    Article  Google Scholar 

  40. Vlachogiannis, J.G., Lee, K.Y.: Closure to discussion on Economic load dispatch: a comparative study on heuristic optimization techniques with an improved coordinated aggregation-based PSO. IEEE Trans. Power Syst. 25, 591–592 (2010)

    Article  Google Scholar 

  41. Amjady, N., Sharifzadeh, H.: Solution of non-convex economic dispatch problem considering valve loading effect by a new modified differential evolution algorithm. Int. J. Electr. Power Energy Syst. 32, 893–903 (2010)

    Article  Google Scholar 

  42. Niknam, T., Mojarrad, H.D., Meymand, H.Z.: A novel hybrid particle swarm optimization for economic dispatch with valve-point loading effects. Energy Convers. Manage. 52, 1800–1809 (2011)

    Article  Google Scholar 

  43. Dieu, V.N., Ongsakul, W., Polprasert, J.: The augmented Lagrange Hopfield network for economic dispatch with multiple fuel options. Math. Comp. Model. 57, 30–39 (2013)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Power Systems, Ho Chi Minh City University of Technology, Ho Chi Minh, Vietnam

    Vo Ngoc Dieu

  2. Institute of Electrical Power Systems and High Voltage Engineering, Technische Universität Dresden, 01069, Dresden, Germany

    Peter Schegner

  3. Energy Field of Study, Asian Institute of Technology, Pathumthani, 12120, Thailand

    Weerakorn Ongsakul

Authors
  1. Vo Ngoc Dieu
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  2. Peter Schegner
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  3. Weerakorn Ongsakul
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Corresponding author

Correspondence to Vo Ngoc Dieu .

Editor information

Editors and Affiliations

  1. Computer Science VŠB-TUO, Department of Computer Science, Faculty of Electrical Engineering and, 17. listopadu 15, Ostrava-Poruba, 708 33, Czech Republic

    Ivan Zelinka

  2. , Department of Fundamental and, University Technology Petronas, Tronoh, 31750, Malaysia

    Pandian Vasant

  3. , Engineering and Information Technology, University Malaysia Sabah, Jalan UMS, Kota Kinabalu, 88400, Malaysia

    Nader Barsoum

Appendix

Appendix

The unit data for 40-unit system with valve point effects are given in Table A1.

Table A1 Unit data for 40-unit system with valve point effects
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The unit data for 10-unit system with multiple fuels is given in Table A2.

Table A2 Unit data for 10-unit system with multiple fuels
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The unit data for 15-unit system with prohibited zones is given in Table A3 and prohibited zones are given in Table A4.

Table A3 Unit data for 15-unit system with prohibited zones
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Table A4 Prohibited zones for 15-unit system
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The unit data for 10-unit system with valve pint effects and multiple fuels is given in Table A5.

Table A5 Unit data for 10-unit system with valve point effects and multiple fuels
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Table 1 Additional parameters of PGPSO
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Table 2 Solution for 40-unit system with VPE
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Table 3 Comparison of best total cost and CPU time for 40-unit system with VPE
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Table 4 Results for 10-unit system with MF
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Table 5 Comparison of best total costs and average CPU times for 10-unit system with MF
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Table 6 Results for 15-unit system with POZ
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Table 7 Comparison of best total cost and average CPU time for 15-unit system with POZ
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Table 8 Results for 10-unit system with VPE and MF
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Table 9 Comparison of best total cost and average CPU time for 10-unit system with VPE and MF
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Table 10 Results for large-scale systems with VPE and MF
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Table 11 Comparison of average total cost and average CPU time for large-scale systems with VPE and MF
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Dieu, V.N., Schegner, P., Ongsakul, W. (2013). Pseudo-Gradient Based Particle Swarm Optimization Method for Nonconvex Economic Dispatch. In: Zelinka, I., Vasant, P., Barsoum, N. (eds) Power, Control and Optimization. Lecture Notes in Electrical Engineering, vol 239. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00206-4_1

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  • DOI: https://doi.org/10.1007/978-3-319-00206-4_1

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