A Piecewise Linearization Approach to Non-Convex and Non-Smooth ‎Combined Heat and Power Economic Dispatch

Document Type : Research paper

Authors

1 Department of Electrical Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran

2 Electical Engineering Department , Engineering Faculty, Razi University, Kermanshah, Iran

3 Department of Electrical Engineering, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran

Abstract

The important role of electricity generation in the power system is evident and is growing more and more with innovative technologies and requirements. Hence, addressing the combined heat and power economic dispatch (CHPED) as one of the relatively new issues in the power system operation and control is more importance. Since the CHPED problem is a non-smooth, highly non-linear, and non-convex one, it is required to solve it so that an optimal global solution can be achieved. In this paper, by applying the piece-wise linearization approach the CHPED problem is solved so that the problem reformulated to a quadratic optimization problem with linear and quadratic constraints. To demonstrate the applicability of the proposed model, four case studies are implemented in the GAMS software environment and the results compared to the literature.

Keywords

References

[1]  A. Ghaedi, H. Gorginpour, and E. Noroozi, “Operation studies of the power systems containing combined heat and power‎ plants”‎, J. Oper. Autom. Power Eng., vol. 9, pp. 160-171, 2020.
[2]  S. D. Beigvand, H. Abdi, and M. La Scala, “Combined heat and power economic dispatch problem using gravitational search algorithm”, Electr. Power Syst. Res., vol. 133, pp. 160-172, 2016.
[3]  P. Hajiamoosha et al., “Stochastic energy management in a renewable energy-based microgrid considering demand response program”, Int. J. Electr. Power Energy Syst., vol. 129, p. 106791, 2021.
[4]  T. Niknam, A. Fard, and A. Baziar, “Multi-objective stochastic distribution feeder reconfiguration problem considering hydrogen and thermal energy production by fuel cell power plants”, Energy, vol. 42, pp. 563-73, 2012.
[5]  A. Elaiw, A. Shehata, and M. Alghamdi, “A model predictive control approach to combined heat and power dynamic economic dispatch problem”, Arabian J. Sci. Eng., vol. 39, pp. 7117-25, 2014.
[6]  T. Niknam et al., “A new multi-objective reserve constrained combined heat and power dynamic economic emission dispatch”, Energy, vol. 42, pp. 530-45, 2012.
[7]  F. Rooijers and R. Amerongen, “Static economic dispatch for co-generation systems”, IEEE Trans. Power Syst., vol. 9, pp. 1392-98, 1994.
[8]  T. Guo, M. Henwood, and M. Ooijen, “An algorithm for combined heat and power economic dispatch”, IEEE Trans. Power Syst., vol. 11, pp. 1778-84, 1996.
[9]  A. Sashirekha et al., “Combined heat and power (CHP) economic dispatch solved using Lagrangian relaxation with surrogate subgradient multiplier updates”, Int. J. Electr. Power Energy Syst., vol. 44, pp. 421-30, 2013.
[10]  P. Havel and T. Šimovič, “Optimal planning of cogeneration production with provision of ancillary services”, Electr. Power Syst. Res., vol. 95, pp. 47-55, 2013.
[11]  S. Makkonen and R. Lahdelma, “Non-convex power plant modelling in energy optimisation”, Europ. J. Oper. Res., vol. 171, pp. 1113-26, 2006.
[12]  H. Abdolmohammadi and A. Kazemi, “A benders decomposition approach for a combined heat and power economic dispatch”, Energy Convers. Manage., vol. 71, pp. 21-31, 2013.
[13]  A. Jubril, A. Adediji, and O. Olaniyan, “Solving the combined heat and power dispatch problem: A semi-definite programming approach”, Electr. Power Compon. Syst., vol. 40, pp. 1362-76, 2012.
[14]  P. Rao, “Combined heat and power economic dispatch: a direct solution”, Electr. Power Compon. Syst., vol. 34, pp. 1043-56, 2006.
[15]  Z. Geem and Y. Cho, “Handling non-convex heat-power feasible region in combined heat and power economic dispatch”, Int. J. Electr. Power Energy Syst., vol. 34, pp. 171-73, 2012.
[16]  G. Piperagkas, A. Anastasiadis, and N. Hatziargyriou, “Stochastic PSO-based heat and power dispatch under environmental constraints incorporating CHP and wind power units”, Electr. Power Syst. Res., vol. 81, pp. 209-18, 2011.
[17]  P. Ahmadi and I. Dincer, “Exergoenvironmental analysis and optimization of a cogeneration plant system using Multimodal Genetic Algorithm (MGA)”, Energy, vol. 35, pp. 5161-72, 2010.
[18]  J. Wang, Y. Jing, and C. Zhang, “Optimization of capacity and operation for CCHP system by genetic algorithm”, Appl. Energy, vol. 87, pp. 1325-35, 2010.
[19]  Y. Song and Q. Xuan, “Combined heat and power economic dispatch using genetic algorithm based penalty function method”, Electr. Machines Power Syst., vol. 26, pp. 363-72, 1998.
[20]  M. Basu, “Bee colony optimization for combined heat and power economic dispatch”, Expert Syst. Appl., vol. 38, pp. 13527-31, 2011.
[21]  B. Ivatloo, M. Dalvand, and A. Rabiee, “Combined heat and power economic dispatch problem solution using particle swarm optimization with time varying acceleration coefficients”, Electr. Power Syst. Res., vol. 95, pp. 9-18, 2013.
[22]  E. Khorram and M. Jaberipour, “Harmony search algorithm for solving combined heat and power economic dispatch problems”, Energy Convers. Manage., vol. 52, pp. 1550-4, 2011.
[23]  A. Vasebi, M. Fesanghary, and S. Bathaee, “Combined heat and power economic dispatch by harmony search algorithm”, Int. J. Electr. Power Energy Syst., vol. 29, pp. 713-19, 2007.
[24]  [24]   T. Jayabarathi et al., “Combined heat and power economic dispatch problem using the invasive weed optimization algorithm”, Frontiers Energy, vol. 8, pp. 25-30, 2014.
[25]  M. Basu, “Artificial immune system for combined heat and power economic dispatch”, Int. J. Electr. Power Energy Syst., vol. 43, pp. 1-5, 2012.
[26]  M. Hagh, S. Teimourzadeh, and M. Alipour, “Combined heat and power dispatch using modified group search optimization method”, Int. Power Syst. Conf., 2013.
[27]  P. K. Roy, C. Paul, and S. Sultana, "Oppositional teaching learning based optimization approach for combined heat and power dispatch”, Int. J. Electr. Power Energy Syst., vol. 57, pp. 392-403, 2014.
[28]  A. Yazdani et al., “Combined heat and power economic dispatch problem using firefly algorithm”, Frontiers  Energy, vol. 7, pp. 133-9, 2013.
[29]  Y. Song, C. Chou, and T. Stonham, “Combined heat and power economic dispatch by improved ant colony search algorithm”, Electr. Power Syst. Res., vol. 52, pp. 115-21, 1999.
[30]  N. Ghorbani, “Combined heat and power economic dispatch using exchange market algorithm”, Int. J. Electr. Power Energy Syst., vol. 82, pp. 58-66, 2016.
[31]  M. Basu, “Combined heat and power economic dispatch by using differential evolution”, Electr. Power Compon. Syst., vol. 38, pp. 996-1004, 2010.
[32]  M. Sudhakaran and S. Slochanal, “Integrating genetic algorithms and tabu search for combined heat and power economic dispatch”, Conf. Convergent Technol. Asia-Pacific Reg., 2003.
[33]  Y. Ouyang, Q. Niu, and Y. Zhang, “Combined heat and power economic dispatch using differential evolution”, Proc. Int. Conf. Network, Communication Comput., 2017.
[34]  H. Shayanfar et al., “Combined heat and power economic dispatch solution using iterative cultural algorithm”, Proc. Int. Conf. Artificial Intell., 2017.
[35]  A. Rastgou and S. Bahramara, “An adaptive modified firefly algorithm to unit commitment problem for large-scale power systems”, J. Oper. Autom. Power Eng., vol. 9, pp. 68-79, 2021.
[36]  A. Rastgou, J. Moshtagh, and S. Bahramara, “Probabilistic power distribution planning using multi-objective harmony search algorithm”, J. Oper. Autom. Power Eng., vol. 6, pp. 111-125, 2018.
[37]  L. Papageorgiou and E. Fraga, “A mixed integer quadratic programming formulation for the economic dispatch of generators with prohibited operating zones”, Electr. Power Syst. Res., vol. 77, pp. 1292-96, 2007.
[38]  M. Dalvand et al., “A two-stage mathematical programming approach for the solution of combined heat and power economic dispatch”, IEEE Syst. J., vol. 14, pp. 2873-81, 2019.
[39]  T. Victoire and A. Jeyakumar, “Reserve constrained dynamic dispatch of units with valve-point effects”, IEEE Trans. Power Syst., vol. 20, pp. 1273-82, 2005.
[40]  M. Alipour, B. Ivatloo, and K. Zare, “Stochastic scheduling of renewable and CHP-based microgrids”, IEEE Trans. Ind. Inform., vol. 11, pp. 1049-58, 2015.
[41]  R. Rosenthal, GAMS: A User’s Guide, GAMS Development Corporation, Washington, 2011.
[42]  L. Cooper and D. Steinberg, Methods and Applications of Linear Programming, firsted., Saunders, United States of America, 1974.
[43]  M. Hagh et al., “Improved group search optimization method for solving CHPED in large scale power systems”, Energy Convers. Manage., vol. 80, pp. 446-56, 2014.
[44]  N. Jayakumar et al., “Grey wolf optimization for combined heat and power dispatch with cogeneration systems”, Int. J. Electr. Power Energy Syst., vol. 74, pp. 252-64, 2016.
Journal of Operation and Automation in Power Engineering
Volume 10, Issue 1
April 2022
Pages 40-53

Files

History

  • Receive Date: 26 November 2020
  • Revise Date: 25 February 2021
  • Accept Date: 12 May 2021

Share

How to cite

Statistics