MILP Approaches to Optimal Design and Operation of Distributed Energy Systems

  • Ryohei YokoyamaEmail author
  • Yuji Shinano
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 13)


Energy field is one of the practical areas to which optimization can contribute significantly. In this chapter, the application of mixed-integer linear programming (MILP) approaches to optimal design and operation of distributed energy systems is described. First, the optimal design and operation problems are defined, and relevant previous work is reviewed. Then, an MILP method utilizing the hierarchical relationship between design and operation variables is presented. In the optimal design problem, integer variables are used to express the types, capacities, numbers, operation modes, and on/off states of operation of equipment, and the number of these variables increases with those of equipment and periods for variations in energy demands, and affects the computation efficiency significantly. The presented method can change the enumeration tree for the branching and bounding procedures, and can search the optimal solution very efficiently. Finally, future work in relation to this method is described.


Energy systems Optimal design and operation Mixed-integer linear programming Branch and bound method Hierarchical approach 



A part of this work has been conducted within the Research Campus Modal funded by the German Federal Ministry of Education and Research (fund number 05M14ZAM) and been supported by the EU COST Action TD 1207. In addition, a part of this work has been supported by the IBM Academic Initiative. The authors would like to thank the anonymous reviewer for his/her valuable comments and suggestions to improve the quality of the paper.


  1. 1.
    Balas, E., Jeroslow, R.: Canonical cuts on the unit hypercube. SIAM J. Appl. Math. 23(1), 61–69 (1972)Google Scholar
  2. 2.
    Buoro, D., Casisi, M., De Nardi, A., Pinamonti, P., Reini, M.: Multicriteria optimization of a distributed energy supply system for an industrial area. Energy 58, 128–137 (2013)CrossRefGoogle Scholar
  3. 3.
    Buoro, D., Casisi, M., Pinamonti, P., Reini, M.: Optimal synthesis and operation of advanced energy supply systems for standard and domotic home. Energy Convers. Manag. 60, 96–105 (2012)Google Scholar
  4. 4.
    Carvalho, M., Serra, L.M., Lozano, M.A.: Optimal synthesis of trigeneration systems subject to environmental constraints. Energy 36(6), 3779–3790 (2011)CrossRefGoogle Scholar
  5. 5.
    Dotzauer, E.: Algorithms for short-term production-planning of cogeneration plants. Ph.D. Dissertation, Linköping University (1997)Google Scholar
  6. 6.
    Fazlollahi, S., Mandel, P., Becker, G., Maréchal, F.: Methods for multi-objective investment and operating optimization of complex energy systems. Energy 45(1), 12–22 (2012)CrossRefGoogle Scholar
  7. 7.
    Horii, S., Ito, K., Pak, P.S., Suzuki, Y.: Optimal planning of gas turbine co-generation plants based on mixed-integer linear programming. Int. J. Energy Res. 11(4), 507–518 (1987)Google Scholar
  8. 8.
    IBM ILOG CPLEX Optimization Studio V12.5.1:
  9. 9.
    Ito, K., Yokoyama, R., Akagi, S., Matsumoto, Y.: Influence of fuel cost on the operation of a gas turbine-waste heat boiler cogeneration plant. Trans. ASME. J. Eng. Gas Turbines Power 112(1), 122–128 (1990)Google Scholar
  10. 10.
    Iyer, R.R., Grossmann, I.E.: Optimal multiperiod operational planning for utility systems. Comput. Chem. Eng. 21(8), 787–800 (1997)Google Scholar
  11. 11.
    Iyer, R.R., Grossmann, I.E.: Synthesis and operational planning of utility systems for multiperiod operation. Comput. Chem. Eng. 22(7–8), 979–993 (1998)Google Scholar
  12. 12.
    Kuester, J.L., Mize, J.H.: Optimization Techniques with FORTRAN. McGraw-Hill, NewYork (1972)Google Scholar
  13. 13.
    Lozano, M.A., Ramos, J.C., Carvalho, M., Serra, L.M.: Structure optimization of energy supply systems in tertiary sector buildings. Energy Build. 41(10), 1063–1075 (2009)Google Scholar
  14. 14.
    Lozano, M.A., Ramos, J.C., Serra, L.M.: Cost optimization of the design of CHCP (combined heat, cooling and power) systems under legal constraints. Energy 35(2), 794–805 (2010)CrossRefGoogle Scholar
  15. 15.
    Owen, J.H., Mehrotra, S.: On the value of binary expansions for general mixed-integer linear programs. Oper. Res. 50(5), 810–819 (2002)Google Scholar
  16. 16.
    Papoulias, S.A., Grossmann, I.E.: A structural optimization approach in process synthesis–I: utility systems. Comput. Chem. Eng. 7(6), 695–706 (1983)Google Scholar
  17. 17.
    Piacentino, A., Barbaro, C., Cardona, F., Gallea, R., Cardona, E.: A comprehensive tool for efficient design and operation of polygeneration-based energy grids serving a cluster of buildings, part I: description of the method. Appl. Energy 111, 1204–1221 (2013)Google Scholar
  18. 18.
    Sheblé, G.B., Fahd, G.N.: Unit commitment literature synopsis. IEEE Trans. Power Syst. 9(1), 128–135 (1994)Google Scholar
  19. 19.
    Van den Bosch, P.P.J., Honderd, G.: A solution of the unit commitment problem via decomposition and dynamic programming. IEEE Trans. Power Appar. Syst. 104(7), 1684–1690 (1985)Google Scholar
  20. 20.
    Voll, P., Hennen, M., Klaffke, C., Lampe, M., Bardow, A.: Exploring the near-optimal solution space for the synthesis of distributed energy supply systems. Chem. Eng. Trans. 35(1), 277–282 (2013)Google Scholar
  21. 21.
    Voll, P., Klaffke, C., Hennen, M., Bardow, A.: Automated superstructure-based synthesis and optimization of distributed energy supply systems. Energy 50, 374–388 (2013)CrossRefGoogle Scholar
  22. 22.
    Wakui, T., Yokoyama, R.: Optimal structural design of residential cogeneration systems in consideration of their operating restrictions. Energy 64, 719–733 (2014)CrossRefGoogle Scholar
  23. 23.
    Yokoyama, R.: Optimal operation of a gas turbine cogeneration plant in consideration of equipment minimum up and down times. Trans. ASME J. Eng. Gas Turbines Power 135(7): Paper No. 071801, 1–8 (2013)Google Scholar
  24. 24.
    Yokoyama, R., Fujiwara, K., Ohkura, M., Wakui, T.: A revised method for robust optimal design of energy supply systems based on minimax regret criterion. Energy Convers. Manag. 84, 196–208 (2014)Google Scholar
  25. 25.
    Yokoyama, R., Hasegawa, Y., Ito, K.: A MILP decomposition approach to large scale optimization in structural design of energy supply systems. Energy Convers. Manag. 43(6), 771–790 (2002)Google Scholar
  26. 26.
    Yokoyama, R., Ito, K.: Optimal operation of a cogeneration plant in consideration of equipment startup/shutdown cost. Trans. ASME J. Energy Res. Technol. 121(4), 254–261 (1999)Google Scholar
  27. 27.
    Yokoyama, R., Ito, K.: Optimal design of gas turbine cogeneration plants in consideration of discreteness of equipment capacities. Trans. ASME J. Eng. Gas Turbines Power 128(2), 336–343 (2006)Google Scholar
  28. 28.
    Yokoyama, R., Ito, K.: Performance evaluation of gas turbine cogeneration plants using a design optimization tool: OPS-design. Proc. ASME Turbo Expo 2006: Paper No. GT2006-90611, 1–10 (2006)Google Scholar
  29. 29.
    Yokoyama, R., Ohkura, M., Wakui, T.: Robust optimal operation of a gas turbine cogeneration plant under uncertain energy demands. Trans. ASME J. Eng. Gas Turbines Power 137(2): Paper No. 022001, 1–11 (2015)Google Scholar
  30. 30.
    Yokoyama, R., Shinano, Y., Taniguchi, S., Ohkura, M., Wakui, T.: Optimization of energy supply systems by MILP branch and bound method in consideration of hierarchical relationship between design and operation. Energy Convers. Manag. 92, 92–104 (2015)Google Scholar
  31. 31.
    Zhou, Z., Liu, P., Li, Z., Ni, W.: An engineering approach to the optimal design of distributed energy systems in China. Appl. Therm. Eng. 53(2), 387–396 (2013)Google Scholar

Copyright information

© Springer Japan 2016

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringOsaka Prefecture UniversitySakaiJapan
  2. 2.Department OptimizationZuse Institute BerlinBerlinGermany

Personalised recommendations