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Thermoeconomic optimization of vertical ground-source heat pump systems through nonlinear integer programming

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  • Retkowski, Waldemar
  • Thöming, Jorg

Abstract

Vertical ground-source heat pump systems (GSHPSs) use the ground’s undisturbed relative constant temperature as a source for space heating of residential and commercial buildings. The design of GSHPSs is focused in finding the optimal depth and amount of boreholes and also the connected power requirement like the amount and size of heat pumps. In this paper a mixed-integer nonlinear programming (MINLP) approach to solve the design problem of a vertical GSHPS is presented. The resulting mathematical model includes the calculation of the total annual costs (TAC) and the coefficient of performance to obtain estimates of both economic and ecological relevance to design an optimal equipment set-up. For desired constraints the numerically optimal values of the design parameters (borehole depth, mass flow rate, number of boreholes, type and number of the heat pumps) were calculated. Two numerical solution alternatives are investigated, namely Generalized Reduced Gradient (GRG2) and evolutionary algorithm. The GRG2 approach provides a more stable and faster optimal solution. Calculated results are presented through a validation example. The evaluation of the proposed objectives and studied sensitivity effects present the applicability of the model. This method was able to improve the TAC about more than 10%.

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  • Retkowski, Waldemar & Thöming, Jorg, 2014. "Thermoeconomic optimization of vertical ground-source heat pump systems through nonlinear integer programming," Applied Energy, Elsevier, vol. 114(C), pages 492-503.
    • Handle: RePEc:eee:appene:v:114:y:2014:i:c:p:492-503
    DOI: 10.1016/j.apenergy.2013.09.012
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    3. Carotenuto, Alberto & Ciccolella, Michela & Massarotti, Nicola & Mauro, Alessandro, 2016. "Models for thermo-fluid dynamic phenomena in low enthalpy geothermal energy systems: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 60(C), pages 330-355.
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    6. Ioan Sarbu & Calin Sebarchievici, 2016. "Performance Evaluation of Radiator and Radiant Floor Heating Systems for an Office Room Connected to a Ground-Coupled Heat Pump," Energies, MDPI, vol. 9(4), pages 1-19, March.
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    13. Zhou, Zhihua & Wu, Shengwei & Du, Tao & Chen, Guanyi & Zhang, Zhiming & Zuo, Jian & He, Qing, 2016. "The energy-saving effects of ground-coupled heat pump system integrated with borehole free cooling: A study in China," Applied Energy, Elsevier, vol. 182(C), pages 9-19.
    14. Dusseault, Bernard & Pasquier, Philippe & Marcotte, Denis, 2018. "A block matrix formulation for efficient g-function construction," Renewable Energy, Elsevier, vol. 121(C), pages 249-260.
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    17. Miglani, Somil & Orehounig, Kristina & Carmeliet, Jan, 2018. "Integrating a thermal model of ground source heat pumps and solar regeneration within building energy system optimization," Applied Energy, Elsevier, vol. 218(C), pages 78-94.
    18. Kuzmic, Nikola & Law, Ying Lam E. & Dworkin, Seth B., 2016. "Numerical heat transfer comparison study of hybrid and non-hybrid ground source heat pump systems," Applied Energy, Elsevier, vol. 165(C), pages 919-929.
    19. Aira, Roberto & Fernández-Seara, José & Diz, Rubén & Pardiñas, Ángel Á., 2017. "Experimental analysis of a ground source heat pump in a residential installation after two years in operation," Renewable Energy, Elsevier, vol. 114(PB), pages 1214-1223.
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    22. Pandey, Navdeep & Murugesan, K. & Thomas, H.R., 2017. "Optimization of ground heat exchangers for space heating and cooling applications using Taguchi method and utility concept," Applied Energy, Elsevier, vol. 190(C), pages 421-438.

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