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Two-stage stochastic, large-scale optimization of a decentralized energy system: a case study focusing on solar PV, heat pumps and storage in a residential quarter

Author

Listed:
  • Hannes Schwarz

    (Karlsruhe Institute of Technology (KIT), Institute for Industrial Production (IIP), Chair of Energy Economics)

  • Valentin Bertsch

    (Economic and Social Research Institute (ESRI)
    Trinity College Dublin)

  • Wolf Fichtner

    (Karlsruhe Institute of Technology (KIT), Institute for Industrial Production (IIP), Chair of Energy Economics)

Abstract

The expansion of fluctuating renewable energy sources leads to an increasing impact of weather-related uncertainties on future decentralized energy systems. Stochastic modeling techniques enable an adequate consideration of the uncertainties and provide support for both investment and operating decisions in such systems. In this paper, we consider a residential quarter using photovoltaic systems in combination with multistage air-water heat pumps and heat storage units for space heating and domestic hot water. We model the investment and operating problem of the quarter’s energy system as two-stage stochastic mixed-integer linear program and optimize the thermal storage units. In order to keep the resulting stochastic, large-scale program computationally feasible, the problem is decomposed in combination with a derivative-free optimization. The subproblems are solved in parallel on high-performance computing systems. Our approach is integrated in that it comprises three subsystems: generation of consistent ensembles of the required input data by a Markov process, transformation into sets of energy demand and supply profiles and the actual stochastic optimization. An analysis of the scalability and comparison with a state-of-the-art dual-decomposition method using Lagrange relaxation and a conic bundle algorithm shows a good performance of our approach for the considered problem type. A comparison of the effective gain of modeling the quarter as stochastic program with the resulting computational expenses justifies the approach. Moreover, our results show that heat storage units in such systems are generally larger when uncertainties are considered, i.e., stochastic optimization can help to avoid insufficient setup decisions. Furthermore, we find that the storage is more profitable for domestic hot water than for space heating.

Suggested Citation

  • Hannes Schwarz & Valentin Bertsch & Wolf Fichtner, 2018. "Two-stage stochastic, large-scale optimization of a decentralized energy system: a case study focusing on solar PV, heat pumps and storage in a residential quarter," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 265-310, January.
    • Handle: RePEc:spr:orspec:v:40:y:2018:i:1:d:10.1007_s00291-017-0500-4
    DOI: 10.1007/s00291-017-0500-4
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    Cited by:

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    3. Lynch, Muireann Á & Devine, Mel & Bertsch, Valentin, 2018. "The role of power-to-gas in the future energy system: how much is needed and who wants to invest?," Papers WP590, Economic and Social Research Institute (ESRI).
    4. Bertsch, Valentin & Devine, Mel & Sweeney, Conor & Parnell, Andrew C., 2018. "Analysing long-term interactions between demand response and different electricity markets using a stochastic market equilibrium model," Papers WP585, Economic and Social Research Institute (ESRI).
    5. Mel T. Devine & Valentin Bertsch, 2023. "The role of demand response in mitigating market power: a quantitative analysis using a stochastic market equilibrium model," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(2), pages 555-597, June.
    6. Klemm, Christian & Vennemann, Peter, 2021. "Modeling and optimization of multi-energy systems in mixed-use districts: A review of existing methods and approaches," Renewable and Sustainable Energy Reviews, Elsevier, vol. 135(C).
    7. Oliver Gregor Gorbach & Jessica Thomsen, 2022. "Comparing the Energy System of a Facility with Uncertainty about Future Internal Carbon Prices and Energy Carrier Costs Using Deterministic Optimisation and Two-Stage Stochastic Programming," Energies, MDPI, vol. 15(10), pages 1-39, May.
    8. Henrik C. Bylling & Salvador Pineda & Trine K. Boomsma, 2020. "The impact of short-term variability and uncertainty on long-term power planning," Annals of Operations Research, Springer, vol. 284(1), pages 199-223, January.
    9. Iegor Riepin & Thomas Mobius & Felix Musgens, 2020. "Modelling uncertainty in coupled electricity and gas systems -- is it worth the effort?," Papers 2008.07221, arXiv.org, revised Sep 2020.
    10. Olivella, Jordi & Domenech, Bruno & Calleja, Gema, 2021. "Potential of implementation of residential photovoltaics at city level: The case of London," Renewable Energy, Elsevier, vol. 180(C), pages 577-585.
    11. Russo, Marianna & Bertsch, Valentin, 2020. "A looming revolution: Implications of self-generation for the risk exposure of retailers," Energy Economics, Elsevier, vol. 92(C).

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