IDEAS home Printed from https://ideas.repec.org/a/eee/energy/v330y2025ics0360544225022765.html

Valuation and optimal operation of power investment projects with and without volume constraints under one-factor model

Author

Listed:
  • Shao, Lingjie
  • Wu, Junle
  • Ma, Jinghan
  • Yu, Shengjie
  • Li, Mengsi

Abstract

In the context of economic liberalization, privatization of energy production projects is increasingly commonplace. Nevertheless, this paper advances the research on optimal valuation and sales strategies for these projects during the operational phase by proposing a more comprehensive framework. This study employs a well-accepted one-factor model to formulate power spot prices and utilizes the dynamic programming principle to deduce the Hamilton–Jacobi–Bellman (HJB) equation that satisfies the valuation function, proving the existence and uniqueness of classical solutions to this equation. Subsequently, we verify through the verification theorem that the value function is the unique solution to the HJB equation and outline the expression that satisfies the optimal power sales strategy. Finally, the finite difference method is adopted to solve the HJB equation, considering both scenarios with and without volume constraints, and a sensitivity analysis is conducted by varying the marginal costs.

Suggested Citation

  • Shao, Lingjie & Wu, Junle & Ma, Jinghan & Yu, Shengjie & Li, Mengsi, 2025. "Valuation and optimal operation of power investment projects with and without volume constraints under one-factor model," Energy, Elsevier, vol. 330(C).
    • Handle: RePEc:eee:energy:v:330:y:2025:i:c:s0360544225022765
    DOI: 10.1016/j.energy.2025.136634
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0360544225022765
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.energy.2025.136634?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Dangl, Thomas, 1999. "Investment and capacity choice under uncertain demand," European Journal of Operational Research, Elsevier, vol. 117(3), pages 415-428, September.
    2. Ioannou, Anastasia & Angus, Andrew & Brennan, Feargal, 2017. "Risk-based methods for sustainable energy system planning: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 74(C), pages 602-615.
    3. Markus Burger & Bernhard Klar & Alfred Muller & Gero Schindlmayr, 2004. "A spot market model for pricing derivatives in electricity markets," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 109-122.
    4. Benth, Fred Espen & Kiesel, Rüdiger & Nazarova, Anna, 2012. "A critical empirical study of three electricity spot price models," Energy Economics, Elsevier, vol. 34(5), pages 1589-1616.
    5. Bøckman, Thor & Fleten, Stein-Erik & Juliussen, Erik & Langhammer, Håvard J. & Revdal, Ingemar, 2008. "Investment timing and optimal capacity choice for small hydropower projects," European Journal of Operational Research, Elsevier, vol. 190(1), pages 255-267, October.
    6. Yang, Ming & Blyth, William & Bradley, Richard & Bunn, Derek & Clarke, Charlie & Wilson, Tom, 2008. "Evaluating the power investment options with uncertainty in climate policy," Energy Economics, Elsevier, vol. 30(4), pages 1933-1950, July.
    7. Chevalier-Roignant, Benoît & Flath, Christoph M. & Kort, Peter M. & Trigeorgis, Lenos, 2021. "Capacity investment choices under cost heterogeneity and output flexibility in oligopoly," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1154-1173.
    8. Kanamura, Takashi & Ohashi, Kazuhiko, 2007. "A structural model for electricity prices with spikes: Measurement of spike risk and optimal policies for hydropower plant operation," Energy Economics, Elsevier, vol. 29(5), pages 1010-1032, September.
    9. Fleten, Stein-Erik & Kristoffersen, Trine Krogh, 2007. "Stochastic programming for optimizing bidding strategies of a Nordic hydropower producer," European Journal of Operational Research, Elsevier, vol. 181(2), pages 916-928, September.
    10. Sonja Salo & Aira Hast & Juha Jokisalo & Risto Kosonen & Sanna Syri & Janne Hirvonen & Kristian Martin, 2019. "The Impact of Optimal Demand Response Control and Thermal Energy Storage on a District Heating System," Energies, MDPI, vol. 12(9), pages 1-19, May.
    11. Khamlich, Imane & Zeng, Kuo & Flamant, Gilles & Baeyens, Jan & Zou, Chongzhe & Li, Jun & Yang, Xinyi & He, Xiao & Liu, Qingchuan & Yang, Haiping & Yang, Qing & Chen, Hanping, 2021. "Technical and economic assessment of thermal energy storage in concentrated solar power plants within a spot electricity market," Renewable and Sustainable Energy Reviews, Elsevier, vol. 139(C).
    12. Niu, Shilei & Insley, Margaret, 2016. "An options pricing approach to ramping rate restrictions at hydro power plants," Journal of Economic Dynamics and Control, Elsevier, vol. 63(C), pages 25-52.
    13. Matt Thompson, 2013. "Optimal Economic Dispatch and Risk Management of Thermal Power Plants in Deregulated Markets," Operations Research, INFORMS, vol. 61(4), pages 791-809, August.
    14. Unger, Elizabeth A. & Ulfarsson, Gudmundur F. & Gardarsson, Sigurdur M. & Matthiasson, Thorolfur, 2018. "The effect of wind energy production on cross-border electricity pricing: The case of western Denmark in the Nord Pool market," Economic Analysis and Policy, Elsevier, vol. 58(C), pages 121-130.
    15. Loukatou, Angeliki & Johnson, Paul & Howell, Sydney & Duck, Peter, 2021. "Optimal valuation of wind energy projects co-located with battery storage," Applied Energy, Elsevier, vol. 283(C).
    16. Muche, Thomas, 2009. "A real option-based simulation model to evaluate investments in pump storage plants," Energy Policy, Elsevier, vol. 37(11), pages 4851-4862, November.
    17. Kitzing, Lena & Juul, Nina & Drud, Michael & Boomsma, Trine Krogh, 2017. "A real options approach to analyse wind energy investments under different support schemes," Applied Energy, Elsevier, vol. 188(C), pages 83-96.
    18. Ma, Yiju & Swandi, Kevin & Chapman, Archie C. & Verbič, Gregor, 2020. "Multi-stage compound real options valuation in residential PV-Battery investment," Energy, Elsevier, vol. 191(C).
    19. Matt Thompson & Matt Davison & Henning Rasmussen, 2004. "Valuation and Optimal Operation of Electric Power Plants in Competitive Markets," Operations Research, INFORMS, vol. 52(4), pages 546-562, August.
    20. Erlwein, Christina & Benth, Fred Espen & Mamon, Rogemar, 2010. "HMM filtering and parameter estimation of an electricity spot price model," Energy Economics, Elsevier, vol. 32(5), pages 1034-1043, September.
    21. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook0601.
    22. Boomsma, Trine Krogh & Meade, Nigel & Fleten, Stein-Erik, 2012. "Renewable energy investments under different support schemes: A real options approach," European Journal of Operational Research, Elsevier, vol. 220(1), pages 225-237.
    23. Arenas-López, J. Pablo & Badaoui, Mohamed, 2020. "The Ornstein-Uhlenbeck process for estimating wind power under a memoryless transformation," Energy, Elsevier, vol. 213(C).
    24. M. T. Barlow, 2002. "A Diffusion Model For Electricity Prices," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 287-298, October.
    25. Hagspiel, Verena & Huisman, Kuno J.M. & Kort, Peter M., 2016. "Volume flexibility and capacity investment under demand uncertainty," International Journal of Production Economics, Elsevier, vol. 178(C), pages 95-108.
    26. Zhang, Mingming & Liu, Liyun & Wang, Qunwei & Zhou, Dequn, 2020. "Valuing investment decisions of renewable energy projects considering changing volatility," Energy Economics, Elsevier, vol. 92(C).
    27. Fred Espen Benth & Jan Kallsen & Thilo Meyer-Brandis, 2007. "A Non-Gaussian Ornstein-Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 153-169.
    28. Chen, Qi & Kuang, Zhonghong & Liu, Xiaohua & Zhang, Tao, 2022. "Energy storage to solve the diurnal, weekly, and seasonal mismatch and achieve zero-carbon electricity consumption in buildings," Applied Energy, Elsevier, vol. 312(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Weron, Rafał, 2014. "Electricity price forecasting: A review of the state-of-the-art with a look into the future," International Journal of Forecasting, Elsevier, vol. 30(4), pages 1030-1081.
    2. Kazuya Ito & Makoto Tanaka & Ryuta Takashima, 2024. "Strategic investment in power generation and transmission under a feed-in premium scheme: a game theoretic real options analysis," Annals of Operations Research, Springer, vol. 343(1), pages 349-372, December.
    3. Godin, Frédéric & Ibrahim, Zinatu, 2021. "An analysis of electricity congestion price patterns in North America," Energy Economics, Elsevier, vol. 102(C).
    4. Deschatre, Thomas & Féron, Olivier & Gruet, Pierre, 2021. "A survey of electricity spot and futures price models for risk management applications," Energy Economics, Elsevier, vol. 102(C).
    5. Michail Chronopoulos & Verena Hagspiel & Stein-Erik Fleten, 2017. "Stepwise investment and capacity sizing under uncertainty," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 447-472, March.
    6. Nadarajah, Selvaprabu & Secomandi, Nicola, 2023. "A review of the operations literature on real options in energy," European Journal of Operational Research, Elsevier, vol. 309(2), pages 469-487.
    7. Truong, Chi & Trueck, Stefan & Pitt, David & Best, Rohan, 2025. "Seasonality and valuation of renewable energy projects in a two factor model," Applied Energy, Elsevier, vol. 389(C).
    8. Hain, Martin & Schermeyer, Hans & Uhrig-Homburg, Marliese & Fichtner, Wolf, 2017. "An Electricity Price Modeling Framework for Renewable-Dominant Markets," Working Paper Series in Production and Energy 23, Karlsruhe Institute of Technology (KIT), Institute for Industrial Production (IIP).
    9. Ernstsen, Rune Ramsdal & Boomsma, Trine Krogh, 2018. "Valuation of power plants," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1153-1174.
    10. Fanone, Enzo & Gamba, Andrea & Prokopczuk, Marcel, 2013. "The case of negative day-ahead electricity prices," Energy Economics, Elsevier, vol. 35(C), pages 22-34.
    11. Nagy, Roel L.G. & Hagspiel, Verena & Kort, Peter M., 2021. "Green capacity investment under subsidy withdrawal risk," Energy Economics, Elsevier, vol. 98(C).
    12. Fred Espen Benth & Jūratė Šaltytė Benth & Steen Koekebakker, 2008. "Stochastic Modeling of Electricity and Related Markets," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6811, September.
    13. Niu, Shilei & Insley, Margaret, 2016. "An options pricing approach to ramping rate restrictions at hydro power plants," Journal of Economic Dynamics and Control, Elsevier, vol. 63(C), pages 25-52.
    14. Kupfer, Stefan & Prysyazhna, Vladlena & Lukas, Elmar & Mölls, Sascha, 2025. "Timing corporate social responsibility investments: A dynamic investment model and empirical evidence," Energy Economics, Elsevier, vol. 143(C).
    15. Zhang, Zixuan & Chronopoulos, Michail & Kyriakou, Ioannis & Dimitrova, Dimitrina S., 2024. "Bi-level optimisation of subsidy and capacity investment under competition and uncertainty," European Journal of Operational Research, Elsevier, vol. 318(1), pages 327-340.
    16. Markus Hess, 2026. "Modeling Electricity Prices with Stochastic Langevin Equations," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 33(1), pages 315-346, March.
    17. Nowotarski, Jakub & Tomczyk, Jakub & Weron, Rafał, 2013. "Robust estimation and forecasting of the long-term seasonal component of electricity spot prices," Energy Economics, Elsevier, vol. 39(C), pages 13-27.
    18. Kroniger, Daniel & Madlener, Reinhard, 2014. "Hydrogen storage for wind parks: A real options evaluation for an optimal investment in more flexibility," Applied Energy, Elsevier, vol. 136(C), pages 931-946.
    19. Maciej Kostrzewski & Jadwiga Kostrzewska, 2021. "The Impact of Forecasting Jumps on Forecasting Electricity Prices," Energies, MDPI, vol. 14(2), pages 1-17, January.
    20. Andreas Welling, 2017. "Green Finance: Recent developments, characteristics and important actors," FEMM Working Papers 170002, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:energy:v:330:y:2025:i:c:s0360544225022765. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/energy .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.