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A non-autonomous optimal control model of renewable energy production under the aspect of fluctuating supply and learning by doing

Author

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  • Elke Moser

    (Vienna University of Technology (TU Wien) Institute of Statistics and Mathematical Methods in Economics (SWM))

  • Dieter Grass

    (Vienna University of Technology (TU Wien) Institute of Statistics and Mathematical Methods in Economics (SWM))

  • Gernot Tragler

    (Vienna University of Technology (TU Wien) Institute of Statistics and Mathematical Methods in Economics (SWM))

Abstract

Given the constantly raising world-wide energy demand and the accompanying increase in greenhouse gas emissions that pushes the progression of climate change, the possibly most important task in future is to find a carbon-low energy supply that finds the right balance between sustainability and energy security. For renewable energy generation, however, especially the second aspect turns out to be difficult as the supply of renewable sources underlies strong volatility. Further on, investment costs for new technologies are so high that competitiveness with conventional energy forms is hard to achieve. To address this issue, we analyze in this paper a non-autonomous optimal control model considering the optimal composition of a portfolio that consists of fossil and renewable energy and which is used to cover the energy demand of a small country. While fossil energy is assumed to be constantly available, the supply of the renewable resource fluctuates seasonally. We further on include learning effects for the renewable energy technology, which will underline the importance of considering the whole life span of such a technology for long-term energy planning decisions.

Suggested Citation

  • Elke Moser & Dieter Grass & Gernot Tragler, 2016. "A non-autonomous optimal control model of renewable energy production under the aspect of fluctuating supply and learning by doing," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(3), pages 545-575, July.
    • Handle: RePEc:spr:orspec:v:38:y:2016:i:3:d:10.1007_s00291-016-0444-0
    DOI: 10.1007/s00291-016-0444-0
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    as
    1. Daron Acemoglu & Philippe Aghion & Leonardo Bursztyn & David Hemous, 2012. "The Environment and Directed Technical Change," American Economic Review, American Economic Association, vol. 102(1), pages 131-166, February.
    2. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Capital accumulation under technological progress and learning: A vintage capital approach," European Journal of Operational Research, Elsevier, vol. 172(1), pages 293-310, July.
    3. Renaud Coulomb & Fanny Henriet, 2010. "Carbon price and optimal extraction of a polluting fossil fuel with restricted carbon capture," PSE Working Papers halshs-00564852, HAL.
    4. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, June.
    5. McDonald, Alan & Schrattenholzer, Leo, 2001. "Learning rates for energy technologies," Energy Policy, Elsevier, vol. 29(4), pages 255-261, March.
    6. Rasmussen, Tobias N., 2001. "CO2 abatement policy with learning-by-doing in renewable energy," Resource and Energy Economics, Elsevier, vol. 23(4), pages 297-325, October.
    7. Chakravorty, Ujjayant & Leach, Andrew & Moreaux, Michel, 2011. "Would hotelling kill the electric car?," Journal of Environmental Economics and Management, Elsevier, vol. 61(3), pages 281-296, May.
    8. Jonathan Kohler, Michael Grubb, David Popp and Ottmar Edenhofer, 2006. "The Transition to Endogenous Technical Change in Climate-Economy Models: A Technical Overview to the Innovation Modeling Comparison Project," The Energy Journal, International Association for Energy Economics, vol. 0(Special I), pages 17-56.
    9. Chakravorty, Ujjayant & Leach, Andrew & Moreaux, Michel, 2008. ""Twin Peaks" in Energy Prices: A Hotelling Model with Pollution and Learning," IDEI Working Papers 52, Institut d'Économie Industrielle (IDEI), Toulouse.
    10. Argote, L. & Epple, D., 1990. "Learning Curves In Manufacturing," GSIA Working Papers 89-90-02, Carnegie Mellon University, Tepper School of Business.
    11. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Anticipation effects of technological progress on capital accumulation: a vintage capital approach," Journal of Economic Theory, Elsevier, vol. 126(1), pages 143-164, January.
    12. Grubler, Arnulf & Messner, Sabine, 1998. "Technological change and the timing of mitigation measures," Energy Economics, Elsevier, vol. 20(5-6), pages 495-512, December.
    13. Dennis Epple & Linda Argote & Rukmini Devadas, 1991. "Organizational Learning Curves: A Method for Investigating Intra-Plant Transfer of Knowledge Acquired Through Learning by Doing," Organization Science, INFORMS, vol. 2(1), pages 58-70, February.
    14. Sabine Messner, 1997. "Endogenized technological learning in an energy systems model," Journal of Evolutionary Economics, Springer, vol. 7(3), pages 291-313.
    15. K. J. Arrow, 1971. "The Economic Implications of Learning by Doing," Palgrave Macmillan Books, in: F. H. Hahn (ed.), Readings in the Theory of Growth, chapter 11, pages 131-149, Palgrave Macmillan.
    16. Chakravorty, Ujjayant & Magne, Bertrand & Moreaux, Michel, 2006. "A Hotelling model with a ceiling on the stock of pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2875-2904, December.
    17. Ujjayant Chakravorty & Bertrand Magne & Michel Moreaux, 2012. "Resource Use under Climate Stabilization: Can Nuclear Power Provide Clean Energy?," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 14(2), pages 349-389, March.
    18. van der Zwaan, B. C. C. & Gerlagh, R. & G. & Klaassen & Schrattenholzer, L., 2002. "Endogenous technological change in climate change modelling," Energy Economics, Elsevier, vol. 24(1), pages 1-19, January.
    19. Kiseleva, Tatiana & Wagener, F.O.O., 2010. "Bifurcations of optimal vector fields in the shallow lake model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 825-843, May.
    20. Berglund, Christer & Soderholm, Patrik, 2006. "Modeling technical change in energy system analysis: analyzing the introduction of learning-by-doing in bottom-up energy models," Energy Policy, Elsevier, vol. 34(12), pages 1344-1356, August.
    21. Grass, D., 2012. "Numerical computation of the optimal vector field: Exemplified by a fishery model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1626-1658.
    22. Deshmukh, M.K. & Deshmukh, S.S., 2008. "Modeling of hybrid renewable energy systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 12(1), pages 235-249, January.
    23. Gerlagh, Reyer & van der Zwaan, Bob, 2003. "Gross world product and consumption in a global warming model with endogenous technological change," Resource and Energy Economics, Elsevier, vol. 25(1), pages 35-57, February.
    24. Reichenbach, Johanna & Requate, Till, 2012. "Subsidies for renewable energies in the presence of learning effects and market power," Resource and Energy Economics, Elsevier, vol. 34(2), pages 236-254.
    25. C. Harmon, 2000. "Experience Curves of Photovoltaic Technology," Working Papers ir00014, International Institute for Applied Systems Analysis.
    26. C. Lanier Benkard, 2000. "Learning and Forgetting: The Dynamics of Aircraft Production," American Economic Review, American Economic Association, vol. 90(4), pages 1034-1054, September.
    27. Nema, Pragya & Nema, R.K. & Rangnekar, Saroj, 2009. "A current and future state of art development of hybrid energy system using wind and PV-solar: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 13(8), pages 2096-2103, October.
    28. Linda Argote & Sara L. Beckman & Dennis Epple, 1990. "The Persistence and Transfer of Learning in Industrial Settings," Management Science, INFORMS, vol. 36(2), pages 140-154, February.
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