Energy Systems

, Volume 10, Issue 2, pp 321–353 | Cite as

Power system portfolio selection under uncertainty

  • Carlo MariEmail author
Original Paper


We present a general methodology for power system portfolio selection under uncertainty in which fossil fuels and CO\(_2\) market prices as assumed as the main sources of risk. The planning problem is developed by considering the power system as a whole in its interactions between dispatchable sources and intermittent renewables, under load demand and power capacity constraints. The portfolio selection is performed taking into account costs and benefits of the power system from a societal perspective. Efficient frontiers and optimal generation portfolios are derived and discussed. Based on USA data, an empirical analysis is developed to illustrate the main features of this approach.


Power system Generation portfolio Non-dispatchable source CVaRD Portfolio frontier 

JEL Classification

G31 G32 G33 M21 Q40 


  1. 1.
    Awerbuch, S., Berger, M.: Applying portfolio theory to EU electricity planning and policy-making. IEA/EET Working Paper EET/2003/03Google Scholar
  2. 2.
    Balietti, A.C.: Trader types and volatility of emission allowance prices. Evidence from EU ETS Phase I. Energy Policy 98, 607–620 (2016)CrossRefGoogle Scholar
  3. 3.
    Bhattacharyya, S.C.: Energy Economics. Springer, London (2011)CrossRefGoogle Scholar
  4. 4.
    Bazilian, M., Roques, F.: Analytical Approaches to Quantify and Value Fuel Mix Diversity. Elsevier, Amsterdam (2008)CrossRefGoogle Scholar
  5. 5.
    Delarue, E., Van den Bergh, K.: Carbon mitigation in the electric power sector under cap-and-trade and renewables policies. Energy Policy 92, 34–44 (2016)CrossRefGoogle Scholar
  6. 6.
    Delarue, E., Van den Bergh, K.: Quantifying CO\(_2\) abatement cost in the power sector. Energy Policy 80, 88–97 (2016)Google Scholar
  7. 7.
    Del Granado, P.C., Wallace, S.W., Pang, Z.: The impact of wind uncertainty on the strategic valuation of distributed electricity storage. Comput. Manag. Sci. 13, 5–27 (2016)CrossRefGoogle Scholar
  8. 8.
    DeLlano-Paz, F., Calvo-Silvosa, A., Iglesias, S., Soares, I.: Energy planning and modern portfolio theory: a review. Renew. Sustain. Energy Rev. 77, 636–651 (2017)CrossRefGoogle Scholar
  9. 9.
    Dixit, A.K., Pindyck, R.: Investment Under Uncertainty. Princeton University Press, Princeton (1994)Google Scholar
  10. 10.
    Du Y., Parsons, J.E.: Update on the cost of nuclear power. MIT Working Paper (2009)Google Scholar
  11. 11.
    EC: Guide to Cost-Benefit Analysis of Investment Projects. European Commission, Brussels (2015)Google Scholar
  12. 12.
    EIA: Annual Energy Outlook 2016. US Energy Information Administration, Department of Energy (2016)Google Scholar
  13. 13.
    EIA: Capital Cost Estimates for Utility Scale Electricity Generating Plants. US Energy Information Administration, Department of Energy (2016)Google Scholar
  14. 14.
    EIA: Levelized Cost and Levelized Avoided Cost of New Generation Resources in the Annual Energy Outlook 2016. US Energy Information Administration, Department of Energy (2016)Google Scholar
  15. 15.
    Feng, Z.H., Zou, L.L., Wei, Y.M.: Carbon price volatility: evidence from EU ETS. Appl Energy 88, 590–598 (2011)CrossRefGoogle Scholar
  16. 16.
    Fuss, S., Szolgayová, J., Khabarov, N., Obersteiner, M.: Renewables and climate change mitigation: irreversible energy investment under uncertainty and portfolio effects. Energy Policy 40, 59–68 (2012)CrossRefGoogle Scholar
  17. 17.
    García-Martos, C., Rodríguez, J., Sánchez, M.J.: Modelling and forecasting fossil fuels, CO\(_2\) and electricity prices and their volatilities. Appl. Energy 101, 363–375 (2013)CrossRefGoogle Scholar
  18. 18.
    Hadjipaschalis, I., Poullikkas, A.: Overview of current and future energy storage technologies for electric power applications. Renew. Sustain. Energy Rev. 13, 1513–1522 (2009)CrossRefGoogle Scholar
  19. 19.
    Hanson, D., Schmalzer, D., Nichols, C., Balash, P.: The impacts of meeting a tight CO\(_2\) performance standard on the electric power sector. Energy Econ. 60, 476–485 (2016)CrossRefGoogle Scholar
  20. 20.
    Hittinger, E., Whitacre, J.F., Apt, J.: Compensating for wind variability using co-located natural gas generation and energy storage. Energy Syst. 1, 417–439 (2010)CrossRefGoogle Scholar
  21. 21.
    Hogue, M.T.: A review of the costs of nuclear power generation. University of Utah, BEBR, Salt Lake City (2012)Google Scholar
  22. 22.
    Huisman, R., Mahieu, Schlichter, F.: Electricity portfolio management: optimal peak/off-peak allocations. Energy Econ. 31, 169–174 (2009)CrossRefGoogle Scholar
  23. 23.
    IEA: IEA Wind-2015 Annual Report. International Energy Agency, Paris (2016)Google Scholar
  24. 24.
    IEA-NEA: Projected Costs of Generating Electricity-2015 Edition. International Energy Agency-Nuclear Energy Agency, Paris (2015)Google Scholar
  25. 25.
    Krokhml, P., Palmquist, J., Uryasev, S.: Portfolio optimization with conditional value-at-risk: objective and constraints. J. Risk 4(2), 43–68 (2002)CrossRefGoogle Scholar
  26. 26.
    Kümmel, R., Lindenberger, D., Weiser, F.: The economic power of energy and the need to integrate it with energy policy. Energy Policy 86, 833–843 (2015)CrossRefGoogle Scholar
  27. 27.
    Liu, M., Wu, F.F.: Portfolio optimization in electricity markets. Electr. Power Syst. Res. 77, 1000–1009 (2007)CrossRefGoogle Scholar
  28. 28.
    Lucheroni, C., Mari, C.: Risk shaping of optimal electricity portfolios in the stochastic LCOE theory. Preprint available on ResearchGate (Lucheroni) (2015).
  29. 29.
    Lucheroni, C., Mari, C.: CO\(_2\) Volatility impact on energy portfolio choice: a fully stochastic LCOE theory analysis. Appl Energy 190, 278–290 (2017)CrossRefGoogle Scholar
  30. 30.
    Madlener, R.: Portfolio optimization of power generation assets. In: Zheng, Q.P., et al. (eds.) Handbook of CO\(_2\) in Power Systems, Springer (2012)Google Scholar
  31. 31.
    Mari, C.: Hedging electricity price volatility using nuclear power. Appl. Energy 113, 615–621 (2014)CrossRefGoogle Scholar
  32. 32.
    Markowitz, H.: Portfolio Selection. J. Financ. 77, 77–91 (1952)Google Scholar
  33. 33.
    Mirrlees, J.A., Stern, N.: Fairly good plans. J. Econ. Theory 4, 268–288 (1972)CrossRefGoogle Scholar
  34. 34.
    MIT: Update of the MIT 2003 The Future of Nuclear Power Study. MIT, Cambridge (2009)Google Scholar
  35. 35.
    Nanduri, V., Kazemzadeh, N.: A survey of carbon market mechanisms and models. In: Zheng, Q.P., et al. (eds.) Handbook of CO\(_2\) in Power Systems, Springer (2012)Google Scholar
  36. 36.
    NREL: Renewable Electricity Futures Study. National Renewable Energy Laboratory, Golden (2012)Google Scholar
  37. 37.
    Rockafellar, R.T., Uryasev, S.: Optimization of conditional value-at-risk. J. Risk 2, 21–41 (2000)CrossRefGoogle Scholar
  38. 38.
    Rockafellar, R.T., Uryasev, S.: The fundamental risk quadrangle in risk management, optimization and statistical estimation. Surv. Oper. Res. Manag. Sci. 18, 33–53 (2013)MathSciNetGoogle Scholar
  39. 39.
    Rockafellar, R.T., Uryasev, S., Zabarankin, M.: Generalized deviations in risk analysis. University of Florida Department of Industrial and Systems Engineering WP No. 2004-4. (2004). SSRN:
  40. 40.
    Roques, F.A., Newbery, D.M., Nuttall, W.J., William, J.: Fuel mix diversification incentives in liberalized electricity markets: a mean–variance portfolio theory approach. Energy Econ. 30, 1831–1849 (2008)CrossRefGoogle Scholar
  41. 41.
    Roy, S.: Uncertainty of optimal generation cost due to integration of renewable energy sources. Energy Syst. 7, 365–389 (2016)CrossRefGoogle Scholar
  42. 42.
    Sarykalin, S., Serraino, G., Uryasev, S.: Value-at-risk vs. conditional value-at-risk in risk management and optimization. In: Informs 2008 Proceedings (2008).
  43. 43.
    Stacy, T.F., Taylor, G.: The Levelized Cost of Electricity from Existing Generation Resources. Institute for Energy Research, Houston (2015)Google Scholar
  44. 44.
    Steinbach, J., Staniaszek, D.: Discounting Rates in Energy System Analysis. Fraunhofer ISI, Karlsruhe (2015)Google Scholar
  45. 45.
    Taylor, G., Tanton, T.: The Hidden Costs of Wind Electricity. American Tradition Institute, Washington (2012)Google Scholar
  46. 46.
    Uryasev, S.: Conditional value-at-risk: optimization algorithms and applications. Financ. Eng. News 14 (2000)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of Chieti-PescaraPescaraItaly

Personalised recommendations