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Robust portfolio optimization for electricity planning: An application based on the Brazilian electricity mix

Author

Listed:
  • Costa, Oswaldo L.V.
  • de Oliveira Ribeiro, Celma
  • Rego, Erik Eduardo
  • Stern, Julio Michael
  • Parente, Virginia
  • Kileber, Solange

Abstract

One of the major challenges of today's policy makers and industry strategists is to achieve an electricity mix that presents a high level of energy security within a range of affordable costs and environmental constraints. Bearing in mind the planning of a more reliable electricity mix, the main contribution of this paper is to consider parameter uncertainties on the electricity portfolio optimization problem. We assume that the expected and the covariance matrix of the costs for the different energy technologies, such as gas, coal, nuclear, oil, biomass, wind, large and small hydropower, are not exactly known. We consider that these parameters belong to some uncertainty sets (box, ellipsoidal, lower and upper bounds, and convex polytopic). Three problems are analyzed: (i) finding a energy portfolio of minimum worst case volatility with guaranteed fixed maximum expected energy cost; (ii) finding an energy portfolio of minimum worst case expected cost with guaranteed fixed maximum volatility of the energy cost; (iii) finding a combination of the expected and variance of the cost, weighted by a risk aversion parameter. These problems are written as quadratic, second order cone programming (SOCP), and semidefinite programming (SDP), so that robust optimization tools can be applied. These results are illustrated by analyzing the efficient Brazilian electricity energy mix considered in Losekann et al. (2013) assuming possible uncertainties in the vector of expected costs and covariance matrix. The results suggest that the robust approach, being by nature more conservative, can be useful in providing a reasonable electricity energy mix conciliating CO2 emission, risk and costs under uncertainties on the parameters of the model.

Suggested Citation

  • Costa, Oswaldo L.V. & de Oliveira Ribeiro, Celma & Rego, Erik Eduardo & Stern, Julio Michael & Parente, Virginia & Kileber, Solange, 2017. "Robust portfolio optimization for electricity planning: An application based on the Brazilian electricity mix," Energy Economics, Elsevier, vol. 64(C), pages 158-169.
    • Handle: RePEc:eee:eneeco:v:64:y:2017:i:c:p:158-169
    DOI: 10.1016/j.eneco.2017.03.021
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    References listed on IDEAS

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    1. Marrero, Gustavo A. & Ramos-Real, Francisco Javier, 2010. "Electricity generation cost in isolated system: The complementarities of natural gas and renewables in the Canary Islands," Renewable and Sustainable Energy Reviews, Elsevier, vol. 14(9), pages 2808-2818, December.
    2. Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    3. Shimon Awerbuch, 2006. "Portfolio-Based Electricity Generation Planning: Policy Implications For Renewables And Energy Security," Mitigation and Adaptation Strategies for Global Change, Springer, vol. 11(3), pages 693-710, May.
    4. Marrero, Gustavo A. & Puch, Luis A. & Ramos-Real, Francisco J., 2015. "Mean-variance portfolio methods for energy policy risk management," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 246-264.
    5. Losekann, Luciano & Marrero, Gustavo A. & Ramos-Real, Francisco J. & de Almeida, Edmar Luiz Fagundes, 2013. "Efficient power generating portfolio in Brazil: Conciliating cost, emissions and risk," Energy Policy, Elsevier, vol. 62(C), pages 301-314.
    6. R.H. Tütüncü & M. Koenig, 2004. "Robust Asset Allocation," Annals of Operations Research, Springer, vol. 132(1), pages 157-187, November.
    7. Costa, O. L. V. & Paiva, A. C., 2002. "Robust portfolio selection using linear-matrix inequalities," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 889-909, June.
    8. Roques, Fabien & Hiroux, Céline & Saguan, Marcelo, 2010. "Optimal wind power deployment in Europe--A portfolio approach," Energy Policy, Elsevier, vol. 38(7), pages 3245-3256, July.
    9. Mari, Carlo, 2014. "Hedging electricity price volatility using nuclear power," Applied Energy, Elsevier, vol. 113(C), pages 615-621.
    10. Delarue, Erik & De Jonghe, Cedric & Belmans, Ronnie & D'haeseleer, William, 2011. "Applying portfolio theory to the electricity sector: Energy versus power," Energy Economics, Elsevier, vol. 33(1), pages 12-23, January.
    11. Jang Ho Kim & Woo Chang Kim & Frank J. Fabozzi, 2014. "Recent Developments in Robust Portfolios with a Worst-Case Approach," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 103-121, April.
    12. Shakouri, Mahmoud & Lee, Hyun Woo & Choi, Kunhee, 2015. "PACPIM: New decision-support model of optimized portfolio analysis for community-based photovoltaic investment," Applied Energy, Elsevier, vol. 156(C), pages 607-617.
    13. Roques, Fabien A. & Newbery, David M. & Nuttall, William J., 2008. "Fuel mix diversification incentives in liberalized electricity markets: A Mean-Variance Portfolio theory approach," Energy Economics, Elsevier, vol. 30(4), pages 1831-1849, July.
    14. Rustem, Berc & Becker, Robin G. & Marty, Wolfgang, 2000. "Robust min-max portfolio strategies for rival forecast and risk scenarios," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1591-1621, October.
    15. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • Q43 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Energy and the Macroeconomy
    • Q48 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Government Policy
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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