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On the Value of Dual-Firing Power Generation Under Uncertain Gas Network Access

  • Boris DefournyEmail author
  • Shu Tu
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 279)

Abstract

This work is concerned with the impact of gas network disruptions on dual-firing power generation. The question is addressed through the following optimization problem. Markets drive the price of gas, oil, and electricity. The log-prices evolve as correlated mean-reverting processes in discrete time. A generating unit has dual-firing capabilities, here in the sense that it can convert either gas or oil to electricity. Oil and gas are subject to different constraints and uncertainties. Gas is obtained in real time through the gas network. Due to gas supply disruptions, gas access is not guaranteed. Oil is stored locally and available in real time. The oil storage capacity is limited onsite. Oil can be reordered to replenish the oil tank, with a lead time between the order time and the delivery time. Oil is paid for at the order time price. In this paper, we formulate the stochastic optimization problem for a risk-neutral operator, and study the sensitivity of the value of the dual-firing generating unit to the gas network availability parameters.

Keywords

Dual-firing Power generation Energy asset management Natural gas-electric coordination Resilience Markov decision processes Optimal control Dynamic programming Stochastic optimization 

MSC (2010):

90B05 90B25 90C15 90C39 90C40 

Notes

Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No. 1610825.

References

  1. 1.
    Bonnans, J., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, New York (2000)zbMATHCrossRefGoogle Scholar
  2. 2.
    Borovkova, S., Schmeck, M.: Electricity price modeling with stochastic time change. Energy Econ. 63, 51–65 (2017)CrossRefGoogle Scholar
  3. 3.
    Carmona, R., Durrleman, V.: Pricing and hedging spread options. SIAM Rev. 45(4), 627–685 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Carmona, R., Durrleman, V.: Generalizing the Black-Scholes formula to multivariate contingent claims. J. Comput. Financ. 9, 42–63 (2005)CrossRefGoogle Scholar
  5. 5.
    Deng, S.: Pricing electricity derivatives under alternative stochastic spot price models. In: 33rd Annual Hawaii International Conference on System Sciences (HICSS), pp. 10–20 (2000)Google Scholar
  6. 6.
    Total Electric Power Industry Summary: U.S. Energy Information Administration. https://www.eia.gov/electricity/annual/
  7. 7.
    Escribano, A., Ignacio Peña, J., Villaplana, P.: Modelling electricity prices: international evidence. Oxford Bull. Econ. Stat. 73(5), 622–650 (2011)CrossRefGoogle Scholar
  8. 8.
    Fiacco, A.V., Kyparisis, J.: Convexity and concavity properties of the optimal value function in parametric nonlinear programming. J. Optim. Theory Appl. 48(1), 95–126 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Fleten, S.E., Näsäkkälä, E.: Gas-fired power plants: investment timing, operating flexibility and CO\(_2\) capture. Energy Econ. 32(4), 805–816 (2010)Google Scholar
  10. 10.
    Geman, H.: Mean reversion versus random walk in oil and natural gas prices. In: Advances in Mathematical Finance, pp. 219–228. Springer (2007)Google Scholar
  11. 11.
    Golub, G., Meyer Jr., C.: Using the QR factorization and group inversion to compute, differentiate, and estimate the sensitivity of stationary probabilities for Markov chains. SIAM J. Algebr. Discret. Methods 7(2), 273–281 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Haneveld, W., Stougie, L., van der Vlerk, M.: Simple integer recourse models: convexity and convex approximations. Math. Program. 108(2), 435–473 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Jaillet, P., Ronn, E., Tompaidis, S.: Valuation of commodity-based swing options. Manag. Sci. 50(7), 909–921 (2004)zbMATHCrossRefGoogle Scholar
  14. 14.
    Knittel, C., Roberts, M.: Financial models of deregulated electricity prices: an application to the California market. Energy Econ. 27(5), 791–817 (2005)CrossRefGoogle Scholar
  15. 15.
    Koeppel, G., Andersson, G.: The influence of combined power, gas, and thermal networks on the reliability of supply. In: 6th World Energy System Conference, pp. 10–12. Torino, Italy (2006)Google Scholar
  16. 16.
    Kong, N., Schaefer, A., Ahmed, S.: Totally unimodular stochastic programs. Math. Program. 138(1–2), 1–13 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Laporte, G., Louveaux, F.: The integer L-shaped method for stochastic integer programs with complete recourse. Oper. Res. Lett. 13(3), 133–142 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Li, T., Eremia, M., Shahidehpour, M.: Interdependency of natural gas network and power system security. IEEE Trans. Power Syst. 23(4), 1817–1824 (2008)CrossRefGoogle Scholar
  19. 19.
    Lien, D.: Moments of ordered bivariate log-normal distributions. Econ. Lett. 20(1), 45–47 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Lucia, J., Schwartz, E.: Electricity prices and power derivatives: evidence from the Nordic power exchange. Rev. Deriv. Res. 5(1), 5–50 (2002)zbMATHCrossRefGoogle Scholar
  21. 21.
    Margrabe, W.: The value of an option to exchange one asset for another. J. Financ. 33(1), 177–186 (1978)CrossRefGoogle Scholar
  22. 22.
    Munoz, J., Jimenez-Redondo, N., Perez-Ruiz, J., Barquin, J.: Natural gas network modeling for power systems reliability studies. In: Proceedings of the 2003 IEEE Power Tech Conference, pp. 1–8. Bologna, Italy (2003)Google Scholar
  23. 23.
    Special Reliability Assessment: Potential bulk power system impacts due to severe disruptions on the natural gas system. North American Electric Reliability Corporation (2017)Google Scholar
  24. 24.
    Ross, S., Zhu, Z.: On the structure of a swing contract’s optimal value and optimal strategy. J. Appl. Probab. 45(1), 1–15 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Schwartz, E.: The stochastic behavior of commodity prices: implications for valuation and hedging. J. Financ. 52(3), 923–973 (1997)CrossRefGoogle Scholar
  26. 26.
    Seneta, E.: Sensitivity of finite Markov chains under perturbation. Stat. Probab. Lett. 17(2), 163–168 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Shapiro, A.: Analysis of stochastic dual dynamic programming method. Eur. J. Oper. Res. 209(1), 63–72 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Shapiro, A., Dentcheva, D., Ruszczyński, A.: Lectures on stochastic programming: modeling and theory. SIAM, Philadelphia, PA (2009)zbMATHCrossRefGoogle Scholar
  29. 29.
    Sun, R., Shylo, O., Schaefer, A.: Totally unimodular multistage stochastic programs. Oper. Res. Lett. 43(1), 29–33 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Webster, M., Schmalensee, R.: Growing concerns, possible solutions: the interdependency of natural gas and electricity systems. Technical report, MIT Energy Initiative (2014)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringLehigh UniversityBethlehemUSA

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