Abstract
To explore the effects of uncertain fuel costs on the bulk energy flows in the US, we introduce stochastic fuel costs in a generalized network flow model of the integrated electric energy system, including coal, natural gas, and electricity generation. The fuel costs are modeled as discretely distributed random variables. A rolling two-stage recourse stochastic programming approach is employed to simulate the decision process involving uncertain costs with forecast updates. All the data are derived from publicly available information for the years 2002, when natural gas prices rose much higher than forecast, and 2006, when gas prices were lower than expected. Government forecasts of the natural gas prices are adapted to generate the scenarios considered in the stochastic formulation. Compared to the expected value solution from the deterministic model, the recourse solution found from the stochastic model for 2002 has higher total cost, lower natural gas consumption and less subregional power trade but a fuel mix that is closer to what actually occurred. The comparisons are qualitatively similar but muted in the 2006 case. The stochastic model assists decision makers to simulate the future flows within the national electric energy system and better understand how they are affected by uncertain fuel costs.
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Beale, E.M.L.: On minimizing a convex function subject to linear inequalities. J. R. Stat. Soc. B 17, 173–184 (1955)
Benders, J.F.: Partitioning procedures for solving mixed integer variables programming problems. Numer. Math. 4, 238–252 (1962)
Bolinger, M., Wiser, R., Golove, W.: Accounting for fuel price risk when comparing renewable to gas-fired generation: the role of forward natural gas prices. Energy Policy 34, 706–720 (2006)
Butler, J.C., Dyer, J.S.: Optimizing natural gas flows with linear programming and scenarios. Decis. Sci. 30(2), 563–580 (1999)
Dantzing, G., Glynn, P.: Parallel processors for planning under uncertainty. Ann. Oper. Res. 22(1), 1–21 (1990)
Dantzing, G.B.: Linear programming under uncertainty. Manag. Sci. 1, 197–206 (1955)
Dupac̆ová, J., Gröwe-Kuska, N., Römisch, W.: Scenario reduction in stochastic programming. Math. Program. 95(3), 493–511 (2003)
EIA: Short-term energy outlook January 2002. http://www.eia.doe.gov/pub/forecasting/steo/oldsteos/jan02.pdf
EIA: The national energy modeling system: an overview (2003). http://www.eia.doe.gov/oiaf/aeo/overview/
EIA: Short-term energy outlook January 2003. http://www.eia.doe.gov/pub/forecasting/steo/oldsteos/jan03.pdf
EIA: Annual energy review (2006). http://www.eia.doe.gov/aer/
EIA: Short-term energy outlook January 2006. http://www.eia.doe.gov/pub/forecasting/steo/oldsteos/jan06.pdf
EIA: Short-term energy outlook January 2007. http://www.eia.doe.gov/pub/forecasting/steo/oldsteos/jan07.pdf
Greengard, C., Ruszczynski, A. (eds.): Decision Making under Uncertainty: Energy and Power. IMA Volumes on Mathematics and Its Applications, vol. 128. Springer, New York (2002)
Hogan, W.W.: Energy policy models for project independence. Comput. Oper. Res. 2, 251–271 (1975)
Infanger, G.: Monte Carlo (importance) sampling within a Benders decomposition algorithm for stochastic linear programs. Ann. Oper. Res. 39(1), 65–95 (1992)
Lavenberg, S.S., Welch, P.D.: A perspective on the use of control variables to increase the efficiency of Monte Carlo simulations. Manag. Sci. 27(3), 322–335 (1981)
Mulvey, J.M., Vladimirou, H.: Solving multistage stochastic networks: an application of scenario aggregation. Networks 21, 619–643 (1991)
Murphy, F., Sen, S.: Qualitative implications of uncertainty in economic equilibrium models. In: Decision Making under Uncertainty: Energy and Power. IMA Volumes on Mathematics and Its Applications, vol. 128, pp. 135–152. Springer, New York (2002)
Murphy, F.H., Conti, J.J., Shaw, S.H., Sanders, R.: Modeling and forecasting energy markets with the intermediate future forecasting system. Oper. Res. 36(3), 406–420 (1988)
Pereira, M.V.F., Pinto, L.M.V.G.: Multi-stage stochastic optimization applied to energy planning. Math. Program. 52, 359–375 (1991)
Quelhas, AM: Economics efficiencies of the flows from the primary resource suppliers to the electric load centers. Ph.D. thesis, Iowa State University (2006)
Quelhas, A., Gil, E., McCalley, J.: A multiperiod generalized network flow model of the US integrated energy system: Part II—simulation results. IEEE Trans. Power Syst. 22(2), 837–844 (2007)
Quelhas, A., Gil, E., McCalley, J., Ryan, S.M.: A multiperiod generalized network flow model of the US integrated energy system: Part I—model description. IEEE Trans. Power Syst. 22(2), 829–836 (2007)
Römisch, W., Shapiro, A.: Stability of stochastic programming problem. In: Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10, pp. 483–554. Elsevier, Amsterdam (2003)
Ruszczyński, A., Shapiro, A.: Stochastic programming model. In: Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10, pp. 1–64. Elsevier, Amsterdam (2003)
Ryan, S.M., Downward, A., Philpott, A., Zakeri, G.: Welfare effects of expansions in equilibrium models of an electricity market with fuel network. IEEE Trans. Power Syst. (2010). doi:10.1109/TPWRS.2009.2039587
Van Slyke, R.M., Wets, R.: L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J. Appl. Math. 17(4), 638–663 (1969)
Wallace, S.W., Fleten, S.E.: Stochastic programming models in energy. In: Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10, pp. 637–677. Elsevier, Amsterdam (2003)
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Wang, Y., Ryan, S.M. Effects of uncertain fuel costs on fossil fuel and electric energy flows in the US. Energy Syst 1, 209–243 (2010). https://doi.org/10.1007/s12667-010-0012-7
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DOI: https://doi.org/10.1007/s12667-010-0012-7