Abstract
We develop a two-stage stochastic integer programming model for the simultaneous optimization of power production and day-ahead power trading in a hydro-thermal system. The model rests on mixed-integer linear formulations for the unit commitment problem and for the price clearing mechanism at the power exchange. Foreign bids enter as random components into the model. We solve the stochastic integer program by a decomposition method combining Lagrangian relaxation of nonanticipativity with branch-and-bound in the spirit of global optimization. Finally, we report some first computational experiences.
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References
Amsterdam Power Exchange (APX). http://www.apx.nl/
E. J. Anderson and A. B. Philpott, “Optimal offer construction in electricity markets,” Mathematics of Operations Research vol. 27, pp. 82–100, 2002.
E. J. Anderson and H. Xu, “Necessary and sufficient conditions for optimal offers in electricity markets,” SIAM Journal on Control and Optimization vol. 41, pp. 1212–1228, 2002.
F. Bolle, “Supply function equilibria and the danger of tacit collusion: The case of spot markets for electricity,” Energy Economics vol. 14, pp. 94–102, 1992.
C. C. Carøe and R. Schultz, “Dual decomposition in stochastic integer programming,” Operations Research Letters vol. 24, pp. 37–45, 1999.
H.-P. Chao and H. G. Huntington, Designing Competitive Electricity Markets, Kluwer, Boston, 1998.
Using the CPLEX Callable Library, CPLEX Optimization, Inc., 1999.
R. Gollmer, M. P. Nowak, W. Römisch, and R. Schultz, “Unit commitment in power generation—A basic model and some extensions,” Annals of Operations Research vol. 96, pp. 167–189, 2000.
R. J. Green and D. M. Newbery, “Competition in the British electricity spot market,” Journal of Political Economy vol. 100, pp. 929–953, 1992.
N. Gröwe-Kuska, K. C. Kiwiel, M. P. Nowak, W. Römisch, and I. Wegner, “Power management in a hydro-thermal system under uncertainty by Lagrangian relaxation,” in C. Greengard and A. Ruszczyński (Eds.), Decision Making under Uncertainty: Energy and Power, IMA volumes in Mathematics and its Applications, vol. 128, Springer-Verlag: New York, 2001, pp. 39–70.
J. B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms, Springer-Verlag: Berlin, 1993.
B. F. Hobbs, “Network models of spatial oligopoly with an application to deregulation of electricity generation,” Operations Research vol. 34, pp. 395–409, 1986.
K. C. Kiwiel, “Proximity control in bundle methods for convex nondifferentiable optimization,” Mathematical Programming vol. 46, pp. 105–122, 1990.
K. C. Kiwiel, User’s Guide for NOA 2.0/3.0: A Fortran Package for Convex Nondifferentiable Optimization, Systems Research Institute, Polish Academy of Sciences: Warsaw, 1994.
W. K. Klein Haneveld and M. H. van der Vlerk, “Stochastic integer programming: General models and algorithms,” Annals of Operations Research vol. 85, pp. 39–57, 1999.
P. D. Klemperer and M.A. Meyer, “Supply function equilibria in oligopoly under uncertainty,” Econometrica vol. 57, pp. 1243–1277, 1989.
F. V. Louveaux and R. Schultz, “Stochastic integer programming,” in A. Ruszczyński and A. Shapiro (Eds), Handbooks in Operations Research and Management Science, 10: Stochastic Programming, Elsevier, Amsterdam, 2003, pp. 213–266.
G. L. Nemhauser and L. A. Wolsey, Integer and Combinatorial Optimization, Wiley, New York, 1988.
M. P. Nowak and W. Römisch, “Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty,” Annals of Operations Research vol. 100, pp. 251–272, 2000.
R. Nürnberg and W. Römisch, “A two-stage planning model for power scheduling in a hydro-thermal system under uncertainty,” Optimization and Engineering vol. 3, pp. 355–378, 2002.
A. Rudkevich, M. Duckworth, and R. Rosen, “Modelling electricity pricing in a deregulated generation industry: The potential for oligopoly pricing in a poolco,” The Energy Journal vol. 19, pp. 19–48, 1998.
R. Schultz, “Stochastic programming with integer variables,” Mathematical Programming vol. 97, pp. 285–309, 2003.
G. B. Sheble and G. N. Fahd, “Unit commitment literature synopsis,” IEEE Transactions on Power Systems vol. 9, pp. 128–135, 1994.
C. Supatgiat, R. Q. Zhang, and J. R. Birge, “Equilibrium values in a competitive power exchange market,” Computational Economics vol. 17, pp. 93–121, 2001.
S. Takriti, J. R. Birge, and E. Long, “A stochastic model for the unit commitment problem,” IEEE Transactions on Power Systems vol. 11, pp. 1497–1508, 1996.
S. Takriti, B. Krasenbrink, and L. S.-Y. Wu, “Incorporating fuel constraints and electricity spot prices into the stochastic unit commitment problem,” Operations Research vol. 48, pp. 268–280, 2000.
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Nowak, M.P., Schultz, R. & Westphalen, M. A Stochastic Integer Programming Model for Incorporating Day-Ahead Trading of Electricity into Hydro-Thermal Unit Commitment. Optim Eng 6, 163–176 (2005). https://doi.org/10.1007/s11081-005-6794-0
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DOI: https://doi.org/10.1007/s11081-005-6794-0