Abstract
Recent changes in the U.S. electric power markets have contributed to volatility in hourly prices and loads. In this paper we consider the position of the electric power retailer who typically contracts with suppliers and end-users and must provide future load requirements to the suppliers. As part of this energy supply chain, the retailer is faced with great uncertainty in both market prices as well as end-user loads. Based on actual data for the PJM market covering Pennsylvania, New Jersey, and Maryland, we develop a probabilistic optimization model to optimize the net profits for the retailer for a forecast time horizon (typically one or more hours) given the cumulative performance in previous time periods (hours). The resulting model is formulated as a mixed integer linear program with binary variables due to the disjunctive nature of certain forward load estimation “bandwidth” tolerance constraints. In addition, we also provide an existence result to this optimization model. Lastly, we present a numerical example of the optimization model to validate its workings and provide some insight into model sensitivities.
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References
Birge, J.R. and F. Louveaux. (1997). Introduction to Stochastic Programming.New York: Springer.
Bower, J. and D.W. Bunn. (2000). "Model-Based Comparisons of Pool and Bilateral Markets for Electricity." The Energy Journal 21, 1-29.
Clemen, R.T. and T. Reilly. (2001). Making Hard Decisions with Decision Tools.Pacific Grove, California: Duxbury Thomson Learning.
Conejo, A.J. and F.J. Prieto. (2001). "Mathematical Programming and Electricity Markets." Sociedad de Estadística e Investigación Operativa, TOP 9, 1-54.
De Wolf, D. and Y. Smeers. (1997). "A Stochastic Version of a Stackelberg-Nash-Cournot Equilibrium Model." Management Science 43(2), 190-197.
Gabriel, S.A., M.F. Genc, and S. Balakrishnan. (2002). "A Simulation Approach to Balancing Annual Risk and Reward in Retail Electrical Power Markets." IEEE Transactions on Power Systems 17(4), 1050-1057.
Gabriel, S.A., P. Sahakij, and S. Balakrishnan. (2004). "Optimal Retailer Load Estimates Using Stochastic Dynamic Programming." ASLE Journal of Energy Engineering 130(1), 1-17.
Genc, M.F. (2001). "Probabilistic Analysis of Electrical Power Retailer Strategies." M.S. dissertation, Dept. Civil & Env. Eng., Univ. of Maryland, College Park, MD, USA.
Gürkan, G., A.Y. Özge, and S.M. Robinson. (1999). "Sample-Path Solution of Stochastic Variational Inequalities." Mathematical Programming 84, 313-333.
Haurie, A., G. Zaccour, J. Legrand, and Y. Smeers. (1987). "A Stochastic Dynamic Nash-Cournot Model for the European Gas Market." Technical Report G-86-24, GERAD, Ecole des Hautes Etudes Commerciales, Montréal, Québec, Canada.
Hobbs, B.F. and Y. Ji. (1999). "Stochastic Programming-Based Bounding of Expected Production Costs for Multiarea Electric Power Systems." Operations Research 47(6), 836-848.
Hull, J.C. (2000). Options, Futures, & Other Derivatives. Upper Saddle River, New Jersey: Prentice-Hall, Inc.
Kanudia, A. and R. Loulou. (1998). "Robust Responses to Climate Change via Stochastic MARKAL: The Case of Québec." European Journal of Operational Research 106, 15-30.
Pérez-Ruiz, J. and A.J. Conejo. (2000). "Multi-Period Probabilistic Production Cost Model Including Dispatch Constraints." IEEE Transactions on Power Systems 15, 502-507.
Sherali, H.D., A.L Soyster, F.H. Murphy, and S. Sen. (1984). "Intertemporal Allocation of Capital Costs in Electric Utility Capacity Expansion Planning under Uncertainty." Management Science 30(1), 1-19.
Takriti, S., J.R. Birge, and E. Long. (1996). "A Stochastic Model for the Unit Commitment Problem." IEEE Transactions on Power Systems 11(3), 1497-1506.
Wallace, S. and S.-E. Fleten. (2002). "Stochastic Programming Models in Energy." Working Paper 01-02, Department of Industrial Economics and Technology Management, Norwegian University of of Science and Technology.
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Gabriel, S.A., Kiet, S. & Balakrishnan, S. A Mixed Integer Stochastic Optimization Model for Settlement Risk in Retail Electric Power Markets. Networks and Spatial Economics 4, 323–345 (2004). https://doi.org/10.1023/B:NETS.0000047111.94897.d4
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DOI: https://doi.org/10.1023/B:NETS.0000047111.94897.d4