Abstract
In this paper, we present a bilevel programming formulation for the problem of strategic bidding under uncertainty in a wholesale energy market (WEM), where the economic remuneration of each generator depends on the ability of its own management to submit price and quantity bids. The leader of the bilevel problem consists of one among a group of competing generators and the follower is the electric system operator. The capability of the agent represented by the leader to affect the market price is considered by the model. We propose two solution approaches for this non-convex problem. The first one is a heuristic procedure whose efficiency is confirmed through comparisons with the optimal solutions for some instances of the problem. These optimal solutions are obtained by the second approach proposed, which consists of a mixed integer reformulation of the bilevel model. The heuristic proposed is also compared to standard solvers for nonlinearly constrained optimization problems. The application of the procedures is illustrated in case studies with configurations derived from the Brazilian power system.
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Alarie, S., Audet, C., Jaumard, B., Savard, G.: Concavity cuts for disjoint bilinear programming. Math. Program. 90, 373–398 (2001)
Anandalingam, G., White, D.J.: A solution method for the linear Stackelberg problem using penalty functions. IEEE Trans. Autom. Control 35, 1170–1173 (1990)
Audet, C., Hansen, P., Jaumard, B., Savard, G.: Links between linear bilevel and mixed 01 programming problems. J. Optim. Theory Appl. 93(2), 273–300 (1997)
Audet, C., Hansen, P., Jaumard, B., Savard, G.: A symmetrical linear maxmin approach to disjoint bilinear programming. Math. Program. 85, 573–592 (1999)
Audet, C., Hansen, P., Jaumard, B., Savard, G.: A branch and cut algorithm for nonconvex quadratically constrained quadratic programming. Math. Program. Ser. A 87, 131–152 (2000)
Baíllo, A., Ventosa, M., Rivier, M., Ramos, A.: Optimal offering strategies for generation companies operating in electricity spot markets. IEEE Trans. Power Syst. 19(2), 745–753 (2004)
Barroso, L.A., Fampa, M., Kelman, R., Pereira, M.V.F., Lino, P.: Market power issues in bid-based hydrothermal dispatch. Ann. Oper. Res. 117, 247–270 (2002)
Brotcorne, L., Labbe, M., Marcotte, P., Savard, G.: A bilevel model and solution algorithm for a freight tariff-setting problem. Transp. Sci. 34(3), 289–302 (2000)
Bushnell, J.: A mixed complementarity model of hydrothermal electricity competition in the western United States. Oper. Res. 51(1), 80–93 (2003)
Conejo, A.J., Prieto, F.J.: Mathematical programming and electricity markets. Soc. Estad. Investig. Oper. TOP 9(1), 1–53 (2001)
Conejo, A.J., Contreras, J., Arroyo, J.M., Torre, S.: Optimal response of an oligopolistic generating company to a competitive pool-based electric power market. IEEE Trans. Power Syst. 17(2), 424–430 (2002)
de la Torre, S., Arroyo, J.M., Conejo, A.J., Contreras, J.: Price maker self-scheduling in a pool-based electricity market: a mixed-integer LP approach. IEEE Trans. Power Syst. 17(4), 1037–1042 (2002)
Feo, A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995)
Fletcher, R., Leyffer, S.: Solving mathematical program with complementarity constraints as nonlinear programs. Optim. Methods Softw. 19(1), 15–40 (2004)
Fudenberg, D., Tirole, J.: Game Theory, 5th printing. MIT Press, Cambridge (1996)
Gill, P.E., Murray, M., Saunders, M.A.: User’s guide for SNOPT 5.3: a fortran package for large-scale nonlinear programming. Report NA 97-5, Department of Mathematics, University of California, San Diego (1997)
Granville, S., Barroso, L.A., Oliveira, G.C., Latorre, M.L., Campodónico, N., Thomé, L.M., Pereira, M.: Stochastic optimization of transmission constrained and large scale hydrothermal systems in a competitive framework. In: Proceedings of the IEEE General Meeting, Toronto (2003)
Hobbs, B.F.: Linear complementarity models of Nash-Cournot competition in bilateral and POOLCO power markets. IEEE Trans. Power Syst. 16(2), 194–202 (2001)
Hobbs, B.F., Helman, U.: Complementarity-based equilibrium modeling for electric power markets. In: Bunn, D. (ed.) Modeling Prices in Competitive Electricity Markets, ch. 3. Wiley, New York (2004)
Hobbs, B.F., Metzler, C.B., Pang, J.: Strategy gaming analysis for electric power systems: an MPEC approach. IEEE Trans. Power Syst. 15, 638–645 (2000)
Hunt, S.: Making Competition Work in Electricity. Wiley, New York (2003)
Kahn, E.: Regulation by simulation: the role of production cost models in electricity planning and pricing. Oper. Res. 43(3), 388–398 (1995)
Kahn, E.: Numerical techniques for analyzing market power in electricity. Electr. J., 34–43 (1998)
Labbé, M., Marcotte, P., Savard, G.: A bilevel model of taxation and its application to optimal highway pricing. Manag. Sci. 44, 1608–1622 (1998)
Labbé, M., Marcotte, P., Savard, G.: On a class of bilevel programs. In: di Pillo, Giannessi (eds.) Nonlinear Optimization and Related Topics, pp. 183–206. Kluwer Academic, Dordrecht (2000)
Lino, P., Barroso, L.A., Fampa, M., Pereira, M.V., Kelman, R.: Bid-based dispatch of hydrothermal systems in competitive markets. Ann. Oper. Res. 120, 81–97 (2003)
Nash, J.F.: Equilibrium points in n-person games. In: Proceedings of NAS 36 (1950)
Pereira, M.V., Pinto, L.M.V.G.: Multi-stage stochastic optimization applied to energy planning. Math. Program. 52, 359–375 (1991)
Pereira, M.V., Granville, S., Fampa, M., Dix, R., Barroso, L.A.: Strategic bidding under uncertainty: a binary expansion approach. IEEE Trans. Power Syst. 20(1), 180–188 (2005)
Perron, S.: Applications jointes de l’optimisation combinatoire et globale, Ph.D. Thesis, École Polytechnique de Montréal (2004)
Ramos, A., Ventosa, M., Rivier, M.: Modeling competition in electric energy markets by equilibrium constraints. Util. Policy 7(4), 233–242 (1999)
The NEOS guide. Available online at http://www-neos.mcs.anl.gov/
Thieu, T.V.: A note on the solution of bilinear problems by reduction to concave minimization. Math. Program. 41, 249–260 (1988)
Visweswaran, V., Floudas, C.A.: New properties and computational improvement of the GOP algorithm for problems with quadratic objective function and constraints. J. Glob. Optim. 3(4), 439–462 (1993)
Weber, J.D., Overbye, T.J.: An individual welfare maximization algorithm for electricity markets. IEEE Trans. Power Syst. 17(3), 590–596 (2002)
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Fampa, M., Barroso, L.A., Candal, D. et al. Bilevel optimization applied to strategic pricing in competitive electricity markets. Comput Optim Appl 39, 121–142 (2008). https://doi.org/10.1007/s10589-007-9066-4
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DOI: https://doi.org/10.1007/s10589-007-9066-4