Strictly and Γ-robust counterparts of electricity market models: Perfect competition and Nash–Cournot equilibria

Operations Research Perspectives - Tập 8 - Trang 100197 - 2021
Anja Kramer1, Vanessa Krebs1,2, Martin Schmidt2,3
1Friedrich-Alexander-Universität Erlangen-Nürnberg, Discrete Optimization, Cauerstr. 11, 91058 Erlangen, Germany
2Energie Campus Nürnberg, Fürther Str. 250, 90429 Nürnberg, Germany
3Trier University, Department of Mathematics, Universitätsring 15, 54296 Trier, Germany

Tài liệu tham khảo

Cottle, 2009 Conejo, 2020, Complementarity, not optimization, is the language of markets, IEEE Open Access J Power and Energy, 7, 344, 10.1109/OAJPE.2020.3029134 Gabriel, 2012 Pang, 2003, Properties of oligopolistic market equilibria in linearized DC power networks with arbitrage and supply function conjectures, 113 Metzler, 2003, Nash-Cournot equilibria in power markets on a linearized DC network with arbitrage: Formulations and properties, Netw Spat Econ, 3, 123, 10.1023/A:1023907818360 Hobbs, 2004, Strategic generation with conjectured transmission price responses in a mixed transmission pricing system-Part I: formulation, IEEE Trans Power Syst, 19, 707, 10.1109/TPWRS.2003.821628 Hobbs, 1999, LCP models of Nash-Cournot competition in bilateral and POOLCO-based power markets, vol. 1, 303 Hobbs, 2004, Complementarity-based equilibrium modeling for electric power markets Hobbs, 2007, Nash-cournot equilibria in electric power markets with piecewise linear demand functions and joint constraints, Oper Res, 55, 113, 10.1287/opre.1060.0342 Hu, 2007, Using EPECs to model bilevel games in restructured electricity markets with locational prices, Oper Res, 55, 809, 10.1287/opre.1070.0431 Jing-Yuan, 1999, Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices, Oper Res, 47, 102, 10.1287/opre.47.1.102 Daxhelet, 2001, Variational inequality models of restructured electricity systems, 85 Hobbs, 2000, Strategic gaming analysis for electric power systems: an MPEC approach, IEEE Trans Power Syst, 15, 638, 10.1109/59.867153 Facchinei, 2003 Çelebi, 2020, Γ-Robust electricity market equilibrium models with transmission and generation investments, Energy Syst Birge, 2011 Soyster, 1973, Technical note—Convex programming with set-inclusive constraints and applications to inexact linear programming, Oper Res, 21, 1154, 10.1287/opre.21.5.1154 Ben-Tal, 2009 Bertsimas, 2011, Theory and applications of robust optimization, SIAM Rev, 53, 464, 10.1137/080734510 Kouvelis, 1997, 10.1007/978-1-4757-2620-6 Bertsimas, 2003, Robust discrete optimization and network flows, Math Program, 98, 49, 10.1007/s10107-003-0396-4 Sim, 2004 Bertsimas, 2004, The price of robustness, Oper Res, 52, 35, 10.1287/opre.1030.0065 Liebchen, 2009, Robust and online large-scale optimization: Models and techniques for transportation systems, 1 Fischetti, 2009, Light robustness, 61 Ben-Tal, 2004, Adjustable robust solutions of uncertain linear programs, Math Program, 99, 351, 10.1007/s10107-003-0454-y Gorissen, 2015, A practical guide to robust optimization, Omega, 53, 124, 10.1016/j.omega.2014.12.006 Chen, 2005, Expected residual minimization method for stochastic linear complementarity problems, Math Oper Res, 30, 1022, 10.1287/moor.1050.0160 Lin, 2006, New reformulations for stochastic nonlinear complementarity problems, Optim Methods Softw, 21, 551, 10.1080/10556780600627610 Chen, 2012, Stochastic variational inequalities: Residual minimization smoothing sample average approximations, SIAM J Optim, 22, 649, 10.1137/110825248 Chen, 2009, Robust solution of monotone stochastic linear complementarity problems, Math Program, 117, 51, 10.1007/s10107-007-0163-z Wu, 2011, Robust solutions to uncertain linear complementarity problems, Acta Math Appl Sin Engl Ser, 27, 339, 10.1007/s10255-010-0033-y Krebs, 2020, Γ-Robust linear complementarity problems, Optim Methods Softw, 10.1080/10556788.2020.1825708 Krebs, 2021, Γ-Robust linear complementarity problems with ellipsoidal uncertainty sets, Int Trans Oper Res Biefel, 2020 Xie, 2014, On robust solutions to uncertain monotone linear complementarity problems (LCPs) and their variants, 2834 Xie, 2016, On robust solutions to uncertain linear complementarity problems and their variants, SIAM J Optim, 26, 2120, 10.1137/15M1010427 Aghassi, 2006, Robust game theory, Math Program, 107, 231, 10.1007/s10107-005-0686-0 Hayashi, 2005, Robust Nash equilibria and second-order cone complementarity problems, J Nonlinear Convex Anal, 6 Nishimura, 2009, Robust Nash equilibria in N-person non-cooperative games: Uniqueness and reformulation, Pac J Optim, 5 Crespi, 2017, Robust games: theory and application to a cournot duopoly model, Decis Econ Finance, 40, 177, 10.1007/s10203-017-0199-3 Perchet, 2014, A note on robust Nash equilibria with uncertainties, RAIRO Oper Res, 48, 365, 10.1051/ro/2014001 Hu, 2013, Existence, uniqueness, and computation of robust Nash equilibria in a class of multi-leader-follower games, SIAM J Optim, 23, 894, 10.1137/120863873 Ordóñez, 2007, Robust wardrop equilibrium, 247 de Frutos, 2011, Endogenous capacities and price competition: The role of demand uncertainty, Int J Ind Organ, 29, 399, 10.1016/j.ijindorg.2010.08.001 Roh, 2009, Market-based generation and transmission planning with uncertainties, IEEE Trans Power Syst, 24, 1587, 10.1109/TPWRS.2009.2022982 van der Weijde, 2012, The economics of planning electricity transmission to accommodate renewables: Using two-stage optimisation to evaluate flexibility and the cost of disregarding uncertainty, Energy Econ, 34, 2089, 10.1016/j.eneco.2012.02.015 Ehrenmann, 2011, Generation capacity expansion in a risky environment: a stochastic equilibrium analysis, Oper Res, 59, 1332, 10.1287/opre.1110.0992 Ralph, 2015, Risk trading and endogenous probabilities in investment equilibria, SIAM J Optim, 25, 2589, 10.1137/110851778 Ralph, 2017 Ruiz, 2015, Robust transmission expansion planning, European J Oper Res, 242, 390, 10.1016/j.ejor.2014.10.030 Jabr, 2013, Robust transmission network expansion planning with uncertain renewable generation and loads, IEEE Trans Power Syst, 28, 4558, 10.1109/TPWRS.2013.2267058 Bertsimas, 2014, Adaptive robust optimization for the security constrained unit commitment problem, IEEE Trans Power Syst, 29, 996, 10.1109/TPWRS.2014.2301352 Zhao, 2012, Robust unit commitment problem with demand response and wind energy, 1 Jiang, 2012, Robust unit commitment with wind power and pumped storage hydro, IEEE Trans Power Syst, 27, 800, 10.1109/TPWRS.2011.2169817 Jiang, 2014, Two-stage network constrained robust unit commitment problem, European J Oper Res, 234, 751, 10.1016/j.ejor.2013.09.028 Mejía-Giraldo, 2014, Adjustable decisions for reducing the price of robustness of capacity expansion planning, IEEE Trans Power Syst, 29, 1573, 10.1109/TPWRS.2013.2295166 Baringo, 2011, Offering strategy via robust optimization, IEEE Trans Power Syst, 26, 1418, 10.1109/TPWRS.2010.2092793 Mather, 2017, Robust Cournot-Bertrand equilibria on power networks, 2747 Campos, 2004, Application of possibility theory to robust cournot equilibrium in electricity market, 409 Van den Bergh, 2014, DC power flow in unit commitment models Wood, 2014 Barquin, 2008, Cournot equilibrium calculation in power networks: An optimization approach with price response computation, IEEE Trans Power Syst, 23, 317, 10.1109/TPWRS.2008.919198 Ehrenmann, 2009, A comparison of electricity market designs in networks, Oper Res, 57, 274, 10.1287/opre.1080.0624 Grimm, 2017, Uniqueness of market equilibrium on a network: A peak-load pricing approach, European J Oper Res, 261, 971, 10.1016/j.ejor.2017.03.036 Krebs, 2018, Uniqueness and multiplicity of market equilibria on DC power flow networks, European J Oper Res, 271, 165, 10.1016/j.ejor.2018.05.016 Krebs, 2018, Uniqueness of market equilibria on networks with transport costs, Oper Res Perspect, 5, 169 Aussel, 2013, Electricity spot market with transmission losses, J Ind Manag Optim, 9, 275, 10.3934/jimo.2013.9.275 Aussel, 2016, Deregulated electricity markets with thermal losses and production bounds: models and optimality conditions, RAIRO Oper Res, 50, 19, 10.1051/ro/2015009 Hashimoto, 1985, A spatial Nash equilibrium model, 20 Mangasarian, 1988, A simple characterization of solution sets of convex programs, Oper Res Lett, 7, 21, 10.1016/0167-6377(88)90047-8