Abstract
This paper presents a review of selected models, methods, and challenges associated with the use of bilevel optimization in problems that involve consumers’ demand response arising in the power sector. The main formulations and concepts of bilevel optimization are presented. The importance of demand response as a “dispatchable” resource in the evolution of power networks to smart grids is emphasized. The hierarchical nature of the interaction between decision-makers controlling different sets of variables in several problems involving demand response is highlighted, which establishes bilevel optimization as an adequate approach to decision support. The main concepts and solution approaches to those problems are underlined, in the context of the theoretical, methodological, and computational issues associated with bilevel optimization.
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References
Afşar S, Brotcorne L, Marcotte P, Savard G (2016) Achieving an optimal trade-off between revenue and energy peak within a smart grid environment. Renew Energy 91:293–301
Alipour M, Zare K, Seyedi H (2018) A multi-follower bilevel stochastic programming approach for energy management of combined heat and power micro-grids. Energy 149:135–146
Alves MJ, Antunes CH (2018) A semivectorial bilevel programming approach to optimize electricity dynamic time-of-use retail pricing. Comput Oper Res 92:130–144
Alves MJ, Antunes CH, Costa JP (2019) New concepts and an algorithm for multiobjective bilevel programming: optimistic, pessimistic and moderate solutions. Oper Res Int J. https://doi.org/10.1007/s12351-019-00534-9
Alves MJ, Antunes CH, Soares I (2020) Optimizing prices and periods in time-of-use electricity tariff design using bilevel programming. In: Paquete L, Zarges C (eds) Evolutionary computation in combinatorial optimization, EvoCOP 2020, lecture notes in computer science. Springer, Berlin
Asensio M, Munoz-Delgado G, Contreras J (2017) A bi-level approach to distribution network and renewable energy expansion planning considering demand response. IEEE Trans Power Systems 32(6):4298–4309
Asimakopoulou GE, Dimeas AL, Hatziargyriou ND (2013) Leader-follower strategies for energy management of multi-microgrids. IEEE Trans Smart Grid 4:1909–1916
Asimakopoulou GE, Vlachos AG, Hatziargyriou ND (2015) Hierarchical decision making for aggregated energy management of distributed resources. IEEE Trans Power Systems 30:255–3264
Aussel D, Brotcorne L, Lepaul S, von Niederhäusern L (2020) A trilevel model for best response in energy demand-side management. Eur J Oper Res 281:299–315
Bard J (1998) Practical bilevel optimization: algorithms and applications. Springer, Berlin
Bialas WF, Karwan MH (1984) Two-level linear programming. Manag Sci 30(8):1004–1020
Bracken J, McGill J (1973) Mathematical programs with optimization problems in the constraints. Oper Res 21:37–44
Bruninx K, Pandžić H, Le Cadre H, Delarue E (2020) On the interaction between aggregators, electricity markets and residential demand response providers. IEEE Trans Power Systems 35(2):840–853
Colson B, Marcotte P, Savard G (2005) Bilevel programming: a survey. Springer, Berlin, pp 87–107
Colson B, Marcotte P, Savard G (2007) An overview of bilevel optimization. Ann Oper Res 153(1):235–256
Dempe S (2002) Foundations of bilevel programming. Springer, Berlin
Dempe S, Dutta J (2012) Is bilevel programming a special case of a mathematical program with complementarity constraints? Math Program 131:37–48
Dempe S, Kalashnikov V, Perez-Valdes G, Kalashnikova N (2015) Bilevel programming: theory, algorithms and applications to energy networks. Springer, Berlin
Deng R, Yang Z, Chow M-Y, Chen J (2015) A survey on demand response in smart grids: mathematical models and approaches. IEEE Trans Ind Inform 11(3):570–582
Escudero LF, Monge JF, Rodriguez-Chia A (2020) On pricing-based equilibrium for network expansion planning. A multi-period bilevel approach under uncertainty. Eur J Oper Res 287(1):262–279
Eurelectric (2014) Flexibility and aggregation requirements for their interaction in the market 2014. https://www.eurelectric.org/media/115877/tf_bal-agr_report_final_je_as-2014-030-0026-01-e.pdf. 2019
Feng C, Li Z, Shahidehpour M, Wen F, Li Q (2020a) Stackelberg game based transactive pricing for optimal demand response in power distribution systems. Electr Power Energy Syst 118:105764
Feng C, Wang Y, Zheng K, Chen Q (2020b) Smart meter data-driven customizing price design for retailers. IEEE Trans Smart Grid 11(3):2043–2054
Fortuny-Amat J, McCarl B (1981) A representation and economic interpretation of a two-level programming problem. J Oper Res Soc 32(9):783–792
Garcia-Herreros P, Zhang L, Misra P, Arslan E, Mehta S, Grossmann IE (2016) Mixed-integer bilevel optimization for capacity planning with rational markets. Comput Chem Eng 86:33–47
Haghifam S, Dadashi M, Zare K, Seyedi H (2020) Optimal operation of smart distribution networks in the presence of demand response aggregators and microgrid owners: a multi follower bi-level approach. Sustain Cities Soc 55:102033
Jia Y, Mi Z, Yu Y, Song Z, Sun C (2018) A bilevel model for optimal bidding and offering of flexible load aggregator in day-ahead energy and reserve markets. IEEE Access 6:67799–67808
Jordehi AR (2019) Optimisation of demand response in electric power systems: a review. Renew Sustain Energy Rev 103:308–319
Kovács A (2019) Bilevel programming approach to demand response management with day-ahead tariff. J Mod Power Syst Clean Energy 7:1632–1643
Li Y, Li K (2019) Incorporating demand response of electric vehicles in scheduling of isolated microgrids with renewables using a bi-level programming approach. IEEE Access 7:116256–116266
Li Y, Yang Z, Li G, Mu Y, Zhao D, Chen C, Shen B (2018) Optimal scheduling of isolated microgrid with an electric vehicle battery swapping station in multi-stakeholder scenarios: a bi-level programming approach via real-time pricing. Appl Energy 232:54–68
Lozano L, Smith JC (2017) A value-function-based exact approach for the bilevel mixed-integer programming problem. Oper Res 65(3):768–786
Luo X, Liu Y, Liu J, Liu X (2020) Energy scheduling for a three-level integrated energy system based on energy hub models: a hierarchical Stackelberg game approach. Sustain Cities Soc 52:101814
Mahmoudi N, Saha TK, Eghbal M (2016) Demand response application by strategic wind power producers. IEEE Trans Power Systems 31:1227–1237
McCormick GP (1976) Computability of global solutions to factorable nonconvex programs: part I - convex underestimating problems. Math Program 10(1):147–175
Meng F, Zeng X-J, Zhang Y, Dent CJ, Gong D (2018) An integrated optimization + learning approach to optimal dynamic pricing for the retailer with multi-type customers in smart grids. Inf Sci 448–449:215–232
Mitsos A (2010) Global solution of nonlinear mixed-integer bilevel programs. J Global Optim 47(4):557–582
Pineda S, Bylling H, Morales JM (2018) Efficiently solving linear bilevel programming problems using off-the-shelf optimization software. Optim Eng 19(1):187–211
Pineda S, Morales JM (2019) Solving linear bilevel problems using big-Ms: not all that glitters is gold. IEEE Trans Power Systems 34(3):2469–2471
Pozo D, Sauma E, Contreras J (2017) Basic theoretical foundations and insights on bilevel models and their applications to power systems. Ann Oper Res 254:303–334
Quashie M, Marnay C, Bouffard F, Joós G (2018) Optimal planning of microgrid power and operating reserve capacity. Appl Energy 210:1229–1236
Rui T, Hu C, Li G, Tao J, Shen W (2019) A distributed charging strategy based on day ahead price model for PV-powered electric vehicle charging station. Appl Soft Comput 76:638–648
Sadati S, Moshtagh J, Shafie-khah M, Rastgou A, Catalão J (2019) Operational scheduling of a smart distribution system considering electric vehicles parking lot: a bi-level approach. Electr Power Energy Syst 105:159–178
Saez-Gallego J, Morales JM, Zugno M, Madsen H (2016) A data-driven bidding model for a cluster of price-responsive consumers of electricity. IEEE Trans Power Systems 31(6):5001–5011
Salyani P, Abapour M, Zare K (2019) Stackelberg based optimal planning of DGs and electric vehicle parking lot by implementing demand response program. Sustain Cities Soc 51:101743
Sekizaki S, Nishizaki I, Hayashida T (2016) Electricity retail market model with flexible price settings and elastic price-based demand responses by consumers in distribution network. Int J Electr Power Energy Syst 81:371–386
Sinha A, Malo P, Deb K (2018) A review on bilevel optimization: from classical to evolutionary approaches and applications. IEEE Trans Evol Comput 22(2):276–295
Soares I, Alves MJ, Antunes CH (2020) Designing time-of-use tariffs in electricity retail markets using a bi-level model – Estimating bounds when the lower level problem cannot be exactly solved. Omega 93:102027
Soares I, Alves MJ, Antunes CH (2019) A population-based approach to the bi-level multifollower problem: an application to the electricity retail market. Int Trans Oper Res. https://doi.org/10.1111/itor.12710
US Department of Energy (2006) Benefits of demand response in electricity markets and recommendations for achieving them. https://eetd.lbl.gov/sites/all/files/publications/report-lbnl-1252d.pdf
Vardakas JS, Zorba N, Verikoukis CV (2015) A Survey on demand response programs in smart grids: pricing methods and optimization algorithms. IEEE Commun Surv Tutor 17(1):152–178
Vicente LN, Calamai PH (1994) Bilevel and multilevel programming: a bibliography review. J Global Optim 5(3):291–306
von Stackelberg H (2011) The theory of the market economy. Springer-Verlag, Berlin
Wei W, Liu F, Mei S (2015) Energy pricing and dispatch for smart grid retailers under demand response and market price uncertainty. IEEE Trans Smart Grid 6(3):1364–1374
White D, Anandalingam G (1993) A penalty function approach for solving bi-level linear programs. J Global Optim 3:397–419
Yoon S-G, Choi Y-J, Park J-K, Bahk S (2016) Stackelberg-game-based demand response for at-home electric vehicle charging. IEEE Trans Veh Technol 65(6):4172–4184
Zhang N, Hu Z, Springe C, Li Y, Shen B (2016) A bi-level integrated generation-transmission planning model incorporating the impacts of demand response by operation simulation. Energy Convers Manag 123:84–94
Zugno M, Morales JM, Pinson P, Madsen H (2013) A bilevel model for electricity retailers' participation in a demand response market environment. Energy Econ 36:182–197
Acknowledgements
This work was partially supported by projects UIBD/00308/2020 and UIDB/05037/2020, and by the European Regional Development Fund through the COMPETE 2020 Programme, FCT—Portuguese Foundation for Science and Technology and Regional Operational Program of the Center Region (CENTRO2020) within projects ESGRIDS (POCI-01-0145-FEDER-016434), SUSPENSE (CENTRO-01-0145-FEDER-000006) and MAnAGER (POCI-01-0145-FEDER-028040).
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Henggeler Antunes, C., Alves, M.J. & Ecer, B. Bilevel optimization to deal with demand response in power grids: models, methods and challenges. TOP 28, 814–842 (2020). https://doi.org/10.1007/s11750-020-00573-y
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DOI: https://doi.org/10.1007/s11750-020-00573-y