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Bilevel optimization to deal with demand response in power grids: models, methods and challenges

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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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Asimakopoulou GE, Dimeas AL, Hatziargyriou ND (2013) Leader-follower strategies for energy management of multi-microgrids. IEEE Trans Smart Grid 4:1909–1916

    Google Scholar 

  • Asimakopoulou GE, Vlachos AG, Hatziargyriou ND (2015) Hierarchical decision making for aggregated energy management of distributed resources. IEEE Trans Power Systems 30:255–3264

    Google Scholar 

  • 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

    Google Scholar 

  • Bard J (1998) Practical bilevel optimization: algorithms and applications. Springer, Berlin

    Google Scholar 

  • Bialas WF, Karwan MH (1984) Two-level linear programming. Manag Sci 30(8):1004–1020

    Google Scholar 

  • Bracken J, McGill J (1973) Mathematical programs with optimization problems in the constraints. Oper Res 21:37–44

    Google Scholar 

  • 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

    Google Scholar 

  • Colson B, Marcotte P, Savard G (2005) Bilevel programming: a survey. Springer, Berlin, pp 87–107

    Google Scholar 

  • Colson B, Marcotte P, Savard G (2007) An overview of bilevel optimization. Ann Oper Res 153(1):235–256

    Google Scholar 

  • Dempe S (2002) Foundations of bilevel programming. Springer, Berlin

    Google Scholar 

  • Dempe S, Dutta J (2012) Is bilevel programming a special case of a mathematical program with complementarity constraints? Math Program 131:37–48

    Google Scholar 

  • Dempe S, Kalashnikov V, Perez-Valdes G, Kalashnikova N (2015) Bilevel programming: theory, algorithms and applications to energy networks. Springer, Berlin

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Jordehi AR (2019) Optimisation of demand response in electric power systems: a review. Renew Sustain Energy Rev 103:308–319

    Google Scholar 

  • Kovács A (2019) Bilevel programming approach to demand response management with day-ahead tariff. J Mod Power Syst Clean Energy 7:1632–1643

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Lozano L, Smith JC (2017) A value-function-based exact approach for the bilevel mixed-integer programming problem. Oper Res 65(3):768–786

    Google Scholar 

  • 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

    Google Scholar 

  • Mahmoudi N, Saha TK, Eghbal M (2016) Demand response application by strategic wind power producers. IEEE Trans Power Systems 31:1227–1237

    Google Scholar 

  • McCormick GP (1976) Computability of global solutions to factorable nonconvex programs: part I - convex underestimating problems. Math Program 10(1):147–175

    Google Scholar 

  • 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

    Google Scholar 

  • Mitsos A (2010) Global solution of nonlinear mixed-integer bilevel programs. J Global Optim 47(4):557–582

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Quashie M, Marnay C, Bouffard F, Joós G (2018) Optimal planning of microgrid power and operating reserve capacity. Appl Energy 210:1229–1236

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Vicente LN, Calamai PH (1994) Bilevel and multilevel programming: a bibliography review. J Global Optim 5(3):291–306

    Google Scholar 

  • von Stackelberg H (2011) The theory of the market economy. Springer-Verlag, Berlin

    Google Scholar 

  • 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

    Google Scholar 

  • White D, Anandalingam G (1993) A penalty function approach for solving bi-level linear programs. J Global Optim 3:397–419

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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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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Correspondence to Carlos Henggeler Antunes.

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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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