Bilevel optimization to deal with demand response in power grids: models, methods and challenges
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Bilevel optimization to deal with demand response in power grids: models, methods and challenges Carlos Henggeler Antunes1 · Maria João Alves2 · Billur Ecer3 Received: 23 December 2019 / Accepted: 13 June 2020 © Sociedad de Estadística e Investigación Operativa 2020
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. Keywords Bilevel optimization · Demand response · Power grids · Power systems Mathematics Subject Classification 90-02 (Research exposition (monographs, survey articles) pertaining to operations research mathematical programming) · 90C26 (Nonconvex programming, global optimization) · 90C90 (Applications of mathematical programming)
* Carlos Henggeler Antunes [email protected]; [email protected]; [email protected] 1
INESC Coimbra, Department of Electrical and Computer Engineering, University of Coimbra, Rua Sílvio Lima, Polo 2, 3030‑290 Coimbra, Portugal
2
CeBER and Faculty of Economics, University of Coimbra, Av. Dias da Silva 165, 3004‑512 Coimbra, Portugal
3
Industrial Engineering Department, Ankara Yildirim Beyazit University, Ankara, Turkey
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1 Introduction Bilevel optimization (BLO) models enable to formulate problems involving noncooperative hierarchical decision processes. These models have their roots in the leader–follower duopoly model presented by Stackelberg in his book “Market Structure and Equilibrium”, first published in German in 1934 (von Stackelberg 2011). For this reason, the solution of a BLO problem is also called Stackelberg equilibrium, although this type of problem had been introduced in the mathematical programming community about 40 years late with the work of Bracken and McGill (1973). In a Stackelberg equilibrium, the leader forms a conjecture about the follower’s reaction and acts in such a way that the ensuing the follower’s behavior provides the leader with an advantage. In a BLO model, the leader (upper level—UL) and the follower (lower level— LL) decision-makers control different sets of variables and have, in general, objective functions displaying some antagonism and being subject to interdependent constraints (i.e., involving variables of both levels). The LL problem belongs to the constraint set of the UL problem
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