IEEE TRANSACTIONS ON SMART GRID, VOL. 7, NO. 2, MARCH 2016 817 Incorporating Price-Responsive Demand in Energy Scheduling Based on Consumer Payment Minimization Ricardo Fernández-Blanco, Member, IEEE, José M. Arroyo, Senior Member, IEEE, Natalia Alguacil, Senior Member, IEEE, and Xiaohong Guan, Fellow, IEEE Abstract—In the restructured power industry, demand respon- siveness is a key factor whose importance will be boosted due to the impetus provided by the development of smart grids. Within the context of pool-based electricity markets, this paper addresses the incorporation of price-responsive demand in multiperiod energy scheduling driven by consumer payment minimization. Although consumer payment minimization has drawn considerable attention mainly in an operational setting and also recently under a planning framework, available models and solution approaches typically neglect demand-side partic- ipation. The proposed scheduling model considers a marginal pricing scheme as well as the effects of both network con- straints and intertemporal constraints associated with generation operation. Modeling demand-side participation leads to bilin- ear payment terms that significantly increase the mathematical complexity of the optimization process. The resulting problem is formulated as a mixed-integer nonlinear bilevel program for which no exact solution technique is currently available. This paper presents a novel methodology by which the origi- nal bilevel and bilinear problem is converted into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software. This transformation is based on the appli- cation of duality theory of linear programming, integer algebra, and Karush–Kuhn–Tucker optimality conditions. The proposed approach has been successfully applied to the IEEE 118-bus system. Index Terms—Bilevel programming, bilinear terms, consumer payment minimization, demand response, energy scheduling, marginal pricing, mixed-integer linear equivalent. Manuscript received September 23, 2014; revised January 23, 2015 and April 13, 2015; accepted April 26, 2015. Date of publication June 18, 2015; date of current version February 17, 2016. This work was supported in part by the Ministry of Science of Spain under CICYT Project ENE2012-30679, in part by the European Commission under Grant 309048 “SiNGULAR”, in part by the Junta de Comunidades de Castilla-La Mancha under Project POII-2014-012-P, and in part by the Universidad de Castilla-La Mancha under Grant GI20152945. Paper no. TSG-00946-2014. R. Fernández-Blanco is with the Department of Electrical Engineering, University of Washington, Seattle, WA 98195-2500 USA (e-mail: ricardo.fcarramolino@gmail.com). J. M. Arroyo and N. Alguacil are with the Departamento de Ingeniería Eléctrica, Electrónica, Automática y Comunicaciones, E.T.S.I. Industriales, Universidad de Castilla-La Mancha, Ciudad Real E-13071, Spain (e-mail: josemanuel.arroyo@uclm.es; natalia.alguacil@uclm.es). X. Guan is with the Systems Engineering Institute, SKLMSE Laboratory, and MOE KLINNS Laboratory, Xi’an Jiaotong University, Xi’an 710049, China, and also with the Center for Intelligent and Networked Systems and TNLIST, Tsinghua University, Beijing 100084, China (e-mail: xhguan@sei.xjtu.edu.cn). Digital Object Identifier 10.1109/TSG.2015.2427584 NOMENCLATURE Indices b Demand bid block. i Generating unit. j Consumer. l Transmission line. n Bus. n(i) Bus where generating unit i is located. n( j) Bus where consumer j is located. o Generation offer block. t Time period. Sets B j Indices of the demand bid blocks of consumer j. F it Feasibility set for the scheduling variables associ- ated with unit i in period t. I Indices of generating units. I n Indices of the generating units located at bus n. J Indices of consumers. J n Indices of the consumers located at bus n. L + t Indices of transmission lines for the constraints imposing the upper bounds on line power flows in period t. L - t Indices of transmission lines for the constraints imposing the lower bounds on line power flows in period t. N Indices of buses. O i Indices of the generation offer blocks of unit i. T Indices of time periods. Constants A ln Sensitivity factor for line l and bus n. C d bjt Price of the bth demand block bid by consumer j in period t. C g oit Price of the oth generation block offered by unit i in period t. n B j Cardinality of B j . n I Number of generating units. n J Number of consumers. n L + t Cardinality of L + t . n L - t Cardinality of L - t . n N Number of buses. n O i Cardinality of O i . n T Number of time periods. 1949-3053 c  2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.