128 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 26, NO. 1, FEBRUARY 2011 Optimal Contract Pricing of Distributed Generation in Distribution Networks Jesús María López-Lezama, Student Member, IEEE, Antonio Padilha-Feltrin, Senior Member, IEEE, Javier Contreras, Senior Member, IEEE, and José Ignacio Muñoz Abstract—This paper proposes a bilevel programming ap- proach to determine the optimal contract price of dispatchable distributed generation (DG) units in distribution systems. Two different agents are considered in the model, namely, the distri- bution company (DisCo) and the owner of the DG. The former seeks the minimization of the payments incurred in attending the forecasted demand, while the latter seeks the maximization of his profit. To meet the expected demand, the DisCo has the option to purchase energy from any DG unit within its network and directly from the wholesale electricity market. A traditional distribution utility model with no competition among DG units is considered. The proposed model positions the DG owner in the outer optimization level and the DisCo in the inner one. This last optimization problem is substituted by its Karush-Kuhn-Tucker optimality conditions, turning the bilevel programming problem into an equivalent single-level nonlinear programming problem which is solved using commercially available software. Tests are performed in a modified IEEE 34-bus distribution network. Index Terms—Bilevel programming, distributed generation, dis- tribution networks. NOMENCLATURE Indices: Bus indexes. Distributed generation unit index. Substation index. Index of line connecting nodes , . Parameters: Wholesale energy price at substation in period [ /MWh]. Length of the time interval [h]. Manuscript received September 21, 2009; revised February 02, 2010. First published May 10, 2010; current version published January 21, 2011. This work was supported in part by the Ministry of Education and Science of Spain grants ENE2006-02664 and HBP2008-0022, the University of Castilla – La Mancha through the Program of Stays of Latin American Professors, CAPES, CNPq (process: 308010/2006-0), Fapesp (process: 2007/07041-3), and Universidad de Antioquia. Paper no. TPWRS-00747-2009. J. M. López-Lezama is with Group of Efficient Energy Manage- ment (GIMEL), Universidad de Antioquia, Medellín, Colombia (e-mail: lezama@udea.edu.co). A. Padilha-Feltrin is with Universidade Estadual Paulista (UNESP), Ilha Solteira SP, Brasil (e-mail: padilha@dee.feis.unesp.br). J. Contreras and J. I. Muñoz are with E.T.S. de Ingenieros Industriales, Uni- versidad de Castilla–La Mancha, 13071 Ciudad Real, Spain (e-mail: Javier.Con- treras@uclm.es; JoseIgnacio.Munoz@uclm.es). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2010.2048132 Impedance of line connecting nodes [ ]. Maximum active power limit in line [MW]. Maximum voltage limit in bus [V]. Minimum voltage limit in bus [V]. Maximum active power limit of DG unit [MW]. Minimum active power limit of DG unit [MW]. Maximum active power limit of substation [MW]. Minimum active power limit of substation [MW]. Production cost of DG unit [ /MWh]. Active power demand in bus in period [MW]. Variables: Active power supplied by substation in period [MW]. Active power supplied by DG unit in period [MW]. Contract price of DG unit [ /MWh]. Voltage magnitude of node in period [V]. Dual variable associated with the constraint of maximum active power flow limit of the line connecting the nodes , in period . Dual variable associated with the constraint of minimum active power flow limit of the line connecting the nodes , in period . Dual variable associated with the constraint of maximum voltage in node in period . Dual variable associated with the constraint of minimum voltage in node in period . Dual variable associated with the constraint of power balance equation in node in period . Dual variable associated with the constraint of maximum active power generated by DG unit in period . 0885-8950/$26.00 © 2010 IEEE