IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 27, NO. 1, FEBRUARY 2012 407 Yearly Maintenance Scheduling of Transmission Lines Within a Market Environment Hrvoje Pandˇ zic ´ , Student Member, IEEE, Antonio J. Conejo, Fellow, IEEE, Igor Kuzle, Senior Member, IEEE, and Eduardo Caro, Student Member, IEEE Abstract—Within a yearly horizon, a transmission system oper- ator needs to schedule the maintenance outages of the set of trans- mission lines due for maintenance. Facing this task, two conflicting objectives arise: on one hand, the transmission system adequacy should be preserved as much as possible, and, on the other hand, market operation should be altered in the least possible manner. To address this scheduling problem, a bilevel model is proposed whose upper-level problem schedules line maintenance outages pursuing maximum transmission capacity margin. This upper-level problem is constrained by a set of lower-level problems that represent the clearing of the market for all the time periods considered within the yearly planning horizon. This bilevel model is conveniently con- verted into a nonlinear mathematical program with equilibrium constraints (MPEC) that can be recast as a mixed-integer linear programming problem solvable with currently available branch- and-cut techniques. Index Terms—Line maintenance scheduling, market envi- ronment, mathematical program with equilibrium constraints (MPEC). NOTATION The main notation used throughout this paper is stated below for quick reference. Other symbols are defined as required in the text. A. Constants Susceptance of line (S). Destination bus of line . Capacity of the th block of the th demand in time period (MW). Capacity of the th block of the th generating unit in time period (MW). Manuscript received January 13, 2011; revised April 28, 2011; accepted June 08, 2011. Date of publication July 14, 2011; date of current version January 20, 2012. The work of H. Pandˇ zic ´ was supported by the National Foundation for Science, Higher Education and Technological Development of the Republic of Croatia through Project O-3554-2010. The work of A. J. Conejo and E. Caro was supported in part by Junta de Comunidades de Castilla-La Mancha through project PCI-08-0102 and in part by the Ministry of Education and Science of Spain through CICYT Project DPI2006-08001. Paper no. TPWRS-00027-2011. H. Pandˇ zic ´ and I. Kuzle are with University of Zagreb, Zagreb, Croatia (e-mail: hrvoje.pandzic@fer.hr; igor.kuzle@fer.hr). A. J. Conejo and E. Caro are with Universidad de Castilla-La Mancha, Ciudad Real, Spain (e-mail: antonio.conejo@uclm.es; eduardo.caro@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.2011.2159743 Weighting factor for line . Parameter used for linearizations (upper-level problem). Maximum number of lines simultaneously in maintenance. Origin bus of line . Number of time periods involving maintenance overlap for lines and . Transmission capacity of line (MW). Number of time periods. Weighting factor for line power flow in loading level . Limit for loading level of line power flow (%). Number of working week time periods required for maintenance of line . Number of weekend time periods required for maintenance of line . Parameter used for linearizations (lower-level problem). Price bid of the th block of the th demand ( /MW). Price offer of the th block of the th generating unit ( /MW). B. Variables Power consumed by the th block of the th demand in time period (MW). Power produced by the th block of the th generating unit in time period (MW). Power flow through line in time period (MW). Power flow for loading level of line in time period (MW). Absolute value of variable . Absolute value of variable . Binary variable that is equal to 1 if line is maintained during time period and 0 otherwise. Voltage angle at bus in time period (rad). 0885-8950/$26.00 © 2011 IEEE