Benders decomposition applied to security constrained unit commitment: Initialization of the algorithm J. Alemany a,⇑ , F. Magnago a,b a Department of Electrical and Electronic Engineering, Universidad Nacional de Río Cuarto, Argentina b Nexant Inc., AZ, USA article info Article history: Received 5 December 2013 Received in revised form 3 August 2014 Accepted 12 October 2014 Available online 12 November 2014 Keywords: Benders decomposition Initialization methodology Mixed integer linear programming Security constrained unit commitment abstract Benders decomposition has been broadly used for security constrained unit commitment problems, despite the fact that it may present convergence difficulties due to instabilities and to the mixed integer nature of the unit commitment problem. The initialization of Benders decomposition has been recognized as a prominent feature for the algorithm enhancement. In this work, a new Benders decomposition ini- tialization methodology is proposed. The objective of the initialization is to include inexpensive network signals that can be added during the initial unit commitment master problem. Numerical simulations using the IEEE-118 and RTS-96 systems are performed to illustrate the benefits of the proposed initiali- zation methodology. Results suggest that the initialization of Benders decomposition applied to security constrained unit commitment problems improves the overall convergence of the algorithm. Ó 2014 Elsevier Ltd. All rights reserved. Introduction The unit commitment (UC) calculation is extensively used in daily power system operation. The UC is an exercise of large-scale, time-varying, non-convex, mixed-integer modeling and optimiza- tion. Security constrained unit commitment (SCUC) is an extension of conventional UC with the inclusion of system network constraints, in both normal and contingency operation states. The main objectives of the SCUC are to ensure not only the economic operation but also the security of the system [1,2]. These two dif- ferent objectives can be separately solved as a two-level optimiza- tion problem. It is a common practice to define a master level, which includes the UC calculation, and the sub-problem level, which checks the network security constraints. Benders Decomposition (BD) is an algorithm that has been broadly used for large-scale optimization problems, particularly for power systems [3,4]. BD has three main advantages: modular- ity, flexibility and robustness. With regard to modularity, master and sub-problems can be separately solved by specialized algorithms, thus providing speed and efficiency on the overall per- formance of the global optimization process. Additionally, Benders flexibility is mainly supported by the different existing power system applications. For example, it is possible to find its application in areas like security constrained economic dispatch [5], generation–transmission planning [6,7], hydrothermal coordination [8,9], and optimal power flow [10,11]. Finally, in rela- tion to robustness, despite the different nature of the master and the sub-problems in SCUC applications, both are essentially solved using Linear Programming (LP) algorithms. This is an important feature because LP algorithms are considered to be among the most mature methodologies in optimization techniques [12]. Nevertheless, since BD is a cutting-plane method [13], it may present instabilities which are translated into delays of the algo- rithm convergence [14,8]. In addition, since the master level is for- mulated as a mixed integer linear problem (MILP), the convergence time is strongly affected by the high computational burden of the master problem [15]. Therefore, there are many research efforts regarding BD improvements [16]. Among the different suggested possibilities, having a better initialization of BD is recognized by several authors as one of the most important enhancements, concluding that it could have a significant effect on BD performance. Several initialization methodologies have been developed. In [17] an initial set of cuts is constructed from routes of an aircraft routing model. The author concluded that the initial cuts are advisable to be used with any network, since there is a reduction in the total computation time. Furthermore, in [18] a strategy to initialize BD with the addition of a series of valid inequalities is developed. The initialization procedure is applied to a fixed charge network problem, and different variants of refinery systems are studied. http://dx.doi.org/10.1016/j.ijepes.2014.10.044 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: jalemany@ing.unrc.edu.ar (J. Alemany). Electrical Power and Energy Systems 66 (2015) 53–66 Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes