2166 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 4, OCTOBER 2009 Distribution Systems Reconfiguration Based on OPF Using Benders Decomposition H. M. Khodr, Member, IEEE, J. Martínez-Crespo, M. A. Matos, Member, IEEE, and J. Pereira Abstract—This paper presents a new and efficient methodology for distribution network reconfiguration integrated with optimal power flow (OPF) based on a Benders decomposition approach. The objective minimizes power losses, load balancing among feeders, and is subject to constraints: capacity limit of branches, minimum and maximum power limits of substations or distributed generators, minimum deviation of bus voltages, and radial optimal operation of networks. A specific approach of the Generalized Benders decomposition algorithm is applied to solve the problem. The formulation can be embedded under two stages: the first one is the Master problem and is formulated as a mixed integer nonlinear programming problem. This stage determines the radial topology of the distribution network. The second stage is the Slave problem and is formulated as a nonlinear programming problem. This stage is used to determine the feasibility of the Master problem solution by means of an OPF and provides information to formulate the linear Benders cuts that connect both problems. The model is programmed in the General Algebraic Modeling System. The effectiveness of the proposal is demonstrated through three examples extracted from the literature. Index Terms—Benders decomposition, distribution system, op- timal power flow (OPF), optimization, reconfiguration. NOMENCLATURE Set of buses of the network. Subset of the load buses of the network. Subset of the PV buses of the network. Subset of load buses where there are capacitor banks. Set of lines connected to bus . Subset of lines that leave node . Subset of lines that enter node . Set of transformers or generators connected at bus . Set of capacitor banks or reactors. Manuscript received June 03, 2008; revised April 03, 2009. Current version published September 23, 2009. This work was supported in part by FCT, in part by FEDER, in part by POCTI, in part by POSI, in part by POCI, in part by POSC, and in part by PTDC. Paper no. TPWRD-00428-2000. H. M. Khodr is with the GECAD-Knowledge Engineering and Decision- Support Research Center of the Electrical Engineering-Polytechnic Institute of Porto (ISEP/IPP), Porto 4200-072, Portugal (e-mail: hmk@isep.ipp.pt). J. Martínez-Crespo is with the Electrical Department of the Universidad Carlos III de Madrid, Madrid 28911, Spain. M. A. Matos and J. Pereira are with INESC Porto and also with the Engi- neering and Economics Faculty, University of Porto, Porto 4200-465, Portugal. Digital Object Identifier 10.1109/TPWRD.2009.2027510 Set of blocks of capacitor banks. Load connected at node (in kilovolt amperes). Apparent power (in kilovolt amperes) of line connected at bus . Maximum power limit established at line connected at bus . Minimum admissible load imposed by standards of the corresponding companies (in kilovolt amperes). Maximal apparent power of each transformation point (in kilovolt amperes). Decision variable to connect line to node . Decision variable to connect transformer/ generator at node . Decision variable to connect block of capacitor at node . Losses cost coefficient due to the power circulating at line connected at bus (in dollars per kilovolt per year). Real power output of the generating unit or transformer at bus . Maximum real power output of generation unit or transformer . Minimum real power output of the generation unit or transformer . Reactive power output of the generating unit or transformer at bus . Maximum reactive power output of the generation unit . Minimum reactive power output of the generation unit . Susceptance of the capacitor connected at bus . Reactive power output of capacitor connected at bus . Bus voltage magnitude at bus . Phase angle at bus . Real term of the element in the bus admittance matrix. 0885-8977/$26.00 © 2009 IEEE Authorized licensed use limited to: Instituto Politecnico do Porto. Downloaded on March 18,2010 at 07:44:47 EDT from IEEE Xplore. Restrictions apply.