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Top1. Introduction
The expansion and increasing of load demand in EDS lead to challenges its planning and operation. The reconfiguration of distribution networks has been investigated as an attractive option to handle problems related to EDS, as the voltage instability. The reconfiguration consists of determining a connected and radial topology for the network through the definition of the statuses, open or closed, of the maneuverable switches.
The EDS voltage stability problem occurs due to the fast voltage drop at the network busbars caused by high feeder loading levels, which limits the increasing of the load supply by the utilities (Mahmoud, 2012). Voltage stability can be defined as the system capacity to maintain the voltages within suitable levels according with the power transfer capacity of the feeders (Guiping et al., 2009). Therefore, voltage stability is a security requirement for electrical power systems.
Problems as blackouts can be caused by unsuitable voltage levels for electrical energy distribution (Mahmoud, 2012). Such problems arise due to high and fast nodal voltage drops and occur with high frequency and severity in EDS (Guiping et al., 2009). Thus, the voltage stability problem has been receiving ever more attention all over the word and there are different feasible options, as the network reconfiguration, as proposed to be investigated in this paper.
Indexes have been proposed in the literature since the 1990s to measure the voltage stability level (Zheng & Kezunovic, 2010). Such indexes consist of numeric parameters that help the operator to monitor the distance between the current system state and the voltage collapse as well as to make decision to avoid collapse.
A voltage stability index is proposed by Chakravorty and Das (2001), which is derived from an equation that addresses the nodal voltages of the distribution branches with each other. The index can vary between '0' and '1' and the authors show that the lower index is the most sensitive to the voltage collapse, leading the system to the instability. Another index is presented by Eminoglu and Hocaoglu (2007), formulated from the active and reactive power flow equations for the network branches. In this case, the lower index is also the most sensitive to the voltage instability, i.e., the critical busbar.
Jasmon and Lee (1993) present a voltage stability index for radial networks that depends on the equivalent impedance of the distribution branches and on the system total load. Several programming models proposed in the literature are based on the Thevenin equivalent of the transmission system (Wiszniewski, 2007) to assess the voltage stability at the connection point between transmission and distribution systems. Such methods allow reducing the problem dimension and the related computational times. However, the impedances of the transformer and the distribution branches impact on the voltage stability indexes.
Following the EDS optimal reconfiguration proposal, a hybrid technique based on the concepts of quantum mechanics and AIS is proposed by Ahmad et al. (2012) to minimize active power losses and to maximize the voltage stability. Studies are presented by considering such objectives separately from each other and by considering them simultaneously through a multiobjective problem with weighting strategy.
The reconfiguration problem requires nonlinear mixed integer mathematical programming comprising continuous and discrete variables for a computational tool supported solution. In this sense, suitable and efficient approaches with such features are necessary, as metaheuristic techniques and bioinspired methods as the AIS, whose application for the problem is investigated by Oliveira et al. (2014) and Resende et al. (2011) for loss minimization. In (Resende et al., 2011), the objective is to minimize technical losses considering a unique load level, whereas Oliveira et al. (2014) include different load levels in the analysis through segmented diary load levels.