Optimal Selection and Location of Fixed-Step Capacitor Banks in Distribution Networks Using a Discrete Version of the Vortex Search Algorithm

Abstract

This paper deals with the problem of the optimal selection of capacitor banks in electrical AC distribution systems for minimizing the costs of energy losses during a year of operation through a discrete version of the vortex search algorithm (DVSA). This algorithm works with a hypersphere with a variable radius defined by an exponential function where a Gaussian distribution is used to generate a set of candidate solutions uniformly distributed around the center of this hypersphere. This center corresponds to the best solution obtained at the iteration t, which is initialized at the center of the solution space at the iterative search beginning. The main advantage of combining the exponential function with the Gaussian distribution is the correct balance between the exploration and exploitation of the solution space, which allows reaching the global optimal solution of the optimization problem with a low standard deviation, i.e., guaranteeing repeatability at each simulation. Two classical distribution networks composed of 33 and 69 nodes were used to validate the proposed DVSA algorithm. They demonstrated that the DVSA improves numerical reports found in specialized literature regarding the optimal selection and location of fixed-step capacitor banks with a low computational burden. All the simulations were carried out in MATLAB software.

Reduction of Losses and Operating Costs in Distribution Networks Using a Genetic Algorithm and Mathematical Optimization

“…A set of rates was created for this, that is supposed to be reported by the network operator to the liquidator or accounts manager in the first 10 days of each year [18]. In order to guarantee the service quality for end customers and increase the economic benefits for network operators, in this work, the implementation of a discrete genetic algorithm for the optimal siting and sizing of fixed-step capacitor banks is proposed for solving the mixed-integer non-linear programming (MINLP) model that represents the problem [11]. Additionally, this mathematical model is implemented using the General Algebraic Modeling System (GAMS) software by comparing the results obtained with the method proposed [19].…”

“…Finally, the authors of [11] presented a master-salve optimization algorithm for the selection and location of fixed-step capacitor banks in distribution systems. In the master stage, a discrete version of the vortex search optimization algorithm was employed that determines the siting and sizing of the capacitors via a unique codification vector.…”

“…The fixed-step capacitor banks siting and sizing problem is represented via an integer codification and the classic optimization method is applied based on the CBGA, which reaches the optimal solution of the problem in minimum computational times when compared with the results reported in [11]. The solution developed from the interaction between the CBGA and the successive approximations method can be implemented in any radial or meshed distribution system.…”

“…It is important to mention that while genetic algorithms have been widely reported in the specialized literature to solve the problem of optimal selection and location of capacitor banks, as presented in the review of the state of the art, the solutions reported get stuck in local optimums due to the binary codification of two stages that are commonly used for node selection, which increases the algorithm's complexity and the possibility to obtain infeasible configurations. Furthermore, in this work, the problem of the binary codification is solved using the discrete codification presented in [11], thus accelerating the computational times and reaching the convergence to the best optimal solution reported in the specialized literature.…”

“…The large percentage of losses found in distribution systems and the high levels of investment, operation, and maintenance required have prompted network operators to perform significant amount of research to determine the most practical and economic solutions for reducing the operative costs associated with energy losses [10,11], as the good management of this issue will greatly impact the system's efficiency and the power supply service's profitability [8]. Network operators have found that locating distributed generators and capacitor banks in parallel is the most popular mechanism to improve the system performance, as these reduce losses and improve voltage profile [12,13].…”