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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. [ABSTRACT FROM AUTHOR]

This paper proposes a new methodology based on the combination of symbiosis organism search (SOS) and neural network algorithm (NNA), named SOS-NNA, for the optimal planning and operation of distributed generations (DGs) and capacitor banks (CBs) in the radial distribution networks (RDNs) considering single- and multi-objective optimization with various equality and inequality constraints. The multi-objective framework is a weighted combination of five component objectives including active power loss, voltage deviation, voltage stability, load balancing, and supply reliability. In addition, practical voltage-dependent non-linear load models are also examined. Two benchmark instances 33 and 69-bus networks have been utilized to evaluate the effectiveness and feasibility of the proposed SOS-NNA via various case studies. The obtained outcomes for different operating cases and test scenarios reveal that the proper combination of optimal power factor DGs (OPF-DGs) and CBs can boost the network performance indexes to an ever-highest degree for all test networks. A cost–benefit analysis is further implemented to evaluate the economic feasibility of the obtained multi-objective solutions. As a result, the proposed SOS-NNA shows a marked improvement regarding the solution quality compared to the recently well-established optimization algorithms as well as outweighs the original NNA in the performance indexes of the solution quality, convergence speed, and statistical results. In addition, the proposed SOS-NNA has been employed for allocating different DG types in RDNs with the consideration of actual 24-h load profiles and the obtained outcomes contribute to the further improvement of yearly energy loss mitigation as well as cost savings. • A new hybrid algorithm SOS-NNA is proposed for distribution systems optimization. • A multi-objective framework relating to five technical objectives is presented. • The best planning and operation solution is given for distribution systems. • Voltage-dependent load model and hourly generation scheduling cases are examined. • The superiority of proposed hybrid algorithm over other algorithms is verified. [ABSTRACT FROM AUTHOR]