This article discusses the problem of minimizing power loss in unbalanced distribution systems through phase-balancing. This problem is represented by a mixed-integer nonlinear-programming mathematical model, which is solved by applying a discretely encoded Vortex Search Algorithm (DVSA). The numerical results of simulations performed in IEEE 8-, 25-, and 37-node test systems demonstrate the applicability of the proposed methodology when compared with the classical Cuh & Beasley genetic algorithm. In addition, the computation times required by the algorithm to find the optimal solution are in the order of seconds, which makes the proposed DVSA a robust, reliable, and efficient tool. All computational implementations have been developed in the MATLAB^® programming environment, and all the results have been evaluated in DigSILENT© software to verify the effectiveness and the proposed three-phase unbalanced power-flow method.

This article reviews the main methodologies employed for the optimal location, sizing, and operation of Distributed Generators (DGs) and Energy Storage Systems (ESSs) in electrical networks. For such purpose, we first analyzed the devices that comprise a microgrid (MG) in an environment with Distributed Energy Resources (DERs) and their modes of operation. Following that, we examined the planning and operation of each DER considered in this study (DGs and ESSs). Finally, we addressed the joint integration of DGs and ESSs into MGs. From this literature review, we were able to identify both the objective functions and constraints that are most commonly used to formulate the problem of the optimal integration and operation of DGs and ESSs in MGs. Moreover, this review allowed us to identify the methodologies that have been employed for such integration, as well as the current needs in the field. With this information, the purpose is to develop new mathematical formulations and approaches for the optimal integration and operation of DERs into MGs that provide financial and operational benefits.

This paper presents an Energy Management System (EMS) for solving the problem regarding the optimal daily operation of Photovoltaic (PV) distributed generators in Alternate Current (AC) distribution grids. To this effect, a nonlinear programming problem (NLP) was formulated which considered the improvement of economic (investment and maintenance costs), technical (energy losses), and environmental (${CO}_2$ emission) grid indices as objective functions, considering all technical and operating constraints for the operation of AC networks with the presence of PV sources. To solve this mathematical formulation, a master–slave methodology was implemented, whose master stage employed the antlion optimizer to find the power dispatch of PV sources in each period of time considered (24 h). In the slave stage, an hourly power flow based on the successive approximations method was used in order to obtain the values of the objective functions and constraints associated with each possible PV power configuration proposed by the master stage. To evaluate the effectiveness and robustness of the proposed methodology, two test scenarios were used, which included three installed PV sources in an urban and a rural network, considering the PV power generation and demand located reported for Medellín and Capurganá, respectively. These systems correspond to connected and standalone grids located in two different regions of Colombia. Furthermore, the proposed methodology was compared with three optimization methodologies reported in the literature: the Chu and Beasley genetic algorithm, the particle swarm optimization algorithm, and the vortex search optimization algorithm. Simulation results were obtained via the MATLAB software for both test scenarios with all the optimization methodologies. It was demonstrated that the proposed methodology yields the best results in terms of solution quality and repeatability, with shorter processing times.

This paper discusses the minimization of the total annual operative cost for a planning period of 20 years composed by the annualized costs of the energy purchasing at the substation bus summed with the annualized investment costs in photovoltaic (PV) sources, including their maintenance costs in distribution networks based on their optimal siting and sizing. This problem is presented using a mixed-integer nonlinear programming model, which is resolved by applying a master–slave methodology. The master stage, consisting of a discrete-continuous version of the Vortex Search Algorithm (DCVSA), is responsible for providing the optimal locations and sizes for the PV sources—whereas the slave stage employs the Matricial Backward/Forward Power Flow Method, which is used to determine the fitness function value for each individual provided by the master stage. Numerical results in the IEEE 33- and 69-node systems with AC and DC topologies illustrate the efficiency of the proposed approach when compared to the discrete-continuous version of the Chu and Beasley genetic algorithm with the optimal location of three PV sources. All the numerical validations were carried out in the MATLAB programming environment.