Abstract
In this work, the implementation of an efficient multi-threading algorithm for calculating the power flow in electricity distribution networks is carried out using recursion and parallel programming. With the integration of renewable energy, energy storage systems and distributed generation, the ability of power flow simulations becomes a crucial factor in finding the best solution in the shortest possible time. We propose the direct use of graph theory to represent distribution network topologies. In this data structure, the traversal algorithms are inherently recursive, thus enabling the development of algorithms with parallel programming to obtain the power flow calculation faster and more efficiently. Results under a 809 buses test system show that the implementation provides additional computation efficiency of 32% with recursion techniques and 27% with parallel programming, due the expense of threads' allocation the combined gain reaches 50%. © 2024 IEEE.

Abstract
The intensification of environmental impacts and the increased economic risks are triggering a technological race towards a low-carbon economy. In this socioeconomic scenario of increasing changes and environmental concerns, microgrids (MGs) play an important role in integrating distributed energy resources. Thus, a planning strategy for grid-connected MGs with distributed energy resources and electric vehicle (EV) charging stations is proposed in this paper. The developedmathematical model aims to defineMGexpansion decisions that satisfy the growing electricity demand (including EV charging demand) at the lowest possible cost; such decisions include investments in PV units, wind turbines, energy storage systems, and EV charging stations. The objective function is based on the interests of the MG owner, considering constraints associated with the main distribution grid. A mixed-integer linear programming model is used to formulate the problem, ensuring the solution's optimality. The applicability of the proposed model is evaluated in the 69-bus distribution grid. Promising results concerning grid-connected MGs were obtained, including the enhancement of energy exchange with the grid according to their needs.