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In this study, the concept of symmetry is introduced by finding the optimal state of a power system. An electric vehicle type load is present, where the supply stores’ electrical energy causes an imbalance in the system. The optimal conditions are related by adjusting the voltage of the bus location. The key variables are the load voltage deviation (LVD), the variation of the load and the power, and the sizing of the distributed photovoltaic (DPV), which are added to the system for power stability. Here, a method to optimize the fast-charging stations (FCSs) and DPV is presented using an optimization technique comparison. The system tests the distribution line according to the bus grouping in the IEEE 33 bus system. This research presents a hypothesis to solve the problem of the voltage level in the system using metaheuristic algorithms: the cuckoo search algorithm (CSA), genetic algorithm (GA), and simulated annealing algorithm (SAA) are used to determine the optimal position for DPV deployment in the grid with the FCSs. The LVD, computation time, and total power loss for each iteration are compared. The voltage dependence power flow is applied using the backward/forward sweep method (BFS). The LVD is applied to define the objective function of the optimization techniques. The simulation results show that the SAA showed the lowest mean computation time, followed by the GA and the CSA. A possible location of the DPV is bus no. 6 for FCSs with high penetration levels, and the best FCS locations can be found with the GA, with the best percentage of best hit counter on buses no. 2, 3, 13, 14, 28, 15, and 27. Therefore, FCSs can be managed and handled in optimal conditions, and this work supports future FCS expansion.

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