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The expected growth of the number of electric vehicles can be challenging for planning and operating power systems. In this sense, distribution networks are considered the Achilles' heel of the process of adapting current power systems for a high presence of electric vehicles. This paper aims at deciding the maximum number of three-phase high-power charging points that can be installed in a low-voltage residential distribution grid. In order to increase the number of installed charging points, a mixed-integer formulation is proposed to model the provision of decentralized voltage support by electric vehicle chargers. This formulation is afterwards integrated into a modified AC optimal power flow formulation to characterize the steady-state operation of the distribution network during a given planning horizon. The performance of the proposed formulations have been tested in a case study based on the distribution network of La Graciosa island in Spain. [ABSTRACT FROM AUTHOR]