This technology refers to a control process for single-controllable low-voltage microgrids (Mgs) (SCM) having centralized communication. The process is based on the “Power-Based Control” (PBC) technique by adapting it to the context of SCMs through a modified PBC process (MPBC). The technology includes a process that provides the following technical effects: (1) sharing of active power and reactive power proportionately to the capacity of distributed energy resources (DERs or DGs) in the MG, for example, rendering the use of batteries based on different technologies (lead-acid, ion-lithium, etc.) compatible; (2) compensation for the current unbalance at the point of common coupling (PAC); (3) allows exploration of battery banks by balancing the charging status of storage elements; (4) allows implementation of the control process without knowing the electrical grid's parameters and topology; (5) is able to deal with the arbitrary connection of inverters into the MG, in addition to other advantages. The technology is applied in the technical field of equipment and infrastructure for the development of MGs.