The central inverter topology presents some advantages such as simplicity, low cost and high conversion efficiency, being the first option for interfacing photovoltaic mini-generation, whose shading and panel orientation studies are evaluated in the project planning phase. When it uses only one power converter, its control structures must ensure synchronization with the grid, tracking the maximum power generation point, appropriate power quality indices, and control of the active and reactive power injected into the grid. This work develops and contributes to mathematical models, the principles of formation of control structures, the decoupling process of the control loops, the treatment of nonlinearities, and the tuning of the controllers of a single-stage photovoltaic system that is integrated into the electrical grid through a three-phase voltage source inverter. Using the parameters and configurations of an actual inverter installed at the power plant CRESP (Reference Center for Solar Energy of Petrolina), mathematical modeling, implementation, and computational simulations were conducted in the time domain using MatLab^® software (R2021b). The results of the currents injected into the grid, voltages, active powers, and power factor at the connection point with the grid are presented, analyzed, and compared with real measurement data during one day of operation.