This paper presents the mathematical modeling and control design procedure of the compressor motor of an air conditioner using the energy from a photovoltaic system combined with the power grid in a DC microgrid. A comprehensive model considers the interconnection of the photovoltaic cells with their associated DC/DC converter, the DC bus, the three-phase squirrel-cage induction motor with its driver, the bidirectional DC/AC converter, the output filter, and the power grid. The state-of-the-art showed that a complete mathematical model of the proposed system is unavailable. Therefore, the mathematical model of the system is compared and validated in simulation with a block diagram in the Matlab/Simulink environment. In addition, several control approaches are used in the whole system to track the maximum power point of the photovoltaic cells, obtain a soft start on the machine, control the velocity using the variable frequency drive, regulate the DC bus voltage, and manage the power flow between the DC bus and the power grid.