This paper presents an optimized control structure for a PV microgrid based on a three-phase quasi-Z source inverter (qZSI) ensuring enhanced power quality in the stand-alone mode of operation. The control strategy adopted consists of three control stages. The first control stage is used to optimize the energy efficiency of the photovoltaic (PV) generator under various irradiation conditions. An indirect control-based maximum power point tracking (MPPT) procedure is implemented. The second controller stabilizes DC-bus voltage to maintain the power balance between the PV energy source and a nonlinear (NL) load demand through a battery connected to the qZSI capacitor via a bidirectional DC/DC converter. The third control stage regulates the output AC voltage and current of the qZSI to their references. A fractional-order PID controller (FOPID) is adopted for all control stages to ensure good tracking under various scenarios: changing irradiation conditions, non-linearity of the load, and its variation. The yellow saddle goatfish algorithm (YSGA) is used to calculate the control parameters. Simulation results are performed to highlight the presented approach performance.