In this paper, a novel perturbation observer based fractional-order PID (PoFoPID) control scheme is proposed for a grid-connected Photovoltaics (PV) inverter to harvest the available maximum solar energy from the PV arrays under various atmospheric conditions. A high-gain state and perturbation observer (HGSPO) is adopted to efficiently estimate the aggregated effect of PV inverter nonlinearities, parameter uncertainties, unmodelled dynamics, stochastic fluctuation of atmospheric conditions, and external disturbances. Then, a fractional-order PID (FoPID) control is employed to fully compensate the perturbation estimate and to significantly improve the dynamical responses of the closed-loop system, in which Yin-Yang-Pair optimization (YYPO) algorithm is used to rapidly and effectively seek its optimal control parameters. Inspiringly, PoFoPID control can simultaneously own the elegant merits of global control consistency and robustness of perturbation observer based control, high reliability and simple structure of FoPID control, as well as the global optimality of YYPO algorithm. Four case studies including the solar irradiation change, temperature variation, power grid voltage drop, and inverter parameter uncertainties are undertaken. Simulation results verify the effectiveness and superiority of the PoFoPID control compared to that of PID control, FoPID control, feedback linearization control (FLC), and sliding-mode control (SMC), respectively. At last, a dSpace based hardware-in-loop (HIL) experiment is carried out to validate the implementation feasibility of PoFoPID control.