To address DC bus voltage fluctuations induced by sudden irradiance variations and load switching in photovoltaic storage microgrids, and to simultaneously enhance the system's anti-disturbance capability, dynamic response speed, and accuracy of current trajectory tracking, dual-loop cooperative control architecture was proposed. For the voltage outer loop, the optimized policy gradient (PG) algorithm was used to investigate the optimization of bandwidth parameters of linear active disturbance rejection control (LADRC), achieves adaptive parameter tuning without relying on an accurate system model. For the current inner loop, finite control set-model predictive control (FCS-MPC) was utilized to integrate a trajectory flexibility factor into the objective function. The comprehensive performance of current deviation and change rate was quantified, overcoming the defect of single performance optimization in traditional MPC. Based on the complementary characteristics of supercapacitors and batteries, the reference current output by the voltage outer loop was filtered and frequency-separated to generate differentiated current reference commands for energy storage units, thereby optimizing the power distribution efficiency of the energy storage system. Finally, simulations were conducted to compare the proposed coordinated control strategy with traditional proportional-integral (PI), MPC, and LADRC strategies, and the superiority of the proposed method was validated by overall performance indicators.