Smart grids and their technologies transform the traditional electric grids to assure safe, secure, cost-effective, and reliable power transmission. Non-linear phenomena in power systems, such as voltage collapse and oscillatory phenomena, can be investigated by chaos theory. Recently, renewable energy resources, such as wind turbines, and solar photovoltaic (PV) arrays, have been widely used for electric power generation. The design of the controller for the direct Current (DC) converter in a PV system is performed based on the linearized model at an appropriate operating point. However, these operating points are everchanging in a PV system, and the design of the controller is usually accomplished based on a low irradiance level. This study designs a fractional-order proportional-integrated-derivative (FOPID) controller using deep learning (DL) with quasi-oppositional Archimedes Optimization algorithm (FOPID-QOAOA) for cascaded DC-DC converters in micro-grid applications. The presented FOPID-QOAOA model is designed to enhance the overall efficiency of the cascaded DC-DC boost converter. In addition, the proposed model develops a FOPID controller using a stacked sparse autoencoder (SSAE) model to regulate the converter output voltage. To tune the hyper-parameters related to the SSAE model, the QOAOA is derived by the including of the quasi-oppositional based learning (QOBL) with traditional AOA. Moreover, an objective function with the including of the integral of time multiplied by squared error (ITSE) is considered in this study. For validating the efficiency of the FOPID-QOAOA method, a sequence of simulations was performed under distinct aspects. A comparative study on cascaded buck and boost converters is carried out to authenticate the effectiveness and performance of the designed techniques.