The increase in renewable energy resource based electricity generation in the past few years can be attributed to dwindling fossil fuels and their negative environmental impact, as well as the exponential expansion of electricity consumption. Furthermore, RERs are environmentally benign and sustainable. This manuscript proposes a hybrid method for managing power in a Hybrid Energy Storage System within a grid-independent Hybrid Renewable Energy System. The proposed hybrid technique combines the Prairie Dog Optimization (PDO) and Multi-scale Attention Convolutional Neural Network, hence named the PDO-MACNN technique. The principal objective of the proposed method is to minimize Total Harmonic Distortion (THD), maintain active power stability among generation and consumption through the charging or discharging of the Hybrid Energy Storage System, and regulate the DC-link voltage within strict bounds. The PDO algorithm is used to optimize the parameters of the three-phase inverter controller, while the MACNN algorithm is used to predict the performance of the hybrid renewable energy systems. The proposed approach is evaluated and compared to other existing methods on the MATLAB platform, demonstrating superior performance to methods like the Whale Optimization Algorithm, Seeker Optimization Algorithm, and Grasshopper Optimization Algorithm. Based on the outcome, it is concluded that the proposed approach achieves a 0.8 % lower THD compared to the existing techniques.