The research investigates power system stability, load balancing, and voltage regulation improvements with BESS. Simulations and experiments utilizing MATLAB/Simulink, ADS, and Python-based machine learning models were used for analysis. Average efficiency, signal linearity, and power gain of the power amplifier were 72.4% with peaks of 87% under ideal conditions. Heat sinks and phase-change materials kept peak operation temperatures below 85°C. The BESS-Lithium Ion-battery integration reduced voltage variations for charging cycles by ±8% to ±2% and improved charge/discharge efficiency to 94.5% and 92.7%, respectively. Envelope Tracking, Load-Pull Optimization, and Adaptive Biasing enhanced efficiency, signal distortion, and power handling capacity dramatically. Neural Networks, Genetic Algorithms, and Reinforcement Learning, which had a 42ms latency, had been used to optimize power conversion and compute efficiency. High-efficiency power amplifiers and BESS improve efficiency, stability, and performance in modern power systems and help build a sustainable and stable grid infrastructure.