Accurate modeling of Battery Energy Storage Systems (BESS) is essential for optimizing system performance, ensuring operational safety, and extending service life in applications ranging from electric vehicles (EV) to large-scale grid storage. However, the simplifications inherent in conventional battery models often hinder optimal system design and operation, leading to conservative performance limits, inaccurate State-of-Energy (SOE) estimation, and reduced overall efficiency. This paper presents a framework for advanced battery modeling, developed to achieve higher fidelity in SOE estimation and improved power-capability prediction. The proposed model introduces a dynamic energy-based representation of the charging and discharging processes, incorporating a functional dependence of instantaneous power on stored energy. Experimental validation confirms the superiority of this modeling framework over existing state-of-the-art models. The proposed approach reduces SOE estimation error to 0.1% and cycle-time duration error to 0.82% compared to the measurements. Consequently, the model provides more accurate predictions of the maximum charge and discharge power limits than state-of-the-art solutions. The enhanced predictive accuracy improves energy utilization, mitigates premature degradation, and strengthens safety assurance in advanced battery management systems.