This paper introduces a physical–chemical model that governs the lithium ion (Li-ion) battery performance. It starts from the model of battery life and moves forward with simplifications based on the single-particle model (SPM), until arriving at a more simplified and computationally fast model. On the other hand, the implementation of this model is developed through MATLAB. The goal is to characterize an Li-ion cell and obtain its charging and discharging curves with different current rates and different cycle depths, as well as its transitory response. In addition, the results provided are represented and compared, and different methods of estimating the state of the batteries are applied. They include the dynamics of the electrolyte and the effects of aging caused by a high number of charging and discharging cycles of the batteries. A complete comparison with the three-parameter method (TPM) is represented in order to demonstrate the superiority of the applied methodology.