The parameter extraction of parameters for Li-ion batteries is regarded as a critical topic for assessing the performance of battery energy storage systems (BESSs). The supply–demand algorithm (SDA) is used in this work to identify a storage system’s unknown parameters. The parameter-extracting procedure is represented as a nonlinear optimization task in which the state of charge (SOC) is approximated using nonlinear features related to the battery current and the initial SOC condition. Furthermore, the open-circuit voltage is approximated using the resulting SOC, which is performed in a nonlinear formula, as well. When used in the dynamic nonlinear BESS model, the SDA was used to verify the fitness values and standard deviation error. Furthermore, the results that were acquired using SDA are compared to recently developed approaches, which are the gradient-based, tuna swarm, jellyfish, heap-based, and forensic-based optimizers. Simulated studies were paired with experiments for the 40 Ah Kokam Li-ion battery and the ARTEMIS driving-cycle pattern. The numerical outcomes showed that the proposed SDA is an approach which is excellent at identifying the parameters. Furthermore, when compared to the other current optimization techniques, for both the Kokam Li-ion batteries and the ARTEMIS drive-cycle pattern, the suggested SDA exhibited substantial precision.