Development of a fast and accurate tool for simulation of batteries is greatly interested in the applications which require real-time estimation of the battery operating status, e.g., battery monitoring, online prognostics, and control. This study proposes three lumped model for the real-time simulation of Lead-acid batteries. The first one, named ordinary lumped model, replaces the elliptic terms in the governing equations with engineering approximations. The second and third models are structure-based lumped models which are developed based on dominant structures (modes) of the acid concentration field. Proper orthogonal decomposition and cluster analysis are utilized as reduced-order models to extract the dominant structures. All models are capable of predicting the transient behavior of lead-acid batteries during charge and discharge processes in terms of acid concentration, state of charge, cell voltage, and electrodes’ porosity and active-area. The proposed models provide good consistency with previous experimental and numerical studies. Moreover, they produce results in a fraction of a second and simulate the battery orders of magnitude (∼103) faster than the finite-volume method. Furthermore, the results show that structure-based lumped models improve the accuracy of ordinary lumped model significantly.