Fields of hybrid electric vehicles (HEVs) and renewable energies require energy storage systems operating in a partial state of charge (PSOC). The ultra-battery combines an asymmetric supercapacitor and a lead-acid battery in a unit cell and is compatible with the PSOC mode. In this study, a mathematical model is presented for numerical simulation of the ultra-battery. The electrochemical model of lead-acid batteries is extended to simulate the ultra-battery. The two key roles of carbon, namely, double layer capacitance and electrodeposition of lead on carbon surfaces, are considered in the present model. A good agreement is observed between the results and experimental data during the validation in a simple discharge, rest and charge process. The high rate partial state of charge (HRPSOC) is also simulated. The HRPSOC results show that double layer capacitance protects the lead part of the negative electrode from being discharged and charged at a high rate. In addition, deposited lead on the carbon surfaces creates a pseudocapacitance effect which shares a considerable part of the current during HRPSOC cycling. Overall, the present model can predict the behavior of the negative electrode and contribution of lead and carbon parts, which is desirable but challenging in experiments. (C) 2019 The Electrochemical Society.