Pb-Acid batteries are excellent candidates for hybrid and electric locomotive, primarily due to their low cost. Model-based design, estimation, and control of a Pb-Acid energy storage system for a locomotive requires the development of efficient and accurate models. This paper presents a first principles model based on the fundamental governing equations of species and charge conservation for a Pb-Acid cell. The governing equations are discretized using a Ritz method to produce a low order and numerically efficient model that simulates over 20 times faster than CFD. The Ritz model outputs variables of interest such as voltage and internal potential, current, and concentration distributions in response to the current input. The Ritz model can be cast in state variable form, making it amenable to systems analysis using Matlab and model-based estimator and controller design. The accuracy of the Ritz model decreases with increasing charge/discharge rate, low or high State of Charge, and increasing charge/discharge time due to linearization of the Butler-Volmer equation, linearization of the open circuit voltage, and constant porosity assumptions, respectively. Finally, the time constant during charge is significantly different than that during discharge due to different specific areas, motivating the use of a time-varying model.

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