Lead (Pb)-acid batteries are a low-cost power source for applications ranging from hybrid and electric vehicles (HEVs) to large-scale energy storage. Efficient simulation, design, and management systems require the development of low order but accurate models. In this paper we develop a reduced-order Pb-acid battery model from first principles using linearization and the Ritz discretization method. The model, even with a low-order discretization, accurately predicts the voltage response to a dynamic pulse current input and outputs spatially distributed variables of interest. A dynamic averaged model is developed from the Ritz model and realized by an equivalent circuit. The circuit resistances and capacitances depend on electrochemical parameters, linking the equivalent circuit model to the underlying electrochemistry of the first principles model.

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