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This paper examines an electrochemistry-based lithium-ion battery model developed by Doyle, Fuller, and Newman. The paper makes this model more tractable and conducive to control design by making two main contributions to the literature. First, we adaptively solve the model's algebraic equations using quasi-linearization. This improves the model's execution speed compared to solving the algebraic equations via optimization. Second, we reduce the model's order by deriving a family of analytic Padé approximations to the model's spherical diffusion equations. The paper carefully compares these Padé approximations to other published methods for reducing spherical diffusion equations. Finally, the paper concludes with battery simulations showing the significant impact of the proposed model reduction approach on the battery model's overall accuracy and simulation speed. This paper examines the problem of developing reduced, electrochemistry-based models of the dynamics of charging and discharging of lithium-ion batteries. The overarching goal of the paper is to develop lithium-ion battery models that satisfy two important but potentially conflicting objectives. First, the models must have the ability to accurately predict the performance of lithium-ion batteries in applications involving potentially complex and rapid charge/discharge cycles, e.g., hybrid vehicle applications. Second, the models must run with sufficient speed to enable battery system design, optimization, and control.Several models have been used to monitor battery state of charge ͑SOC͒ and state of health. 1-4 While these models are very desirable for control and estimation, they do not capture all of the high rate dynamics associated with hybrid vehicle drive cycles. For this one can use an electrochemical battery model. One such model is provided by Doyle, Fuller, and Newman, with the addition of a potential degradation mechanism provided by Ramadass et al. [5][6][7][8] There are two major numerical difficulties with this electrochemical model. The first is the large number of state variables: a finite difference discretization of the model with M points along the width of the cell and N points in the pseudospherical direction has approximately ͑2/3͒ * M * N state variables. The second challenge is the model's nonzero index, represented by approximately ͑2/3͒ * M * N algebraic equations, most of them involving a hyperbolic sine nonlinearity. This results in a large set of differential algebraic equations ͑DAEs͒. Ideally, one would like a model that: ͑i͒ runs quickly with a low number of state variables to enable optimal design and control studies, while ͑ii͒ still retaining the ability to accurately model complex, high rate charge/discharge cycles.Applying model reduction techniques to the above electrochemical battery model can bring it closer to the ideal speed and fidelity goals. Several reductions of this model are already presented in the literature. Some of these reductions pay special attention to the spherical diffusion submodel because it ap...

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