This paper presents a procedure for deriving and tuning a solvable and compact differential-algebraic equation (DAE) model for the LiFePO4-graphite lithium-ion battery cell. A reduced order model can drastically decrease the simulation time with a minimal loss of the prediction accuracy for the lithium-ion battery. This paper proposes a method based on a linear DAE theory for choosing a Galerkin formulation that will produce a solvable ROM from the original higher-order model of the lithium-ion battery cell. Moreover, a systematic tuning of the model parameters using the sensitivity study and the genetic algorithm is demonstrated by exploiting the computational efficiency of the simplified model. When coupled with the model for describing the hysteresis of the battery cell, the tuned model, consisting of 26 DAEs, shows a good agreement with the experimental data from a LiFePO4-graphite battery cell at rates up to 4 C. [GRAPHICS] .