Computational efficiency of solving the DFN battery model using descriptor form with Legendre polynomials and Galerkin projections

This paper evaluates the collective impact of three computational strategies from the literature applied to the Doyle-Fuller-Newman (DFN) lithium-ion battery model, a physics-based model valid for high current rates. The first strategy used is efficient model reformulation, where spatial basis functions are used to represent the distribution of lithium ions and potentials within the battery. The second strategy is quasi-linearization, which is used to lessen the computational burden associated with the nonlinearities of the Butler-Volmer equation. Finally, the combination of the first two strategies furnishes a descriptor-form DAE model of the battery at every integration time step. This paper evaluates the accuracy of these combined methods by evaluating the number of basis functions needed for accurate representation and by evaluating the consistency of the constraint equations when the full model is assembled. The combined methods lead to low computation time with accurate simulations 3-4 times faster than real time on a laptop computer.