A fast fixed-point solution framework for the P2D model of lithium-ion batteries

This paper presents a novel algorithmic framework for efficiently solving the pseudo-two-dimensional (P2D) model of lithium-ion batteries. The proposed approach reformulates the original P2D model, typically expressed as a system of coupled nonlinear partial differential–algebraic equations, into a system of quasilinear partial integro-differential equations (PIDEs). Through this reformulation, intermittent algebraic states, such as local potential and current terms, are effectively eliminated, thereby reducing the model complexity. This enables the identification of a generic fixed-point iterated function for solving the P2D model’s nonlinear algebraic equations. To implement this iterated function, the finite volume method is employed to spatially discretize the PIDE system into a system of ordinary differential equations. An implicit–explicit (IMEX) time integration scheme is adopted, and the resulting quasilinear structure facilitates the development of a single-step numerical integration scheme that admits a closed-form update, providing stable, accurate, and computationally efficient solutions. Unlike traditional gradient-based approaches, the proposed framework does not require the Jacobian matrix and is insensitive to the initial guess error of the solution, making it easier to implement and more robust in practice. Due to its significantly reduced computational cost, the proposed framework is particularly well-suited for simulating large-scale battery systems operated under advanced closed-loop control strategies.