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This paper presents a system-level thermal model of a fluid-cooled Li-Ion battery module. The model is a reduced order model (ROM) identified by results from finite element analysis (FEA)/computational fluid dynamic (CFD) coupling simulation using the linear and time-invariant (LTI) method. The ROM consists of two LTI sub-systems: one of which describes the battery temperature response to a transient battery current, and the other of which takes into account of the battery temperature variation due to a heat flux induced by a varied inlet temperature of the battery cooling circuit. The thermal LTI model can be coupled to an electrical model to build a complete system-level battery ROM. Test examples show that the ROM is able to provide as accurate results as those from FEA/CFD coupling simulations.

Modeling of lithium iron phosphate electrodes calls for appropriate extensions of established model approaches. An electrochemical pseudo two-dimensional and a single-particle model are enhanced to address the phase separating behavior of this material with a variable solid state diffusion model. A particle size distribution model tackles the heterogeneity of the electrode microstructure. Both models are embedded in a framework to describe multi-layer electrode designs featuring segregated material properties. The models are parameterized following literature replicating a good match with measured discharge curves at low, medium and high currents. A simplified version of the rigorous model shows the effort of reparameterization, the computational advantage of model order reduction techniques, the model accuracy and application scope.

The parameterization of the electrochemical pseudo-two-dimensional (P2D) model plays an important role as it determines the acceptance and application range of subsequent simulation studies. Electrochemical impedance spectroscopy (EIS) is commonly applied to characterize batteries and to obtain the exchange current density and the solid diffusion coefficient of a given electrode material. EIS measurements performed with frequencies ranging from 1 MHz down to 10 mHz typically do not cover clearly isolated solid state diffusion processes of lithium ions in positive or negative electrode materials. To extend the frequency range down to 10 μHz, the distribution function of relaxation times (DRT) is a promising analysis method. It can be applied to time-domain measurements where the battery is excited by a current pulse and relaxed for a certain period.