A Reduced-Order Model for the Thermal Dynamics of Li-Ion Battery Cells

Abstract The electro-thermal dynamics of Li-Ion batteries for EVs and PHEVs applications is a topic of critical importance today. For applications related to control and diagnostics, the behavior of a battery pack is typically modeled using an equivalent circuit analogy approach. The model parameters, such as the open-circuit voltage and the battery internal resistance, are generally scheduled with respect to the temperature, which is often regarded as static input to the model. However, due to the internal heat generation and the conductivity of the materials, battery cells are characterized by a time-varying internal temperature that may be considerably different from the measured surface temperature. The phenomenon, often overlooked in these simplified models, must be properly accounted for in control-oriented applications, such as battery pack performance analysis, cell balancing, diagnostics and residual life estimation. This work proposes a control -or energy management- oriented model of the thermal dynamics of a prismatic Li-Ion cell, which predicts the internal temperature. Unlike most control-oriented models based on system identification techniques, the proposed approach defines a one-dimensional boundary-value problem for heat diffusion in unsteady conditions, which is solved by applying the Laplace transform and further reduced to a low-order linear model using the singular perturbation method. The model prediction is validated by comparison with the analytical solution of the boundary-value problem, for different charging/discharging profiles, using data acquired from experimental studies.