An exact solution for rest-period voltage relaxation in Li-ion batteries for applications on battery management systems

Rest-period voltage relaxation in lithium-ion batteries is a non-invasive means to probe the battery's state of charge (SOC) and health without service interruption. However, to apply voltage relaxation as a reliable method for state estimation, an accurate on-board model is needed. The shape of the voltage relaxation depends on a multitude of factors, including the diffusivity and the initial Li concentration profile. By invoking the spherical-diffusion equation for an electrode particle, we solve it for the rest period with homogeneous boundary conditions of no flux at the center and surface. This leads to an analytical expression for the spatiotemporal evolution of Li concentration and, consequently, the SOC during the rest period. The solution is suitable for implementation on battery management systems as it calculates the equilibrium and the transient spatiotemporal profiles of SOC efficiently. The validation of the model predictions against the electrochemical-thermal model-generated data showed >95% accuracy.