Systematic Lumped Modeling of all-Vanadium Redox Flow Batteries

Abstract

Recently, the lumped models for all-vanadium redox flow batteries (VRFBs) have gained a lot of interest among battery designers for system-level studies because of their simplified mathematical approach with the minimum computational procedure. In this paper, we, therefore, aim to systematically derive a reduced lumped mathematical model for VRFB. In essence, we carry out an analysis to arrive reduced lumped model by orderly reducing the distributed three-dimensional (3D) model to one dimensional (1D) model by providing justified conditions/assumptions. Subsequently, from the analytical solution of 1D, we obtain the expression for lumped model. A further analysis and reduction of this analytical lumped model are carried out to obtain a reduced lumped model. We then verify both this analytical and reduced lumped model by comparing the charge-discharge predictions of the lumped model with the distributed model of higher dimensions at different values of current density. A good agreement between the model predictions is obtained, which indicates that the derived lumped model can capture the behavior of a higher dimensional model with high accuracy and without compromising internal physics.