The quasi-steady state of all-vanadium redox flow batteries: A scale analysis

• We present a transient 2D model for a VRFB (conservation of species and charge);
• Carry out scale analysis of the species conservation equation;
• Derive the condition characterizing the quasi-steadiness of VRFB operation;
• Verify it by comparing charge-discharge curve with transient simulations.

In general, mathematical models for all-vanadium redox flow batteries (VRFB) that seek to capture the transport phenomena are transient in nature. In this paper, we carry out scale analysis of VRFB operation and derive the conditions when it can be assumed to be quasi-steady state in nature, i.e., time-dependence only through a boundary condition. We find that it is true for typical tank volume and flow rate employed for VRFBs. The proposed analysis is generic and can also be employed for other types of redox flow batteries.