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A Multiphysics Finite-Element Performance Model of a Vanadium Redox Flow Battery

Numerical models are very important for designing control and monitoring systems, which are needed for the electric grid interfacing. Both 1D and 2D finite element models have been developed in order to reduce computing cost and allow for a real-time simulation of VRFB operations [2]-[4]. In this work novel 1D steady-state and dynamic finite-element model of an all-vanadium redox flow battery are proposed. The reference cell model includes current collectors, positive and negative porous electrodes, where chemical reactions occur, and the polymer membrane for proton conduction. The FEM model incorporates the following multiphysics phenomena: momentum, charge and species conservation, mass transport (Nernst-Plank equation), electric conduction, charge generation (Butler-Volmer equation) inside the porous electrodes, and the proton conduction inside the membrane. In particular, for charge generation the effect of mass transport is taken into account by considering surface concentration of the electrolytes, which differs from bulk concentration. The VRFBs charge and discharge dynamics is taken into account by including reservoir mass balance equations. In such a way the energy storage cell performance can be properly simulated. The independent variables of the model are the electrode and electrolyte potentials and the ionic species concentrations in the porous electrodes. From potentials the overall cell voltage is derived as a function of the State of Charge (SoC) during charge and discharge cycles. The cell runtime and the storage efficiency can be deduced from the voltage time profile of the dynamic model. Numerical results of both the static and the dynamic 1D model are compared with those of 2D models, with the same parameters, showing good agreement. The proposed model is expected to be a useful tool in driving and optimizing the stack design.

**References**

[1] P. Alotto, M. Guarnieri and F. Moro, “Redox flow batteries for the storage of renewable energy: A review,” *Renew. Sust. Energ. Rev*., **29**, (2014): 325–335.

[2] C.L. Chen, H. K. Yeoh and M. H. Chakrabarti, “An enhancement to Vynnycky’s model for the all-vanadium redox flow battery,” *Electrochem. Acta*, **120**, (2014): 167-179.

[3] D. You, H. Zhang, and J. Chen, “A simple model for the vanadium redox battery,” *Electrochem. Acta*, **54**, (2009): 6827-6836.

[4] K. W. Knehr et al., “A Transient Vanadium Flow Battery Model Incorporating Vanadium Crossover and Water Transport Through the Membrane,” *J. Electrochem. Soc.*, **159** (9), (2012): A1446-A1459.