Modeling of Ion Crossover in Vanadium Redox Flow Batteries: A Computationally-Efficient Lumped Parameter Approach for Extended Cycling

Abstract

In this work, we have developed a zero-dimensional vanadium redox flow battery (VRFB) model which accounts for all modes of vanadium crossover and enables prediction of long-term performance of the system in a computationally-efficient manner. Using this model, the effects of membrane thickness on a 1000-cycle operation of a VRFB system have been investigated. It was observed that utilizing a thicker membrane significantly reduces the rate of capacity fade over time (up to ∼15%) at the expense of reducing the energy efficiency (up to ∼2%) due to increased ohmic losses. During extended cycling, the capacity of each simulated case was observed to approach an asymptote of ∼60% relative capacity, as the concentrations in each half-cell reach a quasi-equilibrium state. Simulations also indicated that peak power density and limiting current density exhibit a similar asymptotic trend during extended cycling (i.e., an ∼10-15% decrease in the peak power density and an ∼20-25% decrease in the limiting current density is observed as quasi-equilibrium state is reached Recently, vanadium redox flow batteries (VRFBs) have gained significant interest as one of the most promising electrochemical systems for grid-scale energy storage due to their several advantages over conventional batteries.1,2 Among these advantages, the most important ones are their ability to decouple power and energy rating due to their unique system architecture, and their flexible design.3-6 Despite these advantages, one major challenge which hinders their commercial viability is the relatively higher capital cost of these systems.5 According to a recent study by Pacific Northwest National Laboratory, the current capital cost of a VRFB system is about $350 per kWh for 4-h application, 7 which is much higher than the capital cost target set by government agencies. The current capital cost target of The Department of Energy's Office of Electricity Delivery and Energy Reliability is $250 per kWh, falling to $150 per kWh in the future for a 4-hour energy storage system. 8 One possible approach to reduce the capital cost is to improve the performance of these systems for less material use. To date, the majority of research has focused on improving the performance of individual components, such as developing high power density electrodes 4,[9][10][11][12][13][14][15][16] and exploring high energy capacity electrolytes. [17][18][19][20][21] In line with these studies, another approach to reduce the capital cost is to increase the lifetime of VRFB systems. Currently, the lifetime of these systems is limited by the capacity fade during cycling, which is primarily governed by unwanted active species transport across the membrane (i.e., species crossover). 22 Developing sophisticated mathematical models to mimic the VRFB operation is imperative to investigate the capacity fade and related performance losses in these systems due to lengthy time requirements and practical limitations of experimental cycling analysis. So far, there are several studies reported that ha...

Estimation of Transport and Kinetic Parameters of Vanadium Redox Batteries Using Static Cells

“…Accordingly, the comparison of voltage profiles between model predictions and experimental data and the predicted vanadium ions concentration are presented in Figure 5, 6, and 7. This section also discusses how the proposed approach can contribute to the RFB model development, providing estimation results of a recently published zero-dimensional model which includes only uni-directional migration effects (13). The importance and limitations of the proposed work and further works will be discussed as well.…”

“…In other words, the rate of accumulation of each vanadium ion species (V 2+ , V 3+ , VO 2+ , and VO2 + ) is the sum of the rate of production of the vanadium ions by side reactions, the rate of outflow into the opposite chamber, and the rate of generation or loss at the electrode by the electrochemical reactions. (9,11,13). The cell voltage given by Equation 17 is used in the static cell model (11).…”

“…Models in each category have their own advantages and can be used depending on users' purposes. For example, zero-dimensional models have been developed to be easy to implement, enabling to quickly understand, predict, and control the battery system (9,13). Multi-dimensional models have been implemented with the more detailed physics of the system (3).…”

Open Data, Models, and Codes for Vanadium Redox Batch Cell Systems: A Systems Approach Using Zero-Dimensional Models

“…Models in each category have their own advantages and can be used depending on the users' needs. For example, zero-dimensional models have been developed to be easily implementable, enabling to quickly understand, predict, and control the battery system [3,6,7]. Multidimensional models have been implemented by including more detailed physics of the system [12].…”

A low-cost average valence detector for mixed electrolytes in vanadium flow batteries

“…Theoretical and experimental studies show that there are two mechanisms resulting in the capacity decay of VFBs. [19][20][21][22][23][24][25][26][27][28] One is the imbalance in the vanadium concentration and volume of the positive and the negative electrolytes, which is caused by water and vanadium ions transferring through the separator. The other is the imbalance in the vanadium valences of the positive and the negative electrolytes, which is due to the side reactions including gas evolution reactions and oxidation of V 2+ by the oxygen in the air.…”