Glucosamine-Assisted Functionalization of Carbon Nanotubes for Vanadium Flow Batteries

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Glucosamine-Assisted Functionalization of Carbon Nanotubes for Vanadium Flow Batteries

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  • Research Article
  • Cite Count Icon 254
  • 10.1007/s41918-019-00047-1
Progress and Perspectives of Flow Battery Technologies
  • Jul 11, 2019
  • Electrochemical Energy Reviews
  • Huamin Zhang + 2 more

Flow batteries have received increasing attention because of their ability to accelerate the utilization of renewable energy by resolving issues of discontinuity, instability and uncontrollability. Currently, widely studied flow batteries include traditional vanadium and zinc-based flow batteries as well as novel flow battery systems. And although vanadium and zinc-based flow batteries are close to commercialization, relatively low power and energy densities restrict the further commercial and industrial application. To improve power and energy densities, researchers have started to investigate novel flow battery systems, including aqueous and non-aqueous systems. Here, novel non-aqueous flow batteries possess low conductivity and low safety, limiting further application. Therefore, the most promising systems remain vanadium and zinc-based flow batteries as well as novel aqueous flow batteries. Overall, the research of flow batteries should focus on improvements in power and energy density along with cost reductions. In addition, because the design and development of flow battery stacks are vital for industrialization, the structural design and optimization of key materials and stacks of flow batteries are also important. Based on all of this, this review will present in detail the current progress and developmental perspectives of flow batteries with a focus on vanadium flow batteries, zinc-based flow batteries and novel flow battery systems to provide an effective and extensive understanding of the current research and future development of flow batteries.

  • Research Article
  • Cite Count Icon 20
  • 10.1016/j.est.2023.107246
Definition of multi-objective operation optimization of vanadium redox flow and lithium-ion batteries considering levelized cost of energy, fast charging, and energy efficiency based on current density
  • Mar 30, 2023
  • Journal of Energy Storage
  • Bahman Khaki + 1 more

Definition of multi-objective operation optimization of vanadium redox flow and lithium-ion batteries considering levelized cost of energy, fast charging, and energy efficiency based on current density

  • Research Article
  • Cite Count Icon 57
  • 10.1016/j.joule.2020.11.022
Harnessing Interfacial Electron Transfer in Redox Flow Batteries
  • Dec 21, 2020
  • Joule
  • Tejal V Sawant + 4 more

Harnessing Interfacial Electron Transfer in Redox Flow Batteries

  • Research Article
  • Cite Count Icon 1
  • 10.17170/kobra-20190204145
Comparing Electrical Energy Storage Technologies Regarding Their Material and Carbon Footprint
  • Dec 3, 2018
  • Energies
  • Clemens Mostert + 3 more

The need for electrical energy storage technologies (EEST) in a future energy system, based on volatile renewable energy sources is widely accepted. The still open question is which technology should be used, in particular in such applications where the implementation of different storage technologies would be possible. In this study, eight different EEST were analysed. The comparative life cycle assessment focused on the storage of electrical excess energy from a renewable energy power plant. The considered EEST were lead-acid, lithium-ion, sodium-sulphur, vanadium redox flow and stationary second-life batteries. In addition, two power-to-gas plants storing synthetic natural gas and hydrogen in the gas grid and a new underwater compressed air energy storage were analysed. The material footprint was determined by calculating the raw material input RMI and the total material requirement TMR and the carbon footprint by calculating the global warming impact GWI . All indicators were normalised per energy fed-out based on a unified energy fed-in. The results show that the second-life battery has the lowest greenhouse gas (GHG) emissions and material use, followed by the lithium-ion battery and the underwater compressed air energy storage. Therefore, these three technologies are preferred options compared to the remaining five technologies with respect to the underlying assumptions of the study. The production phase accounts for the highest share of GHG emissions and material use for nearly all EEST. The results of a sensitivity analysis show that lifetime and storage capacity have a comparable high influence on the footprints. The GHG emissions and the material use of the power-to-gas technologies, the vanadium redox flow battery as well as the underwater compressed air energy storage decline strongly with increased storage capacity.

  • Research Article
  • Cite Count Icon 2
  • 10.4028/www.scientific.net/amr.853.291
Design and Test of a Lab-Scale Vanadium Redox Flow Battery Cell Considering Electrolyte Feeding Structure for Solar Energy
  • Dec 1, 2013
  • Advanced Materials Research
  • Andy Kyung Yong Yoon + 2 more

This paper describes the design and test of a lab-scale vanadium redox flow (VRF) battery considering electrolyte feeding and flow structure. The VRB battery has emerged as the promising technology for energy storage technologies. The VRF battery an electrochemical energy storage device chemically, and physically VRF battery is a sandwich type structure, and it consists of a cell stack, two electrolyte reservoirs, two pumps and an electrolyte flow tube. The cell stack has numerous single cells, and it has two half-cells which consist of an electrode, a carbon felt, a sealant PVC frame, and there is an ion-exchange membrane separating two half-cells. The VRF battery is applied electrolyte feeding and flow technology, and one of energy storage system without memory effect and self-discharge. This paper focuses design of liquid electrolyte feeding and flow mechanism, and considering inverse concept of electrolyte feeding structure for the vanadium flow battery. In addition, in order to get the specific flow rate (SFR) of electrolyte, numerous experiments were carried out, and the parameter and governing equations was obtained.

  • Research Article
  • 10.1149/ma2022-01482006mtgabs
(Invited) Optimized Operation of the Vanadium Redox Flow Batteries
  • Jul 7, 2022
  • Electrochemical Society Meeting Abstracts
  • Bahman Khaki

The Redox Flow Battery (RFB) systems are unique chemically, mechanically, and electrically compared to other kinds of batteries. Among RFBs, the Vanadium Redox Flow Batteries (VRFBs) are the most commercialized type. VRFBs are a suitable option for large-scale energy storage with exceptional advantages like the decoupled power and energy design (scalability), long life-time, safe battery chemistry (non-toxic, and non-flammable), etc. The power and energy designs in VRFBs are decoupled, known as the scalability benefit of the VRFBs. This implies more output energy from the battery is possible only by adding more electrolytes to the reservoir tanks.There are only a few research studies in the literature about the optimized operation of the Vanadium redox flow batteries. Most of these papers are not applicable to develop in real practice. The introduced optimized operation algorithms of VRFBs in this lecture can help the participants learn how to improve the performance of the battery and operate the battery more efficiently. Different objective functions are considered in this lecture to be optimized, e.g. minimizing the time duration of battery charging (for fast charging), energy loss, voltage loss, and capacity loss of the battery. The participants can find the results of this useful in optimized operation and implementation of the VRFBs.High charging current density results in faster charging and reduces the capacity fading in Vanadium Redox Flow Batteries (VRFB). On the other hand, it leads to the reduced energy efficiency of the battery. Also, the lower electrolyte flow rate in VRFBs results in less energy consumption by the pumps leading to the higher energy efficiency of the VRFBs. However, higher flow rates have the benefit of reducing voltage loss of VRFBs. To address these trade-offs, closed-loop charge control and flow management in VRFBs are necessary. In this lecture, a multi-objective optimization is proposed in first section to optimize the charging duration and flow management of the VRFB simultaneously during its charging. An innovative method is proposed for modeling pump consumption based on affinity laws for centrifugal pumps, which leads to new electrolyte flow management. Further, three case studies are defined in charging mode on a nine-cell VRFB unit laboratory prototype to validate the proposed optimization's performance, involving the duration of charging, flow management, and energy efficiency of the VRFB. The method is compared with previously published research studies on the optimal operation of VRFBs, which shows the uniqueness and consistency of the proposed optimization method for simultaneous controlling VRFB's charging duration and flow management.Capacity fade in Vanadium Redox Flow Batteries (VRFB) relies on the loss of electrolyte volume in each of charge and discharge cycles. The loss of volume in each cycle, also known as the bulk electrolyte osmosis, is due to Vanadium ions' diffusion from the membrane. The lower electrolyte flow rate in VRFB can reduce capacity fade as the electrolyte's velocity across the membrane decreases. However, the lower electrolyte flow increases the battery’s voltage loss. A new electrolyte flow management is introduced in second section of the lecture to address this trade-off, which considers the decrease of both capacity fade and voltage loss in VRFBs simultaneously. The proposed multi-objective flow management shows a significant reduction of both capacity and voltage losses in VRFBs.Moreover, typically complex electrochemical models and equations are needed to model capacity fade in VRFBs, which are not straightforward to model. The capacity fade modeling can lead to the estimation of available capacity and the battery’s State of Health (SoH). Therefore, a new mathematical model is proposed for the VRFB’s available capacity based on the electrochemical-based capacity fade model results. The model further is developed to estimate the State of Charge (SoC) and the SoH of VRFBs per cycle of charge and discharge.

  • Research Article
  • 10.1149/ma2022-013471mtgabs
A Kinetic Performance-Informed Technoeconomic Assessment-Life Cycle Assessment Model of Ce and V Redox Flow Batteries
  • Jul 7, 2022
  • Electrochemical Society Meeting Abstracts
  • Cailin Buchanan + 1 more

The EIA projects that 60% of cumulative capacity additions in the U.S. by 2050 will be renewable electric generating technologies.1 The use of intermittent renewable energy in the U.S. electricity grid requires energy storage. NREL predicts that for a scenario in which 80% of electricity in the U.S. comes from renewable energy by 2050, 120 GW of energy storage would be needed,2 yet as of 2020, the U.S. has only 24 GW of storage capacity.3 Redox flow batteries (RFBs) are a useful technology for ensuring the smooth integration of renewable energy into the U.S. electricity grid because of their long lifecycles and discharge times. RFBs are currently too expensive for market deployment, however, with the all vanadium RFB (VRFB) costing double the DOE target.4,5 One way to improve the cost effectiveness of RFBs is to explore chemistries that increase the voltage window. The replacement of the VO2+/ VO2 + chemistry at the positive electrode of a VRFB with the Ce3+/Ce4+ chemistry would result in an increased theoretical voltage, but it is unclear how the kinetic, ohmic, and mass transport overvoltages would change. Additionally, studies of the environmental burdens of life cycle phases of Ce RFBs are limited. To advance the most cost effective and least environmentally harmful RFB, in this study, we develop a combined Technoeconomic Assessment-Life Cycle Assessment (TEA-LCA) model that is informed by our performance measurements to compare the levelized cost of electricity (LCOE) and levelized greenhouse gas (LGHG) emissions of VRFBs and Ce-V RFBs.The TEA-LCA model allows the user to select from a list of positive and negative electrode redox chemistries, solvents, electrode materials, and electricity grid generation profiles to calculate the LCOE and LGHG emissions of the battery for the delivery of 1 kWh of energy. A solver function optimizes the current density that minimizes either LCOE or LGHGs. The TEA-LCA model uses a bottom-up approach, in which energy- and power-dependent capital costs and environmental burdens are calculated by converting the amount of material to a kWh basis. Cost estimates are sourced from vendors and GHG emissions are pulled from the GREET database and literature. The amount of active species required to deliver 1 kWh of electricity at a specified discharge time is calculated using the redox couple properties, including redox potential, exchange current density, and limiting currents. These performance parameters are based on measurements collected in lab. The use phase burdens are calculated using the roundtrip efficiency of the battery and the price and GHGs associated with the electricity grid generation mix. End-of-life costs consist of the economic and environmental burdens of recycling and disposing of the battery material and are collected from vendors and GREET.The TEA-LCA model answers important questions related to the optimal operating conditions of an RFB. In addition to comparing the economic and environmental performances of the VRFB and Ce-V RFB, it demonstrates how different electricity grid mixes influence total cost and emissions and highlights the difference in optimal operating current density if cost or GHG emissions are prioritized, e.g., lower current density results in fewer emissions but higher cost in carbon-intensive electricity grid profiles. Preliminary results using literature values show that the Ce-V RFB has an LCOE that is 45% lower than the VRFB LCOE, with capital costs dominating. We will present the finalized LCOE for the VRFB and Ce-V RFB, as well as LGHGs, as a function of discharge time and electricity grid mix. Sensitivity analyses of the input parameters found that for both RFBs, the discount rate, discharge faradaic efficiency, and lifetime of battery had the most influence on LCOE, with a 20% decrease in discharge faradaic efficiency resulting in a 16% increase in LCOE for the VRFB. The results of this TEA-LCA model show that the use of cerium is a viable option for reducing the cost of RFBs to advance their use in renewable energy storage grid applications. Additionally, this model is generalizable to other batteries and electrochemical systems, such as CO2 conversion. Thus, the development of this TEA-LCA model represents not only an advancement to the field of redox flow batteries but also the wider field of electrochemistry. U.S. EIA. Annual Energy Outlook. (2021).Mai, T. et al. Renewable Electricity Futures Study. NREL. (2012).CSS University of Michigan. U. S. Grid Energy Storage Factsheet. (2021).Mongird, K. et al. 2020 Grid Energy Storage Technology Cost and Performance Assessment. (2020).Weber, A. Z. et al. J. Appl. Electrochem. 41, 1137–1164 (2011).Smith, G. F. & Getz, C. A. Ind. Eng. Chem. Res. 10, 191–195 (1938).

  • Research Article
  • Cite Count Icon 60
  • 10.1149/2.0621807jes
Vanadium Redox Flow Battery Using Electrocatalyst Decorated with Nitrogen-Doped Carbon Nanotubes Derived from Metal-Organic Frameworks
  • Jan 1, 2018
  • Journal of The Electrochemical Society
  • Chanho Noh + 5 more

Highly porous zeolitic-imidazole frameworks (ZIFs) are synthesized to produce N-doped mesoporous carbon electrocatalysts via calcination. The N-doped carbon (m-NC) and carbon nanotubes (m-NCNT) are obtained from ZIF-8 and ZIF-67, while the core-shell structure of ZIF-8@ZIF-67 produced with ZIF-8 seeds (m-NC@NCNT) is prepared by hydrothermal method. Chemical and optical evaluations of the catalysts are characterized using BET, FT-IR, XPS, XRD, Raman spectroscopy and SEM/STEM and they are used as the catalysts for redox reactions of vanadium ions and redox flow battery (VRFB) performance. In the utilization, m-NC@NCNT and m-NCNT are effective for improving VO2+/VO2+ redox reaction, although m-NC does not influence that. Even in VRFB tests using the catalysts, charge/discharge potential and energy efficiency (EE) of m-NC@NCNT and m-NCNT are highest, not to mention excellent EE resilience after undergoing tougher cycling condition. These results are due to the large graphitic-N portion of the two catalysts. Namely, electrons produced by the graphitic-N are delocalized, forming pi-conjugated system and vanadium–nitrogen transition state. This state then promotes electron transfer during VO2+/VO2+ redox reaction and VRFB performance.

  • Research Article
  • Cite Count Icon 2
  • 10.1149/1945-7111/ad5252
Fluid Physics Impacting Vanadium and Other Redox Flow Batteries
  • Jun 3, 2024
  • Journal of The Electrochemical Society
  • Clifford M Krowne

The Vanadium redox flow battery (VRFB) has been intensively examined since the 1970s, with researchers looking at its electrochemical time varying electrolyte concentration time variation equations (both tank and cells, for negative and positive half cells), its thermal time variation equations, and fluid flow equations. Chemical behavior of the electrolyte ions has also been intensively examined. Our focus in this treatment is a completely new approach to understanding the physics, chemistry, and electronics of the VRFB. Here, we develop complete theoretical equations by an analytical treatment affecting the fluid flow in the VRFB as well as all other redox flow batteries, providing background derivations applicable for all of the fundamental concepts required to properly understand flow batteries. With these concepts presented, calculations are done to determine actual values for fluid velocity, strain rate, angular fluid velocity, angular momentum, rotational kinetic energy, and gravity effects on fluid velocity in a redox flow battery.

  • Research Article
  • 10.1149/ma2025-01452367mtgabs
(Invited) Lessons from Vanadium Flow Batteries for Non-Vanadium Flow Batteries
  • Jul 11, 2025
  • Electrochemical Society Meeting Abstracts
  • Reed M Wittman + 1 more

Over the last ~40 years Vanadium Redox Flow Batteries (VRFBs) have been the most studied redox flow battery chemistries. This owes to VRFBs being a reasonably easy system to build and run. VRFBs use sulfuric acid that is compatible with off the shelf components that do not need extreme oxygen removal. Crossover impacts are minimized because the active species are vanadium ions at different charge state. Rebalancing is a process of moving electrolyte between tanks and charging to the right state of charge again. Vanadium in the VRFB forms straight forward redox couples on each side of the cell with a relatively simple one electron reaction for both. This has made VRFB an exemplar system to study various inherent properties of flow batteries.All redox flow batteries have inherent issues that has made their scale up and adoption problematic including losses associated with system scaling, mass transport imbalance, and side reactions. These are compounded by a lack of diagnostics to determine system state of health. The foundational issue is system scaling. Flow batteries take a very different form in the field than they are commonly studied in the lab. Lab systems are single cells with active areas on the order of 10s of cm2 while fielded system are stacks of cells each with active areas on the order of m2. As such, issues that were minor, like mass transport, side reactions, internal resistances, and component degradation, in lab scale research becomes large barriers to progress for flow battery commercialization. A lack of system diagnostics inhibits addressing minor issues at the small scale to improve system scaling operations.In this talk we will cover selected lessons from VRFBs research and development, then discuss how those lessons apply to new redox flow batteries. This talk will compile work from existing literature with highlights from work done in our labs at Sandia. Through this work we will develop a chemistry agnostic framework to conduct future flow battery research in. SNL is managed and operated by NTESS under DOE-NNSA contract DE-NA0003525. SAND2024-16717A

  • Dissertation
  • Cite Count Icon 1
  • 10.17918/hexn-t660
Simulation and Modeling of Electrochemical Systems with Pore-scale Analysis
  • Feb 1, 2019
  • Charles P Andersen + 1 more

One of the most important requirements for being able to integrate clean energy generation is storage through new battery technology. For example, to address the issue from intermittent energy sources such as wind and solar power vanadium redox flow batteries (VRFBs) have emerged as promising technology. Another promising technology, particularly for vehicular application, is that of lithium air batteries which boast high energy density (an order of magnitude higher than state of the art Li-ion batteries) but suffer from short cycle life. While the majority of literature covers these energy storage systems in experimental setups experimental identification for the optimal electrode microstructure is challenging, time consuming, and expensive. The primary objective of this dissertation is to apply pore-scale modeling to simulate the effect of key design parameters and operating conditions to optimize cell performance in vanadium redox flow and lithium-air batteries. The motivation behind selecting these battery systems is not only the technological advantages highlighted above but also because they span very different electrode architecture length scales (nanometers for Li-air to millimeters for flow batteries), which will enable the models developed to be utilized in many different systems beyond the specific ones studied here.

  • Research Article
  • Cite Count Icon 106
  • 10.5075/epfl-thesis-4277
Modeling of a vanadium redox flow battery electricity storage system
  • Jan 1, 2009
  • Infoscience (Ecole Polytechnique Fédérale de Lausanne)
  • C Blanc

Today, the electricity industries are facing new challenges as the market is being liberalized and deregulated in many countries. Electricity storage is undoubtedly a disruptive technology that will play, in the near future, a major role in the fast developing distributed generations network. Indeed, electricity storage has many potential applications: management of the supply and demand of electricity, power quality, integration of renewable sources, improvement of the level of use of the transport and distribution network, etc. Over the years, many storage technologies have been investigated and developed, some have reached the demonstrator level and only a few have become commercially available. The pumped hydro facilities have been successfully storing electricity for more than a century; but today, appropriate locations are seldom found. Electrochemical storage is also an effective means to accumulate electrical energy; among the emerging technologies, the flow batteries are excellent candidates for large stationary storage applications where the vanadium redox flow battery (VRB) distinguishes itself thanks to its competitive cost and simplicity. In this ambitious work that encompasses the domains of electricity, electrochemistry and fluid mechanics, we have proposed a novel multiphysics model of the VRB. This model describes the principles and relations that govern the behaviour of the VRB under any set of operating conditions. Furthermore, this multiphysics model is a powerful means to identify and quantify the sources of losses within the VRB storage system; indeed, one of the purposes of this study is to propose strategies of control and operation for a greater effectiveness of the overall storage system. The electrochemical model is based on the electrochemical principles and the study of the VRB chemistry; this model determines the equilibrium voltage from the vanadium concentrations, and the associated activation, concentration, ohmic and ionic overpotentials. Furthermore, the vanadium concentrations within the tank and the stack are constantly determined as a function of the current and the electrolyte flowrate. A simplified model of the internal loss is also proposed. The electrochemical performance was then established through the simulation of a stand alone system composed of a solar source, a VRB and a load. The model determines the stack voltage, the power flows and the vanadium concentrations over a 24 h period. Furthermore, the model was successfully compared with experimental data through a series of charge and discharge cycles at constant currents. Thereafter, the properties of the electrolyte are briefly investigated: in particular their dependence upon the electrolyte composition. Indeed, the viscosity and the density are important parameters of the mechanical model. In order to analyse the battery performance, a mechanical model has been proposed to determine the mechanical power required to flow the electrolytes. This model based on fluid mechanics has an analytical part that predicts the pressure drop within the pipes and the tanks, and a numerical part. Indeed, the stack geometry is so complex that it can not be described analytically; therefore, a numerical model based on finite element method (FEM) is proposed. Hence, the mechanical power necessary to the battery operation is obtained at any operating conditions. The electrochemical and the mechanical models are finally assembled to form the original multiphysics model of the VRB. This model provides a good insight of the battery operation and offers a powerful means to enhance the battery performance. Indeed, there is at constant current an optimal flowrate that maximizes the efficiency. A second series of charge and discharge cycles has determined the efficiency of different control strategies. Finally, the battery operations at constant power were also discussed in details and an optimal operating point has been highlighted.

  • Conference Article
  • 10.2118/222372-ms
Innovation in Battery Energy Storage Systems via Redox Flow Batteries Technology
  • Nov 4, 2024
  • S Atatreh + 3 more

Utility scale energy storage which is cost effective and scalable is required to meet the global energy demand while maintaining global climate goals, including UAE's goal of net zero by 2050. Increasing renewable energy resources results in volatility presented by supply fluctuations and grid-stability challenges which can be addressed through innovative modular Battery Energy Storage Systems (BESS) that has long discharge hours, more than six hours, fast ramp-up rate and has relatively low maintenance cost. Vanadium Redox Flow Batteries (VRFB) provide substantial advantages which support a scalable, efficient utility scale energy storage system that can be commercialized at a competitive Levelized Cost of Storage (LCOS). Our global Innovation centers are collaborating to develop innovative solution to upgrade existing Battery Energy Storage Systems in power plants and other applications via Vanadium Redox Flow Batteries (VRFB) technologies along with wide synergy opportunities for clean technology implementation. Our research focuses on the system integration of large scale VRFB system, power rating of 10-100 MW, to the grids and investigates economics of scale and demand forecasts. Moreover, it aims to study the effect of high temperature in the GCC region on the performance of the cell, stack, and system levels. VRFB provides substantial advantages which support the commercialization regions that are rich with Renewable Energy (RE) resources, like solar and wind, where the surplus production can be stored and used at a feasible cost. Other applications include black start and backup power, also upgrading the existing BESS in large power plants. VRFB systems have the unique advantage to decouple power from capacity and can be designed independently, which supports to adapt to changing market conditions and increase your plants flexibility. Moreover, the lifetime can match the powerplant and offer further aspects such as recycling capacity. It's important to note that studies reveal positive trends on the availability of the element Vanadium through reliable supply chain and stable supply/demand, which can further increase the competitiveness of VRFB. Ongoing and future work includes collaborating with a utility/large energy supplier to study and develop a large-scale MW pilot VRFB system in harsh environment such, high temperature climates, to further co-create breakthrough industrial and commercial solutions in VRFB. Redox Flow Battery (RFB) systems are promising solution for utility scale energy storage solutions with zero emissions and have promising business case to replace diesel generators for backup power black start applications. The results include a complete system analysis and a feasible roadmap for VRFB technology adoption.

  • Research Article
  • Cite Count Icon 52
  • 10.1016/j.electacta.2019.02.062
Revealing sulfuric acid concentration impact on comprehensive performance of vanadium electrolytes and flow batteries
  • Feb 15, 2019
  • Electrochimica Acta
  • Yang Zhao + 3 more

Revealing sulfuric acid concentration impact on comprehensive performance of vanadium electrolytes and flow batteries

  • Research Article
  • Cite Count Icon 5
  • 10.1149/1945-7111/ad4824
Measures of Performance of Vanadium and Other Redox Flow Batteries
  • May 1, 2024
  • Journal of The Electrochemical Society
  • Clifford M Krowne

The Vanadium redox flow battery and other redox flow batteries have been studied intensively in the last few decades. The focus in this research is on summarizing some of the leading key measures of the flow battery, including state of charge (SoC), efficiencies of operation, including Coulombic efficiency, energy efficiency, and voltage efficiency, and energy density. New formulas are presented to allow calculation of energy density, under varying circumstances, including varying ionic electrolyte concentrations, terminal voltage, discharge times and cycle numbers, and electron exchange numbers in the redox chemical reactions. Effects of ionic crossover and side reactions are addressed, and it is shown which forms of energy density are robust against these additional undesirable chemical reactions.

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