Electrolyte Imbalance Determination of a Vanadium Redox Flow Battery by Potential‐Step Analysis of the Initial Charging

Abstract Vanadium redox flow batteries (VRFB) suffer from capacity fades owing to side reactions and crossover effects through the membrane. These processes lead to a deviation of the optimal initial average oxidation state (AOS=+3.5) of vanadium species in both half‐cell electrolytes. To rebalance the electrolyte solutions, it is first necessary to determine the current AOS. In this study, a new method was developed that enables an accurate determination of the AOS. A potential‐step analysis was performed with mixed electrolyte solutions of both half‐cells during the initial charging. The potential was recorded with a simple open‐circuit voltage (OCV) cell, and the potential‐steps were analyzed. A correlation between the duration of the potential plateaus in the OCV and the amount of vanadium ions of a certain oxidation state in the half‐cell electrolytes was found and used to precisely determine the AOS with a maximum error of 3.6 %.


Introduction
The increasing share of renewable energy production comes with the need to overcome the fluctuations in electricity production. In this context,e nergy-storage devices such as batteries are considered to play an increasingly vital role. Amongst batteries, redox flow batteries have interesting properties such as av ery high cycle life, the absence of flammability,a nd perfect suitabilityf or large-scale stationary storagea pplications owing to their setup. [1,2] The most maturer edox flow battery is the vanadium redox flow battery (VRFB), which has been investigated since the 1980s. [3] This redox flow battery uses av anadium electrolyte with different oxidation states in both half-cells.T he redox couples are V 2 + /V 3 + in the negative electrolyte andV O 2 + /VO 2 + (hereinafter referred to as V 4 + /V 5 + )i nt he positivee lectrolyte. Nevertheless, there are mechanismsthat lead to irreversible capacity fades of VRFBs, whicha re still under investigation. [4][5][6] Despite the aging mechanisms that occur in the stacks (e.g., corrosion,i ncrease of electrical resistance), the capacity of each electrolyte is crucial for the overall capacity and therefore the state of health of aV RFB. Side reactions such as hydrogen and carbon dioxide evolution, oxidation of species by oxygen from air, [7,8] crossover processes through the membrane, and volumec hanges during operation can lead to imbalanced capacities of the two electrolytes. [9] However,t he maximum capacity of the VRFB is limited by the electrolyte with the lowest capacity. Therefore, the optimal overall capacity is achievedi f both electrolytes have the same capacity.F or VRFBs, this is the case if both electrolytes have the same volume, the same concentration of vanadium species, and an average oxidation state (AOS) of the vanadium species of + 3.5 (whichm eans that the electrolyte consists of 50 %V 3 + and 50 %V 4 + species only).
There are straightforward methodst hat can be used to balance the volume and vanadiumc oncentration of the electrolytes (mixing,s plitting the electrolytes in two equal portions), whereas balancing the AOS is more demanding:f or example, chemicalt reatment with reducing agents, [10,11] mixing with extra vanadium electrolytes, [12] or electrochemical methods such as electrolysis [13,14] have been investigated. Determining the AOS is required before conducting compensation measures for imbalanced AOS. Different methods for analyzing the AOS in VRFBs have been presented in the literature. The oxidation state of the two electrolytes (or of am ixture of both electrolytes)c an be determined by potentiometric titration. [15] However, fort his method, samples of the electrolytes must be extracted anda nalyzed ex situ. This procedure is time-consuming and needs additional equipment,m aking it unsuitable for industrial applications. Am ore convenientp rocedure is the determination of the concentrations of the vanadium species by Vanadium redox flow batteries (VRFB) suffer from capacity fades owing to side reactions and crossovere ffects through the membrane. These processes lead to ad eviation of the optimal initial average oxidation state (AOS =+3.5) of vanadium speciesi nb oth half-cell electrolytes. To rebalance the electrolyte solutions, it is first necessary to determine the current AOS. In this study,anew method was developed that enables an accurate determination of the AOS. Apotential-step analysis was performed with mixed electrolyte solutionso fb oth halfcells during the initial charging. The potentialw as recorded with as imple open-circuit voltage (OCV) cell, and the potential-steps were analyzed. Ac orrelation between the duration of the potential plateausinthe OCV and the amount of vanadium ions of ac ertain oxidation state in the half-cell electrolytes was found and used to precisely determinet he AOS with am aximum error of 3.6 %.
analyzing the UV/Vis absorption spectra of the electrolytes. [8,[16][17][18] On-linem onitoring is possible by using flowthrough cuvettes, which provides additional information about the state of charge of the VRFB. Li et al. have already proposed an electrolyte recovery based on UV/Vis measurement and electrolysis. [19] Despite the mentioned advantages,e xtra equipment is still needed. Furthermore, the calibrationi sq uite tedious, especially in case of the positivee lectrolyte, in which the V 5 + absorption does not follow Beer's Law. [17] Anothera pproach utilizes as pecial open-circuit voltage (OCV) cell with three half-cells. [20] With this cell it is possible to determine the current oxidation state in each half-cell from the measured OCV and the given AOS. Although this method is "noninvasive" and suitable for on-line determination of the electrolytes, a special electrochemical cell with three half-cells is needed. Additionally, it is only applicable for monitoringt he current oxidation state, whereas the AOS has to be determinedb yp otentiometric titration.
In this study,w ed eveloped an ew method that enables the AOS of the electrolytes to be determined by using as tandard OCV cell. The analysiso ft he potentials teps during the initial chargingo fm ixed electrolytes allows an accurate determination of the AOS. This procedure is straightforward and allows the AOS in VRFB to be determined without the need for special apparatus because most VRFB-systems are already equipped with an OCVc ell for monitoring the state of charge. The suitabilityo ft he method is investigated in as mall labscale cell and verified under real operation conditions in a4cell short-stack VRFB-system.

Results and Discussion
Potential-step analysis during initial charging of mixed electrolytes Knowing that every combination of redoxc ouples in the vanadium electrolyte has its characteristic potential difference, a potential-step analysisd uring the initial charging of mixed electrolytes can be utilized to determine the AOS. An overview of half-cell potentials and potentiald ifferencesi naVRFB is shown in Ta ble 1.
Starting with identical electrolytes with equal volumes and AOS in both half-cells, ap otentiald ifference of approximately 0Vis expected. During the charging process, alteration of the oxidation states in both half-cells occurs.I nt he negative halfcell electrolyte, the vanadium ions are reduced from V 4 + to V 3 + in af irst step, and subsequently,a fter conversion of all V 4 + to V 3 + ,V 3 + is reduced to V 2 + in as econd step. In the positive half-celle lectrolyte, the vanadium ions are oxidized from V 3 + to V 4 + in af irst step, and subsequently from V 4 + to V 5 + in a second step. Dependingo nt he AOS of the initial electrolyte, the second reduction/oxidation step (V 3 + !V 2 + or V 4 + !V 5 + , respectively) will begin at the same time as the first step (for AOS =+3.5) or at ad ifferent time (for AOS ¼ 6 + 3.5).
For an AOS =+3.5 the oxidation states of both half-cell electrolytes will simultaneously change in such aw ay that no intermittent potential plateau can be observed, and the measured OCV will increased irectly from approximately 0t o1 .4 V (1.255 Vi st he theoretical potentiald ifference; the formal potential is 1.4 V [11] ). However,f or imbalanced electrolytes, the second vanadium reduction/oxidation step is reached earlier in one half-cell than in the other one. Therefore, either ap otential plateauo f0 .592 V( for AOS < + 3.5) or 0.663 V( for AOS > + 3.5) is expected owing to the cell potentials caused by the present redox couples (Table 1). When the second oxidation/reductions tep is also reached in the other half-cell, the potential difference between both half-cells increases to approximately 1.4 V. As chematic diagram of the development of the OCV over time during the initial charging of mixed imbalanced electrolytesi naVRFB is shown in Figure 1f or an AOS < + 3.5 (a) and AOS > + 3.5 (b), as well as their derivations.Three plateaus occur in both cases. Each plateau is separated by one of the above-mentionedp otentials teps. The first and third plateau have the same potentialf or every AOS, approximately 0V in the first part and approximately 1.4 Vi nt he thirdp art. Therefore, the second plateau is characteristic for the determination of the AOS.
An AOS < + 3.5 describesa no verall excess of V 3 + ions compared with V 4 + ions in the mixed electrolyte. During the first plateau the reactions from V 4 + to V 3 + (negative electrolyte) and from V 3 + to V 4 + (positive electrolyte) occur simultaneously. At t V 4þ all V 4 + ions in the negative electrolyte are converted to V 3 + ,a nd the predominant reaction in the negative electrolyte changes to further reduction of V 3 + to V 2 + .U ntil t V 3þ is reached, there are still V 3 + ions presenti nt he positive electrolyte. When t V 3þ is reached,a ll V 3 + ions are converted to V 4 + ions in the positive electrolyte, and the oxidation of V 4 + to V 5 + begins. Hence,t he times t V 4þ and t V 3þ characterize the ratio of V 3 + and V 4 + ions in the electrolytes. t V 4þ is proportional to the amount of V 4 + ions in the negative half-cell, whereas t V 3þ correlates with the amount of V 3 + ions in the positiveh alf-cell. Supposinge qual electrolyte volumes and equal overall vanadium concentrations in both half-cells at the beginning of the initial charging, the AOS can be calculated with Equation (1). t V 4þ and t V 3þ are defined as the times of the inflection points IP V 4þ and IP V 3þ (Figure 1), respectively.
In the case of AOS > + 3.5, an overall excess of V 4 + is present in the mixed electrolyte. Analogously,t he first potential step is caused by an oxidation of all V 3 + to V 4 + in the positive Table 1. Overview of standard potentials E 0 at different oxidation states in negative and positive electrolyte and their resulting potential difference DE. [21] Negative electrolyte half-cell electrolyte and the beginning of further oxidation from V 4 + to V 5 + .T he second potentials tep resultsf rom the total reduction of all V 4 + to V 3 + in the negative half-cell electrolyte followed by the beginning of the reductiono fV 3 + to V 2 + .T herefore, the reasonsf or the potential steps are opposite to those described for AOS < + 3.5. Hence, t V 3þ occurs prior to t V 4þ .Ift he AOS equals exactly + 3.5, both inflection points coincide. Only plateaus one and three would be present without any additional potentials tep. This means t V 4þ equals t V 3þ ,a nd Equation (1) will result in AOS =+3.5.
To determine the inflectionp oints, the temporal derivative of the OCV is calculated numerically,a si llustrated in Figure 1 (lowerp art). The maxima in the derivative correspond to the inflection points in the OCV curve marking t V 4þ and t V 3þ .I tw as observed duringv ariouse xperiments that IP V 3þ is steeper than IP V 4þ for both cases. Therefore, the steeper inflection point is induced by the disappearance of V 3 + ions in the positive halfcell electrolyte. Likewise, the inflection point with the shallower slope results from the disappearance of V 4 + ions in the negative half-cell electrolyte. These observations might be caused by different vanadium-iont ransfer rates throught he ion-exchange membrane resulting from the combination of diffusion, migration, and/or electro-osmotic convection processes. However,t he analysis of the vanadium-ion transfer rates or other possible effects are not within the scope of this paper and could be the subjecto ff uture studies. Nevertheless, the slope of the derivatives upports the potential-step analysisb ecause it gives additional evidence for the presence of AOS < + 3.5 or > + 3.5. This is essential because the deviationo ver time in the voltage level of the second plateau might be too high to precisely match the expected voltage of either 0.592 V( for AOS < + 3.5) or 0.663 V( for AOS > + 3.5). Therefore, the average voltage level of plateau 2c annot serve as information whether the AOS of the electrolyte is < + 3.5 or > + 3.5. However,b ya nalyzing the derivative of the measured OCV,t he AOS orientation (< + 3.5 or > + 3.5) can be determined from the slope of the inflection points. Nevertheless, the distinction between AOS < + 3.5 and > + 3.5 is not necessarily required in real-lifea pplications because there is only an occurrence of AOS with values ! + 3.5 under real operation conditions. [22] Validation experiments in lab-scale single cell Validation experimentso ft his new method were performed in al ab-scale single-cell VRFB. For several electrolyte samples with ap redefined AOS, the OCV potentials werem easured duringi nitial charging, and the potential-step analysis was applied. The obtainedO CV potentials for AOS + 3.5 and AOS > + 3.5 are shown in Figures 2a nd 3, respectively.A sd iscussed above,t hree plateausw ere observed in the OCV potential measurements for every sample, which weres eparated by the two inflection points IP V 4þ and IP V 3þ.T he times t V 4þ and t V 3þ were determinedf rom the corresponding peaks in the derivative of the OCV.A st he electrolyte imbalance of the sample increased, the length of plateau 2b ecame longera nd that of plateau 3b ecames horter.T herefore, the length of plateau 3 corresponds to the capacity of the VRFB. [20] For every sample, plateau 2i nt he OCV potential was in the range between approximately 0.6-0.7 V. Because the deviation over time for this measured voltage level is too high to precisely match the expectedv oltage of either 0.592 V( for AOS < + 3.5) or 0.663 V( for AOS > + 3.5), the AOS value was determined by the slope of the inflection points. The steeper inflection point corresponds to ac hange of the vanadium redox pairs in the positive half-cell electrolyte, whereas the shallower inflection point corresponds to ac hange of the vanadium redox pairs in the negative half-cell electrolyte. Therefore, if the first inflection point in the derivativei sf lat (IP 4 + )a nd the second one is steep (IP 3 + ), then the AOS is < + 3.5 and vice versa. The appearance of additional peaks in the derivativei s related to noise effects and can be identified by ac orrelating negative peak.
The obtained times t V 4þ and t V 3þ and the AOS results fort he potential-step analysis for every prepared sample are shown in Ta ble 2. Ag ood alignment between the prepared AOS and the measured AOS was observed. The maximum deviation was obtained for AOS =+3.4 with ad eviation of 0.018.C ompared with other methods, this is below the results of the UV/Visbased AOS detectorp roposed by Li et al.,w ho found am aximum deviation of 0.039 by using their method. [13] Because the possible imbalance in the VRFB only spans a range of 0.5 (in the positive and negative direction in relation to + 3.5), an error of 0.1 in the measured AOS meansa ne rror of 20 %i nt he imbalance detection. Accordingly,t his new methodc an describe electrolyte imbalances with an error of 3.6 %c omparedw ith 5% forp otentiometric titration [22] and 7.8 %f or the UV/Vis detector [13] (in [13] the authors mention an error of 1.28 %, whichi st he relative error;h owever,u sing the error calculation described above results in an imbalance accuracy of 7.8 %). This makes the methodv ery reliable for the determination of AOS and further rebalancings teps.

Application in as hort-stackV RFB-system
To verify the method under real operation conditions, the potential-step analysis of the initial charging for the determination of the AOS was appliedt oafour-cell short-stack VRFBsystem.A fter each 35 cycles,t he electrolytes were mixed and reused. During the subsequent initial charging of the mixed electrolytes the AOS was determined by the potential-step analysisa nd compared with the values determined by the UV/ Vis method. [18] The time-dependent OCV during the initial charginga nd its temporal derivative for the new electrolyte after 35 and 70 cycles are shown in Figure 4.
For every measurement, ap otential plateau at approximately 0.6-0.7 Vw as observed. The temporal length of the potential plateau increased with longer cycling of the electrolyte. This indicated an increasei nt he capacity imbalance between the positive and negative electrolyte. The short potential pla-    teau for the new electrolyte indicated that its AOS was not equal to exactly + 3.5;I P V 4þ occurred before IP V 3þ,w hich indicated an AOS < + 3.5. This observation was in good agreement with the value of AOS =+3.49 derived from the data of the analysisc ertificate of the commercial electrolyte and the UV/ Vis measurement of AOS =+3.497. After 35 and 70 cycles, the peak values in the derivativesw ere reversed, that is, IP V 4þ occurred after IP V 3þ.H ence, the AOS increased with the number of cycles towards values greater than + 3.5. This increase of the AOS during cyclingw as expected and can be explained owing to side reactions that cause an irreversible oxidation of the overall electrolyte and thus represent ac ommon problem in VRFBs. [23] The obtained times t V 4þ and t V 3þ are shown in Ta ble3,t ogether with the calculated AOS values and the values from the UV/Vis measurements. AllA OS values from the potential-step analysisare in the range of the AOS measured by UV/Vis analysis. The maximum deviationb etween two values was 0.029 for the AOS after 70 cycles. In terms of accuracy of the imbalance determination, this means an uncertainty of 5.8% between the two different methods. Even thought he data obtained from the short-stack cyclingi sn oisier than the data of the lab-scale cell cycling, the evaluation is still accurate, and the values t V 4þ and t V 3þ were easy to identify.T hese findings emphasizet he successful application of the potential-step analysise ven for larger systems, showing its high potential for automated maintenancea lgorithms. There is no need for any supplementary equipmento ther than the OCV cell and the voltage measurement, which comes on-board mostV RFB systemsf or state-ofcharge determination.
One constraint is that this new method is only applicable for fully mixed and equallyp arted electrolytes with an equal overall vanadiumc oncentration.H owever,b ecause ion exchange and electrolyte transfer between the two half-cells take place during operation, an electrolyte mixing is recommended at periodic intervals to retract reversible capacity fading. [22] This mixing can be directly utilized to apply the potential-step analysis during the subsequent initial charging of the electrolytes.

Conclusions
An ew potential-step analysis during initial charging of mixed electrolytes was developed for determining the average oxidation state (AOS) in vanadium redox flow batteries (VRFBs). The methodc onsists of as traightforwardp rocess for determining the AOS from the measured open-circuit voltage (OCV) curve. Ac orrelation between the duration of the potential plateaus in the OCV and the amount of vanadium ions of ac ertain oxidation state in the half-cell electrolytes was found and used to calculate the AOS. The potential-step analysis was performed in situ with no need for any additional equipmente xcept for an OCV cell, which is part of many VRFB systems for determining the state of charge. Moreover,t his new method is simple, cost efficient, timesaving, and can predict the AOS with ah igh accuracy of 3.6 %. Precise AOS detection is important for the maintenance of aV RFB because knowledge about the electrolyte imbalance is essential for rebalancing and cycling strategies. Therefore, the proposed methodh as ah igh potential for automated maintenance algorithms in large-scale VRFB systems.

Experimental Section Setup lab-scale cell experiments
The setup for the lab-scale experiments consisted of an in-housedeveloped single-cell assembly with an active area of 4 4cm, two pumps (Simdos 10, KNF Flodos AG, Switzerland), two electrolyte tanks, and as tandard two-compartment OCV cell. Each half-cell was connected by tubes in the following order:e lectrolyte tank, pump, the corresponding half-cell of the OCV cell, and then the cell assembly.F or the electrochemical measurements, ap otentiostat/galvanostat (Solartron Analytical Modulab Pstat, Model 2100 A with Booster 12 V/20A) was utilized. Af umasep FAP-450 (fumatech GmbH, Germany) membrane was used as an ion-conductive separator for the half-cells. Each half-cell consisted of aS IGRACELL GFD 4.6 EA graphite felt (SGL Carbon SE, Germany), aSIGRACELL bipolar plate PV15 (SGL Carbon SE, Germany), and ac opper plate as current collector.T he felts were pretreated at 400 8Cf or 18 hi na ir atmosphere in an oven (P330, Nabertherm GmbH, Germany) and compressed by 20 %i nt he assembly.T he electrolyte tanks were flushed with nitrogen during each experiment. To achieve as table behavior of the membrane, the cell was first cycled 20 times by using ac ommercial vanadium electrolyte [OXKEM, 1.62 m vanadium sulfate (51 %V 3 + ,4 9% V 4 + )i n2m sulfuric acid] with ap umping rate of 100 mL min À1 in the range between 0.7-1.8 V( cell voltage) at AE 93.75 mA cm À2 .F or the standard two-compartment OCV cell, SIGRACELL bipolar plates PV15 (SGL Carbon SE, Germany) were applied as current collectors and aN afion 117( Ion Power GmbH, Germany) membrane was used as as eparator with an active area of 2.36 cm 2 .

Preparation of electrolyte solutions with defined AOS
Electrolyte samples with different AOS were prepared. Twoe lectrolyte solutions (with AOS =+3a nd AOS =+4) were obtained by charging the commercial electrolyte [OXKEM, 1.62 m vanadium sulfate (51 %V 3 + ,4 9% V 4 + )i n2 m sulfuric acid, AOS =+3.49].F or this purpose, first as uccessive charging of 1050 mL electrolyte in each half-cell was performed with 125, 93.75, 62.5, 31.25, and 6.25 mA cm À2 up to ac ell voltage of 1.8 Vt oo btain fully charged electrolytes with oxidation states of V 2 + and V 5 + .F or the preparation of 1Lof 100 %V 3 + electrolyte, 50 mL of the negative half-cell electrolyte (V 2 + )w as removed, and the system was discharged successively with À125, À93.75, À62.5, À31.25, À6.25, and À5mAcm À2 until ac ut-off voltage of 0.8 V. The same procedure Table 3. Obtained times t V4 + and t V3 + and AOSr esults from the potential-step analysis of as hort-stack VRFB-system compared with AOS values determined with the UV/Vis method.

Measurement of the AOS by potential-step analysis in al abscale cell
For the measurement of the AOS of the six electrolyte solutions, 80 mL of the defined AOS samples was filled into each electrolyte tank of the setup. The initial charging was performed with 80 mA cm À2 up to an OCV of 1.4 V. The OCV was recorded and evaluated by applying the potential-step analysis. For every new sample, the whole setup was cleaned with deionized water,a nd the felts and bipolar plates were renewed.

Short-stack VRFB-system experiments
In as econd step, the method was applied to as hort-stack VRFBsystem, as represented in Figure 5. As tack was connected to the peripheral devices, consisting of two electrolyte tanks, two pumps (RD-40, IWAKI Europe GmbH, Germany), ac urrent source and sink (NL1V8C80, Hçcherl &H ackl, Germany), as tandard two-compartment OCV cell, and additional devices for controlling and data logging. The stack was built of four cells with copper endplates on both sides. The flow frames were made of polypropylene with an active electrode area of 726 cm 2 .T he materials for the separator, felts, bipolar plates, and OCV cell were the same as used for the lab-scale setup. The felts were activated with oxygen plasma for 20 min. The system was flushed with nitrogen before 24 Lo ft he commercial vanadium electrolyte [OXKEM, 1.62 m vanadium sulfate (51 %V 3 + ,4 9% V 4 + )i n2m sulfuric acid] was filled into each tank. The electrolytes were pumped through the system;a fterwards, the pumps were turned off, and the system was in idle mode for 72 h to ensure that all components were in contact and soaked with the electrolytes. Subsequently,t he system was repeatedly charged and discharged. Every 35 cycles the electrolytes of both half-cells were mixed and divided into two equal portions. An electrolyte sample of the mixed electrolyte was collected from the system each time, and the AOS was determined by UV/Vis measurements (LAMBDA XLS + UV/Vis Spectrophotometer,P erkinElmer,U SA) fol-lowing as imilar routine as described in [18].S ubsequently,t he potential-step analysis was performed during the initial charging of the mixed electrolytes, and the AOS was calculated.