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Error! No text of specified style in document. 1 Fakultät Technik und Informatik Department Maschinenbau und Produktion Faculty of Engineering and Computer Science Department of Mechanical Engineering and Production Management Niklas Janshen In situ state of charge measurement in vanadium redox flow batteries Bachelorarbeit
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  • Error! No text of specified style in document. 1

    Fakultät Technik und Informatik

    Department Maschinenbau und Produktion

    Faculty of Engineering and Computer Science

    Department of Mechanical Engineering and

    Production Management

    Niklas Janshen

    In situ state of charge measurement in vanadium redox flow batteries

    Bachelorarbeit

  • Error! No text of specified style in document. 2

    Niklas Janshen

    In situ state of charge measurement in vanadium redox flow batteries

    Bachelorarbeit eingereicht im Rahmen der Bachelorprüfung im Studiengang Maschinenbau/Entwicklung und Konstruktion am Department Maschinenbau und Produktion der Fakultät Technik und Informatik der Hochschule für Angewandte Wissenschaften Hamburg Erstprüfer/in: Prof. Dr. Thorsten Struckmann Zweitprüfer/in : M. Eng. Simon Ressel Abgabedatum: 11.11.2016

  • Error! No text of specified style in document. 3

    Zusammenfassung Niklas Janshen Thema der Bachelorthesis

    In situ Ladezustandsbestimmung in Vanadium Redox Flow Batterien

    Stichworte

    Vanadium Redox Flow Batterie, Ladezustandsbestimmung, Elektrolytdichte Kurzzusammenfassung

    Der Ladezustand von All-Vanadium Redox Flow Batterien (VRBs) kann über die Messung von Elektrolyteigenschaften bestimmt werden. Im Rahmen dieser Bachelor Thesis wurde eine Übersicht über die existierenden Methoden der Ladezustandsbestimmung in VRBs erstellt und die Eignung einer Dichtemessung zur Ermittlung des Ladezustands einer VRB evaluiert. Es wurden Lade- und Entladezyklen mit einer 1.6 M Vanadium und 4 M Sulfat Elektrolytlösung analysiert und die Temperaturabhängigkeit der Dichte experimentell bestimmt. Es wurde gezeigt, dass durch die Messung der Elektrolytdichte und Temperatur der Ladezustand der Halbzellen von VRB in situ mit einer Genauigkeit von 2.4 \% für den Anolyten und 7.4 \% für den Katholyten bestimmt werden kann. In der Zukunft kann mit der evaluierten Methode die Kreuzkontamination durch die Membran von VRBs untersucht werden. Zusätzlich kann mit der Vermessung von Elektrolyten unterschiedlicher Zusammensetzung der Anwedungsbereich erweitert werden.

    Niklas Janshen Title of the paper

    In situ state of charge measurement in vanadium redox flow batteries

    Keywords

    Vanadium redox flow batteries, state of charge monitoring, electrolyte density

    Abstract

    The State Of Charge (SOC) of All-Vanadium Redox Flow Batteries (VRB’s) can be monitored by measuring the electrolyte properties. Within this bachelor thesis, an overview on the existing SOC monitoring methods for VRB's was given. The applicability of a method to monitor the SOC of a VRB by measuring the electrolyte density was evaluated. Charge and discharge cycles with an electrolyte solution of 1.6 M vanadium and 4 M total sulfate were analysed and the temperature dependency of the density was determined experimentally. It was shown, that the SOC of both half-cells of a VRB can be monitored in situ with an accuracy of 2.4 \% for the anolyte and 7.4 \% for the catholyte by measuring the density and temperature. In future research, the crossover through the membrane of VRB’s can be studied by utilizing the evaluated method. In addition, the scope of the SOC monitor can be extended by investigating electrolytes with different compositions.

  • List of Abbreviations and Symbols

    a) Symbols

    Symbol Unit Description

    ci [mole l−1] molar concentration or molarity of i

    c [ml % g−1] slope of regression

    d [% K−1] temperature correction factor

    e [%] correction factor

    E0,cell [V ] standard cell potential

    E0,cell′ [V ] formal potential

    Ecell [V ] cell potential

    f [%] y-intercept of regression

    F [C mole−1] Faraday constant

    I [A] current

    Icell [A] cell current

    m g ml−1 ◦C−1 slope of regression

    n [mole] amount of substance

    Q [C] charge

    Qtheo [C] theoretical capacity

    R [J K−1 mole−1] gas constant

    R2 [-] coefficient of determination

    t [s] time

    T [K] temperature

    I

  • V [m3] volume

    z [-] number of electrons per reaction

    γ [-] activity coefficient

    ∆i [-] error of i

    κ [mS cm−1] electrolyte conductivity

    ρ [g ml−1] electrolyte density

    ρ0 [g ml−1] standard electrolyte density

    φ0 [V ] standard reduction potential

    b) Abbreviations

    blablablablablablaAbbreviation Full form

    ch charge

    dch discharge

    EES Electrical Energy Storage

    GfE Gesellschaft für Elektrometallurgie

    IR Infrared

    OCV Open Circuit Potential

    RE Reference Electrode

    SOC State Of Charge

    VRB All-Vanadium Redox Flow Battery

    WE Working Electrode

    II

  • Contents

    List of Abbreviations and Symbols I

    1 Introduction 31.1 The All-Vanadium Redox Flow Battery (VRB) . . . . . . . . . . . . . 3

    1.1.1 Electrochemistry of VRB . . . . . . . . . . . . . . . . . . . . . 41.1.2 Components of the VRB cell . . . . . . . . . . . . . . . . . . . 8

    1.2 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

    2 State of Charge Monitoring Methods & Electrolyte Properties 112.1 Formation,Charge and Discharge of the Electrolyte . . . . . . . . . . . 112.2 SOC Monitoring Methods in VRB . . . . . . . . . . . . . . . . . . . . 142.3 Electrolyte Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

    3 Experimental 253.1 Temperature Dependence of the Electrolyte Density . . . . . . . . . . 25

    3.1.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1.2 Measurement Routine . . . . . . . . . . . . . . . . . . . . . . . 26

    3.2 Charge and Discharge Cycling . . . . . . . . . . . . . . . . . . . . . . . 273.2.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2.2 Measurement Routine . . . . . . . . . . . . . . . . . . . . . . . 28

    4 Electrolyte Density Dependent SOC Monitoring 294.1 Temperature Influence . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.2 Influence of the SOC on the Electrolyte Density . . . . . . . . . . . . . 33

    4.2.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2.2 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.2.3 Measurement Accuracy . . . . . . . . . . . . . . . . . . . . . . 43

    5 Conclusions and Outlook 455.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

    5.1.1 Method comparison . . . . . . . . . . . . . . . . . . . . . . . . 465.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

    5.2.1 Required future research efforts . . . . . . . . . . . . . . . . . . 485.2.2 Crossover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

    Bibliography 56

    1

  • A Appendix IIIA.1 Error Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IIIA.2 Validation of Experimental Set Up . . . . . . . . . . . . . . . . . . . . VIA.3 Measuring Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIIA.4 Data Sheet - GfE Electrolyte . . . . . . . . . . . . . . . . . . . . . . . XI

    2

  • 1 Introduction

    The worlds energy demand is rapidly increasing with the growing population. Si-multaneously fossil fuels are running low and getting harder and more expensive toextract. In addition, by consuming the oil, coal and natural gases of this planet, CO2is emitted. This greenhouse gas is under suspicion to be the biggest contributor toglobal warming. If in the future, the energy demand wants to be met and the CO2emission reduced, the energy production sector will have to change extensively.The International Energy Agency has predicted, that the worlds energy demand willgrow by 33 %, while the need for electricity will grow by over 60 % until 2035 [1].Renewable energies will contribute 30 % to the increase of electricity production from2011 to 2035. While hydro power will hold around 50 % of the shares of the renew-ables, electricity production from wind energy will increase from 10 % to 24 %, whilesolar energy will increase from 1.4 % to 10 % [1].Wind and solar are both abundant sources of energy and accessible in all parts ofthe world, but they are not constantly available. To provide grid stability it is im-portant to generate as much electricity as the demand requires. Due to the difficultyin forecasting solar and especially wind energy production, more attention has beenraised to Electrical Energy Storage (EES).The EES can balance demand and generation by accumulating electric energy dur-ing periods of high production and low demand and introduce electricity into thegrid during periods of the opposite behavior. Additionally, this balancing service iseconomically valuable, because energy can be stored at low prices during off-peaktimes and released with high profit during peak times. Furthermore EES can bean assurance in the case of blackouts and can be used for reliable energy supply inoff-grid regions [2, 3].A promising technology for stationary EES is the redox-flow-battery (RFB) [4], whichstores electrical energy in two redox couples dissolved in electrolytes. A major ad-vantage of the RFB is the separation of power from energy capacity, which makesit possible to match the specific requirements for a variety of applications. The all-vanadium redox flow battery (VRB) is one of the most developed RFB’s [5] and apromising stationary EES technology [2].

    1.1 The All-Vanadium Redox Flow Battery (VRB)

    In the following section the basic principles and underlying electrochemistry of theVRB will be explained and the important components of the VRB will be introduced.In the end, difficulties in operating a VRB will be explained and the thesis objectiveswill be outlined.

    3

  • Figure 1.1: Principle of a VRB [6]

    In figure 1.1 a schematic of a VRB setup, including the processes occurring duringcharging and discharging, is depicted. The VRB consists of two electrolyte cyclesconnected to an electrochemical cell. The latter is divided by an ion exchange mem-brane into half-cells, the negative half-cell on the right side and the positive half-cellon the left side of the figure. The electrolytes are stored in two tanks and are pumpedthrough the half-cells during operation of the battery. The charge transfer takes placeat the electrode surfaces inside both half-cells.The electrolyte is an aqueous solution of vanadium salts in sulfuric acid and is de-noted as anolyte, the electrolyte in the negative- and as catholyte, the electrolyte inthe positive half-cell. To charge or discharge the battery, the cell has to be connectedto a power source or an electrical load.

    1.1.1 Electrochemistry of VRB

    The following section is focussing on the underlying electrochemistry of a VRB. Firstthe important basic terms and definitions of reduction-oxidation-reactions will beexplained, followed by the reactions taking place in a VRB. In the end the equationsused in this thesis will be explained and possible occurring side reactions will beintroduced.

    4

  • Fundamentals and Definitions of Reduction-Oxidation-Reactions

    To simplify the understanding of reduction-oxidation-reactions (redox-reactions) thefollowing fundamentals and definitions are helpful. A redox-reaction is a chemicalreaction in which one or more electrons are transferred between the reacting species.

    Oxidant + e− −−→ Product (1.1)

    Reductant −−→ Product + e− (1.2)

    In a reduction reaction (1.1) the oxidant gains an electron, while in an oxidation re-action (1.2) the reductant loses an electron to another species.Therefore, the oxidantis reduced and the reductant is oxidized. A reduction decreases the oxidation state,while an oxidation increases the oxidation state of the involved species.

    Reductant + Oxidante−−−⇀↽−−e−

    Oxidant + Reductant (1.3)

    When reduction and oxidation reactions appear at both sides of a chemical equationthe reaction is called a redox-reaction(1.3).

    The molarity

    The molarity or molar concentration is an important unit in chemistry when referringto the concentration of electrolytes. The molar concentration ci is defined as the ratioof the number of moles of the solute ni to the volume of the solution V :

    ci =niV

    in

    [mole

    l

    ]or [ M] (1.4)

    Redox Reactions of VRB’s

    When looking at figure 1.1 it can be seen, that the employed redox couples in a VRBare V 2+/V 3+ in the negative half-cell and V 4+/V 5+ in the positive half-cell. Thevanadium ions in the oxidation states 4 and 5 are known to form a V-O bond [7] andtherefore V 4+ occurs as V O2+ and V 5+ is present as V O2

    +. The reactions takingplace in the negative and positive half-cell and the corresponding standard reductionpotentials are the following:

    Negative half-cell

    V3+ + e−charge−−−−−−⇀↽−−−−−−

    dischargeV2+ ;φ−0 = −0.26V (1.5)

    Positive half-cell

    VO2+ + H2Ocharge−−−−−−⇀↽−−−−−−

    dischargeV O2

    + + 2 H+ + e− ;φ0+ = 1.00V (1.6)

    5

  • Overall redox-reaction

    V3+ + VO2+ + H2Ocharge−−−−−−⇀↽−−−−−−

    dischargeV2+ + V O2

    + + 2 H+ ;E0,cell = 1.26V (1.7)

    From the chemical reaction, (1.5) it can be seen, that during charge V 3+ is reducedto V 2+. The electron needed for the reduction is transferred through the outerelectrical circuit from the oxidation of V O2+ to V O2

    + in the positive half-cell. Thetransferred electron leads to an unbalanced charge of the half-cells. To compensatethis, one proton H+ from the catholyte crosses the ion exchange membrane towardsthe anolyte.The opposite reactions occur during discharge of the VRB. The V 2+ is oxidized toV 3+ in the negative half-cell, losing the electron needed for the reduction of V O2

    +

    to V O2+ in the positive half-cell. The electron is transferred through the outerelectrical circuit to the positive half-cell and one proton crosses the membrane fromthe anolyte to the catholyte. When looking at equation (1.6) it can be noticed thatin the positive half-cell during charge two hydrogen ions are produced and one watermolecule is consumed for each oxidized V O2+ ion.In conclusion, a fully charged VRB contains only V 2+ in the negative half-cell andV O2

    + in the positive half-cell, while a fully discharged VRB contains solely V 3+ inthe negative half-cell and V O2+ in the positive half-cell.

    The standard reduction potentials of the negative φ−0 and positive φ0+ half-cell are

    given in equations (1.5) and (1.6), respectively [8]. The potential is the driving forcefor the species to be oxidized or reduced and can experimentally be determined wheneither an electrolyte with V 2+/V 3+ or V O2+/V O2

    + is placed in one half-cell and ismeasured against a standard hydrogen electrode (SHE) in the other half-cell, understandard conditions. These are defined as 298.15 K, 1 M of both redox couples and1 bar pressure. The standard cell potential E0,cell of the VRB cell can be obtainedby:

    E0,cell = φ0+ − φ−0 (1.8)

    The standard cell potential can also be measured between the electrodes of the VRBat standard conditions without current flow.

    Faraday’s Law

    To determine the charge needed to fully charge or discharge the VRB, Faraday’s firstlaw of electrolysis can be applied.

    Q = I · t = z · F · n (1.9)

    According to Faraday the amount of charge Q, which flows through the outer elec-trical circuit can be expressed as the number of electrons per reaction z multipliedwith the Faraday constant F and the moles of the active species n dissolved in theelectrolyte. This amount of charge will be proportional to the applied current Iduring the time t.

    6

  • Nernst Equation

    As mentioned before, the standard cell potential E0,cell can experimentally be de-termined as the voltage measured between the negative and positive electrode in aVRB during standard conditions.By applying the Nernst equation, the cell potential Ecell can be determined theoret-ically for varying conditions [9]:

    Ecell = E0,cell −R · Tz · F

    ln

    [cV O+2

    · cV 2+ · (cH+)2

    cV O2+ · cV 3+·γV O+2

    · γV 2+ · (γH+)2

    γV O2+ · γV 3+

    ](1.10)

    Where ci is the molar concentration and γi the activity coefficients of the vanadiumspecies, c+H the proton concentration in the positive half-cell, R the gas constant andT the temperature. The activity coefficients however cannot directly be measured [9]and to circumvent this lack of information the measurable formal potential E0,cell

    ′ isintroduced:

    E′0,cell = E0,cell +R · Tz · F

    ln

    [γV O+2

    · γV 2+ · (γH+)2

    γV O2+ · γV 3+

    ](1.11)

    By combining equations (1.10) and (1.11), the activity constants can be includedinto the formal potential and the standard cell potential can be determined using thefollowing equation:

    Ecell = E0,cell′ − R · T

    z · Fln

    [cV O+2

    · cV 2+ · (cH+)2

    cV O2+ · cV 3+

    ](1.12)

    Another common way to avoid the use of the activity coefficients is to assume thatthey cancel each other out and are equal to one [9], which leads to:

    Ecell = E0,cell −R · Tz · F

    ln

    [cV O+2

    · cV 2+ · (cH+)2

    cV O2+ · cV 3+

    ](1.13)

    It should be noted however, that the Nernst equation is only valid for zero currentflow in the VRB. Therefore Ecell is denoted as Open Circuit Voltage (OCV), alsooften referred to as open circuit potential.

    State Of Charge (SOC)

    The State Of Charge (SOC) is a characteristic value to indicate how much energy isstored in a battery. The SOC can generally be expressed as the percentage of theamount of stored charge at a certain point Q(x) to the maximum possible storedamount of charge Qtheo, also be referred to as the theoretical capacity:

    SOC(x) =Q(x)

    Qtheo· 100% (1.14)

    7

  • In a VRB the energy is stored within two electrolytes and therefore the SOC of thewhole battery is dependent on both half-cells. When using Faraday’s Law (1.9) theSOC of a VRB can be calculated for each half-cell by:

    Negative half-cell

    SOC =nV 2+

    nV 2+ + nV 3+· 100% (1.15)

    Positive half-cellSOC =

    nV O2+

    nV O2+ + nV O2+· 100% (1.16)

    By using the definition of the molarity (1.4) and assuming that the electrolyte massand volume are constant the SOC of the entire VRB can be calculated by:

    SOC =cV 2+

    cV 2+ + cV 3+· 100% =

    cV O2+

    cV O2+ + cV O2+· 100% (1.17)

    Side Reactions

    The before mentioned chemical equations (1.5), (1.6) were explained under the as-sumption of an ideal behavior. However, in a real operating battery side reactionscan occur.

    2 H+ + 2 e− −−→ H2 (1.18)

    2 H2O −−→ 4 H+ + O2 + 4 e− (1.19)

    Hydrogen evolution (1.18) can occur at low potentials in the negative half-cell, whileoxygen evolution and proton production (1.19) can occur at high potentials in thepositive half-cell [10], both at a high SOC of the VRB. In addition, the rate ofhydrogen evolution is observed to be higher than the rate of oxygen evolution [11].Due to this, more current will flow into the hydrogen evolution reaction in the positivehalf-cell, than into the actual charge of the catholyte. Consequently, the electrolytesin the half-cells will have an unbalanced SOC.

    In addition to the side reactions mentioned above, the V 2+-ion is reported to behighly unstable. Therefore it can either be oxidized by water [7, 12] or by the oxygenin the air [8, 10].

    1.1.2 Components of the VRB cell

    In the following section, the components of a VRB will be introduced and the basicfunction will be explained.

    8

  • Electrode

    As already mentioned, the electron transfer takes place on the surfaces of the elec-trodes of the VRB. The cell potential can be measured between the electrode ofthe positive and the negative half-cell in the absence of current flow. In order toincrease the mass transfer and reduce the pressure drop, often porous graphite feltsare used as electrodes in VRB. During charge or discharge however, a degradation ofthe electrode material can occur [13] which can influence the electrode behavior andtherefore the measured potentials.

    Electrolyte

    In section 1.1.1, the electrolyte was introduced as an aqueous solution of vanadiumsalts in sulfuric acid. Due to the sulfuric acid H2SO4 more protons H

    +, as indicatedby the reaction of the positive half-cell and sulfate ions SO4

    − are present in the solu-tion. The composition of the electrolyte is denoted as the concentration of vanadiumcV and total sulfate cSO4− of the electrolyte.

    Membrane

    As already discussed in section 1.1.1, the ion exchange membrane is responsible forthe transport of protons from one half-cell to the other. Furthermore it plays a crucialrole in the set up of the cell, by separating the negative from the positive half-cell. Ingeneral there are two types of membranes, only permitting certain ions the passage:

    1. Anion exchange membranes

    2. Cation exchange membranes

    The first membranes obviously only permit anions to cross itself, while the secondmembranes only allow cations to pass from one half-cell to the other.However, in operating VRB’s other ions or molecules also happen to migrate throughthe membrane. This process is called crossover and can also be divided into two types:

    1. Selective crossover

    2. Bulk crossover

    Selective crossover describes certain ions or molecules crossing the membrane. There-fore it includes vanadium ions, sulfate ions and water molecules. Bulk crossover oc-curs when the electrolyte in its entirety crosses the membrane. Both types will leadto an imbalance of electrolyte volume of the half-cells and cause an SOC decreasedue to the reaction of the vanadium species with each other. This SOC decrease isoften referred to as self-discharge of the VRB.

    Up to this point two types of imbalances were introduced: a volumetric imbalancebetween the anolyte and catholyte and an imbalance in the SOC’s of the half-cell

    9

  • electrolytes. Both types of imbalance, limit the SOC of the entire cell, because onehalf-cell will limit the charge of the other one. This will lead to a capacity loss andrequires rebalancing methods [11].

    1.2 Thesis Objectives

    When examining the previous section, the following difficulties in the operation of aVRB can be observed:

    Overcharging of the battery will lead to undesirable side reactions.

    Side reactions, bulk and selective crossover can lead to an imbalance and there-fore to a capacity loss.

    The SOC of both half-cells need to be monitored in order to detect imbalancesand whether one half-cell is in danger of overcharging.

    Thesis Objectives

    In order to solve the above listed problems the applicability of a new SOC monitoringmethod should be evaluated. The SOC of a VRB should be monitored by measuringthe electrolyte density and temperature in situ. In detail the following points shouldbe investigated:

    Literature research on existing SOC monitoring methods for VRB’s should bedone and an overview of these should be given. The focus should be on theelectrolyte composition, advantages, limitations and on the feasibility of thosemethods in order to compare them with the new monitoring method.

    The temperature influence on the electrolyte density should be experimentallyinvestigated for the anolyte and catholyte of VRB’s. Therefore an experimentalset up and measurement routine should be developed.

    The applicability of an in situ density and temperature measurement of thepositive and negative electrolyte to monitor the SOC of a VRB should beevaluated.

    The method should be validated in comparison with another validated, existingSOC monitoring method. For that purpose either an OCV or an in situ half-cellpotential measurement should be utilized.

    An outlook should be given, focussing on the possibility of determining thecrossover through the membrane of a VRB, by the application of the evaluatedmethod.

    10

  • 2 State of Charge Monitoring Methods &Electrolyte Properties

    The following chapter is divided into three sections. In the first one the detailedprocesses which occur during charge and discharge of the VRB will be explained.In the second section an overview on the existing SOC monitoring methods will begiven, while in the third section studies on the electrolyte density will be presented.

    2.1 Formation,Charge and Discharge of the Electrolyte

    From the previously introduced redox reaction equations (1.5), (1.6) and (1.7) theexact process taking place in the VRB cell can not be observed yet. They neitherconsider the complete composition of the electrolyte nor the transfer of hydrogenions through the membrane. In the following section, the processes which take placeduring charge and discharge of the VRB will be explained.

    In section 1.1.2, the electrolyte was introduced as an aqueous solution of vanadiumspecies in sulfuric acid. In order to achieve higher energy densities, the vanadiumconcentration can be increased. Thereby, the dissolved V 5+-ions become unstableand can precipitate more easily [14]. To avoid precipitation of vanadium species,in some cases a stabilizing agent is added [15]. To produce electrolytes employedin VRB’s, different vanadium salts and techniques to dissolve them, are used. Theelectrolyte used for experiments in this thesis will be used as an example to explainthe detailed reactions, which occur during charge and discharge of the VRB.

    The electrolyte from Gesellschaft für Elektrometallurgie mbH (GfE), used for mea-surements in this thesis, is produced by the dissolution of 0.8 M vanadyl sulfate(V OSO4) and 0.4 M vanadium(III) sulfate (V2[SO4]3) in a 2 M sulfuric acid solu-tion. Furthermore 0.05 M phosphoric acid (H3PO4) is added to increase the stabilityof the electrolyte. However, in the following section the effect of the phosphoric acidwill be neglected. The ratio of V OSO4 to V2(SO4)3 needs to be 2:1, to obtain asolution with an equal concentration of V 3+ and V O2+ referred to as V 3.5+.

    It should be noted, that in the following processes concerning the electrolyte, the sul-furic acid is assumed to be fully dissociated. However, the acid dissociation generallytakes two steps [7]:

    H2SO4 −−→ H+ +HSO42− (2.1)

    HSO42− −−→ H+ + SO42− (2.2)

    11

  • In the first step (2.1) one bisulfate ion (HSO42−) and one proton is produced for

    each dissociated sulfuric acid molecule. In the second step (2.2) another protonand one sulfate ion (SO4

    −) arise for each dissociated bisulfate ion. Whether thedissociation occurs completely or only to the first step is uncertain [6] and amongstothers dependent on the total sulfate concentration [7].

    Before operating the cell, the formation of the electrolyte has to take place. For thisprocess, the V 3.5+ electrolyte solution is filled into both tanks and charged until theanolyte solely contains V 3+ ions while in the catholyte only V O2+ ions are present.

    2.1.1 Formation of the Electrolyte

    In figure 2.1 the formation of an electrolyte solution of 1M V 3.5+ in variable sulfuricacid concentration is depicted. After a first observation, it can be seen that the dis-solution of one V OSO4 molecule leads to one V O

    2+ ion and one sulfate ion, whilethe dissolution of one V2(SO4)3 molecule results in two V

    3+ ions and three sulfateions. In addition for each dissociated sulfuric acid molecule, two protons and onesulfate ion are produced.For further comprehension of the formation and the transfer of hydrogen throughthe membrane it is helpful to focus on the processes taking place in the negative andpositive half-cell separately.By studying the formation in the negative half-cell, shown in figure 2.1, it can beseen that the V 3+ ions arising from the dissolution of the vanadium(III) sulfate stayin their present form, while the V O2+ ions are split into one oxide ion (O2−) and oneV 4+ ion. The oxide ion forms one water molecule with two protons, available fromthe sulfuric acid dissociation, while the V 4+ ion needs one electron to be reduced toV 3+. The electron needed for the reduction comes from the oxidation of the V 3+ ionin the positive half-cell.When looking at the positive half-cell reactions it can be seen that the V O2+ ionsarising from the dissolution of the vanadyl sulfate stay in their present form, whilethe V 3+ ions are oxidized to V 4+ donating the previously mentioned electron. Toform the V O2+ ion, one water molecule is electrolysed to produce one oxide ion andtwo protons. The V 4+ ion and the oxide ion then form the V O2+ ion, while theprotons stay dissolved and increase the proton concentration of the positive half-cell.The electron transferred through the outer electrical circuit leads to an unbalancedcharge of the half-cells and one proton is transferred through the ion exchange mem-brane. The outer electrical circuit is depicted as a dotted line, the membrane as adouble line and the proton crossing the membrane as a dashed line.After the formation, the electrolyte has an SOC of 0% according to equation (1.17)and can be used for the actual charge and discharge process.

    12

  • 0.5 𝑽𝑶𝑺𝑶𝟒 0.5𝑽𝑶𝑺𝑶𝟒0.25 𝑽𝟐 𝑺𝑶𝟒 𝟑 𝟎. 𝟓𝑽𝟐 𝑺𝑶𝟒 𝟑𝒙 𝑯𝟐𝑶 𝒙 𝑯𝟐𝑶a 𝑯𝟐𝑺𝑶𝟒 a 𝑯𝟐𝑺𝑶𝟒

    Negative half-cell Positive half-cell

    0.5𝑉𝑂2+ 1.25 𝑆𝑂42− 0.5 𝑉3+ 𝑎 2𝐻+ a 𝑆𝑂4

    2− 0.5𝑉𝑂2+1.25 𝑆𝑂42−0.5𝑉3+ a 2𝐻+ a 𝑆𝑂4

    2−0.5𝑂2− 1𝐻+

    2a + 0.5 𝑯+ a+𝟏. 𝟐𝟓 𝑺𝑶𝟒𝟐−

    0.5𝐻+

    𝟏𝑽𝑶𝟐+

    0.5𝑉4+0.5𝑒−

    a + 1.25 𝑺𝑶𝟒𝟐−

    0.5𝑂2−0.5𝑉4+

    𝟏 𝑽𝟑+

    1𝐻+

    (𝒙 − 𝟎. 𝟓 𝑯𝟐𝑶)(𝒙 + 𝟎. 𝟓𝑯𝟐𝑶) 2a + 0.5 𝑯+

    0.5𝑒−

    Figure 2.1: Schematic of the formation process in a VRB for an electrolyte solutionof 1M vanadium in variable sulfuric acid concentration.

    2.1.2 Charge/Discharge of the Electrolyte

    In figure 2.2 the charge and discharge process for the previously mentioned electrolytesolution is depicted. The arrows on the right side of the figure follow the processesoccurring during charge. However, by reversing them the discharge would be shown.On the left side of the figure the SOC and the direction of the charge and dischargeprocess is shown. So from top to bottom the electrolyte starts with 0 % SOC andends with 100% SOC. The starting conditions are the same as those from the endof the formation depicted in figure 2.1. Furthermore the outer electrical circuit isdepicted as a dotted line, the membrane as a double line and the transferred protonas a dashed line.After a first observation of the schematic, it can be seen that the sulfate ions in bothhalf-cells stay in their present form and do not vary in concentration throughout theentire charging process. The same observance can be made for the water moleculesin the negative half-cell.It can also be seen, that the V 3+ ion in the negative half-cell is reduced to V 2+,by receiving the electron of the V O2+ ion from the positive half-cell. The latter isthereby oxidized to V O3+, which forms a V O2

    + ion with an oxide molecule. Theoxide molecule is produced by the electrolysis of one water molecule, which pro-duces two more protons in the positive half-cell. Due to the fact that an electron istransferred through the outer electrical circuit, one proton crosses the ion exchangemembrane to balance the charge of the half-cells.At the time the electrolyte has an SOC of 100% the proton concentration in bothhalf-cells increased, while the water concentration in the positive half-cell decreased.

    After looking at the formation, charge and discharge process as well as the aciddissociation it can be seen, that the proton concentration in both half-cells is de-pendent on the degree of acid dissociation, the total vanadium and the sulfuric acid

    13

  • Negative half-cell Positive half-cell

    2a + 0.5 𝑯+𝟏𝑽𝑶𝟐+a + 1.25 𝑺𝑶𝟒𝟐−𝟏 𝑽𝟑+ (𝒙 − 𝟎. 𝟓 𝑯𝟐𝑶)(𝒙 + 𝟎. 𝟓𝑯𝟐𝑶) 2a + 0.5 𝑯

    +

    1𝑒− 1𝑉𝑂3+ 1𝑂2− 2𝐻+

    𝟏𝑽𝑶𝟐+ (𝒙 −

    𝟏. 𝟓 𝑯𝟐𝑶)𝟏 𝑽𝟐+ (𝒙 + 𝟎. 𝟓𝑯𝟐𝑶)

    1𝑒−

    2a + 1.5 𝑯+

    1𝐻+

    2a + 1.5 𝑯+a + 1.25 𝑺𝑶𝟒𝟐−

    a+𝟏. 𝟐𝟓 𝑺𝑶𝟒

    𝟐−

    a+𝟏. 𝟐𝟓 𝑺𝑶𝟒

    𝟐−

    charge

    disch

    arge

    SOC=0%

    SOC=100%

    Figure 2.2: Schematic of the charge and discharge process for an electrolyte solutionof 1M vanadium in variable sulfuric acid concentration.

    concentration. The increase of the water concentration in the negative half-cell dur-ing formation and the decrease in the positive half-cell during formation and chargeonly depends on the total vanadium concentration. The total sulfate concentrationis dependent on the sulfuric acid and the vanadium sulfate concentration. It shouldbe noted that the effect of the dissociation of water was neglected in this section.After looking at the charge, discharge and formation, it can be seen that the elec-trolyte undergoes significant changes. Due to this, electrolyte properties like viscosity,density, conductivity and pH-value vary during these processes [7].

    2.2 SOC Monitoring Methods in VRB

    In the previous chapter the basic electrochemistry of VRB was introduced, followedby a brief description of the components of the VRB cell. This insight leads toimportant criteria for the assessment of SOC monitoring methods.

    As mentioned in section 1.2, the detection of any imbalances arising from side reac-tions or crossover is a necessary ability of a SOC monitoring system.Whether or not a method can be executed in or ex situ is of importance for the futureimplementation in commercial systems and therefore crucial for the feasibility.Furthermore the advantages or limitations compared to other methods will be dis-cussed in order to compare them with the evaluated method.In addition, the knowledge of the electrolyte composition is critical for comparisonwith own present or future results. As mentioned in section 2.1 different techniquesare used to produce vanadium electrolytes. However, it is assumed, that those willnot influence the electrolyte properties, if the same composition is obtained. Onlyby adding stabilizing agents the electrolyte properties might change. Consequently,

    14

  • SOC monitoring methods

    coulombcounting

    potentiometric

    titration

    via potential

    measurements

    spectroscopic

    methods

    via electrolyte

    properties

    Open Circuit Potential

    electrolyte half-cell potentials

    UV/Vis infrared conductivityother

    absorption transmission

    Figure 2.3: Overview of SOC monitoring methods used in VRB.

    a comparison with results which are obtained with electrolyte solutions of the samecomposition, but without stabilizing agents can be difficult. In the analysed liter-ature, either self produced electrolytes were used without any stabilizing agents orthe 1.6 M vanadium and 4 M total sulfate from GfE was used. Because of this, thetechniques to produce the electrolytes are not mentioned in the following section.The existing SOC monitoring used for VRB’s, which were found during the litera-ture research, are depicted in figure 2.3. Some of them can be further divided intoSOC monitoring by measuring electrolyte properties or potentials and spectroscopicmethods.

    2.2.1 Coulomb Counting

    The cell current integration over time is called coulomb counting. The SOC canhence be determined using a theoretical calculated possible charge amount Qtheo byapplying Faraday’s law (1.9):

    SOC(t) =

    ∫ t0 Idt

    Qtheo· 100% (2.3)

    This is a common method for a rough SOC estimation and was for instance used byAaron et al. [16] for the characterization of their cell design at an SOC of approxi-mately 60 % with an electrolyte solution of 1 M vanadium and 6 M total sulfate.Coulomb counting is a very simple method and easy to apply during operation, butit does not consider any side reactions and therefore any current flowing in those willlead to errors. If these errors are not corrected they will accumulate over each chargeand discharge cycle.

    15

  • 2.2.2 Potentiometric Titration

    For the potentiometric titration the electrolyte needs to be extracted from the VRBand diluted. Afterwards the potential between two electrodes is recorded while theactive species are oxidized with an appropriate oxidant. The recorded voltage isplotted over the titrated volume and any voltage jumps indicate the oxidation statesof the vanadium species.Becker et al. [17] used potentiometric titration for the characterization of the currentdensity distribution at different SOC’s in VRB’s with an electrolyte solution of 1.6M vanadium and 4 M total sulfate purchased from GfE.Petchsingh et al. [18] used potentiometric titration for the calibration of their spec-troscopic SOC monitoring method for the positive half-cell in VRB for varying elec-trolyte compositions, 0.35- 1.6 M vanadium and 4 M total sulfate.Potentiometric titration is a precise method to determine the SOC, but it is only ap-plicable ex situ. It includes also complicated steps and is therefore time-consuming.Furthermore the anolyte and catholyte need to be treated with different oxidantsand diluted in different acids [17, 19].

    2.2.3 SOC Monitoring via Potential Measurements

    Potentiometric titration not only includes potential measurement, but chemical treat-ment as well, the following methods are only dependent on the measurement of po-tentials. These can generally be divided into measuring the cell potential of the VRB,referred to as Open Circuit Voltage (OCV) and the potential of either the anolyteor catholyte, referred to as electrolyte half-cell potentials.

    Open Circuit Voltage (OCV)

    As mentioned in 1.1.1, the SOC in terms of equation (1.17) is dependent on the ratioof V 5+ to V 4+ ions and V 2+ to V 3+ ions. Therefore the SOC can be calculated,dependent on the OCV, using one of the forms of the Nernst equations. As men-tioned before, there are several forms of the Nernst equation. In some studies theproton concentration in the positive half-cell is assumed to be constantly equal toone. In figure 2.4, the OCV over SOC for an electrolyte solution of 1 M vanadiumin 1 M sulfuric acid is shown. The dashed line shows the OCV for a constant protonconcentration of 1 M in the positive half-cell throughout the charge and dischargeprocess while the solid line corresponds to the OCV with a varying proton concen-tration according to the schematic depicted in figure 2.2. Generally, it can be seenthat the OCV increases strongly during the first 5 % of the SOC range. Afterwardsit increases approximately linearly and ends with another strong increase from 95%- 100% SOC. In addition an average deviation of approximately 0.05 V can becalculated between the two depicted graphs.Tang et al. [20] determined the SOC via OCV in order to compare the results witha spectroscopic measured SOC for an electrolyte solution of 1 M vanadium and 5 Mtotal sulfate. The OCV was calculated with an initial proton concentration of 4 M

    16

  • SOC [%]0 10 20 30 40 50 60 70 80 90 100

    OC

    V [

    V]

    0.9

    1

    1.1

    1.2

    1.3

    1.4

    1.5

    1.6

    1.7

    OCV with varying cH+

    OCV

    Figure 2.4: Calculated OCV for an electrolyte solution of 1 M vanadium in 1M sul-furic acid in dependence of the SOC with included cH+ variation, solidline, and without cH+ , dashed line.

    and a standard potential of 1.26 V using equation (1.13) and a mean deviation ofapproximately 7 % between the calculated and the measured OCV values was found.P. Pyka [21] monitored the SOC via OCV measurements for an electrolyte solutionof 1.6 M and 4 M total sulfate from GfE. Two models were compared: one includingthe varying proton concentration with a standard cell potential of 1.26 V using equa-tion (1.13) and one neglecting the proton concentration with a formal potential of1.4 V using equation (1.12). Both were found to be equally precise, while deviationsappeared at an SOC of above 90 %. Furthermore, the formal potential of the secondmodel was adjusted to 1.419 V.

    The above presented SOC monitoring methods using OCV measurements can beused in situ, but they cannot be applied during cell operation.

    Ngamsai et al. [22] determined the SOC via OCV for electrolyte solutions withcompositions of 1.5- 2 M vanadium and 3- 5 M total sulfate for the calibration ofan SOC monitoring method utilizing the electrolyte conductivity. The OCV wasreported to increase with increasing total sulfate concentration and was measured inan OCV-cell. The cell was implemented before the actual cell, which enables SOCmonitoring during cell operation. Nevertheless, in the additional cell more crossovercan occur.

    17

  • In conclusion, SOC monitoring via OCV measurement can be applied without anyadditional equipment, except the OCV-cell, but it cannot detect any imbalance.As shown in figure 2.4, the effect of the varying proton concentration increases theOCV with a constant value. At the moment, the varying proton concentration isneglected, but the formal potential is adjusted to a higher value, the SOC can bemeasured with the same precision. Thereby a known influence is neglected in order touse a less complex model. Furthermore the measured potentials might be influencedby electrode degradation processes [13], which can occur during cell operation.

    Electrolyte Half-Cell Potentials

    By applying the Nernst equation separately to both half-cells the theoretical reduc-tion potentials of the positive φ+ and the negative half-cell φ− can be obtained:

    Negative half-cell

    φ− = φ0− − R · T

    z · Fln

    [cV 2+

    cV 3+

    ](2.4)

    Positive half-cell

    φ+ = φ0+ − R · T

    z · Fln

    [cV O2+

    cV O2+ · (cH+)2

    ](2.5)

    For the measurement of the reduction potentials, now referred to as the electrolytehalf-cell potentials, a reference electrode (RE) with a known potential is needed [23].To measure the electrolyte half-cell potential the reference electrode is placed in shortdistance to a working electrode (WE), both immersed inside the electrolyte. The typeof the reference electrode in the following section is given as RE against WE.Corcuera et al. [11] monitored the SOC via electrolyte half-cell potentials measuredby a Hg/Hg2SO4 in 2 M H2SO4 against a carbon rod immersed in both tanks ofthe VRB. The proton concentration was assumed to be one and with this a formalhalf-cell potential of -0.207 V for the negative and 1.1182 V for the positive half-cellwas measured.Rudolph et al. [24, 25] measured the electrolyte half-cell potentials by the use of aAg/AgCl against a unknown working electrode in the tanks for an electrolyte solutionof 1.6 M vanadium and 4 M total sulfate from GfE. The determined SOC was usedto calibrate an SOC monitoring method, which utilizes an infrared (IR) sensor.

    Depending on the tank size and electrolyte volume used, the two abovementionedmethods can lead to errors, due to stratification of the electrolyte in the tanks.

    P. Pyka [21] monitored the SOC via electrolyte half-cell potentials measured by aHg/HgSO4 in 2.5 M H2SO4 against a glassy carbon rod for an electrolyte solutionof 1.6 M vanadium and 4 M total sulfate from GfE. Flow through RE’s employedafter the cells were used to avoid the stratification in the tanks. For the anolyte, φ0

    was adjusted to -0.289 V and for the catholyte, φ0+ was adjusted to 1.029 V. For

    the positive half-cells good agreements between the calculated and measured SOC

    18

  • values were found until an SOC of 80 %, while for the negative half-cell deviationsunder 10 % and above 90 % were reported.

    By monitoring the half-cell potentials an imbalance can be detected. However, ref-erence electrodes are influenced by the proton concentration [10], which is furtherdependent on the sulfuric acid and vanadium concentration as well as the sulfuricacid dissociation. Additionally, the electrolyte can diffuse into the reference and alterthe potential. Furthermore, to ensure the potential is stable, the RE has to be refer-enced itself after an experiment. Another error can occur due to impurities inside thereference electrode, which can corrosively react with the electrode material, changethe activity of the reacting species or the properties of the electrolyte [23].

    Limitations of SOC monitoring via potential measurement in general are, that thepotential of the VRB around an SOC of 50 % changes very little with increasing ordecreasing SOC. Therefore, in this SOC range small offsets can lead to significanterrors. In addition, the theoretical potentials need to be adjusted to the measuredvalues.

    2.2.4 Spectroscopic Methods

    As already mentioned in section 2.1, the electrolyte changes significantly duringcharging and discharging. From table 2.1 it can be seen, that each of the fouroxidation states of the vanadium species has their specific colour [26]. Spectroscopicmeasurement methods utilize this dependency to measure the SOC via absorptionor transmission spectra.

    UV/Vis Spectroscopy

    Spectroscopic measurements in the visible spectrum of light are called UV/Vis spec-troscopy, which can further be divided into absorption- and transmission spectrameasurements.

    Skyllas et al. [26] monitored the SOC via absorption spectra measurements usinga wavelength of 750 nm for an electrolyte solution of 2 M vanadium and 5 M totalsulfate. The measurement was conducted ex situ on reference solutions and reportedas not feasible for the catholyte due to the high absorbance of the V 4+/V 5+ solution.However for the anolyte a feasibility over the range of 5 - 100 % was reported.P. Pyka [21] monitored the SOC of an electrolyte solution of 1.6 M vanadium and 4M total sulfate from GfE in situ in a bypass utilizing a wavelength of 405 nm. For thepositive half-cell the method was reported as not feasible due to non-linear behaviorof the absorbance spectra.Petchsingh et al. [18] monitored the SOC of the positive half-cell utilizing two wave-lengths and a mathematical model to simulate the spectra of the V 4+/V 5+ solution.Different electrolyte solutions with 0.35- 1.6 M vanadium and 4 M total sulfate were

    19

  • negative half-cell positive half-cell

    oxidation state 2 3 4 5specific colour violet green yellow blue

    Table 2.1: Different colours of the electrolyte corresponding to the oxidation state ofthe vanadium species

    used.Liu et al. [27, 28] monitored the SOC of the positive- and negative half-cell in situ byinvestigating the entire transmission spectra. Different electrolyte solutions with 1.4-1.9 M vanadium and 2.2- 2.8 M total sulfate, confirmed by potentiometric titrationwith an average error of 1.1 %, were used and a dependence of the V 4+/V 5+ spectrabetween an SOC of 50- 100 % on the total sulfate concentration was found.

    Infrared

    Rudolph et al. [24, 25, 29] utilized an IR sensor in the range of 950 nm to monitor theSOC of an electrolyte solution of 1.6 M vanadium and 4 M total sulfate from GfE insitu. The sensor was calibrated using the previously mentioned Ag/AgCl RE. Withthis an error between the calibration curve and the 8th degree polynomial equationof 1 % was reported. For the catholyte the method can only detect 0 % and 100 %SOC.

    In conclusion, spectroscopic methods can monitor the SOC in situ, but additionalequipment is needed. A bypass and an additional pump in case of [21] or a home madetransmission spectrum analytical system in case of [27, 28]. Furthermore, the moni-toring of the positive half-cell is reported to be impossible [21, 26], limited possible[24, 25, 29] or only by establishing a huge database utilizing the entire transmissionspectrum of the catholyte [27]. Also in [18] a series of different electrolyte mixturesneeded to be analysed to establish the monitoring method. Additionally, in [27, 28]at an SOC between 50 % and 100 %, a dependence of the catholyte spectra on thetotal sulfate concentration was found.

    2.2.5 SOC Monitoring via Measurement of Electrolyte Properties

    As mentioned in section 2.1, the electrolyte undergoes changes during the charge anddischarge process. Thereby, after studying the change of electrolyte properties withvarying SOC, the latter can be monitored by measuring the former.

    Conductivity

    Skyllas et al. [26] measured the electrolyte conductivity ex situ of different referencesolutions of 0.5- 2 M vanadium and 4- 5 M total sulfate at 22 ◦C.

    20

  • Ngamsai et al. [22] monitored the SOC in situ via electrolyte conductivity for 1- 2 Mvanadium and 3- 5 M total sulfate solutions. In both studies, the conductivity wasreported to increase with increasing total sulfate concentration and to decrease withincreasing vanadium concentration. In addition, Skyllas et al. [26] monitored theSOC for a 2 M vanadium and 5 M total sulfate electrolyte solution at 10, 20 and 30◦C and a linear increase of the conductivity with increasing SOC for both half-cellswas reported.Corcuera et al. [11] monitored the SOC via electrolyte conductivity for an electrolytesolution of 1.6 M and 4.2 M total sulfate at 10, 22 and 45 ◦C. A Comparison of thecalculated conductivity values with experimental data showed good correlation anda higher precision for the positive half-cell.All in all, the feasibility of the conductivity as an indicator for the SOC was reportedin all studies. Nevertheless, the high dependency of the conductivity on the temper-ature increases the measurement effort. In addition, varying total sulfate, vanadiumand proton concentration, due to crossover or side reactions, will lead to errors ifthey are not considered.

    pH-Value

    As mentioned in section 1.1.2, the hydrogen concentration in both half-cells willideally change during charge and discharge according to figure 2.2. The pH-valuerepresents the amount of hydrogen ions in an aqueous solution.S. Ressel [6] studied the pH-value in dependence of the SOC in situ for an electrolytesolution of 1.6 M and 4 M total sulfate. The pH-value as an SOC monitor was re-ported as feasible for the positive half-cell. The pH-value in the negative half-cellremained constant throughout the experiment.

    Other

    Skyllas et al. [7] presented in two graphs the dependency of the electrolyte viscosityand density on the SOC for a 2 M vanadium and 5 M total sulfate electrolyte at 10,20 and 30 ◦C. However, they referred to a patent from 1990 [30], in which neitherthe two graphs nor the SOC as a function of density and viscosity were mentioned.Therefore it remains uncertain how these values were measured and they will not beconsidered in the following sections.

    Furthermore it should be noted, that the exact determination of the boundaries ofthe SOC range are not easy to obtain. In the end of a charge process, the exactvalue of 100 % SOC is difficult to detect because the possibility of overcharging theVRB. Furthermore at the end of the discharge, the VRB can go below 0 % into theformation region. In conclusion, an indicator is needed to detect whether the batteryis fully charged or discharged. In table 2.2, the indicators for 0 % and 100 % SOC,used in the analysed literature, are listed. The found indicators are explained in thefollowing paragraph.

    21

  • indicator for 100 % SOC specification and reference

    cut off current 4 mA/cm2 [16, 20], 6 mA/cm2 [10]

    change of electrolyte colour [11, 18, 22, 26]

    constant measurement signal OCV [22], electrolyte half-cell potential [18,31], absorption [21]

    indicator for 0 % SOC

    potential jump electrolyte half-cell potential [18]

    maximum in absorption [21, 24]

    reference solution only applicable for the catholyte - dissolutionof V OSO4 in sulfuric acid [10, 26, 31]

    Table 2.2: Indicators for a fully charged and discharged VRB, an SOC of 100 % and0 %, respectively.

    When charging the VRB at a constant voltage, the current drops over the chargingprocess, but it will not reach zero, because of the side reactions. One way to definea fully charged battery is to use a cut off current. However this indicator is highlydependent on the ohmic resistance of the used VRB cell. A cell with a high ohmicresistance will reach the cut off current earlier than one with a lower ohmic resistance.Another common way is to simply take the moment when the colour of the electrolytechanges to violet in case of the anolyte and yellow in case of the catholyte. The thirdfound indicator for a fully charged VRB is the time when a measurement signal, whichrepresents the SOC, stays constant. Measurement signals, which can be utilized forthis purpose are the OCV, the electrolyte half-cell potential and the absorption.As an indicator for 0 % SOC the half-cell potential can be monitored, because afterthe formation process a sharp increase in the potential of both half-cells was reportedand theoretically supported by the Nernst equation. Spectroscopic methods use themaximum in the absorption signal. Another way often used to ensure an SOC of 0% is to dissolve V OSO4 in sulfuric acid to obtain a solution containing only V

    4+.

    2.3 Electrolyte Properties

    In the following section, a short introduction into the aqueous chemistry will begiven, followed by a brief overview of the temperature stability of the vanadiumelectrolyte in order to establish the temperature range for the measurement routinein the following chapter. Afterwards, studies on the density of vanadium electrolytesolutions. They will be used for comparison with own measured densities in order toestimate the effect of crossover on the density.

    In general, aqueous electrolyte solutions are produced by using water as the solvent

    22

  • and adding one or more solutes to produce dissolved cations and anions. In thecase of the VRB, the solutes are vanadium sulfates and sulfuric acid. The chargeof those ions will have an impact on the dipole water molecules and hence disturbthe prior configuration of them. This will cause a change of the physical propertiesof the solution. The ions in the aqueous solution have stronger charges than thehydrogen and oxygen ions of the water and therefore the water molecules are forcedto form hydration spheres around the ions. Within these spheres, the oxygen ionsare oriented towards the positively charged ion, while the hydrogen ion is attractedtowards the negatively charged ion [12]. Hence, in case of the vanadium electrolyte,the oxygen ions are attracted towards the vanadium ions and the hydrogen ions areoriented towards the sulfate ions.

    In [32], Xiao et al. reported that both, V 2+ and V 3+ electrolyte solutions are stableuntil minus 25 ◦C and increase in stability with increasing temperatures. For the V 4+

    and V 5+ electrolyte solutions, the opposite behavior occurred and V 5+ was reportedto precipitate at 35 ◦C.

    Studies on Electrolyte Density

    F. Rahman [14] studied the density of different electrolyte solutions, containing 2-5 M V 5+ and 5- 7 M total sulfate at 20 ◦C. The V 5+ solutions were prepared byelectrolytic oxidation of V 4+ solutions, afterwards analysed by inductively coupledplasma mass spectrometry and adjusted if needed. The measured densities are pre-sented in table 2.3.

    V 5+ concen-tration [M]

    total sulfate concentration [M]

    5 6 7

    3 1.527 1.541 1.5794 1.591 1.619 1.6705 1.657 1.721 1.789

    Table 2.3: Densities of different V 5+ electrolyte solutions at 20 ◦C in g/ml [14]

    A. Mousa [12] studied the densities of V 2+ and V 3+ solutions over a range of 15- 40◦C for various vanadium and total sulfate concentrations in the case of V 3+. TheV 2+ solutions were reported to be highly unstable and therefore only the densitiesat 25 ◦C for 1- 2 M vanadium and 3- 4 M total sulfates were reported. The V 2+

    and V 3+ solutions were prepared by electrolytic reduction of V 4+ solutions and theconcentrations were confirmed by potentiometric titration, with a reported relativeerror of 10 %. The measured densities are presented in table 2.5 and 2.4 for the V 3+-and V 2+ solutions, respectively.

    23

  • cV SO4 [M] ρ [g/ml]

    0.0 1.10721.0 1.21951.5 1.27652.0 1.3349

    Table 2.4: Densities of V 2+ electrolyte solutions at 25 ◦C in g/ml [12]

    Table 2.5: Densities of different V 3+ electrolyte solutions in the range of 15- 40 ◦Cin g/ml [12]

    The V 4+ solutions used for both presented studies were prepared by the reaction ofan equimolar mixture of vanadium trioxide (V2O3) and vanadium pentoxide (V2O5)in diluted sulfuric acid according to equation 2.6 [12, 14]:

    V2O3 + V2O5 + 8H+ −−⇀↽−− 4 VO2+ + 4H2O (2.6)

    The densities were measured, by recording the mass of a glass density bottle withknown volume and a relative error of 2 % in the case of [12].

    From tables (2.5) and (2.3), it can be seen that the density of vanadium solutionsincreases with increasing total sulfate and vanadium concentration. In both studiesthe increase due to higher vanadium concentration was reported to be larger.

    24

  • 3 Experimental

    The effect of the temperature on the electrolyte density was measured within thescope of this thesis. For the investigation of the influence of the SOC on the elec-trolyte density and development of a model to monitor the SOC in dependence ofthe latter, already existing measurement data was used. This data came from a cellcharacterization experiment and was not conducted by the author of this thesis. Inthe following chapter, the experimental set up for the abovementioned experimentswill be introduced and the measurement routines will be explained.

    3.1 Temperature Dependence of the Electrolyte Density

    The densities of three vanadium electrolyte solutions were measured in the temper-ature range of 10- 30 ◦C. The first measurement was conducted on the commer-cially available V 3.5+ electrolyte solution (GfE), consisting of 0.8 M VOSO4, 0.4M V2[SO4]3 in 2 M H2SO4 and 0.05 M H3PO4. The following two measurementswere carried out on V 2+/V 3+ and V 4+/V 5+ solutions at an approximate SOC of50 %, both obtained at a previous measurement from the V 3.5+ electrolyte. Priorto the actual experiment with vanadium electrolyte, the set up was validated usingbi-distilled water. The result of the validation is in appendix A.2, while the datasheet of the V 3.5+ electrolyte is in appendix A.4.

    3.1.1 Setup

    In figure 3.1 a schematic of the experimental set up is shown. The set up consistsof two cycles, the argon and the electrolyte cycle, depicted as a double line and asingle line, respectively. The electrolyte is pumped counter clockwise through thePVC tubing from the lower to the upper glass tank. The upper tank is mountedto a scale, which allows the measurement of the electrolyte mass change throughoutthe experiment. Located between the tanks is a level sensor triggered valve, whichopens in case the lower tank runs dry. Cooling of the electrolyte is realised witha cooling bath, which is filled with salt water and crushed ice. Additionally, twothermal pads are attached around the tubing. A temperature sensor is placed insidethe cooling bath to monitor the temperature reached by the added crushed ice.A heating with several temperature sensors in front and inside allows controllableheating of the electrolyte. The electrolyte density and temperature is measured ina flow through module, DMA 35N Liquid Density Module - Anton Paar, during theentire experiment. The argon cycle enables the measurement to be conducted underargon pressure to avoid the oxidation of V 2+ by the oxygen in the air. In addition,

    25

  • Valve

    Tank 1

    Tank 2

    m

    T1

    T, ρ

    Heating

    Scale

    Density

    module

    Cooling bath

    Level

    sensor

    T2

    Temperature

    sensor 1

    Temperature

    sensor 2

    Ar

    Ar Cycle Electrolyte cycle

    Cooling pad 1

    Cooling Pad 2

    Pump

    Figure 3.1: Experimental set up of the temperature dependence measurement of theelectrolyte density

    the argon pressure can be used to press the electrolyte into the pump head in orderto avoid gas sucking of the pump.

    3.1.2 Measurement Routine

    All three measurements were conducted using the same measurement routine, whichwill be explained in the following section.First the set up was purged with argon gas and the cooling bath was filled withsalt water and crushed ice. Then the cooled thermal packs were applied around thetubing and the pre-cooled electrolyte was filled into the lower tank. Afterwards theelectrolyte was pressed into the pump head by applying argon pressure. The pumpwas set to a flow rate of 4.08 ml/min and the electrolyte was pumped through the setup. After the electrolyte reached 10 ◦C, the cooling devices were detached to heatthe electrolyte up to ambient temperature in approximately 100 minutes. Afterwardsthe electrolyte was heated up in 2 ◦C steps until 30 ◦C in approximately 120 minutes.Subsequently, the procedure was repeated with the same electrolyte in approximatelyhalf the time.

    26

  • Pump 2

    ρ2

    Pump 1

    Ar

    ρ1 

    AnodeCathode

    Valve 1 Valve 2

    Tank 1

    Tank 2 Tank 4

    Tank 3

    TT

    Inlet outerhalf cell

    Outlet inner half cell

    Inlet inner half cell

    Outlet outer half cell

    h

    Electrolyte CycleAr Cycle Power Supply

    Tubu

    lar V

    RB Cell

    Schematic of Tubular Redox Flow Battery Test Rig

    m m

    p1 p2

    p3

    Figure 3.2: Schematic of the VRB test rig used for electrochemical studies[33]

    3.2 Charge and Discharge Cycling

    In order to investigate the influence of the SOC on the electrolyte density, chargeand discharge cycles with the VRB were performed. The experimental set up andthe measurement routine will be explained in the following section.

    3.2.1 Setup

    The charge and discharge cycling measurements were carried out using the test rigdepicted in figure 3.2. The design is similar to the general VRB set up discussed in1.1, but using a four tank system. This enables a batch operation of the cell witha quasi constant SOC. Like in the previously discussed set up, the valve opening iscontrolled via level sensor signal. The valves open simultaneously when one of thelevel sensors detects, that one tank is running dry. The upper tanks are mounted toscales to measure the change of the electrolyte mass throughout the measurement.In addition, using flow through pressure sensors at the half-cell inlets and in theargon cycle, the pressure drop across the cell can be determined. The temperatureand density of the electrolytes are measured at the outlets of the half-cells with flowthrough modules of type DMA 35N Liquid Density Module by Anton Paar. Theelectrochemical measurements are conducted with a potentiostat SP-240 / 4A/1aV,

    27

  • BioLogic©, which is connected to the electrodes. The VRB cell has a tubular designand uses graphite felts as electrodes. The fumapem© F950 cation exchange mem-brane by FUMATECH BWT GmbH Germany, has an active surface area of 15.71cm2.

    3.2.2 Measurement Routine

    First, the set up was purged with argon gas, while 100 ml of the identical V 3.5+

    electrolyte solution, used for the measurements in 3.1, was filled into both lowertanks. Subsequently the system was set under an argon pressure of pAr,rel = 50mbar, the flow rates were set to V̇ = 3.2 ml/min and the electrolyte formationwas conducted at a cell voltage of Ecell= 1.3 V. Once a charge of 2300 mAh wastransferred, Ecell was set to 1.75 V in order to achieve an SOC of approximately 60%, after another 2300 mAh. Afterwards four sequences to derive polarization plotswere conducted, ending at an SOC of approximately 55 %. The VRB was charged to88.4 % SOC, corresponding to a total charge of 5936.3 mAh, at Ecell= 1.8 V and V̇= 6.4 ml/min. Subsequently six charge and discharge cycles with a constant currentdensity of 35 mA/cm2 between cell voltages of 1.7 and 0.8 V were carried out. Inbetween each charge and discharge the OCV was measured for 15 minutes. Thetransferred amount of charge in mAh and the corresponding SOC values, determinedby coulomb counting, are presented in table 3.1.

    cycle number charge (ch) / discharge (dch) transferred charge [mAh] SOC [%]

    1dch -2877.8 21.3ch 1329.7 52.3

    2dch -1239.7 23.4ch 1159.7 50.5

    3dch -1153.8 23.4ch 1154.28 50.5

    4dch -1067.7 23.6ch 1060.2 50.5

    5dch -1055.8 25.7ch 971.1 48.3

    6dch -878.2 27.8ch 859.6 47.9

    Table 3.1: Transferred charge values and corresponding SOC’s for the six conductedcharge and discharge cycles

    28

  • 4 Electrolyte Density Dependent SOCMonitoring

    In the following section, the results from the studies of the temperature and the SOCinfluence on the electrolyte density will be presented and discussed. A method tomonitor the SOC of a VRB will be derived from the results and validated on measureddata. In the end, the accuracy of the measurement method will be discussed.

    In order to investigate the SOC influence on the electrolyte density only the chargeand discharge cycles from the measurement routine, explained in 3.2.2, were taken.In figure 4.1, the cell voltage and the measured densities in the negative and positivehalf-cell over time are shown. Each of the six cycles begins with a discharge in whichthe cell voltage drops to 0.8 V, followed by an OCV measurement and ends witha charge, in which the voltage increases to 1.7 V. The first, highest discharge infigure 4.1, was from 88.4 - 21.3 %, while afterwards the VRB was cycled betweenapproximately 20 - 50 % SOC, according to table 3.1. The SOC monitoring methodwas calibrated using the first charge and discharge cycle and afterwards validated onthe second one. The last cycle was used for another comparison. When looking atfigure 4.1 and table 3.1, it can be seen, that the range in within the SOC changes isdecreasing throughout the measurement. This effect occurs, due to a capacity lossinduced by crossover from one half-cell to the other. When looking at the densitydata in figure 4.1, vertical jumps in the signal can be seen. These jumps occur whengas bubbles move through the density module. Then the density signal drops tozero for a few seconds and usually stabilizes within approximately 20 seconds. Whenlooking at figure 4.1 the following observations can be made:

    The density of the anolyte increases, while the density of the catholyte decreasesduring discharge.

    The opposite behavior occurs during charge, the density of the anolyte de-creases, while the density of the catholyte increases.

    In general, the density measured in the negative half-cell is higher than thedensity measured in the positive half-cell.

    The density in the negative half-cell changes within a larger range, than thedensity in the positive half-cell.

    By analysing the observations it can be concluded, that the V 2+ and V 3+ ions andthe hydration spheres they build, must be more tightly packed within the electrolyte

    29

  • ×1051 1.2 1.4 1.6 1.8 2 2.2

    Voltage [V]

    0.6

    1

    1.4

    Ecell

    Time [s]×105

    1 1.2 1.4 1.6 1.8 2 2.2

    Density [g/ml]

    1.34

    1.36

    1.38

    ρnhc

    ρphc

    Validation ComparisonCalibration

    Figure 4.1: Cell Voltage Ecell and measured densities in negative (ρnhc) and positive(ρphc) half-cell over time during six charge and discharge cycles. Cyclesused for calibrating and validating the SOC on the density as well as thecycle used for a comparison of the result are marked with dashed lines.

    solutions, than the V O2+ and V O2+ ions with their hydration spheres. It is believed,

    that the V-O bond effects the configuration of the molecules and thereby they occupymore space, resulting in a lower density value. Furthermore it can be seen, that inboth half-cell electrolytes, the density is largest when the vanadium ions have thehighest positive charge.

    4.1 Temperature Influence

    In the following section, the temperature influence on the anolyte and catholyte willbe derived from the results of the measurement, which was described in section 3.1.After the first observation of the density behavior during charge and discharge fromthe previous chapter, the following results were predicted.

    The V 2+/V 3+ solution was expected to have the highest density, whilst the V 4+/V 5+

    solution would have the lowest. The V 3.5+ electrolyte solution is a 50:50 mixture ofV 3 and V 4+ ions and therefore the density was predicted to be in between of theother two solutions. Furthermore, it was expected, that the V 2+/V 3+ solution mightchange during the measurement. Due to the instability of the V 2+-ion it was believed,

    30

  • that an oxidation to V 3+ will occur, which would lead to an increase of the density.This will happen especially during heating, due to an increased reaction rate. Therepeated measurements should detect whether or not this effect occurred.

    The densities of the 1.6 M V 2+/V 3+-, V 3.5+- and V 4+/V 5+ and 4M total sulfatesolutions at an approximate SOC of 50 % are depicted in figure 4.2. For a detailedview of the three measurements see appendix A.3. Due to the sensor inertia, tem-perature values were matched to at least 60 seconds in constant density. The firstconduction of each experiment is denoted as 1st measurement, while the repeated isdenoted as 2nd measurement. When looking at figure 4.2, it can be seen, that theresults agree well with the previous discussed expectations and plausibly the densityvalues decrease with increasing temperature. Also, the expected increase of the slopeof the V 2+/V 3+ solution is more pronounced during the 1st measurement. The slopeof the first measurement is -0.000517 gml ·

    1◦C , while the second slope is -0.000604

    gml ·

    1◦C . This is due to the fact, that the 1st measurement took more time and after

    this less V 2+-ions remained in the solution. Thereby less V 2+ could be oxidised toV 3+, resulting in a lesser effect on the slope. The other repeated measurements agreewell with the first conducted ones.

    Temperature [°C] 5 10 15 20 25 30 35

    De

    nsi

    ty

    [g/m

    l]

    1.34

    1.345

    1.35

    1.355

    1.36

    1.365

    1.37

    1.375

    1.38V2+/V3+ 1st measurement

    V2+/V3+ 2nd measurement

    V3.5+ 1st measurement

    V3.5+ 2nd measurement

    V4+/V5+ 1st measurement

    V4+/V5+ 2nd measurement

    V3+ Mousa 1.6M V in 4.4M total sulfate

    Figure 4.2: Measured densities of the 1.6 M V 2+/V 3+-, V 3.5+- and V 4+/V 5+ and 4M total sulfate electrolyte solutions over temperature from the 1st andthe 2nd measurement. The measured densities for a 1.6 M V 3+ and 4.4M total sulfate solution values by A. Mousa [12] are depicted as crosses.

    31

  • In order to investigate the influence of the temperature on the density only theslopes of the lines were analysed. Additionally, the exact SOC’s of the solutions wereunknown, due to the fact that a proper SOC monitoring method was missing at thetime they were produced. The overall assumption is, that the slope will not vary withchanging SOC of the solution. Thereby the temperature will have the same influenceon the electrolyte density at the entire SOC range. Due to this, the SOC during themeasurement needed to be as constant as possible. Therefore, the true value of theslope must be closer to the second measurement of the V 2+/V 3+ solution, becausethe first measurement was more effected by the influence of the SOC. The slopesfor each solution were determined by the linear regression tool LINEST of MicrosoftExcel® 2013. Because of the previous explained reasons, only the 2nd measurementvalues for the V 2+/V 3+ solution were taken. For the V 3.5+ and V 4+/V 5+ solutions,both measurements were analysed, resulting in the regression values shown in table4.1.

    V 2+/V 3+ solution V 4+/V 5+ solution V 3.5+ solution

    m [ gml ·1

    ◦C ] -0.00060 -0.00060 -0.000058standard error 0.00002 0.00002 0.00002absolute rel. error [%] 3.0 3.0 2.7R2 0.995 0.989 0.993

    Table 4.1: Slopes, standard errors, absolute relative error and coefficient of determi-nation R2 of the measurement results of the temperature influence studyfor the V 2+/V 3+, V 4+/V 5+ and V 3.5+ solutions.

    When looking at the table it can be seen, that the slopes of the solutions are veryclose together and are equal for the representatives of the anolyte and catholyte.This leads to the conclusion that the temperature influence is the same for all threeinvestigated solutions. In addition, the low standard errors and the high coefficient ofdetermination indicate a good linear correlation between the density and the temper-ature. To be precise, the density of anolyte and catholyte will decrease with 0.00060± 0.00002 g/ml for an increase of 1 ◦C.

    After comparing the measured results with the data from A. Mousa [12], deviationscan be seen. According to the observations made in the last section, a solutioncontaining solely V 3+ should have a higher density than a V 2+/V 3+ solution. Fur-thermore, Mousa’s solution had a total sulfate concentration, which was 0.4 mole/lhigher, suggesting an even higher density. However, Mousa’s values are found to belower than the V 2+/V 3+ solution and similar to the V 3.5+ solution with a slightlyhigher slope of -0.000674 gml ·

    1◦C . It is believed, that this systematic error arises, due

    to the phosphoric acid (H3PO4) within the electrolyte solution from GfE, which wasintroduced in 2.1.

    32

  • SOC [%]20 40 60 80 100

    Density [g/ml]

    1.365

    1.37

    1.375

    1.38

    1.385

    1.39

    dischargecharge

    (a) Negative half-cell

    SOC [%]20 40 60 80 100

    Density [g/ml]

    1.335

    1.34

    1.345

    1.35

    dischargecharge

    (b) Positive half-cell

    Figure 4.3: Measured density in the negative- (a) and positive half-cell (b) over SOC,determined by coulomb counting, during the first discharge and chargecycle.

    4.2 Influence of the SOC on the Electrolyte Density

    In this section, the results obtained from the charge and discharge cycles will bediscussed and combined with the results of the temperature influence study. Therebythe necessary equations needed for SOC monitoring in dependence of the electrolytedensity of both half-cells will be derived.

    4.2.1 Calibration

    The first cycle, marked in figure 4.1, was used for the calibration of the SOC independency of electrolyte density.

    Influence of Charge and Discharge on the Density

    In a first step to analyse the general behavior, the densities of both half-cells duringthe first cycle were plotted over the SOC, obtained by coulomb counting. The resultis shown in figure 4.3. During discharge, the trends of the densities were expectedto decrease in the positive and increase in the negative half-cell. During charge, thetrend of the density was expected to follow the trend from the discharge, but inthe opposite direction. However, when looking at figure 4.3, it can be seen that thedensities during charge compared to discharge are lower in the case of the negativehalf-cell and higher in the case of the positive half-cell.

    In order to understand and quantify the previous mentioned effect of different den-sity levels during charge and discharge, the density change between the cycles was

    33

  • analysed. As already mentioned, each cycle consists of a discharge process, followedby an OCV measurement for 15 minutes. Subsequently the charge process is con-ducted and another OCV measurement. When looking at figure 4.1, in between thecharge and discharge, the cell voltage drops to OCV, before it decreases becauseof the following discharge. For visualization, the density behavior during the firstchange from charge (ch) to OCV to discharge (dch) is depicted in figure 4.4. It canbe seen, that the density increases in case of the negative and decreases in case ofthe positive half-cell, after the voltage drops to OCV. The same can be seen for thechange from OCV to discharge, when the voltage drops lower. The density behaviorduring the following voltage jumps was analysed:

    discharge voltage to OCV, in between a discharge and a charge process

    charge voltage to OCV, in between a charge and a discharge process

    The voltage jumps between OCV to charge and OCV to discharge were not analysed.In those voltage jumps the density increase and decrease, as a result of the the actualSOC change, overlaps with the effect which wanted to be analysed. This can alsobe seen in figure 4.4, the second density increase for the negative and decrease forthe positive half-cell is more pronounced than the first one. One part of this higherdensity change is due to the voltage jump, the other part is a result of the effect, thatthe electrolyte is charged and discharged, respectively. Nevertheless, the change inthe density during discharge to OCV should happen in the opposite direction as forOCV to discharge. The same argument is valid for the change of the density duringa voltage jump from OCV to charge.

    Time [s]135200 135400 135600

    1.377

    1.3775

    1.378

    1.3785

    1.379

    Density [g/ml] Ch Dch

    OCV

    (a) Negative half-cell

    Time [s]135200 135400 135600

    1,3418

    1,342

    1,3422

    1,3424

    Density [g/ml]

    ChDch

    OCV

    (b) Positive half-cell

    Figure 4.4: Measured densities in the negative- (a) and the positive half-cell (b) dur-ing during the first change from charge to discharge over time.

    34

  • It was detected, that during a voltage drop from charge to OCV the density in thenegative half-cell increased with 0.0004 g/ml, while the density in the positive half-cell decreased with 0.0002 g/ml. The values were obtained by analysing the voltagejumps of three charge to OCV voltage jumps and represent the mean value. Asimilar effect occurred during discharge to OCV, the density in the negative half-celldecreased with approximately 0.0004 g/ml, while the density in the positive half-cellincreased with 0.0002 g/ml. The density variation due to temperature changes, whichoccurred during these jumps, were adjusted. When combining both observed values,the density of the anolyte should be 0.0008 g/ml higher during discharge comparedto charge, while the density of the catholyte should be 0.0004 g/ml lower duringdischarge.

    Establishing of the correlation between SOC and density

    In the last section, it was shown, that the density is dependent on the SOC andwhether the VRB gets charged or discharged. Therefore, by implication the SOCcan be calculated by using the density and by adding a correction factor for eithercharge or discharge.

    In order to derive a dependency between SOC and electrolyte density, certain densityvalues needed to be matched to SOC values. When looking at figure 4.3, it can beseen, that the density for example in the negative half-cell, does not change linearly.During discharge it increases, than stays at a certain level and increases again andso on. This effect is due to the four tank system, which was explained in section3.2. At the time one batch gets charged, the electrolyte is pumped from the lowerto the upper tank, resulting in a constant SOC and density, respectively. After thelower tank is empty, the valve opens and the next batch is charged. Therefore theSOC and density increase to the next level, which results in an increase followed bya constant density signal. Due to this, a constant density value during one batch wasmatched to the SOC at the moment the valve closed at the end of the same batch.

    As discussed in section 4.1, the density is dependent on the temperature as well.Due to this, the density values of the first cycle were adjusted to 25 ◦C. In addition,a dummy variable A was introduced, which has the value 0 during discharge and1 during charge. The thereby obtained array of values is visualised in table 4.2.Now, the SOC can be calculated in dependence of the electrolyte density at 25 ◦Caccording to the following equation:

    SOC = c · ρ+A · e+ f (4.1)

    The slopes c, e and the y-intercept f were calculated using the multiple linearregression tool LINEST of Microsoft Excel® 2013. The results are presented intable 4.3. From the standard errors and coefficients of determination R2 it can beseen, that in general the SOC prediction for the negative half-cell is more accurate

    35

  • SOC [%] A ρnhc(25◦C) ρnhc(25

    ◦C)

    discharge84.50 0 1.3661 1.3461

    ......

    ......

    21.32 0 1.3874 1.3370

    charge24.14 1 1.3859 1.3378

    ......

    ......

    52.10 1 1.3766 1.3417

    Table 4.2: Array used for the regression of the SOC in dependency of the electrolytedensity.

    and has a better linear correlation, than for the positive half-cell. This observationcan be explained by the lesser degree of variation of the density in the positivehalf-cell. Thereby the systematic error of the density module has a higher effect onthe measurement accuracy for the catholyte. Furthermore it can be seen, that therelative errors, for the coefficient e is approximately eight times higher than the otherrelative errors. As analysed in the previous section, the density increase and decreasein between the charge and discharge process is relatively small, which again increasesthe influence of the systematic error of the density module on the measurement ofthis effect. In the following example the suggested SOC change from the densityincrease and decrease due to the voltage jumps, obtained from the analysis of thevoltage jumps will be compared to the corresponding regression values from table 4.3.In section 4.2.1, it was analysed, that the density of the negative half-cell decreaseswith 0.0008 g/ml from the discharge to the charge process without any current flow.According to table 4.3 and with the absence of factor e, that would lead to an SOCincrease of:

    ∆SOC =

    (−2979 ml ·%

    g

    )·(−0.0008 g

    ml

    )= 2.38 % (4.2)

    For the positive half-cell the analysed density increase of 0.0004 g/ml from the dis-charge to the charge process would lead without consideration of factor e to a SOCincrease of:

    ∆SOC = 6998ml ·%

    g· 0.0004 g

    ml= 2.8 % (4.3)

    From that, example it can be seen, that the SOC in the negative half-cell would be2.38 % and the SOC in the positive half-cell would be 2.8 % higher, only because theVRB changed from charge to discharge, but without an actual transferred charge.The factor e was established to correct this mismatch. In table 4.3, the correctionfactor e for the negative half-cell is -2.9 %, which agrees well with the required cor-rection of 2.38 %, obtained in the previous example. For the positive half-cell thecorrection factor e is -5.4 %, which is overestimated, when looking at the needed

    36

  • negative half-cell positive half-cell

    c e f c e f

    value -2979 -2.9 4155 6998 -5.4 -9332standard error 19 0.2 27 168 0.8 225absolute rel. error [%] 0.7 8.1 0.6 2.4 15 2.4R2 0.999 0.992

    Table 4.3: Regression values, standard errors, absolute relative errors and R2 valuesfor the SOC in dependency of the electrolyte density.

    correction of 2.8 % obtained from the previous example. This can repeatedly be ex-plained by the smaller variation of the density in the positive half-cell and the therebyhigher uncertainty of the SOC calculation. Nevertheless, this agreement proves, thatthis effect is measurable and needs to be corrected for the SOC determination.

    Subsequently, it was decided to present the equation in dependency of a standarddensity value ρ0 at 298.15 K, SOC= 50 % and A= 0, which was calculated accordingto the following equation:

    ρ0 =50− fc

    (4.4)

    The densities obtained thereby are:

    ρnhc(298.15 K, SOC= 50 %, A = 0) = 1.3780 g/ml

    ρphc(298.15 K, SOC= 50 %, A = 0)= 1.3407 g/ml

    Up to this point, the SOC can be calculated for densities measured at 298.15 K. Inorder to include the temperature correction, the slopes obtained in section 4.1 wereused. However, only the density variation due to temperature changes was known. Inorder to get the correction factor for the SOC as a result of the temperature variation,the slope m of the regression from section 4.1 was multiplied with the slope c of theprevious discussed regression.

    dT· dSOC

    dρ=dSOC

    dT= m · c = d (4.5)

    By applying equation 4.5 the following values for the temperature correction factord were obtained:

    dnhc = + 1.8

    dphc = − 4.23

    A plausibility check of the algebraic sign of the factor d reveals the following: inthe negative half-cell, at a constant SOC a temperature increase would decreasethe density, which would suggest a higher SOC. In the positive half-cell exactly the

    37

  • opposite occurs. According to this, both algebraic signs need to be changed and theSOC of both half-cells can be calculated using the following two equations:

    SOCnhc = 50 %−2979ml ·%

    g· (ρ−1.3780 g

    ml)−1.800 %

    K· (T −298.15 K)−A ·2.85 %

    (4.6)

    SOCphc = 50 %+6998ml ·%

    g·(ρ−1.3407 g

    ml)+4.23

    %

    K·(T−298.15 K)−A·5.4 % (4.7)

    The dummy factor A can be realised by using the algebraic sign of the cell currentIcell. Then the definition needs to be the following:

    A =1

    2+

    1

    2sign(Icell) (4.8)

    4.2.2 Validation

    In the last section, the equations to calculate the SOC in dependency of the electrolytedensity and temperature were derived. In this section, the applicability of them willbe validated by comparing the SOC determined by coulomb counting to the SOCcalculated by applying equations (4.6) and (4.7). In order to test, whether theapplicability is compromised by crossover, the comparison will be repeated for thesixth cycle.

    In figure 4.5 the calculated SOC via coulomb counting (SOC CC), via density of thenegative (SOC nhc) and positive half-cell (SOC phc) during the second cycle are de-picted. Furthermore the corresponding mean residuals and mean relative deviationsare listed in table 4.4. The mean residual of the negative half-cell was calculatedusing the following equation:

    mean residual =

    ∑ni=1(SOC nhci - SOC CCi)

    n(4.9)

    The mean relative deviation of the negative half-cell was calculated by:

    mean rel. deviation =

    ∑ni=1

    (SOC nhci - SOC CCi

    SOC CCi

    )n

    (4.10)

    The mean residual and mean relative deviation of the positive half-cell are determinedin the same way. It can be seen, that the SOC of the negative half-cell agrees with theSOC of the coulomb counting with a mean relative deviation of 1.4 %. In comparison,the SOC of the positive half-cell has a relative deviation of 7.7 %. One reason forthis, is the general lower accuracy of the SOC calculated from the catholyte density,as mentioned in section 4.2.1.

    For the explanation of another reason, the level sensor signals of both lower tanksduring the entire measurement are depicted in figure 4.6. It can be seen, that when

    38

  • Time [min]

    0 50 100 150 200 250

    SOC [%]


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