2016-04 Impedance-based battery management for … · Impedance-Based Battery Management For Lithium-Oxygen Systems Andreas E. Christensen O2 Li O2 ReLiable LiTHIUM BALANCE BATTERY

Impedance-Based Battery Management For Lithium-Oxygen Systems

Andreas E. ChristensenLi O2O2

ReLiable

LiTHIUM BALANCE BATTERY MANAGEMENT SYSTEMS

Acknowledgements

• Funding The Danish Council for Strategic Research Lithium Balance A/S

• Colleagues The battery group at DTU Energy R&D at Lithium Balance A/S

14Work performed in collaboration with

J. Højberga, P. Norbyb, T. Veggeb a Haldor Topsøe A/S

b DTU Energy - Technical University of Denmark

2

Introduction - Battery Management

Battery Mangement System

• Safe operating window: ‣ Current ‣ Voltage ‣ Temperature

• Performance threshold: ‣ Battery parameter estimation

main methods: the direct, the indirect andthe adaptive. Direct methods include physi-cal parameters such as the battery voltage orimpedance measurements, indirect methods usecoulomb counting with some form of simple cal-ibration to reduce the accumulated errors, andadaptive methods can combine both direct andindirect methods and apply corrections. Thesemethods all give the state of charge (SoC) for abattery, which is analogous to the volume of fuel,but since secondary batteries are used for hun-dreds to thousands of cycles, the fuel “health”must also be known. This is known as state ofhealth (SoH) of a battery.

2 State of HealthState of Health (SoH) is the generic term de-scribing the performance of the battery relativeto its new state, or its specifications. There is noagreed mathematical definition of SoH enshrinedin an international standard, but there are somegenerally accepted definitions.

SoHcapacity

=current total capacity

rated total capacity(1)

Capacity fade – SoH in applications where thekey limitation is the available energy such a elec-tric vehicles that need range or energy storage so-lutions which require endurance, is measured asthe percentage of the original or rated battery ca-pacity available between the fully charged stateand the fully discharged state.

SoHpower

=current available power

initial available power(2)

Power fade – SoH in hybrid vehicles and energybuffering systems (grid regulation) and the likefocus on the battery’s ability to deliver power.The thermal window of operation is fixed and thepower capability within the thermal window ofoperation is determined by the increase in dis-sipated power due to the internal impedance ofthe battery. The SoH in such applications isdefined as a function of the increase of batteryimpedance compared to the reference value [3].Since P = U · I and U = R · I , where R is thetotal battery resistance as a function of SoC andtemperature, equation (2) becomes

SoHpower

=U

2x

R

x

U

20

R0

=R0 · U2

x

Rx

· U20

(3)

where the index 0 is the initial and x the currentvalue. If the measurements are then made at thesame voltage as the initial level the expressionreduces to

SoHpower

=R0

Rx

(4)

The power fade can thus be expressed as a func-tion of the increase in total battery resistance. Itis common to see the above parameters used to-gether to form the overall SoH.

2.1 AgeingAgeing can be divided into two principle types:Cycle related ageing (cycle life) and calendarrelated ageing (calendar life). During the firstcharge cycle of a lithium-ion battery the elec-trolyte reacts with both the anode and the cath-ode to form a film, the solid electrolyte interface(SEI). This is a chemical reaction that continuesthroughout the life of the battery and is acceler-ated at elevated temperatures. The effect of theSEI on carbon anodes is well documented [4].The ever thickening film increases the internal re-sistance at all temperatures, but is worse at lowtemperatures where it becomes less porous to thepassage of Li+ ions which may lead to metal-lic lithium dendrites being deposited on the sur-face of the electrode. These dendrites lead to aloss of active material as well as pose a dangerby creating internal short circuits or acting as areaction amplifier during thermal runaway. SEIlayers form on cathodes, but to a lesser extentand their impact on battery performance is not asmarked [4].

2.2 Cycle lifeThe rocking chair mechanism that all lithium-ionbattery chemistries utilize sees Li+ ions migrat-ing between intercalation sites in the positive andnegative electrodes via the medium of the elec-trolyte. For charging, this typically means mov-ing from the cathode (positive) electrode to theanode (negative).Dependent on the nature of the electrode mate-rial the intercalation sites may occupy a differentvolume when there is a Li+ ion present, com-pared to when the intercalation sites are unoc-cupied. This expansion and contraction of thestructure can lead to exfoliation whereby surfaceelements of the electrode material microstructuremay crack and crumble reducing the active mate-rial of the electrode, creating a capacity reduction[4]. This can be seen in many electrode materi-als including carbon and cobalt. This is why it isoften possible to increase the cycle life of a bat-tery by optimizing the depth of discharge win-dow such that you keep the level of strain ex-perienced by the electrodes/cycle within certainlimits.The separator in the lithium-ion batteries acts tokeep the positive and negative electrodes sepa-rate to prevent internal shorting while still allow-ing the easy migration of Li+ ions between theelectrodes. The porous material of the separa-tor becomes contaminated with element of theelectrode materials as well as Li+ ions being de-posited as metallic lithium on the separator. Thisleads to reductions in active electrode material aswell as reduction in the porosity of the separatorleading to an increase in internal resistance.

EVS27 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium 2



SoHcapacity




SoHpower



SoC =current total capacity

initial total capacity(3)


SoHpower

=U

2x

R

x

U

20

R0

=R0 · U2

x

Rx

· U20

(4)


SoHpower

=R0

Rx

(5)



2.2 Cycle lifeThe rocking chair mechanism that all lithium-ionbattery chemistries utilize sees Li+ ions migrat-ing between intercalation sites in the positive andnegative electrodes via the medium of the elec-trolyte. For charging, this typically means mov-ing from the cathode (positive) electrode to theanode (negative).Dependent on the nature of the electrode mate-rial the intercalation sites may occupy a differentvolume when there is a Li+ ion present, com-pared to when the intercalation sites are unoc-cupied. This expansion and contraction of thestructure can lead to exfoliation whereby surfaceelements of the electrode material microstructuremay crack and crumble reducing the active mate-rial of the electrode, creating a capacity reduction[4]. This can be seen in many electrode materi-als including carbon and cobalt. This is why it isoften possible to increase the cycle life of a bat-tery by optimizing the depth of discharge win-dow such that you keep the level of strain ex-perienced by the electrodes/cycle within certainlimits.The separator in the lithium-ion batteries acts tokeep the positive and negative electrodes sepa-rate to prevent internal shorting while still allow-ing the easy migration of Li+ ions between theelectrodes. The porous material of the separa-tor becomes contaminated with element of the




SoHcapacity




SoHpower






SoHpower

=U

2x

R

x

U

20

R0

=R0 · U2

x

Rx

· U20

(4)


SoHpower

=R0

Rx

(5)







SoHcapacity




SoHpower






SoHpower

=U

2x

R

x

U

20

R0

=R0 · U2

x

Rx

· U20

(4)


SoHpower

=R0

Rx

(5)





• State of Charge (SoC)The remaining energy left in the battery

• State of Health (SoH)The health of the battery

• Coulomb counting: counting electrons

• Any error in measuring results in accumulated errors

Introduction - Parameters

3

Q =

!∞

−∞

I dt Qdiscrete =ns!

n=0

(In) ·∆T

Qdiscrete =ns!

n=0

(In + Ierr) ·∆T

SoC-OCV calibration for Li-ion (LiCoO2)

3800 mV

54 % SOC

4

Discharge and open-circuit voltages

5

9154 Chem. Commun., 2013, 49, 9152--9154 This journal is c The Royal Society of Chemistry 2013

the first discharging. The first stage near 1.5 V reflected thereaction of Mg2+ with iodine (i.e., it acted as an Mg–iodinebattery), showing the reduction of I3

! (I3! + 2e! - 3I!). The

discharge capacity of the Mg–I2 battery was 100 mA h g!1,which was determined by the amount of dissolved iodine in theelectrolyte. The second stage at about 1.25 V revealed thedischarging of the Mg–O2 battery. The total discharge capacitywas 2131 mA h g!1-cathode (black line in Fig. 4). The dischargevoltage of the Mg–iodine and Mg–air batteries was lower thanthe theoretical values calculated from the potentials of theiodine redox couple (+0.4 V vs. NHE) or four-electron reductionof oxygen (0.2 V vs. NHE) and of Mg2+/Mg (!2.37 V vs. NHE).The drop in voltage was caused by the formation of a solidelectrolyte interface (SEI) on the Mg anode. When the polarityof the current was reversed during the charging process, the cellvoltage increased to about 1.8 V, and a plateau was observed atabout 2.2 V. The total charge capacity was 1590 mA h g!1, andthe reversibility against discharging was 74.6%. In the seconddischarge–charge cycle, the electrochemical discharge andcharge capacities were 1364 mA h g!1 and 1028 mA h g!1,respectively (pink line), becoming 940 mA h g!1 and 736 mA h g!1,respectively (green line), in the third cycle. On the other hand, theMg–O2 battery without iodine had a large discharge capacity of2280 mA h g!1, but showed no charging behavior (blue line).

In order to identify the formation and decomposition ofMgO in our Mg–O2 battery we analyzed the cathode surfaces afterdischarging, and after discharging–charging. White precipitateparticles with size on the order of several microns were observedin the samples. It was found that the size of these white precipitateparticles was diminished upon charging (ESI,† Fig. S4). Theprecipitates at the cathodes were identified using Raman spectro-scopy and TOF-SIMS (time of flight-secondary ion mass spectro-metry). The Raman data are presented in the ESI,† Fig. S5, alongwith the Raman signals of MgO and MgO2. Although MgO2 gave asignal at 1137 cm!1 due to peroxide vibration, MgO had no Ramansignal. In sample B (from only discharging), a Raman signal at

147 cm!1 due to triiodide vibration was detected. In sample A(from discharging–charging), the triiodide vibration was notdetected, indicating the complete conversion of I3

! to I2. The SIMSspectra of the cathodes before and after discharging are displayedin ESI,† Fig. S6. The signals of the sample after only discharging, atm/z = 24 for positive ions and m/z = 16 for negative ions, had strongintensities compared with the sample before discharging. From theexperimental data in ESI,† Fig. S4–S6, it was concluded that thewhite precipitates were mainly MgO, which was decomposedduring electrical charging.

Molecular complexes between iodine and organic solventshave been investigated extensively for the past several decades.Our work has revealed a new application for these molecularcomplexes, i.e., as a catalyst for the decomposition of metaloxides. In addition, we have succeeded in charging a non-aqueous Mg–O2 battery using the iodine–DMSO complex asan O2-electrode catalyst. The basic mechanism of electro-chemical charging by use of the complex could be exploitedto design multivalent metal–O2 batteries.

Notes and references1 P. G. Bruce, S. A. Freunberger, L. J. Hardwick and J.-M. Trascon,

Nat. Mater., 2012, 11, 19.2 P. Hartmann, C. L. Bender, M. Vracar, M. K. Durr, A. Garsuch,

J. Janek and P. Adelhelm, Nat. Mater., 2012, 12, 228.3 K. Takechi, T. Shiga and T. Asaoka, Chem. Commun., 2011, 47, 3463.4 K. M. Abraham and Z. Jiang, J. Electrochem. Soc., 1996, 143, 1.5 D. T. Sawyer and J. S. Valentine, Acc. Chem. Res., 1981, 14, 393.6 L. Rongti, P. Wei and M. Sano, Metall. Mater. Trans. B, 2003, 34, 433.7 M. S. Mohamed, T. Yabe, C. Basandash, Y. Sato, Y. Mori, L. Shi-Hua,

H. Sato and S. Uchida, J. Appl. Phys., 2008, 104, 113110.8 T. J. Novak, E. J. Poziomek, W. A. Mosher and R. A. Mackay,

J. Phys. Chem., 1976, 80, 2609.9 R. P. Lang, J. Phys. Chem., 1974, 78, 1657.

10 S. Nagakura, J. Am. Chem. Soc., 1958, 80, 520.11 R. S. Mulliken, J. Am. Chem. Soc., 1950, 72, 600.12 S. B. Sharp and G. I. Gellene, J. Phys. Chem. A, 1997, 101, 2192.13 A. E. Johnson and A. B. Myers, J. Phys. Chem., 1996, 100, 7778.14 T. Shiga, Y. Kato, M. Inoue and K. Takechi, J. Power Sources, 2012,

217, 538.15 R. M. Munavu, J. Org. Chem., 1980, 45, 3341.16 M. I. McCarthy, R. B. Gerber and M. Shapiro, J. Chem. Phys., 1990,

92, 7708.17 N. Sun and K. J. Klabunde, J. Am. Chem. Soc., 1999, 121, 5587.18 P. K. Stoimenov, V. Zaikovski and K. J. Klaubende, J. Am. Chem. Soc.,

2003, 125, 12907.19 R. S. Drago, B. Wayland and R. L. Carlson, J. Am. Chem. Soc., 1963,

85, 3125.20 H. Tsubomura and J. M. Kliegman, J. Am. Chem. Soc., 1960, 82, 1314.21 D. D. Wagman, W. H. Evans, V. B. Parker, R. H. Schumm,

I. Halow, S. M. Bailey, K. L. Churney and R. I. Nuttal, The S tablesof chemical thermodynamic properties, J. Phys. Chem. Ref. Data,1982, 11(Suppl 2), 260.

22 S. A. Freunberger, Y. Chen, Z. Peng, J. M. Griffin, L. J. Hardwick,F. Barde, P. Novak and P. G. Bruce, J. Am. Chem. Soc., 2011,133, 8040.

23 M. J. Trahan, S. Mukerjee, E. J. Plichta, M. S. Hendrickson andK. M. Abraham, J. Electrochem. Soc., 2013, 160, A259.

24 Y. Chen, S. A. Freunberger, Z. Peng, F. Barde and P. G. Bruce,J. Am. Chem. Soc., 2012, 134, 7952.

25 K. Takechi, S. Higashi, F. Mizuno, H. Nishikoori, H. Iba andT. Shiga, ECS Electrochem. Lett., 2012, 1, A27.

Fig. 4 Discharge–charge curves of the non-aqueous Mg–O2 battery with iodineat 60 1C. The black, pink, green, and red lines correspond to the first, second, thirdand fourth cycles, respectively. The blue line represents a discharging–chargingprofile in the absence of iodine.

ChemComm CommunicationLi

Mg Al

Na

[1] B. D. McCloskey, J. M. Garcia, A. C. Luntz, Chemical and Electrochemical Differences in Nonaqueous Li-O2 and Na-O2 Batteries, The Journal of Physical Chemistry Letters 5 (7) (2014) 1230–1235. [2] R. Revel, T. Audichon, S. Gonzalez, Non-aqueous aluminium-air battery based on ionic liquid electrolyte, Journal of Power Sources 272 (c) (2014) 415–421. [3] T. Shiga, Y. Hase, Y. Kato, M. Inoue, K. Takechi, A rechargeable non-aqueous Mg-O2 battery, Chemical Communications 49 (80) (2013) 9152– 9154.

2.2

2.25

2.3

2.35

2.4

OCV

Prior findings

6

reactions are very slow, and if the EIS excitation signal is sufficiently small, the

impedance signal from the positive electrode becomes capacitive at the relevant90

frequencies (see insert in Figure 2). This means that the capacitance can be

determined by the simple expression shown in Equation 1.23

C =−1

2πf · Zim(1)

where f is the AC perturbation frequency and Zim is the imaginary part of the

corresponding impedance. It is important that other impedance contributions

from processes with similar time constants do not overlap at the frequency used95

for the calculation. A frequency of 10 mHz was chosen because it was the highest

frequency (and hence shortest measurement time) with the main contribution

from the positive electrode capacitance.

2.2. Relating capacitance to the discharge processes

The capacitance of the positive electrode is determined by the electrochem-100

ical double layer capacitance that reflects the ability of the system to store

electrical charge by rearranging the charges in the carbon (electrons) and in the

electrolyte (ions). The value is proportional to the surface area and depends on

the choice of electrolyte, the concentration of charged species in the electrolyte

(salt concentration) and deposits on the carbon surface. For a Li-O2 battery,105

Li2O2 is deposited on the surface during discharge and as Li2O2 is a dielec-

tric, the capacitance of the surface will change. The capacitance of XC72 is

12.6 F g-1c in an organic aprotic electrolyte as reported by Barbieri et al., which

corresponds to 5.4 µF cm-2, using a measured BET area of 235 m2 g-1.24 The

capacitance of the Li2O2 layer is calculated using Equation 2.110

C = ϵrϵ0A

d(2)

where ϵr is the relative permittivity, ϵ0 is the vacuum permittivity, A is the

area of the layer and d is the thickness of the layer. The relative permittivity of

Li2O2 has been determined to be 35 by Gerbig et al.25, and using these values it

can be calculated that going from a pristine carbon surface without Li2O2 to ∼6

5

[5] M. Orazem, B. Tribollet, Electrochemical impedance spectroscopy, John Wiley & Sons, 2008

death. During charge, the OCV was 2.85 V, but it increasedslightly toward the end of charge where it reached 3.2 V.3.1. Discharge to Sudden Death at 250 μA. EIS

measurements from the first discharge at 250 μA (220 μ/cm2)are shown in Figure 2a−d. The spectra were measured whiledrawing a current, which means that the SODs shown in Figure2 and Table 1 are approximate values. Three arcs aredistinguished in the Nyquist plot in Figure 2a. They werealmost constant in the first part of the discharge but changed asthe potential decreased near the end of discharge. The threeidentified impedance contributions are labeled Z1, Z2, and Z3,and, on the basis of a fit to the equivalent circuit given in eq 3and shown in Figure S4a in the Supporting Information, thecorresponding peak frequencies, resistances, and pseudocapa-citances are calculated. The values from two of thesecalculations are given in Table 1.It is seen that R1 is constant through the discharge, whereas

R2 and R3 increase and C3* decreases. The decrease of C3* andincrease of R3 through the discharge could be a blocking of thecathode surface. The magnitudes of the pseudocapacitances

indicate that Z1 originates from an anode process, and Z2 andZ3 originate from cathode processes. The cathode blocking andidentification of reaction processes in the impedance spectra arediscussed further in Section 4.1.The peak frequencies changed between different current

densities and close to sudden death. In all of our measurements,however, f1 was between 100 Hz and 10 kHz, f 2 was between 2and 100 Hz, and f 3 was between 20 mHz and 1 Hz. Theseintervals are shown in Figure 2c,d, and the clear separationhelps in identifying the different impedance contributions.

3.2. Discharge to Sudden Death at 20 μA.We decreasedthe discharge current to 20 μA (18 μA/cm2) to increase thestability of the system during the impedance measurements, seeFigure 3. When comparing this with the previous discharge at250 μA presented in Figure 2, it is important to note that boththe capacity and the polarization resistance, Rp, are significantlylarger in the 20 μA discharge.On the basis of a fit using eq 3, representing the equivalent

circuit presented in Figure S4a in the Supporting Information,the resistance and pseudocapacitance parameters of Z1, Z2, and

Figure 2. Nyquist plot (a) and (b) and Bode-like plot (c) and (d) of impedance measurements during a 250 μA (220 μA/cm2) constant currentdischarge. The approximate SODs are shown in (e) and in the legends of (a) and (b). Three processes are identified and named Z1, Z2, and Z3, andthe corresponding peak frequencies are within the gray intervals marked in (c) and (d) at all current densities and SODs investigated.

Table 1. Peak Frequencies, Resistances, and Pseudocapacitances from Selected Impedance Fita

f1 [Hz] f 2 [Hz] f 3 [Hz] R1 [Ω] R2 [Ω] R3 [Ω] C1* [mF] C2* [mF] C3* [mF]

discharge at 250 μA0.16 mAh 733 5.4 93 × 10−3 96 56 145 2.3 × 10−3 0.53 10.20.51 mAh 605 3.4 184 × 10−3 94 92 188 2.8 × 10−3 0.45 4.0

discharge at 20 μA0.5 mAh 470 1.15 5.5 × 10−3 109 50 1007 3.1 × 10−3 2.8 19.31.9 mAh 464 1.12 9.9 × 10−3 107 158 2131 3.2 × 10−3 0.6 2.02.3 mAh 479 1.1 × 10−3 114 14 097 2.9 × 10−3 0.8

charge at 250 μA0.03 mAh 678 9.6 267 × 10−3 65 166 497 3.6 × 10−3 76 × 10−3 1.00.42 mAh 983 14.0 19 × 10−3 255 105 700 0.6 × 10−3 99 × 10−3 9.0

aThe expected capacitances for the full anode and cathode are 10 μF and 25 mF, respectively. Typical values of n are n1 = 0.77, n2 = 0.86, and n3 =0.78.

ACS Applied Materials & Interfaces Research Article

DOI: 10.1021/am5083254ACS Appl. Mater. Interfaces 2015, 7, 4039−4047

4042

[4] An Electrochemical Impedance Spectroscopy Investigation of the Overpotentials in Li–O2 Batteries Jonathan Højberg, Bryan D. McCloskey, Johan Hjelm, Tejs Vegge, Keld Johansen, Poul Norby, and Alan C. Luntz, ACS Applied Materials & Interfaces 2015 7 (7), 4039-4047

• Low frequency response is from positive electrode

• Capacitance from EIS:

Supplementary Information: Impedance-based BatteryManagement for Metal-O2 Systems

Andreas E. Christensena,c,∗, Jonathan Højbergb,c, Poul Norbyc, Tejs Veggec

aLithium Balance A/S, Baldershøj 26C, 2635 Ishøj, DenmarkbHaldor Topsøe A/S, Nymøllevej 55, 2800 Kgs. Lyngby, Denmark

cDTU Energy, Frederiksborgvej 399, 4000 Roskilde, Denmark

S1. Li2O2 capacitance

Figure S1: Calculation of capacitance depending on Li2O2 layer thickness, showing where

capacitance is 50 % of the initial 12.6 F g-1c

The calculation of capacitance is based on a simple model with two capaci-

tances: the capacitance of the pristine carbon electrode, and the capacitance of

the Li2O2 layer deposited on the carbon electrode. Equation 2 in the manuscript

and a calculation of two capacitances in series is used to calculate the total ca-

pacitance depending on the Li2O2 layer thickness. The final formula is:

Ctotal(d) =

!1

ϵrϵ0A/d+

1

CXC72

"−1

(1)

Where ϵr is the relative permittivity, ϵ0 is the vacuum permittivity, A is the area

of the layer, d is the thickness of the Li2O2 layer, and CXC72 is the capacitance

of XC72 in an aprotic electrolyte. For the case where d = 0 only the capacitance

of XC72 is used, all other calculations use: ϵr = 35,1 ϵ0 = 8.9 · 10−12, A = 235

m2 g-1, and CXC72 = 12.6 F g-1c .2

∗Corresponding author.Email address: [email protected] (Andreas E. Christensen)

Preprint submitted to Journal of The Electrochemical Society April 8, 2015

Cap

acita

nce

[F/g

]

02468

101214

0 2 4 6 8 10 12

50 %

100 %

Li2O2 layer [nm]













Ctotal(d) =

!1

ϵrϵ0A/d+

1

CXC72

"−1

(1)





m2 g-1, and CXC72 = 12.6 F g-1c .2















Ctotal(d) =

!1

ϵrϵ0A/d+

1

CXC72

"−1

(1)





m2 g-1, and CXC72 = 12.6 F g-1c .2















Ctotal(d) =

!1

ϵrϵ0A/d+

1

CXC72

"−1

(1)





m2 g-1, and CXC72 = 12.6 F g-1c .2















Ctotal(d) =

!1

ϵrϵ0A/d+

1

CXC72

"−1

(1)





m2 g-1, and CXC72 = 12.6 F g-1c .2















Ctotal(d) =

!1

ϵrϵ0A/d+

1

CXC72

"−1

(1)





m2 g-1, and CXC72 = 12.6 F g-1c .2



Model

7

• System with XC72 and Li2O2• Series capacitances configuration• Initial capacitance: 12.6 F/g• 50 % capacitance: ~6 nm

Li2O2

CC

- - - - - -

+ + + + + +

[6] Barbieri, Hahn, Herzog & Kotz. Capacitance limits of high surface area activated carbons for double layer capacitors. Carbon N. Y. 43, 1303–1310 (2005). [7] Gerbig, O., Merkle, R. & Maier, J. Electron and ion transport in Li2O2. Adv. Mater. 25, 3129–3133 (2013).

Model

8

CC

- - - - - -+ + + + + +

CCLi2O2- - -

+ + +- - -+ + +

Li2O2

CC

- - - - - -

+ + + + + +

OCV

Udischarge

Capacitance

Capacity

Voltage

Capacitance

reactions are very slow, and if the EIS excitation signal is suciently small, the

impedance signal from the positive electrode becomes capacitive at the relevant90

frequencies (see insert in Figure 2). This means that the capacitance can be

determined by the simple expression shown in Equation 1.23

C =1

2f · Zim(1)

where f is the AC perturbation frequency and Zim is the imaginary part of the

corresponding impedance. It is important that other impedance contributions

from processes with similar time constants do not overlap at the frequency used95

for the calculation. A frequency of 10 mHz was chosen because it was the highest

frequency (and hence shortest measurement time) with the main contribution

from the positive electrode capacitance.

2.2. Relating capacitance to the discharge processes

The capacitance of the positive electrode is determined by the electrochem-100

ical double layer capacitance that reflects the ability of the system to store

electrical charge by rearranging the charges in the carbon (electrons) and in the

electrolyte (ions). The value is proportional to the surface area and depends on

the choice of electrolyte, the concentration of charged species in the electrolyte

(salt concentration) and deposits on the carbon surface. For a Li-O2 battery,105

Li2O2 is deposited on the surface during discharge and as Li2O2 is a dielec-

tric, the capacitance of the surface will change. The capacitance of XC72 is

12.6 F g-1c in an organic aprotic electrolyte as reported by Barbieri et al., which

corresponds to 5.4 µF cm-2, using a measured BET area of 235 m2 g-1.24 The

capacitance of the Li2O2 layer is calculated using Equation 2.110

C = r0A

d(2)

where r is the relative permittivity, 0 is the vacuum permittivity, A is the

area of the layer and d is the thickness of the layer. The relative permittivity of

Li2O2 has been determined to be 35 by Gerbig et al.25, and using these values it

can be calculated that going from a pristine carbon surface without Li2O2 to 6

5

Experiments

• Constant current discharge at 130 mA/gc • OCV during experiment: 2.83 V

9

0 100 200 300 400 Capacity [mAhg-1]

5

6

7

8

C [F

g-1 ]

2.70 V 2.69 V

2.67 V

2.63 V

2.32 V

10

9

500 600

C

C

0 0.5 Re(Z) [ΩgC] 0

0.5

1

1.5

-Im(Z

) [Ω

g C]

0 0.5 Re(Z) [ΩgC]

0

0.5

1

1.5

-Im(Z

) [Ω

g C] 10 mHz

2.69 V

Experiments

10

0 400 800 1200 2

4

6

8

10

Staircase Charging

Drive cycle 1 Drive cycle 2

Constant current

Variable current

Capacity [mAhg-1] C

C [F

g-1 ]

C

13 mAgC 39 mAgC 130 mAgC 130 mAgC 390 mAgC

-1

-1

-1

-1

-1

Experiments

11

0.0 0.2 0.4 0.6 0.8 1.0 Normalized capacity

0.4

0.6

0.8

1.0

Nor

mal

ized

cap

acita

nce

130 mAgC Staircase Charging Drive cycle 1 Drive cycle 2

-1 g-1

b

13 mAgC 39 mAgC 130 mAgC 130 mAgC 390 mAgC

0.0 0.2 0.4 0.6 0.8 1.0 Normalized capacity

0.4

0.6

0.8

1.0

Nor

mal

ized

cap

acita

nce

a

-1

-1

-1

-1

-1

• Experimental data normalised: • Capacitance normalised to initial value • Capacity normalised to sudden death at 2.2 V

Example: Calibration of SoC

130 mAgC-1

100 80 60 40 20 0SoC [%]

0.4

0.6

0.8

1.0

Nor

mal

ised

capa

cita

nce

130 mAgC

Drive cycle 1Drive cycle 2

-1g-1

Figure SI4

Calibration: 0,83: 18% - 25% SoC

18% SoC

Actual SoC BMS with calibration BMS without calibration Calibration

0 20 40 60 80

100

SoC

[%]

6am Time

6pm 6am 6pm

b

Example: Calibration of SoC

13• Without full charge, calibration keeps SoC within 5 % of actual SoC

Degradation over cycling

14

Current collector

Li2O2

Current collector

Discharged Charged

Li2CO3

0 Cycle no.

0.6

0.8

1.0

Nor

mal

ized

cap

acita

nce

0.7

0.9

5 10 15

Cathode Li2O2

Cathode Discharged Charged

Li2CO3

d

• Presence of Li2CO3 on positive electrode: • Decrease in active area for Li2O2 deposition • Increased overpotential due to charge transport limitations

through Li2O2

[8] Mekonnen, Y. S. et al. Communication: The influence of CO2 poisoning on overvoltages and discharge capacity in non-aqueous Li-Air batteries. J. Chem. Phys. 140, (2014). [9] McCloskey, B. D. et al. Limitations in Rechargeability of Li-O2 Batteries and Possible Origins. J. Phys. Chem. Lett. 3, (2012). [10] Ottakam Thotiyl, M. M., Freunberger, S. a., Peng, Z. & Bruce, P. G. The carbon electrode in nonaqueous Li-O2 cells. J. Am. Chem. Soc. 135, (2013). [11] Gallant, B. M. et al. Chemical and Morphological Changes of Li–O2 Battery Electrodes upon Cycling. J. Phys. Chem. C 116, 20800–20805 (2012).

Summary

• Capacitance of positive electrode changes as function of discharge.

• SoC and SoH estimation based on calibration using capacitance of positive electrode.

• Prolonged battery usage due to better estimation of remaining energy.

• Primary focus on Li-O2, other metal-O2 systems show similar behaviour.

15

Current collector

Li2O2

Current collector

Discharged Charged

Li2CO3

0 Cycle no.

0.6

0.8

1.0

No

rma

lize

d c

ap

aci

tance

0.7

0.9

5 10 15

Cathode Li2O2

Cathode Discharged Charged

Li2CO3

d

Actual SoC BMS with calibration BMS without calibration Calibration

0 20 40 60 80

100

So

C [

%]

6am Time

6pm 6am 6pm

b

Li

Mg Al

Na

Li O2O2

ReLiable

LiTHIUM BALANCEBATTERY MANAGEMENT SYSTEMS

Acknowledgements

• Funding The Danish Council for Strategic Research Lithium Balance A/S

• Colleagues The battery group at DTU Energy R&D at Lithium Balance A/S

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