New Advances In Lithium Ion Battery Fuel Gauging Final
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New Advances In Lithium Ion Battery Fuel Gauging Final

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A paradigm shift how fuel gauging is done in lithium ion batteries.

A paradigm shift how fuel gauging is done in lithium ion batteries.

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New Advances In Lithium Ion Battery Fuel Gauging Final New Advances In Lithium Ion Battery Fuel Gauging Final Document Transcript

  • New Advances in Lithium Ion Battery Monitoring Jörn Tinnemeyer Vice President - Research & Development Cadex Electronics Inc. 22000 Fraserwood Way, Richmond BC, Canada V6W 1J6 Joern.Tinnemeyer@cadex.com or www.cadex.comAbstract: In the last decade, lithium ion batteries have Importantly, though, the praises of Li-ion batteries mustdominated the market place: first being used in portable be tempered by several key disadvantages in using thisconsumer products, and now in more industrial and chemistry. Namely, they safely operate within a verytransport-based applications. One necessary requirement limited range of conditions; that is, the manufacturers ofof lithium ion batteries -- irrespective of the particular Li-ion battery packs must be vigilant when developing theapplication of interest -- is to gauge how much energy the protection circuitry and a safe milieu for the batterybattery contains and how long a given application can (McDowall et al., 2007, Van Schalkwijk et al., 2002).run before the battery needs to be recharged. The precisemonitoring and management of lithium ion batteries has The precise monitoring and management of Li-ionproven to be difficult to achieve, especially as the battery batteries also presents a noteworthy problem -- thisstarts to age. Here, I describe a novel patented approach problem being the focus of this article. Irrespective of thethat Cadex Electronics Inc., is developing, which assesses application being considered, the end-user needs to knowthe state of charge and state of health of lithium ion when the battery is fully charged and when the batterybatteries by directly measuring the concentration of lithium will run out of power. Intuitively speaking, everyone whoions across different states of charge. Directly assessing uses cellular phones, laptops, or MP3 players knows thatthe material state of the battery assures very precise predicting when a battery will run out of charge can bemonitoring -- conservatively speaking, +/- 5% accuracy, elusive, especially as the battery gets older. Within theirrespective of which lithium ion chemistries are tested. field of battery management and monitoring, several techniques have been developed that monitor the state ofKeywords: state of charge; lithium ion; magnetic charge of Li-ion batteries and new techniques are up-and-susceptibility, magnetic field measurements coming. Importantly though, not all techniques are equivalent in their precision or ability to monitor different Li-ion chemistries. Owing to the fundamental role ofIntroduction battery chemistry, I begin this article by providing a brief review of Li-ion chemistries and construction (see also Aurbrach et al., 2007, McDowall 2008, Van SchalkwijkIn our portable world, we use batteries to keep our 2002, Wittingham 2004), then I review the advantageselectronic devices functioning and we monitor the state of and disadvantages of current techniques, and I describe athe battery to assure that the equipment will operate as we patented technology that Cadex Electronics is developingexpect. Over the last decade, the applications that use that offers the same advantages, without sharing thelithium ion batteries have diversified dramatically. disadvantages.Initially, lithium ion batteries (for the remainder of thispaper, I will refer to these as Li-ion batteries) were usedas the primary power source in electronic devices that Lithium Ion Construction and Consequences forbenefited from light and powerful batteries -- such as Battery Managementlaptop computers and cellular phones. Now, Li-ionbatteries are used in a gamut of different electronictechnologies, from power tools to transport vehicles. This Li-ion batteries are not uniform in construction, ratherexponentiating presence of Li-ion batteries in the they may be better characterized as a family of batteries,marketplace makes sense because they effectively store each possessing its own unique characteristics. Li-ionenergy (high energy, low weight) with no memory effect, batteries differ in two fundamental ways -- chemistry andthey are cheap to produce, and they are consumable (i.e., construction.possess a limited lifespan), which benefits the retailersthrough the sale of replacement batteries or new The name of a particular Li-ion battery is derived fromtechnological devices (Scuilla 2007, Whittingham 2004). the substances from which it is made, such as ‘lithium manganese’, ‘lithium cobalt’, and ‘lithium iron
  • phosphate’ batteries (see Table 1). For most Li-ionbatteries, the cathode contains the unique chemistries.For example, lithium manganese oxide (LiMn2O4) is thecathode material used in lithium manganese batteries,whereas lithium cobalt oxide (LiCoO2) is the cathodematerial used in lithium cobalt batteries. The anodematerials tend to be more conserved across different Li-ion batteries. Most often, layered carbon (graphite) isused to construct the anode.Full name Chemical Abbrev. Short form Note definitionLithium Cobalt LiCoO2 LCO Li-cobalt Cell phoneOxide (60% Co) laptop, cameraLithium LiMn2O4 LMO Li-Manganese (IV) manganese,Oxide1 also spinelLithium Iron LiFePO4 LFP Li- Power tools,Phosphate phosphate e-bikes, EV,Lithium Nickel LiNiMnCoO2 NMC NMC medical, Figure 1 - Lithium ion transport between anode andManganese (10-20% Co) hobbyist cathode (Teki et al., 2009)Cobalt Oxide 1Lithium Nickel LiNiCoAlO2 NCA NCA InCobalt Aluminum 9% Co) development, Moreover, these differences in construction play a vitalOxide less role in the diffusion characteristics of the lithium ions.Lithium Titanate Li5Ti5O13 LTO Li-titanate commonly used Figure 3 illustrates the impedance spectroscopy curves for both the prismatic and polymer designs.1. Li[NixMnxCo1-2x]O2 is a more accurate description of NCA, where xis typically 1/3Table 1 - Examples of lithium ion battery chemistriesThese differences in chemistry assure that many simple,generalized attempts to monitor and manage Li-ion Figure 2 - Prismatic (left) and polymer (right)batteries are less than ideal (see more below). Indeed, the constructions of lithium ion batteries.difficulty in effectively monitoring some of the uniquechemistries (e.g., lithium iron phosphate, and lithiumnickel manganese cobalt oxide) have thwarted their use in As stated above, differences in chemistry and constructionthe marketplace, even though these chemistries are, have noteworthy consequences for the differentotherwise, very powerful (Deutsche Bank, 2009). That techniques that monitor and manage Li-ion batteries,said, Li-ion batteries function in a similar way despite insofar that they hinder generalized battery managementthese differences in chemistry. Figure 1 highlights this and monitoring solutions. Consider voltagesimilarity in function: the lithium ions shuttle between the measurements. Voltage measurements have been used foranode electrode and cathode electrode as the cell charges decades as a simple means to monitor and manage Li-ionand discharges, respectively. batteries (and preceding rechargeable battery chemistries). Be that as it may, voltage measurements fall flat for someLi-ion batteries also differ in their construction. For the particular types of Li-ion batteries. For example, thepurposes of battery monitoring and management, the relatively constant voltage output of lithium irondifferent forms of cell construction also limit the efficacy phosphate batteries makes this chemistry resistant toof generalized algorithms. Two types of battery cell useful voltage measurements when determining state ofconstruction are most common: prismatic cells (Fig. 2 charge. In the following sections, I highlight many of theleft) and polymer (or pouch) cells (Fig. 2 right). Prismatic different techniques that are currently employed, and acells have an outer metal casing that adds weight and novel patented technique that Cadex Electronics isdurability to the battery’s construction, whereas polymer developing that monitors and manages all Li-ion batteries.cells are light-weight and flexible (Tarascon et al., 2001).
  • before an accurate measure of voltage can be obtained. Polymer The voltage-based fuel gauge is constructed by measuring 0.025 Prismatic the voltage of the battery across different states of charge-Imaginary Impedance (Ohm) and then generating an electromotive force curve (EMF curve), which is used to estimate the residual energy contained within the battery. 0.015 This method, albeit being simple to implement and possessing strong intuitive appeal, has several shortcomings. Consider Figure 4. The solid line 0.005 illustrates the EMF curve of a battery that is in perfect state of health (a brand new battery). The dashed line illustrates the EMF curve of a battery that is in a 70% 0.12 0.14 0.16 0.18 state of health (an old battery at a state, in which battery Real Impedance (Ohm) monitoring is notoriously difficult). Importantly, the lines do not overlap perfectly; therefore, the same curve may not be used as the battery ages. Figure 3 - Impedance spectroscopy differences between prismatic and polymer constructions 4.2Fuel Gauges: State of Charge vs. State of Health 100% SoH 70% SoH 4.0A fundamental task of a battery management system is to 3.8report how much energy remains in the battery (how Battery Voltage (V)much time the user can expect the application to continue 3.6operating). Such fuel gauges calculate the state of chargeof the battery -- the ratio of remaining energy in the 3.4battery compared to the maximum energy the battery canstore at that time. The total amount of energy that the 3.2battery can possibly hold is called the state of health. Bothstate of charge and state of health are highly dynamic and 3.0interdependent. With respect to their dynamic nature, 20 40 60 Battery SoC (%) 80 100state of charge is modified by polarization currents,whereas the state of health decreases (significantly) as the Figure 4 EMF curves for two batteries at differentage of the battery increases. With regards to their states of healthinterdependence, without knowing state of health, it isimpossible to know state of charge because the maximalamount of energy the battery contains (i.e., state of health)is part of the ratio that determines state of charge. This shortcoming of voltage measurements has long been identified (Pop et al., 2007). To compensate for this problem, mathematical aging models have beenVoltage and the Electromotive Force Curve developed to account for the age of the battery. However, even with the mathematical models implemented, voltage measurements are imprecise -- more than +/-10%Voltage was the first technique that was implemented to divergences have been reported (Pop et al., 2007).monitor and manage battery systems (Buchmann, 2001),and it is one that is still in use today. The battery’s Another problem when using voltage measurements andvoltage originates from the half reactions of each EMF curves is the amount of time the user must waitelectrode, which in turn depends on the composition of before the reading is meaningful (i.e., before the voltagethe electrodes. For Li-ion batteries, this has two asymptotes). For most batteries, at least 30-60 minutesconsequences. First, as the cathode material changes in must elapse before the EMF curve accurately estimatesits composition, the battery voltages change also. Second, state of charge (Coleman et al., 2007). For most users,as the battery discharges (or charges), the composition of this timeframe is impractical. Indeed, if there is anythe electrodes change, which, again, leads to changes in current draw (polarization) or if the voltage is monitoredvoltage. For both reasons, the battery must rest -- stand shortly after a polarization event, the voltage reading iswithout any current polarization -- for at least 30 minutes incorrect. Once again, mathematical models are used to correct for this shortcoming, but the models must consider View slide
  • scores of conditions; as such, one model cannot ..1 effectively manage all situations and/or all applications. Figure 5 illustrates a much more significant problem in using voltage measurements and EMF curve estimations Here, α is the initial state of charge, which is typically -- the inability to generalize this technique across different 100%, CN is the capacity of the battery, δ is an efficiency Li-ion chemistries. This graph plots the difference rating to account for any loss (typically 1) and I is the between the battery’s state of charge and its voltage. As flow of current. What is most important is CN. The value illustrated with the solid line, lithium cobalt batteries yield is dynamic and it decreases as the battery’s state of health a clear stepwise trend across state of charge -- the higher decreases. If the battery is not fully discharged after the state of charge, the higher the voltage. Lithium iron being maximally charged, then a proper calculation is not phosphate batteries (dashed line), by contrast, yield (at possible and the coulomb counter becomes less and less best) a truncated version of this pattern -- vast changes in accurate (Coleman et al., 2007). This is a serious state of charge are accompanied by small changes in shortcoming because, in most instances, it is very rare to voltage. Simply put, voltage measurements cannot be fully charge and fully discharge a battery; henceforth, a used for all variants of Li-ion batteries. significant drift in the coulomb counter is difficult to avoid. As the signal drifts, the efficacy of coulomb counting decreases. 4.0 Other issues with coulomb counting have been identified, albeit much less problematic. Namely, coulomb counting LiCoO2 is less effective when the battery self-discharges or is 3.8 LiFePO4 subject to temperature changes (Aurbach et al., 2002). Moreover, as the battery ages, so too does the efficacy ofBattery Voltage (V) coulomb counting measurements, since δ is a dynamic 3.6 value that also is dependent on age. Importantly, though, these losses in precision owing to temperature fluctuations 3.4 and battery aging are of minor consequence when compared to the significant loss in precision that can accompany a drift in the signal: a drifting signal can 3.2 produce a 100% discrepancy between the measured and actual amount of energy in the battery, whereas these other issues may affect the precision of coulomb counting 3.0 by less than 1% per month (Takeno et al., 2005). 20 40 60 80 100 Battery SoC (%) Resistance Figure 5 - EMF curves for two different lithium ion chemistries For both voltage measurements and coulomb counting (albeit less so), the state of health of the battery influences the efficacy of battery monitoring and management: new All told, despite the ease of implementing voltage batteries (100% state of health) are easy to gauge, measurements and EMF estimations to monitor and whereas older batteries (85% state of health and below) manage battery systems; in practice, this method is are notoriously difficult to gauge. To account for changes limited in its ability to measure the energy housed in a in state of health, fuel gauging techniques often measure battery under most conditions. the resistance of a battery as the primary means to index state of health. Coulomb Counting Another technique that has been implemented in battery management and monitoring is coulomb counting -- quite literally, counting the amount of charge that flows in and out of the battery. Similar to voltage measurements, coulomb counting has intuitive appeal and it is easy to implement (especially with today’s µ-controllers). The measurement is made using the following equation: View slide
  • After cycle 1 Another significant issue in using impedance After cycle 50 measurements is that a direct coupling exists between 0.025 After cycle 200 state of health and state of charge; namely, there is an-Imaginary Impedance (Ohm) After cycle 800 increase in resistance as the battery ages and discharges. Hence it is unknown which circumstance is causal. This interdependence is highlighted in Figure 8. 0.015 Fresh - SoC 100% After cycle 800 - SoC 100% 0.025 Fresh - SoC 0% -Imaginary Impedance (Ohm) After cycle 800 - SoC 0% 0.005 0.015 0.12 0.14 0.16 0.18 Real Impedance (Ohm)Figure 6 - Complex impedance changes for a lithium 0.005 cobalt oxide battery 0.12 0.14 0.16 0.18For some Li-ion chemistries, the impedance measured in Real Impedance (Ohm)the battery is an effective way to assess the battery’s stateof health. As shown in Figure 6, lithium cobalt oxideevidences clear stepwise changes in the real impedance Figure 8 - Complex impedance data as a function of(or resistance) of the battery, as the number of cycles state of charge and state of healthincreases.For other chemistries, impedance measurements are less As noteworthy in this figure, the battery’s state of chargeeffective in determining state of health. As highlighted in dominates the impedance spectrum, and makes it difficultFigure 7, the impedance measured from lithium to identify the different states of health that are present.manganese oxide batteries yields an ambiguous The complex methods that one can adopt to tease out staterelationship to the number of cycles the battery has of health from these data are computationally intensiveexperienced. and, as such, impractical for most consumer products or industrial applications. Accordingly, rather than relying on the normal discharge currents, most applications now After cycle 200 use an excitation pulse present on the device to assess After cycle 600 changes in the impedance spectrum. Although this 0.025-Imaginary Impedance (Ohm) technique is much more effective for some Li-ion chemistries that show a systematic increase in resistance as the battery ages, it cannot improve the reliability of battery monitoring for chemistries that do not have this 0.015 relationship. Direct Magnetic Measurements 0.005 Despite differences in chemistry, all Li-ion batteries work 0.12 0.14 0.16 0.18 in the same basic way -- energy is released when lithium Real Impedance (Ohm) ions diffuse towards the cathode (see Fig. 1). Thus, as the battery discharges, the anode will contain fewer lithium ions (McDowall, 2008). This change in composition canFigure 7 - Complex impedance changes for a lithium be exploited to directly assess how much energy the manganese oxide battery battery contains.Simply put, before resistance measurements can be usedto index state of health, one must be assured that a reliable The magnetic susceptibility of a substance is an index ofrelationship exists between resistance and battery aging; the magnetization M of this substance as it is placedotherwise, there is little purpose in taking these within a particular magnetic field strength H. Thismeasurements. relationship may be restated as,
  • ..2 in which... dB represents the vector quantity that describes the magnetic field at the desired point;As highlighted in Table 2, the magnetic susceptibilities oflithium and carbon are very different: lithium is a I is the current;paramagnetic substance -- its presence will enhance themagnetic field; whereas, carbon is a diamagnetic dl is a vector quantity of an infinitesimal current element insubstance -- its presence will minimize the magnetic field. the direction of the field potential;Importantly, lithium and carbon are the predominantchemistries that are present at the anode of the battery and is the magnetic susceptibility dependent on thecan be effectively used to index the amount of energy that material;the battery contains. is the unit vector in the direction to where the magnetic Anode Electrode Magnetic Susceptibilities (xm/106 cm3 / mol) field is to be calculated; and Lithium 14.2 r is the distance to the calculation point. If we consider a current loop with a radius of R, and we Carbon -6 wish to measure the field at a particular point x, the equation can be simplified to: Table 2 Negative electrode susceptibilities ..5To measure this change in magnetic susceptibility, anexcitation field is needed to stimulate the metals and asensor is needed that is capable of registering these minutechanges in the magnetic field. To create an excitationfield, a coil is used to generate eddy currents. These eddy which allows us to easily assess the material properties ofcurrents produce magnetic fields that are enhanced by the anode.paramagnetic materials or reduced by diamagneticmaterials. In the case of Li-ion batteries, an enhancementin the magnetic field indicates that there are more lithium A sensor is then used to measure these changes in theions at the anode or, in layman’s terms, the battery is more magnetic field. Magnetic field sensor technology hasfully charged. By contrast, a reduction in the magnetic changed significantly over the last decade, driven mainlyfield indicates that carbon is the predominant chemistry at by hard drive read head development. Magnetic tunnelingthe anode or the battery is in a lesser state of charge. junction sensors are, currently, the state of the art. The sensors are built by separating two alloys, CoFeB, by anBy using the definition, insulator of MgO that is only a few atoms thick. A biasing voltage is created between the metals, by allowing current to flow across the insulator. The likelihood of quantum ..3 tunneling is directly related to electron spin alignment, which can be manipulated and controlled by introducing external magnetic fields, with the following consequence: as the strength of the magnetic field increases, the electronwe can determine the magnetic field absorption. The spin alignment increases, and more electrons may tunneldegree of penetration into the metal, or skin depth, is given across the insulator. As more electrons tunnel across theby δ. The permeability of the material is represented by µ insulator, the resistance of the device falls (Schrag et al.,and the conductivity by σ. The frequency, f, reflects the 2006). Accordingly, the magnetoresistance of the sensor isdepth of the material being sampled. Since equation 3 is the first indication of its performance: for example,inversely proportional, we know that deeper penetration of anisotropic sensors have 2-3% magnetoresistance, whereasthe material occurs at lower frequencies. giant sensors have 15-20% magnetoresistance. By contrast, sensors that implement magnetic tunnel junctions have a magnetoresistance of 200% (Schrag et al., 2006).The magnetic field produced by a coil follows Biot-Savart’sLaw, Finally, a fuzzy logic algorithm is applied to the outputs ..4 from the sensor to provide an estimate of the state of charge of the battery.
  • measurements effectively track their state of charge. In fact, the precision is so effective that no data smoothing or Efficacy of Direct Magnetic Measurements. computational modeling is necessary to see the pattern -- the raw data show the compelling relationship between At Cadex Electronics Inc., we have developed a working state of charge and changes in the magnetic field. prototype of this technology, which is patent pending. The algorithm first degausses the coil by running a AC signal Another Li-ion chemistry that has proven to be difficult to at a particular frequency and then reducing the amplitude monitor is lithium nickel manganese cobalt oxide -- a type to zero. A frequency of 20 Hz is then applied and the of battery that is often used in electrical bicycles and in resultant change in the magnetic field is measured. This medical instruments. Like lithium iron phosphate degauss-excitation cycle is repeated for number of batteries, the magnetic sensor is very effective in tracking different frequencies in order to sample a volume of the state of charge of the battery. This effectiveness can material. be observed in the raw data (not shown, but similar to Fig. 9) and in the calculation of the state of charge (using a Figure 9 provides a striking example of how changes in fuzzy logic inference algorithm) and the actual state of the magnetic field correspond to the state of charge of the charge, as shown in Figure 10. battery. In this example, a lithium iron phosphate battery was tested during a full charge-discharge cycle, with the magnetic field measurements being probed at 20 Hz. 100 75 Estimated SoC(%) 1 Discharge 10A Charge 5ARelative Magnetic Field Units 50 0.75 25 0.5 0 0.25 25 50 75 100 Measured SoC (%) 0 30 60 90 120 150 180 Figure 10 - State of charge estimation using Time (min) 0 magnetic susceptibility measurements on a lithium nickel manganese battery Figure 9 - Magnetic field measurements of a lithium iron phosphate battery undergoing a charge As evidenced in this figure, the error with respect to the discharge cycle. actual state of charge measurements was significantly less than 5%. Initially the battery was fully charged. Then the battery One critical feature of this magnetic sensor technology was discharged at 10A for 300 seconds. Next, the current must be reiterated -- none of these measurements involved was removed and the battery was measured. This process voltage data or coulomb counting -- the magnetic sensor was repeated until the battery was fully discharged. Once directly and precisely measures the ratio of lithium ions discharged, the battery was charged using 5A before the and carbon ions at the anode. battery was charged using constant voltage. As evidenced in this figure, there is a very predominant signal and an excellent correlation evidenced across the Conclusion entire state of charge. Our patented magnetic sensor technology affords several It is with good reason that I chose a lithium iron benefits when compared to other battery monitoring phosphate battery to highlight the efficacy of our techniques: it is more accurate; its accuracy is independent magnetic sensor. As illustrated in Figure 5 and described of the age or condition of the battery; and, it allows all Li- above, these batteries are notoriously difficult to monitor ion chemistries to be precisely monitored and managed -- -- other techniques that attempt to gauge the amount of even chemistries that have proven to be difficult to monitor energy remaining in these batteries are ineffective. using other techniques. Moreover, the magnetic sensor Indeed, the inability to precisely monitor lithium iron does not share the same shortcomings as voltage or phosphate batteries have limited their station in the coulomb counting techniques, insofar that the magnetic marketplace. By contrast, our magnetic field sensor does not depend on voltage signals or the current
  • flow in the battery and it does not require predefined aging McDowall J., Understanding Lithium Ion Batteries,models to remain accurate, as do the other techniques. Battcon Conference Proceedings, June 2008.These features of our magnetic sensor technology arefactual because we directly measure the battery material McDowall J., Biensan M., Spigai B., Broussely M.,composition as it changes, and relate this information to the Industrial Lithium Ion Battery Safety - What Are theuser. Tradeoffs?, Intelec Conference Proceedings, 2007. Pop, V., Bergveld,H.J., Danilov, D., Regtien, P.P.L.,OpOne important feature of our new technology has not been Het Veld, J.H.G., Danilov, D., & Notten, P.H.L. Batterymentioned yet, but is noteworthy -- our patented magnetic aging and its influence on the electromotive force.sensor technology is equally easy to implement and costs Journal of the Electrochemical Society, 154(8), A744-approximately the same amount of money to produce as A750, 2007voltage sensors and coulomb counting techniques. Ramadass, P., Durairajan, A., Haran, B., White, R., Popov, B., Studies in Capacity Fade of Spinel-Based Li-ionAs the world becomes more portable, we are becoming Batteries. Journal of the Electrochemical Society, 149(1)more and more reliant on battery technologies. This trend A54-A60, 2002.will only increase because up-and-coming ‘green’automotive technologies also emphasize the use of Scuilla C., The Commercialization of Lithium Batterybatteries. As we increase our demands of batteries, the Technology”, Battcon Conference Proceedings, 2007.necessity to precisely monitor and manage the batterybecomes increasingly important. For a moment, imagine Schrag, B.D., Carter, M.J., Liu, X., Hoftun, J.S., & Xiao,the annoyance we have all experienced when a ‘fully G., Magnetic current imaging with magnetic tunnelcharged’ cellphone or a computer looses its power within junction sensors: case study and analysis, Proceedings ofminutes. Now imagine the annoyance you might feel if the the 2006 International Symposium for Testing and Failuresame situation occurred as you used your car! Such Analysis,2006.imprecision would and could not be tolerated. At CadexElectronics, we are developing technologies that assure Takeno K., Ichimura M., Takano K., Yamaki J., Influencevery precise battery management and monitoring because of cycle capacity deterioration and storage capacitywe do not guess at what is happening inside the battery -- deterioration on Li-Ion batteries used in mobile cellwe measure it directly. phones, Journal of Power Sources, Vol. 142, Mar. 2005. Tarascon, J.M., Armand, M., Issues and challenges facingReferences rechargeable lithium batteries. Nature, 414, 359-367.,Aurbach D., Markovsky B., Rodkin A., Cojocaru M., 2001.Levi E., Kim H., An analysis of lithium ion batteries afterprolonged cycling, Electrochimica Acta, Vol. 12, May Teki, R., Datta, M.K., Krishnan, R., Parker, T.C., Lu, T.,2002. Kumta, P.N., Koratkar, N., Nanostructured Silicon Anodes for Lithium Ion Rechargeable Batteries. Small, 5(20),Aurbach D., Markovsky B., Salitra G., Markevich E., 2236-2242, 2009.Talyossef Y., Koltypin M., Nazar L., Ellis B., KovachevaD., Review on electrode-electrolyte solutions interactions, Van Schalkwijk W.A., Scrosati B., Advances in lithium-related to cathode materials for Li-ion batteries, Journal ion batteries, Springer, 2002.of Power Sources, Vol 165-2, March 2007. Wittingham M.S., Lithium Batteries and Cathode Chemistries, Chemical Revue, Vol 104, 2004.Buchmann I., Batteries in the Portable World 2nd Edition,Cadex Electronics Inc., 2001. Zhang D, Haran, B.S., Durairajan, A., White, R.E., Podrazhansky, Y., Popov, B.N., Studies on Capacity fadeColeman M., Lee C. K., Zhu C., Gerard W. G., State-of- of lithium-ion batteries. Journal of Power Sources, 91,Charge Determination from EMF Voltage Estimation: 122-129, 2000.Using Impedance, Terminal Voltage and Current for Lead-Acid and Lithium-Ion Batteries, IEEE Transactions onIndustrial Electronics, Vol. 54, No. 5, Oct. 2007.Deutsche Bank, Electric Cars: Plugged In 2, GlobalMarkets Research, November 2009.