Patent Publication Number: US-8531158-B2

Title: Method and apparatus for assessing battery state of health

Description:
TECHNICAL FIELD 
     This disclosure is related to monitoring lithium-ion battery systems. 
     BACKGROUND 
     The statements in this section merely provide background information related to the present disclosure and may not constitute prior art. 
     Lithium-ion batteries are employed to provide high power and high energy densities in portable applications including, e.g., mobile devices, computing devices, and propulsion systems for vehicles. Power and energy management of lithium-ion batteries relies upon accurate determination of battery parameters including state of charge (SOC) and state of health (SOH) in real-time. Known systems for determining SOC and SOH may include an adaptive algorithm to provide real time prediction of SOC and SOH with associated errors due to inaccuracies in estimating the SOC. 
     SOC refers to stored electrical charge of a battery system, indicating available electric power for work relative to that which is available when the battery is fully charged. SOC may be viewed as a thermodynamic quantity, enabling one to assess the potential energy of the system. SOC may be used for purposes of regulating power flow from the battery pack to generate mechanical work, balanced with mechanical power originating from an internal combustion engine. 
     To better control the propulsion battery systems in vehicles for long battery life and good fuel economy, onboard systems determine and process battery parameters such as the open-circuit voltage (OCV), battery ohmic resistance, battery capacitance, and other parameters to determine SOC. However, OCV and other battery internal parameters are not directly measurable during vehicle operation. 
     It is known in the art to use a predetermined calibration table to regulate a battery pack, which has pre-determined parameters that are based on a standard vehicle or an experimental vehicle. It is known to use Coulomb counting to determine an SOC value of a battery system. Coulomb counting may be implemented when an initial SOC and a current efficiency is known, which may have inaccuracies. It is known to use differential voltage analysis, i.e., dV/dQ vs. V, to determine the source of capacity fade for lithium-ion batteries. It is known to use differential charge analysis, i.e., dQ/dV vs. Q, to determine the capacity fade for lithium-ion batteries and to quantify the composition change in materials. 
     SUMMARY 
     A method for monitoring a lithium-ion battery cell includes monitoring a battery cell voltage and a corresponding state of charge of the battery cell during an electric power event which may include either an electric power charge event or an electric power discharge event. A measured potential-derivative is determined by differentiating the battery cell voltage in relation to the corresponding state of charge of the battery during the electric power event. The measured potential-derivative is compared with a preferred anode potential-derivative of an anode charge curve (for electric power discharge events) or an anode discharge curve (for electric power charge events), and with a preferred cathode potential-derivative of a cathode charge curve (for electric power charge events) or a cathode discharge charge curve (for electric power discharge events). A first state of health parameter of the battery cell corresponding to the comparison of the measured potential-derivative with the preferred anode potential-derivative of the anode curve is determined. And, a second state of health parameter of the battery cell corresponding to the comparison of the measured potential-derivative with the preferred cathode potential-derivative of the cathode curve is determined. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       One or more embodiments will now be described, by way of example, with reference to the accompanying drawings, in which: 
         FIG. 1  is a schematic diagram of an equivalent circuit of a lithium-ion battery cell, in accordance with the disclosure; 
         FIG. 2  schematically shows a flowchart depicting a process for monitoring and evaluating components that affect SOH of the battery cell using a differential curve technique, in accordance with the disclosure; 
         FIG. 3  is a graphical plot of data associated with charge/discharge characteristics for an exemplary battery cell including a full cell discharge, a cathode discharge response curve vs. lithium, and an anode charge response curve vs. lithium, in accordance with the disclosure; 
         FIG. 4  is a graphical plot of a cathode discharge response curve and a corresponding preferred cathode potential-derivative in accordance with the disclosure; 
         FIG. 5  is a graphical plot of an anode charge response curve and a corresponding preferred anode potential-derivative, in accordance with the disclosure; 
         FIG. 6  is a graphical plot of the preferred anode potential-derivative  355  and measured potential-derivative calculated from a measured discharge voltage profile of a battery cell, in accordance with the disclosure; and 
         FIG. 7  is a graphical plot of the preferred cathode discharge response curve and the preferred cathode potential-derivative, a measured cathode discharge response curve and the measured cathode potential-derivative, in accordance with the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Referring now to the drawings, wherein the showings are for the purpose of illustrating certain exemplary embodiments only and not for the purpose of limiting the same,  FIG. 1  schematically shows a diagram of an equivalent circuit (or model)  200  of a lithium-ion battery cell  100 . The equivalent circuit  200  has a first node  202  and a second node  204 , with a measurable battery voltage  207  (V) existing between the nodes. The first node  202  corresponds to a cathode (positive) electrode preferably fabricated from FePO 4 , e.g., a graphite-FePO 4  cell. The second node  204  corresponds to an anode (negative) electrode preferably fabricated from graphite, e.g., a graphite-FePO 4  cell. A voltage device  206 , such as a voltmeter, may be disposed between the first node  202  and the second node  204  to obtain a reading of the measured battery voltage  207  (V). An electric current measuring device  208  measures an electric current  209  (I) at first node  202 . Electrical current flowing into the first node  202  represents a positive charging current for equivalent circuit  200 . The dashed arrow represents this positive charging current. 
     The equivalent circuit  200  includes a series resistance  210  (R) disposed between a third node  212  and first node  202 . A capacitance  214  (C) arranged in parallel with a resistance  216  (Rct) are disposed between third node  212  and a fourth node  218 . Capacitance  214  (C) represents an internal double layer capacitance of the battery model. Resistance  216  (Rct) represents a charge transfer resistance of the battery model. The voltage  211  across capacitance  214  and resistance  216  is referred to as a double layer voltage (Vdl) and is an internal voltage that cannot be readily measured in a practical battery. There may also be a contribution to the open circuit voltage due to hysteresis in the battery cell  100 , by which past electrical currents influence the magnitude of the open circuit voltage (OCV). 
     The equivalent circuit  200  includes a battery voltage source  220  disposed between the fourth node  218  and the second node  204 . The open circuit voltage  224  (OCV) is defined between fourth node  218  and second node  204 , and represents an open terminal voltage of the battery voltage source  220 , which cannot be readily measured under normal operating conditions because the battery voltage source  220  is connected to an electrical system. The measured battery voltage (V)  207  may be represented by the relationship:
 
 V=OCV+Vdl+IR   [1]
 
     A control module may be suitably configured to determine battery parameters for the lithium-ion battery cell  100  based upon measurable battery parameters, namely, the measured battery voltage (V)  207 , the measured current  209  (I) and a measured battery temperature. 
     During a discharging event of a lithium battery, e.g., the battery cell  100 , lithium ions are moving from the anode electrode to the cathode electrode. Thus, the cathode electrode is discharging by a lithium intercalation process and the anode electrode is charging by a lithium deintercalation process. During a charging event of the lithium battery cell  100 , lithium ions are moving from the cathode electrode to the anode electrode. Thus, the cathode electrode is charging by a lithium deintercalation process and the anode electrode is discharging by a lithium intercalation process. 
     The relationship between battery voltage V battery , cathode voltage V cathode  and anode voltage V anode  may be expressed as follows.
 
 V   battery   =V   cathode   −V   anode   [2]
 
     A derivative as a function of the charge storage, Q may be expressed as follows. 
     
       
         
           
             
               
                 
                   
                     
                       [ 
                       
                         
                           ⅆ 
                           V 
                         
                         
                           ⅆ 
                           Q 
                         
                       
                       ] 
                     
                     battery 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             ⅆ 
                             V 
                           
                           
                             ⅆ 
                             Q 
                           
                         
                         ] 
                       
                       cathode 
                     
                     - 
                     
                       
                         [ 
                         
                           
                             ⅆ 
                             V 
                           
                           
                             ⅆ 
                             Q 
                           
                         
                         ] 
                       
                       anode 
                     
                   
                 
               
               
                 
                   [ 
                   3 
                   ] 
                 
               
             
           
         
       
     
     A differential curve technique is applied to directly monitor the state of health (SOH) of the lithium-ion battery cell  100 . This includes analyzing derivatives of an OCV-SOC relationship of a battery cell during an extended discharge event, wherein OCV is the open circuit voltage and SOC is one of state of charge and a state of discharge of the battery cell. The differential curve technique provides information related to individual OCV-SOC behaviors of the cathode and the anode of the battery cell, and provides information related to a magnitude of active lithium loss. This information enhances the accuracy of SOC and SOH monitoring of the lithium-ion battery cell. The source of the cell aging may also be determined based upon the information related to the loss of cathode material, anode material and active lithium. 
     The differential curve technique includes determining one of a potential-derivative, i.e., dV/dQ vs. Q and an associated differential voltage curve, and a charge-capacity-derivative, i.e., dQ/dV vs. V and an associated differential charge curve. Either may be used to monitor the SOH of the battery cell by determining and analyzing distinctive signature peaks from the respective differential voltage or charge curve. The signature peaks in the differential voltage curve relate to phase transitions of the electrode materials. The signature peaks in the differential charge curve indicate the phase equilibria of the electrode materials. 
     The electrochemical behaviors of each of the cathode and the anode are deconvoluted from charge/discharge characteristics of the battery cell and quantified based upon the magnitude and voltage position shifting of peaks identified in either of the differential curves. As capacity of the battery cell fades, information on loss of cathode material, anode material and active lithium is obtained. 
       FIG. 2  schematically shows a flowchart depicting a process for monitoring and evaluating components that affect SOH of the battery cell  100  using a differential curve technique. It is appreciated that there are three measurable components that affect SOH of a battery cell, including a cathode capacity, an anode capacity, and an amount of active lithium. The process depicted in the flowchart is useful to extract the cathode capacity, the anode capacity, and the amount of active lithium in a battery cell, and is described with reference to the battery cell  100  described in  FIG. 1 . The terms cell, battery and battery cell are used interchangeably throughout. 
     Table 1 is provided as a key for the flowchart set forth in  FIG. 2 , wherein the numerically labeled blocks and the corresponding functions are set forth as follows. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 FIG. 2 
               
            
           
           
               
               
            
               
                 BLOCK 
                 BLOCK CONTENTS 
               
               
                   
               
               
                 105 
                 Develop calibration on new battery cell 
               
               
                 110 
                 Measure data, determine a cathode 
               
               
                   
                 discharge response curve and an anode 
               
               
                   
                 charge response curve 
               
               
                 120 
                 Determine preferred cathode potential- 
               
               
                   
                 derivative and preferred anode potential- 
               
               
                   
                 derivative 
               
               
                 125 
                 Monitor SOH 
               
               
                 130 
                 Measure battery cell discharge to determine 
               
               
                   
                 measured discharge voltage profile 
               
               
                 140 
                 Calculate measured potential-derivative 
               
               
                 145 
                 Compare measured potential-derivative 
               
               
                   
                 with the preferred anode potential- 
               
               
                   
                 derivative 
               
               
                 150 
                 Compare measured signature peaks to 
               
               
                   
                 determine total anode capacity 
               
               
                 155 
                 Calculate total anode capacity 
               
               
                 160 
                 Evaluate cathode 
               
               
                   
                 Compare measured potential-derivative 
               
               
                   
                 with the preferred cathode potential- 
               
               
                   
                 derivative 
               
               
                 165 
                 Determine total cathode capacity 
               
               
                 170 
                 Determine SOH associated with losses of 
               
               
                   
                 cathode, anode, and active lithium 
               
               
                   
               
            
           
         
       
     
     The flowchart includes developing a calibration ( 105 ) to determine relationships of the positive and negative electrodes for developing an ideal calibration curve for an embodiment of the battery cell having a mixed oxide cathode and a graphite anode. The calibration ( 105 ) to determine relationships of the positive and negative electrodes for developing ideal calibration curve(s) may be developed on a representative battery cell and implemented for purposes of monitoring and controlling other battery cells in use. 
     A calibration process for a new battery cell includes measuring battery parameters correlated with charge/discharge characteristics of the mixed-oxide cathode and the graphite anode against a known counter electrode, e.g., a lithium metal ( 110 ). The measured and analyzed battery parameters to determine charge/discharge characteristics for an exemplary battery are described with reference to  FIG. 3 , with OCV indicating the open circuit voltage, which is determined as described with reference to  FIG. 1  and SOC and Q indicating a state of charge or charge capacity of the battery. The measured data includes a cathode discharge response curve  340  and an anode charge response curve  345 , which are shown with reference to  FIG. 3 . 
       FIG. 3  is a graphical plot of data associated with charge/discharge characteristics for an exemplary battery cell, including electrical potential V ( 310 ) shown on the y-axis plotted in relation to a charge capacity ( 315 ) shown on the x-axis. The data is illustrative. Depicted data include full cell discharge  311 , a cathode discharge response curve  340  of the cathode of the new battery cell vs. lithium, and an anode charge response curve  345  of the anode of the new battery cell vs. lithium. The charge/discharge characteristics are measured at a slow charge/discharge rate (e.g., &lt;C/20) to obtain equilibrium curves, yielding half-cell data, i.e., one of the cathode and the anode, OCV-SOC curves that depict OCV-SOC relations of the cathode and the anode for the new battery cell, i.e., the cathode discharge response curve  340  and the anode charge response curve  345 . 
     Derivatives of the cathode discharge response curve  340  and the anode charge response curve  345  are also determined and correlated to the SOC ( 120 ). Derivatives may include the potential-derivative of the electric potential calculated for the differential voltage, i.e., dV/dQ vs. Q, or, alternatively, the charge-capacity-derivative of the electric charge capacity calculated for the differential charge, i.e., dQ/dV vs. V. 
     Preferred signature peaks associated with the derivatives of the cathode discharge response curve  340  and the anode charge response curve  345  are identified and used in subsequent evaluations. By taking the derivatives of the cathode discharge response curve  340  and the anode charge response curve  345 , signature peaks may be captured that are representative of the cathode and the anode. 
       FIG. 4  is a graphical plot of electrical potential V ( 310 ) and a potential-derivative of the electric potential dV/dQ ( 320 ), both shown on the y-axis, plotted against discharge capacity ( 325 ), which is shown on the x-axis. The discharge capacity ( 325 ) may be in units of amp-hours, or normalized to 100% discharge, or other suitable units. Depicted data includes cathode discharge response curve  340  and a corresponding preferred cathode differential voltage curve  350 , also referred to as preferred cathode discharge-derivative  350 . The preferred cathode differential voltage curve  350  is a potential-derivative of the cathode discharge response curve  340 , which provides a characteristic electrical potential response for the mixed-oxide cathode discharge against the known counter electrode, i.e., dV/dQ vs. SOC of the cathode discharge. 
       FIG. 5  is a graphical plot of electrical potential V ( 310 ) and a potential-derivative of the electric potential dV/dQ ( 320 ), both shown on the y-axis, plotted against charge capacity ( 315 ), which is shown on the x-axis. The charge capacity ( 315 ) may be in units of amp-hours, or normalized to 100% charge, or other suitable units. Depicted data includes the anode charge response curve  345  and a corresponding preferred anode differential voltage curve  355 , also referred to as a preferred anode potential-derivative  355 . The preferred anode differential voltage curve  355  is a potential-derivative of the anode charge response curve  345 . The preferred anode potential-derivative  355 , i.e., dV/dQ vs. SOC of the anode charge has two peaks  360  and  365  that are located at points on the charge capacity ( 315 ) that differ by approximately 0.33, or 33% of the total normalized charge capacity, and is referred to herein as a preferred total anode capacity. It is appreciated that the two peaks  360  and  365  and their difference is meant to be illustrative only. The peaks  360  and  365  may be identified as the preferred signature peaks for the graphite anode  360  and  365 , and employed for evaluating health of the battery cell during ongoing operation. 
     Alternatively, the OCV-SOC curves may be analyzed using the charge-capacity-derivative, i.e., dQ/dV vs. V. Signature peaks for the potential-derivative, i.e., dV/dQ vs. Q correspond to phase transitions in the electrode materials, whereas signature peaks for the charge-capacity-derivative dQ/dV vs. V indicate phase equilibria of the electrode materials. 
     Referring again to  FIG. 2 , during ongoing operation a state of health (SOH) of the battery is monitored during an electric power event ( 125 ). The method is described with reference to gathering battery data during an electric power event that is primarily a battery discharge event to generate a discharge voltage profile. An exemplary battery discharge event occurs during operation of a hybrid or electrically-powered vehicle when battery power is used for vehicle propulsion. The method applies equally to gathering battery data during an electric power event that is primarily a battery charge event to generate a charge voltage profile. This includes using the preferred cathode potential-derivative  350  shown in  FIG. 4  and the preferred anode potential-derivative  355  shown in  FIG. 5 . 
     Discharge of the battery cell is measured during operation that includes a low rate of discharge to determine a measured discharge voltage profile. Measured data associated with the discharge of the battery cell are described in Table 2 ( 130 ). 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
             
            
               
                   
                 Time 
                 Current 
                 Voltage 
                 Temp 
                 OCV 
                 SOC, Q 
               
               
                   
                 (Sec) 
                 (Amps) 
                 (V) 
                 (C) 
                 (V) 
                 (Ah) 
               
               
                   
               
            
           
         
       
     
     The measured data includes measuring battery parameters across the terminals of the battery cell during an extended discharge event, including current  208  and voltage  207  and a battery temperature (Temp) as a function of elapsed time as described with reference to  FIG. 1 . It is appreciated that data associated with charging of the battery cell may be measured at a low rate of battery charge to determine a measured charge voltage profile using the same data as described in Table 2. 
     The measured battery parameters are used to determine a measured discharge voltage profile that is correlated to the state of charge Q, i.e., OCV vs. Q, wherein OCV is the open-circuit voltage and Q is the state of charge ( 130 ). An example extended discharge event may include a discharge event from greater than 80% SOC to less than 20% SOC. A battery state estimator may be applied to the measured battery parameters to estimate the battery states including the open-circuit voltage OCV and the state of charge Q. Battery state estimators are known and not described in detail herein. 
     A measured potential-derivative (dV/dQ vs. Q) is calculated from the measured discharge voltage profile of the battery, preferably using differential analysis methods ( 140 ). 
     Signature peaks for the graphite anode electrode are identified by comparing the measured potential-derivative (dV/dQ vs. Q) derived from the measured discharge voltage profile of the battery cell with the preferred anode potential-derivative  355 , i.e., dV/dQ vs. SOC of the anode electrode ( 145 ). This is shown in  FIG. 6 . 
       FIG. 6  is a graphical plot of the potential-derivative of the electric potential dV/dQ ( 320 ), shown on the y-axis, plotted against the charge capacity ( 315 ), which is shown on the x-axis. The depicted data includes the preferred potential-derivative  355  of an anode charge curve and the measured potential-derivative of a cell discharge curve (dV/dQ vs. Q)  370  that is calculated from the measured discharge voltage profile of the battery cell. The preferred anode potential-derivative  355  includes preferred signature peaks  360  and  365  of an anode. The measured potential-derivative of the cell discharge curve (dV/dQ vs. Q)  370  includes measured signature peaks  375  and  380 . 
     Referring again to  FIG. 2 , the measured potential-derivative of the cell discharge curve  370  calculated from the measured discharge voltage profile of the battery also includes the two measured signature peaks  375  and  380 , which are identified and shown with reference to  FIG. 6  ( 145 ). The distance between the signature peaks  375  and  380 , preferably measured in units of Amp-hours or another suitable metric, represents a fraction (e.g. 33%) of the total anode capacity. A total measured anode capacity is thus determined. 
     The measured signature peaks  375  and  380  in the measured charge-derivative  370  are quantitatively compared with the preferred signature peaks  360  and  365  of the preferred potential-derivative of the anode charge curve  355  to determine total anode capacity ( 150 ). Quantitatively comparing the measured signature peaks includes comparing the total measured anode capacity for the measured signature peaks with the preferred total anode capacity, with the comparison preferably made in units of Amp-hours difference between the signature peaks. Quantitatively comparing the measured signature peaks also includes aligning one of the measured signature peaks, e.g., peak  380 , with a corresponding one of the preferred signature peaks for the preferred anode charge-derivative  355 , e.g., peak  365 , to determine the position of the anode electrode with respect to the complete battery cell. 
     Quantitatively comparing the measured signature peaks  375  and  380  in the measured potential-derivative  370  with the preferred signature peaks  360  and  365  of the preferred anode potential-derivative  355  further includes aligning the respective peaks to determine the position of the anode with reference to the battery cell, which permits deconvoluting the OCV-SOC relationship of the anode in relation to the battery cell. 
     A total graphite anode capacity may be calculated as a ratio of the total anode capacity for the measured signature peaks and the preferred total anode capacity ( 155 ). The total graphite anode capacity is useable as an indicator of graphite anode loss. A shift in the positions of one or both of the measured signature peaks in relation to the preferred signature peaks  360  and  365  for the graphite anode is calculated, and is an indication of lithium loss and total capacity loss when compared to the preferred total anode capacity. Shrinkage in distance between the signature peaks reflects graphite anode loss. A leftward shift of the positions of the peaks, excluding shrinkage, indicates an amount of lithium loss or total capacity loss. Suitable analytical processes, e.g., ratiometric comparisons, may be employed to calculate parameters correlatable to the total graphite anode capacity, the lithium loss and the total capacity loss. 
     Measurements associated with the cathode are also evaluated, including quantitatively comparing a measured potential-derivative with the preferred cathode potential-derivative ( 160 ). This includes comparing measured signature peaks in the potential-derivative with preferred signature peaks to determine a total cathode capacity ( 165 ). This includes calculating the OCV-SOC relationship of the cathode electrode using the previously determined cell discharge voltage, i.e., the data associated with Table 2, and a deconvoluted OCV-SOC relationship of the anode in relation to the battery cell, i.e., V anode (SOC) described herein. 
     A cathode voltage response is determined by adding the cell voltage, i.e., OCV or V battery (SOC), and the deconvoluted anode voltage V anode (SOC) together at each specific SOC for the data described with reference to Table 2. 
     The cathode voltage response is described by the following arithmetic relationship.
 
 V   cathode ( SOC )= V   battery ( SOC )+ V   anode ( SOC )  [4]
 
     Similarly, the potential-derivative for the cathode voltage response may be determined as follows.
 
 dV/dQ   cathode   =dV/dQ   battery   +dV/dQ   anode   [5]
 
     The measurements associated with the cathode are evaluated, including quantitatively comparing the measured potential-derivative for the cathode voltage response, i.e., dV/dQ cathode  with the preferred cathode potential-derivative of a discharge curve  350 . Illustrative data is shown with reference to  FIG. 7 . 
       FIG. 7  is a graphical plot of a potential-derivative of the electric potential dV/dQ ( 320 ) and electric potential V ( 310 ), shown on the y-axis, plotted against the discharge capacity ( 330 ), which is shown on the x-axis. The depicted data includes the preferred calculated cathode discharge response curve  340  and the preferred calculated cathode potential-derivative  350 . The depicted data also includes the measured cathode discharge response curve  390  and the measured cathode differential voltage curve  395 , both of which are calculated from the measured discharge voltage profile of the exemplary battery  370 , i.e., V battery (SOC) and the negative electrode voltage V anode (SOC) together at each specific SOC for the measured data that has been obtained as described with reference to Table 2. 
     During in-use operation of the battery cell, changes in position and size of the peaks at the anode and the cathode are monitored using the differential dV/dQ analysis. Capacity fading behaviors of the anode and the cathode and information on the active lithium loss are determined by monitoring the shifting in peak position(s), shrinking magnitude of the peaks, and shrinking in distance between the peaks. 
     The method described with reference to  FIG. 2  may also be applied to monitor the lithium-ion battery cell  100  during an electric power charging event. This includes monitoring the battery voltage and a corresponding state of charge of the battery cell during the charging event, as described with reference to Table 2 using analytical methods that are analogous to those described with reference to  FIG. 2 . A measured potential-derivative is determined by differentiating the battery voltage in relation to the corresponding state of charge of the battery during the electric power charge event. The measured potential derivative is compared with a preferred anode potential-derivative of the anode discharge curve. The measured potential derivative is also compared with a preferred cathode potential-derivative of the cathode charge curve. A first state of health parameter of the lithium-ion battery cell may be determined, and corresponds to the comparison of the measured potential-derivative with the preferred potential-derivative of the anode discharge curve. A second state of health parameter of the lithium-ion battery cell may be determined, and corresponds to the comparison of the measured potential-derivative with the preferred cathode potential-derivative of the cathode charge curve. 
     Alternatively or in addition, monitoring the lithium-ion battery cell includes monitoring battery voltage and a corresponding charge capacity of the battery cell during either electric power charge event or an electric power discharge event, as previously described with reference to the data described in Table 2, using analytical methods that are analogous to those described with reference to  FIG. 2 . A measured charge-capacity-derivative may be determined by differentiating the charge capacity in relation to the corresponding battery voltage during the electric power event. The measured charge-capacity-derivative is compared with a preferred charge-capacity-derivative of an anode curve. The measured charge-capacity-derivative is compared with a preferred charge-capacity-derivative of a cathode curve. A first state of health parameter of the lithium-ion battery cell is determined and corresponds to the comparison of the measured charge-capacity-derivative with the preferred charge-capacity-derivative of the anode curve. A second state of health parameter of the lithium-ion battery cell is determined that corresponds to the comparison of the measured charge-capacity-derivative with the preferred charge-capacity-derivative of the cathode curve. Comparing the measured charge-capacity-derivative with the preferred charge-capacity-derivative of the anode curve may include identifying preferred signature peaks of the preferred charge-capacity-derivative of the anode curve, identifying measured signature peaks of the measured charge-capacity-derivative, and determining an anode capacity corresponding to the measured signature peaks relative to the preferred signature peaks. In addition, comparing the measured charge-capacity-derivative with the preferred charge-capacity-derivative of the cathode curve may include integrating the measured charge-capacity-derivative, integrating the preferred charge-capacity-derivative of the cathode curve, and comparing the integrated measured charge-capacity-derivative with the preferred charge-capacity-derivative of the cathode curve. 
     Referring again to  FIG. 2 , a total cathode capacity may be determined as a ratio of a total cathode capacity for the measured signature peaks and a preferred total cathode capacity ( 165 ). The total cathode capacity is useable as an indicator of cathode material loss. 
     This analysis permits a determination of SOH of the battery in terms of a loss of cathode electrode, a loss of anode electrode, and a loss of active lithium, which indicates a total capacity loss ( 170 ). 
     The process for monitoring and evaluating components that affect SOH of the battery cell  100  using a differential curve technique described herein is preferably executed using algorithms and predetermined calibrations stored in an on-vehicle control module. 
     Control module, module, control, controller, control unit, processor and similar terms mean any suitable one or various combinations of one or more of Application Specific Integrated Circuit(s) (ASIC), electronic circuit(s), central processing unit(s) (preferably microprocessor(s)) and associated memory and storage (read only, programmable read only, random access, hard drive, etc.) executing one or more software or firmware programs, combinational logic circuit(s), input/output circuit(s) and devices, appropriate signal conditioning and buffer circuitry, and other suitable components to provide the described functionality. The control module has a set of control algorithms, including resident software program instructions and calibrations stored in memory and executed to provide the desired functions. The algorithms are preferably executed during preset loop cycles. Algorithms are executed, such as by a central processing unit, and are operable to monitor inputs from sensing devices and other networked control modules, and execute control and diagnostic routines to control operation of actuators. Loop cycles may be executed at regular intervals, for example each 3.125, 6.25, 12.5, 25 and 100 milliseconds during ongoing engine and vehicle operation. Alternatively, algorithms may be executed in response to occurrence of an event. 
     The disclosure has described certain preferred embodiments and modifications thereto. Further modifications and alterations may occur to others upon reading and understanding the specification. Therefore, it is intended that the disclosure not be limited to the particular embodiment(s) disclosed as the best mode contemplated for carrying out this disclosure, but that the disclosure will include all embodiments falling within the scope of the appended claims.