Patent Publication Number: US-2016231387-A1

Title: Estimating Battery Cell Parameters

Description:
BACKGROUND 
     This background is provided for the purpose of generally presenting a context for the instant disclosure. Unless otherwise indicated herein, material described in the background is neither expressly nor impliedly admitted to be prior art to the instant disclosure or the claims that follow. 
     Batteries are often used as a power source for mobile computing and electronic devices. Typically, a run-time of the mobile device is determined by a capacity of the device&#39;s batteries, from which power is drawn until the batteries are unable to support operations of the mobile device. In most cases, an estimation of run-time or remaining battery capacity is displayed to a user of the device to inform the user of an expectation of device availability or need to recharge the device. 
     These estimations of run-time, an effective battery capacity, or other battery-related characteristics, however, are often inaccurate due to the dynamic variability of not only properties of the batteries, but the ways in which the mobile device draws power. Additionally, once manufactured into a mobile device, retrieving real-time information on the characteristics of a battery is often precluded by simplicity of traditional battery interface circuitry. Accordingly, the inaccurate estimation of run-time or effective battery capacity can adversely affect user experience when a mobile device unexpectedly resets or shuts down due to a battery&#39;s inability to provide sufficient power for the operations of the device. 
     SUMMARY 
     This document describes techniques and apparatuses for estimating battery cell parameters. The estimated battery parameters can be used to build or update a model of the battery cell, which can be leveraged to optimize energy extraction from the battery cell. By so doing, energy stored in the battery cell can be used more efficiently to extend a run-time of a device drawing power from the battery cell. In some embodiments, voltage of a battery cell is measured while two different amounts of current are drawn from the battery cell. An internal resistance of the battery cell is then estimated based on the amounts of current drawn and the measured voltages of the battery cell. In other embodiments, voltage of battery cell is measured when an application load current to the battery cell is interrupted and at a later point in time when the voltage relaxes after the interruption. A capacitance or concentration resistance of the battery cell is then estimated based on the load current and the measured voltages of the battery cell. In these or other embodiments, the battery cell for which parameters are estimated may be isolated from other battery cells of a device or be a device&#39;s sole battery cell. 
     This summary is provided to introduce simplified concepts that are further described below in the Detailed Description. This summary is not intended to identify essential features of the claimed subject matter, nor is it intended for use in determining the scope of the claimed subject matter. Techniques and/or apparatuses for estimating battery parameters are also referred to herein separately or in conjunction as the “techniques” as permitted by the context, though techniques may include or instead represent other aspects described herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments enabling estimation of battery parameters are described with reference to the following drawings. The same numbers are used throughout the drawings to reference like features and components: 
         FIG. 1  illustrates an example environment in which techniques for estimating battery parameters can be implemented. 
         FIG. 2  illustrates an example battery system capable of implementing estimation of battery parameters. 
         FIG. 3  illustrates an example battery cell configuration in accordance with one or more embodiments. 
         FIG. 4  illustrates an example method for estimating internal resistance of a battery cell. 
         FIG. 5  illustrates an example discharge current profile and associated voltage measurements. 
         FIG. 6  illustrates an example charge current profile and associated voltage measurements. 
         FIG. 7  illustrates an example method for estimating capacitance or concentration resistance of a battery cell. 
         FIG. 8  illustrates example relaxation voltage profiles for various amounts of discharge current. 
         FIG. 9  illustrates example relaxation voltage profiles for various amounts of charge current. 
         FIG. 10  illustrates example models for estimating open circuit potential of a battery cell based on discharge data. 
         FIG. 11  illustrates comparisons of experimental data and model data for estimating open circuit potential after battery discharge. 
         FIG. 12  illustrates example models for estimating open circuit potential of a battery cell based on charging data. 
         FIG. 13  illustrates comparisons of experimental data and model data for estimating open circuit potential after battery charging. 
         FIG. 14  illustrates an example method of calculating parameters for multiple batteries. 
         FIG. 15  illustrates an example device in which techniques of estimating battery parameters can be implemented. 
     
    
    
     DETAILED DESCRIPTION 
     Overview 
     This document describes techniques and apparatuses for estimating battery cell parameters. These apparatuses and techniques may enable estimation of battery parameters such as internal resistance, capacitance, or concentration resistance, which effect a battery cell&#39;s ability to provide power. The estimated battery parameters can then be used to construct or update a model of the battery cell that more-accurately reflects or predicts the battery cell&#39;s future performance under various conditions. In some embodiments, these techniques and apparatuses enable estimation of a battery cell&#39;s internal resistance based on amounts of current drawn from, or applied to, the battery cell and respective voltage measurements made therewith. The techniques and apparatuses may also enable estimation of a battery cell&#39;s capacitance or concentration resistance based on an amount of current drawn from, or applied to, the battery cell and voltage measurements made after the application of current is interrupted. Further, the techniques and apparatuses may also isolate a battery cell from other battery cells in order to enable the estimation of battery parameters. These are but a few examples of many ways in which the techniques estimation of battery parameters, others of which are described below. 
     Example Operating Environment 
       FIG. 1  illustrates an example operating environment  100  in which techniques for estimating battery parameters can be embodied. Operating environment  100  includes a computing device  102 , which is illustrated with three examples: a smart phone computer  104 , a tablet computing device  106 , and a laptop computer  108 , though other computing devices and systems, such as netbooks, smart watches, fitness accessories, electric vehicles, Internet-of-Things (IoT) devices, wearable computing devices, media players, and personal navigation devices may also be used. 
     Computing device  102  includes computer processor(s)  110  and computer-readable storage media  112  (media  112 ). Media  112  includes an operating system  114  and applications  116 , which enable various operations of computing device  102 . Operating system  114  manages resources of computing device  102 , such as processor  110 , media  112 , and the like (e.g., hardware subsystems). Applications  116  comprise tasks or threads that access the resources managed by operating system  114  to implement various operations of computing device  102 . Media  112  also includes battery manager  132 , the implementation and use of which varies and is described in greater detail below. 
     Computing device  102  also includes power circuitry  120  and battery cell(s)  122 , from which computing device  102  can draw power to operate. Generally, power circuitry  120  may include firmware or hardware configured to enable computing device  102  to draw operating power from battery cells  122  or to apply charging power to battery cells  122 . Battery cells  122  may include any suitable number or type of rechargeable battery cells, such as lithium-ion (Lion), lithium-polymer (Li-Poly), lithium ceramic (Li-C), and the like. Implementations and uses of power circuitry  120  and battery cells  122  vary and are described in greater detail below. 
     Computing device  102  may also include display  124 , input mechanisms  126 , and data interfaces  128 . Although shown integrated with the example devices of  FIG. 1 , display  124  may be implemented separate from computing device  102  via a wired or wireless display interface. Input mechanisms  126  may include gesture-sensitive sensors and devices, such as touch-based sensors and movement-tracking sensors (e.g., camera-based), buttons, touch pads, accelerometers, and microphones with accompanying voice recognition software, to name a few. In some cases, input mechanisms  126  are integrated with display  124 , such an in a touch-sensitive display with integrated touch-sensitive or motion-sensitive sensors. 
     Data interfaces  128  include any suitable wired or wireless data interfaces that enable computing device  102  to communicate data with other devices or networks. Wired data interfaces may include serial or parallel communication interfaces, such as a universal serial bus (USB) and local-area-network (LAN). Wireless data interfaces may include transceivers or modules configured to communicate via infrastructure or peer-to-peer networks. One or more of these wireless data interfaces may be configured to communicate via near-field communication (NFC), a personal-area-network (PAN), a wireless local-area-network (WLAN), or wireless wide-area-network (WWAN). In some cases, operating system  114  or a communication manager (not shown) of computing device  102  selects a data interface for communications based on characteristics of an environment in which computing device  102  operates. 
       FIG. 2  illustrates an example battery system  200  capable of implementing aspects of the techniques described herein. In this particular example, battery system  200  includes battery manager  118 , power circuitry  120 , and battery cells  122 . In some embodiments, battery manager is implemented in software (e.g., application programming interface) or firmware of a computing device by a processor executing processor-executable instructions. Alternately or additionally, components of battery manager  118  can be implemented integral with other components of battery system  200 , such as power circuitry  120  and battery cells  122  (individual or packaged). 
     Battery manager  118  may include any or all of the entities shown in  FIG. 2 , which include battery monitor  202 , parameter estimator  204 , current load monitor  206 , workload estimator  208 , and load allocator  210 . Battery monitor  202  is configured to monitor characteristics of battery cells  122 , such as voltage, current flow, remaining capacity (e.g., state-of-charge), full charge capacity (which decreases as cycle count increases), temperature, age (e.g., time or charging cycles), and the like. Battery monitor  202  may also determine or have access to respective configuration information for battery cells  122 , such as cell manufacturer, chemistry type, rated capacity, voltage and current limits (e.g., cutoffs), and the like. Battery monitor  202  may store and enable other entities of battery manager  118  to access this battery cell configuration information. 
     Parameter estimator  204  is configured to estimate parameters of battery cells  122 , such as internal resistance, capacitance, or concentration resistance. In some cases, parameter estimator estimates these parameters based on characteristics of the battery cells that are monitored by battery monitor  202 , such as current flow and voltage. The implementation and use of battery monitor  202  varies and is described below in greater detail. 
     Current load monitor  206  monitors an amount of current drawn from one or more of battery cells  122  by computing device  102 . In some cases, current load monitor  206  monitors individual amounts of current drawn from each respective one of battery cells  122 . Current load monitor  206  may also monitor an amount of current applied to one or more of battery cells  122  by computing device  102  during charging. In at least some embodiments, current load monitor  206  provides real-time information indicating an amount of current drawn from a battery cell, such as at a rate on the order of milliseconds or seconds. 
     Workload estimator  208  estimates an amount of current that may be consumed when computing device  102  performs various tasks or operations. The estimated amount of current may be based on tasks that computing device  102  is performing, scheduled to perform, likely to perform, and so on. For example, workload estimator may receive information from operating system  114  that indicates a set of tasks are scheduled for execution by resources of computing device  102 . Workload estimator  208  may also include or have access to information that describes relationships between power consumption of hardware components and their respective workloads. Based on the set of tasks, workload estimator  208  estimates or forecasts an amount of current that computing device  102  will consume to perform the tasks. In some cases, workload estimator  208  provides a current consumption forecast over time based on a schedule or predicted order of execution for the tasks. 
     Load allocator  210  is configured to determine an amount of current to draw from each battery cell  122 . In some cases, load allocator  210  determines a load allocation scheme based on information received from other entities of battery manager  118 , such as current and forecast power demands of computing device  102 , and respective characteristics, states-of-charge, internal resistances for battery cells  122 . A load allocation may be configured to draw power from all or a subset of battery cells  122  based on the aforementioned information to maximize an efficiency of drawing power from multiple battery cells. 
     Although shown as disparate entities, any or all of battery monitor  202 , parameter estimator  204 , current load monitor  206 , workload estimator  208 , and load allocator  210  may be implemented separate from each other or combined or integrated in any suitable form. For example, any of these entities, or functions thereof, may be combined generally as battery manager  118 , which can be implemented as a program application interface (API) or system component of operating system  114 . 
     Battery system  200  also includes power circuitry  120 , which provides an interface between battery manager  118  and battery cells  122 . Generally, power circuitry  120  may include hardware and firmware that enables computing device  102  to draw power from (e.g., discharge), apply power to (e.g., charge) battery cells  122 , and implement various embodiments thereof. In this particular example, power circuitry  120  includes charging circuitry  212 , sensing circuitry  214 , and isolation circuitry  216 . 
     Charging circuitry  120  is configured to provide current by which battery cells  122  are charged. Charging circuitry may implement any suitable charging profile such as constant current, constant voltage, custom profiles provided by battery manager  118 , and the like. In at least some embodiments, charging circuitry  212  is capable of providing different amounts of current to different respective battery cells being charged concurrently. 
     Sensing circuitry  214  is configured to sense or monitor operational characteristics of battery cells  122 . These operational characteristics may include a voltage level, an amount of current applied to, or an amount of current drawn from a respective one of battery cells  122 . In some cases, sensing circuitry  214  may be implemented integral with charging circuitry  120 , such as part of a charging controller or circuit that includes sensing elements (e.g., analog-to-digital converters (ADCs), amplifiers, and sense resistors). 
     Power circuitry  120  also includes isolation circuitry  216 , which enables battery manager  118  to isolate single or subsets of battery cells  122 . While isolated, single battery cells or subsets of battery cells may be charged or discharged concurrently. For example, charging current can be applied to a battery cell isolated by isolation circuitry  216  while computing device  102  draws operating power from all or a subset of the remaining battery cells. In some cases, isolation circuitry is implemented as multiplexing circuitry that switches between battery cells  122  to facilitate connection with an appropriate set of power circuitry for battery cell sensing, current consumption, or current application. 
     Battery cells  122  may include any suitable number or type of battery cells. In this particular example, battery cells  122  include battery cell  1   218 , battery cell  2   220 , battery cell n  222 , and battery cell N  224 , where N may be any suitable integer. In some cases, computing device may include a single battery cell  122  to which the techniques described herein can be applied without departing from the spirit of the disclosure. In other cases, battery cells  122  may include various homogeneous or heterogeneous combinations of cell shape, capacity, or chemistry type. 
     Example types of battery chemistry may include lithium-ion, lithium-polymer, lithium ceramic, flexible printed circuit Li-C (FPC-LiC), and the like. Each of battery cells  122  may have a particular or different cell configuration, such as a chemistry type, shape, capacity, packaging, electrode size or shape, series or parallel cell arrangement, and the like. Accordingly, each of battery cells  122  may also have different parameters, such as internal resistance, capacitance, or concentration resistance. 
       FIG. 3 . Illustrates an example battery cell configuration  300  in accordance with one or more embodiments. Battery cell configuration  300  includes battery cell- 1   302 , battery cell- 2   304 , battery cell- 3   306 , and battery cell- 4   308 , each of which may be configured as any suitable type of battery. Additionally, each of battery cells  302  through  308  is configured with a respective parallel bulk capacitance  310  through  316  (e.g., super capacitor), which can be effective to mitigate a respective spike of current load on a given battery. 
     Each of battery cells  302  through  308  may provide (or receive) a respective amount of current from computing device  102 , which are shown as current I 1    318 , current I 2    320 , current I 3    322 , and current I 4    324 . These individual currents are multiplexed via battery switching circuit  326  (switching circuit  326 ), the summation of which is current I Device    328 . Here, note that switching circuit  326  is but one example implementation of isolation circuitry  216  as described with respect to  FIG. 2 . In some cases, such as normal device operation, battery switching circuit  326  switches rapidly between battery cells  302  through  308  effective to draw current or power from each of them. In other cases, battery switching circuit  236  may isolate one of batteries  302  through  306  and switch between a subset of the remaining batteries to continue powering computing device  102 . 
       FIG. 3  also illustrates example battery model  330 , which may be used to model any battery cell or battery described herein. Generally, battery model  330  can be used to estimate or predict parameters of a battery that effect the battery&#39;s ability to provide power for computing device  102 . In some cases, these battery parameters are dynamic and may not be directly observable or measurable by traditional sensing techniques. Battery model  330  includes an ideal voltage source that provides power and has an open circuit voltage  332  (V O    332 ). When a battery is not providing current, an open circuit potential of the battery may be approximate to open circuit voltage  332 . 
     Battery model  330  also includes direct current (DC) internal resistance  334  (R DCIR    334 ), capacitance  336  (C  336 ), and concentration resistance  338  (R Conc.    338 ). Battery current  340  (I  340 ) is formed by capacitance current (I C    342 ) and concentration resistance current  338  (I R    344 ), which are effected by capacitance  336  and concentration resistance  338 , respectively. Battery voltage  346  (V  346 ) represents the terminal voltage for battery model  330  and can be effected by the losses associated with the other parameters, such as when current passes through concentration resistance  338  and internal resistance  334 . 
     Example Methods 
     The methods described herein may be used separately or in combination with each other, in whole or in part. These methods are shown as sets of operations (or acts) performed, such as through one or more entities or modules, and are not necessarily limited to the order shown for performing the operation. For example, the techniques may estimate an internal resistance based on an amount of current drawn from, or applied to, a battery cell and measured instances of the battery cell&#39;s voltage. The techniques may also estimate a concentration resistance or capacitance based on an amount of current drawn from, or applied to, a battery cell and instances of the battery cell&#39;s voltage that are measured at particular times after the application of the current. These are but a few examples that may be implemented using the techniques described herein. In portions of the following discussion, reference may be made to the operating environment  100  of  FIG. 1 , the battery system  200  of  FIG. 2 , the battery cell configuration  300  of  FIG. 3 , and other methods and example embodiments described elsewhere herein, reference to which is made for example only. 
       FIG. 4  depicts method  400  for estimating an internal resistance of a battery cell, including operations performed by battery manager  118  or parameter estimator  204 . 
     At  402 , a battery cell is isolated from another battery cell of a computing device. The battery cell may be isolated from the other battery cell with any suitable switching circuitry or isolation circuitry. It should be noted that isolation of the battery cell is optional and that other operations described herein may be performed using one or more un-isolated battery cells. In some cases, the battery cell is isolated from multiple other battery cells arranged in a parallel or series configuration (e.g., two series by four parallel or 2S4P). While the battery cell is isolated, the computing device may continue to draw operating current from, or apply charging current to, the other battery. 
     By way of example, consider battery cell configuration  300 . Here, assume that battery cell configuration  300  is implemented in laptop computer  108 , which is operating from battery power. When discharging the batteries, switching circuit  326  switches between battery cells  302  through  308  to draw current from each of the battery cells. Here, parameter estimator  204  isolates, via switching circuit  326 , battery cell- 1   302  from battery cells  304  through  308 , which may continue to provide operational current to laptop computer  108 . 
     At  404 , a first amount of current is drawn the isolated battery cell. The first amount of current may be any suitable amount of current, such as a discharge current ranging from C amps to C/20 amps, where C is a capacity of the battery cell in amp-hours. In some cases, the first amount of current is based on a known amount of current consumed by components of the device at a particular activity level. For example, the amount of current may be current consumed while the device&#39;s CPU is at a highest power state and the device&#39;s display is at full brightness. Alternately, the first amount of current may be applied to the isolated battery cell. In some cases, the amount of current is applied in accordance with a constant-current charge profile. In such cases, the application of the first amount of current may be substantially stable and constant. 
     In the context of the present example and as illustrated by current graph  500  of  FIG. 5 , parameter estimator  204  draws, via isolation circuitry  216 , current I 1    502  (e.g., operational current) from battery cell- 1   302 . Although isolated from battery cells  304  through  308 , switching circuit  326  switches between voltage regulation circuitry (not shown) and battery cell- 1   302  to enable current I 1    502  to be drawn from battery cell- 1   302 . Alternately, for cases in which current is applied to a battery cell, consider current graph  600  of  FIG. 6 . Here, parameter estimator  204  would apply, via charging circuitry  212 , current I 1    602  (charging current as denoted by negative values) to the battery cell. 
     At  406 , a first instance of the isolated battery cell&#39;s voltage is measured while the first amount of current is drawn. The isolated battery cell&#39;s voltage may be measured at any point in time while the first amount of current is drawn. Continuing the ongoing example and as illustrated by voltage graph  504 , parameter estimator  204  measures, via sensing circuitry  214 , voltage V 1    506  of battery cell- 1   302  while current I 1    502  is drawn. Alternately, a first instance of the isolated battery cell&#39;s voltage can be measured while a first amount of current is applied to the isolated battery. An example of this is illustrated by voltage graph  604 , in which voltage V 1    606  of the battery cell is measured while current I 1    602  is applied. 
     At  408 , a second amount of current is drawn from the isolated battery cell. The second amount of current may be any suitable amount that is different from the first amount of current, such as a different amount of discharge current consumed by components of the device. Alternately, the drawing of the first amount of current may be interrupted, effective to halt the discharge any current from the battery cell. The second amount of current is drawn for at least a particular amount of time, such as from approximately one second to approximately ten seconds. In the context of the present example, parameter estimator  204  interrupts the discharge of current I 1    502  from battery cell- 1   302  from time t 1  to time t 2 , during which current I 2    508  being drawn from battery cell- 1   302  is approximately zero amps. 
     Alternately, a second amount of current can be applied to the isolated battery cell. The second amount of current may be any suitable amount that is different from the first amount of current, such as a different amount of charge current. Alternately, the application of the first amount of current may be interrupted, effective to halt the application any charging current to the battery cell. The second amount of current is applied for at least a particular amount of time, such as from approximately one second to approximately ten seconds. Returning to current graph  600 , the application current I 1    602  is interrupted from time t 1  to time t 2 , during which current I 2    608  applied to the battery cell is approximately zero amps. 
     At  410 , a second instance of the isolated battery cell&#39;s voltage is measured while the second amount of current is drawn. Alternately, the second instance of voltage may be measured while no current is drawn, such as when discharging is interrupted. The isolated battery cell&#39;s voltage may be measured at any point in time while the second amount of current is drawn, or not drawn in the case of discharge interruption. In the context of the present example, parameter estimator  204  measures, via sensing circuitry  214 , voltage V 2    510  of battery cell- 1   302  while current I 2    508  is drawn. 
     In the alternate case of current application, a second instance of the isolated battery cell&#39;s voltage is measured while the second amount of current is applied. In some cases, the second instance of voltage is measured while no current is applied, such as when charging is interrupted. The isolated battery cell&#39;s voltage may be measured at any point in time while the second amount of current is applied, or not applied in the case of charge interruption. Returning to voltage graph  604 , voltage V 2    610  of the battery cell is measured while current I 2    508  is applied. 
     At  412 , an internal resistance of the isolated battery cell is estimated based on the amounts of current drawn and the measured instances of the voltage. Because the isolation circuitry or switching circuitry permits the isolation of the battery cell, other battery cells of the computing device may continue to charge or provide operating power while this and the other preceding operations are performed. Extending Ohm&#39;s Law to estimate the internal resistance (IR) of the isolated battery cell based on the values of  FIG. 5  yields Equation 1. 
     
       
         
           
             
               
                 
                   
                     
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     Continuing the ongoing example, parameter estimator  204  applies V 1    506 , V 2    510 , I 1    502 , and I 2    508  to Equation 1 to estimate an IR of battery cell- 1   302 . Parameter estimator  204  can then update a battery model of battery cell- 1   302  with the estimated internal resistance. By so doing, battery manager  118  can predict an ability of battery cell- 1   302  to provide current under various conditions. 
     Alternately, an internal resistance of the isolated battery cell can be estimated based on the amounts of current applied and the measured instances of the voltage. Extending Ohm&#39;s Law to estimate the IR of the isolated battery cell based on the values of  FIG. 6  yields Equation 2. 
     
       
         
           
             
               
                 
                   
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     Optionally at  414 , the isolated battery cell is switched back into operation with other battery cells of the computing device. In some cases, this may include switching the isolated battery cell back into circuit with the other battery cell of the computing device, which may be charging. Alternately, the isolated battery cell may be switched back in with the other battery cell to provide operating current for the computing device. Concluding the present example, parameter estimator combines, via switching circuit  326 , battery cell- 1   302  with battery cells  304  through  308 , which may continue to charge or provide operational current to laptop computer  108 . 
       FIG. 7  depicts method  700  for estimating a capacitance or concentration resistance of a battery cell, including operations performed by battery manager  118  or parameter estimator  204 . 
     At  702 , a battery cell is isolated from another battery cell of a computing device. The battery cell may be isolated from the other battery cell with any suitable switching circuitry or isolation circuitry. In some cases, the battery cell is isolated from multiple other battery cells arranged in a parallel or series configuration. While the battery cell is isolated, the computing device may continue to draw operating current from, or apply charging current to, the other battery. 
     At  704 , a known amount of current is drawn from the isolated battery cell effective to discharge the isolated battery cell. The known amount of current may be any suitable amount of current, such as current consumed by components of the computing device. By way of example, consider current graph  800  of  FIG. 8  in which current  702  is drawn from an isolated battery cell. Here, assume that current  802  comprises approximately 375 mA of current drawn from the isolated battery cell by setting components of a device to known states (e.g., display to full brightness). Alternately, a known amount of current can be applied to isolated battery cell, such as charging current. In some cases, the known amount of current is based on a constant-current charging profile of the battery cell. An example of this alternate case illustrated by current graph  900  of  FIG. 9 , in which current  902  is applied to the battery cell (charging denoted by negative current values). 
     At  706 , the drawing of the known amount of current is ceased effective to interrupt discharge of the isolated battery cell. In some cases, drawing of the current is ceased by switching the isolated battery cell out of a discharge circuit. This can be effective to allow a voltage of the isolated battery cell to stabilize or relax. In the context of discharging current from a battery cell, the discharge of current  802  is halted at time  804 , which is located at zero seconds on the time axis of current graph  800 . In the alternate case of applying current, the application of the current can be ceased effective to interrupt the charging of the isolated battery cell. Returning to current graph  900 , the application of current  902  is halted at time  904 , which is located at zero seconds on the time axis of current graph  900 . 
     At  708 , a first instance of the isolated battery cell&#39;s voltage is measured after ceasing to draw the current. This first instance of the voltage may be measured immediately after ceasing to draw the current from the isolated battery cell. As shown in voltage graph  806 , voltage  808  is measured at the terminal of the battery cell at time zero after the discharge of current  802  is interrupted. Alternately, a first instance of the isolated battery cell&#39;s voltage can be measured after ceasing to apply the known amount of current. An example of this is illustrated by voltage graph  906 , in which voltage  908  (e.g., terminal voltage) is measured at time zero after interrupting the application of current  902 . 
     At  710 , a duration of time is waited effective to allow the voltage of the isolated battery cell to stabilize. Waiting for longer durations of time may allow for a more-accurate measurement of the isolated battery cell&#39;s change in voltage. In some cases, the duration of time waited ranges from 120 seconds to an hour after charging is interrupted. In other cases, the duration of time is much shorter, such as approximately 60 seconds to 120 seconds. In the context of the present example, assume the amount of time waited is 3500 seconds, or approximately 58 minutes, as shown in voltage graph  806  or  906 . 
     At  712 , a second instance of the isolated battery cell&#39;s voltage is measured after waiting for the duration of time. As noted at operation  710 , the duration of time may range from 60 to 120 seconds, or up to an hour or more. Continuing the ongoing example, voltage  810  is measured after waiting 3500 seconds from ceasing to discharge current  802 . As additional examples, voltage profile  812  and voltage profile  814  illustrate voltage relaxation associated with discharge rates of 0.2 C and 0.7 C respectively. 
     In the alternate case of applying current to the battery cell, a second instance of voltage may also be measured after waiting for the durations of time as described with respect to operation  712 . Here, voltage  910  is measured after waiting 3500 seconds from ceasing the application of charging current  902 . As additional examples, voltage profile  912  and voltage profile  914  illustrate voltage relaxation associated with charge rates of 0.2 C and 0.7 C respectively 
     At  714 , a capacitance or concentration resistance of the isolated battery cell is estimated based on the known amount of current and the measured instances of the voltage. In cases in which the voltage of the isolated battery cell is provided ample time to relax (e.g., ˜1 hour), concentration resistance may be calculated using Equation 3. 
     
       
         
           
             
               
                 
                   
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                    
                   3 
                 
               
             
           
         
       
     
     In the context discharging current, concentration resistance of the isolated battery cell can be determined from current  802 , voltage  808 , and voltage  810 . Here, these values for use in Equation 3 are illustrated in  FIG. 8  as ΔI  816  and ΔV  818 . In the case of charging current, concentration resistance can be calculated using similar value of  FIG. 9 , which are shown as ΔI  916  and ΔV  918 . 
     In some embodiments, a relaxed voltage or steady-state potential of an isolated battery cell may be predicted from data collected over shorter durations of time. In some cases, this can be effective to accurately estimate concentration resistance or capacitance without having to wait for voltage of a battery cell to fully relax or stabilize. In such cases, concentration resistance or capacitance may be estimated based on data collected over as few as 60 seconds, 120 seconds, or 600 seconds. 
     Steady state potential of the battery cell can be estimated by linearizing a voltage (open circuit potential (OCP)) relaxation curve and fitting (A and B values) the linearization as shown in Equation 4, which may be applied to values associated with discharging battery cells. A graphical representation of Equation 4 is illustrated in  FIG. 10  at  1000 , which shows a log of potential vs. the square root of time. 
       −ln(OCP− V )= A√{square root over (t)}+B    Equation 4
 
     Because OCP is not accurately known, an estimation for OCP can be made by altering OCP to maximize R 2  as shown at  1002 , which includes a fit with experimental results  1004 . Further, from this fit model and as illustrated in  FIG. 11 , a comparison can be made between results of the fit model and experimental data as shown in voltage graph  1100 . Here, notice that within 120 seconds, the model fits well with the experimental results. Extrapolating the comparison to one hour, however, may result in a slight increase in error as shown in voltage graph  1102 . 
     With a model capable of estimating OCP, concentration resistance can also be found using Equation 5. 
     
       
         
           
             
               
                 
                   
                     
                       OCP 
                       - 
                       
                         V 
                         0 
                       
                     
                     
                       Δ 
                        
                       
                           
                       
                        
                       I 
                     
                   
                   = 
                   
                     R 
                     Concentration 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   5 
                 
               
             
           
         
       
     
     Capacitance of the battery cell can also be determined by finding a time constant for Equation 4, which can be solved for and written as Equation 6 as shown below. 
     
       
         
           
             
               
                 
                   
                     
                       Att 
                       = 
                       0 
                     
                     , 
                     
                       V 
                       = 
                       
                         V 
                         0 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       Att 
                       = 
                       
                         
                           t 
                           1 
                         
                         = 
                         τ 
                       
                     
                     , 
                     
                       V 
                       = 
                       
                         V 
                         1 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       V 
                       1 
                     
                     = 
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             
                               1 
                               e 
                             
                           
                           ) 
                         
                          
                         
                           ( 
                           
                             OCP 
                             - 
                             
                               V 
                               0 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         V 
                         0 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     τ 
                     = 
                     
                       
                         ( 
                         
                           
                             
                               - 
                               
                                 ln 
                                  
                                 
                                   ( 
                                   
                                     OCP 
                                     - 
                                     
                                       V 
                                       1 
                                     
                                   
                                   ) 
                                 
                               
                             
                             - 
                             B 
                           
                           A 
                         
                         ) 
                       
                       2 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     τ 
                     = 
                     
                       C 
                       * 
                       IR 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     C 
                     = 
                     
                       τ 
                       IR 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   6 
                 
               
             
           
         
       
     
     In the alternate case of applying current to a battery cell, steady state potential of the battery cell may be estimated by performing a similar linearization, which is shown in Equation 7. A graphical representation of Equation 7 is illustrated in  FIG. 12  at  1200 , which shows a log of potential vs. the square root of time. 
       −ln( V −OCP)= A√{square root over (t)}+B    Equation 7
 
     An estimation for OCP can be made by altering OCP to maximize R 2  as shown at  1202 , which includes a fit with experimental results  1204 . Further, from this fit model and as illustrated in  FIG. 13 , a comparison can be made between results of the fit model and experimental data as shown in voltage graph  1300 . Here, notice that within 120 seconds, the model fits well with the experimental results. Extrapolating the comparison to one hour, however, may result in a slight increase in error as shown in voltage graph  1302 . 
     With a model capable of estimating OCP, concentration resistance can also be found using Equation 8. 
     
       
         
           
             
               
                 
                   
                     
                       
                         V 
                         0 
                       
                       - 
                       OCP 
                     
                     
                       Δ 
                        
                       
                           
                       
                        
                       I 
                     
                   
                   = 
                   
                     R 
                     Concentration 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   8 
                 
               
             
           
         
       
     
     Capacitance of the battery cell can also be determined by finding a time constant for Equation 7, which can be solved for and written as Equation 9 as shown below. 
     
       
         
           
             
               
                 
                   
                     
                       Att 
                       = 
                       0 
                     
                     , 
                     
                       V 
                       = 
                       
                         V 
                         0 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       Att 
                       = 
                       
                         
                           t 
                           1 
                         
                         = 
                         τ 
                       
                     
                     , 
                     
                       V 
                       = 
                       
                         V 
                         1 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       V 
                       1 
                     
                     = 
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             1 
                             e 
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           
                             V 
                             0 
                           
                           - 
                           OCP 
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     τ 
                     = 
                     
                       
                         ( 
                         
                           
                             
                               - 
                               
                                 ln 
                                  
                                 
                                   ( 
                                   
                                     
                                       V 
                                       1 
                                     
                                     - 
                                     OCP 
                                   
                                   ) 
                                 
                               
                             
                             - 
                             B 
                           
                           A 
                         
                         ) 
                       
                       2 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     τ 
                     = 
                     
                       C 
                       * 
                       IR 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     C 
                     = 
                     
                       τ 
                       IR 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   9 
                 
               
             
           
         
       
     
     Accordingly, the capacitance or concentration resistance of the isolated battery cell can be estimated with the model described herein. By so doing, a duration of time for which discharging or charging is interrupted can be minimalized. Once the capacitance or concentration resistance is estimated, method  700  may optionally switch the isolated battery cell back into circuit with other battery cells of the computing device. 
     Once internal resistance, capacitance, or concentration resistance are estimated for a battery cell, a model of the battery cell can be constructed or updated with the estimated values. By so doing, performance (present or future) of the battery cell can be more-accurately predicted. In some cases, the model of the battery cell can be leveraged to enable more efficient use of the battery cell. 
     For example, battery manager  118  can estimate future battery performance based on a model and a state-of-charge of a battery cell. Using information provided by current load monitor  206  and workload estimator  208 , battery manager  118  can predict how the battery cell will perform under different loads (e.g., an ability to provide current). Based on the predicted performance of the battery cells, load allocator  210  can then optimally distribute system current draw across one or more of the battery cells to maximize battery efficiency or minimize internal battery losses associated with the parameters described herein. 
       FIG. 14  depicts method  1400  for calculating battery parameters for multiple batteries, including operations performed by battery manager  118  or battery monitor  202 . 
     At  1402 , system current of a computing device is drawn from multiple batteries of the computing device. The multiple batteries may be configured as a homogeneous combination of batteries or a heterogeneous combination of batteries having different chemistry types or different capacities. Alternately, charging current may be applied to the multiple batteries of the computing device. 
     At  1404 , one of the multiple batteries is isolated from the multiple batteries for parameter characterization. The battery may be isolated by any suitable switching or isolation circuitry. In some cases, the battery is isolated from other batteries in series and other batteries in parallel. Alternately or additionally, the battery may be isolated from bulk capacitance connected in parallel with the battery. 
     Optionally at  1406  and while the battery is isolated, system current continues to be drawn from the other multiple batteries by which the computing device operates. Alternately, charging current may be applied to the other multiple batteries while the battery is isolated. 
     At  1408 , the battery is allowed to rest for a predetermined amount of time. This can be effective to permit properties of the battery to stabilize, such as temperature, voltage, and the like. 
     At  1410 , voltage of the battery is polled under the discharge or application of predefined current profiles. The predefined current profiles may include varying amounts of current or an interruption in the discharge or application of current, such as those described herein. In some cases, a predefined current profile may be configured to enable a particular battery parameter to be calculated, such as internal resistance, capacitance, or concentration resistance. 
     At  1412 , parameters for the battery are calculated based on results of the polling. The results of the polling may include multiple voltage measurements made at particular points during application of a predefined current profile. From operation  1412 , method  1400  may return to operation  1402  in order to calculate parameters of another one of the multiple batteries of the computing device. 
     Aspects of these methods may be implemented in hardware (e.g., fixed logic circuitry), firmware, a System-on-Chip (SoC), software, manual processing, or any combination thereof. A software implementation represents program code that performs specified tasks when executed by a computer processor, such as software, applications, routines, programs, objects, components, data structures, procedures, modules, functions, and the like. The program code can be stored in one or more computer-readable memory devices, both local and/or remote to a computer processor. The methods may also be practiced in a distributed computing environment by multiple computing devices. 
     Example Device 
       FIG. 15  illustrates various components of example device  1500  that can be implemented as any type of mobile, electronic, and/or computing device as described with reference to the previous  FIGS. 1-10  to implement techniques of estimating battery cell parameters. In embodiments, device  1500  can be implemented as one or a combination of a wired and/or wireless device, as a form of television client device (e.g., television set-top box, digital video recorder (DVR), etc.), consumer device, computer device, server device, portable computer device, user device, communication device, video processing and/or rendering device, appliance device, gaming device, electronic device, and/or as another type of device. Device  1500  may also be associated with a user (e.g., a person) and/or an entity that operates the device such that a device describes logical devices that include users, software, firmware, and/or a combination of devices. 
     Device  1500  includes communication modules  1502  that enable wired and/or wireless communication of device data  1504  (e.g., received data, data that is being received, data scheduled for broadcast, data packets of the data, etc.). Device data  1504  or other device content can include configuration settings of the device, media content stored on the device, and/or information associated with a user of the device. Media content stored on device  1500  can include any type of audio, video, and/or image data. Device  1500  includes one or more data inputs  1506  via which any type of data, media content, and/or inputs can be received, such as user-selectable inputs, messages, music, television media content, recorded video content, and any other type of audio, video, and/or image data received from any content and/or data source. 
     Device  1500  also includes communication interfaces  1508 , which can be implemented as any one or more of a serial and/or parallel interface, a wireless interface, any type of network interface, a modem, and as any other type of communication interface. Communication interfaces  1508  provide a connection and/or communication links between device  1500  and a communication network by which other electronic, computing, and communication devices communicate data with device  1500 . 
     Device  1500  includes one or more processors  1510  (e.g., any of microprocessors, controllers, and the like), which process various computer-executable instructions to control the operation of device  1500  and to enable techniques for estimating battery cell parameters. Alternatively or in addition, device  1500  can be implemented with any one or combination of hardware, firmware, or fixed logic circuitry that is implemented in connection with processing and control circuits which are generally identified at  1512 . Although not shown, device  1500  can include a system bus or data transfer system that couples the various components within the device. A system bus can include any one or combination of different bus structures, such as a memory bus or memory controller, a peripheral bus, a universal serial bus, and/or a processor or local bus that utilizes any of a variety of bus architectures. Device  1500  may be configured to operate from any suitable power source, such as battery cells  122 , power circuitry  120 , various external power sources, and the like. 
     Device  1500  also includes computer-readable storage media  1514 , such as one or more memory devices that enable persistent and/or non-transitory data storage (i.e., in contrast to mere signal transmission), examples of which include random access memory (RAM), non-volatile memory (e.g., any one or more of a read-only memory (ROM), flash memory, EPROM, EEPROM, etc.), and a disk storage device. A disk storage device may be implemented as any type of magnetic or optical storage device, such as a hard disk drive, a recordable and/or rewriteable compact disc (CD), any type of a digital versatile disc (DVD), and the like. Device  1500  can also include a mass storage media device  1516 . 
     Computer-readable storage media  1514  provides data storage mechanisms to store device data  1504 , as well as various device applications  1518  and any other types of information and/or data related to operational aspects of device  1500 . For example, an operating system  1520  can be maintained as a computer application with the computer-readable storage media  1514  and executed on processors  1510 . Device applications  1518  may include a device manager, such as any form of a control application, software application, signal-processing and control module, code that is native to a particular device, a hardware abstraction layer for a particular device, and so on. 
     Device applications  1518  also include any system components or modules to implement the techniques, such as battery manager  118  and any combination of components thereof. 
     CONCLUSION 
     Although embodiments of techniques and apparatuses of estimating of battery cell parameters have been described in language specific to features and/or methods, it is to be understood that the subject of the appended claims is not necessarily limited to the specific features or methods described. Rather, the specific features and methods are disclosed as example implementations of estimating battery cell parameters.