Method for charging a battery and corresponding system

Abstract

A method for charging an accumulator, comprising: iteratively determining a plurality of charge profiles of the accumulator; iteratively determining the accumulator swell based on the plurality of charge profiles; and setting a charging current during a subsequent charging of the accumulator; wherein the iterative determination of a plurality of charge profiles comprises: determining a first charge profile of the accumulator; and, after discharging the accumulator, determining a second charge profile of the accumulator, the method further comprising: determining a first range of interest by comparing the first and second charge profiles; and setting a charging current in the first range of interest during the subsequent charging of the accumulator, each of the first and second charge profiles defining a relationship between a state of charge and an accumulator swell;wherein the first charging profile is defined by a first data set comprising charge value data and swelling value data, wherein the subsequent charging profile is defined by a second data set comprising charge value data and swelling value data; characterized in that the first area of ​​interest is determined by comparing the swelling value data of the first and second data sets with the charge value data of the first data set, which correspond to the charge value data of the second data set.

Description

TECHNICAL FIELDThe present invention relates to a method for charging an accumulator according to the preamble of claim 1 or 2, as known from US 2018 / 0 149 462 A1 and WO 2020 / 097 271 A1, and to a corresponding system.BACKGROUNDLithium ion batteries may be used in electromobility and portable electronics implementations, among others, where the lithium ions move between negative and positive electrodes during discharge (e.g., from anode to cathode). Lithium ion batteries may be subject to swelling during charging and / or discharging. Some aspects of swelling may be reversible, while other aspects of swelling may be irreversible. The battery life may be extended if the irreversible aspect(s) can be(can) minimized.SUMMARYThe invention provides a method for charging an accumulator according to claims 1 and 2 and a corresponding system according to claims 13 and 14, respectively.BRIEF DESCRIPTION OF THE DRAWINGSFIG. 1 is a schematic diagram illustrating a lithium ion secondary battery in a mobile device. FIG. 2A is a perspective view of a pouch cell for a lithium ion battery. FIG. 2B is a perspective view of the pouch cell having swelling. FIG. 3A is a perspective view of a prismatic cell for a lithium ion secondary battery with some layers stripped. FIG. 3B is a schematic end view of the prismatic cell having swelling. FIG. 4 is a perspective view of an accumulator inspection device. FIG. 5 is a plan view of the battery testing apparatus shown in FIG. 4. FIG. 6 is a flow chart illustrating the process of charging the lithium-ion battery to minimize swelling. FIG. 7 is a graph of a plurality of charging profiles illustrating the threshold value versus state of charge. FIG. 8 is a graph of the potential versus time profile of a cell of a lithium-ion battery. Fig. 9 is a graph of a plurality of profiles of potential versus time of the cell of Fig. 8. FIG. 10 is a graph of a plurality of current versus time profiles corresponding to the plurality of potential versus time profiles of FIG. 9. FIG. 11 is a flowchart illustrating a parameterization process of a physics-based charge cycle model. FIG. 12 is a schematic diagram illustrating a laptop computer including an accumulator management system and a lithium ion accumulator. FIG. 13 is a schematic diagram illustrating a vehicle including an accumulator management system and a lithium ion accumulator.DETAILED DESCRIPTIONEmbodiments of the present disclosure will be described herein. It is to be understood, however, that the disclosed embodiments are merely examples and other embodiments may take various and alternative forms. The figures are not necessarily to scale; some features could be exaggerated or minimized to show the details of particular components. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art to variously employ the embodiments. As those skilled in the art will recognize, various features illustrated and described with respect to any one of the figures may be combined with features illustrated in one or more other figures to produce embodiments that are not expressly illustrated or described. The combinations of illustrated features provide representative embodiments for typical applications. However, various combinations and modifications of the features consistent with the teachings of this disclosure could be desired for particular applications or implementations.Lithium ion batteries may swell during charging and discharging (e.g., a case or cell wall may expand outward). This swelling may be reversible or irreversible. Reversible swelling may refer to swelling that subsides, whereas irreversible swelling may refer to swelling that does not subside. Once an accumulator has experienced a predetermined amount of irreversible swelling, it may be at the end of its useful life. Disclosed herein is an accumulator charging method that uses threshold measurements to regulate the charging of the accumulator to minimize permanent degradation of the accumulator. This technique can be used for so-called 'fast charging' - thereby reducing the duration of a charging mode while minimizing the degradation of the accumulator. Further disclosed is a parameterization process of a physics-based charge cycle model based on measurements of the swelling of the accumulator.FIG. 1 illustrates both a mobile device 4 carrying and using a lithium-ion battery 6 to power the electronics therein and a battery management system 8 comprising one or more processors 10 and a memory 12, the memory 12 storing data and instructions executable by the one or more processors 10 and which, when executed, perform one or more of the methods described herein. The mobile device 4 may be a mobile phone or a smart phone, and is only an example of hardware that may use the lithium ion battery 6. Other electronics or electronics environments are contemplated herein.The accumulator management system 8 may be any suitable device that monitors and / or controls the accumulator charge and / or discharge, e.g., to maximize the useful life of the accumulator 6. The processor(s) 10 and / or the memory 12 of the system 8 may be a computer or other computing device. The processor 10 (processors 10) may be programmed to process and / or execute digital instructions to perform at least some of the tasks described herein. Non-limiting examples of the processor(s) 10 include one or more of a microprocessor, microcontroller, or controller, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), one or more electrical circuits comprising discrete digital and / or analog electronic components arranged to perform predetermined tasks or instructions, etc., to name just a few. In at least one example, processor(s) 10 reads from memory 12 and / or executes(s) multiple sets of instructions, which may be embodied as a computer program product stored in a non-transitory computer readable storage medium (such as memory 12). Some non-limiting examples of the instructions are described in the process(s) below and illustrated in the drawings. These and other instructions may be executed in any suitable order unless otherwise specified. The instructions and the example processes described below are merely embodiments and are not intended to be limiting.The memory 12 may include volatile and / or nonvolatile memory devices. Non-transitory storage devices may include any non-transitory, computer-usable or computer-readable medium, any non-transitory, computer-usable or computer-readable storage device, any non-transitory, computer-usable or computer-readable storage article, or the like, including non-transitory (e.g., non-transitory) memory. Non-limiting examples of non-volatile memory devices include read only memory (ROM), erasable programmable read only memory (EPROM), electrically erasable programmable read only memory (EEPROM), optical disks, magnetic disks (such as hard disk drives, floppy disks, magnetic tape, etc.), solid state memory (e.g., metal oxide semiconductor field effect transistors (MOSFETs) with floating gate, flash memory (e.g., NAND flash, solid state drives, etc.), and even some types of random access memory (RAM) (such as ferroelectric RAM). According to one example, non-transitory memory devices may store one or more sets of instructions, which may be embodied as software, firmware, or other suitable programming instructions executable by processor(s) 10, including, but not limited to, the instruction examples set forth herein.Volatile storage devices may include any non-transitory, computer-usable or computer-readable medium, any non-transitory, computer-usable or computer-readable storage device, any non-transitory, computer-usable or computer-readable storage article, or the like, that includes non-transitory memory (e.g., may require power to maintain stored information). Non-limiting examples of volatile memories include universal random access memory (RAM), static RAM (SRAM), dynamic RAM (DRAM), or the like.Thus, the battery management system 8 may be embodied as hardware and software. According to one example, the system 8 may monitor real-time functions in the mobile device 4. In other examples, aspects and functions of the accumulator management system 8 may be embodied in a laboratory test apparatus, as described below.As shown in FIGS. 1 and 2A, the lithium-ion battery 6 (the "battery") may include one or more cells 14, each cell 14 using lithium ions to move charge between an anode electrode 16 and a cathode electrode 18, and including a negative terminal 20 and a positive terminal 22 coupled to the respective electrodes 16, 18, respectively. The accumulator 6 may have any suitable configuration - e.g. such as one or more pouch cells, one or more prismatic cells or one or more cylindrical cells. FIG. 2A illustrates a pouch cell 14 typically comprising a body 26 comprising a perimeter frame 28 from which the ports 20, 22 protrude and two main (opposite) sides 30, 32, wherein the sides 30, 32 may translate outward due to the generation of internal gases (swelling), as shown in FIG. 2B.Another example of a cell is shown in FIG. 3A. An accumulator 6' may for example comprise a prismatic cell 14' comprising a body 26' typically shaped like a relatively flattened box having two main sides 30', 32'. The body 26' may include an anode electrode 16' and a cathode electrode 18' (shown as stripped layers). FIG. 3B schematically illustrates the prismatic cell 14' having swelling.There are also other examples of the cells. For example, a cylindrical cell (not shown) may comprise a body, typically having a tubular structure comprising concentrically arranged cathode and anode electrodes. According to the current state of the art, the bodies of pouch and prismatic cells are more prone to swelling than cylindrical cells; consequently, irreversible swelling in pouch and prismatic cells 14, 14' can be more minimized. Apart from this, the present disclosure may be applied to any suitable cell type including cylindrical cells and / or other cell configurations developed so far that may experience undesirable swelling.FIGS. 4-5 illustrate a test apparatus 40 that can be used to demonstrate evidence of the functional principle to perform at least a portion of the methods described herein, or both. The test apparatus 40 may include a pair of supports 42, 44, one or more supports 46, 48, one or more trays 50, 52, and a plurality of sensors coupled to the processor(s) 10 (four sensors 54, 56, 58, 60 are shown herein). In the arrangement, the posts 42, 44 are upright plates with the beams 46, 48 extending between the posts 42, 44 and holding one or more cells 14 (such as the two pouch cells 14 shown). Here, the beams 46, 48 are coupled to the posts 42, 44 and hang the cells 14 therebetween. The tray 50 may support the sensors 54, 58 and may extend between the supports 42, 44 on one side of the supports 46, 48, whereas the tray 52 may support the sensors 56, 60 and may extend between the supports 42, 44 on an opposite side of the supports 46, 48. Each sensor 54-60 may be identical; therefore, only one is described.The sensor 54 may be any suitable sensor for detecting the movement of the pouch cell 14. Non-limiting examples include a displacement sensor, a pressure sensor, or a non-contact sensor (e.g., a Hall effect sensor, a laser sensor, etc.). In the illustration, each cell 14 has two displacement sensors, each comprising a piston (p54, p56, p58, p60) - the piston p54 of the sensor 54 abutting, for example, the main side 30 (of the cell 14) and the piston of the sensor 56 abutting the main side 32. The plungers p58, p60 may similarly abut the main sides of the other cell 14. In this manner, the sensors 54, 56 (or the sensors 58, 60) may detect the swelling of the pouch cell 14(s). The resolution of the sensors 54- 60 may be as small as 1 μm.The test apparatus 40 may include other components (not shown) for collecting data regarding the current to the pouch cell 14, the voltage of the pouch cell 14, the charging duration, etc. The text device 40 may include, for example, wires (not shown) for connection to the terminals 20, 22, an ammeter (not shown), a voltmeter (not shown), a temperature sensor (attached to the cell 14), and the like. According to one example, the data of the sensors 54- 60 may be received by the battery management system 8 in a laboratory environment. In other embodiments, the mobile device 4 (or other suitable electronic device) may include the sensors 54- 56, a temperature sensor, an ammeter, a voltmeter, etc. Thus, processor(s) 10 and memory 12 may be used to evaluate swelling with respect to other charging parameters.FIG. 6 illustrates an illustrative process 600 for determining a charging profile that optimizes charging speed while also minimizing irreversible swelling. The process 600 may be performed using the battery management system 8 - e.g., the instructions stored in the memory 12 and executed by the processor(s) 10. To illustrate process 600, the features of pouch cell 14 are used; however, it should be appreciated that prismatic cell 14' or any other suitable cell may be used instead. Further, unless expressly stated, the instructions may be executed in any suitable order and / or at least partially concurrently. Before a detailed description of the process 600 is provided, some aspects of the physical and chemical processes are set forth with respect to a lithium ion cell 14.The volume changes of the body 26 of the cell 14 (e.g., swelling or contracting) may occur due to a reaction within the body 26 due to the release of gases and / or heat that may occur during the phase change of an intercalation or deintercalation process. Thus, for example, swelling may refer to an outward extension of the body 26 (or sides 30, 32). Swelling may occur, for example, during charging (e.g., due to parasitic reactions due to overcharging and / or fast charging) or during discharging (e.g., due to deep discharging). Additionally, elevated temperatures, cell damage, or other factors may contribute to swelling. In the cases of pouch and prismatic cells, the major sides 30, 32 may swell outward (e.g., 10-100 μm during a particular charge cycle).For example only, the anode electrode 16 of the pouch cell 14 may include graphite layers. A majority of the expansion may occur at the anode electrode 16 when lithium ions are introduced into the graphite layers. In particular, the irreversible swelling may be due to mechanical stress (due to expansion) and deposition of metallic lithium on the anode electrode 16 (e.g., resulting in a reduced capacity for ion transport). Further, the degree of irreversible swelling may correspondingly increase as the electric current (e.g., in a charging mode) is higher (e.g., so-called quick charging).The process 600 may begin with block 605. In block 605, a counter value (N) may be set to one (1) - e.g., N=1. Each value of N may represent a different load profile.In block 610, which may follow, the processor(s) 10 may determine an Nthload profile during a load mode, where the load profile may be a 'reference load profile'. A charging mode may refer to a higher potential electrically coupled to the terminals 20, 22 of the cell 14 such that the cell 14 may increase its electrical charge level. The charging mode may be performed during a charging cycle, wherein a charging cycle refers to a time interval in which the charging occurs, the cycle ending when the charging is ended and / or the discharging starts. A reference charging profile may refer to a charging profile used to determine a subsequent current profile (e.g., during a next charging cycle). Each load profile may include a dataset including load value data and threshold value data as illustrated by the graphically depicted datasets in FIG. 7 (e.g., a first dataset, a second dataset, a third dataset, etc.).The block 610 may include blocks 615, 620, 625, and 630. Further, block 610 may include executing a clock (e.g., a timer) that may correspond to events during the cycle. Each will again be discussed.According to an embodiment of the block 610, a first Nthload profile of the block 610 may include relatively slow charging during the charging mode. The relatively slow charging mode may relate to, for example, charging in which the current is controlled to be less than or equal to a predetermined threshold THR 1, for example, to satisfy C / 10 CCCV (e.g., 1 coulomb / 10 CCCV (constant charge)). Further, according to one embodiment, the relatively slow charging may include a duration (t REF) of the charging mode that is longer than a duration (t CH MODE) of any subsequent charging cycles. According to this embodiment, the reference charge profile may be compared to each subsequent charge profile to determine an optimal charge profile that minimizes swelling of the cell 14. In at least this embodiment, process 600 occurs in a laboratory environment and using test apparatus 40; however, as explained in other embodiments, this is not necessary.At block 615, a state of charge (SOC) value may be monitored by the processor(s) 10 during block 610. For example, as shown in equation (1), the charge value SOC N(j) may be a ratio of the current charge (Q curr, in coulomb) to a maximum charge (Q max, in coulomb), where Q max may refer to a maximum charge capacity (e.g., when the accumulator is closer to the beginning of its useful life). Thus, the charge value may be expressed as a percentage, e.g., a charge value of 0-10% may refer to a minimum charge (e.g., deep discharge), while a charge value of 100% may refer to a maximum (e.g., full) charge. The charge value (for these and other cycles) may be stored in memory 12.In some embodiments, processor(s) 10 may determine (via a voltmeter measurement and a capacity of cell 14) an incremental series of charge values, e.g., between 1-100%, where each value (j) is a predetermined increment (such as 1%, 2%, 5%, or the like). Thus, in an example where the increment is 1%, the values of j may be 1%, 2%, 3%,... 100% is the total amount of 100% is the total. As will be further explained below, other values of the block 610 (determining an Nthload profile) may be correlated with each increment of the load value. For example, as will be explained below, a threshold value (S N(j)) and a charge current value (I N(j)) may be correlated with the state-of-charge value SOC N(j).In block 620, the processor(s) 10 may monitor the threshold (S N(j)) during block 610, via the data from the sensors, such as sensors 54- 56 (or 58- 60). According to a non-limiting example, the threshold value (S N(j)) may be stored in memory 12 for each increment of the charge value SOC N(j) - processor 10 may (processors 10) store, for example, in memory 12 for each state of charge value SOC N(1), SOC N(2), SOC N(3),..., SOC N(100) threshold values S N(1), S N(2), S N(3),..., S N(100).At block 625, the processor(s) 10 may determine and / or monitor, via an ammeter (not shown), the charging current values (I N(j)) during block 610. According to a non-limiting example, the charging current (I N(j)) for each increment of the state-of-charge value SOC N(j) may be stored in the memory 12 - the processor 10 (the processors 10) may, for example, store the current values I N(1), I N(2), I N(3),..., I N(100) in the memory 12 for each state of the state-of-charge value SOC N(1), SOC N(2), SOC N(3), ..., SOC N(100).During the determination of the Nthload profile, the monitored results of blocks 615, 620, and 625 may be provided repeatedly to block 630, which may follow blocks 615, 620, 625. At block 630, the processor(s) 10 may determine a threshold state-of-charge ratio (S N(j) / SOC N(j)). Where the Nthload profile (e.g., N=1) may be determined for all j. An example load profile for both N=1 (as well as the load profiles for N=2 and N=3 and N=4, as discussed below) is graphically depicted in FIG. 7.After the block 610, the process 600 may proceed to the block 640. At block 640, the processor(s) 10 may determine whether at least two load profiles have been determined (e.g., whether N≥2). If N is not greater than or equal to two (2), then the process 600 may proceed to block 650. Otherwise, the process 600 may proceed to block 660.In block 650, the value of N may be incremented (e.g., by one (1)) -such that N=1+1=2. Further, a value of j may be reset (e.g., to one (1) or another value corresponding to the increment). Thereafter, the process 600 may loop back to block 610 and determine the next Nthload profile (e.g., for N=2).In a loop back to block 610, processor(s) 10 may determine threshold value (S N(j)) charging current (I N(j)) and threshold state of charge ratio (S N(j) / SOC N(j) for N=2; where, as discussed above, FIG. 7 graphically depicts a charging profile for N=2. Continuing with the above example, the charging mode may be a predetermined duration (t CH MODE) that is shorter than the duration (t REF) - e.g., to determine a faster charging cycle to improve user experience. After re-executing block 610, at block 640, process 600 may proceed to block 660 (now, upon repeating block 640, N may be greater than or equal to 2).At block 660, the processor(s) 10 may compare two charging profiles (e.g., a charging profile associated with N=1 (e.g., a first charging profile) and a charging profile associated with N=2 (e.g., a second charging profile)), and identify one or more regions of interest 70 N in the threshold state-of-charge ratios (S N(j) / SOC N(j)) ( of N=1 and N=2) by comparing the reference charging profile (e.g., N=1) to an immediately preceding charging profile (e.g., N=2). For example, processor 10 (processors 10) may identify a range of threshold state-of-charge ratios (S N(j) / SOC N(j) for all j that represents a significant deviation - e.g., since a deation of current in such areas of interest may be directly related to a way to minimize swelling in subsequent charge cycles.FIG. 6 illustrates that block 660 may include blocks 665, 670, and 675. According to an embodiment shown in block 665, the region(s) 70 N of interest may be determined using a standard deviation technique. For example, a standard deviation (σ) for the differences of S 1(j) / SOC 1(j) and S 2(j) / SOC 2(j) may be calculated for all j.Process 600 may proceed from block 665 to block 670 if the standard deviation (σ) is greater than a threshold THR 2 (determining a region of interest 70 N( e.g., for N=2)). Conversely, if the standard deviation (σ) is not greater than the threshold THR, then the process 600 may proceed from block 665 to block 675 (not determining an area of interest 70 N).Block 680 may follow. At block 680, the processor(s) 10 may set the charging current in the region of interest 70 N( for N=2) for a subsequent charging profile (e.g., for N=3-i.e., a charging profile subsequent to the current charging profile). Adjusting the charging current during the region of interest may include decreasing and / or increasing the charging current throughout the charging cycle. For example, the current may be decreased - e.g., in regions of interest 70 N- as process 600 proceeds via block 670; and similarly, e.g., in some examples, the current could be increased as process 600 proceeds via block 675. According to one embodiment, this adjustment of current may be determined according to equation (2), with a control loop being executed by the processor(s) 10 to determine a desired current profile. Equation (2). I k( soc)=F(I k - 1( soc), T, S k - 1( soc); S ref( soc)), where I k(soc) represents the charging current for a next subsequent charging cycle k according to a function F, where T represents the temperature of the cell 14, where S k-1( soc) represents a thickness of the cell 14 (e.g., due to swelling) in the charging cycle being performed, and where S ref( soc) represents a thickness of the cell 14 (e.g., due to swelling) in the reference charging cycle.Accordingly, a degree of swelling can be determined using the two thicknesses [S k-1( soc) and S ref( soc)]. Wherein the current may be controlled with respect to state of charge (SOC).Equation (3) illustrates another embodiment of block 680 that adjusts current in a next subsequent charge cycle. Equation (3) may take account of the aging of cell 14 in various increments of the lifetime of cell 14. For example, as will be explained below, prior to executing process 600, a predetermined number n of different ages of cell 14 may be determined, each of which ages may correspond to a percentage threshold reduction in cell capacity (e.g., THR3=2%, or the like). Equation (3). I k( soc) = F(I k - 1( soc), T, S k - 1( soc); S refM( soc)), wherein I k( soc) represents the charging current for a next subsequent charging cycle k according to a function F, wherein T represents the temperature of the cell 14, wherein S k - 1( soc) represents a thickness of the cell 14 (e.g., due to swelling) in the charging cycle just performed, wherein S refM( soc) represents a thickness of the cell 14 (e.g., due to swelling) in the reference charging cycle, wherein M is a largest m ≤ k, m ∈ {1,..., n}.Equation (4) illustrates a calculation implementing the function F in equation (3), where a proportional gain K T is temperature dependent and also reaches a target charging duration (e.g., duration (t CH MODE)) in cycle k.In block 690, which may follow, the processor(s) 10 may determine to recharge the accumulator 6, e.g., after a discharge cycle. In at least one example, block 690 may record reversible swelling - e.g., processor 10 (processors 10) may determine in this manner whether irreversible swelling has been minimized. Ideally, the irreversible swelling may be zero; however, according to one embodiment, irreversible swelling less than a predetermined threshold (THR4) may be considered optimized. According to one example, irreversible swelling may be minimized if no region of interest 70 N has been determined in block 660. According to one example, block 690 determines whether optimization of the charging mode has occurred. The processor 10 (the processors 10) may determine to loop (via the block 695) back to the block 610 if irreversible swelling is not yet optimized, or alternatively, the processor (the processors) 10 may determine to end the process 600 (e.g., if irreversible swelling is optimized).If the process 600 is not ended - but instead returns in a loop, block 695 may follow. Block 695 may be similar or identical to block 650; therefore, for brevity, this block will not be described again.After the block 695, the block 610 may be repeated, e.g., according to a charge mode having a duration (t CH MODE) ( e.g., N=3). The blocks described above may be repeated - e.g., block 610, followed by blocks 660 and 680, 690 and 695. In repeating block 680, the two load profiles that may be compared may be those associated with N=1 (a first load profile) and N=3 (a third load profile). Upon later returning to a loop, processor 10 (processors 10) may compare N=1 with N=4, N=1 with N=5, etc. Finally, the threshold state-of-charge ratio may be smoothed (e.g., the curve may be smoothed - indicating less irreversible swelling).Before discussing other embodiments of the process 600, FIGS. 8-10 will be described. FIG. 8 illustrates a potential profile (e.g., voltage versus time) for the charge cycle associated with N=1. The duration (t REF) may be, for example, about 550 minutes, during which duration the potential of the cell 14 may increase from about 3.5 V to 4.4 V.FIGS. 9-10 illustrate a potential profile (e.g., voltage versus time) and a current profile (e.g., current versus time), respectively, for N=2, N=3, and N=4, as described below. FIGS. 9-10 illustrate the duration (t CH MODE) as 0 to about 120 minutes when the cell 14 is charged from about 3.7 V to 4.4 V; however, this is merely an example. Further, FIG. 9 illustrates a voltage spike 62 at a time (e.g., ~24 minutes) that may occur as the charging current changes (as shown in FIG. 10 ), where the charging current is changed in response to a deviation in dynamic swelling with respect to a reference protocol or previous charging cycle (e.g., as shown in FIG. 7 ). Equations (2), (3), and / or (4) above may be used to smooth such deviations, resulting in less irreversible swelling.There are also other embodiments of the process. For example, according to a process 600' (also FIG. 6 ), similar blocks may be executed (such as those shown in FIG. 6 ); however, each of the charge cycles may have a common duration (e.g., each have duration t CH MODE ), and a new reference charge cycle may be used each time block 660 is repeated. A common duration may refer to a duration that is within a threshold duration of another (e.g., 3%, 5%, etc.). In process 600', the processor(s) 10 compare each subsequent charge cycle to a charge cycle immediately before, rather than comparing each subsequent charge cycle (N=2, N=3, etc.) to a single reference charge cycle (e.g., N=1) -- where the immediately preceding charge cycle may be the reference charge cycle. For example, a charge cycle (associated with N=2) may be compared to a charge cycle associated with (N=1) at block 660, while a charge cycle associated with (N=3) may be compared to a charge cycle associated with (N=2) at block 660, etc. Accordingly, equations (2), (3), and (4) may be applied similarly as discussed above, except that S ref( soc) or S refM( soc) may refer to the immediately preceding charge cycle (e.g., rather than just N=1).According to at least one additional embodiment, process 600 is first executed (e.g., in a laboratory environment) to determine an appropriate initial charge profile that is programmed into accumulator management system 8. Thereafter, the battery 6 is installed in a device (such as the mobile device 4) and coupled to the battery management system 8 (also in the mobile device 4). Then, the process 600' is used in the mobile device 4-e.g. outside the laboratory environment. In this example, using the initial charge profile (which may be, e.g., the optimized charge profile determined using blocks 605- 695 of blocks 600), subsequent charge profiles are determined - e.g., to extend the useful life of the accumulator 6.According to another embodiment, a process 1100 of parameterization may be performed using the processor(s) 10; an example of which is shown in FIG. 11. Parameterization may refer to identifying one or more parameters for the model equations for the accumulator 6. According to one example, the parameterization may: (a) compare the voltage behavior of an experimental charge cycle to a physics-based charge cycle model (e.g., a computer simulation); and (b) compare the Li plating trends during an experimental charge cycle to swelling measurements (e.g., an indicator of Li plating). Herein, a physics-based charge cycle model may refer to a model having states indicating when Li plating occurs. According to an example, the process 1100 may take place in a laboratory environment - e.g., performing some load cycles, collecting the data therefrom, and then adjusting the parameter(s) of the model.The process 1100 may begin with block 1110-which may include blocks 1120, 1130, 1140, 1150, and 1160. At block 1110, the processor(s) 10 may iteratively and incrementally execute i→N charging cycles, each charging cycle having a different C rate, each of the different C rates being a measure of a rate at which the accumulator is charged with respect to its maximum capacity.Block 1120 indicates that the state of charge (SOC) of the cell 14 of the accumulator 6 is 0%. In block 1130, cell 14 is loaded at a unique C rate. At block 1140, the processor(s) 10 may store in memory 12 (during charging) the cycle parameter data used to parameterize the model, such as voltage data, time data, swelling data, etc.; further, the processor(s) 10 may store electrochemical accumulator parameters, such as anode material diffusion coefficient, cathode material diffusion coefficient, reaction rate constant, accumulator material sheet resistances, etc. The block 1150 may include discharging the accumulator 6. Wherein, in block 1160 that may follow, the processor(s) 10 may determine(s) whether an index i is equal to N iterations of charging and discharging. If it is not, the process 1100 loops back and repeats the block 1110. If i=N, the process 1100 proceeds to block 1170. In block 1170, the processor(s) 10 may determine a cost function that accounts for (e.g., corresponds to) a binary indication of the thresholds. And at block 1180, the processor(s) 10 may use the collected 1110 data (e.g., including the cycle parameter data) to optimize the cost function for the battery model parameters (e.g., for the electrochemical battery parameters). A mathematical embodiment of a physics-based model (and process 1100) is described below.Equation (5) illustrates a cost function calculation that takes into account both the physics-based model and the experimental data.In Equation (Sentence) (5), J i is a cost function, x and z denote differential and algebraic states of the model, f (e.g., a differential equation), g (e.g., an algebraic equation), h (e.g., an output equation) are respectively vectors relating to functions constituting an electrochemical structure of an electrochemical accumulator model p, i relates to the number of the experiment, where N relates to a total number of the experiments - each having different C rates according to a CCCV protocol, x i relates to an initial condition of an i-th experimental charge cycle, p* relates to a result of optimization of the model, wherein a set P may define an upper limit and a lower limit for the parameter variation. The functions f, g, h may be derived using model order reduction techniques from the Li ion physical-based accumulator model, which consists of coupled partial differential equations with algebraic constraints; a non-limiting example of such a physical-based model may be found in U.S. Application Serial No. 12 / 396,918 (US 2010 0 225 325 A1), which is incorporated herein by reference in its entirety.The aim of equation set (5) is to find the best set of parameters of the electrochemical accumulator model p, so that the difference between the prediction of the accumulator model and the experimental measurement is minimized. The costs to be minimized are detected by the function J i. The total cost is the sum of the individual costs of each experiment. The cost function may represent the deviation between the model prediction and the measurement. For example, the deviation of the measured versus the predicted voltage or the deviation of the measured versus the predicted temperature. By optimizing via the set of parameters, it is possible to minimize the deviation error between the model signals and the measurement signals. The constraints of the optimization problem are such that the output of the accumulator model y model is generated by a set of mathematical equations defining the accumulator operations and for any initial condition x i(0). The equations of the accumulator model are then represented by the differential or algebraic equations having the functions f, g.The parameters of the electrochemical accumulator model that are adjusted and are part of the parameter vector p may include the following: a diffusion coefficient, a sheet resistance, an activation energy for diffusion and / or kinetics, a reaction rate constant (e.g., corresponding to the anode material and / or a cathode material), a volume fraction of the active material (e.g., in an anode electrolyte and / or a cathode electrolyte), the Bruggeman coefficients (e.g., for an anode separator and / or a cathode separator), the transport properties of the electrolyte (such as the diffusion coefficients and / or the transfer numbers), a contact resistance, and the model thermal properties (such as the heat capacity, the heat transfer coefficients, etc.). Some functional forms relating to the constants of the ionic conductivity of the electrolyte and the electrical conductivity in the anode and / or the cathode may typically be set during the parameterization process. The above-listed accumulator parameters then influence the electrical behavior (such as the voltage behavior) and the temperature behavior of the accumulator model.One non-limiting set of C rates that may be used includes 1C-4C.When executed by the processor(s) 10, an output (y model) of the physics-based model may be defined by equation (6), while an output (y exp) of the experiment may be defined by equation (7). For the sake of simplicity, the number i of the experiment is hidden in the following equations. The relevant equations below may nevertheless be incremented N times. Equation (6). y model= [ V model, T model], wherein V model is a voltage function of the model during a charging cycle, wherein T model is a temperature function of the model during the charging cycle. Equation (7). y exp= [ V exp, T exp], wherein V exp is a voltage function of the experiment during a charge cycle, wherein T exp is a temperature function of the experiment during the charge cycle.A structure of the cost function (J) is illustrated by equation (8). Equation (8) wherein w 1 and w 2 are predetermined weights.A trend during incremental charging may include a change in the crystal structure of the Li plating. To take such a factor into account, equation (8) may be modified according to equation (9). Equation (9). J = w 1| V model- V exp|2+ w 2| T model- T exp|2+ w 3| μ(x, z) - α exp|, wherein w 1, w 2 and w3 are predefined weights, wherein αexp=1 for the respective experimental charging cycle when swelling is observed, wherein αexp=0 when swelling is not observed, wherein a function μ(x, z) has a binary output (0 or 1) depending on a state of the model. For example, the weights w 1, w 2, w 3 may be chosen to normalize the various error functions in the cost function. w 3= 1 would normalize the plating error prediction, where w 1, w 2 may be based on the target RMS error for the voltage and temperature dynamics.With regard to μ(x,z), if z is k< 0 at any time during charging, (x,z) = 1, where z k refers to a kthelement of the model / vector z; otherwise, μ(x,z) = 0.A number of the electrochemical model parameters may be improved by minimizing a voltage error between the model and the experiment, while also monitoring trends in internal states (such as anode overvoltage), Li plating observed from the swelling experiments, and the like. Minimizing voltage fault and / or avoiding anode overvoltage may be an advantage in the areas of fast charging and power prediction. Model-based fast charging strategies typically rely on controlling anode overvoltage during charging above a 0 mV limit. Thus, a better estimate of anode overvoltage from improved model parameterization may result in fast charging protocols that achieve a target charging time while minimizing battery aging. Similarly, to estimate how much power may be recovered during braking events and used to charge the battery, an estimate of the anode overvoltage is required to prevent triggering harmful side reactions such as Li plating.Using the model set forth in equations (5)-(7) and (9), the processor(s) 10 may partially validate an internal state of the model by detecting features indicative of undesired side reactions (e.g., irreversible swelling due to Li plating). By identifying irreversible swelling in a model, loading profiles that minimize irreversible plating can be determined in a computer-aided laboratory environment. It should also be appreciated that developing and using the battery management system 8 using the above-mentioned model may better estimate the state of charge (SOC) and the state of function (SOH).In at least one embodiment, model is developed in a laboratory environment and then later programmed into processor(s) 10 (of battery management system 8) to regulate charging during useful life of cell.Thus, techniques for charging Li-ion batteries while minimizing irreversible swelling have been described. Further, a parameterization model has been described that promotes the determination of charging profiles that minimize irreversible swelling.The processes, methods, or algorithms disclosed herein may be available to / implemented by a processing device, controller, or computer, which may include any existing programmable electronic control unit or dedicated electronic control unit. Similarly, the processes, methods, or algorithms can be stored as data and instructions executable by a controller or computer in many forms including, but not limited to, information permanently stored in non-writable storage media such as ROM devices and information alterably stored in writeable storage media such as floppy disks, magnetic tapes, CDs, RAM devices, and other magnetic and optical media. The processes, methods, or algorithms can also be implemented in an executable software object. Alternatively, the processes, methods, or algorithms can be embodied in whole or in part using suitable hardware components, such as application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), state machines, controllers or other hardware components or devices, or a combination of hardware, software, and firmware components.While exemplary embodiments have been described above, it is not intended that these embodiments describe all possible forms encompassed by the claims. The words used in the specification are words of description rather than limitation, and it is recognized that various changes may be made without departing from the spirit and scope of the disclosure. As previously described, the features of various embodiments may be combined to form further embodiments of the invention that may not be explicitly described or illustrated. While various embodiments could have been described as providing advantages or being preferred over other embodiments or prior art implementations with respect to one or more desired characteristics, those skilled in the art recognize that one or more features or characteristics can be compromised to achieve desired overall system characteristics, which depend on the specific application and implementation. These features may include cost, strength, durability, life cycle cost, marketability, appearance, packaging, size, serviceability, weight, machability, ease of assembly, etc. As such, insofar as embodiments have been described as less desirable than other embodiments or prior art implementations with respect to one or more characteristics, these embodiments are not outside the scope of the disclosure and may be desirable for particular applications.

Claims

A method of charging an accumulator, comprising: iteratively determining a plurality of charging profiles of the accumulator; based on the plurality of charging profiles, iteratively determining swelling of the accumulator; and adjusting a charging current during subsequent charging of the accumulator; wherein iteratively determining a plurality of charging profiles comprises: determining a first charging profile of the accumulator; and after discharging the accumulator, determining a second charging profile of the accumulator, the method further comprising: determining a first range of interest by comparing the first and second charging profiles; and adjusting a charging current in the first range of interest during subsequent charging of the accumulator, wherein each of the first and second charging profiles defines a relationship between a state of charge and swelling of the accumulator; wherein the first charging profile is defined by a first data set comprising charging value data and swelling value data, the subsequent charging profile being defined by a second data set comprising charging value data and swelling value data; characterized in that the first region of interest is determined by comparing the swelling value data of the first and second data sets with the charging value data of the first data set corresponding to the charging value data of the second data set.A method of charging an accumulator, comprising: iteratively determining a plurality of charging profiles of the accumulator; based on the plurality of charging profiles, iteratively determining swelling of the accumulator; and adjusting a charging current during subsequent charging of the accumulator; wherein iteratively determining a plurality of charging profiles comprises: determining a first charging profile of the accumulator; and after discharging the accumulator, determining a second charging profile of the accumulator, the method further comprising: determining a first range of interest by comparing the first and second charging profiles; and adjusting a charging current in the first range of interest during subsequent charging of the accumulator, wherein each of the first and second charging profiles defines a relationship between a state of charge and swelling of the accumulator; wherein the first charging profile is defined by a first data set comprising charging value data and swelling value data, wherein the subsequent charging profile is defined by a second data set comprising charging value data and swelling value data; characterized in that the first region of interest is determined based on data of the swelling value of the first data set differing more than a threshold from the data of the swelling value of the second data set for corresponding charging value data of the first and second sets.The method of claim 1 or 2, wherein the adjusting further comprises calculating a decrease in charging current for the subsequent charging of the accumulator within the first range of interest; and providing a decreased charging current based on the calculated decrease.The method of claim 1 or 2, wherein the first charging profile is a predetermined slow charging profile, wherein the second charging profile is a predetermined faster charging profile.The method of claim 4, wherein the faster charging profile is 4-5 times faster than the slow charging profile.The method of claim 1 or 2, wherein a duration of the first and second loading profiles have a common duration with respect to each other.The method of claim 1 or 2, further comprising: determining a third charging profile of the accumulator using the adjusted charging current; determining a second region of interest by comparing the first and third charging profiles; and adjusting a charging current in the second region of interest during charging of the accumulator after the third charging profile.The method of claim 7, further comprising: iteratively determining additional charging profiles of the accumulator; iteratively and correspondingly determining additional regions of interest; setting a charging current in the additional regions of interest during the respective subsequent charging; and if the additional regions of interest are less than a threshold, then storing a final charging profile.The method of claim 1 or 2, further comprising: determining, using the adjusted charging current, a third charging profile of the accumulator; determining a second region of interest by comparing the second and third charging profiles; and adjusting a charging current in the second region of interest during charging of the accumulator after the third charging profile.The method of claim 9, further comprising: iteratively determining additional charging profiles of the accumulator; iteratively and correspondingly determining additional regions of interest; setting a charging current in the additional regions of interest during the respective subsequent charging; and if the additional regions of interest are less than a threshold, then storing a final charging profile.The method of claim 1 or 2, wherein the accumulator comprises a pouch cell or a prismatic cell.The method of claim 1 or 2, wherein the accumulator is a lithium ion accumulator.A system comprising: one or more processors; and a memory coupled to the one or more processors and storing a plurality of instructions executable by the one or more processors, wherein the method of any one of claims 1 to 12 is executable by the plurality of instructions.A system comprising: one or more processors; and a memory coupled to the one or more processors and storing a plurality of instructions executable by the one or more processors to determine an electrochemical accumulator model, the plurality of instructions comprising: iteratively executing a charge and discharge cycle of an accumulator; for each charge and discharge cycle: charging at a unique C rate; and storing cycle parameter data; and optimizing a cost function for electrochemical accumulator parameters using the cycle parameter data, wherein the cost function accounts for swelling of the accumulator.

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