A method to approximate the fast charging algorithm for lithium-ion batteries based on electrochemical battery model

Abstract

A method for approximating a fast charging algorithm for a lithium-ion battery based on an electrochemical battery model is provided. A method, system, and non-transitory computer-readable medium for determining a pseudo-optimal charging algorithm for a specific battery are disclosed. The electrochemical battery model is characterized based on the physical characteristics of the specific battery. An optimal charging curve for the specific battery is determined using a highly accurate electrochemical battery model. A pseudo-optimal charging curve that closely approximates the optimal charging curve is determined. However, the pseudo-optimal charging curve is composed of simple building blocks that are easily and efficiently implemented in embedded applications with limited computing power / memory. An optimization process is used to determine optimal control parameters, trigger conditions and thresholds for the simple building blocks, and adaptation parameters for adapting the pseudo-optimal charging curve as the battery ages.

Description

Technical Field

[0001] The devices and methods disclosed in this document relate to battery charging, and more particularly, to methods for charging lithium-ion (Li-ion) batteries. Background Art

[0002] Unless otherwise indicated herein, the materials described in this section are not prior art to the claims in this application and are not admitted to be prior art by inclusion in this section.

[0003] A battery is an electrochemical energy storage device that converts chemical energy into electrical energy and vice versa. One specific type of battery is the Li-ion battery. Lithium-ion batteries are desirable energy storage devices for portable electronic devices, electric and hybrid electric vehicles, among other devices and systems, because of their high specific energy compared to other electrochemical energy storage devices.

[0004] A key requirement for widespread adoption of battery technology is to provide fast charging times without accelerating the degradation of available capacity. State-of-the-art charging systems typically employ some variation of the constant current constant voltage (CCCV) charging process. In the CCCV charging process, a constant current is applied to the battery until a certain voltage is reached. After reaching a specific voltage, the constant voltage is maintained until the charging current drops below a specified threshold, at which point the battery is considered fully charged. This charging process is robust and simple to implement, however it also suffers from relatively long charging times. More sophisticated charging strategies can provide faster charging times, but typically require complex real-time calculations, making such strategies impractical for embedded applications with limited memory and processing power. Summary of the invention

[0005] A method for approximating an optimal charging curve for a specific battery is disclosed. The method includes: storing an electrochemical battery model in a memory, the electrochemical battery model being parameterized based on physical characteristics of the specific battery; determining, using a processor, a first charging curve using the electrochemical battery model, the first charging curve minimizing the charging time of the specific battery and minimizing the degradation of the specific battery; and determining, using the processor, a first set of parameters defining a second charging curve, the second charging curve being formed by an ordered sequence of charging stages that approximate the first charging curve, each charging stage in the ordered sequence being characterized by: (i) a corresponding first parameter in the first set of parameters indicating a corresponding control strategy to be used to control the charging current during the corresponding charging stage, (ii) a corresponding second parameter in the first set of parameters indicating a control parameter value of the corresponding control strategy, (iii) a corresponding third parameter in the first set of parameters indicating a corresponding trigger condition that, when satisfied, triggers the end of the corresponding charging stage, and (iv) a corresponding fourth parameter in the first set of parameters indicating a threshold parameter value of the corresponding trigger condition.

[0006] A system for approximating an optimal charging curve for a specific battery is disclosed. The system includes: a data storage device configured as a plurality of instructions, the plurality of instructions including instructions corresponding to an electrochemical battery model, the electrochemical battery model being parameterized based on physical characteristics of the specific battery; and at least one processor operably connected to the data storage device. The at least one processor is configured to execute the plurality of instructions on the data storage device to: determine a first charging curve using the electrochemical battery model, the first charging curve minimizing the charging time of the specific battery and minimizing the degradation of the specific battery; and determine a first set of parameters defining a second charging curve, the second charging curve being formed by an ordered sequence of charging stages that approximate the first charging curve, each charging stage in the ordered sequence being characterized by: (i) a corresponding first parameter in the first set of parameters indicating a corresponding control strategy to be used to control the charging current during the corresponding charging stage, (ii) a corresponding second parameter in the first set of parameters indicating a control parameter value of the corresponding control strategy, (iii) a corresponding third parameter in the first set of parameters indicating a corresponding trigger condition, the corresponding trigger condition triggering the end of the corresponding charging stage when satisfied, and (iv) a corresponding fourth parameter in the first set of parameters indicating a threshold parameter value of the corresponding trigger condition.

[0007] A non-transitory computer-readable medium for approximating an optimal charging curve for a specific battery is disclosed. The computer-readable medium stores a plurality of instructions configured to cause at least one processor, when executed, to: store an electrochemical battery model in a memory, the electrochemical battery model being parameterized based on physical characteristics of the specific battery; determine a first charging curve using the electrochemical battery model, the first charging curve minimizing the charging time of the specific battery and minimizing the degradation of the specific battery; and determine a first set of parameters defining a second charging curve, the second charging curve being formed by an ordered sequence of charging stages that approximate the first charging curve, each charging stage in the ordered sequence being characterized by: (i) a corresponding first parameter in the first set of parameters indicating a corresponding control strategy to be used to control the charging current during the corresponding charging stage, (ii) a corresponding second parameter in the first set of parameters indicating a control parameter value of the corresponding control strategy, (iii) a corresponding third parameter in the first set of parameters indicating a corresponding trigger condition that, when satisfied, triggers the end of the corresponding charging stage, and (iv) a corresponding fourth parameter in the first set of parameters indicating a threshold parameter value of the corresponding trigger condition. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] The foregoing aspects and other features of a method of approximating an optimal charging curve for a particular battery are explained in the following description read in conjunction with the accompanying drawings.

[0009] Figure 1 A block diagram of an exemplary embodiment of a computing system for determining a pseudo-optimal charging algorithm for a particular battery is shown.

[0010] Figure 2 A logic flow diagram of a method for determining a pseudo-optimal charging algorithm for a particular battery is shown.

[0011] Figure 3 Plots illustrating optimal charging curves for an exemplary lithium-ion battery at the beginning and end of life are shown.

[0012] Figure 4 Plots illustrating pseudo-optimal charging curves for an exemplary lithium-ion battery at the beginning and end of life are shown.

[0013] Figure 5 Experimental results comparing the performance of an OEM-recommended charging regimen with the performance of a pseudo-optimal charging curve for an exemplary lithium-ion battery are shown.

[0014] Figure 6 A battery charging system utilizing a pseudo-optimal charging curve is shown.

[0015] Figure 7 A logic flow diagram of a method for operating a battery charging system to utilize a pseudo-optimal charging curve is shown. DETAILED DESCRIPTION

[0016] For the purpose of promoting an understanding of the principles of the present disclosure, reference will now be made to the embodiments illustrated in the accompanying drawings and described in the following written specification. It should be understood that no limitation of the scope of the present disclosure is thereby intended. It should also be understood that the present disclosure includes any changes and modifications to the illustrated embodiments, and includes additional applications of the principles of the present disclosure as would normally occur to a person skilled in the art to which the present disclosure pertains.

[0017] A battery management system (BMS) based on an electrochemical cell model provides a path to the most efficient use of Li-ion batteries by utilizing model equations that reflect the physical behavior of the battery's interior. In particular, the equations of the electrochemical cell model, etc., can be designed to accurately capture all relevant mechanisms that lead to aging or other undesirable processes, such as (but not limited to) lithium plating, battery swelling, solid-electrolyte interface (SEI) layer growth, or gas generation due to electrolyte decomposition. Therefore, the electrochemical cell model can be used to accurately identify the boundary conditions for efficient use of the battery, and can therefore be used to improve charging speed while minimizing aging and other undesirable processes.

[0018] However, utilizing electrochemical battery models in a BMS faces certain challenges. First, the performance of the BMS in terms of accurate state of charge estimation, power prediction, and online strategies for fast charging is directly related to the quality of the model parameters in the initial model and the adaptation of the model parameters as the battery ages. However, validating the results of algorithms that estimate electrochemical battery model parameters is a time-consuming process that requires specific experimental techniques. Second, algorithms for state and parameter estimation based on electrochemical battery models are computationally intensive for real-time implementation because such models will likely involve coupled nonlinear partial differential equations (PDEs) that are numerically solved through model reduction techniques with algebraic constraints. Finally, in order to fully appreciate the benefits of using a BMS based on an electrochemical battery model for fast charging strategies, it is imperative to adapt the model parameters as the battery ages.

[0019] The development, implementation, and validation of such algorithms are typically challenging and remain unsolved for online deployment in products. Disclosed herein is a method and system that maintains the same benefits of electrochemical battery models for fast charging applications while utilizing simpler and more easily implemented building blocks for charge profile generation, as well as adaptation rules that ensure safe and efficient operation of the battery during charging. As discussed in more detail below, a complex electrochemical battery model is used offline to determine the optimal charge profile for a specific battery, and the optimal charge profile is systematically and closely approximated by using functional building blocks that can be easily implemented in embedded applications with limited memory and processing power.

[0020] System for synthesizing pseudo-optimal charging curves

[0021] Figure 1 A block diagram of an exemplary embodiment of a computing system 10 for determining a pseudo optimal charging curve for a particular battery is shown. The computing system 10 is typically provided in a housing, cabinet, or the like 12 configured in a typical manner for computing devices. In the illustrated embodiment, the computing system 10 includes a processor 14, a memory 16, a display 18, a user interface 20, and a network communication module 22. However, it will be appreciated that the illustrated embodiment of the computing system 10 is only one exemplary embodiment of the computing system 10 and is merely representative of any of the various ways or configurations of a personal computer, laptop, server, or any other data processing system operating in the manner described herein.

[0022] The processor 14 is configured to execute instructions to operate the computing system 10 to implement features, functionality, characteristics, etc. as described herein. To this end, the processor 14 is operably connected to the memory 16, the display 18, the user interface 20, and the network communication module 22. The processor 14 generally includes one or more processors, which can operate in parallel or otherwise in coordination with each other. It will be appreciated by those of ordinary skill in the art that a "processor" includes any hardware system, hardware mechanism, or hardware component that processes data, signals, or other information. Therefore, the processor 14 may include a system having a central processing unit, a plurality of processing units, or a dedicated circuit for implementing a particular functionality.

[0023] The memory 16 may have any device type capable of storing information accessible by the processor 14, such as a memory card, ROM, RAM, writable memory, read-only memory, hard drive, disk, flash memory, or any of a variety of other computer-readable media that function as data storage devices as will be recognized by those of ordinary skill in the art. The memory 16 is configured to store program instructions 24 for execution by the processor 14, and data 26. The program instructions 24 include at least a charge curve synthesis program 28. The charge curve synthesis program 28 includes at least some instructions corresponding to at least one electrochemical battery model 30. In at least one embodiment, the data 26 includes battery characterization data 32 corresponding to at least one specific battery. The charge curve synthesis program 28 is configured to enable the computing system 10 to determine the optimal charge curve of at least one specific battery using at least one electrochemical battery model 30 and the battery characterization data 32 of at least one specific battery. The charge curve synthesis program 28 is configured to further enable the computing system 10 to synthesize a pseudo-optimal charge curve consisting of a sequence of functional building blocks that closely approximate the optimal charge curve.

[0024] The network communication module 22 of the computing system 10 provides an interface that allows communication with any of a variety of devices using a variety of means, and may include one or more modems, transceivers, network adapters, etc. In particular, the network communication module 22 may include a local area network port that allows communication with any of a variety of local computers housed in the same or nearby facilities. In some embodiments, the network communication module 22 also includes a wide area network port that allows communication with a remote computer via the Internet. Alternatively, the computing system 10 communicates with the Internet via an independent modem and / or router of a local area network. In one embodiment, the network communication module is equipped with a Wi-Fi transceiver or other wireless communication device. Therefore, it will be appreciated that communication with the computing system 10 may occur via wired communication or via wireless communication. Communication may be accomplished using any of a variety of known communication protocols.

[0025] The computing system 10 can be operated locally or remotely by a user. To facilitate local operation, the computing system 10 may include a display 18 and a user interface 20. Via the user interface 20, the user can access instructions including the charging curve synthesis program 28, and can collect data from the memory 16 and store data to the memory 16. In at least one embodiment, the display 18 may include an LCD display screen, etc. In at least one embodiment, the user interface 20 may appropriately include a mouse or other pointing device, a keyboard or other keypad, a speaker, and a microphone, as will be recognized by a person of ordinary skill in the art. It will be appreciated that the display 18 and the user interface 20 may be integrated on or within the housing 12, or may be an external device operably connected via a connector (not shown) disposed on the housing 12. Alternatively, in some embodiments, the user can remotely operate the computing system 10 from another computing device, which communicates with the computing system 10 via a network communication module 22 and has a similar display and user interface.

[0026] Charging curve synthesis program

[0027] A method for operating the computing system 10 is described below. In particular, a method for operating the processor 14 to determine a pseudo-optimal charging algorithm for a particular battery is described. In the description of the method, the statement that the method is performing a task or function refers to a general-purpose processor, etc. (e.g., processor 14) executing programming instructions (e.g., charging curve synthesis program 28 and / or electrochemical battery model 30) stored in a non-transitory computer-readable storage medium (e.g., memory 16), which is operatively connected to a controller or processor to manipulate data or operate one or more components in the computing system 10 to perform the task or function. It will be appreciated that some or all of the operations in the method can also be performed by a remote server or cloud processing infrastructure. In addition, the steps of the method can be performed in any feasible time order, regardless of the order shown in the figure or the order in which the steps are described.

[0028] Figure 2 A logic flow diagram of a method 100 for determining a pseudo-optimal charging algorithm for a particular battery is shown. The method 100 improves the operation of the computing system 10, and more specifically the operation of the processor 14 of the computing system 10, by advantageously enabling the processor 14 to determine an optimal charging curve for a particular battery and systematically derive a pseudo-optimal charging curve comprised of a sequence of functional building blocks that closely approximates the optimal charging curve and is adapted over time as the battery ages. As will be discussed in more detail below, once the pseudo-optimal charging curve is derived, it can be used to improve the operation of a charging circuit or battery management system of a device employing a particular battery by achieving faster charging and / or minimizing degradation and other undesirable processes.

[0029] Method 100 begins with the following steps: characterizing a specific battery for which a pseudo-optimal charging curve is to be determined (block 110), and once the battery has been characterized, parameterizing an electrochemical battery model based on the characterization of the specific battery (block 130). In particular, with respect to the detailed embodiments described herein, computing system 10 is configured to receive, measure, or otherwise acquire characteristic data about a specific battery. In at least one embodiment, the specific battery is a specific lithium-ion battery. Processor 14 is configured to store characteristic data about the specific battery (referred to herein as battery characterization data 32) in memory 16.

[0030] Electrical and electrochemical tests are performed on a particular battery to parameterize the physically based electrochemical battery model 30. In some embodiments, one such electrical test includes a series of slow charge and discharge steps to characterize the capacity of a particular battery, as well as other parameters associated with steady-state battery behavior. In other embodiments, additional electrical tests involving different charge, discharge rates, current pulses of varying duration and amplitude at different temperatures are used to obtain data to fit the dynamic and kinetic parameters of the electrochemical battery model 30.

[0031] Characteristic data 32 derived from electrical testing may include information such as current-voltage-temperature curves, open circuit voltage-state of charge measurements, energy capacity measurements, impedance measurements, and expansion measurements. Characteristic data 32 may include the value of such a parameter as a function of another parameter (e.g., as a function of battery voltage, battery current, state of charge, or time). In some embodiments, additional characteristic data 32 may be manufacturer specification information defined by the manufacturer and published in documentation for a particular battery, such as steady-state and dynamic current limits, steady-state and dynamic voltage limits, safe operating temperature range, nominal voltage, nominal capacity, and geometric and material properties.

[0032] In some embodiments, the processor 14 is configured to receive some or all of the characteristic data 32 about a specific battery via a data port that is operably connected to a measurement tool, sensor, etc. that is operated to measure some or all of the characteristic data 32 about a specific battery. In some embodiments, the processor 14 is configured to read some of the characteristic data 32 from a data file stored on the memory 16. In some embodiments, the processor 14 is configured to receive some or all of the characteristic data 32 about a specific battery from another computing device via the network communication module 22. In some embodiments, the processor 14 is configured to receive some of the characteristic data 32 about a specific battery as input manually entered by a user via the user interface 20.

[0033] The processor 14 is configured to determine values ​​of undefined parameters of the electrochemical cell model 30 based on the characteristic data 32. In particular, the electrochemical cell model 30 includes one or more equations that model multiple physical quantities and phenomena about the battery, such as battery voltage, battery current, battery temperature, battery state of charge, lithium ion flux, concentrations of solid phases and electrolytes, and potentials in solid phases and electrolytes. The equations of the electrochemical cell model 30 are designed to capture the main electrochemical reactions that characterize the operation of the battery, as well as all relevant mechanisms that lead to aging or other undesirable processes, such as (but not limited to) lithium plating, battery swelling, solid-electrolyte interface (SEI) layer growth, or gas generation due to electrolyte decomposition. The equations of the electrochemical cell model 30 include one or more undefined / unknown parameters that vary depending on the specific battery to be modeled. In at least one embodiment, the processor 14 is configured to determine the undefined parameters of the electrochemical cell model 30 by an optimization routine that attempts to minimize the difference between experimental battery measurements (e.g., voltage, current, temperature, etc.) and corresponding model-based predictions.

[0034] Once the electrochemical cell model has been parameterized for a particular battery, the method 100 continues with the following steps: determining an optimal charging curve for the particular battery based on the parameterized electrochemical cell model (block 150). In particular, with respect to the detailed embodiments described herein, the processor 14 is configured to use the electrochemical cell model 30 to determine an optimal charging curve that minimizes the charging time of the particular battery and minimizes degradation / aging of the particular battery. As used herein, the term "charging curve" is a data plot, a plurality of parameters, values ​​or data points, one or more functions or equations, etc., which defines the battery current, battery voltage, and / or battery state of charge of the battery over time and / or as a function of time during at least a portion of the charging process in which current flows into the battery. The processor 14 is configured to calculate an optimal charging curve for a particular battery that minimizes the charging time under the constraints of the current limit and voltage limit specified by the battery manufacturer by maximizing the input charging current to the battery, and at the same time minimizes side reactions that may potentially cause lithium plating or otherwise age the battery faster. In one embodiment, the relative importance / priority of minimizing charging time and minimizing degradation / aging can be weighted based on user input. In some embodiments, the processor 14 is further configured to use the optimal electrochemical curve at the beginning of life (BoL) in a closed-loop environment to calculate a plurality of additional optimal charging curves as the battery ages until the battery reaches its end of life (EoL). In particular, the processor 14 is configured to calculate a set of N optimal charging curves, where each optimal charging curve corresponds to a different degradation / aging level of a particular battery. Figure 3A plot 152 is shown illustrating optimal charging curves 154 and 156 for an exemplary lithium-ion battery. Charging curve 154 (shown as a solid line) represents the optimal charging curve for an exemplary lithium-ion battery at the beginning of life. Charging curve 156 (shown as a dashed line) represents the optimal charging curve for an exemplary lithium-ion battery at the end of life.

[0035] Back to Figure 2 Once the optimal charging curve has been determined, the method 100 continues with the following step: determining a pseudo-optimal charging curve that includes a sequence of functional building blocks that closely approximate the optimal charging curve (box 170). In particular, as previously mentioned, the optimal charging curve derived from the electrochemical battery model 30 can be approximated using simple building blocks. The processor 14 is configured to determine at least one pseudo-optimal charging curve, which is formed by an ordered sequence of charging curve building blocks that closely approximate (multiple) optimal charging curves. More specifically, the processor 14 is configured to determine a set of parameters that define and / or characterize the ordered sequence of charging curve building blocks that form the pseudo-optimal charging curve. In at least some embodiments, the adaptation rules are used to provide multiple different pseudo-optimal charging curves as the battery ages.

[0036] As used herein, a "charge profile building block" (which may also be referred to herein as a "charge phase", "functional building block", "functional block", "simple building block" and / or "building block") refers to a segment or portion of a charge profile that is characterized by: (i) a specific control strategy for regulating the charging current applied to the battery, and (ii) a specific trigger condition for ending the specific segment or portion of the charge profile and transitioning to the next charge profile building block or, in the case of the last charge profile building block in the sequence, ending the charging process. The specific control strategy of the charge profile building block is executed with respect to at least one control parameter having a defined target value. Likewise, the specific trigger condition of the charge profile building block (which may also be referred to herein as a switching criterion) is evaluated with respect to at least one threshold parameter having a defined threshold. In at least some embodiments, the control parameters and threshold parameters of each charge profile building block are adapted as a function of the battery state of health or some other battery parameter indicative of the state of health, such that the control parameters and threshold parameters are adapted over time. An optimal charge profile can be closely approximated by such a sequence of charge profile building blocks, which is referred to herein as a "pseudo-optimal charge profile".

[0037] In at least one embodiment, each charging curve building block of the pseudo optimal charging curve is characterized by at least four different parameters. The first parameter (also referred to herein as a "control strategy") indicates the corresponding control strategy to be used to control the charging current during the corresponding building block. Exemplary control strategies include (but are not limited to) constant current (CC), constant current ramp (CdI), constant voltage (CV) and constant voltage ramp (CdV). The second parameter (also referred to herein as a "control parameter") indicates the control parameter value of the corresponding control strategy, such as the target current amplitude, the target current change rate, the target voltage amplitude and the target voltage change rate. The third parameter (also referred to herein as a "trigger condition") indicates the corresponding type of trigger condition, which will cause the corresponding building block to end when it is met. Exemplary trigger conditions include (but are not limited to) current-based trigger conditions, voltage-based trigger conditions, charge state-based trigger conditions, temperature-based trigger conditions and duration-based trigger conditions. Finally, the fourth parameter (also referred to herein as a "threshold parameter") indicates the threshold parameter value of the corresponding trigger condition, such as a current threshold parameter, a voltage threshold parameter, a charge state threshold parameter, a temperature threshold parameter and a duration threshold parameter. Exemplary combinations of these control strategies and trigger conditions used in the charging profile building block are summarized in Table 1 below.

[0038]

[0039] In the function block using the constant current control strategy, the battery charging current is maintained at a value controlled by the current amplitude control parameter CC. Mag The battery charging current is controlled by the current slope control parameter CdI. Mag The defined constant slope increases or decreases monotonically until the corresponding trigger condition is met. In the function block using the constant voltage control strategy, the battery charging current is adjusted to keep the battery voltage at a value controlled by the voltage amplitude control parameter CV. Mag In the function block using the constant voltage ramp control strategy, the battery charging current is adjusted so that the battery voltage is controlled by the voltage slope control parameter CdV Mag The defined constant slope increases or decreases monotonically until the corresponding trigger condition is met.

[0040] In the function block using the voltage trigger condition, the control strategy of the corresponding function block responds to the battery voltage exceeding the voltage threshold parameter V 触发 In the function block using the current trigger condition, the control strategy of the corresponding function block responds to the battery current falling to the value defined by the current threshold parameter I 触发In a function block using a state of charge (SOC) trigger condition, the control strategy of the corresponding function block responds to the state of charge (SOC) of the battery exceeding the state of charge (SOC) threshold parameter SOC 触发 In the function block using the temperature trigger condition, the control strategy of the corresponding function block responds to the battery temperature exceeding the temperature threshold parameter T 触发 In a function block utilizing a time trigger condition, the control strategy of the corresponding function block responds to the time since the start of the function block exceeding the duration threshold parameter t 触发 The value ends.

[0041] In order to minimize battery degradation, it is critical to adapt the control parameters (the second parameter discussed above) and threshold parameters (the fourth parameter discussed above) of the charging curve building blocks according to the battery temperature and / or battery degradation / aging. Therefore, in at least one embodiment, the processor 14 is further configured to calculate optimal values ​​of parameters of a plurality of adaptation functions according to the battery temperature and / or battery degradation / aging, the adaptation functions being used to adjust the values ​​of the control parameters and threshold parameters of each charging curve function block.

[0042] Below we describe exemplary adaptation functions of control parameters of each exemplary charging control strategy and exemplary adaptation functions of threshold parameters of each exemplary trigger condition. Exemplary adaptation functions f1-f9 are summarized in Table 2 below.

[0043] Control parameters and threshold parameters of the charging profile building block Adaptation rules Current amplitude for constant current control strategy #timg# Current slope of constant current ramp control strategy #timg# Voltage amplitude for constant voltage control strategy #timg# Voltage slope of constant voltage ramp control strategy #timg# Voltage thresholds for voltage-based trigger conditions #timg# Current threshold for current-based trigger conditions #timg# SOC threshold based on SOC trigger condition #timg# Temperature thresholds for temperature-based trigger conditions #timg# Duration threshold for time-based trigger conditions #timg#

[0044] Table 2.

[0045] As described in Table 2, the constant current amplitude parameter CC Mag is defined as an arbitrary function f1 that depends on the battery temperature T, the battery state of health SoH, and one or more arbitrary constant current amplitude adaptation parameters CC 适配 . Current slope parameter CdI Mag is defined as an arbitrary function f2 that depends on the battery temperature T, the battery state of health SoH, and one or more arbitrary current slope adaptation parameters CdI 适配 . Constant voltage amplitude parameter CV Mag is defined as an arbitrary function f3 that depends on the battery temperature T, the battery state of health SoH, and one or more arbitrary constant voltage amplitude adaptation parameters CV 适配 Finally, the voltage slope parameter CdV Mag is defined as an arbitrary function f4 that depends on the battery temperature T, the battery state of health SoH, and one or more arbitrary voltage slope adaptation parameters CdV适配 .

[0046] Similarly, the voltage threshold parameter V 触发 is defined as an arbitrary function f5 that depends on the battery state of health SoH and one or more arbitrary voltage threshold adaptation parameters V 适配 Current threshold parameter I 触发 is defined as an arbitrary function f6 that depends on the battery state of health SoH and one or more arbitrary current threshold adaptation parameters I 适配 . Charge state threshold parameter SOC 触发 is defined as an arbitrary function f7 that depends on the battery state of health SoH and one or more arbitrary state of charge threshold adaptation parameters SOC 适配 . Temperature threshold parameter T 触发 is defined as an arbitrary function f8 that depends on the battery state of health SoH and one or more arbitrary temperature threshold adaptation parameters T 适配 Finally, the duration threshold parameter t 触发 is defined as an arbitrary function f9 that depends on the battery state of health SoH and one or more arbitrary duration threshold adaptation parameters t 适配 .

[0047] The adaptation functions f1-f9 may be predefined and stored in the memory 16. 适配 An exemplary adaptation function for adapting the parameters may take the form of exemplary equation (1):

[0048] (1),

[0049] One or more adaptation parameters K 适配 The magnitude variable K includes the parameter value indicating the beginning of a particular battery life. 初始 and a scaling parameter K for scaling the parameter depending on the battery state of health SoH 缩放 The battery state of health SoH may be defined in a conventional manner as a function of capacity, nominal capacity, impedance, nominal impedance, etc. It will be appreciated that the adaptation functions f1-f9 may take many different forms, depending on the parameters being adapted, and may incorporate features of an equivalent circuit battery model, etc. Additionally, as seen above, some adaptation functions may also depend on the battery temperature T.

[0050] The processor 14 is configured to calculate corresponding control parameters (e.g. CC Mag , CdI Mag 、CV Mag or CdV Mag ) and the corresponding threshold parameters (such as V 触发,I 触发 , SOC 触发 、T 触发 or 触发 ) which, at least with respect to the optimal charging curve at the beginning of life (i.e., the optimal charging curve corresponding to the least amount of degradation), (i) minimizes the difference between the optimal charging curve and the pseudo-optimal charging curve, and (ii) minimizes the difference between the degradation / aging of the specific battery caused by the optimal charging curve and the degradation / aging of the specific battery caused by the pseudo-optimal charging curve.

[0051] Furthermore, the processor 14 is configured to calculate the adaptation parameter values ​​(eg CC 适配 , CdI 适配 、CV 适配 or CdV 适配 and V 适配 ,I 适配 , SOC 适配 、T 适配 or 适配 ), the adaptation function is used to adapt the control parameters and threshold parameters constructed for each charging curve in the ordered sequence of optimal charging curves after the start of life, and the adaptation parameter values ​​(i) minimize the difference between each optimal charging curve and the corresponding adapted pseudo-optimal charging curve at each degradation amount, and (ii) minimize the difference between the degradation / aging of the specific battery caused by each optimal charging curve and the degradation / aging of the specific battery caused by the corresponding adapted pseudo-optimal charging curve at each degradation amount.

[0052] Therefore, the processor 14 is configured to determine, for each charging profile building block, at least the control parameter CC Mag , CdI Mag 、CV Mag or CdV Mag and threshold parameter V 触发 ,I 触发 , SOC 触发 、T 触发 or 触发 The initial value of the corresponding adaptation parameter CC is determined 适配 , CdI 适配 、CV 适配 or CdV 适配 and V 适配 ,I 适配 , SOC 适配 、T 适配 or 适配 The adaptation parameters are used to adapt the control parameters and the threshold parameters, respectively, as the specific battery ages and / or degrades.

[0053] In at least one embodiment, the processor 14 is configured to calculate the control parameters and threshold parameters of each charging curve building block, as well as the adaptation parameters of the adaptation function by solving a minimization and / or optimization problem. For example, given a set of optimal charging curves within N cycles, one can decide which type of building block (i.e., which control strategy and trigger condition) to use to form a pseudo-optimal charging curve that approximates the optimal charging curve. The selection of control strategies and trigger conditions for each block is discussed in further detail below. Once the sequence of building blocks is fixed (the same sequence is used for all cycles), the following minimization equation (2) can be used to calculate the optimal values ​​of control parameters, threshold parameters, and adaptation parameters based on current, voltage, temperature, state of charge, state of health, capacity, impedance, etc.:

[0054] (2).

[0055] In equation (2), l Indicates the number of cycles in N cycles, A l,k Marking the loops in the best curve l The aging index k at Marking loops in pseudo-optimal curves l The aging index k at Represents a loop l The best charging curve in Represents a loop l The pseudo-optimal charging curve in . Equation (2) is solved to determine the optimal values ​​of the control parameters, threshold parameters and adaptation parameters. The minimization problem of equation (2) is subject to the current, voltage and temperature limits specified by the specific battery manufacturer. We note that the aging indicator A l,k It is an overpotential representation of the undesirable side reactions that cause capacity loss and battery aging, and is related to the internal state of the electrochemical cell model. A l,k Such side reactions represented include (but are not limited to) lithium plating, cell swelling, solid-electrolyte interface (SEI) layer growth or gas generation due to electrolyte decomposition. Equation (2) guarantees the best approximation of the optimal electrochemical charging curve, so that the pseudo-optimal curve has a very similar aging behavior over the battery life.

[0056] As discussed above, in at least one embodiment, the processor 14 is configured to determine control parameters and threshold parameters for each charging profile building block, as well as adaptation parameters for adjusting the control parameters and threshold parameters. In some embodiments, the type of control strategy and trigger condition for each charging profile building block is predefined or preselected before determining the control parameters, threshold parameters, and adaptation parameters.

[0057] In particular, in some embodiments, the processor 14 is configured to receive, for each building block in the ordered sequence forming the pseudo optimal charging curve, the following via an input device such as the user interface 20 or the network communication module 22: the value of a first parameter indicating a control strategy to be used for the corresponding building block and the value of a third parameter indicating a trigger condition to be used for the corresponding building block. The first parameter of each building block in the ordered sequence forming the pseudo optimal charging curve may, for example, take possible values: CC, CdI, CV or CdV. Similarly, the third parameter of each building block in the ordered sequence forming the pseudo optimal charging curve may, for example, take possible values: V_TRIG, I_TRIG, SOC_TRIG, TEMP_TRIG or TIME_TRIG.

[0058] However, the optimization process embodied in equation (2) discussed above can be generalized and / or adapted to also identify an optimal value of a third parameter that indicates the type of trigger condition to be used for each respective building block. In particular, in some embodiments, the processor 14 is configured to collectively determine the value of the respective third parameter indicating the type of trigger condition to be used for each respective building block, the value of the third parameter (i) minimizing the difference between the optimal charging curve and the pseudo-optimal charging curve, and (ii) minimizing the difference between the degradation / aging of the particular battery caused by the optimal charging curve and the degradation / aging of the particular battery caused by the pseudo-optimal charging curve. An example of this method is provided below in Table 3.

[0059] Threshold parameters for trigger conditions Identification of trigger conditions and threshold adaptation rules Voltage thresholds for voltage-based trigger conditions #timg# Current threshold for current-based trigger conditions #timg# SOC threshold based on SOC trigger condition #timg# Temperature thresholds for temperature-based trigger conditions #timg# Duration threshold for time-based trigger conditions #timg#

[0060] Table 3.

[0061] In Table 3, the trigger condition flag flag V 、flag I 、flag SOC 、flag T and flag t Take a value from the set {0,1}. If the specific trigger condition flag has a value of 1, the corresponding trigger condition is used for the corresponding charging curve building block. On the contrary, if the specific trigger condition flag has a value of 0, the corresponding trigger condition is not used for the corresponding charging curve building block. In some embodiments, the processor 14 is configured to use these functions or the like in conjunction with equation (2) to determine the trigger condition flag flag V 、flag I 、flag SOC 、flag T and flag t The optimization process is performed on the trigger condition flag flag.V 、flag I 、flag SOC 、flag T and flag t The trigger condition is performed under the constraint that only one of the building blocks can have the value 1. In this way, a third parameter indicating the type of trigger condition to be used for each building block can be determined together with the control parameter, the threshold parameter and the adaptation parameter, as discussed above.

[0062] Similarly, the optimization process embodied in equation (2) discussed above can also be generalized and / or adapted to also identify an optimal value of a first parameter indicating a control strategy to be used for each respective building block, and to determine an optimal number of different building blocks in a sequence. In particular, in some embodiments, the processor 14 is further configured to collectively determine a value of a respective first parameter indicating a control strategy to be used for each respective building block, the value of the first parameter (i) minimizing the difference between the optimal charging curve and the pseudo-optimal charging curve, and (ii) minimizing the difference between the degradation / aging of a particular battery caused by the optimal charging curve and the degradation / aging of the particular battery caused by the pseudo-optimal charging curve.

[0063] Continue to refer Figure 2 Once the pseudo-optimal charging curve is determined, the method 100 continues with the following steps: verifying the pseudo-optimal charging curve by simulation and / or experiment (box 190). In particular, with respect to the detailed embodiments described herein, the processor 14 is configured to compare the optimal charging curve and the pseudo-optimal charging curve at different degradation amounts in order to verify the pseudo-optimal charging curve. In addition, in some embodiments, the processor 14 is configured to perform simulations using an electrochemical battery model 30 that utilizes the optimal charging curve and the pseudo-optimal charging curve, and compare various performance metrics such as charging time, degradation rate, etc. In some embodiments, the processor 14 is configured to operate the display 18 to display a visual comparison of the optimal charging curve and the pseudo-optimal charging curve or a visual comparison of certain performance metrics for evaluation by a user. In some embodiments, the processor 14 is configured to similarly compare the pseudo-optimal charging curve and its performance metrics with the charging scheme recommended by the OEM.

[0064] Figure 4A plot 172 is shown illustrating a visual comparison of pseudo-optimal charging curves 174 and 176 of an exemplary lithium-ion battery with the optimal charging curves 154 and 156. Charging curve 174 (shown as a solid line) represents the determined pseudo-optimal charging curve of the exemplary lithium-ion battery at the beginning of life. Charging curve 176 (shown as a dashed line) represents the determined pseudo-optimal charging curve of the exemplary lithium-ion battery at the end of life. Charging curves 174 and 176 are formed by an ordered sequence of charging phases, which include: (1) a first constant current phase, (2) a first current ramp phase, (3) a second current ramp phase, (4) a second constant current phase, and (5) a constant voltage phase. As can be seen, pseudo-optimal charging curves 174 and 176 closely approximate the optimal charging curves 154 and 156 determined using the electrochemical battery model 30.

[0065] Similarly, the pseudo-optimal charging curve can be verified experimentally. In particular, Figure 5 Experimental results comparing the performance of an OEM-recommended charging scheme with the performance of a pseudo-optimal charging curve for an exemplary lithium-ion battery are shown. In particular, an exemplary lithium-ion battery (a cell phone battery) was used to obtain these experimental results. According to the manufacturer's specifications, the battery cell has a nominal capacity of 2.8Ah, a maximum voltage of 4.4V, and an OCP rating of 4.8A. Additionally, according to the manufacturer's specifications, the battery cell temperature should not exceed 40 degrees Celsius. The OEM-recommended fast charging algorithm consists of a constant current of 3.105A, up to 4.3V, and then de-rating the current to 1.89A, up to 4.4V, and holding the voltage at 4.4V until the current reaches 100mA. This results in a charging time of approximately 125 minutes from 0% to 100% state of charge.

[0066] A pseudo optimal charging curve was derived according to the method discussed above, with the goal of maintaining the same charging time similar to the OEM recommended fast charging algorithm while significantly improving the cycle life of the battery. The details of the pseudo optimal charging curve derived for a cell phone battery are given below in Table 4.

[0067] Control strategy Control parameters and adaptation rules Trigger conditions Threshold parameters and adaptation rules Constant current 3.105[A] SOC 0.17 Current ramp -12e-4[A / s] SOC 0.36 * Nominal capacity / Capacity [A] Current ramp -4e-4[A / s] Current 1.2 * Nominal capacity / capacity [A] Constant current 1.2 * Nominal capacity / capacity [A] Voltage 4.4[V] Constant voltage 4.4V Current 0.120[A]

[0068] Table 4.

[0069] To compare the performance of the pseudo-optimal charge profile with respect to the OEM-recommended charging regimen, the batteries were cycled according to the following test plan. The cycle test consisted of a sequence of: (1) charging the battery, (2) allowing the battery to rest for a 30-minute rest period, (3) discharging the battery with a typical cellular phone usage profile, and (4) allowing the battery to relax for 30 minutes before starting another cycle. All tests were performed in a temperature-controlled environment at 25 degrees Celsius.

[0070] Plot 192 shows a comparison of the degraded battery capacity when using a pseudo optimal charging curve (illustrated with larger dots) over several cycles with the degraded battery capacity when using the OEM recommended charging scheme (illustrated with smaller dots). Plot 194 shows a comparison of the evolution of the charging time when using a pseudo optimal charging curve (illustrated with larger dots) over several cycles with the evolution of the charging time when using the OEM recommended charging scheme (illustrated with smaller dots). Plot 196 shows a comparison of the evolution of the expansion expansion when using a pseudo optimal charging curve (illustrated with a solid dotted line) over several cycles with the evolution of the expansion expansion when using the OEM recommended charging scheme (illustrated with a dotted line).

[0071] As can be seen, the pseudo-optimal charging curve has a similar charging time to the OEM-recommended charging scheme at the beginning of life, and maintains the same charging time throughout the experiment. In contrast, the charging time of the OEM-recommended charging scheme decreases in the first 50 cycles due to battery cell capacity loss, and then increases due to significant impedance growth. Additionally, the experimental results also confirm the significant improvement in reducing the thickness expansion rate when using the pseudo-optimal charging curve. This is because the side reactions that cause accelerated aging are effectively mitigated, thereby reducing their byproducts.

[0072] Leveraging Pseudo-Optimal Charging Profiles in Embedded Applications

[0073] Figure 6 A battery charging system 200 utilizing a pseudo optimal charging curve is shown. The system 200 includes a battery 202 configured to store electrochemical energy. The battery 202 includes one or more electrochemical cells 204 arranged in parallel and / or in series to form the battery 202. In one embodiment, the battery 202 is a lithium ion battery and the electrochemical cells 204 are lithium ion cells. The battery 202 includes a positive battery terminal 206 and a negative battery terminal 208, and the battery 202 provides an output voltage and an output current via the positive battery terminal 206 and the negative battery terminal 208. Additionally, the battery 202 is configured to be charged via the positive and negative battery terminals 206, 208.

[0074] The system 200 also includes a power supply 210 and a charging circuit 212. The power supply 210 is configured to apply a charging current and / or a charging voltage to the battery 202 via the positive and negative battery terminals 206, 208 during the charging process. In some embodiments, the power supply 210 is configured to provide a predetermined constant direct current (DC) voltage or current. In some embodiments, the power supply 210 is an alternating current (AC) voltage or current source. In one embodiment, the power supply 210 is a local power grid (mains) configured to provide a single-phase or three-phase AC voltage having a predetermined frequency (such as 50 Hz or 60 Hz) and a predetermined nominal voltage (such as a nominal voltage between 110-127 volts or 220-240 volts).

[0075] The charging circuit 212 is connected between the power source 210 and the battery 202 and is configured to convert, regulate and / or control the charging current and / or charging voltage applied to the battery 202 by the power source 210. In some embodiments, the charging circuit 212 includes a charging controller 214 and a memory 216 associated with or connected to the charging controller 214. The charging circuit 212 also includes various circuits and hardware configured to convert, regulate and / or control the charging current and / or charging voltage applied to the battery 202 by the power source 210. The circuits and hardware may include components such as contactors, relays, transistors, transformers, diodes, capacitors, inductors, and resistors arranged in a conventional manner. In some embodiments, additional power conversion circuits may be arranged between the power source 210 and the charging circuit 212, such as a separate AC / DC converter.

[0076] The charge controller 214 is configured to operate switches and other components of the charging circuit 212 in order to convert, regulate and / or control the charging current and / or charging voltage applied by the power source 210 to the battery 202. In one embodiment, the charge controller 214 includes a processor configured to execute program instructions stored on the memory 216. The memory 216 can be of any device type capable of storing information accessible by the charge controller 214, such as a memory card, ROM, RAM, writable memory, read-only memory, hard drive, disk, flash memory, or any of a variety of other computer-readable media that act as data storage devices as will be recognized by those of ordinary skill in the art. Additionally, those of ordinary skill in the art will recognize that a "controller" or "processor" includes any hardware system, hardware mechanism, or hardware component that processes data, signals, or other information. The charge controller 214 may include a system having a central processing unit, multiple processing units, dedicated circuits for implementing specific functionality, or other systems.

[0077] The system 200 also includes a current sensor 218, a voltage sensor 220, and a temperature sensor 222, which are configured to monitor the battery current, battery voltage, and battery temperature, respectively, at least during the charging process. The charging controller 214 is operably connected to the current sensor 218, to the voltage sensor 220, and to the temperature sensor 222, and is configured to receive measurement signals corresponding to the battery current, battery voltage, and battery temperature. In one embodiment, the current sensor 218 includes a shunt resistor arranged in series with the battery 202, which provides a voltage proportional to the battery current. In one embodiment, the current sensor 218 includes a Hall effect sensor, which is arranged in series with the battery 202 and is configured to measure the battery current. The voltage sensor 220 is connected in parallel with the battery 202 and is configured to measure the battery voltage across the positive and negative battery terminals 206, 208 of the battery 202. In some embodiments, the voltage sensor is also configured to measure the voltage of a single battery cell 204 of the battery 202. In some embodiments, charge controller 214 is configured to determine, calculate, and / or estimate additional battery parameters, such as state of charge, state of health, impedance, capacity, open circuit voltage, and / or resting voltage.

[0078] The memory 216 is configured to store pseudo-optimal parameters 224 that define and / or characterize an ordered sequence of charge profile building blocks that form the pseudo-optimal charge profile determined in the manner described above, and an adaptation function that defines control parameters and threshold parameters for adapting each charge profile building block as the battery 202 ages / degrades.

[0079] Figure 7A logic flow diagram of a method 300 for operating a battery charging system 200 to utilize a pseudo optimal charging curve is shown. In particular, the charging controller 214 is configured to operate the charging circuit 212 with reference to the pseudo optimal parameters 224 to implement the functional building blocks of the pseudo optimal charging curve. The charging controller 214 is configured to select the first and / or next functional block in the sequence defined by the pseudo optimal parameters 224 (block 310). The charging controller 214 is configured to receive measured values ​​of voltage, current, and temperature from the sensors 218, 220, and 222 as inputs and calculate the state of charge and / or state of health of the battery 202 (block 320). Based on the measured values ​​of voltage, current, and temperature and the calculated values ​​of the state of charge and / or state of health, the charging controller 214 is configured to adapt the control parameters and threshold parameters of the pseudo optimal parameters 224 with reference to the adaptation parameters and their adaptation functions defined in the pseudo optimal parameters 224 (blocks 330 and 340). The charging controller 214 is configured to charge the battery according to the charging strategy of the functional block defined by the pseudo optimal parameters 224 (block 350). In at least some embodiments, the charging controller 214 is configured to operate the charging circuit 212 using closed-loop feedback control based on the measured battery current and / or the measured battery voltage to implement the functional building block. In particular, the charging controller 214 is configured to vary the charging current based on the difference (error) between the measured battery current and / or the measured battery voltage and the target battery current and / or the target battery voltage. In this way, the charging controller 214 is configured to control the charging current so as to track the target battery current or target battery voltage as indicated by the pseudo optimal parameters 224. When the battery is charged, the charging controller 214 is configured to continuously or periodically check whether a trigger condition is met by comparing the corresponding threshold parameter with the corresponding measured or calculated value (block 360). Once the trigger condition is met, the charging controller 214 is configured to check whether it is the end of the sequence (block 370). If more function blocks remain in the sequence, the charge controller 214 is configured to select the next function block (returning to block 310). Otherwise, if no function blocks remain in the sequence, the charging process ends. By utilizing the pseudo-optimal charging curve defined by the pseudo-optimal parameters 224, the operation of the charge controller 214 is improved and the charging time and / or battery degradation is reduced.

[0080] The methods, processes, and program instructions (e.g., charging curve synthesis program 28) described herein improve the operation of the processor 14 and the computing system 10 as a whole, separately, or in combination by enabling the processor 14 and / or the computing system 10 to systematically derive a pseudo-optimal charging curve for a specific battery, thereby enabling the implementation of a strategy based on a complex model-based algorithm in real time in a computationally constrained environment. As discussed above, the method 100 improves the state of the art of algorithms for applications (such as consumer electronic devices) where it is not possible to run a complete physics-based electrochemical model online. The method 100 helps design a BMS strategy for battery charging that adapts to the battery aging behavior. Using the systematic approximation method technology, the features and advantages of a physics-based BMS can be captured in a computationally efficient manner. The pseudo-optimal charging curve derived using the method 100 keeps a specific battery within an operating regime that prevents accelerated aging during charging (i.e., there is no lithium plating that causes capacity degradation and safety issues, and there are no other undesirable reactions that cause battery swelling, SEI growth, etc.), while minimizing charging time without relying on a computationally expensive physics-based BMS.

[0081] In at least one embodiment, a non-transitory copy of the programming instructions for a single one of the above methods and processes (e.g., the charge curve synthesis program 28) may be placed in a non-transitory storage device (such as, for example, the memory 16) during manufacture, or in the field via, for example, a distribution medium (not shown) such as a compact disk (CD) or via a network communication module 22 (from a remote server). That is, one or more distribution media having the program implemented therein may be employed to distribute the program to various computing devices.

[0082] Although the present disclosure has been illustrated and described in detail in the drawings and the foregoing description, it should be considered illustrative rather than restrictive in nature. It should be understood that only preferred embodiments have been presented and that all changes, modifications and additional applications that fall within the spirit of the present disclosure are desired to be protected.

Claims

1. A method for approximating an optimal charging curve for a specific battery, the method comprising: storing in a memory an electrochemical cell model describing physical processes of the battery that cause aging, the electrochemical cell model being parameterized based on physical characteristics of a specific battery; determining, with a processor, a first charging profile using the electrochemical cell model, the first charging profile minimizing charging time for the specific cell and minimizing degradation of the specific cell; and determining, with a processor, a first set of parameters defining a second charging profile, the second charging profile being formed by an ordered sequence of charging phases approximating the first charging profile, each charging phase in the ordered sequence being characterized by: (i) a respective first parameter in the first set of parameters indicating a respective control strategy to be used to control charging current during the respective charging phase, (ii) a respective second parameter in the first set of parameters indicating a control parameter value of the respective control strategy, (iii) a respective third parameter in the first set of parameters indicating a respective trigger condition that, when satisfied, triggers an end to the respective charging phase, and (iv) a respective fourth parameter in the first set of parameters indicating a threshold parameter value for the respective trigger condition; Determining the first set of parameters defining the second charging curve also includes: For each charging stage in the ordered sequence, a value of a corresponding second parameter and a value of a corresponding fourth parameter are calculated that (i) minimizes a difference between the first charging profile and the second charging profile, and (ii) minimizes a difference between degradation of the specific battery caused by the first charging profile and degradation of the specific battery caused by the second charging profile.

2. The method of claim 1 , wherein determining a first set of parameters defining a second charging curve further comprises: For each charging phase in the ordered sequence, a value of a corresponding third parameter is received via an input device.

3. The method of claim 1 , wherein determining a first set of parameters defining a second charging curve further comprises: For each charging stage in the ordered sequence, a value of a corresponding third parameter is calculated that (i) minimizes the difference between the first charging profile and the second charging profile, and (ii) minimizes the difference between the degradation of the specific battery caused by the first charging profile and the degradation of the specific battery caused by the second charging profile.

4. The method of claim 1 , wherein determining a first set of parameters defining a second charging curve further comprises: For each charging phase in the ordered sequence, a value of a corresponding first parameter is received via an input device.

5. The method of claim 1 , wherein determining a first set of parameters defining a second charging curve further comprises: For each charging stage in the ordered sequence, a value of a corresponding first parameter is calculated that (i) minimizes a difference between the first charging profile and the second charging profile, and (ii) minimizes a difference between degradation of the specific battery caused by the first charging profile and degradation of the specific battery caused by the second charging profile.

6. The method according to claim 1, wherein determining the first charging curve further comprises: A plurality of first charging curves that minimize charging time of the specific battery and minimize degradation of the specific battery are determined using the electrochemical battery model, each first charging curve in the plurality of first charging curves corresponding to a different amount of degradation of the specific battery.

7. The method of claim 6, wherein determining a set of parameters defining a second charging curve further comprises: A first set of parameters defining a second charging curve is determined, the second charging curve being formed by an ordered sequence of charging phases that approximates a charging curve of the plurality of first charging curves that corresponds to a minimum amount of degradation for the particular battery.

8. The method according to claim 7, further comprising: A second set of parameters for adapting a second charging curve depending on the amount of degradation of the specific battery is determined using a processor, such that when adapted using the second set of parameters based on the corresponding amount of degradation of the specific battery, the adapted second charging curve approximates a charging curve of the plurality of first charging curves that corresponds to the corresponding amount of degradation of the specific battery.

9. The method of claim 8, wherein determining a second set of parameters for adapting a second charging curve further comprises: Calculating (i) a value of a fifth parameter in a second set of parameters of a first adaptation function, the first adaptation function being configured to adapt a second parameter in the first set of parameters depending on an amount of degradation of the specific battery, and (ii) a value of a sixth parameter in the second set of parameters of a second adaptation function, the second adaptation function being configured to adapt a fourth parameter in the first set of parameters depending on an amount of degradation of the specific battery, the value of the fifth parameter, and the value of the sixth parameter: minimizing a difference between the plurality of first charging profiles and a second charging profile, the second charging profile being adapted based on a respective amount of degradation of the particular battery corresponding to each of the plurality of first charging profiles; and A difference between degradation of a specific battery caused by each of the plurality of first charging profiles and degradation of the specific battery caused by a second charging profile is minimized, the second charging profile being adapted based on a respective degradation amount of the specific battery corresponding to each of the plurality of first charging profiles.

10. The method of claim 9, wherein the first adaptation function is configured to adapt a second parameter of the first set of parameters depending on an amount of degradation of a specific battery and depending on a temperature of the battery.

11. The method according to claim 1, wherein: For at least one charging stage in the ordered sequence, the corresponding first parameter has one of the following: (i) a first value indicating that the charging current during the corresponding at least one charging stage is to maintain a constant current defined by the corresponding second parameter, (ii) a second value indicating that the battery voltage of the specific battery during the corresponding at least one charging stage is to maintain a constant voltage defined by the corresponding second parameter, (iii) a third value indicating that the rate of change of the charging current during the corresponding at least one charging stage is to maintain a constant current change rate defined by the corresponding second parameter, and (iv) a fourth value indicating that the rate of change of the battery voltage during the corresponding at least one charging stage is to maintain a constant voltage change rate defined by the corresponding second parameter.

12. The method according to claim 1, wherein: For at least one charging stage in the ordered sequence, the corresponding third parameter has one of the following: (i) a first value indicating that the corresponding at least one charging stage is to be terminated in response to the battery voltage of the specific battery exceeding the voltage threshold defined by the corresponding fourth parameter, (ii) a second value indicating that the corresponding at least one charging stage is to be terminated in response to the charging current dropping below the current threshold defined by the corresponding fourth parameter, (iii) a third value indicating that the corresponding at least one charging stage is to be terminated in response to the charge state of the specific battery exceeding the charge state threshold defined by the corresponding fourth parameter, (iv) a fourth value indicating that the corresponding at least one charging stage is to be terminated in response to the temperature of the specific battery exceeding the temperature threshold defined by the corresponding fourth parameter, and (v) a fifth value indicating that the corresponding at least one charging stage is to be terminated in response to the duration of the corresponding at least one charging stage exceeding the duration threshold defined by the corresponding fourth parameter.

13. The method of claim 1 , further comprising, prior to determining the first charging curve: receiving, with a processor, characteristic data defining physical characteristics of a particular battery; and Values ​​of undefined parameters of the electrochemical cell model are determined based on the characteristic data.

14. The method according to claim 1, further comprising: The display device is operated to display a visual comparison of the first charging curve and the second charging curve.

15. A system for approximating an optimal charging curve for a specific battery, the system comprising: a data storage device configured with a plurality of instructions, the plurality of instructions including instructions corresponding to an electrochemical battery model that models battery physical processes that cause aging, the electrochemical battery model being parameterized based on physical characteristics of a particular battery; and at least one processor operably connected to the data storage device, the at least one processor configured to execute the plurality of instructions on the data storage device to: determining a plurality of first charging curves using the electrochemical cell model, the first charging curves minimizing a charging time for the specific battery and minimizing degradation of the specific battery, each first charging curve in the plurality of first charging curves corresponding to a different amount of degradation of the specific battery; A first set of parameters defining a second charging curve is determined, the second charging curve being formed by an ordered sequence of charging stages that approximate a charging curve from among the plurality of first charging curves corresponding to a minimum degradation amount for a specific battery, each charging stage in the ordered sequence being characterized by: (i) a corresponding first parameter from the first set of parameters indicating a corresponding control strategy to be used to control charging current during the corresponding charging stage, (ii) a corresponding second parameter from the first set of parameters indicating a control parameter value of the corresponding control strategy, (iii) a corresponding third parameter from the first set of parameters indicating a corresponding trigger condition that, when satisfied, triggers the end of the corresponding charging stage, and (iv) a corresponding fourth parameter from the first set of parameters indicating a threshold parameter value for the corresponding trigger condition.

16. A non-transitory computer-readable medium for approximating an optimal charging curve for a specific battery, the computer-readable medium storing a plurality of instructions configured to, when executed, cause at least one processor to: store in a memory an electrochemical battery model that models battery physical processes that cause aging, the electrochemical battery model being parameterized based on physical characteristics of the specific battery; determining a first charging curve using the electrochemical cell model, the first charging curve minimizing charging time for the specific cell and minimizing degradation of the specific cell; and determining a first set of parameters defining a second charging profile, the second charging profile being formed by an ordered sequence of charging phases approximating the first charging profile, each charging phase in the ordered sequence being characterized by: (i) a respective first parameter in the first set of parameters indicating a respective control strategy to be used for controlling the charging current during the respective charging phase, (ii) a respective second parameter in the first set of parameters indicating a control parameter value of the respective control strategy, (iii) a respective third parameter in the first set of parameters indicating a respective trigger condition that, when satisfied, triggers the end of the respective charging phase, and (iv) a respective fourth parameter in the first set of parameters indicating a threshold parameter value of the respective trigger condition; Wherein, for at least one charging stage in the ordered sequence, the corresponding first parameter has one of the following items: (i) a first value indicating that the charging current during the corresponding at least one charging stage is to maintain a constant current defined by the corresponding second parameter, (ii) a second value indicating that the battery voltage of a specific battery during the corresponding at least one charging stage is to maintain a constant voltage defined by the corresponding second parameter, (iii) a third value indicating that the rate of change of the charging current during the corresponding at least one charging stage is to maintain a constant current change rate defined by the corresponding second parameter, and (iv) a fourth value indicating that the rate of change of the battery voltage during the corresponding at least one charging stage is to maintain a constant voltage change rate defined by the corresponding second parameter.

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