Lithium-ion battery lossless fast charging method and system based on multi-frequency sinusoidal nonlinear characterization

Abstract

The present invention provides a lossless fast charging method and system for lithium-ion batteries based on multi-frequency sinusoidal nonlinear characterization, and relates to the technical field of battery charging optimization. The lossless fast charging method performs nonlinear characterization of lithium-ion batteries based on dynamic in-situ multi-frequency sinusoidal impedance spectroscopy; decomposes the frequency-domain voltage nonlinear response of the lithium-ion battery into even-order and odd-order responses to obtain the lithium precipitation boundary when the battery is charged; based on the lithium precipitation boundary, a lossless fast charging strategy for lithium-ion batteries is designed: the charging of lithium-ion batteries is divided into a pre-charging stage, a fast charging stage, and a floating charging stage, and a preset charging strategy is executed in each stage. The present invention determines the lithium precipitation boundary based on the dynamic in-situ multi-frequency sinusoidal impedance spectroscopy, so that the battery can avoid lithium precipitation while charging quickly, shortens the charging time, improves safety, and effectively protects the battery.

Description

Technical Field

[0001] The present invention relates to the technical field of battery charging optimization, and in particular to a lossless fast charging method and system for lithium-ion batteries based on multi-frequency sinusoidal nonlinear characterization. Background Art

[0002] Lithium-ion batteries have the advantages of high energy density and long cycle life, and have become the main driving power source for new energy vehicles. It only takes 10 minutes to fill up a gasoline-powered car, while the charging time of an electric car is usually measured in hours. Therefore, fast charging capability has become one of the key indicators of the electric vehicle and power battery industry.

[0003] The main method of fast charging is to increase the charging rate. However, high-rate charging will cause lithium plating, which will accelerate the performance degradation of the battery, resulting in a decrease in capacity and power, and cause a series of safety issues.

[0004] Therefore, lossless fast charging is a way to balance high-rate charging capabilities without lithium plating. In order to ensure the safe and long-lasting use of lithium-ion batteries, the charging strategy responsible for the battery management system needs to be further optimized to effectively detect and control lithium plating in lithium batteries under high-rate charging. Summary of the invention

[0005] Purpose of the invention: To propose a lossless fast charging method and system for lithium-ion batteries based on multi-frequency sinusoidal nonlinear characterization to solve the above-mentioned problems existing in the prior art.

[0006] In the first aspect, a lossless fast charging method for lithium-ion batteries based on multi-frequency sinusoidal nonlinear characterization is proposed, and the steps are as follows:

[0007] S1, using odd-numbered frequency random phase multi-frequency sinusoidal signal, plus constant current, to put the battery in working state, to construct a multi-frequency sinusoidal current excitation signal;

[0008] S2. Based on dynamic in-situ multi-frequency sinusoidal impedance spectroscopy, the nonlinear characterization of lithium-ion batteries is performed to obtain the voltage response of lithium-ion batteries;

[0009] S3, decomposing the voltage response of the lithium ion battery into even-order and odd-order responses, and calculating the lithium precipitation boundary when the lithium ion battery is charged;

[0010] S4. Based on the lithium plating boundary, a lossless fast charging strategy for lithium-ion batteries is designed: the charging of lithium-ion batteries is divided into a pre-charging stage, a fast charging stage, and a floating charging stage, and a preset charging strategy is implemented in each stage.

[0011] In a further embodiment of the first aspect, step S1 further includes: suppressing the fundamental frequency of the 0th harmonic; suppressing all even-order harmonics within the considered bandwidth, recorded as even-order detection harmonics; and randomly selecting and suppressing any one of each group of three consecutive odd-order harmonics, recorded as odd-order detection harmonics; grouping all odd-order harmonics into groups of three odd-order harmonics and randomly suppressing one of each group; obtaining a zero-mean odd-frequency random phase multi-frequency sinusoidal signal in the frequency domain, which is the multi-frequency sinusoidal signal.

[0012] In a further embodiment of the first aspect, the expression of the multi-frequency sinusoidal current excitation signal i(t) in step S1 is as follows:

[0013]

[0014] In the formula, i 0 is the DC current signal; f is the frequency of the excited signal; A m and φ m are the amplitude and phase of the mth harmonic respectively.

[0015] In a further embodiment of the first aspect, the voltage response expression of the lithium ion battery is as follows:

[0016]

[0017]

[0018] Where U [p] (k) represents the input of the pth cycle; Y [p] (k) represents the output of the pth cycle; is the designed ideal multi-frequency sinusoidal signal; Z BLTVA (*) is the frequency response equation of the linear part of the lithium battery system; jω is the complex frequency variable; Y S (k) is the nonlinear disturbance of the system, i.e., the nonlinearity of the lithium battery system; and Represent the measurement errors of the actual environment and hardware equipment in the input and output spectra, respectively.

[0019] In a further embodiment of the first aspect, in the process of constructing the multi-frequency sinusoidal current excitation signal, some odd harmonics and all even harmonics are suppressed, so that only the system nonlinear disturbance V S (k) and measurement error Appears at the corresponding frequency position; taking into account the measurement error under normal conditions The intensity is much smaller than the nonlinear disturbance V S (k), thereby separating the nonlinearity of the lithium battery from the output spectrum.

[0020] In a further embodiment of the first aspect, in step S3, the system nonlinear disturbance V of the lithium ion battery is S (k) According to the suppressed odd and even order harmonics corresponding to the frequency decomposition into odd order nonlinear response V S (H supp,odd ) and even-order nonlinear response V S (H supp,even ).

[0021] Calculate the relative coefficient of even and odd nonlinear response amplitudes If the odd-order nonlinear response amplitude is greater than the even-order nonlinear response amplitude, it is determined that lithium deposition occurs in the lithium battery. The expression is as follows:

[0022]

[0023] In a further embodiment of the first aspect, the state of charge of the lithium-ion battery is between 0 and 20%, which is defined as the pre-charge stage; the state of charge of the lithium-ion battery is between 20 and 80%, which is defined as the fast charge stage; the state of charge of the lithium-ion battery is between 80 and 100%, which is defined as the floating charge stage;

[0024] In the pre-charging stage, a constant current mode is adopted, and the constant current is i 0 ;

[0025] In the fast charging stage, a fused multi-frequency sinusoidal current excitation signal is used to prevent the occurrence of lithium deposition. When the lithium-ion battery is charged with a sinusoidal current mean value I k When charging, when the sinusoidal current reaches the average value I k Before the corresponding lithium deposition boundary, adjust the current sine mean value to I k+1 , where I k+1 k , repeat the above process until charging is completed;

[0026] During the floating charge stage, a constant voltage method is used for supplementary charging until the battery is fully charged.

[0027] The second aspect of the present invention provides a lossless fast charging system for lithium-ion batteries, which includes four components: a signal design module, a voltage response acquisition module, a lithium precipitation boundary acquisition module, and a charging strategy execution module.

[0028] The signal design module uses an odd-numbered frequency random phase multi-frequency sinusoidal signal and a constant current to keep the battery in working condition, thereby constructing a multi-frequency sinusoidal current excitation signal.

[0029] The voltage response acquisition module performs nonlinear characterization of lithium-ion batteries based on dynamic in-situ multi-frequency sinusoidal impedance spectroscopy to obtain the voltage response of lithium-ion batteries; ​

[0030] The lithium deposition boundary acquisition module decomposes the voltage response of the lithium ion battery into even-order and odd-order responses, and calculates the lithium deposition boundary when the lithium ion battery is charged;

[0031] The charging strategy execution module designs a lossless fast charging strategy for lithium-ion batteries based on the lithium plating boundary: the charging of lithium-ion batteries is divided into a pre-charging stage, a fast charging stage, and a floating charging stage, and a preset charging strategy is executed in each stage.

[0032] As a third aspect of the present invention, a computer-readable storage medium is proposed, which stores at least one executable instruction. When the executable instruction is executed on an electronic device, the electronic device executes the lossless fast charging method for lithium-ion batteries disclosed in the first aspect and its further embodiments.

[0033] Compared with traditional technical solutions, the present invention adopts a lossless fast charging method and system for lithium-ion batteries based on multi-frequency sinusoidal nonlinear characterization, which ensures that lithium plating does not occur in the battery during the fast charging process, extends the battery life, improves battery safety, and greatly improves the battery charging speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 The invention is a flow chart of a method for lossless fast charging of lithium-ion batteries based on multi-frequency sinusoidal impedance spectroscopy.

[0035] Figure 2 It is a schematic diagram of a dynamic in-situ odd-frequency random-phase multi-frequency sinusoidal signal design method.

[0036] Figure 3 This is a schematic diagram of the design of a dynamic in-situ multi-frequency sinusoidal fast charging process.

[0037] Figure 4 It is a schematic diagram of the multi-frequency sinusoidal nonlinear characterization and analysis method.

[0038] Figure 5 It is a schematic diagram of dynamic in-situ multi-frequency sinusoidal fast charging voltage (20%-80% SOC). DETAILED DESCRIPTION

[0039] In the following description, a large number of specific details are provided to provide a more thorough understanding of the present invention. However, it is apparent to those skilled in the art that the present invention can be implemented without one or more of these details. In other examples, in order to avoid confusion with the present invention, some technical features known in the art are not described.

[0040] Embodiment 1:

[0041] Figure 1This is a flow chart of the lossless fast charging technology for lithium-ion batteries based on multi-frequency sinusoidal impedance spectroscopy. Figure 1 As shown, lossless fast charging includes the following steps.

[0042] Firstly, a dynamic in-situ multi-frequency sinusoidal current excitation signal is designed. Then, the nonlinear characterization of lithium-ion batteries is performed based on the dynamic in-situ multi-frequency sinusoidal impedance spectrum. Then, the frequency-domain voltage nonlinear response of lithium-ion batteries is decomposed into even-order and odd-order responses, and the lithium precipitation boundary during battery charging is obtained by calculating the relative coefficients of the amplitudes of the odd and even nonlinear responses. Finally, a lossless fast charging strategy for lithium-ion batteries is designed, and fast charging is performed according to the lossless fast charging strategy.

[0043] The multi-frequency sinusoidal excitation signal adopts a dynamic in-situ odd-frequency random-phase multi-frequency sinusoidal signal. The odd-order frequency random sinusoidal signal can realize rapid detection of lithium-ion batteries and simultaneously provide odd-order and even-order voltage nonlinear responses.

[0044] The odd-order frequency random phase multi-frequency sinusoidal signal characterizes the nonlinearity in the fast charging process of the lithium-ion battery by suppressing all even-order harmonics and part of odd-order harmonics in the frequency domain.

[0045] The dynamic in-situ multi-frequency sinusoidal impedance spectroscopy, as a frequency domain analysis method for non-destructive testing, can accurately characterize the nonlinear response of lithium-ion batteries in a dynamic situation, that is, during a fast charging process.

[0046] The lithium deposition boundary is the current boundary that causes lithium deposition in the lithium battery during charging, and the lithium deposition charging current boundary is the maximum charging current that does not trigger lithium deposition at different temperatures and different states of charge. The lithium deposition boundary is based on the odd-order and even-order nonlinear responses obtained by characterizing the lithium-ion battery. By calculating the relative coefficients of the odd-order and even-order nonlinear response amplitudes, if the even-order nonlinear response amplitude rapidly increases to be greater than the odd-order nonlinear response amplitude, it is determined that lithium deposition has occurred in the lithium battery at this time.

[0047] The lossless fast charging method divides the charging process into three stages: pre-charging stage, fast charging stage, and floating charging stage:

[0048] The pre-charging stage is when the state of charge of the lithium-ion battery is 0-20%, the fast charging stage is when the state of charge of the lithium-ion battery is 20-80%, and the floating charging stage is when the state of charge of the lithium-ion battery is 80-100%.

[0049] (1) The pre-charging stage adopts a constant current method, and the constant current is I 0 ;

[0050] (2) The fast charging stage uses a fused multi-frequency sinusoidal current excitation signal. To prevent lithium deposition, when the lithium-ion battery is charged with a sinusoidal current mean value Ik When charging, when the sinusoidal current reaches the average value I k Before the corresponding lithium deposition boundary, adjust the current sine mean value to I k+1 , where I k+1 k , repeat the above process until charging is completed;

[0051] (3) During the floating charge stage, the battery is charged at a constant voltage until it is fully charged.

[0052] Embodiment 2:

[0053] Combined with Example 1, refer to Figures 2 to 4 This embodiment discloses a lossless fast charging method for lithium-ion batteries based on multi-frequency sinusoidal impedance spectroscopy, the steps are as follows:

[0054] Step 1: Design a dynamic in-situ multi-frequency sinusoidal current excitation signal.

[0055] In one embodiment of the present invention, an odd-order frequency random phase multi-frequency sinusoidal signal is used as an excitation, coupled with a constant current i 0 Used to keep the battery in working condition, the expression is as follows:

[0056]

[0057] In the formula, i 0 is the DC current signal; f is the frequency of the excited signal, A m and φ m are the amplitude and phase of the mth harmonic respectively.

[0058] Odd-order frequency random phase multi-frequency sinusoidal signals are used to detect nonlinear responses by suppressing specific harmonics in the frequency domain.

[0059] First, in order to obtain a zero-mean current signal, the fundamental frequency of the 0th harmonic is suppressed to ensure the steady state of the battery. Then, in the zero-mean odd-frequency random-phase multi-frequency sinusoidal signal, all even harmonics within the bandwidth under consideration are suppressed, and any one of each group of three consecutive odd harmonics is randomly selected and suppressed. Finally, in order to reduce the nonlinear interaction of odd harmonics, all odd harmonics are grouped into three odd harmonics and one of each group is randomly suppressed. These suppressed harmonics are called detection harmonics because the responses appearing in these harmonics can be checked in the output voltage response.

[0060] In an embodiment of the present invention, the random odd harmonics used for the current excitation signal are: H exc ={1,5,7,9,13......}.

[0061] ​Step 2: Characterize the nonlinearity of lithium-ion batteries based on dynamic in-situ multi-frequency sinusoidal impedance spectroscopy.

[0062] First, in an embodiment of the present invention, under dynamic in-situ conditions, the voltage response of the lithium-ion battery is as follows:

[0063]

[0064]

[0065] Where: is the designed ideal multi-frequency sinusoidal signal; Z BLTVA (*) is the frequency response equation of the linear part (i.e., impedance) of the lithium battery system, i.e., the best linear time-varying approximation (BLTVA) of the battery impedance under dynamic conditions; jω is a complex frequency variable; Y S (k) is the nonlinear disturbance of the system, i.e., the nonlinearity of the lithium battery system; and Represent the measurement errors of the actual environment and hardware equipment in the input and output spectra, respectively.

[0066] Since some odd and all even harmonics are suppressed in the signal design, only the system nonlinear disturbance Y is present in the output spectrum. S (k) appears at the corresponding frequency position. According to the energy intensity at the corresponding odd-even detection frequency position, the nonlinear response of the lithium-ion battery can be determined.

[0067] In the time domain and frequency domain, the drift voltage (OCV drift) of lithium-ion batteries is expressed as follows:

[0068]

[0069] Where: V 0 (k) is OCV drift, B p (k) is a finite set of basis functions. Then the voltage response V(k) can be expressed as:

[0070]

[0071] in,

[0072] Where: N P is the order; θ p (k′) is the battery calculation parameter, V s (k) is a nonlinear perturbation.

[0073] The expression for the voltage spectrum around the excitation frequency can be written in matrix form as follows:

[0074] V=Kθ+N V

[0075] Where: V, θ, N V Represent the measured voltage, parameter, noise and unmodeled components respectively; K is the regression coefficient. Next, the optimal parameters are estimated in the least squares sense, and the calculation process is as follows:

[0076]

[0077] The sample variance of the nonlinear perturbation part is as follows:

[0078]

[0079] Step 3: Decompose the frequency domain voltage nonlinear response of the lithium-ion battery into even-order nonlinear response V according to the frequency corresponding to the detected harmonic S (H supp,even ) and odd-order nonlinear response V S (H supp,odd ), the lithium plating boundary during battery charging is obtained by calculating the relative coefficients of the even and odd nonlinear response amplitudes.

[0080] By calculating the relative coefficients of even and odd nonlinear response amplitudes Its expression is as follows:

[0081]

[0082] If the even-order nonlinear response amplitude increases rapidly to be greater than the odd-order nonlinear response amplitude, it is determined that lithium plating has occurred in the lithium battery.

[0083] Step 4: Design a lossless fast charging strategy for lithium-ion batteries.

[0084] The lossless fast charging strategy described above divides the charging process into three stages: pre-charging stage, fast charging stage, and floating charging stage:

[0085] First, in the pre-charge stage, that is, when the state of charge of the lithium-ion battery is between 0% and 20%, a constant current method is adopted, and the constant current is I 0 ;

[0086] Then, in the fast charging stage, when the state of charge of the lithium-ion battery is between 20% and 80%, the fused multi-frequency sinusoidal current excitation signal is used to prevent the occurrence of lithium deposition. k When charging, when the sinusoidal current reaches the average value I k Before the corresponding lithium deposition boundary, adjust the current sine mean value to I k+1 , where I k+1 k , repeat the above process until charging is completed;​

[0087] Finally, in the floating charge stage, that is, when the state of charge of the lithium-ion battery is between 80% and 100%, a constant voltage method is used for supplementary charging until the battery is fully charged.

[0088] Embodiment 3:

[0089] The present embodiment discloses a lossless fast charging system for lithium-ion batteries, which includes four components: a signal design module, a voltage response acquisition module, a lithium precipitation boundary acquisition module, and a charging strategy execution module. The signal design module uses an odd-order frequency random phase multi-frequency sinusoidal signal, plus a constant current, to put the battery in a working state, and constructs a multi-frequency sinusoidal current excitation signal; the voltage response acquisition module performs nonlinear characterization of the lithium-ion battery based on the dynamic in-situ multi-frequency sinusoidal impedance spectrum to obtain the voltage response of the lithium-ion battery; the lithium precipitation boundary acquisition module decomposes the voltage response of the lithium-ion battery into even-order and odd-order responses, and calculates the lithium precipitation boundary when the lithium-ion battery is charged; the charging strategy execution module designs a lossless fast charging strategy for the lithium-ion battery based on the lithium precipitation boundary: the charging of the lithium-ion battery is divided into a pre-charging stage, a fast charging stage, and a floating charging stage, and each stage executes a preset charging strategy.

[0090] Embodiment 4:

[0091] The present embodiment discloses a computer-readable storage medium, in which at least one executable instruction is stored. When the executable instruction is run on an electronic device, the electronic device performs the operation of the lossless fast charging method for lithium-ion batteries as described in the above embodiment. More specific examples of computer-readable storage media in the present disclosure may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. The computer-readable storage medium may include a data signal propagated in a baseband or as part of a carrier wave, in which a readable program code is carried. This propagated data signal may take a variety of forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination of the above. The readable signal medium may also be any readable medium other than a readable storage medium, which may send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, an apparatus, or a device.

[0092] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes may be made to it in form and detail without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A lossless fast charging method for lithium-ion batteries based on multi-frequency sinusoidal nonlinear characterization, characterized in that: The steps include: S1. Use an odd-numbered frequency random phase multi-frequency sinusoidal signal and a constant current to put the battery in working state, and construct a multi-frequency sinusoidal current excitation signal; specifically including: Suppress the fundamental frequency of the 0th harmonic; Suppress all even-order harmonics within the bandwidth under consideration, recorded as even-order detected harmonics ; All odd harmonics are grouped into three odd harmonics and one of them in each group is randomly suppressed, which is recorded as the odd-order detection harmonic. ; A zero-mean odd-frequency random-phase multi-frequency sinusoidal signal in the frequency domain is obtained, and superimposed with a constant direct current, that is, a multi-frequency sinusoidal current excitation signal; the multi-frequency sinusoidal current excitation signal The expression is as follows: ； In the formula, is a DC current signal; is the frequency of the excited signal, and are the amplitude and phase of the mth harmonic respectively; In the process of constructing the multi-frequency sinusoidal current excitation signal, some odd harmonics and all even harmonics are suppressed, so only the system nonlinear disturbance is present in the output spectrum. and measurement error Appear at the corresponding frequency position; Taking into account the measurement error under normal conditions The intensity is much smaller than the nonlinear disturbance of the system , thereby separating the nonlinearity of the lithium battery from the output spectrum; S2. Based on the dynamic in-situ multi-frequency sinusoidal impedance spectrum, the lithium-ion battery is nonlinearly characterized to obtain the voltage response of the lithium-ion battery; the voltage response expression of the lithium-ion battery is as follows: ； ； In the formula, represents the input of the pth cycle; represents the output of the pth cycle; is the designed ideal multi-frequency sinusoidal signal; is the frequency response equation of the linear part of the lithium battery system; is a complex frequency variable; is the nonlinear disturbance of the system, that is, the nonlinearity of the lithium battery system; and Respectively represent the measurement errors of the actual environment and hardware equipment in the input and output spectra; S3, decomposing the voltage response of the lithium ion battery into even-order and odd-order responses, and calculating the lithium precipitation boundary when the lithium ion battery is charged; specifically comprising: The nonlinear perturbation of the lithium-ion battery system Decomposing the suppressed odd-order and even-order harmonics into odd-order nonlinear responses and even-order nonlinear responses according to their corresponding frequencies; Calculate the relative coefficient of the odd-order and even-order nonlinear response amplitudes. If the odd-order nonlinear response amplitude is greater than the even-order nonlinear response amplitude, it is determined that lithium deposition occurs in the lithium battery. The expression is as follows: ； In the formula, Relative coefficients representing even and odd order nonlinear response amplitudes; represents odd-order nonlinear response; represents an even-order nonlinear response; S4. Based on the lithium plating boundary, a lossless fast charging strategy for lithium-ion batteries is designed: the charging of lithium-ion batteries is divided into a pre-charging stage, a fast charging stage, and a floating charging stage, and a preset charging strategy is implemented in each stage; specifically, the strategy includes: The state of charge of lithium-ion batteries is between 0 and 20%, which is defined as the pre-charge stage; The state of charge of lithium-ion batteries is between 20% and 80%, which is defined as the fast charging stage; The state of charge of a lithium-ion battery is between 80% and 100%, which is defined as the floating charge stage; In the pre-charging stage, a constant current method is adopted, and the constant current is ; In the fast charging stage, a fused multi-frequency sinusoidal current excitation signal is used to prevent the occurrence of lithium deposition. When the lithium-ion battery is charged with a dynamic in-situ multi-frequency sinusoidal current When charging, the dynamic in-situ multi-frequency sinusoidal current is reached Before the corresponding lithium deposition boundary, adjust the current sine mean to ,in, < , until charging is completed; During the floating charge stage, a constant voltage method is used for supplementary charging until the battery is fully charged.

2. The method for lossless fast charging of lithium-ion batteries according to claim 1, characterized in that: Also includes: Monitor the battery's voltage, temperature, state of charge, internal resistance, and impedance information in real time, and adjust the lithium plating boundary and corresponding charging procedures in real time.

3. A lithium-ion battery lossless fast charging system, used to execute the lithium-ion battery lossless fast charging method according to claim 1 or 2, characterized in that: include: Signal design module; The signal design module uses an odd-numbered frequency random phase multi-frequency sinusoidal signal and a constant current to put the battery in a working state, thereby constructing a multi-frequency sinusoidal current excitation signal; A voltage response acquisition module; the voltage response acquisition module performs nonlinear characterization on the lithium-ion battery based on a dynamic in-situ multi-frequency sinusoidal impedance spectrum to obtain a voltage response of the lithium-ion battery; A lithium deposition boundary acquisition module; the lithium deposition boundary acquisition module decomposes the voltage response of the lithium ion battery into even-order and odd-order responses, and calculates the lithium deposition boundary when the lithium ion battery is charged; Charging strategy execution module; The charging strategy execution module designs a lossless fast charging strategy for lithium-ion batteries based on the lithium plating boundary: the charging of lithium-ion batteries is divided into a pre-charging stage, a fast charging stage, and a floating charging stage, and a preset charging strategy is executed in each stage.

4. A computer-readable storage medium, characterized in that: The storage medium stores at least one executable instruction, and when the executable instruction is executed on the electronic device, the electronic device executes the lossless fast charging method for lithium-ion batteries as claimed in claim 1 or 2.

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