Distributed battery balancing system and method based on fractional-order dynamics estimation

Abstract

The present invention aims to provide a distributed battery balancing system and method based on fractional-order dynamic estimation with simplified calculation process, small error and high control accuracy. The present invention includes a BMS, which is based on the single-cell balancing module of the Buck-Boost converter and is constructed using an A-C2C balancing architecture. It is assumed that the battery pack is composed of i batteries connected in series, the number of single-cell balancing modules is i-1, and the x-th single-cell balancing module is respectively connected to the two ends of the x-th and x+1-th batteries connected in series and the series connection points of the x-th and x+1-th batteries, and each single-cell balancing module and the BMS communicate through the CAN bus; the method is: the BMS estimates the SOC, calculates the balancing current size of each single-cell balancing module, and then sends the corresponding balancing instruction to the single-cell balancing module, and finally completes the corresponding action. The present invention can be applied to the field of battery management technology.

Description

Technical Field

[0001] The present invention relates to the technical field of battery management, and in particular to a distributed battery balancing system and method based on fractional-order kinetic estimation. Background Art

[0002] Battery balancing technology is the main method to solve the problem of battery pack imbalance. Battery balancing technology relies on the balancing circuit to redistribute the charge between each battery cell to achieve the consistency of the power parameters of each battery cell. The realization of battery balancing needs to rely on the balancing circuit, and also requires a certain balancing strategy.

[0003] In the actual application of power battery systems, the number of single cells connected in series often reaches more than 100. It is difficult for a single balancing circuit to complete the balancing task of the entire battery pack. At this time, multiple balancing circuits are required to be connected in a specific way to form a specific balancing architecture to complete the overall balancing of the battery pack. The main advantages of ordinary passive balancing are its simple structure, easy use and low cost. However, its resistance energy consumption generates heat, resulting in unnecessary energy waste. In addition, the dissipated heat further exacerbates the battery imbalance phenomenon. Due to its energy consumption and heat dissipation problems, it is not common and its application prospects are not good.

[0004] Active balancing technology has the advantages of less heat generation, high efficiency, and the ability to achieve complex balancing control, and is gradually gaining more and more attention from academia and industry. Therefore, most common balancing architectures are active balancing. According to the connection method of the balancing circuit and the difference in the energy transfer path, there are three common active balancing architectures:

[0005] 1. Adjacent Cell to Cell (A-C2C)

[0006] 2. Direct Cell to Cell (D-C2C)

[0007] 3. Cell to Pack (C2P) architecture.

[0008] The traditional A-C2C balancing strategy is to balance the battery pack after the charging and discharging process stops and the battery pack is in a static state. At this time, the imbalance of the battery pack has already occurred. The traditional balancing strategy redistributes the charge between batteries by "taking more and supplementing less" to achieve energy consistency between batteries. However, due to the estimation error of the traditional battery model, this imbalance will occur and further expand.

[0009] In addition, the traditional battery equivalent model is represented by an integer-order model, and the electrochemical behavior in some batteries is either approximated by a large number of resistors and capacitors (RC) networks or by relaxation time. However, this type of model requires a large number of high-order mathematical approximations to simulate these electrochemical behaviors, which makes the mathematical model related to the calculation load extremely complicated and increases the amount of calculation for system calibration. Moreover, according to some literature, even if a fifth-order RC network system is used, the phase of the zero point cannot be captured very accurately.

[0010] In view of this, it is necessary to design a new battery balancing module to supplement the deficiencies of the existing solutions. Summary of the invention

[0011] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a distributed battery balancing system and method based on fractional-order dynamics estimation with simplified calculation process, small error and high control accuracy.

[0012] The technical solution adopted by the distributed battery balancing system based on fractional-order dynamic estimation of the present invention is that the present invention includes a BMS, which is based on a single-cell balancing module of a Buck-Boost converter and is constructed using an A-C2C balancing architecture. Assuming that the battery pack is composed of i batteries in series, the number of the single-cell balancing modules is i-1, and the i-1 single-cell balancing modules are connected in series with E1 to E2. i-1 The x-th single-cell balancing module is respectively connected to the two ends of the x-th and x+1-th batteries connected in series and the series connection point of the x-th and x+1-th batteries, wherein 1≤x≤i-1, and x and i are both natural numbers. Each single-cell balancing module communicates with the BMS through a CAN bus. The BMS estimates the SOC according to the voltage and temperature data of the battery, and calculates the balancing current required by each single-cell balancing module, and then sends the corresponding balancing instruction to the single-cell balancing module, and finally the corresponding single-cell balancing module completes the corresponding balancing action.

[0013] Furthermore, the single-cell balancing module based on the Buck-Boost converter is composed of an MCU, a driver, a first field effect transistor (QiH), a second field effect transistor (QiL), an inductor (Li) and a comparator, wherein the BMS monitors the voltage and temperature information of the battery; assuming that V1 and V2 are the voltages of the two batteries, after being sent to the BMS for judgment, the corresponding balancing current value i_ref is obtained and sent to the balancing module with the corresponding module number through the CAN bus.

[0014] The method for balancing a battery pack using the distributed battery balancing system based on fractional-order kinetic estimation comprises the following steps:

[0015] a. Replace the ideal capacitor in the first-order RC model with a fractional-order capacitor and establish a fractional-order electrochemical kinetic equivalent model for the battery. In this fractional-order electrochemical kinetic equivalent model, The open circuit voltage source of the battery is represented by R 0 The ohmic internal resistance of the battery is expressed as R P The Faraday impedance of the battery is expressed as C d Reflects the double-layer characteristics of the interface and is expressed as fractional capacitance, using U d The polarization voltage across the RC circuit is expressed as I Indicates the current flowing through the battery. It is assumed to be positive during discharge and negative during charge. V(t) Represents the terminal voltage of the battery. The state equation and output equation of the equivalent model of fractional-order electrochemical kinetics are expressed as:

[0016] …… (1),

[0017] …… (2),

[0018] in, is a differential operator, representing the order of the fractional-order capacitor The operation process can be written as , Represents the impedance characteristic coefficient of fractional capacitor, jω is the imaginary number of the angular frequency;

[0019] b. Choose the Grunwald-letnikov definition to implement the fractional calculus process. The definition of Grunwald-letnikov fractional calculus is as follows:

[0020] ……(3);

[0021] In the above formula, GL is the abbreviation of Grunwald-letnikov, which is used as the superscript of fractional differentials. is the order of the fractional capacitor, t0 represents the starting time, f(t) represents the function to be fractionally differentiated or integrated, h represents the step size, t represents the battery discharge time, j represents an integer index used to represent the item in the difference sequence, is the generalized binomial coefficient;

[0022] When the step size h is chosen to be small enough, the limit operation in the formula is approximately ignored, and the fractional derivatives and integrals under the Grunwald-Letnikov definition are directly calculated by the following formula:

[0023] …… (4),

[0024] in, is the coefficient of the binomial, and its recursive relationship is as follows:

[0025] ;

[0026] The polarization voltage across the RC circuit in the battery model is U d As a function of fractional differentiation or integration under the fractional definition of formula (4) f(t) ,right U d Perform fractional derivatives or integration to obtain the polarization voltage across the RC circuit using the Grunwald-letnikov fractional derivative. U d Numerical solution of ;

[0027] c. According to formula (1) and formula (4), the discretized state equation of the equivalent circuit of the fractional-order model is expressed as:

[0028] …… (5),

[0029] Formula (5) can be further written as:

[0030] …… (6),

[0031] In the formula, at time t, ∈R is the state vector, ∈R is the system input;

[0032] in: , represents the fractional impedance, Q is the impedance characteristic coefficient of the fractional capacitor;

[0033] Discretize the output equation into:

[0034] …… (7),

[0035] in, ∈R is the system output,

[0036] Finally, from Eq. and jointly determine the discrete state equations and output equations of the fractional order model;

[0037] d. Assume that the SOC of the battery is defined as follows:

[0038] …… (8),

[0039] In the formula, is the SOC at time t, is the initial SOC, is the Coulomb efficiency, is the battery capacity, is the current, and the discharge current in the formula is set to be positive;

[0040] e. Based on the discrete state equation, output equation and SOC definition of the above fractional-order model, the following is derived through computer modeling: Identification table and Identification table, where The identification table shows the relationship between the order of the fractional order model and the battery SOC. The identification table shows the relationship between the coefficients of the fractional order model and the battery SOC. Identification table and The parameter ranges in the identification table are selected based on the fitting results and battery characteristics;

[0041] f. Under the fractional order model, according to the above discrete state equation, output equation, Identification table and The identification table estimates the battery SOC value;

[0042] g. After calculating the SOC of each single cell, calculate the range between adjacent cells and maintain the SOC between them to be consistent. In order to control the SOC change rate of each battery during charging, the current of each battery is balanced. It is calculated by the following formula:

[0043] ,

[0044] in, k i It is a parameter reflecting the inherent characteristics of the battery, n is the number of batteries, and I is the total current;

[0045] In the A-C2C balancing architecture, the actual balancing current of the ith battery is obtained by Kirchhoff's law as the balancing current difference between two adjacent single-cell balancing modules;

[0046] The balancing current required for each single cell is calculated by the following formula:

[0047] ,

[0048] in, is the SOC value of each single battery, is the capacity of each single cell, For the equilibrium time, is the average SOC value of all modules, is the balancing current;

[0049] h. Each single-unit balancing module operates according to the calculated balancing current and finally completes the balancing action.

[0050] Furthermore, the specific steps of step f are as follows:

[0051] f1. Select the initial coefficient within the setting range , according to the least squares method, when the coefficient is fixed to When , and from Identify the battery in the table ,

[0052] f2.According to Identification table, at known order and battery When , the coefficient is retrieved , let the coefficient Calculate according to the following formula

[0053] ;

[0054] f3. The coefficient Use as the new coefficient and repeat steps f1 and f2 until the coefficient and order converge to a fixed value, and the battery SOC is estimated.

[0055] Further, in step a, the impedance of the fractional-order capacitor having a fractional-order characteristic is defined as:

[0056] ,

[0057] Where Z is the impedance, is the impedance characteristic coefficient of the fractional capacitor, is the imaginary angular frequency, is the order of the fractional capacitor, The characteristics of the fractional capacitor are between resistance and capacitance. When the order of the fractional derivative approaches 0, its characteristics are closer to resistance; when the order of its fractional derivative approaches 1, its characteristics are closer to integer-order capacitors.

[0058] The beneficial effects of the present invention are as follows: the present invention proposes a distributed battery balancing system and method based on fractional-order dynamics estimation for a lithium battery pack (power battery pack). On the traditional battery model, it is improved to an estimation model based on fractional-order dynamics, as well as a calculation method and balancing strategy for the SOC change rate. The digitally controlled balancing circuit used in the present invention is more conducive to the implementation of complex balancing control strategies. It is based on the single-cell balancing module of the Buck-Boost converter and is constructed using an A-C2C balancing architecture. The BMS estimates the SOC based on the voltage and temperature data, and calculates the balancing current required for each single-cell balancing module, and then sends the corresponding balancing instruction to the single-cell balancing circuit, and finally the corresponding single-cell balancing circuit completes the corresponding action. The calculation process of the present invention is simple, the error is small, and the control accuracy of each balancing circuit is higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a simplified principle block diagram of the monomer balancing module of the present invention;

[0060] Figure 2 It is a simplified structural block diagram of the system of the present invention;

[0061] Figure 3 is an equivalent model diagram of the fractional-order electrochemical power battery;

[0062] Figure 4 It is a schematic diagram of the steps of the iterative method for estimating battery SOC under the fractional order model;

[0063] Figure 5 It is the BMS control block diagram;

[0064] Figure 6 is the a-SOC identification table;

[0065] Figure 7 is the Q-SOC identification table;

[0066] Figure 8 is a diagram showing the effect of performing SOC estimation and actual SOC according to the fractional order model in the embodiment;

[0067] Fig. 9 It is a diagram showing the effect of performing balancing current estimation based on a fractional-order model and the balancing current actually required in the embodiment. DETAILED DESCRIPTION

[0068] like Figure 2As shown in the figure, in the present invention, the distributed battery balancing system includes a BMS, which is based on a single-cell balancing module of a Buck-Boost converter and is constructed using an A-C2C balancing architecture. Assuming that the battery pack is composed of i batteries in series, the number of single-cell balancing modules is i-1, and the i-1 single-cell balancing modules are connected in series from E1 to E2. i-1 The x-th single-cell balancing module is respectively connected to the two ends of the x-th and x+1-th batteries connected in series and the series connection point of the x-th and x+1-th batteries, wherein 1≤x≤i-1, and x and i are both natural numbers. Each single-cell balancing module communicates with the BMS through a CAN bus. The BMS estimates the SOC according to the voltage and temperature data of the battery, and calculates the balancing current required by each single-cell balancing module, and then sends the corresponding balancing instruction to the single-cell balancing module, and finally the corresponding single-cell balancing module completes the corresponding balancing action.

[0069] like Figure 1 As shown, the single-cell balancing module based on the Buck-Boost converter is composed of an MCU, a driver, a first field effect transistor QiH, a second field effect transistor QiL, an inductor Li and a comparator, wherein the BMS monitors the voltage and temperature information of the battery; V1 and V2 are the voltages of the two batteries, which are sent to the BMS for programmed judgment, and then the corresponding balancing current value i_ref is calculated, and sent to the balancing module with the corresponding module number through the CAN bus. The digitally controlled balancing circuit of the present invention is more conducive to realizing complex balancing control strategies. The BMS can monitor the voltage and temperature information of the battery; V1 and V2 will be sent to the BMS for programmed judgment, and then the corresponding balancing current value i_ref will be calculated, and sent to the balancing module with the corresponding module number through the CAN bus. Then, the balancing module will work with the specified balancing current to complete this balancing action. In this embodiment, the driver realizes amplification and electrical isolation of the control signal sent by the controller, which can be realized by circuit implementation or chip control, such as IXDN609SI, UCC21520, etc., depending on the specific solution. The comparator uses a classic comparator, and a voltage follower is connected in series to increase reliability.

[0070] The method for balancing a battery pack using the distributed battery balancing system based on fractional-order kinetic estimation comprises the following steps:

[0071] a. Replace the ideal capacitor in the first-order RC model with a fractional-order capacitor and establish a fractional-order electrochemical kinetic equivalent model for the battery. In this fractional-order electrochemical kinetic equivalent model, represents the open circuit voltage source of the battery, which is a function of the battery temperature and state of charge; R0 Indicates the ohmic internal resistance of the battery, which is affected by factors such as electrolyte, diaphragm, active materials and temperature; R P Represents the Faraday impedance of the battery, which includes charge transfer impedance, diffusion mass transfer impedance and other impedances related to the basic process of the electrode; C d Reflects the double-layer characteristics of the interface and is expressed as fractional capacitance, using U d The polarization voltage across the RC circuit is expressed as I Indicates the current flowing through the battery. It is assumed to be positive during discharge and negative during charge. V(t) Indicates the terminal voltage of the battery.

[0072] Here, fractional-order capacitors are used to express the phenomenon of battery polarization. The impedance of fractional-order capacitors with fractional-order characteristics is defined as:

[0073] ,

[0074] Where Z is the impedance, is the impedance characteristic coefficient of the fractional capacitor, is the imaginary angular frequency, is the order of the fractional capacitor, The characteristics of the fractional capacitor are between resistance and capacitance. When the order of the fractional derivative approaches 0, its characteristics are closer to resistance; when the order of its fractional derivative approaches 1, its characteristics are closer to integer-order capacitors.

[0075] The state equation and output equation of the fractional-order electrochemical kinetic equivalent model are expressed as:

[0076] …… (1),

[0077] …… (2),

[0078] in, is a differential operator, representing the order of the fractional-order capacitor The operation process can be written as , Represents the impedance characteristic coefficient of fractional capacitor, jω is the imaginary number of the angular frequency.

[0079] b. Choose the Grunwald-letnikov definition to implement the fractional calculus process. The definition of Grunwald-letnikov fractional calculus is as follows:

[0080] …… (3),

[0081] In the above formula, GL is the abbreviation of Grunwald-letnikov, which is used as the superscript of fractional differentials. is the order of the fractional capacitor, t0 represents the starting time, f(t) represents the function to be fractionally differentiated or integrated, f ( t ) is a variable t A function is a differentiable (for derivatives) or integrable (for integrals) mathematical object defined in time or space. h represents the step size, t represents the battery discharge time, and j represents an integer index used to represent the items in the difference sequence. In the Grunwald-Letnikov definition, it starts from 0 and increases to a certain value, which depends on the time point t considered and the step size h. is the generalized binomial coefficient.

[0082] In a microcomputer system, if the step size h is small enough and the limit operation in the formula is approximately ignored, the fractional derivatives and integrals under the Grunwald-Letnikov definition are directly calculated by the following formula:

[0083] …… (4),

[0084] in, is the coefficient of the binomial, and its recursive relationship is as follows:

[0085] ;

[0086] The polarization voltage across the RC circuit in the battery model is U d As a function of fractional differentiation or integration under the fractional definition of formula (4) f(t) ,right U d Perform fractional derivatives or integration to obtain the polarization voltage across the RC circuit using the Grunwald-letnikov fractional derivative. U d Numerical solution of .

[0087] c. According to formula (1) and formula (4), the discretized state equation of the equivalent circuit of the fractional-order model is expressed as:

[0088] …… (5),

[0089] Formula (5) can be further written as:

[0090] …… (6),

[0091] In the formula, at time t, ∈R is the state vector, ∈R is the system input;

[0092] in: , represents the fractional impedance, Q is the impedance characteristic coefficient of the fractional capacitor, where Q is a frequency-dependent As a function of the number of iterations n, Q is actually Identify the coefficient Q in the table, which is a function of n;

[0093] Discretize the output equation into:

[0094] …… (7),

[0095] in, ∈R is the system output,

[0096] Finally, from Eq. and Together they determine the discrete state equations and output equations of the fractional-order model.

[0097] d. Assume that the SOC of the battery is defined as follows:

[0098] …… (8),

[0099] In the formula, is the SOC at time t, is the initial SOC, is the Coulomb efficiency, which is the ratio of the battery discharge capacity to the charge capacity during the same cycle. is the battery capacity, is the current, and the discharge current in the formula is set to be positive.

[0100] e. Based on the discrete state equation, output equation and SOC definition of the above fractional-order model, the following is derived through computer modeling: Identification table and Identification table, where The identification table shows the relationship between the order of the fractional order model and the battery SOC. The identification table shows the relationship between the coefficients of the fractional order model and the battery SOC. Identification table and The parameter range in the identification table is selected according to the fitting results and battery characteristics. In this embodiment, the SOC of different α and Q values ​​under the fractional order model is usually modeled and calculated by tools such as matlab or Python. Then the model and test data are fitted to correct the parameters. There are many ways, such as gradient descent and Newton's method. The goal of fitting the model is usually to minimize a certain metric between the predicted value of the model and the actual observed value. For example, mean square error (MSE), cross entropy loss (Cross-Entropy Loss) and Hinge loss. This has ready-made toolboxes or function libraries in tools such as matlab and Python that are directly adopted.

[0101] f. Under the fractional order model, according to the above discrete state equation, output equation, Identification table and The identification table estimates the battery SOC value. Here, the specific steps of the iterative method for estimating the battery SOC under the fractional order model based on the discrete state equation and the output equation are as follows:

[0102] f1. Select the initial coefficient within the setting range , integers are usually chosen for convenience of calculation. According to the least squares method, when the coefficients are fixed to When , and from Identify the battery in the table ,

[0103] f2.According to Identification table, at known order and battery When , the coefficient is retrieved , let the coefficient Calculate according to the following formula

[0104] ;

[0105] f3. The coefficient Use as the new coefficient and repeat steps f1 and f2 until the coefficient and order converge to a fixed value, and the battery SOC is estimated.

[0106] g. After calculating the SOC of each single cell, calculate the range between adjacent cells and maintain the SOC between them to be consistent. In order to control the SOC change rate of each battery during charging, the current of each battery is balanced. It is calculated by the following formula:

[0107] ,

[0108] in,k i It is a parameter that reflects the inherent characteristics of the battery. It is determined by the properties of the battery itself and is not affected by the charge and discharge state or current size. k i The difference in the value directly leads to the difference in the rate of change of the SOC (state of charge) of each battery in the same battery pack. This difference usually manifests itself as a mismatch in battery capacity. This also explains why the imbalance problem in the battery pack is more common in battery packs that have been used for a certain period of time and show signs of aging. As the battery ages, k i The discrete degree will gradually increase. n is the number of batteries, I is the total current. The above formula is used to express the balancing current of each battery expected value.

[0109] In the A-C2C balancing architecture, the actual balancing current of the ith battery is obtained by Kirchhoff's law as the balancing current difference between two adjacent single-cell balancing modules;

[0110] The balancing current required for each single cell is calculated by the following formula:

[0111] ,

[0112] in, is the SOC value of each single battery, is the capacity of each single cell, For the equilibrium time, is the average SOC value of all modules, is the balancing current.

[0113] h. Each single-unit balancing module operates according to the calculated balancing current and finally completes the balancing action.

[0114] By obtaining the SOC of each single battery from the fractional-order model described above, the balancing current value required by each single battery balancing module can be estimated. Figure 5 The control block diagram of BMS is shown in Figure 1. Then each single cell balancing module will act according to the calculated balancing current.

[0115] like Figure 6 and Figure 7 As shown, the two figures show the a-SOC identification table and the Q-SOC identification table. The specific modeling process is obtained through computer simulation and modeling programming process. In specific implementation, ready-made toolboxes or function libraries can be used in tools such as matlab and Python for simulation and modeling.

[0116] According to the fractional order model, the tracking effect of SOC and balancing current is shown in Figure 8 shown. Figure 8 This is a tracking effect diagram of the SOC based on the fractional-order model. It can be seen that good estimation accuracy is maintained under Gaussian interference and nonlinear changes in random parameters.

[0117] Fig. 9 This is a calculation effect diagram of the balanced current based on the fractional-order model. It can be seen that good calculation accuracy is maintained under Gaussian interference and nonlinear changes in random parameters.

[0118] The present invention proposes a balancing strategy for a lithium battery pack (power battery pack) and a module design and system construction method thereof. Based on the traditional battery model, it is improved to an estimation model based on fractional-order dynamics, and the calculation method and balancing strategy of its SOC change rate are introduced. The balancing architecture of the present invention selects the A-C2C balancing architecture, and the topology mode selects the Buck-Boost converter as the single-cell balancing module. Compared with the traditional analog control scheme, the digitally controlled balancing circuit used in the present invention is more conducive to the implementation of complex balancing control strategies. In the present invention, the BMS adopts a fractional-order dynamic estimation method for the SOC estimation of the power battery to reduce the estimation error of the traditional battery model that gradually deviates from the original fractal state due to changes in aging and charge density.

[0119] Finally, it should be emphasized that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various changes and modifications. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for balancing a battery pack, wherein a distributed battery balancing system based on fractional-order dynamics estimation is used to balance the battery pack, wherein the distributed battery balancing system based on fractional-order dynamics estimation includes a BMS, which is based on a single-cell balancing module of a Buck-Boost converter and is constructed using an A-C2C balancing architecture. Assuming that the battery pack is composed of i batteries in series, the number of the single-cell balancing modules is i-1, and the i-1 single-cell balancing modules are connected in the order of E1 to E2. i-1 The x-th single-cell balancing module is respectively connected to the two ends of the x-th and x+1-th batteries connected in series and the series connection point of the x-th and x+1-th batteries, wherein 1≤x≤i-1, and x and i are both natural numbers, and each single-cell balancing module communicates with the BMS through a CAN bus. The BMS estimates the SOC according to the voltage and temperature data of the battery, and calculates the balancing current required by each single-cell balancing module, and then sends the corresponding balancing instruction to the single-cell balancing module, and finally the corresponding single-cell balancing module completes the corresponding balancing action; It is characterized in that The method comprises the following steps: a. Replace the ideal capacitor in the first-order RC model with a fractional-order capacitor and establish a fractional-order electrochemical kinetic equivalent model for the battery. In this fractional-order electrochemical kinetic equivalent model, The open circuit voltage source of the battery is represented by R 0 The ohmic internal resistance of the battery is expressed as R P The Faraday impedance of the battery is expressed as C d Reflects the double-layer characteristics of the interface and is expressed as fractional capacitance, using U d The polarization voltage across the RC circuit is expressed as I Indicates the current flowing through the battery. It is assumed to be positive during discharge and negative during charge. V(t) Represents the terminal voltage of the battery. The state equation and output equation of the equivalent model of fractional-order electrochemical kinetics are expressed as: ……（1）， ……（2）， in, is a differential operator, representing the order of the fractional capacitor The operation process can be written as , Represents the impedance characteristic coefficient of fractional capacitor, jω is the imaginary number of the angular frequency; b. Choose the Grunwald-letnikov definition to implement the fractional calculus process. The definition of Grunwald-letnikov fractional calculus is as follows: ……（3）， In the above formula, GL is the abbreviation of Grunwald-letnikov, which is used as the superscript of fractional differentials. is the order of the fractional capacitor, t0 represents the starting time, f(t) represents the function to be fractionally differentiated or integrated, h represents the step size, t represents the battery discharge time, j represents an integer index used to represent the item in the difference sequence, is the generalized binomial coefficient; When the step size h is chosen to be small enough, the limit operation in the formula is approximately ignored, and the fractional derivatives and integrals under the Grunwald-Letnikov definition are directly calculated by the following formula: ……（4）， in, is the coefficient of the binomial, and its recursive relationship is as follows: ； The polarization voltage across the RC circuit in the battery model is U d As a function of fractional differentiation or integration under the fractional definition of formula (4) f(t) ,right U d Perform fractional derivatives or integration to obtain the polarization voltage across the RC circuit using the Grunwald-letnikov fractional derivative. U d Numerical solution of ; c. According to formula (1) and formula (4), the discretized state equation of the equivalent circuit of the fractional-order model is expressed as: ……（5）， Formula (5) can be further written as: ……（6）， In the formula, at time t, ∈R is the state vector, ∈R is the system input; in: , represents the fractional impedance, Q is the impedance characteristic coefficient of the fractional capacitor; Discretize the output equation into: ……（7）， in, ∈R is the system output, Finally, from Eq. and jointly determine the discrete state equations and output equations of the fractional order model; d. Assume that the SOC of the battery is defined as follows: ……（8）， In the formula, is the SOC at time t, is the initial SOC, is the Coulomb efficiency, is the battery capacity, is the current, and the discharge current in the formula is set to be positive; e. Based on the discrete state equation, output equation and SOC definition of the above-mentioned fractional-order model, the following is derived through computer modeling: Identification table and Identification table, where The identification table shows the relationship between the order of the fractional order model and the battery SOC. The identification table shows the relationship between the coefficients of the fractional order model and the battery SOC. Identification table and The parameter ranges in the identification table are selected based on the fitting results and battery characteristics; f. Under the fractional order model, according to the above discrete state equation, output equation, Identification table and The identification table estimates the battery SOC value; g. After calculating the SOC of each single cell, calculate the range between adjacent cells and maintain the SOC between them to be consistent. In order to control the SOC change rate of each battery during charging, the current of each battery is balanced. It is calculated by the following formula: ， in, k i It is a parameter reflecting the inherent characteristics of the battery, n is the number of batteries, and I is the total current; In the A-C2C balancing architecture, the actual balancing current of the ith battery is obtained by Kirchhoff's law as the balancing current difference between two adjacent single-cell balancing modules; The balancing current required for each single cell is calculated by the following formula: ， in, is the SOC value of each single battery, is the capacity of each single cell, For the equilibrium time, is the average SOC value of all modules, is the balancing current; h. Each single-unit balancing module operates according to the calculated balancing current and finally completes the balancing action.

2. A method for balancing a battery pack according to claim 1, characterized in that: The specific steps of step f are as follows: f1. Select the initial coefficient within the setting range , according to the least squares method, when the coefficients are fixed to When , and from Identify the battery in the table , f2.According to Identification table, at known order and battery When , the coefficient is retrieved , let the coefficient Calculate according to the following formula ； f3. The coefficient Use as the new coefficient and repeat steps f1 and f2 until the coefficient and order converge to a fixed value, and the battery SOC is estimated.

3. A method for balancing a battery pack according to claim 1, characterized in that: In step a, the impedance of the fractional-order capacitor with fractional-order characteristics is defined as: ， Where Z is the impedance, is the impedance characteristic coefficient of the fractional capacitor, is the imaginary angular frequency, is the order of the fractional capacitor, , the characteristics of the fractional capacitor are between the resistor and the capacitor, and when the order of the fractional derivative approaches 0, its characteristics are closer to the resistor; When the order of its fractional derivative approaches 1, the characteristics are closer to those of an integer-order capacitor.

4. A method for balancing a battery pack according to claim 1, characterized in that: The single-cell balancing module based on Buck-Boost converter is composed of MCU, driver, first field effect transistor (QiH), second field effect transistor (QiL), inductor (Li) and comparator, wherein the BMS monitors the voltage and temperature information of the battery; V1 and V2 are set as the voltages of the two batteries, which are sent to the BMS for judgment, and the corresponding balancing current value i_ref is obtained, and is sent to the single-cell balancing module with the corresponding module number through the CAN bus.

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