A method for constructing a lithium battery voltage model based on fractional-order transfer function

Abstract

The present invention discloses a method for constructing a lithium battery voltage model based on a fractional-order transfer function, the method comprising: step one, the fractional-order transfer function can select one or two fractional-order transfer functions; step two, the order configuration of the fractional-order transfer function is performed, and the variables other than the analytical solution of the fractional-order transfer function in the lithium battery state equation are converted into constants to calculate the initial values ​​of the parameters; step three, the analytical solution parameters are assigned to obtain the influence of the parameter change on the analytical solution value; step four, the optimal transfer function is selected from one or two fractional-order transfer functions based on the comprehensive fitting accuracy and model complexity to configure the model; step five, the integer-order approximation of the fractional-order transfer function model is realized by using an improved Oustaloup filter, and the model is transplanted on multiple platforms. The beneficial effect of the present invention is that the above method can effectively solve the technical problem of poor accuracy of the voltage output characteristics of the existing lithium battery equivalent circuit model.

Description

Technical Field

[0001] The present invention relates to the technical field of voltage model construction for lithium battery detection of electric vehicles, and in particular to a lithium battery voltage model construction method based on fractional-order transfer function. Background Art

[0002] With the increasing popularity of new energy electric vehicles, the detection of the status of electric vehicles is particularly important, especially the detection of the status of the power module of electric vehicles. Since the power of electric vehicles mainly comes from batteries, the battery management system is the core of the power module of electric vehicles. An accurate and efficient lithium battery model is crucial to the operation of the battery management system, which plays a key role in diagnosing the current status of lithium batteries. It is of great significance to extend the life of the battery pack, balance the inconsistency between monomers, improve the energy utilization rate of the vehicle, and reduce the risk of spontaneous combustion.

[0003] However, the internal mechanism of lithium batteries is complex. Although the electrochemical model is highly accurate, it has too many parameters and is not suitable for vehicle-mounted battery management systems. The black box model that incorporates neural networks does not require research on the internal mechanism of the battery, but requires a large amount of data training in the early stages, and the training cost is high. Although the equivalent circuit model is simple, the output voltage characteristics have major defects. There will be obvious voltage inflection points at the beginning and end of charging and discharging, and because the recovery voltage of the traditional equivalent circuit model is lower than the actual value, errors will accumulate under working conditions. Summary of the invention

[0004] The purpose of the present invention is to solve the above problems and to design a lithium battery voltage model construction method based on fractional-order transfer function, which is suitable for power lithium batteries with a terminal voltage range of 2.5V to 4.2V.

[0005] A method for constructing a lithium battery voltage model based on a fractional-order transfer function, the method comprising the following steps:

[0006] Step 1: Use HPPC test to obtain the characteristic data of lithium battery input current and output voltage, and record the relationship between open circuit voltage and SOC after one hour of standing still after discharge. Use the least squares method and fifth-order polynomial to fit U oc Correspondence with SOC;

[0007] Construct one and two fractional-order transfer functions, as shown in equations (1) and (2), a n , b, c n are unknown parameters respectively, and the hyperparameters α and β are fractional orders in the interval (0, 1):

[0008]

[0009]

[0010] Step 2: Introduce fractional calculus - Letnikov definition, perform inverse Laplace transform on one- and two-term fractional transfer functions, assign orders and calculate initial values;

[0011] The Laplace inverse transform analytical solution of formula (1) after the term is shifted is:

[0012]

[0013] Similarly, the Laplace inverse transform analytical solution of the shifted term in equation (2) is:

[0014]

[0015] The state equation of the discharge process of the fractional-order transfer function model is:

[0016]

[0017] Where k = 1 or 2, ΔU c is the voltage mutation value;

[0018] The hyperparameters α and β are in the interval (0, 1). Exceeding the interval will easily cause the analytical solution to diverge. Taking k = 2 in formula (5) as an example, replace U in formula (5) OC The polynomial formed by shifting the terms of R0I is set to a constant Q c , construct the system of equations:

[0019]

[0020] According to the experimental data obtained, let the hyperparameters α = 0.4, β = 0.1, and substitute them into equation (6); take two moments t = 1 and 0.1, and get the equation system:

[0021]

[0022] According to formula (7), we can obtain a set of initial values ​​of parameters a2=139, b=2.7, c2=4.5 of formula (3), so that U in formula (3) g2 (t) is in a convergent state in the interval [0, 20τ1] and exhibits power function characteristics, and the initial value is established;

[0023] Similarly, the initial values ​​of the parameters of formula (4) are a1=139, c1=4.5;

[0024] Step 3: Identification analysis from the perspective of numerical optimization:

[0025]

[0026] Because U gk(t) function has a high complexity. It is difficult to search for parameter iteration direction directly by calculating vector differential operators. Combining the analytical solution characteristics of equations (3) and (4), a n The value is the denominator of each item, b, c n For each molecule, a n and b, c n The influence of the change on the analytical solution, and the parameter iteration direction is summarized by three iterations;

[0027] U g2 The sensitivity to the change of a2 value is low, and the iteration step range is selected in the interval (0, 1); the sensitivity to the change of b and c2 values ​​is high, and the iteration step range is selected in the interval (0, 0.1). In order to ensure good convergence, the parameter segmentation identification is performed, and the number of iterations is 200 or the error ΔU max The iteration is terminated when ε is less than 0.02.

[0028] Step 4: Compare the fitting accuracy of the analytical solutions of one fractional-order transfer function and two fractional-order transfer functions, and select the optimal G according to the parameter complexity. k (S) Modular scheme;

[0029] Three SOC intervals are selected for fitting analysis. A certain span should be ensured between the SOC intervals. When the absolute error of fitting between one or two fractional-order transfer functions and the experimental data does not exceed 2%, one fractional-order transfer function should be selected. When the absolute error exceeds 2%, two fractional-order transfer functions will be considered. Two sets of parameters are used to configure the discharge process and voltage recovery process of the fractional-order transfer function model respectively. Based on the negative response of the fractional-order transfer function, the parameters of the voltage drop curve in the discharge stage are identified; based on the positive response of the fractional-order transfer function, the parameters of the voltage recovery curve in the static stage are identified.

[0030] Step 5: construct a fractional-order filter. The mathematical model of the filter is:

[0031]

[0032] Where m and n are weighted parameters; the zero poles and gain are:

[0033]

[0034] Where μ is the order of the fractional operator, ω1 and ω h are the upper and lower limits of the frequency band selected according to requirements, and N is the filter order;

[0035] The fractional-order transfer function is approximated by integer order through the above filter method. To ensure the high-order approximation effect, the filter order is N; the step response time is long, and a lower frequency band lower limit is selected; to ensure the approximation effect at the initial moment, a higher frequency band upper limit is selected;

[0036] The fractional-order parameters obtained by step 3 identification are input into the selected fractional-order transfer function, and the fractional-order transfer function is input into the improved Oustaloup filter for integer-order approximation to obtain an N-th order integer-order transfer function.

[0037] Among them, the step 1 is to reduce the U caused by different charge and discharge states. oc -SOC error, the mean value of the charge and discharge open circuit voltage is used for parameter identification.

[0038] Beneficial Effects

[0039] The method for constructing a lithium battery terminal voltage model based on a fractional-order transfer function produced by the technical solution of the present invention has the following advantages:

[0040] This method uses a fractional-order transfer function to establish an equivalent model based on the RC equivalent circuit model. This model can better solve the problem of poor accuracy of the voltage output characteristics of the lithium battery equivalent circuit model. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a graph of HPPC experimental data required for establishing the lithium voltage model of the present invention;

[0042] Figure 2 It is an equivalent model diagram of the fractional-order transfer function of the lithium battery of the present invention;

[0043] Figure 3 It is a characteristic diagram of variable parameter output value of the fractional order transfer function of the present invention;

[0044] Figure 4 is the parameter identification flow chart of the present invention;

[0045] Figure 5 This is a comparison chart of the fitting effects of one-order and two-order fractional transfer functions;

[0046] Figure 6 This is a comparison chart of the output effects of the fractional-order transfer function model and the second-order RC model based on a 0.5C current;

[0047] Figure 7 This is the output effect diagram of the fractional order filter;

[0048] Figure 8 This is a comparison chart of the output effect verification of the fractional-order transfer function model and the second-order RC model based on a 1.25C high current;

[0049] Fig. 9 is a relationship table between the open circuit voltage and the SOC of the present invention;

[0050] Fig.10 It is a fractional-order transfer function model parameter identification result table described in the present invention. DETAILED DESCRIPTION

[0051] The present invention will be described in detail below in conjunction with the accompanying drawings. Figure 1-10 As shown;

[0052] The innovation of the present application is to construct one-term and two-term fractional-order transfer functions, as shown in equations (1) and (2):

[0053]

[0054]

[0055] Perform inverse Laplace transform on one- and two-term fractional-order transfer functions, configure the order and calculate the initial value;

[0056] Introducing fractional calculus -Letnikov definition:

[0057]

[0058] Fractional Laplace transform formula:

[0059]

[0060] The two-parameter Mittag-Leffler function has the form:

[0061]

[0062] The Gamma function is:

[0063]

[0064] Combining equations (3) to (6), the Laplace inverse transform analytical solution of equation (1) after the term shift is calculated as:

[0065]

[0066] Similarly, the Laplace inverse transform analytical solution of the shifted term in equation (2) is:

[0067]

[0068] The state equation of the discharge process of the fractional-order transfer function model is:

[0069]

[0070] Where k = 1 or 2, ΔU c is the voltage mutation value;

[0071] For α and β, the values ​​are in the interval [0, 1]. If the values ​​are outside the interval, the analytical solution may diverge. Taking k = 2 in equation (9) as an example, in order to find the initial value of stable convergence, U in equation (9) is OC The polynomial formed by shifting the terms of R0I is set to a constant Q c , construct the system of equations:

[0072]

[0073] Let α = 0.4, β = 0.1, substitute into equation (10); take two moments t = 1, 0.1, and get the equation system:

[0074]

[0075] According to formula (11), we can obtain a set of initial parameter values ​​of formula (8) a2 = 139, b2 = 2.7, c2 = 4.5, so that U in formula (8) g2 (t) is in a convergent state in the interval [0, 20τ1] and exhibits power function characteristics, and the initial value is established;

[0076] Similarly, the initial values ​​of the parameters of formula (7) are a1=139, c1=4.5;

[0077] Identification analysis from the perspective of numerical optimization:

[0078]

[0079] Where θ is the decision vector composed of the optimization model parameters:

[0080] θ=[δ1,δ2,δ3...δ n ] (13)

[0081] Because U gk (t) function has a high complexity. It is difficult to search for parameter iteration direction directly by calculating vector differential operators. Combining the analytical solution characteristics of equations (7) and (8), a n The value is the denominator of each item, b, c n For each molecule, a n and b, c n The influence of the change on the analytical solution is summarized by three iterations. At the same time, in order to facilitate the parameter identification of the terminal voltage data during the discharge process of the lithium battery, -U gk (t) conducting analysis;

[0082] According to experimental data, U g2 The sensitivity to the change of a2 value is low, and the iteration step size is selected as 0.5; the sensitivity to the change of b and c2 values ​​is high, and the step size should be selected as 0.05. To ensure good convergence, the parameter segmentation identification is performed, and the number of iterations is 200 or the error ΔU max The iteration is terminated when <ε, ε can be set to 0.01;

[0083] Compare the fitting accuracy of the analytical solutions of one fractional-order transfer function and two fractional-order transfer functions, and select the optimal G based on the parameter complexity. k (S) Modular scheme;

[0084] Three SOC intervals are selected for fitting analysis, and the SOC intervals are [90%, 80%], [50%, 40%], and [20%, 10%] respectively. When the fitting error between the two does not exceed 2%, a fractional-order transfer function should be selected. Figure 5 The relative error of the fitting effects of the two fractional-order transfer functions shown is less than 2%, so a fractional-order transfer function is selected for model configuration, and the parameter identification results are:

[0085] Two sets of parameters are used to configure the discharge process and voltage recovery process of a fractional-order transfer function model respectively. The discharge process parameters are given in Table 2, so only the voltage recovery process parameters need to be configured. Based on the positive response of the fractional-order transfer function, the voltage recovery curve in the static stage is identified by parameters, and the state equation is:

[0086] U(t)=U g1 (t)+U OC (soc) (14)

[0087] With 90% SOC as the starting state, 0.25C constant current discharge for 1440s and rest for 4000s; a fractional order model is used to fit the rest process, and the parameter identification results are: a = 131.5, c = 10.7;

[0088] Construct a fractional-order filter, and the mathematical model of the filter is:

[0089]

[0090] Where m and n are weighted parameters; the zero poles and gain are:

[0091]

[0092] Where μ is the order of the fractional operator, ω1 and ω h are the upper and lower limits of the frequency band selected according to requirements, and N is the filter order;

[0093] The fractional-order transfer function is approximated by integer order through the above filter method. To ensure the high-order approximation effect, the filter order N = 9; the step response time is long, so a lower frequency band lower limit is selected; to ensure the approximation effect at the initial moment, a higher frequency band upper limit is selected, and the frequency band upper and lower limits are 10 -8 ~10 8 (rad / s);

[0094] Input the parameters a1 and c1 identified by equation (14) into a fractional-order transfer function:

[0095]

[0096] Input equation (17) into the improved Oustaloup filter and we get:

[0097]

[0098] Example 1

[0099] The above fractional-order model is verified under the condition of room temperature 26°C and a fast discharge experiment of lithium battery is carried out with a large current of 1.25C. The lithium battery SOC is discharged from 100% to 0%, and the battery terminal voltage data U is extracted. The second-order RC model and a fractional-order model are used for verification.

[0100] The specific method is: discharge for 50 minutes and then stand for 25 minutes. In the discharge stage, the voltage fitted by the fractional-order model is smoother than the voltage fitted by the second-order RC model in [0, 50s], and the error is within 0.08V. After 3000s, it enters the standstill stage. The voltage transition of the fractional-order model is smooth, with good output characteristics, and the relative error is reduced by 8.9% compared with the second-order RC model.

[0101] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions. The sentence "includes an element defined by ... does not exclude the existence of other identical elements in the process, method, article or device including the element".

[0102] The above technical solutions only reflect the preferred technical solutions of the technical solutions of the present invention. Some changes that may be made to certain parts thereof by technicians in this technical field all reflect the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. A method for constructing a lithium battery voltage model based on a fractional-order transfer function, characterized in that: The method comprises the following steps: Step 1: the fractional order transfer function may select one fractional order transfer function or two fractional order transfer functions; Step 2: Perform order configuration of the fractional transfer function in the interval (0, 1), and convert the variables in the lithium battery state equation except the fractional analytical solution order transfer function into constants to calculate the initial values ​​of the parameters; Step 3: Assign values ​​to the analytical solution parameters to obtain the influence of parameter changes on the analytical solution values, and perform parameter identification based on the gradient descent method according to this feature; Step 4, comprehensively consider the fitting accuracy and model complexity to select the optimal transfer function from one or two fractional-order transfer functions to configure the model; Step 5, using the improved Oustal oup filter to realize the integer-order approximation of the fractional-order transfer function model, and realize the model multi-platform transplantation; In the step 1, the characteristic data of the input current and output voltage of the lithium battery are obtained by HPPC test, and the relationship between the open circuit voltage and SOC after standing for one hour after discharge is recorded. The least squares method and the fifth-order polynomial fitting U oc Correspondence with SOC; In step 1, the U oc -SOC error, using the mean value of the charge and discharge open circuit voltage for parameter identification; Construct one and two fractional-order transfer functions, as shown in equations (1) and (2), a n , b, c n are unknown parameters (n=1, 2), α and β are fractional orders in the interval (0, 1): In step 2, fractional calculus is introduced for one and two fractional transfer functions. ld-Letnikov definition, perform Laplace inverse transform, configure the specific values ​​of fractional orders α and β, substitute the analytical expression into the lithium battery state equation, and calculate the initial values ​​of the denominator an, b, and cn parameters; In step 3, identification analysis is performed from the perspective of numerical optimization. gk (t) The function has a high complexity. It is difficult to search for the parameter iteration direction directly by calculating the vector differential operator. Combining the characteristics of the time domain analytical solution of the fractional-order transfer function, the influence of parameter changes on the analytical solution is analyzed separately, and the parameter iteration direction is summarized by the three-time parameter reduction iteration scheme. In step 4, the fitting accuracy of one fractional-order transfer function and two fractional-order transfer function analytical solutions are compared, and the optimal G is selected in combination with the parameter complexity. k (S) Module solution: select three SOC intervals for fitting analysis. When the absolute fitting error between one fractional-order transfer function analytical solution and two fractional-order transfer function analytical solutions does not exceed 2%, one fractional-order transfer function should be selected. When the absolute error exceeds 2%, consider using two fractional-order transfer functions.

2. The method for constructing a lithium battery voltage model based on a fractional-order transfer function according to claim 1, characterized in that: In the step five, a fractional-order filter is constructed, and the fractional-order transfer function is approximated by an integer order through a filter method. The fractional-order filter selected by this method is an improved Oustaloup filter.

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