A lithium battery parameter identification method based on innovation increment detection least square method

Abstract

The present application relates to lithium battery parameter identification technical field, disclose a kind of lithium battery parameter identification method based on innovation increment detection least square method, step one: setting the active autoregressive model of single-input single-output system to be identified:step two: setting error vector, set evaluation function;Wherein, the minimum value of evaluation function is obtained when the estimated value is least square estimate;Step three: initialization is carried out to autoregressive model, from the k time, the value of k-1 time and k-2 time is initialized, and the observed vector and the estimated vector are calculated;Step four: update gain factor and the value of the covariance matrix of observation matrix;Step five: calculate innovation and innovation increment, define characteristic parameter for judging whether to modify forgetting factor, when characteristic parameter is greater than zero, modify forgetting factor;Step six: calculate the estimated vector, recursive least square estimate calculation formula, solve the battery parameter of each step based on innovation increment detection least square method.

Description

Technical Field

[0001] This invention relates to the field of lithium battery parameter identification technology, specifically to a lithium battery parameter identification method based on the least squares method of innovation increment detection. Background Technology

[0002] In recent years, traditional gasoline-powered vehicles, which rely on fossil fuels for energy, have been gradually phased out of the market due to their consumption of large amounts of non-renewable energy and the resulting exhaust emissions, which have become a major source of urban environmental pollution. Electric vehicles, as an environmentally friendly mode of transportation, are beginning to gradually replace traditional gasoline-powered vehicles. The State of Charge (SOC) of an electric vehicle's battery is a crucial aspect of electric vehicle technology development, as it is equivalent to the fuel gauge in a gasoline vehicle and is a vital parameter of the electric vehicle's battery management system. Its accuracy directly affects the vehicle's energy management control strategy and the electric vehicle's performance, thus impacting vehicle reliability and cost. A suitable battery model is the foundation and key to SOC estimation. Utilizing a battery model can effectively reflect the correspondence between external battery parameters and the battery's internal state. By establishing an accurate battery model and employing precise battery SOC estimation methods, it is possible to improve the vehicle's energy management control strategy and the electric vehicle's performance, which is of great significance for the simulation, design, and optimization of electric vehicles. Regarding battery system modeling, low-order RC models, with fewer parameters, cannot accurately describe battery characteristics, while high-order RC models have too many parameters, resulting in complex calculations and the potential for overfitting. Currently, the second-order Thevenin equivalent circuit model is commonly used. For parameter identification of the second-order Thevenin equivalent circuit model, the most commonly used method is the Exponentially Weighted Recursive Least Square (EWRLS) method proposed by JDPark. However, its application in parameter identification for lithium batteries has the following problems:

[0003] (1) In actual lithium battery SOC estimation, the innovation is usually small, which causes the forgetting factor update formula to fail and lose its effect on correcting the parameters.

[0004] (2) It is difficult to obtain a suitable value for the sensitivity gain. When the sensitivity gain is too large, although it has good tracking characteristics for significant changes in the system, it will amplify the impact of noise on the system, resulting in an increase in parameter identification error. When the sensitivity gain is too small, it can obtain high accuracy under stable continuous input, but it cannot cope with large changes in the system.

[0005] (3) The algorithm updates the forgetting factor in each iteration, but lacks a suitable evaluation mechanism to determine whether the calculated forgetting factor has a positive effect on the convergence of the system error.

[0006] This invention addresses the shortcomings of the EWRLS algorithm by proposing a least squares method based on innovation increment detection optimization for parameter identification of the second-order Thevenin equivalent circuit model of a battery, starting from the determination of innovation increment. Summary of the Invention

[0007] The purpose of this invention is to provide a lithium battery parameter identification method based on innovation increment detection least squares method. Based on the EWRLS algorithm, a lithium battery parameter identification method based on innovation threshold detection least squares method is proposed.

[0008] The objective of this invention can be achieved through the following technical solutions:

[0009] A lithium battery parameter identification method based on innovation increment detection least squares is proposed, wherein the auto-regressive with extra inputs (ARX) model of the single-input single-output system to be identified is defined as follows:

[0010] (1)

[0011] in:

[0012] (2)

[0013] (3)

[0014] The ARX model is a time series analysis method that estimates the output y at time k based on the input-output quantities k-1 times prior to time k. It can also be written in the following form:

[0015] (4)

[0016] Step 2: Define the error vector Evaluation function for:

[0017] (5)

[0018] (6)

[0019] Wherein the error Let N be the difference between the output and the estimate, and N be the total number of measurements. Make the evaluation function... The estimated value obtained when the minimum value is reached This is the least squares estimate. Therefore, the evaluation function... right Differentiate:

[0020] (7)

[0021] when When it is a regular matrix, the least squares estimate is obtained. for:

[0022] (8)

[0023] Step 3: Initialize before starting the algorithm.

[0024] Initialize the forgetting factor ,for and Assigning initial values ​​typically involves setting the initial value of the covariance matrix. Least squares estimate .in Let be the identity matrix, and 'a' be a very large real number. Assume the algorithm starts from the ... Starting from the next step, initialize the first... Second and third The value of the second time.

[0025] Step 4: Calculation and .

[0026] Based on the parameters calculated in the previous step and the system described by equation (4), we have

[0027] (9)

[0028] in, It is the observation vector. The vector being estimated can be represented as:

[0029] (10)

[0030] in, For system output, For system input, For the error. Assuming the measurement process occurs N times in total starting from time n, it can be rewritten as:

[0031] (11)

[0032] in, It is the output vector. It is a noise vector. It is the observation matrix, as shown in formulas (1.8) and (1.9).

[0033] (12)

[0034] (13)

[0035] Step 5: Update the gain factor The covariance matrix of the observation matrix The value of .

[0036] The update formulas are shown in equations (14) and (15) below:

[0037] (14)

[0038] (15)

[0039] Step 6: Calculate the new information and the new information increment, and define the characteristic parameters. Used to determine whether to correct the forgetting factor.

[0040] Define the information during system operation It is the difference between the observed measurement and the predicted measurement, where the predicted measurement is calculated from the current prior state estimate, which in turn is calculated from the previous posterior state estimate. The formula is defined as shown in (15).

[0041] (15)

[0042] The increment of new information is defined by the following formula:

[0043] (16)

[0044] This is the innovation increment, representing the difference between the innovation value at the k-th iteration and the innovation value at the (k-1)-th iteration. However, relying solely on the innovation increment to determine whether the system is moving towards reducing error is unreasonable. For example, define the innovation value as follows:

[0045] (17)

[0046] In this example, the information increment is as follows:

[0047] (18)

[0048] It is easy to see that the systematic error decreases from the (k-1)th iteration to the kth iteration. From the kth iteration to the (k+1)th iteration, the systematic error first decreases to 0 and then increases to 1. However, the increment of the information cannot reflect this increase in error. Therefore, a characteristic parameter is introduced. Its definition is as follows:

[0049] (19)

[0050] When the feature parameters At this point, we believe that the new information, whether positive or negative, tends to increase, meaning the system error is continuously expanding. Therefore, it is necessary to adjust the forgetting factor at this stage. Make adjustments to reduce its size to improve the system's fast tracking performance. Conversely, when the characteristic parameters... At this point, we assume that the information decreases continuously as the recursion progresses, and the forgetting factor is appropriate. We inherit the forgetting factor from the previous recursion and do not change it.

[0051] Step 7: Calculate the characteristic parameters from Step 6. At that time, the forgetting factor is modified according to the formula.

[0052] To obtain a suitable forgetting factor value, the following formula is proposed for its calculation:

[0053] (20)

[0054] In the formula It is new information. All are constants. To achieve minimum precision in the information, different values ​​can be used to adapt to different data and parameter identification scenarios. The values ​​of the constants in the forgetting factor evaluation function can be changed according to different needs to improve algorithm performance. The basic principles of parameter selection are analyzed below.

[0055] Choose one of the three different sets of parameters from Table 1, such as Figure 2 As shown, different image analyses are performed. The value of this parameter will affect the value of the forgetting factor in the system, so that it can be used as a reference when using this method for parameter identification with different data. It should be noted that... A value of 0.001 is typically chosen to amplify the information and prevent it from being too small, which could cause the algorithm to fail.

[0056] Table 1. Parameter selection values ​​for the forgetting factor formula.

[0057]

[0058] Figure 2 The study demonstrates the variation trends of the forgetting factor under three different parameters, restricting the domain of the new information to [-10, 10]. Different change patterns in the expected forgetting factor values ​​are observed when the error value is large. For example, when the error value is large, such as... Figure 2 When the mean square error is -7.575, a relatively small forgetting factor value must be maintained to reduce the weight of historical data; different forgetting factor values ​​are obtained by substituting the new value into a function with different parameters: When a data point falls within the light blue area of ​​the graph, it indicates a smaller AFFRLS error. In this case, we want the forgetting factor value to be closer to 1. In summary, and It largely meets the requirements for changes in the forgetting factor.

[0059] Step 8: Calculation And according to calculate .

[0060] The formula for calculating the recursive least squares estimate is:

[0061] (twenty one)

[0062] Battery parameter identification typically uses the equivalent circuit diagram of a second-order Thevenin equivalent circuit model, as shown in Figure 3.

[0063] in, It is the open-circuit voltage, which characterizes the potential difference between the positive and negative electrodes when no current flows through the battery, i.e., the equilibrium electrode potential. It is the internal resistance in ohms, which characterizes the contact resistance of the electrode materials, electrolyte, and separator of the power battery. It can cause a jump in the terminal voltage when current flows through it. and These are the electrochemical polarization internal resistance and the electrochemical polarization capacitance, respectively. and These are the concentration range internal resistance and concentration range capacitance, respectively. This is the electrochemical polarization voltage; It is the concentration gradient polarization voltage; its mathematical model can be described as:

[0064] (twenty two)

[0065] (twenty three)

[0066] Discretizing the above two equations and performing a Laplace transform yields:

[0067] (twenty four)

[0068] The system's transfer function is:

[0069] (25)

[0070] in, The transfer function is discretized using the bilinear transform principle. The bilinear transform expression and the discrete transfer function are as follows:

[0071] (26)

[0072] (27)

[0073] The difference equation is calculated according to equation (24):

[0074] (28)

[0075] According to equations (9) and (10):

[0076] (29)

[0077] The expression for the bilinear inverse transform is:

[0078] (30)

[0079] The discrete transfer function undergoes a bilinear inverse transform, and equation (25) can be transformed into:

[0080] (31)

[0081] Comparing equations (23) and (25), we can obtain:

[0082] (32)

[0083] After rearranging the above equation, we get:

[0084] (33)

[0085] Step 9: At this point, one iteration of the algorithm is complete. Following these steps, the battery parameters for each step can be solved using the least squares method based on incremental innovation detection.

[0086] The beneficial effects of this invention are as follows: The charge and discharge data of lithium iron phosphate batteries under the same group were used to identify circuit parameters using the proposed incremental detection least squares method, forgetting factor recursive least squares (FFRLS), and exponentially weighted recursive least squares (EWRLS). Unstable data with a SOC below 20% were removed. The relationship curve between open-circuit voltage and battery capacity was fitted to a polynomial of SOC using a built-in MATLAB function. This significantly improved both the speed and accuracy of the identification. Attached Figure Description

[0087] The invention will now be further described with reference to the accompanying drawings.

[0088] Figure 1This is a flowchart of a lithium battery parameter identification method based on the least squares method of innovation increment detection according to the present invention;

[0089] Figure 2 This is a graph showing the variation of the forgetting factor with innovation under different parameters in a lithium battery parameter identification method based on innovation increment detection least squares method of the present invention;

[0090] Figure 3 This is the equivalent circuit diagram of the second-order Thevenin model in the lithium battery parameter identification method based on the least squares method of innovation increment detection in this invention;

[0091] Figure 4 This is a graph showing the change in the forgetting factor during the parameter identification process of the least squares method based on the innovation increment detection method in the lithium battery parameter identification method of the present invention.

[0092] Figure 5 This is a comparison chart of the parameter identification errors of the innovation increment detection least squares method and the FFRLS algorithm in the lithium battery parameter identification method based on innovation increment detection least squares method of the present invention;

[0093] Figure 6 This is a comparison chart of parameter identification errors between the IVFFRLS algorithm and the EWRLS algorithm in a lithium battery parameter identification method based on the incremental detection least squares method of the present invention;

[0094] Figure 7 This invention relates to an open-circuit voltage curve in a lithium battery parameter identification method based on the least squares method of incremental information detection.

[0095] Figure 8 This invention relates to an ohmic internal resistance method for lithium battery parameter identification based on the least squares method of innovation increment detection. Identification results;

[0096] Figure 9 This invention relates to a lithium battery parameter identification method based on innovation increment detection least squares, specifically the polarization internal resistance. Identification results;

[0097] Figure 10 This invention relates to a lithium battery parameter identification method based on innovation increment detection least squares, specifically the polarization internal resistance. Identification results;

[0098] Figure 11 This invention relates to a lithium battery parameter identification method based on the least squares method of innovation increment detection, specifically the polarization capacitance. Identification results;

[0099] Figure 12This invention relates to a lithium battery parameter identification method based on the least squares method of innovation increment detection, specifically the polarization capacitance. Identification results. Detailed Implementation

[0100] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0101] Please see Figures 1-12 As shown, this invention is a lithium battery parameter identification method based on the innovation increment detection least squares method, comprising the following steps:

[0102] Step 1: Obtain the charge and discharge data of lithium iron phosphate batteries at room temperature (25℃). Import the data into MATLAB in the order of voltage, current, time, and temperature. Take the first 80% of the data for identification. The identification is inaccurate when the SOC is below 20%.

[0103] The total battery capacity is obtained by integrating the battery charging and discharging current with respect to time. Then, the state of charge (SOC) at each time is determined by the ampere-hour integration method. Finally, the polynomial relating the open-circuit voltage and the battery capacity is obtained by function fitting.

[0104] Step 2: Establish a second-order Thevenin equivalent circuit model of the battery, such as... Figure 7 As shown, where, Open-circuit voltage, representing the potential difference between the positive and negative electrodes of a battery when no current flows through it, i.e., the equilibrium electrode potential. The internal resistance in ohms characterizes the contact resistance of components such as electrode materials, electrolyte, and separator in a power battery. It causes a jump in terminal voltage when current flows through it. and These are the electrochemical polarization internal resistance and the electrochemical polarization capacitance, respectively. and These are the concentration range internal resistance and concentration range capacitance, respectively. This is the electrochemical polarization voltage; It is the concentration difference polarization voltage;

[0105] Its mathematical modules are:

[0106] (36)

[0107] (37)

[0108] Discretizing the above two equations and performing a Laplace transform yields:

[0109] (38)

[0110] The system's transfer function is:

[0111] (39)

[0112] in, The transfer function is discretized using the bilinear transformation principle. The bilinear transformation expression and the discrete transfer function are as follows:

[0113] (40)

[0114] (41)

[0115] The difference equation is calculated according to equation (38):

[0116] (42)

[0117] According to equations (28) and (29):

[0118] (43)

[0119] Step 3: Initialize before starting the algorithm.

[0120] Initialize the forgetting factor ,for and Assign initial values, set the initial values ​​for the covariance matrix. ,in , Given an identity matrix, the initial value is estimated using least squares. Construct the initial data vector. ,filling Initial data at time;

[0121] Constructing the initial data vector ,filling Initial data at time. and Connect them together and expand them into a single one using zero padding. Matrix of size ,from Start using it immediately. Initialize the parameters to be identified. More accurate initial values ​​can help the algorithm converge quickly. In this case, set all the parameters to be identified to zero.

[0122] Step 4: Activate the algorithm and calculate according to formula (43). Update the gain factor Covariance Matrix ;

[0123] Calculate and fill in the values ​​of voltage and current obtained from the previous two recursions according to formula (43). ;

[0124] Update the gain factor according to the following recursive formulas (44) and (45). Covariance Matrix

[0125] (44)

[0126] (45)

[0127] Step 5: Calculate the new information and the new information increment, and define the characteristic parameters. Used to determine whether to correct the forgetting factor;

[0128] New It is the difference between the observed measurement and the predicted measurement, where the predicted measurement is calculated from the current prior state estimate, which is calculated from the previous posterior state estimate. The calculation formula is shown in (46).

[0129] (46)

[0130] The increment of new information is defined by the following formula:

[0131] (47)

[0132] This is the innovation increment, representing the difference between the innovation value of the k-th innovation and the innovation value of the (k-1)-th innovation. The characteristic parameters are calculated according to equation (48). And determine whether to update the forgetting factor;

[0133] (48)

[0134] Step 5, if the feature parameters If the previous forgetting factor is inherited, it will remain unchanged. Conversely, if the characteristic parameters... Then, the forgetting factor is updated according to formula (49). Where , , , To achieve the minimum precision of the information, different values ​​can be changed to adapt to different data and parameter identification scenarios.

[0135] (49)

[0136] Step 6: Calculate the value of the parameter to be identified in this step according to formula (50).

[0137] (50)

[0138] Step 7: Run the recursive algorithm in a loop to complete the battery parameter identification, and output the identification results. Figure 7 Open circuit voltage curve Figure 8 Ohmic resistance Identification results Figure 9 Polarization resistance Identification results Figure 10 Polarization resistance Identification results Figure 11 Polarized capacitor Identification results Figure 12 Polarized capacitor Identification results.

[0139] It should be noted that the charging and discharging data of lithium iron phosphate batteries under the same group were used to identify circuit parameters using the innovation increment detection least squares method, the forgetting factor recursive least squares method (FFRLS), and the exponentially weighted recursive least squares method (EWRLS) proposed in this paper, respectively, and unstable data parts with SOC below 20% were removed.

[0140] like Figure 4 The graph shown illustrates the change in the forgetting factor value during the least squares parameter identification process for incremental information detection. Throughout the parameter identification process, the forgetting factor is updated or inherited from the previous forgetting factor based on the value of the feature parameters. Furthermore, even with very small system errors, there is no failure issue, and the forgetting factor can still be effectively updated.

[0141] like Figure 5The comparison chart showing the parameter identification errors of the innovation increment detection least squares method and the FFRLS algorithm demonstrates that, for the same set of data, the accuracy of the innovation increment detection least squares method is significantly higher than that of FFRLS. The calculated mean absolute error (MAE) of the innovation increment detection least squares method is 1.42E⁻⁴, while the MAE of the FFRLS algorithm is 1.51E⁻⁴. The root mean square error (RMSE) of the innovation increment detection least squares method is 8.11E⁻⁴, while the RMSE of the FFRLS algorithm is 8.14E⁻⁴. Because the data used for parameter identification is relatively stable and unstable data with a SOC below 20% has been removed, both algorithms have relatively low MAE and RMSE levels. However, the innovation increment detection least squares method still shows a clear advantage in accuracy. The formulas for calculating MAE and RMES are shown below:

[0142]

[0143] .

[0144] like Figure 6 The graph comparing the parameter identification errors of the IVFFRLS and EWRLS algorithms shows that, with initial values ​​set to 0, the innovation increment detection least squares method converges faster than the EWRLS algorithm. This demonstrates the speed advantage of the innovation increment detection least squares method, enabling it to track significant system changes well and quickly. In the latter half of the algorithm, when data changes tend to stabilize, the innovation increment detection least squares method shows similar estimation errors to the EWRLS algorithm, and may even be more accurate than the EWRLS algorithm.

[0145] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A method for identifying lithium battery parameters based on innovation increment detection least squares method, characterized in that, Includes the following steps: Step 1: Define the source regression model for the identified single-input single-output system: Among them, the model estimates the output y at time k based on the input and output quantities before time k (k-1 times); Step 2: Set the error vector and define the evaluation function; Among them, the estimate obtained when the evaluation function reaches its minimum value is the least squares estimate; Step 3: Initialize the regression model. Starting from the kth iteration, initialize the values ​​of the k-1th and k-2th iterations, and calculate the observed vector and the estimated vector. Step 4: Update the values ​​of the gain factor and the covariance matrix of the observation matrix; Step 5: Calculate the new information and the increment of the new information, and define a feature parameter to determine whether to correct the forgetting factor. If the feature parameter is greater than zero, modify the forgetting factor. The new information is the difference between the observed measurement and the predicted measurement, that is: ； in, Represents new information. For system output, It is the observation vector; The formula for calculating the incremental information is: ； in, It is the interest increment, representing the difference between the interest value of the k-th time and the interest value of the (k-1)-th time; Set feature parameters ; ； When the feature parameters At this point, the value of the new information, whether positive or negative, tends to increase, meaning the system error is continuously expanding. Therefore, it is necessary to adjust the forgetting factor at this time. Make adjustments to reduce its size to improve the system's fast tracking performance; When the feature parameters If the new information decreases continuously as the recursion proceeds, then the forgetting factor is considered appropriate. Feature parameters At that time, the forgetting factor is modified according to the formula; That is, through the formula: ； in, It is the forgetting factor, in the formula It is new information. All are constants. To achieve the minimum precision of the information, different values ​​can be changed to adapt to different data and parameter identification scenarios; Step 6: Calculate the estimated vector, recursively derive the least squares estimation formula, and solve for the battery parameters at each step based on the innovation increment detection least squares method.

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