A lithium battery parameter identification and state joint estimation method considering wide temperature

Abstract

The application discloses a lithium battery parameter identification and state joint estimation method considering wide temperature, and the method is as follows: obtaining open-circuit voltage and SOC of the battery from battery charging and discharging experiments, fitting to obtain a U OCV -SOC curve, thereby establishing a first-order RC equivalent circuit model of the battery, obtaining a spatial state equation; determining a T-alpha relationship through a parameter identification module based on an improved recursive least square method, and determining a T-mu relationship through a state estimation module based on an improved unscented Kalman filter; obtaining a real-time temperature of the battery, determining whether a given temperature changes through a temperature discriminator, and then obtaining a parameter identification best forgetting factor alpha and a state estimation best forgetting factor mu according to the T-alpha and T-mu relationships respectively; feeding back the alpha to the model parameter identification module to update the model parameters; and feeding back the updated model parameters and the mu to the state estimation module to further update the battery state estimation value, so that a more accurate SOC value is obtained.

Description

Technical Field

[0001] This invention relates to the field of power battery management, and in particular to high-precision estimation of power battery system parameters and state of charge. Background Technology

[0002] Today's automobiles are evolving towards electrification, intelligence, connectivity, and sharing, with electric vehicles undoubtedly being a hot research area and their safety receiving significant attention. A crucial aspect of electric vehicle safety is the power battery system. Within this system, estimating the battery's state of charge (SOC) is a critical issue. This invention primarily addresses the joint estimation of battery parameters and SOC, where the battery model parameters correspond to the battery's internal resistance R0 and polarization resistance R... p Polarization capacitor C p and open circuit voltage U OCV .

[0003] Currently, SOC estimation often employs filtering methods based on lithium battery models. The core idea of ​​this approach is to combine existing battery models with current state control theories to estimate SOC with higher accuracy and broader applicability. Kalman filtering, a widely used method, constructs a linear system state equation and compares the system's input and output data to make an optimal estimate. However, most existing techniques are based on simulations and experiments under specific dynamic operating conditions and temperatures. SOC estimation results under the full operating temperature range of a power battery often deviate from reality. This is because battery parameters vary significantly under different temperatures and aging conditions, and the parameters and states of the battery model are coupled. Therefore, researchers have proposed various joint estimation methods for model parameters and SOC. Among these, recursive least squares methods are commonly used for parameter estimation, while Kalman-type filters are still employed for SOC estimation. To address the data saturation problem, some scholars have introduced forgetting factors α and μ into the parameter identification and state estimation processes, respectively, namely Recursive Least Square with Forgetting Factor (FFRLS) and Kalman Filter with Decaying Memory (or Kalman Filter with Forgetting Factor).

[0004] In other fields, for FFRLS, some researchers have proposed establishing formulas for real-time updates of the forgetting factor α. However, lithium batteries are susceptible to temperature variations, and previously established empirical formulas for the forgetting factor recursion do not consider changes in battery temperature T. Even with real-time updates to the recursive forgetting factor α, the obtained α is not necessarily the optimal or near-optimal value for the corresponding temperature T, and the real-time recursive calculation is computationally intensive. For the attenuation factor (also known as the forgetting factor) μ in a Kalman filter with attenuation memory, a constant value is usually empirically set and applied to various temperatures T, which is also not necessarily the optimal or near-optimal value for each temperature T. Therefore, there is currently a lack of an efficient method for determining the forgetting factor applicable to the joint estimation of lithium battery parameters and states over a wide temperature range. Summary of the Invention

[0005] The problem addressed by this invention is to provide a high-precision method for jointly estimating lithium battery parameters and state considering a wide temperature range. The battery parameter identification stage uses FFRLS, specifically a parameter identification module based on an improved recursive least squares method to identify battery model parameters. The state estimation stage uses an unscented Kalman filter (UKF) with a forgetting factor, specifically an unscented Kalman filter-based state estimation module to estimate the battery's state of charge.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] S1. Obtain battery experimental data through lithium battery charge and discharge experiments, including the battery open-circuit voltage U. OCV Terminal voltage U L State of charge (SOC), current (I), and temperature (T) are determined by the battery's U. OCV The SOC experimental data were fitted to obtain U OCV -SOC relationship, establish the first-order RC equivalent circuit model of the battery, and obtain the battery space state equation;

[0008] S2. Based on the battery experimental data obtained from the battery charge and discharge experiment, and combined with the battery space state equation, the temperature T-parameter forgetting factor α relationship is determined by the parameter identification module based on the improved recursive least squares method.

[0009] S3. Based on the battery model parameters obtained by the parameter identification module based on the improved recursive least squares method, the battery model parameters include the battery internal resistance R0 and the polarization internal resistance R. p Polarization capacitor C p and open circuit voltage U OCV Based on the battery experimental data obtained from the battery charge and discharge experiment, and combined with the battery space state equation, the temperature T-state forgetting factor μ relationship is determined by the state estimation module based on the improved unscented Kalman filter.

[0010] S4. Obtain the real-time battery temperature, determine whether the given temperature has changed through the temperature discriminator, and then obtain the optimal parameter forgetting factor α and the optimal state forgetting factor μ according to the T-α and T-μ relationship respectively. Feed α back to the parameter identification module to update the battery model parameters. The updated battery model parameters are then fed back to the state estimation module together with μ to further update the battery state estimate, that is, to obtain a more accurate SOC prediction value.

[0011] In step S1, within the common operating temperature range of lithium batteries (-10℃~50℃), the following tests are conducted at 10℃ intervals: battery capacity test, open circuit voltage test, and dynamic operating condition test (UDDS test) at the charge / discharge rate recommended by the battery manufacturer. The battery current is measured under the dynamic operating condition. ,Voltage And temperature T; combined with capacity experiment and open circuit voltage experiment, the battery U at each sampling point is obtained. OCV And SOC, U is obtained by fitting using the following formula. OCV -SOC relation:

[0012]

[0013] These are parameters to be determined.

[0014] In step S1, the first-order RC equivalent circuit model of the lithium battery is obtained according to Kirchhoff's laws.

[0015]

[0016]

[0017] In the formula, U L U is the battery terminal voltage. OCV U is the battery open-circuit voltage. P R is the polarization voltage, I is the battery current, R0 is the battery internal resistance, and R p C p These are the polarization internal resistance and polarization capacitance, respectively.

[0018] After discretization, the state-space equation of the battery system is obtained as follows:

[0019] = + +

[0020] = - - +

[0021] In the formula, the subscript k represents the data at time k, and T s w represents the time for data collection during the experiment. k With v k It is Gaussian white noise with zero mean and covariances Q and R. Q represents the Coulomb efficiency. N Indicates battery capacity.

[0022] In step S2, the steps to generate the T-α relation are as follows:

[0023] 1) Linearize the battery model:

[0024] = - + + +

[0025] In the formula, The coefficients related to the battery model parameters are as follows:

[0026]

[0027] In the formula, T s Given the sampling time interval, the corresponding parameter matrix is ​​obtained from equation (1). and data matrix for

[0028]

[0029] In the formula, k is the index of the sampling time;

[0030] 2) Initialize U OCV R0, R p and C p The four battery model parameters that need to be identified, along with the covariance matrix P, are converted using equation (2). That is, the initial values ​​of the parameter matrix are obtained. Covariance Matrix Meanwhile, the initial value α0 of the forgetting factor α is given;

[0031] 3) Substitute the battery current and voltage data under dynamic operating conditions to update the battery terminal voltage measurement. ;

[0032] 4) Parameter and error covariance matrix update:

[0033]

[0034]

[0035]

[0036] In the formula, These are the predicted values ​​of the parameter matrix from the previous time step. This is the predicted value of the battery terminal voltage at this moment. This is the gain coefficient. It is the covariance matrix;

[0037] 5) Convert the parameter matrix The inverse transformation yields the required battery model parameters:

[0038]

[0039] 6) Calculate the predicted battery terminal voltage using equation (1) based on the identified battery model parameters. and with the measured value The mean absolute error (MAE) and root mean square error (RMSE) were compared and calculated:

[0040] MAE=

[0041] RMSE= 2

[0042] in , used to evaluate the quality of the identification results, where N is a natural number;

[0043] 7) Determine the optimal forgetting factor at the current temperature: Since α is a value greater than 1 and not easily too large, first, let α be taken in equal intervals of 0.001 between 1.00 and 1.10. Substitute each α value into steps 4) to 6), and then find the forgetting factor α with the best identification effect based on MAE and RMSE, which will be used as the current temperature T. k The optimal parameter for forgetting factor α is... k ;

[0044] 8) Using different temperatures T j The dynamic operating condition data is updated by modifying the initial parameters and their corresponding covariance matrices. Steps 3) to 7) are repeated to obtain the temperature T. j The corresponding optimal parameter is the forgetting factor α. j Where j is a natural number greater than 1, and finally T- is obtained by fitting a seventh-order polynomial. Relationship:

[0045]

[0046] in .

[0047] In step S3, the steps for generating the T-μ relation are as follows:

[0048] 1) Set the initial value of SOC to 1, the number of state variables to 2, and the state variable x = [SOC, U p Up represents the polarization voltage, and the observed variables are set as the battery model parameters R0 and R... p C p and U OCV ;

[0049] 2) Regarding SOC, U p And initialize the corresponding process noise variance Q and measurement noise variance R;

[0050] 3) Connect SOC and U p Perform sigma conversion and calculate its weights. :

[0051] ① Initialize the mean and covariance using the following formulas:

[0052]

[0053]

[0054] ;

[0055] ② Generate 2n+1 sigma points Calculate the corresponding weights :

[0056]

[0057] In the formula, This is a scaling factor; its value is modified to reduce prediction error. (Sampling points) and It has an approximately Gaussian distribution, where Representation matrix The List;

[0058]

[0059] In the formula, m represents the auxiliary scaling factor, n represents the dimension of the state variable, and λ = ε 2 (n+m)-n, The value range is 10 -4 ≤ <1; These are state distribution parameters; These are the weights of the variance and the mean, respectively.

[0060] 4) Calculate the Kalman gain:

[0061] ① Calculate the result of the nonlinear transformation of these sigma points. The specific formula is as follows:

[0062]

[0063]

[0064] The state variable at time k is predicted by the state variable at time k-1 through the nonlinear state equation f(). These are the updated predicted values ​​of the state variables;

[0065] ② Update of state variable covariance, the specific formula is as follows:

[0066] - ) - )T]+Q k

[0067] In the formula, P is the covariance matrix. Q k Let k be the process noise variance at time k;

[0068] ③ Update the observed variables, the specific formula is as follows:

[0069]

[0070]

[0071] Updated predicted values ​​for observed variables;

[0072] ④ Error covariance update: A forgetting factor μ is introduced into the observation noise covariance matrix. The specific formula is as follows:

[0073] - ) - )T]+R k

[0074]

[0075] - ) - )T]

[0076] In the formula R k is the observation noise variance at time k, and μ is the state forgetting factor;

[0077] ⑤ Kalman gain update, the specific formula is as follows:

[0078]

[0079] This represents the ratio of model prediction error to measurement error;

[0080] 5) Calculate and update the system state and covariance based on the Kalman gain:

[0081]

[0082]

[0083] In the formula, ;

[0084] 6) Obtain the predicted SOC value from step 5), and compare it with the reference SOC value SOCr to obtain the mean absolute error (MAE) and root mean square error (RMSE) of SOC, respectively.

[0085] SOC MAE =

[0086] SOC RMSE = 2

[0087] in SOCg is the predicted SOC value;

[0088] 7) Determine the optimal state forgetting factor at the current temperature: First, let the state forgetting factor μ be taken in intervals of 0.01 from 1.00 to 1.30. Substitute each μ value into steps 4) to 6), and then according to SOC... MAE and SOC RMSE To find the state forgetting factor α that provides the best recognition effect, and use it as the current temperature T k The optimal parameter for forgetting factor μ is... k ;

[0089] 8) Repeat the data from -10℃ to 50℃, and repeat steps 4) to 7) above to obtain the temperature T. j The corresponding optimal parameter is the forgetting factor μ. j The T-μ relationship was obtained by fitting a seventh-order polynomial:

[0090]

[0091] In the formula,

[0092] In step S4, the temperature discriminator is designed as follows: Let the temperature difference ΔT = T k -T k-1 Tk The real-time battery temperature at this moment, T k-1 The value is the battery's real-time temperature at the previous moment. If ΔT is greater than 0.5℃, then at T... k The forgetting factor is updated at temperature T; otherwise, it is updated at temperature T. k-1 The forgetting factor is updated at temperature.

[0093] The lithium battery parameter identification and state estimation method proposed in this invention, which considers the wide temperature range, has the following advantages compared with traditional methods: It adopts a forgetting factor algorithm that varies with temperature for battery model parameter identification and state estimation, which can adapt to the changes in battery operating environment temperature and improve the SOC estimation accuracy under full operating temperature conditions. Attached Figure Description

[0094] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0095] In the attached diagram:

[0096] Figure 1 This is a diagram of the first-order RC equivalent circuit of the present invention;

[0097] Figure 2 This is a flowchart of the method of the present invention;

[0098] Figure 3 shows the online parameter identification results of the present invention under 25℃ and DST conditions.

[0099] Figure 4 shows the SOC estimation and error analysis under different forgetting factors according to the present invention. Detailed Implementation

[0100] The following detailed description, in conjunction with the accompanying drawings, of the lithium battery parameter identification and state joint estimation method considering a wide temperature range provided by the present invention.

[0101] In a preferred embodiment of the present invention, an unused lithium battery of model 4.1V / 2Ah is used as the research object, and the dynamic operating condition adopted is DST condition. Its initial capacity is assumed to be 100%.

[0102] 1. Modeling and Experimentation

[0103] ① To address the shortcomings of the internal resistance model, and considering the polarization effect of lithium batteries, an RC module was connected in parallel with the original circuit, forming a first-order RC equivalent circuit model. Compared to the internal resistance model, the first-order RC equivalent circuit model better reflects the dynamic changes inside the battery. Its specific structure is shown in the attached figure. Figure 1 As shown. Where U OCVR represents the battery open-circuit voltage, which is not considered a constant value here. R0 represents the battery's internal resistance in ohms. p and C p These represent the battery's polarization resistance and polarization capacitance, respectively. The ohmic internal resistance R0 can change in a short time, thus reflecting the voltage change during charging and discharging. With the addition of an RC circuit, the RC module can represent the gradual decrease or increase of the battery's internal voltage after charging or discharging is complete. The first-order RC equivalent circuit model is structurally simple but has high accuracy, and therefore has wide applications.

[0104] ② The first-order RC equivalent circuit model needs to identify the ohmic internal resistance R0 and the polarization internal resistance R. p Polarization capacitor C p and open circuit voltage U OCV According to Kirchhoff's laws, the following relationship can be obtained:

[0105] (1)

[0106] (2)

[0107] Combining equations (1) and (2), and after discretization, the state-space equations of the battery system are obtained as shown in equations (3) and (4):

[0108] = + + (3)

[0109] = - - + (4)

[0110] In the formula, the subscript k represents the data at time k, and T s w represents the time for data collection during the experiment. k With v k It is Gaussian white noise with zero mean and covariances Q and R. Q represents the Coulomb efficiency. N Indicates battery capacity.

[0111] ③ The following tests were conducted at the three temperatures mentioned above: battery capacity test, OCV test, and dynamic operating condition test (DST). In this invention, a unidirectional pulse plus intermittent resting method was used to obtain the open-circuit voltage. First, the battery was charged to its upper voltage limit using a unidirectional pulse, maintaining a constant temperature throughout the process until the battery was fully charged. Then, it was allowed to rest for 1 hour to allow the battery to reach a potential equilibrium state. Next, the battery was discharged with a current of 1A for 12 minutes, at which point the SOC in the battery circuit was considered to have reached 90% of its initial value. It was then allowed to rest for another hour. Repeating the above steps yielded the open-circuit voltage value from 100% to 0% SOC. The open-circuit voltage test results at 25℃ are shown in Figure 3.

[0112] The open-circuit voltage and SOC at each sampling point were obtained by combining the capacity experiment and the OCV experiment. U was obtained by fitting the following equation (5). OCV -SOC relation.

[0113] (5)

[0114] 2. The temperature-parameter forgetting factor (T-α) relationship is determined by a parameter identification module based on an improved recursive least squares method.

[0115] ① The above state-space equations are transformed to obtain

[0116] = - + + + (6)

[0117] Among them , , Specifically as formula (7):

[0118] (7)

[0119] The corresponding parameter matrix and data matrix for:

[0120] (8)

[0121] In the formula The open-circuit voltage is obtained using a recursive algorithm. From the above formula, the four parameters that originally needed to be identified are transformed into... , , , After each parameter is identified, it needs to be converted into the required parameters through calculation. The specific conversion formula (9) is as follows:

[0122] (9)

[0123] ② Initialize U OCV R0, R p and C p The document outlines four parameters to be identified, along with their covariance matrix, and provides initial values ​​for the forgetting factor. It uses a 25°C temperature as an example. =[0.25 0.95 -0.002 0.0018], , .

[0124] ③ Obtain offline dynamic operating condition current and voltage data. The current and voltage data obtained through dynamic operating condition experiments are repeatedly used to identify parameters using the following recursive least squares formula until no new data is available.

[0125] (10)

[0126] (11)

[0127] (12)

[0128] The changes of the identification parameters over time are obtained, as shown in Figure 3. The predicted terminal voltage is calculated using the identification parameters through formula (5). The mean absolute error and root mean square error are calculated by comparing the predicted value with the measured value, which are used to evaluate the quality of the identification results.

[0129] MAE= (13)

[0130] RMSE= 2 (14)

[0131] ④ Change the forgetting factor in increments of 0.001 between 1.00 and 1.10. To identify the forgetting factors that have the best identification effect As the optimal forgetting factor at this temperature, the forgetting factor was ultimately adjusted by fine-tuning parameters under standard 25°C conditions. When the value is 1.031, the parameter identification effect is relatively good. Figure 3 shows the online identification results of the present invention under 25℃ and DST conditions.

[0132] ⑤ Using dynamic operating condition data at different temperatures, the above experimental process was repeated by adjusting the initial parameters and the corresponding covariance matrix. Current and voltage data under 10℃ and DST conditions were imported, and finally adjusted to the forgetting factor. When the value is 1.053, the parameter identification effect is good. Similarly, the current and voltage data of 40℃ and DST conditions are imported and finally adjusted to the forgetting factor. When the value is 1.004, the parameter identification effect is good. Therefore, we conclude that when using a parameter with a forgetting factor... When using recursive least squares for parameter identification, the forgetting factor The changes are small, and the temperature should be appropriately reduced as it increases. T- was obtained using polynomial fitting. Relationship:

[0133] (15)

[0134] 3. The temperature-state forgetting factor (T-μ) relationship is determined by a state estimation module based on an improved unscented Kalman filter.

[0135] ① Set the initial value of SOC to 1, and the number of state variables to 2. The state variable x = [SOC, U p The observed variables are set as battery model parameters R0 and R1. p C p and U OCV .

[0136] ② Perform SOC, U p And the corresponding initialization of noise Q and R. In this example, the initial noise is set to R = 0.0001, U p =0. Initialize Q= P= .

[0137] ③ Next, following the steps of the unscented transformation calculation, first compare SOC and U p Perform sigmaization and calculate the weights, while simultaneously calculating the corresponding Kalman gain and updating the state-space equation and covariance matrix.

[0138] S1. Initialize the mean and covariance.

[0139] [0.9,0] (16)

[0140] (17)

[0141] S2. Generate 2n+1 sigma points and calculate the corresponding weights.

[0142] (18)

[0143] (19)

[0144] Where n=2 represents the dimension of the state variables, =0.5 is the dispersion coefficient. In practice, the value should be as small as possible, as a smaller value is closer to the overall sample level; β=2 represents the prior distribution coefficient, and when the distribution is Gaussian, β=2 is optimal; m=2 is an auxiliary scaling factor to ensure that m+n≠0. It is the scaling factor:

[0145] (20)

[0146] S3. Calculate the result of the nonlinear transformation of these sigma points, using the following formula:

[0147] (twenty one)

[0148] (twenty two)

[0149] S4. The specific formula for updating the covariance of state variables is as follows:

[0150] - ) - ) T ]+Q k (twenty three)

[0151] S5. Update the observed variables, the specific formula is as follows:

[0152] (twenty four)

[0153] (25)

[0154] S6. Error covariance update: A forgetting factor μ is introduced into the observation noise covariance matrix. The specific formula is as follows:

[0155] - ) - )T]+R k (26)

[0156] (27)

[0157] - ) - )T] (28)

[0158] S7. Kalman gain update, the specific formula is as follows:

[0159] (29)

[0160] S8. State update and covariance update, the specific formulas are as follows:

[0161] = + ( (30)

[0162] = (31)

[0163] After execution, the estimated terminal voltage value is compared with the actual terminal voltage value, and the error is used to update the error matrix. This process is repeated until the lithium battery discharges completely.

[0164] ④ The 25℃, DST condition was selected as the standard operating condition. Experience shows that the forgetting factor μ is a value greater than 1, but not excessively large. Values ​​of μ = 1.00 to 1.30 were used to estimate the SOC of the lithium battery at equal intervals of 0.01. When the forgetting factor μ is large, the SOC estimation in the latter half of the estimation has a significant error. When μ = 1.08, the overall SOC estimation error is controlled within 2%, showing a good estimation effect. Therefore, μ = 1.08 was taken as the final value for SOC state estimation at 25℃. Figure 4 shows the state estimation and error analysis under different forgetting factors according to this invention.

[0165] ⑤ The temperature of the DST operating condition was changed accordingly to obtain the SOC state estimation effect and error analysis diagram at different temperatures, in order to explore the influence of temperature on the forgetting factor μ. When changing the temperature, the initial state covariance matrix and the process noise and observation noise parameters should be changed accordingly. Finally, when μ was adjusted to 1.11 at 10 degrees and μ was adjusted to 1.13 at 40 degrees, better state estimation results were obtained. Polynomial fitting was used to obtain T- Relationship:

[0166] (32)

[0167] 4. Achieve accurate SOC estimation through online experimental calls.

[0168] At a given temperature, such as 15°C, the optimal forgetting factor at that temperature is calculated by fitting a relational formula. , After determining the forgetting factor, repeat the above parameter identification and state estimation algorithms to achieve a more accurate SOC estimation result.

[0169] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for joint parameter identification and state estimation of lithium batteries considering a wide temperature range, the method comprising the following steps: S1. Obtain battery experimental data through lithium battery charge and discharge experiments, including the battery open-circuit voltage U. OCV Terminal voltage U L State of charge (SOC), current (I), and temperature (T) are determined by the battery's U. OCV The SOC experimental data were fitted to obtain U OCV -SOC relationship, establish the first-order RC equivalent circuit model of the battery, and obtain the battery space state equation; S2. Based on the battery experimental data obtained from the battery charge and discharge experiment, and combined with the battery space state equation, the temperature-parameter forgetting factor (T-α) relationship is determined by the parameter identification module based on the improved recursive least squares method. S3. Based on the battery model parameters obtained by the parameter identification module based on the improved recursive least squares method, the battery model parameters include the battery internal resistance R0 and the polarization internal resistance R. p Polarization capacitor C p and open circuit voltage U OCV Based on the battery experimental data obtained from the battery charge and discharge experiment, and combined with the battery space state equation, the temperature-state forgetting factor (T-μ) relationship is determined by the state estimation module based on the improved unscented Kalman filter. S4. Obtain the real-time battery temperature, determine whether the given temperature has changed through the temperature discriminator, and then obtain the optimal parameter forgetting factor α and the optimal state forgetting factor μ according to the T-α and T-μ relationship respectively. Feed α back to the parameter identification module to update the battery model parameters. The updated battery model parameters are then fed back to the state estimation module together with μ to further update the battery state estimation value, that is, to obtain a more accurate SOC prediction value. The method for parameter identification and joint state estimation of lithium batteries considering a wide temperature range is characterized by the following steps for generating the T-α relationship: 1) Linearizing the battery model yields: = - + + + (1) In the formula, The coefficients related to the battery model parameters are calculated as follows: (2) In the formula, T s Given the sampling time interval, the corresponding parameter matrix is ​​obtained from equation (1). and data matrix for (3) In the formula, k is the index of the sampling time; 2) Initialize U OCV R0, R p and C p The four battery model parameters that need to be identified, along with the covariance matrix P, are converted using equation (2). That is, the initial values ​​of the parameter matrix are obtained. Covariance Matrix Meanwhile, the initial value α0 of the forgetting factor α is given; 3) Substitute the battery current and voltage data under dynamic operating conditions to update the battery terminal voltage measurement. ; 4) Parameter and error covariance matrix update: (4) (5) (6) In the formula, These are the predicted values ​​of the parameter matrix from the previous time step. This is the predicted value of the battery terminal voltage at this moment. This is the gain coefficient. It is the covariance matrix; 5) Convert the parameter matrix The inverse transformation yields the required battery model parameters: (7) 6) Calculate the predicted battery terminal voltage using equation (1) based on the identified battery model parameters. and with the measured value The mean absolute error (MAE) and root mean square error (RMSE) were compared and calculated: IS= (8) RMSE= 2 (9) in This is used to evaluate the quality of the identification results; 7) Determine the optimal forgetting factor at the current temperature: Since α is a value greater than 1 and not easily too large, first, let α be taken in equal intervals of 0.001 between 1.00 and 1.

10. Substitute each α value into steps 4) to 6), and then find the forgetting factor α with the best identification effect based on MAE and RMSE, which will be used as the current temperature T. k The optimal parameter for forgetting factor α is... k ; 8) Using different temperatures T j The dynamic operating data is updated by updating the initial parameters and their corresponding covariance matrix, and steps 3) to 7) above are repeated to obtain the temperature T. j The corresponding optimal parameter is the forgetting factor α. j Where j is a natural number greater than 1, and finally T- is obtained by fitting a seventh-order polynomial. Relationship: (10) in .

2. The method for joint estimation of lithium battery parameters considering a wide temperature range, as described in claim 1. Its features are, The steps for generating the T-μ relationship are as follows: 1) Set the initial value of SOC to 1, the number of state variables to 2, and the state variable x = [SOC, U p Up represents the polarization voltage, and the observed variables are set as the battery model parameters R0 and R... p C p and U OCV ; 2) Regarding SOC, U p And initialize the corresponding process noise variance Q and measurement noise variance R; 3) Connect SOC and U p Perform sigma conversion and calculate its weights. : Step 1: Initialize the mean and covariance: (11) (12) ； The second step is to generate 2n+1 sigma points. Calculate the corresponding weights : (13) In the formula, This is a scaling factor; its value is modified to reduce prediction error. (Sampling points) and It has an approximate Gaussian distribution. Representation matrix The List; (14) In the formula, m represents the auxiliary scaling factor, n represents the dimension of the state variable, and λ = ε 2 (n+m)-n, The value range is 10 -4 ≤ <1; These are state distribution parameters; These are the weights of the variance and the mean, respectively. 4) Calculate the Kalman gain: The first step is to update the state variables, using the following formula: (15) (16) It is formed by the state variables at time k-1 through the nonlinear state equation The state variables at time k obtained after prediction, These are the updated predicted values ​​of the state variables; The second step is to analyze the covariance of the state variables. Updated, the specific formula is as follows: - ) - ) T ]+Q k (17) In the formula, P is the covariance matrix, Q k Let k be the process noise variance at time k; The third step is to update the observed variables, using the following formula: (18) (19) In the formula, The state variable is measured by the equation The subsequent prediction yields new predicted values ​​for the observed variables. These are the updated predicted values ​​of the observed variables; The fourth step is error covariance update. A state forgetting factor μ is introduced into the observation noise covariance matrix. The specific formula is as follows: - ) - )T]+R k (20) (21) - ) - )T] (22) In the formula R k It is the variance of the observation noise at time k. Step 5: Kalman gain update, the specific formula is as follows: (23) This represents the ratio of model prediction error to measurement error; 5) Update the system state and covariance based on the Kalman gain: (24) (25) In the formula, ; 6) Obtain the predicted SOC value of the battery from step 5), and then compare it with the reference value SOCr to obtain the mean absolute error of SOC (MAE) and the root mean square error of SOC (RMSE). SOC MAE = (26) SOC RMSE = 2 (27) in SOCg is the predicted SOC value; 7) Determine the optimal state forgetting factor at the current temperature: First, let the state forgetting factor μ be taken in intervals of 0.01 from 1.00 to 1.

30. Substitute each μ value into steps 4) to 6), and then according to SOC... MAE and SOC RMSE To find the state forgetting factor α that provides the best recognition effect, and use it as the current temperature T k The optimal parameter for forgetting factor μ is... k ; 8) Repeat the data from -10℃ to 50℃, and repeat steps 4) to 7) above to obtain the temperature T. j The corresponding optimal parameter is the forgetting factor μ. j The T-μ relationship was obtained by fitting a seventh-order polynomial: (28) In the formula, 3. The method for joint estimation of lithium battery parameters and state considering a wide temperature range according to claim 1, characterized in that, The temperature discriminator is designed as follows: Let the temperature difference ΔT = T k -T k-1 T k The real-time battery temperature at this moment, T k-1 The value is the battery's real-time temperature at the previous moment. If ΔT is greater than 0.5℃, then at T... k The forgetting factor is updated at temperature T; otherwise, it is updated at temperature T. k-1 The forgetting factor is updated at temperature.

4. The method for joint estimation of lithium battery parameters and state considering a wide temperature range according to claim 1, characterized in that, The U OCV The SOC relationship is derived as follows: Within the common operating temperature range of lithium batteries (-10℃ to 50℃), the following tests are conducted at 10℃ intervals: battery capacity test, open-circuit voltage test, and dynamic stress test at the charge / discharge rates recommended by the battery manufacturer. The battery current is measured under dynamic conditions. ,Voltage And temperature T; combined with capacity experiment and open circuit voltage experiment, the battery U at each sampling point is obtained. OCV And SOC, U is obtained by fitting using the following formula. OCV -SOC relation: (29) These are parameters to be determined.

5. The method for joint estimation of lithium battery parameters and state considering a wide temperature range according to claim 1, characterized in that, The battery space state equation is as follows: Based on Kirchhoff's laws, the first-order RC equivalent circuit model of a lithium battery is obtained. (30) (31) In the formula, U L U is the battery terminal voltage. OCV U is the battery open-circuit voltage. P R is the polarization voltage, I is the battery current, R0 is the battery internal resistance, and R p C p These are the polarization internal resistance and polarization capacitance, respectively. After discretization, the state-space equation of the battery system is obtained as follows: = + + (32) = - - + (33) In the formula, the subscript k represents the data at time k, and T s w represents the time for data collection during the experiment. k With v k It is Gaussian white noise with zero mean and covariances Q and R. Q represents the Coulomb efficiency. N Indicates battery capacity.

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