Lithium battery internal temperature and surface temperature estimation method based on migration model

Abstract

The invention relates to the technical field of lithium ion batteries, and provides a lithium battery internal temperature and surface temperature estimation method based on a migration model. The method comprises the steps of obtaining charging and discharging data of a single lithium battery, constructing a basic model, performing SOC-OCV fitting, performing parameter identification through machine learning, obtaining a fitting relation between basic model parameters and internal and external temperatures, constructing a migration model, correcting the internal and external temperatures of the battery, and finally obtaining the internal and external temperatures of the lithium ion battery. According to the method for estimating the internal temperature and the surface temperature of the lithium battery based on the migration model, the migration model is introduced, the influence of the working environment temperature and the aging state on internal parameters of the battery is fully considered, and the problem of particle degradation of a traditional particle filtering algorithm is avoided by using a particle filtering algorithm based on particle weight selection optimization; the rapid migration construction of the lithium battery electrothermal coupling model and the rapid acquisition of the lithium battery temperature state in the whole life cycle are realized, the demand for a large amount of new modeling data is reduced, and the calculation speed is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of state estimation of vehicle lithium-ion batteries, and particularly to a method for estimating the internal temperature and surface temperature of a lithium battery based on a migration model. Background Art

[0002] As an excellent energy storage device, lithium batteries (lithium-ion batteries) have currently become the main power source of new energy vehicles, and their safety performance has accordingly become the focus of attention. During the operation of electric vehicles, lithium-ion batteries often work under complex working conditions, and the battery temperature state changes accordingly. Therefore, accurate estimation of the battery temperature state is crucial for ensuring the safe operation of the battery and the vehicle. At the same time, accurate estimation of the battery temperature state is also the key point for the efficient control of the thermal management system.

[0003] At the current stage, the main method for obtaining the temperature state of a single lithium battery cell is to place temperature sensors inside and on the surface of the battery. However, placing sensors in a large number of modules in a real vehicle will increase costs and the risk of control management failure. Currently, the main methods for estimating the internal temperature state of lithium-ion batteries are as follows: using simulation software to establish a battery finite element model and performing simulation analysis on the heat generation and heat release temperature change mechanism inside the lithium battery. This method only considers the ideal environment under experimental conditions and ignores various complex external factor interferences during real vehicle operation, and the results are too idealized; although the data-driven research method is more realistically feasible, it requires a large amount of real vehicle operation data to support model training; establishing partial differential equations based on the electrochemical reaction mechanism of lithium batteries can reflect the reactions inside the battery, but usually requires a large number of experiments to calibrate its electrochemical parameters, and the parameter dependence is strong, the model structure is complex, and the calculation amount is large. In addition, the complex working environment temperature change and its own aging state will further increase the difficulty of its accurate estimation. Therefore, it is of great practical significance to achieve accurate and efficient internal and external temperature state estimation of the battery within a wide temperature working range during the entire service process. Summary of the Invention

[0004] (1) Technical problems to be solved by the present invention

[0005] Aiming at the deficiencies of the prior art, the present invention provides a method for estimating the internal temperature and surface temperature of a lithium battery based on a transfer model. The transfer model greatly reduces the amount of data required by traditional battery temperature estimation methods. Only a reference transfer model for ambient temperature and aging state needs to be established, and model information under other ambient temperatures and aging states can be obtained through online transfer. In practical applications, the internal temperature and surface temperature of the battery can be estimated quickly. When the battery temperature is abnormal, the battery temperature status can be timely fed back to the battery management system, saving a lot of time for thermal management and greatly increasing the safety of in-vehicle operation. It has the advantages of small computational amount, high accuracy and strong practicability, and solves the above technical problems.

[0006] (2) Technical solution of the present invention

[0007] To achieve the above object, the present invention provides the following technical solution: A method for estimating the internal temperature and surface temperature of a lithium battery based on a transfer model, comprising the following steps:

[0008] S1: Obtain the charge and discharge data of a lithium-ion single battery under full-life wide temperature conditions, including current, voltage, surface temperature and tab temperature data. The specific steps are as follows: Perform cyclic charge and discharge aging tests on different batteries of the same model. Use constant current and constant voltage to fully charge the battery, let it stand for 30 s, and then discharge it to the battery cut-off voltage. Repeat the above process. Discharge the battery to 90% and 80% of the nominal battery capacity respectively, and then conduct working condition experiments in the temperature range of -20°C to 60°C, namely UDDS-FUDS working condition and HPPC working condition experiments, and collect the current, voltage, surface temperature and tab temperature data of the single battery, namely UDDS-FUDS working condition and HPPC working condition experiment data. Among them, the UDDS-FUDS working condition experiment data is used for model parameter identification, transfer model construction, temperature estimation and verification, and the HPPC working condition experiment data is used for fitting the relationship between SOC and open circuit voltage OCV.

[0009] S2: Construct an equivalent circuit model and a battery thermal model as a basic electro-thermal coupling model. Among them, the equivalent circuit model is a second-order RC equivalent circuit model, and the battery thermal model includes a heat generation model and a heat transfer model. The heat generation model uses the simplified Bernardi equation as the heat generation model, and uses a two-state lumped parameter thermal model as the heat transfer model to simulate the heat transfer inside the battery, and discretely express the second-order RC equivalent circuit model, the simplified Bernardi equation and the two-state lumped parameter thermal model;

[0010] S3: Curve fitting: Use the experimental data under the HPPC working condition to obtain the relationship curve between SOC and open circuit voltage OCV through sixth-order polynomial fitting. The fitting expression is as follows:

[0011]

[0012] Among them, represents the polynomial fitting parameter, represents the sum of the entire sixth-order polynomial, represents different power terms of SOC;

[0013] Under normal temperature and brand-new state, based on the experimental data of UDDS-FUDS working conditions obtained from S1, the recursive least squares method with forgetting factor is used to identify the parameters of the second-order RC equivalent circuit and thermal model established in S2. The identified parameters are the parameters of the basic electro-thermal coupling model, and the identification process is as follows:

[0014] Under normal temperature and brand-new state, based on the experimental data of UDDS-FUDS working conditions obtained from S1, the recursive least squares method with forgetting factor is used to identify the parameters of the second-order RC equivalent circuit and thermal model established in S2. The identification process is as follows:

[0015] Let the model parameter vector be θ = [α β γ] T

[0016] The observation vector is:

[0017]

[0018] The recurrence formula is:

[0019]

[0020]

[0021] In the formula, K is the gain matrix; P is the covariance matrix; is the system estimation reference value; y(k + 1) is the actual observation value of the system; is the observation value matrix; Δt is the sampling time interval of 1 s;

[0022] The internal heat generation power Q of the battery c can be estimated according to the Bernardi equation, and the heat capacity C of the aluminum-plastic film on the battery surface air can be obtained from the data provided by the battery manufacturer, and its value is a constant value,

[0023]

[0024] From the above formula, the parameter C can be obtained c , R c , R air .

[0025] S4. Obtain the fitting relationship between the parameters of the basic electro-thermal coupling model and the internal and external temperatures of the battery: Based on the internal and external temperature values of the battery obtained from the experiments in S1 and the electro-thermal coupling model parameters identified by FFRLS in S3, use the neural network fitting method to obtain the relationship curves between the model parameters and the internal temperature and surface temperature of the battery respectively;

[0026] S5. Build a migration model and correct the internal temperature and surface temperature of the single battery. Based on the fitting relationship between the basic model parameters and the internal temperature and surface temperature of the battery, build a migration framework. Under different ambient temperatures and aging conditions, complete the online migration of the migration factor through the weighted selection particle filter algorithm, so as to migrate the inaccurate internal temperature and surface temperature values of the single battery and obtain the true internal temperature and surface temperature values under the influence of ambient temperature and aging.

[0027] As a preferred technical solution of the present invention, the working condition charge and discharge data of the lithium-ion single battery at different ambient temperatures and different aging states collected in step S1 include: voltage, current, surface temperature, and tab temperature data.

[0028] As a preferred technical solution of the present invention, the discretized expression of the second-order RC equivalent circuit model established in step S2 is:

[0029]

[0030] In the above formula, U t (k) represents the terminal voltage of the circuit at the current moment; U ocv (k) represents the open-circuit voltage of the circuit at the current moment; I(k) represents the current of the circuit at the current moment; U1(k), U2(k) represent the terminal voltages corresponding to the polarization resistance and capacitance at the current moment; U1(k + 1), U2(k + 1) represent the terminal voltages corresponding to the polarization resistance and capacitance at the next moment; (k) represents the state quantity at the current moment; (k + 1) represents the state quantity at the next moment; R0 is the ohmic internal resistance; R1, R2 represent the polarization resistances; C1, C2 represent the polarization capacitances; τ1, τ2 represent the time constants; Δt represents the sampling time interval of 1 s.

[0031] In step S2, the discretized expression of the heat generation equation is:

[0032]

[0033] In the above formula, T(k) represents the core temperature of the battery at the current moment, and T represents the core temperature of the battery.

[0034] The discretized expression of the heat transfer equation is:

[0035]

[0036] In the above formula, Qc (k) represents the heat generation power of the single cell at the current moment; C c represents the heat capacity of the battery; R c represents the thermal resistance between the inside and the surface of the battery; C air represents the heat capacity of the battery surface housing; R air represents the thermal resistance between the battery surface and the external environment; T c (k), T s (k), T air (k) represent the internal temperature of the battery, the surface temperature of the battery, and the ambient temperature around the battery at the current moment, respectively.

[0037] As a preferred technical solution of the present invention, the steps of obtaining the SOC-OCV fitting curve and identifying the basic model parameters using the FFRLS algorithm in step S3 are as follows:

[0038] S3.1. Extract the voltage and current data of the single cell in the HPPC condition experiment in step S1, and use the 6th-order polynomial fitting method to fit the relationship curve between the open-circuit voltage OCV and SOC.

[0039] S3.2. Respectively use the FFRLS algorithm to obtain the internal parameters of the electrical model and the thermal model. The identified parameters of the electrical model are the ohmic internal resistance R0, the electrochemical polarization resistance R1, the electrochemical polarization capacitance C1, the concentration difference polarization resistance R2, and the concentration difference polarization capacitance C2; the identified parameters of the thermal model are: the battery heat capacity C c , the thermal resistance R c between the inside and the surface of the battery, the heat capacity C air of the battery surface housing, and the thermal resistance R air .

[0040] Under the condition of normal temperature and brand new state, based on the UDDS-FUDS condition experiment data obtained in S1, use the recursive least squares method with a forgetting factor to identify the parameters of the second-order RC equivalent circuit and the thermal model established in S2. The identification process is as follows:

[0041] Let the model parameter vector be θ = [α β γ] T ;

[0042] The observation vector is:

[0043]

[0044] The recurrence loop formula is:

[0045]

[0046]

[0047] In the formula, K is the gain matrix; P is the covariance matrix; is the system estimation reference value; y(k + 1) is the actual system observation value; is the observation value matrix; Δt is the sampling time interval of 1 s;

[0048] The internal heat generation power Q of the battery c can be estimated according to the Bernardi equation. The heat capacity C of the aluminum-plastic film on the battery surface air can be obtained according to the data provided by the battery manufacturer, and its value is a fixed value.

[0049]

[0050] The parameter C can be obtained from the above formula c , R c , R air .

[0051] As a preferred technical solution of the present invention, the step S4 uses the neural network fitting method to fit the basic model parameters and the internal and external temperatures of the battery as follows:

[0052] S4.1. Prepare training data. Respectively, the internal and external temperature data T of the battery obtained from the experiment c , T s are used as input data, and the electrical model and thermal model parameters obtained by identifying using the FFRLS algorithm, i.e., the ohmic internal resistance R0, the electrochemical polarization resistance R1, the electrochemical polarization capacitance C1, the concentration difference polarization resistance R2, the concentration difference polarization capacitance C2, the battery heat capacity C c , the thermal resistance R between the inside of the battery and the battery surface c , the thermal resistance R between the battery surface and the external environment air are used as the target output data.

[0053] S4.2. Create a neural network. Create a feedforward neural network, select a network with a single hidden layer, and select an appropriate number of hidden nodes through cross-validation, and specify the number of hidden layer nodes as 10.

[0054] S4.3. Set the neural network parameters. Set the training function to use the Levenberg-Marquardt algorithm. This algorithm is an optimization algorithm for solving nonlinear least squares problems and is widely used in fields such as curve fitting and parameter estimation. It combines the advantages of the gradient descent method and the Gauss-Newton method and can flexibly adjust the optimization strategy in different situations; set the normalization ranges of the input and output.

[0055] S4.4. Train the neural network and the neural network model, and use the train function for fitting. This function is usually used in machine learning or deep learning frameworks to train the model. Its main role is to adjust the parameters of the model through optimization algorithms to minimize the loss function. During the training process, the weights and biases of the network are adjusted to make the network output match the target data as closely as possible.

[0056] S4.5. Evaluate the model performance and visualize the results. After training, draw a comparison graph between the real target data and the prediction results of the neural network to evaluate the model performance through comparison.

[0057] As a preferred technical solution of the present invention, the formula for constructing the transfer model in step S5 is as follows: Construct the transfer model between the internal temperature T of the battery c and the parameters of the basic model as follows:

[0058]

[0059] Construct the transfer model between the surface temperature T of the battery s and the parameters of the basic model as follows:

[0060]

[0061] In the above formula, X = [x1, x2, x 3, …, x 22 represents 22 undetermined transfer factors; T air , β represents the influence factors of the model affected by the ambient temperature and battery aging; represents the parameter corrected based on the transfer model at the current moment for the corresponding parameter, * represents each parameter of the model, k represents the state quantity at the current moment, m represents being corrected by the transfer model; g * (T i c / s,k , T air , β) represents the function for correcting each battery model parameter, T i c / s,k represents the inaccurate internal and external temperature values of the battery under the influence of ambient temperature and aging; f * (x1T i c / s,k +x2, T air , β) represents the mapping relationship between each model parameter and the internal and external temperature of the battery, x1T i c / s,k +x2 represents the corrected internal and external temperature values of the battery; I k represents the current at time k.

[0062] As a preferred technical solution of the present invention, step S5 completes the online migration of the migration factor through the weighted selection particle filter algorithm, thereby correcting the inaccurate internal and external temperature values of the single battery to obtain the accurate internal and external temperature values under the influence of the ambient temperature and aging. The specific steps are as follows:

[0063] S5.1. As time progresses, the migration factor matrix X = [x1, x2, x 3, …, x 22 follows a Gaussian distribution. Therefore, this matrix is used as the state variable of the system, and the terminal voltage of the battery is used as the observable of the system. The discrete state equation of the system is established as follows:

[0064]

[0065]

[0066]

[0067]

[0068] In the above formula, x 1,k , x 2,k , x 3,k ……, x 22,k and U t,k are the state equation and the observation equation of the system respectively. x ×,k represents the ×th migration factor at the kth moment, and x ×,k-1 represents the ×th migration factor at the (k - 1)th moment. is the system noise. is the variance of the system measurement noise. Rand is a number randomly generated among N particles. represents the output value of the ith particle system at the kth moment;

[0069] S5.2. Particle initialization. N initial particles are generated using the prior probability p(x k ): Their weights are where x k is the particle at the kth moment, is the ith particle at the kth moment, and δ(·) is the Dirichlet function.

[0070] S5.3. Next, predict the particle state. Predict the state of N particles at the kth moment through the state x k-1 at the (k - 1)th moment and calculate the predicted terminal voltage value corresponding to each , where is the system noise at the (k - 1)th moment.

[0071]

[0072] S5.4. Update the particle weights.

[0073]

[0074] In the above formula, is the system output value of the i-th particle at time k, and U t,k is the terminal voltage at time k, represents the particle weight at the current time, represents the updated particle weight, and σ 23 represents the standard deviation of the system measurement noise, and exp represents the natural logarithm.

[0075] S5.5. Select the best. Select the N particles with the largest weights among the N S particles.

[0076] S5.6. Normalize the particle weights.

[0077]

[0078] In the above formula, is the weight of the N S particles after update, is the normalized particle weight, is the updated particle weight in step S5.4, l represents the number of particles, represents the summation of the internal N S data.

[0079] S5.7. Filtering estimation, calculate the posterior probability density p(x S |U k | 1,k ) of the selected N

[0080]

[0081] In the above formula, U 1,k represents the actual voltage of U1 at time k, is the state of the N S particles at time k, and x k is the state of the N particles at time k.

[0082] S5.8. Weight restoration and normalization.

[0083]

[0084] In the above formula, is the normalized weight of all particles.

[0085] S5.9. Calculate the terminal voltage of the model.

[0086]

[0087] S5.10. Estimate the internal and external temperatures.

[0088]

[0089] In the above formula, is the exact internal temperature value affected by the ambient temperature and aging state, is the exact surface temperature value affected by the ambient temperature and aging state, is the state of the first particle at time k, is the state of the second particle at time k, is the normalized weight of all particles.

[0090] S5.11. Filter and denoise the estimated values of the internal temperature and surface temperature in the migration model. The Savitzky–Golay filter is used, which smooths the signal by polynomial fitting of local data points, can effectively remove high-frequency noise and retain the trend of the signal. The internal and external temperatures calculated by the migration model are used as the input of the filter to smooth and denoise the internal temperature and surface temperature values obtained in step S5.10.

[0091] Compared with the prior art, the present invention provides a method for estimating the internal temperature and surface temperature of a lithium battery based on a migration model, having the following beneficial effects:

[0092] 1. The present invention uses the simplified Bernardi equation as the heat generation model and the two-state lumped parameter heat model as the heat transfer model to simulate the internal heat transfer of the lithium-ion battery. The two models are coupled with the basic electrical model second-order RC equivalent circuit model as the basic heat model to construct a complete basic electro-thermal coupling model.

[0093] 2. The present invention uses a machine learning method. By considering the influence of different aging degrees of the battery and the working ambient temperature on the electro-thermal model parameters, a migration model is built on the basis of the fitting relationship between the parameters of the basic electro-thermal coupling model and the internal temperature and surface temperature. The influence degrees of the ambient temperature and aging on the model accuracy are set as uncertain quantities, and the existing model parameters are corrected by the slope and deviation, and then the real model parameters are obtained, and the basic model is linearly changed. By online determining the migration factor, the online determination of the real parameter information of the model is realized. Further, by migrating the inaccurate internal temperature and surface temperature values, the exact internal temperature and surface temperature values affected by temperature and aging can be obtained, making the lithium-ion battery have a good application prospect in the field of electric vehicles. Description of the Drawings

[0094] Figure 1 This is a schematic diagram of the process of the present invention;

[0095] Figure 2 This is a schematic diagram of the second-order RC equivalent circuit model of the present invention;

[0096] Figure 3 This is a schematic diagram of the electro-thermal coupling model of the present invention. Specific embodiments

[0097] Next, in combination with the accompanying drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

[0098] Please refer to Figures 1-3 , a method for estimating the internal temperature and surface temperature of a lithium battery based on a migration model, including the following steps:

[0099] S1: Obtain the charge and discharge data of a lithium-ion monomer battery under full-life wide temperature conditions, including the current, voltage, surface temperature, and tab temperature data of the monomer battery.

[0100] The specific steps are as follows: Conduct cyclic charge and discharge aging tests on different batteries of the same model. Use constant current and constant voltage to fully charge the battery, let it stand for 30 s, and then discharge it to the cut-off voltage of the battery. Repeat the above process. Discharge the battery to 90% and 80% of the nominal battery capacity respectively, and then conduct a working condition experiment in the temperature range of -20°C to 60°C to collect the current, voltage, surface temperature, and tab temperature data of the monomer battery; The UDDS-FUDS working condition experiment data is as follows:

[0101] Table 1 Experimental record data

[0102]

[0103] S2. Construct an equivalent circuit model and a battery thermal model of the lithium-ion monomer battery, where the equivalent circuit model is a second-order RC equivalent circuit model, and the battery thermal model includes a heat generation model and a heat transfer model.

[0104] Specifically, the simplified Bernardi equation is used as the heat generation model, and the two-state lumped parameter thermal model is used as the heat transfer model to simulate the heat transfer inside the battery, and the second-order RC equivalent circuit model, the heat generation model, and the heat transfer model are discretely expressed;

[0105] The discretized expression of the second-order RC equivalent circuit model established in step S2 is:

[0106]

[0107] In the above formula, U t (k) represents the terminal voltage of the circuit at the current moment; U ocv (k) represents the open-circuit voltage of the circuit at the current moment; I(k) represents the current of the circuit at the current moment; U1(k), U2(k) represent the terminal voltages corresponding to the polarization resistance and capacitance at the current moment; U1(k + 1), U2(k + 1) represent the terminal voltages corresponding to the polarization resistance and capacitance at the next moment; (k) represents the state quantity at the current moment; (k + 1) represents the state quantity at the next moment; R0 is the ohmic internal resistance; R1, R2 represent the polarization resistances; C1, C2 represent the polarization capacitances; τ1, τ2 represent the time constants; Δt represents the sampling time interval of 1 s.

[0108] In step S2, the discretized expression of the heat generation equation is:

[0109]

[0110] In the above formula, T(k) represents the core temperature of the battery at the current moment, and T represents the core temperature of the battery.

[0111] The discretized expression of the heat transfer equation is:

[0112]

[0113] In the above formula, Q c (k) represents the heat generation power of the single battery at the current moment; C c represents the heat capacity of the battery; R c represents the thermal resistance between the inside of the battery and the battery surface; C air represents the heat capacity of the battery surface housing; R air represents the thermal resistance between the battery surface and the external environment; T c (k), T s (k), T air (k) represent the internal temperature of the battery, the surface temperature of the battery, and the ambient temperature around the battery at the current moment, respectively.

[0114] S3. Steps for obtaining the SOC-OCV fitting curve and identifying the basic model parameters using the FFRLS algorithm are as follows:

[0115] S3.1. Extract the voltage and current data of the single battery in the HPPC working condition in step S1, and use the 6th-order polynomial fitting method to fit the relationship curve between the open-circuit voltage OCV and SOC.

[0116] Curve fitting: Using the experimental data under the HPPC condition, the relationship curve between SOC and OCV is obtained by fitting with a sixth-order polynomial. The fitting expression is as follows:

[0117]

[0118] Among them, represents the polynomial fitting parameter, represents the sum of the entire sixth-order polynomial, represents the different power terms of SOC;

[0119] S3.2. Respectively use the FFRLS algorithm to obtain the internal parameters of the electrical model and the thermal model. The identification parameters of the electrical model are the ohmic internal resistance R0, the electrochemical polarization resistance R1, the electrochemical polarization capacitance C1, the concentration difference polarization resistance R2, and the concentration difference polarization capacitance C2; the identification parameters of the thermal model are: the battery heat capacity C c , the thermal resistance R c between the inside of the battery and the battery surface, the heat capacity C air of the battery surface housing, and the thermal resistance R air between the battery surface and the external environment.

[0120] Under the normal temperature and brand-new state, based on the experimental data of the UDDS-FUDS condition obtained in S1, use the recursive least squares method with a forgetting factor to identify the parameters of the second-order RC equivalent circuit and the thermal model established in S2. The identification process is as follows:

[0121] Let the model parameter vector be θ = [α β γ] T

[0122] The observation vector is:

[0123]

[0124] The recurrence loop formula is:

[0125]

[0126]

[0127] In the formula, K is the gain matrix; P is the covariance matrix; is the system estimation reference value; y(k + 1) is the system actual observation value; is the observation value matrix; Δt is the sampling time interval of 1 s;

[0128] The internal heat generation power Q c of the battery can be estimated according to the Bernardi equation. The heat capacity C air of the aluminum-plastic film on the battery surface can be obtained according to the data provided by the battery manufacturer, and its value is a fixed value.

[0129]

[0130] The parameter C can be obtained from the above formula c and R c and R air .

[0131] S4. Obtain the fitting relationship between the parameters of the basic electro-thermal coupling model and the internal and external temperatures of the battery: Based on the internal and external temperature values of the battery obtained from the experiment in S1 and the electro-thermal coupling model parameters identified by FFRLS in S3, the relationship curves between the model parameters and the internal temperature and surface temperature of the battery are obtained respectively by the neural network fitting method;

[0132] Step S4 specifically includes the following steps:

[0133] S4.1. Prepare the training data. Respectively, the internal and external temperature data T c and T s obtained from the experiment are used as the input data, and the parameters of the electrical model and thermal model identified by using the FFRLS algorithm, namely the ohmic internal resistance R0, the electrochemical polarization resistance R1, the electrochemical polarization capacitance C1, the concentration polarization resistance R2, the concentration polarization capacitance C2, the battery heat capacity C c , the thermal resistance R c between the inside and the surface of the battery, and the thermal resistance R air between the surface of the battery and the external environment are used as the target output data.

[0134] S4.2. Create a neural network. Create a feedforward neural network, select a network with a single hidden layer, and select an appropriate number of hidden nodes through cross-validation, specifying the number of hidden layer nodes as 10.

[0135] S4.3. Set the neural network parameters. Set the training function to use the Levenberg-Marquardt algorithm, which is an optimization algorithm for solving nonlinear least squares problems and is widely used in fields such as curve fitting and parameter estimation. It combines the advantages of the gradient descent method and the Gauss-Newton method and can flexibly adjust the optimization strategy in different situations; set the normalization ranges of the input and output.

[0136] S4.4. Train the neural network. Train the neural network model and use the train function for fitting. This function is usually used in machine learning or deep learning frameworks to train the model. Its main role is to adjust the parameters of the model through the optimization algorithm to minimize the loss function. The training process will adjust the weights and biases of the network to make the network output match the target data as much as possible.

[0137] S4.5. Evaluate the model performance and visualize the results. After training is completed, draw a comparison graph between the real target data and the neural network prediction results to evaluate the model performance through comparison.

[0138] S5. Build a transfer model and correct the internal and external temperatures of the single cell: Based on the fitting relationship between the basic electro-thermal coupling model parameters obtained in S4 and the internal and external temperatures of the battery, build a transfer framework. Under different environmental temperatures and aging conditions, complete the online transfer of the transfer factor through the weighted selection particle filter algorithm to transfer the inaccurate internal and external temperature values of the single cell, and obtain the accurate internal and external temperature values under different environmental temperatures and aging states. The formula for building the transfer model is as follows:

[0139] Build the transfer model between the internal temperature T of the battery c and the basic model parameters as follows:

[0140]

[0141] Build the transfer model between the surface temperature T of the battery s and the basic model parameters as follows:

[0142]

[0143] In the above formula, X = [x1, x2, x 3, …, x 22 represents 22 undetermined transfer factors; T air , β represents the influencing factors of the model affected by the surrounding environmental temperature and battery aging; represents the parameter corrected based on the transfer model at the current moment of the corresponding parameter. * represents each parameter of the model, k represents the state quantity at the current moment, and m represents the correction through the transfer model; g * (T i c / s,k , T air , β) represents the function for correcting each battery model parameter. T i c / s,k represents the inaccurate internal and external temperature values of the battery under the influence of environmental temperature and aging; f * (x1T i c / s,k + x2, T air , β) represents the mapping relationship between each model parameter and the internal and external temperatures of the battery. x1T i c / s,k + x2 represents the corrected internal and external temperature values of the battery; I k represents the current at time k.

[0144] Step S5 specifically includes the following steps:

[0145] S5.1. As time progresses, the migration factor matrix X = [x1, x2, x 3, …, x 22 follows a Gaussian distribution. Therefore, this matrix is taken as the state variable of the system, and the terminal voltage of the battery is taken as the observable of the system. The discrete state equation of the system is established as follows:

[0146]

[0147]

[0148]

[0149]

[0150] In the above formula, x 1,k , x 2,k , x 3,k ……, x 22,k and U t,k are the state equation and the observation equation of the system respectively. x ×,k represents the ×-th migration factor at time k, and x ×,k-1 represents the ×-th migration factor at time k - 1. is the system noise, is the variance of the system measurement noise. Rand is to randomly generate a number among N particles. represents the output value of the i-th particle system at time k;

[0151] S5.2. Particle initialization. Using the prior probability p(x k ), N initial particles are generated: Their weights are where x k is the particle at the k-th moment, is the i-th particle at the k-th moment, and δ(·) is the Dirichlet function.

[0152] S5.3. Next, predict the particle state. Predict the state k-1 of N particles at time k through the state x at time k - 1, and calculate the predicted terminal voltage value corresponding to each , where is the system noise at time k - 1.

[0153]

[0154] S5.4. Update the particle weights.

[0155]

[0156] In the above formula, is the system output value of the i-th particle at time k, and U t,k is the terminal voltage at time k, represents the particle weight at the current time, represents the updated particle weight, and σ 23 represents the standard deviation of the system measurement noise, and exp represents the natural logarithm.

[0157] S5.5, Selective preference. Select the N S particles with the largest weights among the N particles.

[0158] S5.6, Particle weight normalization.

[0159]

[0160] In the above formula, is the weight of the N S particles after update, is the normalized particle weight, is the weight of the particles updated in step S5.4, l represents the number of particles, represents the sum of the internal N S data.

[0161] S5.7, Filtering estimation, calculate the posterior probability density p(x S |U k | 1,k ) of the selected N

[0162]

[0163] In the above formula, U 1,k represents the actual voltage of U1 at time k, is the state of the N S particles at time k, and x k is the state of the N particles at time k.

[0164] S5.8, Weight restoration and homogenization.

[0165]

[0166] In the above formula, is the normalized weight of all particles.

[0167] S5.9, Calculate the terminal voltage of the model.

[0168]

[0169] S5.10, Internal and external temperature estimation.

[0170]

[0171] In the above formula, is the accurate internal temperature value affected by the ambient temperature and aging state, is the accurate surface temperature value affected by the ambient temperature and aging state, is the state of the first particle at time k, is the state of the second particle at time k, is the normalized weight of all particles.

[0172] S5.11. Filter and denoise the estimated values of the internal temperature and surface temperature in the migration model. The Savitzky–Golay filter is used. It smooths the signal by polynomial fitting of local data points, can effectively remove high-frequency noise and retain the trend of the signal. Take the internal and external temperatures calculated by the migration model as the input of the filter, and smooth and denoise the internal temperature and surface temperature values obtained in step S5.10.

[0173] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for estimating the internal temperature and surface temperature of a lithium battery based on a migration model, characterized in that: It includes the following steps: S1: Obtain the charge and discharge data of a single lithium-ion battery under full-life wide-temperature conditions, including the current, voltage, surface temperature, and tab temperature data of the single battery; S2. Construct an equivalent circuit model and a battery thermal model for the single lithium-ion battery. The equivalent circuit model is a second-order RC equivalent circuit model, and the battery thermal model includes a heat generation model and a heat transfer model; S3. SOC-OCV curve fitting: Using the experimental data under the HPPC condition, obtain the relationship curve between SOC and OCV through sixth-order polynomial fitting. The fitting expression is as follows: Among them, represents the polynomial fitting parameter, represents the sum of the entire sixth-order polynomial, represents different power terms of SOC; Under normal temperature and brand-new state, based on the UDDS-FUDS condition experimental data obtained in S1, use the recursive least squares method with a forgetting factor to identify the parameters of the second-order RC equivalent circuit and thermal model established in S2. The identification process is as follows: Let the model parameter vector be: θ = [α β γ] T , The observation vector is: The recurrence formula is: where K is the gain matrix; P is the covariance matrix; is the system estimation reference value; y(k + 1) is the actual system observation value; is the observation value matrix; Δt is the sampling time interval of 1 s; The internal heat generation power Q of the battery c can be estimated according to the Bernardi equation. The heat capacity C of the aluminum-plastic film on the battery surface air can be obtained from the data provided by the battery manufacturer, and its value is a fixed value The parameter C can be obtained from the above formula c , R c , R air ; S4. Obtain the fitting relationship between the basic electro-thermal coupling model parameters and the internal and external temperatures of the battery: Based on the internal and external temperature values of the battery obtained from the experiment in S1 and the electro-thermal coupling model parameters identified by FFRLS in S3, use the neural network fitting method to obtain the relationship curves between the model parameters and the internal temperature and surface temperature of the battery respectively; S5. Construct a migration model and correct the internal and external temperatures of the single battery: Based on the fitting relationship between the basic electro-thermal coupling model parameters and the internal and external temperatures of the battery obtained in S4, build a migration framework. Under different environmental temperatures and aging conditions, complete the online migration of the migration factor through the weighted particle filter algorithm to migrate the inaccurate internal and external temperature values of the single battery, and obtain the accurate internal and external temperature values under different environmental temperatures and aging states.

2. The method for estimating the internal temperature and surface temperature of a lithium battery based on a migration model according to claim 1, wherein The charge and discharge data of the single lithium-ion battery under different environmental temperatures and different aging states collected in S1 include: voltage, current, surface temperature, and tab temperature data.

3. A method for estimating the internal temperature and surface temperature of a lithium battery based on a migration model according to claim 1, characterized in that, The second-order equivalent circuit model established in S2 is: The discretized model expression of the second-order RC equivalent circuit model is: In the above formula, U t (k) represents the terminal voltage of the circuit at the current moment; U ocv (k) represents the open-circuit voltage of the circuit at the current moment; I(k) represents the current of the circuit at the current moment; U1(k), U2(k) represent the terminal voltages corresponding to the polarization resistance and capacitance at the current moment; U1(k + 1), U2(k + 1) represent the terminal voltages corresponding to the polarization resistance and capacitance at the next moment; (k) represents the state quantity at the current moment; (k + 1) represents the state quantity at the next moment; R0 is the ohmic internal resistance; R1, R2 represent the polarization resistances; C1, C2 represent the polarization capacitances; τ1, τ2 represent the time constants; Δt represents the sampling time interval of 1 s; In step S2, the discretized expression of the heat generation equation is: In the above formula, T(k) represents the current core temperature of the battery, and T represents the core temperature of the battery; The discretized expression of the heat transfer equation is: In the above formula, Q c (k) represents the heat generation power of the single cell at the current moment; C c represents the heat capacity of the battery; R c represents the thermal resistance between the inside and the surface of the battery; C air represents the heat capacity of the battery surface housing; R air represents the thermal resistance between the battery surface and the external environment; T c (k), T s (k), T air (k) represent the internal temperature of the battery, the surface temperature of the battery, and the ambient temperature around the battery at the current moment, respectively.

4. A method for estimating the internal temperature and surface temperature of a lithium battery based on a migration model according to claim 1, characterized in that, The steps of obtaining the SOC-OCV fitting curve and identifying the basic model parameters using the FFRLS algorithm in S3 are as follows: S3.

1. Extract the voltage and current data of the single battery in S1 during the HPPC condition experiment, and use the sixth-order polynomial fitting method to fit the relationship curve between the open-circuit voltage OCV and SOC; S3.

2. Respectively use the FFRLS algorithm to obtain the internal parameters of the electrical model and the thermal model, where the identification parameters of the electrical model are the ohmic internal resistance R0, the electrochemical polarization resistance R1, the electrochemical polarization capacitance C1, the concentration difference polarization resistance R2, and the concentration difference polarization capacitance C2; the identification parameters of the thermal model are: the battery heat capacity C c , the thermal resistance R between the inside of the battery and the battery surface c , the heat capacity C of the battery surface housing air , the thermal resistance R between the battery surface and the external environment air .

5. The method for estimating the internal temperature and surface temperature of a lithium battery based on a migration model according to claim 1, wherein The steps of using the neural network fitting method in S4 to fit the basic model parameters and the internal and external temperatures of the battery are as follows: S4.

1. Prepare training data, and use the internal and external temperature data T of the battery obtained from the experiment c , T s as input data, and use the electrical model and thermal model parameters Ohmic internal resistance R0, electrochemical polarization resistance R1, electrochemical polarization capacitance C1, concentration polarization resistance R2, concentration polarization capacitance C2, battery heat capacity C c , the thermal resistance R between the inside of the battery and the battery surface c , the thermal resistance R between the battery surface and the external environment air as the target output data; S4.

2. Create a neural network, create a feedforward neural network, select a network with a single hidden layer, and select an appropriate number of hidden nodes through cross-validation, and specify the number of hidden layer nodes as 10; S4.

3. Set the neural network parameters, set the training function, and use the Levenberg-Marquardt algorithm. This algorithm is an optimization algorithm for solving nonlinear least squares problems and is widely used in curve fitting and parameter estimation fields. It combines the advantages of the gradient descent method and the Gauss-Newton method and can flexibly adjust the optimization strategy under different circumstances; set the normalization ranges of the input and output; S4.

4. Train the neural network, train the neural network model, and use the train function for fitting. This function is usually used in machine learning or deep learning frameworks to train the model. Its main function is to adjust the parameters of the model through the optimization algorithm to minimize the loss function. The training process will adjust the weights and biases of the network to make the network output match the target data as much as possible; S4.

5. Evaluate the model performance and visualize the results. After training, draw a comparison graph between the real target data and the neural network prediction results to evaluate the model performance through comparison.

6. The method for estimating the internal temperature and surface temperature of a lithium battery based on a migration model according to claim 1, wherein The S5 constructs the internal battery temperature T c The migration model between the basic model parameters is as follows: Construct the battery surface temperature T s The migration model between the In the above formula, X = [x1, x2, x 3, …, x 22 represents 22 undetermined migration factors; T air , β represents the influence factors of the model affected by the surrounding environmental temperature and battery aging; represents the parameter corrected based on the migration model at the current moment of the corresponding parameter. * represents each parameter of the model, k represents the state quantity at the current moment, and m represents being corrected by the migration model; g * (T i c / s,k , T air , β) represents the function for correcting each battery model parameter. T i c / s,k represents the inaccurate internal and external battery temperature values under the influence of environmental temperature and aging; f * (x1T i c / s,k + x2, T air , β) represents the mapping relationship between each model parameter and the internal and external battery temperature. x1T i c / s,k + x2 represents the corrected internal and external battery temperature value; I k represents the current at time k.

7. A method for estimating the internal temperature and surface temperature of a lithium battery based on a migration model according to claim 1, characterized in that The above S5 completes the online migration of the migration factor through the weighted particle filter algorithm, thereby correcting the inaccurate internal and external temperature values of the single battery to obtain the accurate internal temperature and surface temperature values under the influence of the ambient temperature and aging. The specific steps are as follows: S5.

1. As time goes by, the migration factor matrix X = [x1, x2, x 3, …, x 22 , follows a Gaussian distribution. Therefore, this matrix is taken as the state variable of the system, and the terminal voltage of the battery is taken as the observable of the system. The discrete state equation of the system is established as follows: In the above formula, x 1,k , x 2,k , x 3,k ……, x 22,k and U t,k are the state equation and the observation equation of the system respectively. x ×,k represents the ×-th migration factor at time k, and x ×,k-1 represents the ×-th migration factor at time k - 1. is the system noise. is the variance of the system measurement noise. Rand generates a number randomly among N particles. represents the output value of the i-th particle system at time k; S5.

2. Particle initialization. Using the prior probability p(x k ), N initial particles are generated: Their weights are where x k is the particle at the k-th moment, is the i-th particle at the k-th moment, and δ(·) is the Dirichlet function; S5.

3. Next, predict the particle state. Predict the states of N particles at time k through the state x at time k-1 k-1 and calculate the predicted terminal voltage value corresponding to each where is the system noise at time k-1; ​ S5.

4. Update the particle weights: In the above formula, is the system output value of the i-th particle at the k-th moment, and U t,k is the terminal voltage at the k-th moment, represents the particle weight at the current moment, represents the updated particle weight, and σ 23 represents the standard deviation of the system measurement noise, and exp represents the natural logarithm; S5.

5. Optimal selection. Select the N particles with the largest weights among the N particles; S particles; S5.

6. Normalize the particle weights: In the above formula, is the N after update S particle weights, is the normalized particle weight, is the updated particle weight in step S5.4, l represents the number of particles, represents the sum of the internal N S data; S5.

7. Filtering estimation, calculating the posterior probability density p(x S |U k ) of the selected N 1,k particles: In the above formula, U 1,k represents the actual voltage of U1 at time k, is the state of N S particles at time k, and x k is the state of N particles at time k; S5.

8. Weight restoration and normalization: In the above formula, is the normalized weight of all particles; S5.

9. Calculate the terminal voltage of the model. S5.

10. Estimate the internal and external temperatures: In the above formula, is the precise internal temperature value affected by the environmental temperature and aging state, is the precise surface temperature value affected by the environmental temperature and aging state, is the state of the first particle at time k, is the state of the second particle at time k, is the normalized weight of all particles; S5.

11. Perform filtering and noise reduction processing on the estimated values of the internal temperature and surface temperature in the migration model: Use the Savitzky–Golay filter, which smooths the signal by polynomial fitting of local data points, can effectively remove high-frequency noise and retain the trend of the signal; use the internal and external temperatures calculated by the migration model as the input of the filter to perform smoothing and noise reduction processing on the internal temperature and surface temperature values obtained in S5.10.

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