Online estimation method of multi-point internal temperature of square lithium battery based on ASRUKF

Abstract

The present invention relates to the technical field of lithium-ion battery state estimation, and discloses a method for online estimation of the internal temperature of multiple points of a square lithium battery based on ASRUKF. The method is based on a second-order RC equivalent circuit model and a three-heat source heat generation model, combined with a two-state lumped heat transfer model, to construct an electrothermal coupling model for a lithium battery; and the model parameters are identified to achieve accurate modeling of the internal temperature estimation of lithium-ion batteries under a wide temperature range over the entire life cycle; a multi-point temperature heat transfer model is established, and the temperature of representative regions is discretized to obtain the system state space equation and measurement equation, to achieve multi-point temperature estimation of square batteries; an adaptive square root unscented Kalman filter algorithm is integrated to estimate the internal temperature of different points of a square lithium battery, and the estimated internal temperature is used as feedback to update the circuit model parameters, to achieve coupling of the electrothermal model and online estimation of the internal temperature of multiple points.

Description

Technical Field

[0001] The invention relates to the technical field of lithium-ion battery state estimation, and in particular to an ASRUKF-based online estimation method for multi-point internal temperature of a square lithium battery. Background Art

[0002] With the development of electric vehicle technology and the expansion of the market, the safety and reliability of lithium-ion batteries as the internal power components of electric vehicles have attracted much attention. As a power source, lithium batteries often need to work under complex driving conditions, and the battery temperature state changes accordingly. Accurately estimating the internal temperature of lithium batteries under different working environments is crucial to ensure the safe use of batteries.

[0003] In practical applications, the internal temperature state of battery cells can only be obtained through built-in sensors, but installing sensors in batteries used in groups on vehicles will undoubtedly increase costs and the risk of loss of control. At present, the research approaches for estimating the internal state of batteries mainly include: establishing a finite element model based on simulation software to simulate and analyze the heat generation and heat transfer mechanism inside lithium batteries. This method cannot fully consider the influence of various external factors in practical applications, and the results are too idealized; although the data-driven research method is more realistic, it requires a large amount of historical data to support model training; although the partial differential equation based on the chemical reaction mechanism of lithium batteries can fully reflect the reaction kinetics behavior inside the battery, it requires a large amount of partial differential calculations, has strong parameter dependence, and the model is complex and has a large amount of calculation; based on the resistance and capacitance characteristics of lithium batteries, an equivalent circuit model is established, and the internal charge and discharge characteristics of lithium batteries are simulated by a combination of electronic components, and the internal temperature of the battery is estimated by coupling with the thermal model. The physical meaning is clear, the model is simple, and the result is highly accurate. Among them, the square battery has a large area, and the heating conditions in different areas inside the battery are different. Excessive local temperature may cause thermal runaway of the battery starting from a point.

[0004] At present, there is still a lack of research on multi-point temperature estimation of square batteries. It is very meaningful to establish an electrothermal coupling model that conforms to realistic application scenarios and covers a wide temperature operating range within the entire cycle life cycle of the battery to accurately estimate the internal temperature of the battery and enable online application. Summary of the invention

[0005] 1. Technical issues to be resolved

[0006] In view of the shortcomings of the prior art, the present invention provides an online estimation method for multi-point internal temperature of a square lithium battery based on ASRUKF, which has the advantages of small calculation amount, high accuracy and strong robustness, and solves the above technical problems.

[0007] (II) Technical solution

[0008] To achieve the above object, the present invention provides the following technical solution: an online estimation method for multi-point internal temperature of a square lithium battery based on ASRUKF, comprising the following steps:

[0009] S1: Obtain the charge and discharge data of lithium-ion single cells under full life and wide temperature conditions. The specific steps are as follows: perform cyclic charge and discharge aging tests on different batteries of the same model, fully charge the battery using constant current and constant voltage, let it stand for 30 seconds, and then discharge it to the battery cut-off voltage. Repeat the above process to discharge the battery to 95%, 85%, and 80% of the nominal capacity, respectively, and then perform working condition experiments within the temperature range of -20℃ to 60℃, and record the battery's current, voltage, representative area, and lug temperature;

[0010] S2. Establish an equivalent circuit model and a thermal model, wherein 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 a simplified three-heat source heat generation model to represent the heat generation inside the battery, and uses a two-state lumped parameter thermal model as a heat transfer model to represent the heat transfer inside the battery. The second-order RC equivalent circuit model, the simplified three-heat source heat generation model, and the two-state lumped parameter thermal model are discretized. After discretization, a lithium-ion battery internal temperature estimation model is established to obtain the state space equation and measurement equation of the system;

[0011] S3. Model parameter identification: Using the experimental data under HPPC working conditions, the relationship curve between SOC and OCV is obtained through 6th-order polynomial fitting. The fitting expression is as follows:

[0012]

[0013] in, represents the polynomial fitting parameters, represents the sum of the entire sixth-order polynomial, Represents different powers of SOC;

[0014] Under different aging conditions at a wide temperature, based on the battery charge and discharge experimental data obtained by S1, the FFRLS algorithm is used to perform parameter identification on the second-order RC equivalent circuit and parameter thermal model established in S2. The identification process is as follows:

[0015] Calculation error:

[0016] e(k)=y(k)-φ T (k)θ(k-1)

[0017] Calculate the gain vector:

[0018]

[0019] Update the parameter vector:

[0020] θ(k)=θ(k-1)+K(k)e(k)

[0021] Update the covariance matrix:

[0022]

[0023] Among them, e(k) represents the prediction error at the current moment, y(k) represents the system output at the current moment, φ(k) is the system regression vector at the current moment, and φ T (k) is the transpose of φ(k), H(k-1) represents the covariance at the previous moment, θ(k) is the parameter vector at the current moment, θ(k-1) represents the parameter vector at the previous moment, K(k) is the gain vector at the current moment, H(k) is the system covariance matrix at the current moment, and λ is the forgetting factor;

[0024] S4, online estimation of the internal temperature of different points of the square lithium battery based on the ASRUKF algorithm: Based on the system state space equation and measurement equation obtained in S2, the terminal voltage and open circuit voltage output by the second-order RC equivalent circuit model are substituted into the three-heat source heat generation model to calculate the battery heat generation power, and then the two-state lumped parameter thermal model is combined with the ASRUKF algorithm to estimate the internal temperature of multiple points of the lithium battery;

[0025] S5. Coupling of equivalent circuit model and thermal model and updating of model parameters: resistance and capacitance parameters R0, R1, R2, C1, C2 in the second-order RC equivalent circuit model and thermal parameter R in the heat transfer model c , C c It will change with the temperature of the battery, and update the parameters identified based on S3 under different temperature gradients.

[0026] As a preferred technical solution of the present invention, the expression of the second-order RC equivalent circuit model in step S2 is as follows:

[0027] U OCV (t) = U TOV (t)-R0I(t)-U1(t)-U2(t)

[0028]

[0029] Among them, U OCV (t) represents the open circuit voltage at time t, U TOV(t) represents the terminal voltage at time t, I(t) represents the current at time t, U1(t) and U2(t) represent the polarization voltage at time t, R0 represents the battery ohmic internal resistance, R1 and R2 represent polarization resistance, C1 and C2 represent polarization capacitance, τ1 and τ2 represent time constants, e represents a natural constant, Δt represents the sampling time interval, and the second-order RC equivalent circuit model is discretized using the Euler method, and the obtained expression is as follows:

[0030]

[0031] Among them, U OCV (k) is the current battery open circuit voltage, U TOV (k) is the battery terminal voltage at the current moment, I(K) is the battery current at the current moment, I(K-1) represents the battery current at the previous moment, R0 is the battery ohm internal resistance, U1(k) and U2(k) are the terminal voltages corresponding to the polarization resistors R1 and R2 and polarization capacitors C1 and C2 at the current moment, U1(k-1) and U2(k-1) are the terminal voltages corresponding to the polarization resistors R1 and R2 and polarization capacitors C1 and C2 at the previous moment, τ1 and τ2 are time constants, (k) represents the state quantity at the current moment, and (k-1) represents the state quantity at the previous moment;

[0032] The simplified three-heat source heat generation model is expressed as follows:

[0033]

[0034] Among them, Q c (t) represents the heat generation power of the battery cell at time t, U OCV (t) represents the open circuit voltage at time t, U TOV (t) represents the terminal voltage at time t, I(t) represents the current at time t, Q n (t), Q p (t) represents the heat generation power of the two tabs at time t, T 3c (t) represents the internal temperature of the battery at time t, Indicates U OCV To T 3c The partial derivative, R e , R p , R n Represent the internal resistance of the battery cell, positive electrode and negative electrode respectively. Discretize the simplified three-heat source heat generation model, and the expression obtained is as follows:

[0035]

[0036] Among them, Q c (k) represents the heat generation power of the battery cell at the current moment, I(k) is the battery current at the current moment, UOCV (k) is the current battery open circuit voltage, U TOV (k) is the battery terminal voltage at the current moment, Q n (k), Q p (k) respectively represent the heat generation power of the two tabs at the current moment;

[0037] The two-state lumped parameter thermal model expression is as follows:

[0038]

[0039] Among them, T 1c (t), T 2c (t), T 3c (t), T 4c (t) represents the internal temperature of the four measurement points of the battery at time t, R c Represents the internal resistance between the battery surface and the interior, C c Indicates the internal resistance of the battery surface shell, T p (t) represents the positive electrode lug temperature at time t, T n (t) represents the negative electrode lug temperature at time t, T 1s (t), T 2s (t), T 3s (t), T 4s (t) represents the surface temperature of the four measurement points on the battery surface at time t. The discretization expression of the two-state lumped parameter thermal model is as follows:

[0040]

[0041] in, Respectively represent the estimated internal temperature of the four measurement points of the battery at the current moment, T 1s (k), T 2s (k), T 3s (k), T 4s (k) represents the surface temperature of the four measurement points of the battery at the current moment, R c Represents the internal resistance between the battery surface and the interior, C c Indicates the internal resistance of the battery surface shell;

[0042] The internal temperature estimation model of lithium-ion batteries is established, and the state space equation and measurement equation of the system are obtained as follows:

[0043]

[0044] Among them, X k represents the current state vector, A represents the state transfer matrix; B is the system control matrix; u k-1 is the control quantity at the previous moment; Z kV is the state vector measured at the current moment; k-1 is the measurement noise matrix R at the previous moment k-1 Covariance of white Gaussian measurement noise T xs,k-1 Represents the transformation matrix from state quantity to observation quantity.

[0045] As a preferred technical solution of the present invention, the expression of the state transfer matrix is ​​as follows:

[0046]

[0047] The expression of the current state vector is as follows:

[0048]

[0049] The expression of the system control matrix is ​​as follows:

[0050]

[0051] The expression of the control quantity at the current moment is as follows:

[0052] u k =[Q p (k) T 1s (k) T p (k) Q n (k) T 2s (t) T n (k) Q c (k) T 3s (k)] T

[0053] Among them, T 1c (t), T 2c (t), T 3c (t), T 4c (t) represents the internal temperature of the four measurement points of the battery at time t, R c Represents the internal resistance between the battery surface and the interior, C c Indicates the internal resistance of the battery surface shell, T p (t) represents the positive electrode lug temperature at time t, T n (t) represents the negative electrode lug temperature at time t, T 1s (t), T 2s (t), T 3s (t), T 4s (t) represents the surface temperature of the four measurement points on the battery surface at time t, Q n (k), Q p (k) represents the heat generation power of the two tabs at the current moment.

[0054] As a preferred technical solution of the present invention, step S4 specifically includes the following steps:

[0055] S4.1. Initialization of state function. The specific expression is as follows:

[0056]

[0057] Among them, x0 represents the state vector at time 0, represents the expected value of the state vector, E[*] represents the mathematical expectation of the calculated parameters, P0 represents the initial value of the error covariance matrix, the superscript T represents the transpose, chol(P0) represents the Cholesky decomposition of P0, S0 represents the initial value of the square root, represents the initial value of process noise, represents the initial value of the measurement noise, Q0 and R0 represent the process noise and measurement noise at time 0, respectively;

[0058] S4.2, Sigma point weight selection, the specific expression is as follows:

[0059]

[0060] Among them, γ represents the scale factor, represents the mean weight of the 0th Sigma point, represents the covariance weight of the 0th Sigma point, i represents the sequence number of other Sigma points, Represents the mean weight of other Sigma points, represents the covariance weight of other Sigma points, α represents the state parameter, L represents the state variable dimension, and k represents the quadratic scaling parameter;

[0061] The expression for constructing the Sigma point is as follows:

[0062]

[0063] in, represents the state vector at the previous moment, S k represents the square root value at the current moment, γ represents the proportional factor, and χ k-1 represents the vector composed of the Sigma points at the previous moment, and L represents the dimension of the state variable;

[0064] S4.3, time update, the expression for calculating the state estimate and the square root error covariance is as follows:

[0065]

[0066] in, Represents the Sigma point of the current state estimate, represents the current estimated covariance matrix, qr[*] represents the Perform QR decomposition, f(χ k-1 ,u k-1 ) represents the state transition function of the system, S k represents the updated covariance matrix, cholupdate(*) represents the cholupdate function used to update the covariance matrix, Q k represents the process noise at the current moment;

[0067] S4.4, Sigma point resampling, the expression is as follows:

[0068]

[0069] Predict the observed values ​​of the system:

[0070]

[0071] in, represents the estimated observation value, h[ζ k ] represents the observation function, and the state Sigma point ζ k Mapped to the observation space, represents the current state estimate, e k Represents the residual at the current moment;

[0072] Estimation of measurement noise:

[0073]

[0074] Where R represents the measurement noise covariance matrix, R ** represents the updated measurement noise covariance matrix, R * represents the further updated measurement noise covariance matrix, represents the final updated measurement noise covariance matrix, d k represents the scalar gain factor, d k =(1-b) / (1-b k+1 ), b represents the forgetting factor, b k+1 represents the forgetting factor at the next moment, represents the predicted observation value vector obtained by Sigma point propagation, and diag(*) represents the construction of a diagonal matrix;

[0075] Updates to the variance matrix and error covariance:

[0076]

[0077] Among them, S * y,k is the updated observation error covariance matrix, S* y,k is the observation error covariance matrix after further update, P xy,k is the cross covariance matrix between the state quantity and the observation quantity;

[0078] Calculate the Kalman gain matrix and update the estimator and variance:

[0079]

[0080] Update of process noise:

[0081]

[0082] in, represents the process noise covariance matrix at the previous moment, Q ** represents the updated process noise covariance matrix, Q * represents the further updated process noise covariance matrix, Represents the final updated process noise covariance matrix.

[0083] Compared with the prior art, the present invention provides an online estimation method for multi-point internal temperature of a square lithium battery based on ASRUKF, which has the following beneficial effects:

[0084] 1. The present invention adopts a three-heat source heat generation model through the heat generation model, which characterizes the heat generation of the tab and the inside of the battery respectively, and can fully describe the different characteristics of heat generation in different areas of the square lithium battery during the charging and discharging process. It is coupled with the second-order RC equivalent circuit model to accurately describe the resistance-capacitance characteristics and heat generation characteristics of the battery. The model has low calculation complexity, which can improve the calculation efficiency while ensuring accuracy. The ASRUKF algorithm is integrated to estimate the multi-point internal temperature of the square lithium battery. The adaptive mechanism and square root filtering method are combined to achieve more stable temperature estimation in high noise or nonlinear systems.

[0085] 2. The present invention considers the influence of external temperature on the parameters of the electrothermal model under different aging degrees of the battery, adopts battery circuit parameters that match the current temperature state of the battery under full cycle life to calculate the terminal voltage and open circuit voltage, considers the influence of different working environment temperatures of the lithium battery on the model parameters, uses the currently estimated internal temperature as feedback to update the circuit model parameters online, and dynamically adjusts the model parameters to adapt to the changes in the actual working environment temperature, thereby improving the accuracy and real-time performance of temperature estimation. Considering the large area of ​​square lithium batteries and the uneven internal heat generation, combined with experimental analysis, representative heating areas are modeled, and a heat generation and heat transfer model from the tabs to the inside of the battery is established to achieve online estimation of the multi-point internal temperature of square lithium batteries. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 It is a schematic diagram of the process of the present invention;

[0087] Figure 2 It is a schematic diagram of the second-order RC equivalent circuit model of the present invention;

[0088] Figure 3 It is a schematic diagram of the heat generation model of three heat sources of the present invention. DETAILED DESCRIPTION

[0089] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0090] See also Figure 1-3 , an online estimation method of multi-point internal temperature of square lithium battery based on ASRUKF, comprising the following steps:

[0091] S1: Obtain the charge and discharge data of lithium-ion single cells under full life and wide temperature conditions. The specific steps are: perform cyclic charge and discharge aging tests on different batteries of the same model, fully charge the battery using constant current and constant voltage, let it stand for 30 seconds, and then discharge it to the battery cut-off voltage. Repeat the above process, discharge the battery to 95%, 85%, and 80% of the nominal capacity, respectively, and then perform working condition experiments in the temperature range of -20℃ to 60℃, record the battery's current, voltage, representative area, and lug temperature. The experimental data are recorded as follows:

[0092] Table 1 Experimental record data

[0093]

[0094] S2. Establish an equivalent circuit model and a thermal model, wherein 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 a simplified three-heat source heat generation model to represent the heat generation inside the battery, and uses a two-state lumped parameter thermal model as a heat transfer model to represent the heat transfer inside the battery. The second-order RC equivalent circuit model, the simplified three-heat source heat generation model, and the two-state lumped parameter thermal model are discretized. After discretization, a lithium-ion battery internal temperature estimation model is established to obtain the state space equation and measurement equation of the system. The expression of the second-order RC equivalent circuit model in step S2 is as follows:

[0095] U OCV (t) = U TOV (t)-R0I(t)-U1(t)-U2(t)

[0096]

[0097] Among them, U OCV (t) represents the open circuit voltage at time t, U TOV (t) represents the terminal voltage at time t, I(t) represents the current at time t, U1(t) and U2(t) represent the polarization voltage at time t, R0 represents the battery ohmic internal resistance, R1 and R2 represent polarization resistance, C1 and C2 represent polarization capacitance, τ1 and τ2 represent time constants, e represents a natural constant, Δt represents the sampling time interval, and the second-order RC equivalent circuit model is discretized using the Euler method, and the obtained expression is as follows:

[0098]

[0099] Among them, U OCV (k) is the current battery open circuit voltage, U TOV (k) is the battery terminal voltage at the current moment, I(K) is the battery current at the current moment, I(K-1) represents the battery current at the previous moment, R0 is the battery ohm internal resistance, U1(k) and U2(k) are the terminal voltages corresponding to the polarization resistors R1 and R2 and polarization capacitors C1 and C2 at the current moment, U1(k-1) and U2(k-1) are the terminal voltages corresponding to the polarization resistors R1 and R2 and polarization capacitors C1 and C2 at the previous moment, τ1 and τ2 are time constants, (k) represents the state quantity at the current moment, and (k-1) represents the state quantity at the previous moment;

[0100] The simplified three-heat source heat generation model is expressed as follows:

[0101]

[0102] Among them, Q c (t) represents the heat generation power of the battery cell at time t, U OCV (t) represents the open circuit voltage at time t, U TOV (t) represents the terminal voltage at time t, I(t) represents the current at time t, Q n (t), Q p (t) represents the heat generation power of the two tabs at time t, T3(t) represents the internal temperature of the battery at time t, Indicates U OCV To T 3c The partial derivative, R e , R p , R n Represent the internal resistance of the battery cell, positive electrode and negative electrode respectively. Discretize the simplified three-heat source heat generation model, and the expression obtained is as follows:

[0103]

[0104] Among them, Q c (k) represents the heat generation power of the battery cell at the current moment, I(k) is the battery current at the current moment, U OCV (k) is the current battery open circuit voltage, U TOV (k) is the battery terminal voltage at the current moment, Q n (k), Q p (k) respectively represent the heat generation power of the two tabs at the current moment;

[0105] The two-state lumped parameter thermal model expression is as follows:

[0106]

[0107] Among them, T 1c (t), T 2c (t), T 3c (t), T 4c (t) represents the internal temperature of the four measurement points of the battery at time t, R c Represents the internal resistance between the battery surface and the interior, C c Indicates the internal resistance of the battery surface shell, T p (t) represents the positive electrode lug temperature at time t, T n (t) represents the negative electrode lug temperature at time t, T 1s (t), T 2s (t), T 3s (t), T 4s (t) represents the surface temperature of the four measurement points on the battery surface at time t. The discretization expression of the two-state lumped parameter thermal model is as follows:

[0108]

[0109] in, Respectively represent the estimated internal temperature of the four measurement points of the battery at the current moment, T 1s (k), T 2s (k), T 3s (k), T 4s (k) represents the surface temperature of the four measurement points of the battery at the current moment, R c Represents the internal resistance between the battery surface and the interior, C c Indicates the internal resistance of the battery surface shell;

[0110] The internal temperature estimation model of lithium-ion batteries is established, and the state space equation and measurement equation of the system are obtained as follows:

[0111]

[0112] Among them, Xk represents the current state vector, A represents the state transfer matrix; B is the system control matrix; u k-1 is the control quantity at the previous moment; Z k V is the state vector measured at the current moment; k-1 is the measurement noise matrix R at the previous moment k-1 Covariance of white Gaussian measurement noise T xs,k-1 Represents the conversion matrix from state quantity to observation quantity;

[0113] The expression of the state transfer matrix is ​​as follows:

[0114]

[0115] The expression of the current state vector is as follows:

[0116]

[0117] The expression of the system control matrix is ​​as follows:

[0118]

[0119] The expression of the control quantity at the current moment is as follows:

[0120] u k =[Q p (k) T 1s (k) T p (k) Q n (k) T 2s (t) T n (k) Q c (k) T 3s (k)] T

[0121] Among them, T 1c (t), T 2c (t), T 3c (t), T 4c (t) represents the internal temperature of the four measurement points of the battery at time t, R c Represents the internal resistance between the battery surface and the interior, C c Indicates the internal resistance of the battery surface shell, T p (t) represents the positive electrode lug temperature at time t, T n (t) represents the negative electrode lug temperature at time t, T 1s (t), T 2s (t), T 3s (t), T 4s (t) represents the surface temperature of the four measurement points on the battery surface at time t, Q n (k), Qp (k) respectively represent the heat generation power of the two tabs at the current moment;

[0122] S3. Model parameter identification: Using the experimental data under HPPC working conditions, the relationship curve between SOC and OCV is obtained through sixth-order polynomial fitting. The fitting expression is as follows:

[0123]

[0124] in, represents the polynomial fitting parameters, represents the sum of the entire sixth-order polynomial, Represents different powers of SOC;

[0125] Under different aging conditions at a wide temperature, based on the battery charge and discharge experimental data obtained by S1, the FFRLS algorithm is used to perform parameter identification on the second-order RC equivalent circuit and parameter thermal model established in S2. The identification process is as follows:

[0126] Calculation error:

[0127] e(k)=y(k)-φ T (k)θ(k-1)

[0128] Calculate the gain vector:

[0129]

[0130] Update the parameter vector:

[0131] θ(k)=θ(k-1)+K(k)e(k)

[0132] Update the covariance matrix:

[0133]

[0134] Among them, e(k) represents the prediction error at the current moment, y(k) represents the system output at the current moment, φ(k) is the system regression vector at the current moment, and φ T (k) is the transpose of φ(k), H(k-1) represents the covariance at the previous moment, θ(k) is the parameter vector at the current moment, θ(k-1) represents the parameter vector at the previous moment, K(k) is the gain vector at the current moment, H(k) is the system covariance matrix at the current moment, and λ is the forgetting factor;

[0135] S4, online estimation of the internal temperature of different points of the square lithium battery based on the ASRUKF algorithm: Based on the system state space equation and measurement equation obtained in S2, the terminal voltage and open circuit voltage output by the second-order RC equivalent circuit model are substituted into the three-heat source heat generation model to calculate the battery heat generation power, and then the two-state lumped parameter thermal model is combined with the ASRUKF algorithm to estimate the internal temperature of multiple points of the lithium battery;

[0136] Step S4 specifically includes the following steps:

[0137] S4.1. Initialization of state function. The specific expression is as follows:

[0138]

[0139] Among them, x0 represents the state vector at time 0, represents the expected value of the state vector, E[*] represents the mathematical expectation of the calculated parameters, P0 represents the initial value of the error covariance matrix, the superscript T represents the transpose, chol(P0) represents the Cholesky decomposition of P0, S0 represents the initial value of the square root, represents the initial value of process noise, represents the initial value of the measurement noise, Q0 and R0 represent the process noise and measurement noise at time 0, respectively;

[0140] S4.2, Sigma point weight selection, the specific expression is as follows:

[0141]

[0142] Among them, γ represents the scale factor, represents the mean weight of the 0th Sigma point, represents the covariance weight of the 0th Sigma point, i represents the sequence number of other Sigma points, Represents the mean weight of other Sigma points, represents the covariance weight of other Sigma points, α represents the state parameter, L represents the state variable dimension, and κ represents the quadratic scaling parameter;

[0143] The expression for constructing the Sigma point is as follows:

[0144]

[0145] in, represents the state vector at the previous moment, S k represents the square root value at the current moment, γ represents the proportional factor, and χ k-1 represents the vector composed of the Sigma points at the previous moment, and L represents the dimension of the state variable;

[0146] S4.3, time update, the expression for calculating the state estimate and the square root error covariance is as follows:

[0147]

[0148] in, Represents the Sigma point of the current state estimate, represents the current estimated covariance matrix, qr[*] represents the Perform QR decomposition, f(χ k-1 ,u k-1 ) represents the state transition function of the system, S k represents the updated covariance matrix, cholupdate(*) represents the cholupdate function used to update the covariance matrix, Q k represents the process noise at the current moment;

[0149] S4.4, Sigma point resampling, the expression is as follows:

[0150]

[0151] Predict the observed values ​​of the system:

[0152]

[0153] in, represents the estimated observation value, h[ζ k ] represents the observation function, and the state Sigma point ζ k Mapped to the observation space, represents the current state estimate, e k Represents the residual at the current moment;

[0154] Estimation of measurement noise:

[0155]

[0156] Where R represents the measurement noise covariance matrix, R ** represents the updated measurement noise covariance matrix, R * represents the further updated measurement noise covariance matrix, represents the final updated measurement noise covariance matrix, d k represents the scalar gain factor, d k =(1-b) / (1-b k+1 ), b represents the forgetting factor, b k+1 represents the forgetting factor at the next moment, represents the predicted observation value vector obtained by Sigma point propagation, and diag(*) represents the construction of a diagonal matrix;

[0157] Updates to the variance matrix and error covariance:

[0158]

[0159] Among them, S * y,k is the updated observation error covariance matrix, S * y,k is the observation error covariance matrix after further update, P xy,k is the cross covariance matrix between the state quantity and the observation quantity;

[0160] Calculate the Kalman gain matrix and update the estimator and variance:

[0161]

[0162] Update of process noise:

[0163]

[0164] in, represents the process noise covariance matrix at the previous moment, Q ** represents the updated process noise covariance matrix, Q * represents the further updated process noise covariance matrix, represents the final updated process noise covariance matrix;

[0165] S5. Coupling of equivalent circuit model and thermal model and updating of model parameters. During operation, the internal temperature of the battery will change with the change of current and voltage, and the physical parameters of the battery will also change accordingly. The resistance and capacitance parameters R0, R1, R2, C1, C2 in the second-order RC equivalent circuit model and the thermal parameter R in the heat transfer model c , C c It needs to be updated as the temperature changes, so that the current, voltage and other parameters in the current state can be passed to the thermal model to calculate the heat generation power, and the new battery current temperature state T can be estimated. The estimated result of T is fed back to the equivalent circuit model to update the resistance and capacitance parameters, thereby realizing the coupling of the electrical model and the thermal model.

[0166] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An online estimation method for multi-point internal temperature of square lithium batteries based on ASRUKF, characterized by: The following steps are involved: S1: Obtain the charge and discharge data of lithium-ion single cells under full life and wide temperature conditions. The specific steps are as follows: perform cyclic charge and discharge aging tests on different batteries of the same model, fully charge the battery using constant current and constant voltage, let it stand for 30 seconds, and then discharge it to the battery cut-off voltage. Repeat the above process to discharge the battery to 95%, 85%, and 80% of the nominal capacity, respectively, and then perform working condition experiments within the temperature range of -20℃ to 60℃, and record the battery's current, voltage, representative area, and lug temperature; S2. Establish an equivalent circuit model and a thermal model, wherein 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 a simplified three-heat source heat generation model to represent the heat generation inside the battery, and uses a two-state lumped parameter thermal model as a heat transfer model to represent the heat transfer inside the battery. The second-order RC equivalent circuit model, the simplified three-heat source heat generation model, and the two-state lumped parameter thermal model are discretized. After discretization, a lithium-ion battery internal temperature estimation model is established to obtain the state space equation and measurement equation of the system; S3. Model parameter identification: Using the experimental data under HPPC working conditions, the relationship curve between SOC and OCV is obtained through sixth-order polynomial fitting. The fitting expression is as follows: in, represents the polynomial fitting parameters, represents the sum of the entire sixth-order polynomial, Represents different powers of SOC; Under different aging conditions at a wide temperature, based on the battery charge and discharge experimental data obtained by S1, the FFRLS algorithm is used to perform parameter identification on the second-order RC equivalent circuit and parameter thermal model established in S2. The identification process is as follows: Calculation error: e(k)=y(k)-φ T (k)θ(k-1) Calculate the gain vector: Update the parameter vector: θ(k)=θ(k-1)+K(k)e(k) Update the covariance matrix: Among them, e(k) represents the prediction error at the current moment, y(k) represents the system output at the current moment, φ(k) is the system regression vector at the current moment, and φ T (k) is the transpose of φ(k), H(k-1) represents the covariance at the previous moment, θ(k) is the parameter vector at the current moment, θ(k-1) represents the parameter vector at the previous moment, K(k) is the gain vector at the current moment, H(k) is the system covariance matrix at the current moment, and λ is the forgetting factor; S4, online estimation of the internal temperature of different points of the square lithium battery based on the ASRUKF algorithm: Based on the system state space equation and measurement equation obtained in S2, the terminal voltage and open circuit voltage output by the second-order RC equivalent circuit model are substituted into the three-heat source heat generation model to calculate the battery heat generation power, and then the two-state lumped parameter thermal model is combined with the ASRUKF algorithm to estimate the internal temperature of multiple points of the lithium battery; S5. Coupling of equivalent circuit model and thermal model and updating of model parameters: resistance and capacitance parameters R0, R1, R2, C1, C2 in the second-order RC equivalent circuit model and thermal parameter R in the heat transfer model c , C c It will change with the temperature of the battery, and update the parameters identified based on S3 under different temperature gradients.

2. The method for online estimation of multi-point internal temperature of a square lithium battery based on ASRUKF according to claim 1, characterized in that: The expression of the second-order RC equivalent circuit model in step S2 is as follows: U OCV (t)=U TOV (t)-R0I(t)-U1(t)-U2(t) Among them, U OCV (t) represents the open circuit voltage at time t, U TOV (t) represents the terminal voltage at time t, I(t) represents the current at time t, U1(t) and U2(t) represent the polarization voltage at time t, R0 represents the battery ohmic internal resistance, R1 and R2 represent polarization resistance, C1 and C2 represent polarization capacitance, τ1 and τ2 represent time constants, e represents a natural constant, Δt represents the sampling time interval, and the second-order RC equivalent circuit model is discretized using the Euler method, and the obtained expression is as follows: Among them, U OCV (k) is the current battery open circuit voltage, U TOV (k) is the battery terminal voltage at the current moment, I(k) is the battery current at the current moment, I(k-1) represents the battery current at the previous moment, R0 is the battery ohm internal resistance, U1(k) and U2(k) are the terminal voltages corresponding to the polarization resistors R1 and R2 and polarization capacitors C1 and C2 at the current moment, U1(k-1) and U2(k-1) are the terminal voltages corresponding to the polarization resistors R1 and R2 and polarization capacitors C1 and C2 at the previous moment, τ1 and τ2 are time constants, (k) represents the state quantity at the current moment, and (k-1) represents the state quantity at the previous moment; The simplified three-heat source heat generation model is expressed as follows: Among them, Q c (t) represents the heat generation power of the battery cell at time t, U OCV (t) represents the open circuit voltage at time t, U TOV (t) represents the terminal voltage at time t, I(t) represents the current at time t, Q n (t), Q p (t) represents the heat generation power of the two tabs at time t, T 3c (t) represents the internal temperature of the battery at time t, Indicates U OCV To T 3c The partial derivative, R e , R p , R n Represent the internal resistance of the battery cell, positive electrode and negative electrode respectively. Discretize the simplified three-heat source heat generation model, and the expression obtained is as follows: Among them, Q c (k) represents the heat generation power of the battery cell at the current moment, I(k) is the battery current at the current moment, U OCV (k) is the current battery open circuit voltage, U TOV (k) is the battery terminal voltage at the current moment, Q n (k), Q p (k) respectively represent the heat generation power of the two tabs at the current moment; The two-state lumped parameter thermal model expression is as follows: Among them, T 1c (t), T 2c (t), T 3c (t), T 4c (t) represents the internal temperature of the four measurement points of the battery at time t, R c Represents the internal resistance between the battery surface and the interior, C c Indicates the internal resistance of the battery surface shell, T p (t) represents the positive electrode lug temperature at time t, T n (t) represents the negative electrode lug temperature at time t, T 1s (t), T 2s (t), T 3s (t), T 4s (t) represents the surface temperature of the four measurement points on the battery surface at time t. The discretization expression of the two-state lumped parameter thermal model is as follows: in, Respectively represent the estimated internal temperature of the four measurement points of the battery at the current moment, T 1s (k), T 2s (k), T 3s (k), T 4s (k) represents the surface temperature of the four measurement points of the battery at the current moment, R c Represents the internal resistance between the battery surface and the interior, C c Indicates the internal resistance of the battery surface shell; The internal temperature estimation model of lithium-ion batteries is established, and the state space equation and measurement equation of the system are obtained as follows: Among them, X k represents the current state vector, A represents the state transfer matrix, B is the system control matrix, u k-1 is the control quantity at the previous moment, Z k is the measured state vector at the current moment, V k-1 is the measurement noise matrix at the previous moment, R k-1 Covariance of white Gaussian measurement noise, T xs,k-1 Represents the transformation matrix from state quantity to observation quantity.

3. The method for online estimation of multi-point internal temperature of a square lithium battery based on ASRUKF according to claim 2, characterized in that: The expression of the state transfer matrix is ​​as follows: The expression of the current state vector is as follows: The expression of the system control matrix is ​​as follows: The expression of the control quantity at the current moment is as follows: u k =[Q p (k) T 1s (k) T p (k) Q n (k) T 2s (k) T n (k) Q c (k) T 3s (k)] T Among them, T 1c (k), T 2c (k), T 3c (k), T 4c (k) represents the internal temperature of the four measurement points of the battery at the current moment, R c Represents the internal resistance between the battery surface and the interior, C c Indicates the internal resistance of the battery surface shell, T p (k) represents the current positive electrode lug temperature, T n (k) represents the negative electrode lug temperature at time k, Q n (k), Q p (k) represents the heat generation power of the two tabs at the current moment, T 1s (k), T 2s (k), T 3s (k) represents the current temperature of the 1st, 2nd and 3rd measuring points on the battery surface respectively.

4. The method for online estimation of multi-point internal temperature of a square lithium battery based on ASRUKF according to claim 1, characterized in that: The step S4 specifically comprises the following steps: S4.

1. Initialization of state function. The specific expression is as follows: Among them, x0 represents the state vector at time 0, x^0 represents the expected value of the state vector, E[*] represents the mathematical expectation of the calculation parameters, P0 represents the initial value of the error covariance matrix, the superscript T represents the transpose, chol(P0) represents the cholesky decomposition of P0, S0 represents the initial value of the square root, represents the initial value of process noise, represents the initial value of the measurement noise, Q0 and R0 represent the process noise and measurement noise at time 0, respectively; S4.2, Sigma point weight selection, the specific expression is as follows: Where γ represents the scaling factor, represents the mean weight of the 0th Sigma point, represents the covariance weight of the 0th Sigma point, i represents the sequence number of other Sigma points, Represents the mean weight of other Sigma points, represents the covariance weight of other Sigma points, α represents the state parameter, L represents the state variable dimension, and κ represents the quadratic scaling parameter; The expression for constructing the Sigma point is as follows: in, represents the state vector at the previous moment, S k represents the square root value at the current moment, γ represents the proportional factor, and χ k-1 represents the vector composed of the Sigma points at the previous moment, and L represents the dimension of the state variable; S4.3, time update, the expression for calculating the state estimate and the square root error covariance is as follows: in, Represents the Sigma point of the current state estimate, Represents the current estimated covariance matrix, qr[*] represents the Perform QR decomposition, f(χ k-1 ,u k-1 ) represents the state transfer function of the system, S k represents the updated covariance matrix, cholupdate(*) represents the cholupdate function used to update the covariance matrix, Q k represents the process noise at the current moment; S4.4, Sigma point resampling, the expression is as follows: Predict the observed values ​​of the system: in, represents the estimated observation value, h[ζ k ] represents the observation function, and the state Sigma point ζ k Mapped to the observation space, represents the current state estimate, e k Represents the residual at the current moment; Estimation of measurement noise: Where R represents the measurement noise covariance matrix, R ** represents the updated measurement noise covariance matrix, R * represents the further updated measurement noise covariance matrix, represents the final updated measurement noise covariance matrix, d k represents the scalar gain factor, d k =(1-b) / (1-b k+1 ), b represents the forgetting factor, b k+1 represents the forgetting factor at the next moment, represents the predicted observation value vector obtained by Sigma point propagation, and diag(*) represents the construction of a diagonal matrix; Updates to the variance matrix and error covariance: Among them, S * y,k is the updated observation error covariance matrix, S y,k is the observation error covariance matrix after further update, P xy,k is the cross covariance matrix between the state quantity and the observation quantity; Calculate the Kalman gain matrix and update the estimator and variance: Update of process noise: in, represents the process noise covariance matrix at the previous moment, Q ** represents the updated process noise covariance matrix, Q * represents the further updated process noise covariance matrix, Represents the final updated process noise covariance matrix.

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