A lithium-ion battery lithium deposition diagnosis method and system based on electrochemical model and Kalman filter online estimation of negative electrode overpotential

Abstract

The present invention discloses a lithium-ion battery lithium deposition diagnosis method and system for online estimation of negative electrode overpotential based on an electrochemical model and a Kalman filter. The method comprises the following steps: combining a battery SP+thermal coupling model to establish a wide-rate simplified electrochemical model based on parameter correction; constructing an EKF-based negative electrode overpotential estimation framework based on the wide-rate simplified electrochemical model; and performing closed-loop correction on the negative electrode overpotential based on the negative electrode overpotential estimation framework to complete lithium deposition diagnosis of the lithium-ion battery.

Description

Technical Field

[0001] The present invention belongs to the field of negative electrode overpotential estimation of lithium-ion batteries, and specifically relates to a lithium-ion battery lithium plating diagnosis method and system for online estimation of negative electrode overpotential based on an electrochemical model and Kalman filtering. Background Art

[0002] As battery capacities and power levels continue to increase, battery abuse is increasingly susceptible to safety issues such as thermal runaway. Among the many causes of thermal runaway, internal short circuits are a significant factor, and lithium plating is a key cause of these internal short circuits. When batteries are charged at high currents and low temperatures, metallic lithium precipitates on the surface of the battery's negative electrode, forming lithium dendrites. This process, known as "lithium plating," reduces the number of available lithium ions in the battery, leading to irreversible capacity degradation. More importantly, excessive dendrite growth can pierce the separator, triggering internal short circuits and safety issues. Therefore, online estimation of the microscopic kinetics of lithium plating is crucial for monitoring battery safety risks and defining safe operating conditions for battery abuse.

[0003] Lithium deposition in batteries can be directly observed using microscopic instruments. However, direct instrument-based observation of lithium deposition is not only complex and expensive, but also cannot be performed online within the battery system. Some instruments (such as XPS) even require the battery to be disassembled for testing. Furthermore, certain externally measurable battery characteristics (such as relaxation voltage or impedance spectroscopy) are correlated with internal lithium deposition, but the complex operating conditions of the battery can significantly affect the correlation between external characteristics and lithium deposition, resulting in poor versatility. Furthermore, this method can only diagnose lithium deposition after it has already occurred or is occurring, and cannot prevent it from occurring. According to reaction kinetics, lithium deposition occurs when the difference between the solid-phase potential and the liquid-phase potential at the negative electrode surface, i.e., the battery's negative electrode overpotential, is negative. Therefore, lithium deposition can be indirectly observed by measuring the negative electrode overpotential of a battery with a reference electrode. This method can directly measure the potential conditions for the lithium deposition side reaction, but the three-electrode battery is expensive, and its long-term reliability and stability are difficult to guarantee, so it has not yet been promoted within the industry. The battery's electrochemical model has the ability to calculate the battery's negative electrode overpotential. However, the process of using the model to calculate the negative electrode overpotential is essentially "open-loop" and highly dependent on the completeness of the model's mathematical description and the accuracy of parameter identification. Furthermore, the calculation error will continue to accumulate as the model runs online for a long time. Therefore, it is very necessary to combine the model with an optimization algorithm (such as the Kalman filter algorithm), using the negative electrode overpotential as the state value and the battery terminal voltage as the observation value, to construct a closed-loop structure to accurately estimate and predict the battery's negative electrode overpotential and accurately diagnose lithium plating in lithium-ion batteries. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a lithium-ion battery lithium plating diagnosis method and system based on electrochemical model and Kalman filter for online estimation of negative electrode overpotential. In combination with the existing battery model, based on the parameter screening and correction of the model, a wide-rate simplified electrochemical model based on parameter correction is proposed; on the basis of the model, a negative electrode overpotential calculation equation is proposed. Based on the EKF algorithm principle, the negative electrode overpotential is used as the state quantity, and the negative electrode overpotential is corrected by the terminal voltage, thereby realizing closed-loop correction of the negative electrode overpotential.

[0005] To achieve the above object, the present invention provides the following solution: a lithium ion battery lithium deposition diagnosis method based on electrochemical model and Kalman filter online estimation of negative electrode overpotential, comprising the following steps:

[0006] Combined with the battery SP+thermal coupling model, a wide-rate simplified electrochemical model based on parameter correction is established;

[0007] Based on the wide-rate simplified electrochemical model, an EKF-based negative electrode overpotential estimation framework is constructed;

[0008] Based on the negative electrode overpotential estimation framework, closed-loop correction is performed on the negative electrode overpotential to complete the lithium plating diagnosis of lithium-ion batteries.

[0009] Preferably, the method for establishing a wide-rate simplified electrochemical model based on parameter correction includes:

[0010] Use an ohmmeter to measure the internal resistance R ohm ;

[0011] The open circuit voltage curve is formed by extracting the voltage data points at the end of the shelf life, and the least squares fitting method is used to obtain the initial lithium insertion concentration fraction y0 of the positive electrode, the initial lithium insertion concentration fraction x0 of the negative electrode, and the total capacity Q of the positive electrode. p , total negative electrode capacity Q n 、Total battery capacity Q all ;

[0012] Combined with the pre-tested ohmic internal resistance R ohm By extracting the voltage mutation ΔU, the least square method is used to identify P act ;

[0013] At the end of short-time constant current charge and discharge, extract the data point voltage and combine it with the reaction polarization overpotential η act , Ohmic polarization overpotential η ohm To calculate (E ocv -η act ) value, and complete the positive electrode solid phase diffusion time constant τ p , negative electrode solid phase diffusion time constant τ n , liquid phase diffusion coefficient P con identification;

[0014] Using the transient data under the identification condition and combining the existing parameter identification results, the concentration polarization overpotential η at different times is calculated. con , and then identify the liquid phase diffusion time constant τ e , and finally all electrochemical parameters are obtained, and a wide-rate simplified electrochemical model based on parameter correction is established.

[0015] Preferably, the method for constructing a negative electrode overpotential estimation framework based on EKF includes:

[0016] Calculate the negative electrode overpotential using a wide-rate simplified electrochemical model;

[0017] Based on the EKF algorithm, a closed-loop filtering framework is constructed with the negative electrode overpotential as the state variable and the battery terminal voltage as the observation value.

[0018] Preferably, the method for calculating the negative electrode overpotential by using a wide-rate simplified electrochemical model includes:

[0019]

[0020] Among them, η n is the reaction polarization overpotential at the solid-liquid interface of the negative electrode; R is the ideal gas constant; T is the temperature; F is the Faraday constant; Q n is the total capacity of the negative electrode; c0 is the initial lithium ion concentration; P act is the reaction polarization coefficient; I is the current.

[0021] Preferably, based on the negative electrode overpotential estimation framework, a closed-loop correction is performed on the negative electrode overpotential to complete the method for diagnosing lithium deposition in a lithium-ion battery, comprising:

[0022] Using the state variables and input variables at time k-1, the prior estimate of the system state at time k is calculated through the state equation f(·);

[0023] Based on the prior estimate of the system state, updating the error covariance matrix estimate;

[0024] Calculate the Kalman gain based on the updated error covariance matrix estimate;

[0025] Observation error evaluation is performed based on the calculated Kalman gain;

[0026] Based on the evaluated observation error, the system state is corrected to obtain the posterior estimate;

[0027] Based on the posterior estimated value, performing covariance matrix correction of the state variable;

[0028] The expression of the state equation f(·) is as follows:

[0029]

[0030] in, is the prior value of the state variable at the kth moment, is the battery current at the kth moment, is the difference between the negative electrode overpotential at the kth moment and the negative electrode overpotential at the k-1th moment;

[0031] Based on the prior estimate of the system state, the method for updating the error covariance matrix estimate is:

[0032]

[0033] Among them, P k|k-1 , Q k are the prior estimates of the covariance matrix of the state variables at time k and the covariance matrix of the process noise at time k-1, A k is the state transfer coefficient degenerated from the state transfer matrix, φ Δ is the negative electrode overpotential;

[0034] Based on the updated error covariance matrix estimate, the Kalman gain calculation method is:

[0035] K k =P k|k-1 C k Τ (C k P k|k-1 C k Τ +R k ) -1

[0036]

[0037] Among them, K k 、R k is the Kalman gain matrix and observation noise covariance matrix at time k, C k is the observation transfer coefficient degenerated from the observation transfer matrix;

[0038] Based on the calculated Kalman gain, the method for evaluating the observation error is:

[0039]

[0040] Where g(·) is the observation equation, is the observation error at the kth moment, z k is the voltage measurement value at the kth moment, is the reaction polarization overpotential at the positive electrode solid-liquid interface at the kth moment, is the potential of the positive electrode at a certain lithium insertion concentration at the kth moment, is the concentration polarization overpotential at the kth moment, R SEI,n I is the SEI film resistance R SEI,n The voltage drop caused by R ohm is the ohmic polarization internal resistance, I is the current;

[0041] Based on the evaluated observation error, the system state is corrected and the method for obtaining the posterior estimate is as follows:

[0042]

[0043] in, Estimate the posterior value for the state;

[0044] Based on the posterior estimated value, the method for correcting the covariance matrix of the state variable is:

[0045] P k|k =(1-K k C k )P k|k-1 .

[0046] The present invention also provides a lithium ion battery lithium deposition diagnosis system based on electrochemical model and Kalman filter online estimation of negative electrode overpotential, the system is used for the method described, comprising: a model construction module, a framework construction module and a diagnosis module;

[0047] The model building module is used to combine the battery SP+thermal coupling model to establish a wide-rate simplified electrochemical model based on parameter correction;

[0048] The framework building module is used to build an EKF-based negative electrode overpotential estimation framework based on the wide-rate simplified electrochemical model;

[0049] The diagnostic module is used to perform closed-loop correction on the negative electrode overpotential based on the negative electrode overpotential estimation framework to complete the lithium plating diagnosis of the lithium-ion battery.

[0050] Preferably, the process of establishing a wide-rate simplified electrochemical model based on parameter correction includes:

[0051] Use an ohmmeter to measure the internal resistance R ohm ;

[0052] The open circuit voltage curve is formed by extracting the voltage data points at the end of the shelf life, and the least squares fitting method is used to obtain the initial lithium insertion concentration fraction y0 of the positive electrode, the initial lithium insertion concentration fraction x0 of the negative electrode, and the total capacity Q of the positive electrode. p , total negative electrode capacity Q n 、Total battery capacity Q all ;

[0053] Combined with the pre-tested ohmic internal resistance R ohm By extracting the voltage mutation ΔU, the least square method is used to identify P act ;

[0054] At the end of short-time constant current charge and discharge, extract the data point voltage and combine it with the reaction polarization overpotential η act , Ohmic polarization overpotential η ohm To calculate (E ocv -η act ) value, and complete the positive electrode solid phase diffusion time constant τ p , negative electrode solid phase diffusion time constant τ n , liquid phase diffusion coefficient P con identification;

[0055] Using the transient data under the identification condition and combining the existing parameter identification results, the concentration polarization overpotential η at different times is calculated. con , and then identify the liquid phase diffusion time constant τ e , and finally all electrochemical parameters are obtained, and a wide-rate simplified electrochemical model based on parameter correction is established.

[0056] Preferably, the process of constructing the negative electrode overpotential estimation framework based on EKF includes:

[0057] Calculate the negative electrode overpotential using a wide-rate simplified electrochemical model;

[0058] Based on the EKF algorithm, a closed-loop filtering framework is constructed with the negative electrode overpotential as the state variable and the battery terminal voltage as the observation value.

[0059] Preferably, the process of calculating the negative electrode overpotential by using a wide-rate simplified electrochemical model includes:

[0060]

[0061] Among them, η n is the reaction polarization overpotential at the solid-liquid interface of the negative electrode; R is the ideal gas constant; T is the temperature; F is the Faraday constant; Q n is the total capacity of the negative electrode; c0 is the initial lithium ion concentration; P act is the reaction polarization coefficient; I is the current.

[0062] Preferably, based on the negative electrode overpotential estimation framework, the negative electrode overpotential is corrected in a closed loop to complete the process of diagnosing lithium deposition in lithium-ion batteries, including:

[0063] Using the state variables and input variables at time k-1, the prior estimate of the system state at time k is calculated through the state equation f(·);

[0064] Based on the prior estimate of the system state, updating the error covariance matrix estimate;

[0065] Calculate the Kalman gain based on the updated error covariance matrix estimate;

[0066] Observation error evaluation is performed based on the calculated Kalman gain;

[0067] Based on the evaluated observation error, the system state is corrected to obtain the posterior estimate;

[0068] Based on the posterior estimated value, performing covariance matrix correction of the state variable;

[0069] The expression of the state equation f(·) is as follows:

[0070]

[0071] in, is the prior value of the state variable at the kth moment, is the battery current at the kth moment, is the difference between the negative electrode overpotential at the kth moment and the negative electrode overpotential at the k-1th moment;

[0072] Based on the prior estimate of the system state, the method for updating the error covariance matrix estimate is:

[0073]

[0074] Among them, P k|k-1 , Q k are the prior estimates of the covariance matrix of the state variables at time k and the covariance matrix of the process noise at time k-1, A k is the state transfer coefficient degenerated from the state transfer matrix, φ Δ is the negative electrode overpotential;

[0075] Based on the updated error covariance matrix estimate, the Kalman gain calculation method is:

[0076] K k =P k|k-1 C k Τ (C k P k|k-1 C k Τ +R k ) -1

[0077]

[0078] Among them, K k 、Rk is the Kalman gain matrix and observation noise covariance matrix at time k, C k is the observation transfer coefficient degenerated from the observation transfer matrix;

[0079] Based on the calculated Kalman gain, the method for evaluating the observation error is:

[0080]

[0081] Where g(·) is the observation equation, is the observation error at the kth moment, z k is the voltage measurement value at the kth moment, is the reaction polarization overpotential at the positive electrode solid-liquid interface at the kth moment, is the potential of the positive electrode at a certain lithium insertion concentration at the kth moment, is the concentration polarization overpotential at the kth moment, R SEI,n I is the SEI film resistance R SEI,n The voltage drop caused by R ohm is the ohmic polarization internal resistance, I is the current;

[0082] Based on the evaluated observation error, the system state is corrected and the method for obtaining the posterior estimate is as follows:

[0083]

[0084] in, Estimate the posterior value for the state;

[0085] Based on the posterior estimated value, the method for correcting the covariance matrix of the state variable is:

[0086] P k|k =(1-K k C k )P k|k-1 .

[0087] Compared with the prior art, the present invention has the following beneficial effects:

[0088] The present invention combines the existing battery model with the parameter screening and correction of the model to propose a wide-rate simplified electrochemical model based on parameter correction; on the basis of the model, a negative electrode overpotential calculation equation is proposed. Based on the EKF algorithm principle, the negative electrode overpotential is used as the state quantity, and the negative electrode overpotential is corrected by the terminal voltage, thereby realizing a closed-loop correction of the negative electrode overpotential. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0090] Figure 1 This is a schematic diagram of the structure of a lithium-ion battery according to an embodiment of the present invention;

[0091] Figure 2 Schematic diagram of the identification working condition of an embodiment of the present invention, wherein (a) is a schematic diagram of current excitation, and (b) is a schematic diagram of voltage response;

[0092] Figure 3 Schematic diagram of the effect of parameters on voltage in an embodiment of the present invention, where (a) is the parameter τ p Schematic diagram of the influence curve on voltage, (b) is the parameter τ n Schematic diagram of the influence curve on voltage, (c) is the parameter τ e Schematic diagram of the influence curve on voltage, (d) is the parameter P con Schematic diagram of the influence curve on voltage, (e) is the parameter P act Schematic diagram of the voltage impact curve, (f) is the parameter R ohm Schematic diagram of the impact curve on voltage;

[0093] Figure 4 This is a schematic diagram of the CPSO algorithm according to an embodiment of the present invention;

[0094] Figure 5 Schematic diagram of the fitting results of the embodiment of the present invention, where (a) is P act Schematic diagram of fitting results, (b) is τ n Schematic diagram of fitting results;

[0095] Figure 6 Schematic diagram of voltage simulation curves under different rate constant current discharge conditions of an embodiment of the present invention, wherein (a) is a schematic diagram of the uncorrected SP+ model, and (b) is a schematic diagram of the corrected SP+ model;

[0096] Figure 7 This is a schematic diagram of the internal structure of a three-electrode battery according to an embodiment of the present invention;

[0097] Figure 8 Schematic diagram of lithium plating of a three-electrode battery according to an embodiment of the present invention;

[0098] Figure 9 Schematic diagram of the negative electrode overpotential curve of a three-electrode battery under low-rate working conditions according to an embodiment of the present invention;

[0099] Figure 10Schematic diagram of the comparison curve of the frequency modulation working current, negative electrode overpotential and terminal voltage in an embodiment of the present invention, wherein (a) is a schematic diagram of the frequency modulation working current, (b) is a schematic diagram of the negative electrode overpotential estimation curve; (c) is a schematic diagram of the terminal voltage estimation curve. DETAILED DESCRIPTION

[0100] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0101] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0102] Example 1:

[0103] This embodiment provides a lithium ion battery lithium deposition diagnosis method based on electrochemical model and Kalman filter online estimation of negative electrode overpotential, comprising the following steps:

[0104] Combined with the battery SP+thermal coupling model, a wide-rate simplified electrochemical model based on parameter correction is established;

[0105] Based on the wide-rate simplified electrochemical model, an EKF-based negative electrode overpotential estimation framework is constructed;

[0106] Based on the negative electrode overpotential estimation framework, the negative electrode overpotential is corrected in a closed loop to complete the lithium deposition diagnosis of the lithium-ion battery (if the negative electrode overpotential is less than 0, it is considered that the battery has deposited lithium).

[0107] In this embodiment, the lithium-ion battery is composed of positive and negative electrodes, a separator, positive and negative current collectors, and an electrolyte distributed throughout the entire battery. The basic structure of the battery is as follows: Figure 1 shown.

[0108] The SP+ model further considers the influence of liquid-phase diffusion of active lithium ions based on the SP model. It simplifies the series of partial differential equations describing the internal diffusion process of the battery into algebraic equations, thereby balancing the model's computational efficiency and simulation accuracy. The SP+ model describes the internal mechanisms of lithium-ion batteries from five perspectives: the basic working process, solid-phase diffusion, liquid-phase diffusion, reaction polarization, and ohmic polarization. Table 1 presents the mathematical formula for the model, with parameters and variables listed in Tables 2 and 3, respectively.

[0109] Table 1 Basic description of the model

[0110]

[0111]

[0112] Table 2 Model parameters

[0113]

[0114] Table 3 Model variables

[0115]

[0116] In order to complete the model simulation process, a certain amount of preliminary offline identification work needs to be done. The battery geometric parameters can be obtained by reviewing relevant literature, consulting battery manufacturers, etc., and no identification is required. The SP+ model parameters that need to be obtained by identification methods are shown in Table 2. There are 11 parameters that need to be identified in the SP+ model. It is difficult to use optimization algorithms (such as least squares method) to accurately identify such a large parameter set, and the identification results are not accurate enough. The present invention decouples the polarization overpotential from the measured terminal voltage by applying a series of specially designed current excitations to the battery. The current excitation and voltage response forms in the parameter identification condition are as follows: Figure 2 As shown. The current excitation consists of a combination of multiple stages of constant current charge and discharge and a rest period. Each stage is set to constant current discharge for 20 minutes, constant current charge for 10 minutes, and rest for 15 minutes. The charge and discharge current rate range is 0.05C to 0.4C to reduce the battery temperature rise and avoid the influence of temperature on the parameter identification results. The specific parameter identification sequence is as follows: First, use an ohmmeter to measure R ohm ; Secondly, by extracting Figure 2 The voltage data points at the end of the shelf period shown in (b) form the open circuit voltage curve, and the least squares fitting method is used to obtain y0, x0 and Q p , Q n , Q all ; From the formula in Table 1, we can see that Figure 2 The instantaneous voltage change ΔU caused by the sudden current in the rectangle in (b) is determined by the ohmic polarization overpotential and the reaction polarization overpotential. Therefore, combined with the pre-tested ohmic internal resistance, the voltage mutation ΔU can be extracted and the P can be identified using the least squares method. act ;exist Figure 2 (b) At the end of the medium- and short-term constant current charge and discharge, the solid-liquid phase diffusion process has entered a stable stage. The voltages of these data points can be extracted and combined with η act ,η ohm To calculate (E ocv -η act ) and complete the τ p , τ n 、P con Identification; Using the transient data under the identification condition and combining the existing parameter identification results, η at different times can be calculatedcon , and then identify τ e , and finally all electrochemical parameters are obtained. Repeating the above parameter identification process at different ambient temperatures can obtain the temperature-affected τ at different ambient temperatures. p , τ n 、P act 、P con and R ohm value, and perform temperature fitting based on formula (1).

[0117]

[0118] Where X is the parameter τ p , τ n 、P act 、P con and R ohm Correction value with temperature; X ref is the value of X at the reference temperature; λ is the activation energy coefficient of the parameter; T ref is the reference temperature; T is the battery temperature.

[0119] In order to ensure that the SP+ thermal coupling model has high accuracy in a wide current rate range, it is necessary to adjust the parameters according to the applied current. Since the model contains more than a dozen parameters, it is not feasible to correct all of them. Therefore, it is necessary to select the characteristic parameters that have a greater impact on the model simulation as the parameters to be corrected to achieve the adaptability of the model to a wide rate range. Among the 11 parameters described in Table 2, y0, x0, Q p , Q n and Q all By affecting the deintercalation and insertion of lithium ions in the positive and negative active particles, E ocv and U app From the physical meanings described in Table 2, it can be inferred that they are mainly related to the battery type specifications and do not need to be corrected with the current rate. The remaining parameters τ p , τ n , τ e 、P con 、P act and R ohm The terminal voltage simulation curves are shown as follows: Figure 3 As shown in (a)-(f).

[0120] The discrete degree of the voltage curve cluster indicates the influence of each parameter on the terminal voltage simulation. Figure 3 As shown, the parameter that has the greatest impact on voltage is τ n and P act , which affect the upper SOC and lower SOC ranges respectively. Therefore, by modifying the parameter τ n and Pact It is expected to improve the accuracy of the SP+ model over a wide magnification range.

[0121] Based on the SP+ model parameters obtained by existing identification, under different rate constant current discharge conditions, the optimization goal is to minimize the terminal voltage mean absolute error (MAE). Figure 4 The CPSO algorithm shown in the figure obtains the appropriate τ under different rate conditions. n and P act The specific identification process is as follows:

[0122] (1) Set the total number of particles N, the number of subgroups n, and the number of particles in each subgroup N in the multi-constraint particle swarm optimization algorithm. s and evolutionary algebra M gen , randomly generate a K-th generation particle group containing N particles within the parameter value range of the set lithium-ion battery electrochemical model, the initial value of K is 1, and the position of the K-th generation particle group is P0 = (X1, X2, X3, ..., X N ), each particle position in the K-th generation particle swarm represents a model parameter vector X i =(P act_i ,τ n_i ), i=1,2,3,…,N, the velocity of the Kth generation particle is Q0=(V1,V2,V3,…,V N ), V i =(0,0),i=1,2,3,…,N;

[0123] (2) Calculate the fitness of each particle position in the Kth generation particle swarm as shown in formula (2). In the formula, F(X i ) is the fitness of each particle position in the K-th generation particle swarm, U app_i is the terminal voltage of the lithium-ion battery calculated by the i-th particle model parameter vector, V cell is the battery terminal voltage measured during actual operation, and sum is the number of measured terminal voltage data points. Arrange the fitness of each particle position in the Kth generation particle swarm in ascending order;

[0124]

[0125] (3) Select the first particle from the fitness of the particles in ascending order as the local optimal particle of the first subgroup, calculate the Euclidean distance between the first particle and each of the remaining N-1 particles, and obtain a total of N-1 Euclidean distances. From the N-1 Euclidean distances, select the N / n-1 particles corresponding to the largest N / n-1 Euclidean distances and establish a subgroup together with the first particle;

[0126] (4) The remaining N-3 particles establish subgroups according to step (3) until the number of remaining particles is less than N s , complete the establishment of n subgroups. Record the individual optimal particle P in the Kth generation particle swarm best (P best1 ,P best2 ,P best3 ,…,P bestN ) and the local optimal particle G best (G best1 ,G best2 ,G best3 ,…,G bestN ), the individual optimal particle is the position vector of N particles in the first generation;

[0127] (5) Using the velocity and position update equations, the individual optimal particle and the local optimal particle, the position of the K-th generation particle swarm is evolved to obtain the position of the new generation particle swarm. After iteration, each particle in each sub-swarm is represented as shown in the following formula. i K Represents the speed of the i-th particle in the K-th generation of evolution, K=1,2…M gen , X i K represents the position of the i-th particle at the K-th generation of evolution, ω is the inertia weight coefficient, c1 and c2 are learning factors, r1 and r2 are random numbers in the range of 0 to 1, ξ is the convergence factor, P besti K , i=1,2…N is the individual optimal value of the i-th particle evolving from the 1st generation to the Kth generation, g besti K , i=1,2…N is the local optimal value of the subgroup to which the particle belongs from the 1st generation to the Kth generation. If the model parameter vector in the position of the new particle group exceeds the parameter value range set at the beginning, it should be readjusted as shown in formula (6) and then step (6) should be executed. (i,z) Indicates the coordinate of the i-th particle in the z-th dimension when updated to the current generation, σ is a random number between 0 and 1, X z min The lower limit of the parameter value range of the lithium-ion battery electrochemical model for the z-th dimension coordinate of the particle position, X z max The upper limit of the parameter value range of the lithium-ion battery electrochemical model for the z-th dimension coordinate of the particle position is set. In the process of obtaining the parameter data set about temperature offline, X z max With X z max They are shown in formula (7) respectively.

[0128]

[0129] (6) Execute steps (2) to (5), record the current individual optimum and local optimum, compare the fitness of each particle in the total swarm with the fitness of the particle corresponding to the previous iteration, and save the particle with the smaller fitness as the individual optimum of the latest particle swarm;

[0130] (7) Until the maximum number of iterations M is completed gen Or the optimal fitness reaches a preset value in advance, and the particle position with the minimum fitness in the latest iteration is obtained, and the model parameter vector in the minimum particle position is used as the identification result.

[0131] Then, a quartic polynomial as shown in the following equation is used as the fitting function to construct the correction relationship between the parameter and the magnification. Where C is the current magnification, and a1, b1, c1, d1, e1, a2, b2, c2, d2, and e2 are the unknown coefficients of the fitting equation.

[0132]

[0133] In this embodiment, to reduce the negative electrode overpotential calculation error caused by open-loop model simulation, a closed-loop filtering framework is constructed with the negative electrode overpotential as the state variable and the battery terminal voltage as the observation value. First, the negative electrode overpotential calculation equation is proposed using the SP+ model.

[0134] According to the reaction kinetics of lithium-ion batteries, the governing equation for the negative electrode reaction polarization overpotential is:

[0135] η n =φ s -φ l -U n -R SEI,n I (9)

[0136] Among them, η n is the reaction polarization overpotential at the solid-liquid interface of the negative electrode; U n is the potential of the negative electrode at a certain lithium insertion concentration; φ s is the solid phase potential of the negative electrode; φ l is the negative electrode liquid phase potential. R SEI,n I is the SEI film resistance R SEI,n The voltage drop caused by SEI is difficult to describe quantitatively, so the battery ohmic internal resistance is used to approximate this parameter. Equation (9) can be improved to: Δ is the negative electrode overpotential. When it is negative, it is considered that lithium deposition will occur in the battery:

[0137] φ Δ =φ s -φ l =η n +U n +Rohm I (10)

[0138] At the solid-liquid interface of the battery negative electrode, if the lithium ion concentration on the surface of the active particles and the lithium ion concentration in the liquid phase are known, the electrochemical reaction polarization overpotential can be reversely solved based on the reaction ion flow density, as shown in Equation (11):

[0139]

[0140] Among them, k n is the reaction rate constant at the negative electrode; R is the ideal gas constant; T is the temperature; F is the Faraday constant; m n is an intermediate variable; is the maximum lithium ion concentration of the negative electrode; is the lithium ion concentration on the negative electrode surface; c0 is the initial lithium ion concentration; j n is the reaction ion current density at the negative electrode, which is calculated as follows

[0141]

[0142] Among them, R n is the radius of the negative electrode active particles.

[0143] Under the assumption that the reaction is uniformly distributed at the negative electrode, the reaction ion flow density at the solid-liquid interface of the negative electrode can be approximated by formula (13):

[0144] j n ≈IR n / 3F(1-ε n -ε f,n )l n A(13)

[0145] Among them, ε n is the porosity of the negative electrode material; ε f,n is the volume fraction of the negative electrode filling material; l n is the length of the negative electrode region; A is the area of ​​the negative electrode sheet.

[0146] In the SP+ model, the parameters in equations (11) and (13) can be integrated and replaced by P act =R n / k n , and Then η n It can be obtained by the following formula, where x surf is the amount of lithium embedded on the negative electrode surface:

[0147]

[0148] Combined with formula (14), the negative electrode overpotential can be obtained from formula (10).

[0149] The Kalman filter algorithm is a mathematical method for state estimation, originally proposed by Rudolf E. Kalman in 1960. The algorithm provides the best estimate of the system state by combining the system's dynamic model and measurement data. Its basic principle is to achieve state estimation through prediction and update steps. The prediction step uses the system's dynamic model to predict the next state and estimate the covariance of the prediction error. The update step uses the latest measurement data to correct the predicted state estimate and fuses the prediction and measurement information through the Kalman gain. EKF is an extension of the Kalman filter algorithm and is applicable to nonlinear system state estimation problems. Unlike the standard Kalman filter that targets the dynamic model and measurement model of linear systems, the EKF is mainly applicable to nonlinear system models, and its general model is:

[0150] Let the p-dimensional state variable vector be x k ∈R p×1 , k represents the time sequence number, and the evolution of state variables over time is described by the state equation:

[0151] The state equation and observation equation are shown in Equations (15) and (16).

[0152]

[0153] Where x k t k The system state transition variable at time z k t k The observed comparison quantity at the moment, u k is the parameter required by the state equation, v k are the parameters required by the observation equation. f(·) is the temporal state transition relationship between the system state variables, and g(·) represents the mapping relationship between the system state transition variables and the observed comparison values. In the EKF algorithm, f(·) and g(·) are nonlinear functions. k , ε k They are respectively represented as t k The process noise of the state transfer equation and the observation noise of the observation equation represent the model’s characterization error of the actual system and the observation error of the sensor sampling. Their covariances are Q k 、R k , the two are independent of each other.

[0154] The linearization of nonlinear systems is based on the Taylor expansion method. k Taking the first-order Taylor expansion at all times, we can get formula (17), and then sort it out to get formula (18), where A k is the system state transfer matrix, C k is the observation matrix.

[0155]

[0156] To perform closed-loop prediction of the negative electrode overpotential based on the EKF algorithm, it is necessary to clearly define the negative electrode overpotential as the state variable and the terminal voltage as the observation variable. The specific process is as follows:

[0157] (1) Predict the system state and obtain a priori estimated value of the system state.

[0158] Using the state variables and input variables at time k-1, the prior estimate of the system state at time k is calculated through the state equation f(·), as shown in Equation (19), where h(·) is composed of several nonlinear equations, and its specific form is the same as the lithium deposition potential description equation in the model.

[0159]

[0160] in, is the priori value of the state variable at the kth moment, which is the negative electrode overpotential in the present invention, is the battery current at the kth moment, It is the difference between the negative electrode overpotential at the kth moment and the negative electrode overpotential at the k-1th moment.

[0161] (2) Update the estimated value of the error covariance matrix.

[0162] As shown in formula (20), P k|k-1 , Q k are the prior estimates of the covariance matrix of the state variables at time k and the covariance matrix of the process noise at time k-1, respectively, where A k The calculation formula for the state transfer coefficient degenerated from the state transfer matrix is ​​as follows:

[0163]

[0164] (3) Perform Kalman gain calculation.

[0165] As shown in formula (22), K k 、R k is the Kalman gain matrix and observation noise covariance matrix at time k, where C k The calculation formula for the observation transfer coefficient degenerated from the observation transfer matrix is ​​as follows:

[0166] K k =P k|k-1 C k Τ (C k P k|k-1 C k Τ +R k ) -1(twenty two)

[0167]

[0168] (4) Conduct observation error assessment.

[0169] Using the prior estimate of the system state obtained in step (1) and the input variable at time k, the theoretical output at time k is calculated through the observation equation g(·), and the observation error is obtained by comparing it with the observed value, as shown in formula (24), where η p is the reaction polarization overpotential at the positive electrode solid-liquid interface; U p is the potential of the positive electrode at a certain lithium insertion concentration. In the model, the reaction polarization overpotential at the positive electrode is calculated using formula (25):

[0170]

[0171] Where g(·) is the observation equation, is the observation error at the kth moment, z k is the voltage measurement value at the kth moment, is the reaction polarization overpotential at the positive electrode solid-liquid interface at the kth moment, is the potential of the positive electrode at a certain lithium insertion concentration at the kth moment, is the concentration polarization overpotential at the kth moment, R SEI,n I is the SEI film resistance R SEI,n The voltage drop caused by R ohm is the ohmic polarization internal resistance, and I is the current.

[0172] (5) Correct the system state and obtain the posterior estimate.

[0173] The system state prior estimate obtained in step (1) is corrected, and the updated system state posterior estimate is shown in formula (26).

[0174]

[0175] in, Estimate the posterior for the state.

[0176] (6) Correct the covariance matrix of the state variables.

[0177] The covariance matrix correction method of the state variables is shown in formula (27).

[0178] P k|k =(1-K k C k )P k|k-1 (27)

[0179] Example 2

[0180] The present invention also provides a lithium ion battery lithium deposition diagnosis system based on electrochemical model and Kalman filter online estimation of negative electrode overpotential, the system is used to implement the method described, including: a model construction module, a framework construction module and a diagnosis module;

[0181] The model building module is used to combine the battery SP+thermal coupling model to establish a wide-rate simplified electrochemical model based on parameter correction;

[0182] The framework building module is used to build an EKF-based negative electrode overpotential estimation framework based on the wide-rate simplified electrochemical model;

[0183] The diagnostic module is used to perform closed-loop correction on the negative electrode overpotential based on the negative electrode overpotential estimation framework to complete the lithium plating diagnosis of the lithium-ion battery.

[0184] In this embodiment, the process of establishing a wide-rate simplified electrochemical model based on parameter correction includes:

[0185] Use an ohmmeter to measure the internal resistance R ohm ;

[0186] The open circuit voltage curve is formed by extracting the voltage data points at the end of the shelf life, and the least squares fitting method is used to obtain the initial lithium insertion concentration fraction y0 of the positive electrode, the initial lithium insertion concentration fraction x0 of the negative electrode, and the total capacity Q of the positive electrode. p , total negative electrode capacity Q n 、Total battery capacity Q all ;

[0187] Combined with the pre-tested ohmic internal resistance R ohm By extracting the voltage mutation ΔU, the least square method is used to identify P act ;

[0188] At the end of short-time constant current charge and discharge, extract the data point voltage and combine it with the reaction polarization overpotential η act , Ohmic polarization overpotential η ohm To calculate (E ocv -η act ) value, and complete the positive electrode solid phase diffusion time constant τ p , negative electrode solid phase diffusion time constant τ n , liquid phase diffusion coefficient P con identification;

[0189] Using the transient data under the identification condition and combining the existing parameter identification results, the concentration polarization overpotential η at different times is calculated. con , and then identify the liquid phase diffusion time constant τ e, and finally all electrochemical parameters are obtained, and a wide-rate simplified electrochemical model based on parameter correction is established.

[0190] In this embodiment, the process of constructing the negative electrode overpotential estimation framework based on EKF includes:

[0191] Calculate the negative electrode overpotential using a wide-rate simplified electrochemical model;

[0192] Based on the EKF algorithm, a closed-loop filtering framework is constructed with the negative electrode overpotential as the state variable and the battery terminal voltage as the observation value.

[0193] In this embodiment, the process of calculating the negative electrode overpotential using the wide-rate simplified electrochemical model includes:

[0194]

[0195] Among them, η n is the reaction polarization overpotential at the solid-liquid interface of the negative electrode; R is the ideal gas constant; T is the temperature; F is the Faraday constant; Q n is the total capacity of the negative electrode; c0 is the initial lithium ion concentration; P act is the reaction polarization coefficient; I is the current.

[0196] In this embodiment, based on the negative electrode overpotential estimation framework, closed-loop correction of the negative electrode overpotential is performed to complete the process of lithium deposition diagnosis in lithium-ion batteries, including:

[0197] Using the state variables and input variables at time k-1, the prior estimate of the system state at time k is calculated through the state equation f(·);

[0198] Based on the prior estimate of the system state, updating the error covariance matrix estimate;

[0199] Calculate the Kalman gain based on the updated error covariance matrix estimate;

[0200] Observation error evaluation is performed based on the calculated Kalman gain;

[0201] Based on the evaluated observation error, the system state is corrected to obtain the posterior estimate;

[0202] Based on the posterior estimated value, performing covariance matrix correction of the state variable;

[0203] The expression of the state equation f(·) is as follows:

[0204]

[0205] in, is the priori value of the state variable at the kth moment, which is the negative electrode overpotential in the present invention, is the battery current at the kth moment, is the difference between the negative electrode overpotential at the kth moment and the negative electrode overpotential at the k-1th moment;

[0206] Based on the prior estimate of the system state, the method for updating the error covariance matrix estimate is:

[0207]

[0208]

[0209] Among them, P k|k-1 , Q k are the prior estimates of the covariance matrix of the state variables at time k and the covariance matrix of the process noise at time k-1, A k is the state transfer coefficient degenerated from the state transfer matrix, φ Δ is the negative electrode overpotential;

[0210] Based on the updated error covariance matrix estimate, the Kalman gain calculation method is:

[0211] K k =P k|k-1 C k Τ (C k P k|k-1 C k Τ +R k ) -1

[0212]

[0213] Among them, K k 、R k is the Kalman gain matrix and observation noise covariance matrix at time k, C k is the observation transfer coefficient degenerated from the observation transfer matrix;

[0214] Based on the calculated Kalman gain, the method for evaluating the observation error is:

[0215]

[0216] Where g(·) is the observation equation, is the observation error at the kth moment, z k is the voltage measurement value at the kth moment, is the reaction polarization overpotential at the positive electrode solid-liquid interface at the kth moment, is the potential of the positive electrode at a certain lithium insertion concentration at the kth moment, is the concentration polarization overpotential at the kth moment, R SEI,n I is the SEI film resistance R SEI,n The voltage drop caused by R ohm is the ohmic polarization internal resistance, I is the current;

[0217] Based on the evaluated observation error, the system state is corrected and the method for obtaining the posterior estimate is as follows:

[0218]

[0219] in, Estimate the posterior for the state.

[0220] Based on the posterior estimated value, the method for correcting the covariance matrix of the state variable is:

[0221] P k|k =(1-K k C k )P k|k-1 .

[0222] Example 3

[0223] In order to specifically illustrate the method used in the present invention, a 50Ah lithium iron phosphate battery model and the negative electrode overpotential estimation process are used as implementation cases in the present invention. The specific parameters of the battery are shown in Table 4.

[0224] Table 4 Battery parameters

[0225]

[0226] In order to obtain the selected parameters P act and τ n Regarding the fitting equation of the rate, combined with the 0.5C / 1C / 1.5C / 2C / 3C / 4C rate constant current discharge conditions, the P under different rate conditions is obtained. act and τ n The optimal value of . Figure 5 The comparison results of the optimal value obtained by CPSO algorithm and the fitting value using the fourth-order polynomial fitting equation are given. As can be seen from the figure, the τ calculated by the fitting equation is n and P act The values ​​are very close to the parameters obtained by the optimization algorithm, indicating the feasibility of the fitting results. Table 5 shows the model parameter identification results at an ambient temperature of 20℃.

[0227] Table 5 Parameter identification results

[0228]

[0229] Figure 6Comparison curves comparing the simulated and measured voltages of LFP prismatic cells using the uncorrected and corrected electrochemical models are shown. The simulated terminal voltage and temperature curves obtained using the corrected SP+ model agree well with the experimental curves. Table 6 shows the voltage MAEs using the corrected and uncorrected SP+ models. As shown in the table, the voltage MAEs of the corrected SP+ model are within 23mV, demonstrating good accuracy. Compared to the uncorrected SP+ model, accuracy is significantly improved at high rates.

[0230] Table 6 Voltage MAE (mV) of the corrected model and the uncorrected model

[0231]

[0232] To verify the effectiveness of the negative electrode overpotential estimation method proposed in this invention, a three-electrode battery needs to be fabricated to complete experimental measurements. The current reference design mainly uses a lithium plating process based on a copper wire substrate. The reference substrate is an ultrafine copper wire with a wire diameter of 20 μm, which is on the order of magnitude of the diaphragm size and can be roughly assumed to have no effect on the internal structure of the battery. The preparation method of the three-electrode battery is as follows:

[0233] (1) Take a section of copper wire and fold it in half. Remove the paint from the two tips of the fork, exposing the conductive end for lithium plating. The two branches of the fork will be buried inside the battery, providing two measurement channels, which serve as backup for each other. Because the copper wire is too thin, there is a risk of it breaking when passing through the top cover, so the copper wire is placed in a hot melt tube.

[0234] (2) Take a small piece of diaphragm and stick the two paint-removed copper wire tips on the diaphragm to avoid internal short circuit when the copper wire is subsequently placed in the battery.

[0235] (3) Place the separator with copper wire between the battery coils. Note that the separator should be placed between the negative electrode and the separator. Figure 7 shown.

[0236] (4) Assemble the coil core with three electrodes, weld the top cover, punch a hole in the top cover to facilitate the extension of the hot melt tube, and seal it with glue.

[0237] (5) After the three-electrode battery is packaged, filled with liquid, and physically tested, the tip of the reference electrode outside the battery is stripped of paint and spot welded to the upper electrode to complete the entire three-electrode battery.

[0238] After the three-electrode battery is completed, the reference electrode needs to be plated with lithium to obtain the required lithium-copper reference electrode. That is, lithium metal is plated on the copper wire by electrochemical deposition using the copper wire as the substrate. When plating lithium, in order to ensure the uniformity of the lithium plating layer, the positive electrode of the battery is first used as the positive electrode and the copper wire as the negative electrode. The copper wire is charged with a constant small current of 400μA for 1 hour. Figure 8 (a) As shown; After the end, the negative electrode of the battery is used as the positive electrode and the copper wire is used as the negative electrode to charge at 400μA for 1h. Figure 8 (b) As shown. After the lithium plating is completed, the copper wire can be used as a lithium copper reference electrode to provide Li / Li + The electric potential.

[0239] The lithium plating effect of the reference electrode has a great influence on the accuracy of key experimental data, so the effectiveness of the lithium-copper reference electrode needs to be verified. Figure 9 The negative electrode overpotential curve under a 0.02C discharge-charge current condition is shown. Due to the low current, the measured negative electrode overpotential is approximately Un, the graphite potential, and its trend is generally consistent with existing research. As can be seen from the figure, the graphite potential curve is mainly divided into three plateaus. As the lithium concentration x in LixC6 increases, the three plateaus correspond to the 1L-3L, 3L-2, and 2-1 phase transitions, respectively. The number represents the number of graphene layers embedded between the lithium layers; L refers to the liquid state, indicating that the embedded lithium has no planar order, that is, it is randomly distributed in the gaps between the graphene sheets.

[0240] The present invention uses a typical frequency modulation working condition as a verification working condition. The frequency modulation working condition generally uses power as input. For the convenience of the experiment, the frequency modulation current can be obtained based on Ohm's law in combination with the nominal voltage. Figure 10 For the proposed closed-loop method, the estimated negative electrode overpotential, terminal voltage and temperature are compared with the measured values ​​of the three-electrode battery, as shown in Figure 2. Figure 10 As shown in (b) and (c).

[0241] Depend on Figure 10 It can be seen that the simulated curves for the negative electrode overpotential, terminal voltage, and temperature obtained using the method described in this invention are in good agreement with the experimental curves. As shown in Table 7, the absolute average errors between the predicted and measured negative electrode overpotential and terminal voltage values ​​do not exceed 10.5 mV and 24 mV, respectively, demonstrating high accuracy.

[0242] Table 7 Errors between predicted and measured values ​​of negative electrode overpotential and terminal voltage

[0243]

[0244] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A lithium-ion battery lithium deposition diagnosis method based on electrochemical model and Kalman filter online estimation of negative electrode overpotential, characterized in that: The following steps are involved: Combined with the battery SP+thermal coupling model, a wide-rate simplified electrochemical model based on parameter correction is established; Based on the wide-rate simplified electrochemical model, an EKF-based negative electrode overpotential estimation framework is constructed; Based on the negative electrode overpotential estimation framework, closed-loop correction is performed on the negative electrode overpotential to complete the lithium plating diagnosis of lithium-ion batteries; The method of constructing the EKF-based negative electrode overpotential estimation framework includes: Calculate the negative electrode overpotential using a wide-rate simplified electrochemical model; Based on the EKF algorithm, a closed-loop filtering framework is constructed with the negative electrode overpotential as the state variable and the battery terminal voltage as the observation value; Methods for calculating negative electrode overpotential using wide-rate simplified electrochemical models include: Among them, η n is the reaction polarization overpotential at the solid-liquid interface of the negative electrode; R is the ideal gas constant; T is the temperature; F is the Faraday constant; is the total capacity of the negative electrode; c0 is the initial lithium ion concentration; P act is the reaction polarization coefficient; is the current, is the amount of lithium embedded on the negative electrode surface; Based on the negative electrode overpotential estimation framework, a method for performing closed-loop correction on the negative electrode overpotential to complete lithium deposition diagnosis in a lithium-ion battery includes: Using the state variables and input variables at time k-1, the prior estimate of the system state at time k is calculated through the state equation f(·); Based on the prior estimate of the system state, updating the error covariance matrix estimate; Calculate the Kalman gain based on the updated error covariance matrix estimate; Observation error evaluation is performed based on the calculated Kalman gain; Based on the evaluated observation error, the system state is corrected to obtain the posterior estimate; Based on the posterior estimated value, performing covariance matrix correction of the state variable; The expression of the state equation f(·) is as follows: in, is the prior value of the state variable at the kth moment, is the battery current at the kth moment, is the difference between the negative electrode overpotential at the kth moment and the negative electrode overpotential at the k-1th moment; Based on the prior estimate of the system state, the method for updating the error covariance matrix estimate is: Among them, P k|k-1 is the prior estimate of the covariance matrix of the state variables at time k, Q k is the process noise covariance matrix at time k, A k is the state transfer coefficient degenerated from the state transfer matrix, is the negative electrode overpotential; Based on the updated error covariance matrix estimate, the Kalman gain calculation method is: Among them, K k 、R k is the Kalman gain matrix and observation noise covariance matrix at time k, C k is the observation transfer coefficient degenerated from the observation transfer matrix; Based on the calculated Kalman gain, the method for evaluating the observation error is: Where g(·) is the observation equation, is the observation error at the kth moment, is the voltage measurement value at the kth moment, is the reaction polarization overpotential at the positive electrode solid-liquid interface at the kth moment, is the potential of the positive electrode at a certain lithium insertion concentration at the kth moment, is the concentration polarization overpotential at the kth moment, R SEI,n I is the SEI film resistance R SEI,n The voltage drop caused by R ohm is the ohmic polarization internal resistance, I is the current; Based on the evaluated observation error, the system state is corrected and the method for obtaining the posterior estimate is as follows: in, Estimate the posterior value for the state; Based on the posterior estimated value, the method for correcting the covariance matrix of the state variable is: 。 2. The method for diagnosing lithium deposition in lithium-ion batteries based on online estimation of negative electrode overpotential using an electrochemical model and Kalman filtering according to claim 1, characterized in that: Methods for establishing a wide-rate simplified electrochemical model based on parameter correction include: Use an ohmmeter to measure the internal resistance R ohm ; The open circuit voltage curve is formed by extracting the voltage data points at the end of the shelf life, and the least squares fitting method is used to obtain the initial lithium insertion concentration fraction y0 of the positive electrode, the initial lithium insertion concentration fraction x0 of the negative electrode, and the total capacity Q of the positive electrode. p , total negative electrode capacity Q n 、Total battery capacity Q all ; Combined with the pre-tested ohmic internal resistance R ohm By extracting the voltage mutation ΔU, the least square method is used to identify P act ; At the end of short-time constant current charge and discharge, extract the data point voltage and combine it with the reaction polarization overpotential η act , Ohmic polarization overpotential η ohm To calculate (E ocv -η act ) value, and complete the positive electrode solid phase diffusion time constant τ p , negative electrode solid phase diffusion time constant τ n , liquid phase diffusion coefficient P con Identify, where E ocv is the open circuit potential; Using the transient data under the identification condition and combining the existing parameter identification results, the concentration polarization overpotential η at different times is calculated. con , and then identify the liquid phase diffusion time constant τ e , and finally all electrochemical parameters are obtained, and a wide-rate simplified electrochemical model based on parameter correction is established.

3. A lithium-ion battery lithium deposition diagnostic system based on an electrochemical model and Kalman filtering for online estimation of negative electrode overpotential, the system being used to implement the method according to any one of claims 1 to 2, characterized in that: include: Model building module, framework building module and diagnosis module; The model building module is used to combine the battery SP+thermal coupling model to establish a wide-rate simplified electrochemical model based on parameter correction; The framework building module is used to build an EKF-based negative electrode overpotential estimation framework based on the wide-rate simplified electrochemical model; The diagnostic module is used to perform closed-loop correction on the negative electrode overpotential based on the negative electrode overpotential estimation framework to complete the lithium deposition diagnosis of the lithium-ion battery; The process of building the EKF-based negative electrode overpotential estimation framework includes: Calculate the negative electrode overpotential using a wide-rate simplified electrochemical model; Based on the EKF algorithm, a closed-loop filtering framework is constructed with the negative electrode overpotential as the state variable and the battery terminal voltage as the observation value; The process of calculating the negative electrode overpotential using a wide-rate simplified electrochemical model includes: Among them, η n is the reaction polarization overpotential at the solid-liquid interface of the negative electrode; R is the ideal gas constant; T is the temperature; F is the Faraday constant; is the total capacity of the negative electrode; c0 is the initial lithium ion concentration; P act is the reaction polarization coefficient; is the current, is the amount of lithium embedded on the negative electrode surface; Based on the negative electrode overpotential estimation framework, a closed-loop correction of the negative electrode overpotential is performed to complete the process of lithium plating diagnosis in lithium-ion batteries, including: Using the state variables and input variables at time k-1, the prior estimate of the system state at time k is calculated through the state equation f(·); Based on the prior estimate of the system state, updating the error covariance matrix estimate; Calculate the Kalman gain based on the updated error covariance matrix estimate; Observation error evaluation is performed based on the calculated Kalman gain; Based on the evaluated observation error, the system state is corrected to obtain the posterior estimate; Based on the posterior estimated value, performing covariance matrix correction of the state variable; The expression of the state equation f(·) is as follows: in, is the prior value of the state variable at the kth moment, is the battery current at the kth moment, is the difference between the negative electrode overpotential at the kth moment and the negative electrode overpotential at the k-1th moment; Based on the prior estimate of the system state, the method for updating the error covariance matrix estimate is: Among them, P k|k-1 is the prior estimate of the covariance matrix of the state variables at time k, Q k is the process noise covariance matrix at time k, A k is the state transfer coefficient degenerated from the state transfer matrix, is the negative electrode overpotential; Based on the updated error covariance matrix estimate, the Kalman gain calculation method is: Among them, K k 、R k is the Kalman gain matrix and observation noise covariance matrix at time k, C k is the observation transfer coefficient degenerated from the observation transfer matrix; Based on the calculated Kalman gain, the method for evaluating the observation error is: Where g(·) is the observation equation, is the observation error at the kth moment, is the voltage measurement value at the kth moment, is the reaction polarization overpotential at the positive electrode solid-liquid interface at the kth moment, is the potential of the positive electrode at a certain lithium insertion concentration at the kth moment, is the concentration polarization overpotential at the kth moment, R SEI,n I is the SEI film resistance R SEI,n The voltage drop caused by R ohm is the ohmic polarization internal resistance, I is the current; Based on the evaluated observation error, the system state is corrected and the method for obtaining the posterior estimate is as follows: in, Estimate the posterior value for the state; Based on the posterior estimated value, the method for correcting the covariance matrix of the state variable is: 。 4. The lithium ion battery lithium deposition diagnosis system for online estimation of negative electrode overpotential based on electrochemical model and Kalman filter according to claim 3 is characterized in that: The process of establishing a wide-rate simplified electrochemical model based on parameter correction includes: Use an ohmmeter to measure the internal resistance R ohm ; The open circuit voltage curve is formed by extracting the voltage data points at the end of the shelf life, and the least squares fitting method is used to obtain the initial lithium insertion concentration fraction y0 of the positive electrode, the initial lithium insertion concentration fraction x0 of the negative electrode, and the total capacity Q of the positive electrode. p , total negative electrode capacity Q n 、Total battery capacity Q all ; Combined with the pre-tested ohmic internal resistance R ohm By extracting the voltage mutation ΔU, the least square method is used to identify P act ; At the end of short-time constant current charge and discharge, extract the data point voltage and combine it with the reaction polarization overpotential η act , Ohmic polarization overpotential η ohm To calculate (E ocv -η act ) value, and complete the positive electrode solid phase diffusion time constant τ p , negative electrode solid phase diffusion time constant τ n , liquid phase diffusion coefficient P con Identify, where E ocv is the open circuit potential; Using the transient data under the identification condition and combining the existing parameter identification results, the concentration polarization overpotential η at different times is calculated. con , and then identify the liquid phase diffusion time constant τ e , and finally all electrochemical parameters are obtained, and a wide-rate simplified electrochemical model based on parameter correction is established.

Images