Lithium battery state estimation method and system based on PNGV model and DEKF algorithm

Abstract

The invention discloses a lithium battery state estimation method and system based on a PNGV model and a DEKF algorithm, and the method comprises the steps: firstly, carrying out the systematic offline test of a battery, and obtaining an open-circuit voltage-state of charge curve of the battery and the equivalent capacitance of a second-order PNGV equivalent circuit model; secondly, discretizing a continuous state equation of the model into a difference equation through bilinear transformation, and identifying other model parameters of the battery in different charge states by applying a recursive least square method; and finally, constructing a state filter and a parameter filter by adopting a double-extended Kalman filtering algorithm, and realizing collaborative estimation of the charge state and the health state through data interaction and feedback of the two filters. According to the method, through a progressive process of parameter identification and cooperative state estimation, the problems of time-varying characteristics and state coupling of battery model parameters are effectively solved, and the joint estimation precision and robustness of the state of charge and the state of health of the lithium battery under complex working conditions are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of battery management technology and state estimation, specifically involving a joint estimation method and system for the state of charge (SOC) and state of health (SOH) of lithium-ion batteries based on a second-order PNGV equivalent circuit model and a dual extended Kalman filter (DEKF) algorithm. Background Technology

[0002] With the continuous expansion of lithium-ion battery applications, the operational safety, reliability, and lifespan management of electrochemical energy storage systems are becoming increasingly prominent issues, placing higher demands on the state estimation capabilities of battery management systems (BMS). Among these, the state of charge (SOC) and state of health (SOH), as key indicators reflecting the battery's remaining energy and aging level, are the core foundation for achieving safe battery operation, optimized energy scheduling, and lifespan management. In actual operation, lithium-ion batteries are subjected to complex and variable operating conditions, influenced by factors such as changes in charge / discharge rates, ambient temperature fluctuations, and aging effects, resulting in significant nonlinear and time-varying characteristics in their internal parameters. Insufficient accuracy in SOC and SOH estimation can easily lead to overcharging, over-discharging, or decreased capacity utilization, not only reducing system efficiency but also potentially posing safety risks. Therefore, achieving high-precision estimation of SOC and SOH under complex operating conditions and battery aging is a critical technical problem that urgently needs to be solved in the current battery management field.

[0003] Current mainstream methods for estimating the state of charge (SOC) of batteries mainly include the ampere-hour integral method, methods based on equivalent circuit models, and data-driven methods. Among these, methods based on equivalent circuit models are widely used in engineering practice because they can achieve a good balance between the physical meaning of the model and computational complexity. The commonly used second-order RC equivalent circuit model has the advantages of simple structure and low computational cost, but it has limitations in describing the terminal voltage drift characteristics exhibited by the battery under long-term load, and it is difficult to accurately reflect the dynamic changes in open-circuit voltage caused by the accumulation of load current. In contrast, the second-order PNGV equivalent circuit model, by adding a large-capacity capacitor in series with the second-order RC model, provides a more efficient solution. C bThis capacitor can characterize the change of open-circuit voltage as a function of the load current integral, thus compensating for the shortcomings of traditional models in handling DC response and accumulated error, and enabling more accurate simulation of the nonlinear voltage response of batteries under complex operating conditions. However, for parameter identification of the second-order PNGV equivalent circuit model, existing research often uses curve fitting, which often suffers from large calculation errors and low identification efficiency. Furthermore, current SOC estimation based on the PNGV equivalent circuit model mostly employs a single extended Kalman filter algorithm. Due to the highly nonlinear characteristics of lithium batteries, their internal resistance, capacitance, and other parameters dynamically change with SOC, ambient temperature, and state of health (SOH). There is a strong coupling relationship between SOC and SOH; if SOC estimation is performed solely using fixed model parameters determined offline, battery aging will lead to a significant decrease in estimation accuracy. Summary of the Invention

[0004] To address the shortcomings of the existing technologies, the present invention aims to provide a lithium battery state estimation method and system based on the PNGV model and DEKF algorithm. By utilizing the time-varying model parameters of the battery and through data interaction and feedback between the state filter and the parameter filter, the method achieves collaborative estimation of the state of charge and the state of health.

[0005] To achieve the above-mentioned objectives, the present invention proposes the following technical solution: Firstly, a lithium battery state estimation method based on the PNGV model and the DEKF algorithm includes the following steps: S1. Steps for obtaining battery reference characteristic parameters: Conduct systematic offline testing on lithium-ion batteries. The offline testing includes maximum capacity testing, low-current constant-current charge-discharge testing, and hybrid power pulse characteristic testing to calibrate the open-circuit voltage-state-of-charge relationship curve of the battery. The equivalent capacitance parameters of the open-circuit voltage change caused by current accumulation are characterized by a second-order PNGV equivalent circuit model using a formula. S2. Model parameter identification and update steps: Construct the discretized difference equation of the second-order PNGV equivalent circuit model, and apply the recursive least squares method to recursively identify the model parameters of the battery under different charging states based on the current and voltage data of the battery under the mixed power pulse characteristic test. The model parameters include ohmic internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance and concentration polarization capacitance. S3. Co-estimation steps of state and parameters: Construct the system state-space equation based on the second-order PNGV equivalent circuit model; Employ a dual extended Kalman filter algorithm to simultaneously construct and run a first state extended Kalman filter and a second parameter extended Kalman filter; wherein, the first state extended Kalman filter estimates the system state vector including the state of charge, electrochemical polarization voltage, concentration polarization voltage, and equivalent capacitance voltage based on the system state-space equation; the second parameter extended Kalman filter estimates the model parameter vector including the ohmic internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance, concentration polarization capacitance, equivalent capacitance, and maximum battery capacity; the first state extended Kalman filter and the second parameter extended Kalman filter share the system output equation, and achieve co-estimation of the lithium battery's state of charge and health state through interactive state and parameter estimation values.

[0006] In some implementations, the parameter identification using the recursive least squares method in step S2 specifically includes: Construct the difference equation: ,in, , n For discrete time points, express n Open circuit voltage at any moment express n Battery terminal voltage at any time, express n The voltage across the equivalent capacitor at any given time, I ( n )for n Discharge current at any given moment k 1 to k 5 represents the coefficient to be identified; Define the observation column vector: With intermediate parameter column vector ; Based on the recursive formula: Online update of the estimated values ​​of the intermediate parameter column vector With covariance matrix P ( n ),in, K ( n ) is the gain matrix, I It is the identity matrix; Based on the updated coefficients k 1 to k 5. Calculate the values ​​of the ohmic internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance, and concentration polarization capacitance.

[0007] In some implementations, the specific implementation of the double extended Kalman filter algorithm in the cooperative state estimation stage of S3 includes: The state equation of the first state filter is obtained by discretization based on a second-order PNGV model, and the state vector includes the state of charge, electrochemical polarization voltage, concentration polarization voltage, and equivalent capacitance voltage; the state vector of the second parameter filter includes model parameters. ,in, Q ( n )for n The maximum usable capacity of the battery at any given time; The interaction between the two filters is based on the coupled observation equations, with the parametric filter using the state estimate from the previous time step to calculate the parametric Jacobian matrix. The parameters are then updated; the updated parameters are passed to the state filter in real time to calculate the state Jacobian matrix. It also performs state estimation, and the two processes run alternately to achieve coordinated estimation of the state and parameters.

[0008] In some embodiments, in the step of obtaining the battery reference characteristic parameters, the equivalent capacitance... C b The calibration is achieved in the following way: Calculate the charge change based on the test data of the hybrid power pulse characteristics. and the corresponding open-circuit voltage change ,in, Apply the terminal voltage to the pulse load moment before the pulse load. This is the terminal voltage during the recovery period after the pulse ends; The equation is derived based on the law of energy conservation. Inversion calculation of equivalent capacitance C b The value of .

[0009] In some implementations, the interaction between the two filters is achieved in the following manner: The observation equation of the first state-extended Kalman filter with respect to the Jacobian matrix of the state vector The Jacobian matrix of the observation equation of the second parameter extended Kalman filter with respect to the parameter vector. They are coupled through the following relationship: ; in Through recursive relationships The update allows for feedback correction of the parameter estimates based on the state estimation results.

[0010] Secondly, this invention proposes a lithium battery state estimation system based on the PNGV model and the DEKF algorithm, used to implement the method described in any of the above, including a hardware module for progressive processing: The battery unit is a lithium-ion battery. The sensor module is configured to acquire the current and voltage data of the battery in real time; it is used to perform the battery reference characteristic parameter acquisition steps: to conduct systematic offline testing on the lithium-ion battery, the offline testing including maximum capacity testing, low current constant current charge and discharge testing and hybrid power pulse characteristic testing, in order to calibrate the open circuit voltage-state of charge relationship curve of the battery and obtain the equivalent capacitance of the second-order PNGV equivalent circuit model; A processing module, connected to the sensor module, includes: The parameter identification unit is used to perform recursive least squares method to identify the model parameters of the second-order PNGV equivalent circuit model as the state of charge changes. The identification and updating steps of the model parameters are as follows: construct the discretized difference equation of the second-order PNGV equivalent circuit model, and apply the recursive least squares method to identify the model parameters of the battery under different states of charge based on the current and voltage data of the battery under the mixed power pulse characteristic test. The model parameters include ohmic internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance, concentration polarization capacitance and equivalent capacitance characterizing capacity decay. The state estimation unit is used to perform a dual extended Kalman filter algorithm to collaboratively estimate the state of charge (SOC) and health state. The collaborative estimation steps for state and parameters are as follows: The system state-space equation is constructed based on a second-order PNGV equivalent circuit model; a dual extended Kalman filter algorithm is used to simultaneously construct and run a first state extended Kalman filter and a second parameter extended Kalman filter; wherein, the first state extended Kalman filter estimates the system state vector including the SOC, electrochemical polarization voltage, concentration polarization voltage, and equivalent capacitance voltage based on the system state-space equation; the second parameter extended Kalman filter estimates the model parameter vector including the ohmic internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance, concentration polarization capacitance, equivalent capacitance, and maximum battery capacity; the first state extended Kalman filter and the second parameter extended Kalman filter share the system's output equation and achieve collaborative estimation of the lithium battery's SOC and health state through interactive state and parameter estimation values.

[0011] The output module is used to display or transmit the state estimation results.

[0012] In some embodiments, the processing module includes a processor and a memory, the memory storing a computer program that, when executed by the processor, implements the steps of any of the methods described.

[0013] In some implementations, the system is integrated into a battery management system and applied to electric vehicles, electrochemical energy storage power stations, or distributed energy systems.

[0014] Thirdly, the present invention proposes a non-transitory computer-readable storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the lithium battery state estimation method based on the PNGV model and DEKF algorithm as described in any one of the claims.

[0015] Fourthly, an electronic device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the lithium battery state estimation method based on the PNGV model and DEKF algorithm as described in any one of the claims.

[0016] Compared with the prior art, the technical solution provided by the present invention has the following significant advantages: 1) High model accuracy and stronger representation ability: By adopting a second-order PNGV equivalent circuit model, an equivalent capacitance is introduced on the basis of the traditional second-order RC model. C b This model can accurately characterize the dynamic changes in open-circuit voltage and the drift characteristics of terminal voltage caused by the cumulative effect of load current. This model structure better reflects the actual nonlinear dynamic characteristics of lithium batteries, providing a guarantee for high-precision state estimation from the model's foundation, and overcoming the limitations of traditional RC models in describing voltage response under long-term loads.

[0017] 2) Strong parameter tracking capability and good model adaptability: The recursive least squares method is applied to parameter identification of the PNGV model. By discretizing the model and constructing difference equations, the gain matrix and covariance matrix are updated recursively using the RLS algorithm, enabling fast and accurate tracking of ohmic internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance, and concentration polarization capacitance. This allows the identified battery model to account for changes in internal characteristics caused by battery aging, operating conditions, and temperature fluctuations, fundamentally solving the problem of decreased estimation accuracy with increasing usage time due to fixed model parameters.

[0018] 3) Significantly improved state estimation accuracy and robustness: The core lies in the construction of a collaborative estimation architecture using dual extended Kalman filters. The system state (SOC, etc.) is estimated through a state filter, while the model parameters are estimated through a parameter filter. The two filters interact via the Jacobian matrix, forming a dual closed-loop optimization mechanism of "parameters updating the model, and state updates providing feedback to optimize parameters." This design achieves collaborative estimation of SOC and SOH, significantly reducing interference caused by inaccurate parameters. Even under complex operating conditions where model parameters exhibit uncertainty and time-varying characteristics, the joint estimation results of SOC and SOH maintain high accuracy and robustness.

[0019] 4) Forming a progressive optimization closed loop to systematically solve key technical problems: This invention organically integrates the three steps of "offline experimentation - parameter identification - collaborative state estimation" into a progressive closed-loop processing flow. The parameter identification step provides accurate model parameters for collaborative state estimation, while the results of state estimation are fed back and optimize the basis of parameter identification. This systematic approach improves the overall performance of state estimation and effectively solves the industry problem that a single algorithm or fixed model cannot cope with the nonlinear and time-varying characteristics of batteries.

[0020] The adaptive dynamic estimation and update step of the model parameters provides high-precision model parameters that are updated in real time for the collaborative decoupling estimation step of state and parameters. The two form a closed-loop progressive process from online parameter identification to collaborative state estimation. Attached Figure Description

[0021] Figure 1 This is a flowchart of the lithium battery state estimation method based on the PNGV model and dual extended Kalman filtering of the present invention.

[0022] Figure 2 This is a second-order PNGV equivalent circuit model diagram of a lithium-ion battery.

[0023] Figure 3 This is a schematic diagram of the current and voltage curves in the HPPC experiment.

[0024] Figure 4 This is a block diagram of the lithium battery state estimation system based on the PNGV model and dual extended Kalman filtering of the present invention. Detailed Implementation

[0025] The following will combine Figure 1 The embodiments of the present invention will be described in detail.

[0026] Example 1: As Figure 1 As shown, the lithium battery state estimation method based on the PNGV model and dual extended Kalman filter of the present invention has the following specific steps: Step 1, Battery Baseline Characteristic Parameter Acquisition Steps: A systematic offline testing experiment is conducted on the lithium-ion battery. The offline tests include maximum capacity testing, low-current constant-current charge-discharge testing, and hybrid power pulse characteristic testing to calibrate the battery's open-circuit voltage-state-of-charge relationship curve and obtain the equivalent capacitance of the second-order PNGV equivalent circuit model. Specifically, the offline tests include: Step 1-1: Perform a maximum capacity test to determine the battery's nominal capacity; Steps 1-2: Perform small-current constant-current charge-discharge tests, including small-current charge-discharge experiments on lithium-ion batteries at a rate of 0.05C. By acquiring charge-discharge data and utilizing the characteristic that the ohmic voltage and polarization effect are opposite and cancel each other out during the averaging process, the open-circuit voltage data of the battery is calculated. That is, when the charging and discharging data are summed, the summed data is divided by 2 to obtain the open-circuit voltage data of the battery, thereby calibrating the OCV-SOC curve. Steps 1-3: Perform hybrid power pulse characteristic testing, including hybrid power pulse characteristic (HPPC) testing of lithium-ion batteries, to excite the battery dynamic response and obtain model parameters.

[0027] Step 2, Adaptive Dynamic Estimation and Update of Model Parameters: Construct the discretized difference equations of the second-order PNGV equivalent circuit model, and apply the recursive least squares method to recursively identify the model parameters of the battery under different states of charge based on the current and voltage data of the battery under mixed power pulse characteristic test. The model parameters include ohmic internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance, and concentration polarization capacitance. The parameter identification process of lithium-ion batteries based on recursive least squares is described in detail below: First, the parameters are obtained through experimental measurement. and corresponding , This indicates the change in charge of the battery during HPPC testing (in coulombs). This indicates the change in the battery's open-circuit voltage at the start and end of the change in charge. Equivalent capacitance C b The definition is shown in formula (1): (1); Based on equation (1), equation (2) is derived using the principle of energy conservation: (2); Change in open-circuit voltage Then it is calculated by the following formula (3): (3); In equation (1), for Figure 3 middle Apply the terminal voltage to the pulse load moment before the pulse load. This is the terminal voltage during the recovery period after the pulse ends.

[0028] like Figure 2 The diagram shows the second-order PNGV equivalent circuit used in this invention. This model is mainly composed of the open-circuit voltage. Equivalent capacitance C b Ohm resistance R 0 and parallel RC circuits (parameters) R 1. C 1. R 2. C 2) Composition.

[0029] In this model, the direction of the discharge current is defined as positive. Assume the nominal capacity of the lithium battery is... Q , its in t The state of charge at time t is SOC ( t Based on this circuit model, and according to Kirchhoff's voltage and current laws, the battery state-space equation and output equation can be derived in the continuous time domain, as shown in equations (4) and (5), respectively. t For time, I ( t ) represents the discharge current. U Cb ( t () is the equivalent capacitance voltage, U OCV ( t ) is the open circuit voltage, R 0 represents the internal resistance in ohms. R 1 is the electrochemical polarization resistance, C 1 is an electrochemically polarized capacitor, R 2 is the concentration polarization resistor, C 2 is the concentration polarization capacitor, U 1( t )and U 2( t The voltage of the RC parallel circuit is: (4); (5); By performing Laplace transforms on equations (4) and (5), the state-space equations of the second-order PNGV equivalent circuit model in the complex frequency domain are obtained as shown in equation (6): (6); in, sFor the Laplace transform operator, I ( s ) represents the discharge current. U Cb ( s () is the equivalent capacitance voltage, U OCV ( s ) is the open circuit voltage, R 0 represents the internal resistance in ohms. R 1 is the electrochemical polarization resistance, C 1 is an electrochemically polarized capacitor, R 2 is the concentration polarization resistor, C 2 is the concentration polarization capacitor, U 1( s )and U 2( s The voltage of the RC parallel circuit is: By rearranging the frequency domain equation (6), we can obtain the expression shown in equation (7): (7); Further, equation (7) can be written in transfer function form, as shown in equation (8): (8); Next, find a common denominator on the right-hand side of equation (8) to transform it into the standard transfer function form, as shown in equation (9): (9); The standard form of the transfer function G (s) characterizes the input-output relationship of the second-order PNGV equivalent circuit model in the complex frequency domain, laying a clear mathematical model foundation for online parameter identification based on discrete system theory.

[0030] To facilitate analysis and derivation, some coefficients in equation (9) are expressed as intermediate variables, and the time constant is set to... , As shown below: (10); in, a to e These are parameters for the continuous domain model, serving as intermediate variables for the second-order PNGV equivalent circuit model. Furthermore, make the output response Then equation (9) can be rearranged into the standard form of the transfer function, as shown in equation (11): (11); Using the bilinear transformation method, the mapping relationship is shown in equation (12): (12); in,T The sampling interval is... Z For complex variables in the discrete domain; Complete the transfer function in the continuous domain G (s) The transformation from the continuous domain to the discrete domain yields the discrete domain transfer function. G (z) Expression, denoted as (13): (13); in, to These are discrete parameters to be identified, containing all parameter information from the second-order PNGV model. These coefficients can be obtained from the continuous domain model parameters. a to e The specific representation is shown in equation (14): (14); in, Y (z) represents the voltage drop inside the battery module. T The sampling period is a to e For the continuous domain model parameters defined according to equation (10), equations (13) and (14) together constitute the subsequent online parameters. The discrete difference equation form upon which the recursive least squares method in number identification relies.

[0031] By inversely deducing from the bilinear transformation formula (12), the following relationship can be obtained: (15); Substituting equation (15) into the discrete domain transfer function equation (13), the corresponding continuous domain transfer function can be derived. G ( s The expression is as follows: (16); Based on the principle that the coefficients of terms with the same power in the numerator and denominator of equations (16) and (11) are equal, the following system of equations can be established: (17); This set of equations shows the discrete identification parameters. to With continuous domain model parameters a to e The mathematical mapping relationship between them provides a theoretical basis for recovering physical model parameters from online identification results.

[0032] The time constant can be obtained by solving the system of equations (17). and The expression is as follows: (18); Furthermore, based on equations (17) and (18), the calculation formulas for each physical parameter in the model can be obtained: (19); To facilitate subsequent recursive identification, the discrete domain transfer function (13) is rewritten in the following form: (20); in, To output the response, I ( z ) represents the discharge current.

[0033] Expanding and rearranging equation (20), we obtain the difference equation that is easy to implement in the time domain, as shown below: (twenty one); Equation (21) is the basic equation upon which the recursive least squares method is used for parameter identification in the future.

[0034] Applying the time-shifting property of the z-transform, operators in the z-domain are... Corresponding to sequences in the time domain The corresponding time-domain difference equation can be obtained from equation (21), where n Representing discrete moments: (twenty two); Define data variable matrix The matrix of coefficients to be estimated in the time-domain difference equation as follows: (twenty three); (twenty four); Equation (22) can then be written in the form of the following matrix: (25); in, express n The observed voltage value at time [time]. Representing the battery model n The input column vector at time t, express n The column vector of model parameters to be identified at time (25) forms the basis for subsequent parameter identification using the recursive least squares method.

[0035] Recursive Least Squares (RLS) identifies parameters by calculating the model parameter estimates that minimize the sum of squared errors between the observed and predicted values ​​of the linear model.

[0036] Recursive Least Squares (RLS) is an algorithm that identifies parameters through iterative calculations. Its core idea is to estimate the unknown parameters in a linear model by minimizing the sum of squared errors between the observed data and the model's predicted values.

[0037] Consider the following linear model: (26); in, Indicates the first i Observed values ​​of terminal voltage, The first battery model i The input vector corresponding to each sample This represents the vector of parameters to be identified. This represents the error. The algorithm updates the parameter estimates recursively, making the objective function... Minimize, thereby achieving optimization of model parameters. M Real-time, adaptive identification.

[0038] Before processing m When there are only a few observations, the linear model (26) can be expressed in a compact matrix form: (27); in, express m A ×1 observation column vector, express n’ A data matrix of size 5 This represents a 5×1 vector of parameters to be identified. express m An error vector of ×1.

[0039] Equation (27) transforms the parameter estimation problem of the recursive least squares method into a matrix expression based on batch data, providing a basis for deriving its recursive update formula.

[0040] Definition based on the previous m Cost function of observations The sum of squares of the errors between the recursive least squares predicted output and the measured output is expressed in matrix form as follows: (28); By analyzing the cost function Regarding the parameter vector to be identified The gradient is obtained as follows: (29); And set the gradient above to zero, that is Thus, the normal equation is obtained: (30); Solving equation (30) yields the result based on the cutoff date. m The least squares estimate of all observations at time t is denoted as . : (31); Assuming it has been obtained m Parameter estimation at time 1 When m Get new data points at all times. When ), then m Extended data matrix at time step and extended observation vector It can be recursively expressed as: (32); To achieve online recursive updates of parameters and avoid direct inversion operations, we define... m The parameter covariance matrix at time 1 as follows: (33); matrix Characterized m Uncertainty in time parameter estimation.

[0041] Based on the recursive relation (32) and the definition of the covariance matrix (33). m inverse of the covariance matrix at time t can be m Data matrix at time 1 With new observation vector The details are as follows: (34); Combination The definition of , equation (34) can be further simplified as: (35); Equation (35) represents the recursive update relation for the inverse of the covariance matrix. For direct solution... To avoid matrix inversion, we introduce the matrix inversion lemma (Sherman-Morrison formula): (36); This formula provides for matrices of the form "original matrix". A An efficient method for inverting a matrix with a low-rank update term "UV".

[0042] Corresponding to equation (35) with the matrix inversion lemma (36), let , , The covariance matrix can be directly derived from this. The recursive calculation formula is as follows: (37); intermediate variable parameter estimates The recursive update derivation is as follows. Equation (31) can be simplified to: (38); according to m The estimated value at time 1 is defined as follows: (39); and then: (40); Substituting equation (40) into equation (38), we get: (41); Substituting equation (35) into equation (41), we get: (42); Expanding and rearranging equation (42), we obtain the recursive update formula for the intermediate variable parameter estimation: (43); To simplify the expression, a gain matrix is ​​defined. : (44); Gain matrix using covariance covariance matrix The recursive formula can be further simplified to: (45); In summary, equations (43), (44), and (45) together constitute the core iterative update equation set of the standard recursive least squares (RLS) method.

[0043] so, n The core iterative formula of the recursive least squares method at each time step is shown in equation (46): (46); in, This is the gain coefficient matrix. Let covariance matrix be the variance matrix. I It is an identity matrix.

[0044] By recursively executing formula (46), five parameters to be estimated can be identified online. to Then, based on the mapping relationship between these parameters and the parameters of the battery equivalent circuit model, specific physical parameters such as ohmic internal resistance, polarization resistance, and polarization capacitance are obtained.

[0045] Consider as Figure 3 The second-order PNGV equivalent circuit model is shown, where the first filter is used to estimate the system's state vector. The corresponding discrete-time state-space equation and output equation of this model can be expressed as follows: (47); in, n Indicates time, Let be the system state vector. , These are the system matrix and the input matrix, respectively. This indicates process noise, caused by sensor measurement errors. This indicates system noise, stemming from factors such as model simplification and inaccurate parameters. For observation output, For system input, and Both are multidimensional random variables that follow a normal distribution, denoted as and respectively. and Its covariance matrix can be expressed as: and .

[0046] Step 3, Co-estimation of SOC and SOH of lithium-ion energy storage power station batteries based on dual extended Kalman filtering: To simultaneously estimate the battery's state of charge (SOC) and state of health (SOH), this step employs a dual extended Kalman filter algorithm. The first filter is used to estimate the system's state vector. Based on the second-order PNGV model, the following discrete-time state-space equations can be established: The state vector is defined as: ; System state transition matrix With control matrix Represented as: , ; in, For battery charging and discharging efficiency, T The sampling interval is... and Let be the time constants of the two RC circuits, and have . and .

[0047] Define the system input quantity (current) as The observed measurement (terminal voltage) is Then the state equation of the system With observation equation These can be written in the following function forms: ; ; in, This is a vector containing time-varying parameters such as ohmic internal resistance, polarization resistance, polarization capacitance, and equivalent capacitance. The above equations provide a complete mathematical model foundation for the subsequent construction of state filters and parameter filters, and for achieving coordinated decoupling estimation of SOC and SOH.

[0048] .

[0049] The second filter estimates the model parameters, using the slowly changing parameters in the battery model as a parameter column vector. θ The following discrete state-space system equations and output observation equations can be obtained: In this step, the mathematical model of the second filter (parameter filter) is established based on the following state-space equations: (48); in, and The modeling error and the observation error both follow a zero-mean normal distribution, i.e. , Its corresponding covariance matrix is ​​defined as: and .

[0050] The parameter vector to be estimated Specifically: ; The key step in parametric filtering is to calculate the Jacobian matrix of the observation equation with respect to the parameter vector. The complete derivation is as follows: ; In the formula, the term The recurrence relation is given by the following formula: ; and Related to the filter gain of the previous time step: ; in, for n Posterior state estimation at time 1 for nThe prior state estimate at time t, i.e.; for n The system input at time 1 typically refers to the battery load current. for n The prior parameter estimates at time 1, i.e., the predicted values ​​before parameter measurement and updates, for n The state Kalman gain matrix at time 1 is used in the state filter to balance the predicted state with the measured value and correct for state estimation errors. Difference, for n The observation equation at time t is the Jacobian matrix of the parameter vector.

[0051] The above formulas together constitute the prediction error covariance in the parametric filter. The complete theoretical basis of recursive updates ensures the ability to track the time-varying characteristics of model parameters online.

[0052] Furthermore, in step 3, the algorithm flow for estimating the battery SOC using the dual extended Kalman filter is as follows: 1-Initialization: The initial values ​​for the state column vector are: ; Its corresponding error covariance matrix is: ; Assign initial values ​​to the parameter column vector: ; Its corresponding error covariance matrix is: ; in, parameter vector The initial estimate, E ( ) is the mathematical expectation operator. This is the initial estimate of the state vector x.

[0053] 2-Prior estimation: Parameter prediction update: Based on the parameter evolution model, update the parameter vector. θ A one-step prediction is performed using its error covariance matrix: ; in, Let be the covariance matrix of the parametric process noise. for n Posterior estimate of the parameter vector at time 1 In order to be in n Prior estimation of parameter vectors at time t. forn The posterior estimate of the parameter estimation error covariance matrix at time 1. for k Prior estimation of the parameter estimation error covariance matrix at time t.

[0054] State prediction update: Based on the state estimate from the previous time step, the system input, and the predicted parameters, update the state vector. x A one-step prediction is performed using its error covariance matrix: ; in, for n Posterior estimation of the state vector at time 1 This is the posterior estimate from the previous time step. From n 1 to n The state transition matrix at time t, for n 1 to n The input matrix at time step, for n Load current at time 1 State transition matrix The transpose of the matrix, for n State-process noise covariance matrix at time 1 for n Prior estimation of parameter vectors at time t.

[0055] 3-Measurement Update: State Kalman gain State vector (include and ) and its error covariance matrix (include and Posterior correction: ; in, Let Jacobian matrix be the observation function with respect to the state vector. The state measurement noise covariance matrix is... for n Posterior estimate of the state covariance matrix at time t. for n Prior estimation of the state covariance matrix at time t. I It is an identity matrix.

[0056] Parameter Kalman gain Parameter vector (include and ) and its error covariance matrix (include and Posterior correction: ; in, Let Jacobian matrix be the observation function with respect to the parameter vector. The noise covariance matrix is ​​used to measure parameters.

[0057] 4-Iterative Loop: After completion n State vector at time step With parameter vector After the posterior estimation, the time index is updated to Then return to step 2 - prior estimation and step 3 - measurement update and continue execution. By iterating in this way, continuous online collaborative estimation and tracking of battery state of charge (SOC) and model parameters can be achieved.

[0058] Example 2: Figure 4 As shown, the lithium battery state estimation system based on the PNGV model and dual extended Kalman filtering of the present invention, used to implement the method of any embodiment, includes a hardware module for progressive processing: Battery cell 100 is a lithium-ion battery; The sensor module 200 is configured to acquire the current and voltage data of the battery in real time; it is used to perform the battery reference characteristic parameter acquisition steps: to conduct systematic offline testing on the lithium-ion battery, the offline testing including maximum capacity testing, low current constant current charge and discharge testing and hybrid power pulse characteristic testing, in order to calibrate the open circuit voltage-state of charge relationship curve of the battery and obtain the initial parameters of the second-order PNGV equivalent circuit model. Processing module 300, connected to the sensor module, includes: The parameter identification unit 310 is used to perform online identification of the time-varying parameters of the second-order PNGV equivalent circuit model using the recursive least squares method. The adaptive dynamic estimation and update steps of the model parameters are as follows: the discretized difference equation of the second-order PNGV equivalent circuit model is constructed, and the recursive least squares method is applied to identify the time-varying model parameters of the battery online based on the real-time collected battery current and voltage data. The time-varying model parameters include ohmic internal resistance, polarization resistance, polarization capacitance, and equivalent capacitance characterizing capacity decay. The state estimation unit 320 is used to perform a dual extended Kalman filter algorithm to collaboratively estimate the state of charge (SOC) and health state. The collaborative and decoupled estimation steps for state and parameters are as follows: Based on the time-varying model parameters updated online in the previous step, a system state-space model is constructed; based on the time-varying characteristics of the battery parameters, a parameter evolution model is constructed; using the dual extended Kalman filter algorithm, a first state extended Kalman filter and a second parameter extended Kalman filter are simultaneously constructed and run. Specifically, the first state extended Kalman filter, based on the online-updated time-varying model parameters and the system state-space model, estimates a system state vector including the SOC, polarization voltage, and equivalent capacitance voltage; the second parameter extended Kalman filter, based on the parameter evolution model, estimates a model parameter vector including the ohmic internal resistance, polarization resistance, polarization capacitance, equivalent capacitance, and maximum battery capacity; the first state extended Kalman filter and the second parameter extended Kalman filter share the system's output equations and achieve collaborative and decoupled estimation of the SOC and health state through interaction between state estimation errors and parameter prediction values. Output module 400 is used to display or transmit state estimation results; The output of the parameter identification unit is connected to the state estimation unit, forming a progressive data stream from parameter identification to state estimation. Furthermore, the processing module 300 includes a processor and a memory, the memory storing a computer program that, when executed by the processor, implements the steps of any of the methods described.

[0059] Furthermore, the system is integrated into a battery management system and applied to electric vehicles, electrochemical energy storage power stations, or distributed energy systems.

[0060] In summary, the technical implementation route of this invention can be summarized as follows: 1. Battery modeling based on a second-order PNGV equivalent circuit model: A second-order PNGV model is used to replace the second-order RC equivalent circuit model, and a large-capacity capacitor is added in series. C b This capacitor is used to accurately characterize the dynamic changes in open-circuit voltage and the terminal voltage drift characteristics caused by the integral of the load current. The model structure includes an ohmic internal resistance. R 0. Two sets of RC parallel circuits R 1. C 1. R 2. C 2 and equivalent capacitance C b It can simulate the nonlinear voltage response of a battery under long-term load and complex operating conditions more accurately than traditional models, and solves the limitations of traditional RC models in describing cumulative errors, while keeping the computational complexity of the model relatively low.

[0061] 2. Online Model Parameter Identification Based on Bilinear Transform and Recursive Least Squares (RLS): To overcome the nonlinear characteristics of battery parameters changing with aging and environmental factors, this invention employs an online parameter identification scheme based on Recursive Least Squares (RLS). The key aspect lies in its mathematical processing flow: First, a continuous-time domain state equation is constructed based on Kirchhoff's laws. Then, the continuous transfer function is discretized using Laplace transform and bilinear transform, deriving a difference equation containing model parameter information. Next, the observation matrix and parameter matrix are constructed, and the gain coefficient matrix is ​​updated in real-time using the recursive least squares method. K Covariance Matrix P This enables rapid tracking and accurate identification of the model's resistance and capacitance parameters.

[0062] 3. SOC and SOH Co-estimation Architecture Based on Dual Extended Kalman Filters: This invention constructs two parallel extended Kalman filters to achieve decoupled estimation of state and parameters. The first filter is used to estimate the battery's system state (SOC), taking current as input and voltage as observation; the second filter uses slowly changing parameters in the battery model as the state vector. The key to this architecture lies in the data interaction mechanism between the two filters: the output of the parametric filter updates the model parameters in the state equation in real time, while the error correction of the state filter, in turn, optimizes the parameter estimation. This dual closed-loop structure takes into account changes in model parameters, significantly improving the robustness and accuracy of the joint estimation of SOC and SOH.

[0063] Example 3: A non-transitory computer-readable storage medium storing a computer program that, when executed by a processor, implements a lithium battery state estimation method based on the PNGV model and DEKF algorithm according to Example 1 of the present invention. The present invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate methods for implementing the state estimation of lithium batteries according to Example 1 of the present invention. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0064] Example 4: An electronic device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements a lithium battery state estimation method based on the PNGV model and DEKF algorithm according to Example 1 of the present invention. These computer program instructions may also be stored in a computer-readable storage medium capable of directing a computer or other programmable data processing device to operate in a specific manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process... Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0065] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0066] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0067] This invention is not limited to the embodiments described above. The above description of specific embodiments is intended to illustrate and explain the technical solutions of this invention. The specific embodiments described above are merely illustrative and not restrictive. Without departing from the spirit and scope of the claims, those skilled in the art can make many specific modifications based on the teachings of this invention, and these modifications all fall within the scope of protection of this invention.

Claims

1. A method for estimating the state of a lithium battery based on the PNGV model and the DEKF algorithm, characterized in that, Includes the following steps: S1. Steps for obtaining battery reference characteristic parameters: Conduct systematic offline testing on lithium-ion batteries. The offline testing includes maximum capacity testing, low-current constant-current charge-discharge testing, and hybrid power pulse characteristic testing to calibrate the open-circuit voltage-state-of-charge relationship curve of the battery. The equivalent capacitance parameters of the open-circuit voltage change caused by current accumulation are characterized by a second-order PNGV equivalent circuit model using a formula. S2. Model parameter identification and update steps: Construct the discretized difference equation of the second-order PNGV equivalent circuit model, and apply the recursive least squares method to identify the model parameters of the battery under different charging states based on the current and voltage data of the battery under the mixed power pulse characteristic test. The model parameters include ohmic internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance and concentration polarization capacitance. S3. Co-estimation steps of state and parameters: Construct the system state-space equation based on the second-order PNGV equivalent circuit model; Employ a dual extended Kalman filter algorithm to simultaneously construct and run a first state extended Kalman filter and a second parameter extended Kalman filter; wherein, the first state extended Kalman filter estimates the system state vector including the state of charge, electrochemical polarization voltage, concentration polarization voltage, and equivalent capacitance voltage based on the system state-space equation; the second parameter extended Kalman filter estimates the model parameter vector including the ohmic internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance, concentration polarization capacitance, equivalent capacitance, and maximum battery capacity; the first state extended Kalman filter and the second parameter extended Kalman filter share the system output equation, and achieve co-estimation of the lithium battery's state of charge and health state through interactive state and parameter estimation values.

2. The lithium battery state estimation method based on the PNGV model and DEKF algorithm according to claim 1, characterized in that, In S2, the application of recursive least squares method for parameter identification specifically includes: Construct the difference equation: ,in, n is a discrete time point. Represents the open-circuit voltage at time n. Represents the battery terminal voltage at time n. Let I(n) represent the voltage across the equivalent capacitor at time n, I(n) represent the discharge current at time n, and k1 to k5 represent the coefficients to be identified. Define the observation column vector: With intermediate parameter column vector ; Based on the recursive formula: Update the estimated value of the intermediate parameter column vector. Let K(n) be the covariance matrix, where K(n) is the gain matrix and I is the identity matrix. The values ​​of the ohmic internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance, and concentration polarization capacitance are calculated based on the updated coefficients k1 to k5.

3. The lithium battery state estimation method based on the PNGV model and DEKF algorithm according to claim 1, characterized in that, In S3, the specific implementation of the double extended Kalman filter algorithm in the cooperative state estimation stage includes: The state equation of the first state filter is obtained by discretization based on the second-order PNGV model, and the state vector includes the state of charge, electrochemical polarization voltage, concentration polarization voltage and equivalent capacitance voltage. The state vector of the second parameter filter includes time-varying model parameters. ,in, Let be the ohmic internal resistance of the battery at time n; Let be the electrochemical polarization resistance of the battery at time n; Let be the concentration polarization resistance of the battery at time n; Let be the electrochemical polarization capacitance of the battery at time n; Let be the concentration polarization capacitance of the battery at time n; Let be the equivalent capacitance of the battery at time n; Q(n) is the maximum usable capacity of the battery at time n. The interaction between the two filters is based on the coupled observation equations, with the parametric filter using the state estimate from the previous time step to calculate the Jacobian matrix. The parameters are then updated; the updated parameters are passed in real time to the state filter for calculating the Jacobian matrix. It also performs state estimation, and the two processes run alternately to achieve coordinated estimation of the state and parameters.

4. The lithium battery state estimation method based on the PNGV model and DEKF algorithm according to claim 1, characterized in that, In the step of obtaining the battery reference characteristic parameters, the equivalent capacitance C b The calibration is achieved in the following way: Calculate the charge change based on the test data of the hybrid power pulse characteristics. and the corresponding open-circuit voltage change ,in, Apply the terminal voltage to the pulsed load moment before the pulse. This is the terminal voltage during the recovery period after the pulse ends; The equation is derived based on the law of energy conservation. Inversion calculation of equivalent capacitance C b The value of .

5. The lithium battery state estimation method based on the PNGV model and DEKF algorithm according to claim 3, characterized in that, The interaction between the two filters is achieved in the following way: The observation equation of the first state-extended Kalman filter with respect to the Jacobian matrix of the state vector The Jacobian matrix of the observation equation of the second parameter extended Kalman filter with respect to the parameter vector. They are coupled through the following relationship: ； in Through recursive relationships The update allows for feedback correction of the parameter estimates based on the state estimation results.

6. A lithium battery state estimation system based on the PNGV model and the DEKF algorithm, used to implement the method described in any one of claims 1-5, characterized in that, Includes hardware modules for progressive processing: The battery unit is a lithium-ion battery. The sensor module is configured to acquire the current and voltage data of the battery in real time; it is used to perform the battery reference characteristic parameter acquisition steps: to conduct systematic offline testing on the lithium-ion battery, the offline testing including maximum capacity testing, low current constant current charge and discharge testing and hybrid power pulse characteristic testing, in order to calibrate the open circuit voltage-state of charge relationship curve of the battery and obtain the initial parameters of the second-order PNGV equivalent circuit model. A processing module, connected to the sensor module, includes: The parameter identification unit is used to perform recursive least squares method to identify the model parameters of the second-order PNGV equivalent circuit model as the state of charge changes. The identification and updating steps of the model parameters are as follows: construct the discretized difference equation of the second-order PNGV equivalent circuit model, and apply the recursive least squares method to identify the model parameters of the battery under different states of charge based on the current and voltage data of the battery under the mixed power pulse characteristic test. The model parameters include ohmic internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance, and concentration polarization capacitance. The state estimation unit is used to perform a dual extended Kalman filter algorithm to collaboratively estimate the state of charge (SOC) and health state. The collaborative estimation steps for state and parameters are as follows: The system state-space equation is constructed based on a second-order PNGV equivalent circuit model; a dual extended Kalman filter algorithm is used to simultaneously construct and run a first state extended Kalman filter and a second parameter extended Kalman filter; wherein, the first state extended Kalman filter estimates a system state vector including the SOC, electrochemical polarization voltage, concentration polarization voltage, and equivalent capacitance voltage based on the system state-space equation; the second parameter extended Kalman filter estimates a model parameter vector including the ohmic internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance, concentration polarization capacitance, equivalent capacitance, and maximum battery capacity; the first state extended Kalman filter and the second parameter extended Kalman filter share the system's output equation and achieve collaborative estimation of the lithium battery's SOC and health state through interactive state and parameter estimations; The output module is used to display or transmit the state estimation results.

7. The lithium battery state estimation system based on the PNGV model and DEKF algorithm according to claim 6, characterized in that, The processing module includes a processor and a memory, the memory storing a computer program that, when executed by the processor, implements the steps of the method as described in any one of claims 1-5.

8. The lithium battery state estimation system based on the PNGV model and DEKF algorithm according to claim 6, characterized in that, The system is integrated into a battery management system and can be applied to electric vehicles, electrochemical energy storage power stations, or distributed energy systems.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, the computer program being executed by a processor to implement the lithium battery state estimation method based on the PNGV model and DEKF algorithm as described in any one of claims 1 to 5.

10. An electronic device, comprising: The memory, the processor, and the computer program stored in the memory and executable on the processor thereon, wherein the processor, when executing the computer program, implements the lithium battery state estimation method based on the PNGV model and the DEKF algorithm as described in any one of claims 1 to 5.

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