A joint estimation method for lithium-ion battery state

Abstract

The present invention discloses a method for jointly estimating the state of a lithium-ion battery, which mainly relates to a method for jointly estimating the SOC and SOH of a lithium-ion battery based on an adaptive double extended Kalman filter algorithm (SVDDAEKF) with singular value decomposition. The method aims to accurately estimate the SOC and SOH values ​​of a lithium-ion battery. In order to solve the problem of filter divergence caused by abnormal disturbances, inaccurate initial values, and rounding errors due to limited bytes of a single-chip computer, the state quantity covariance matrix is ​​subjected to singular value decomposition based on a common extended Kalman filter algorithm, thereby overcoming the problem of non-positive definiteness of the error covariance matrix. The SVDDAEKF algorithm is used to jointly estimate the SOC and SOH of the battery based on a battery equivalent circuit model. The present invention can avoid the common Kalman filter algorithm from losing its positive definiteness during the iteration of the covariance matrix due to the limitation of the bytes of the single-chip computer, thereby causing filter divergence, and adjust the process noise covariance in real time, thereby improving the accuracy and convergence speed of the algorithm in estimating the state of charge.

Description

Technical Field

[0001] The present invention relates to a method for jointly estimating the state of a lithium-ion battery, and belongs to the technical field of research on a method for jointly estimating the SOC and SOH of a lithium-ion battery. Background Art

[0002] Due to environmental concerns, countries around the world have set carbon neutrality goals. To address these challenges, research related to clean energy has become a hot topic in recent years. Compared to traditional batteries such as lead-acid and nickel-cadmium batteries, lithium-ion batteries offer a range of advantages, including high specific energy, low self-discharge, rapid charge and discharge, non-toxicity, no memory effect, and a long service life. Consequently, lithium-ion batteries are becoming increasingly popular and are now widely used in electric vehicles. Batteries, motors, and electronic controls are the three core components of electric vehicles and directly determine the overall performance of the vehicle. While lithium-ion batteries offer advantages such as long cycle life, high specific energy, and no memory effect, they still face several key challenges. A safe and reliable battery management system is crucial for electric vehicles, with state of charge (SOC) being one of its core functions. Accurate SOC estimation is a major challenge. The accuracy of SOC estimation directly determines the effectiveness of the battery management system's control strategy.

[0003] Current SOC estimation methods are primarily categorized as follows: 1) direct measurement; 2) data-driven methods; and 3) model-based estimation methods. Direct measurement methods currently mostly combine the ampere-hour integration method and the open-circuit voltage method. The initial SOC of the battery is obtained by allowing the battery to rest for a long period of time, and the SOC value is then obtained by integrating the current. However, this method requires a long period of rest to obtain the initial SOC value, making it inconvenient to implement in practice. It is also sensitive to initial values ​​and interference, leading to uncorrectable error accumulation. Data-driven methods use large amounts of data to understand the internal dynamics of the battery. Commonly used data-driven methods include neural networks, fuzzy logic, and support vector machines. However, data-driven methods require high computational costs, and the accuracy of the estimation depends heavily on the training data. Model-based estimation methods are currently the most widely used methods, primarily using a set of state-space equations. Currently, the Kalman filter algorithm and its improved algorithms are primarily used to apply the model to SOC estimation. Model-based estimation methods are currently the mainstream approach and a key focus of current research.

[0004] There are several types of SOH estimation methods: 1) Aging mechanism identification methods based on frequency-domain equivalent circuit models; 2) Neural network algorithms based on black-box models; and 3) Filter estimation algorithms based on time-domain equivalent circuit models. Aging mechanism identification methods based on frequency-domain equivalent circuit models estimate SOH by identifying internal aging mechanisms and external characteristic parameters. The former primarily refers to the battery's internal physicochemical parameters, while the latter primarily refers to the test curves of the charge and discharge process, internal resistance, and available capacity of the battery. Neural network algorithms based on black-box models primarily include estimation based on analytical models and artificial neural network estimation. These methods require large amounts of data for training. Filter estimation algorithms based on time-domain equivalent circuit models offer high accuracy and are combined with online algorithms, making them popular among many scholars. Summary of the Invention

[0005] In response to the problems existing in the current technology, the present invention provides a method for jointly estimating the state of a lithium-ion battery, which solves the current technical difficulties in accurately estimating the SOC and SOH of lithium-ion batteries.

[0006] To achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: a method for jointly estimating the state of a lithium-ion battery, comprising the following steps:

[0007] Step 1: Read the initial SOC and capacity values ​​of the battery.

[0008] Step 2: Establish a second-order equivalent circuit model of the lithium-ion battery and derive the state space equation of the model based on Kirchhoff's voltage law.

[0009] Step 3: Collect open circuit voltage data and state of charge data to obtain the relationship between the two. Based on the model, discretize the model equation and rewrite the discretized equation into least squares form. Then, use the bias-compensated least squares method with forgetting factor (BCFFRLS) and combine it with the relationship between open circuit voltage and state of charge. Identify the model parameters through the input battery current, voltage and other data.

[0010] Step 4: Improve the ordinary extended Kalman, perform singular value decomposition on the error covariance matrix, and update the noise error covariance matrix in real time.

[0011] Step 5: Based on the obtained initial values ​​and model parameters, the multi-scale calculation formulas for joint estimation of battery SOC and SOH are established using the Adaptive Extended Kalman Matrix (SVDAEKF) based on singular value decomposition and the Adaptive Extended Kalman Matrix (AEKF). SOH can be expressed as the maximum available capacity of the battery at this moment. Therefore, the battery SOH can be estimated by estimating the maximum available capacity of the battery at this moment, which can be expressed as: First, the capacity estimation module runs, passing the estimated capacity value and the collected current and voltage values ​​to the SOC estimation module to calculate the SOC value. Simultaneously, the observed values ​​obtained during the SOC estimation process are passed to the capacity estimation module to participate in the calculation and estimate the capacity. Because capacity changes slowly while SOC changes constantly, a multi-timescale approach is adopted, estimating capacity at a macroscale and SOC at a microscale. The capacity is updated every 60 seconds, while the SOC value is updated every 1 second.

[0012] In the above scheme, the battery state space equation in step 2 includes the state equation and the observation equation, which can be expressed as:

[0013]

[0014] Where t is the sampling time, R0 is the ohmic internal resistance of the battery, R1, R2 and C1, C2 are the polarization resistance and polarization capacitance of the battery respectively, τ1, τ2 are the polarization time constants and τ1=R1C1, τ2=R2C2, U1, U2 are the terminal voltages of the two RC links, C max is the rated capacity of the battery, U oc is the open circuit voltage of the battery, i is the operating current of the battery, U t is the battery terminal voltage, ω is the process noise, ν is the measurement noise, and SOC is the state of charge of the battery. The dual time scales k and l describe the macroscopic time scale and the microscopic time scale respectively, which can be regarded as: k,l t k,l =t k,0 +l×Δt(1≤l≤L z ) The state of the system at the moment, L z is the scale conversion limit, that is, a macro scale equals L z A microscopic time scale.

[0015] In the above scheme, the relationship between the open circuit voltage OCV and the state of charge SOC of the battery in step 3 is obtained by the static method, which is to discharge the battery intermittently from a full charge and obtain the open circuit voltage of the battery by static method.

[0016] Furthermore, polynomial fitting of OCV and SOC was performed using Matlab fitting tools to obtain the relationship between OCV and SOC:

[0017]

[0018] In the above scheme, the model parameters described in step 3 include battery capacity, battery polarization internal resistance, polarization capacitance, concentration polarization internal resistance, and concentration polarization capacitance. The present invention collects data through a dynamic stress test (DST) of the battery and identifies the parameters using a bias-compensated least squares method with a forgetting factor.

[0019] The parameter identification process of the bias-compensated least squares method with forgetting factor is as follows:

[0020] Parameter initialization:

[0021] Among them, θ BC (0) is the initial value of the least squares method for deviation compensation, θ LS (0) is the initial value of the least squares identification with forgetting factor, J(0) is the initial value of the cost function, and P(0) is the initial value of the covariance matrix.

[0022] Calculate the estimated error:

[0023] Update the system gain matrix:

[0024] Parameter estimation without considering noise: θ LS (k+1)=θ LS (k)+K(k+1)e(k+1)

[0025] Error criterion function calculation:

[0026] Average weighted variance estimation of voltage signal noise:

[0027] Update the system error covariance:

[0028] Update the parameter estimates after bias compensation:

[0029] Output the parameter result θ of the least squares method with the forgetting factor. BC (k+1), then according to the following formula:

[0030]

[0031] Calculate the model parameters R0, R1, C1, R2, and C2.

[0032] In the above scheme, the improvement to the EKF described in step 4 includes performing SVD decomposition on the covariance matrix. The specific process of the improved algorithm is as follows:

[0033] x k+1|k=Ax k +Bu k

[0034]

[0035] U k+1|k =V′ k 、D k+1|k =D′ k

[0036]

[0037]

[0038]

[0039]

[0040] K k+1 =U k+1 (D k+1 ) 2 (U k+1 ) T C T L k+1 L k+1 T

[0041]

[0042] x k+1 =x k+1k +K k+1 e k

[0043] In the above scheme, the SOH estimation in step five is characterized by the battery capacity, and the capacity is estimated using the adaptive extended Kalman filter algorithm. In actual battery operation, the SOH changes very slowly relative to the SOC. Therefore, a multi-scale method is used to estimate the SOC on a macro time scale and the capacity on a micro time scale.

[0044] In the above scheme, the adaptive extended Kalman filter algorithm described in step 5 is as follows:

[0045] Initialization: x0, P0, R0, Q0

[0046] Time update: x k+1|k =Ax k +Bu k

[0047] Error covariance matrix prediction: P k+1|k =AP k AT +Q k

[0048] Noise matrix update:

[0049] Calculate the Kalman filter gain: K k+1 =P k+1|k C T (CP k+1|k C T +R k+1 ) -1

[0050] Observation update: x k+1 =x k+1|k +K k+1 (y k+1 -g(x k+1|k ,u k ))

[0051] Error covariance matrix update: P k+1 =(IK k+1 C)P k+1|k

[0052] Noise matrix update:

[0053] Furthermore, in parameter estimation, the state space equation of the system is:

[0054]

[0055] In the above scheme, the SOC and SOH collaborative estimation framework described in step 5 is:

[0056] Set the capacity observer AEKF respectively θ and state observer SVDAEKF χ Initial value:

[0057]

[0058] Where θ 0,0 , Capacity observer AEKF θ The initial capacity value, error covariance matrix initial value and system noise covariance matrix initial value; χ 0,0 , They are state observers SVDIEKF χ The initial value of the state, the initial value of the error covariance matrix and the initial value of the system noise covariance matrix, is the decomposition matrix of the initial error covariance matrix; is the observation noise covariance, and satisfies but When the estimation starts, the value at time (0) is converted to the value at time (k-1), and the value at time (0, 0) is converted to the value at time (k-1, l-1).

[0059] Capacity observer AEKF based on macroscopic time scale θ Time update:

[0060]

[0061] For microscopic time scale series, l=1,2,...,L z , when l reaches the scale conversion limit L z , that is, completing the cyclic calculation of the micro time scale under a macro time scale and entering the next macro time scale, that is, the conversion of k→k+1.

[0062] SVDAEKF state observer based on microscopic time scale χ Time update:

[0063] χ k,l+1|l =A k,l χ k,l +B k,l u k,l

[0064] State estimation innovation matrix update: e k,l =y k,l -g(x k,l+1|l ,θ k+1|k ,u k,l )

[0065] in,

[0066] Make matrix M1 and perform singular value decomposition:

[0067] Get the decomposition matrix of the prediction error covariance matrix:

[0068] Observation error covariance matrix update:

[0069] Make the matrix M2 and perform singular value decomposition: in

[0070] The updated singular value decomposition matrix of the error covariance matrix is:

[0071] Kalman filter gain:

[0072] Process noise covariance matrix update:

[0073] State Estimation:

[0074] Microscopic time scale cycle calculation (l=1:L z ) and scale conversion (when l=L z hour):

[0075]

[0076] At this point, a micro time scale cycle calculation under a macro time scale is completed. The next step is to return to the macro time scale to perform measurement updates of capacity estimation.

[0077] Capacity estimation innovation matrix update:

[0078]

[0079] Measurement error covariance matrix update:

[0080] Kalman filter gain update:

[0081] in,

[0082]

[0083] Capacity Estimate Revisions:

[0084] Error covariance matrix update:

[0085] At this point, the multi-time-scale estimation of the state and capacity at time k is completed, and we are ready to enter the estimation at time k+1.

[0086] The present invention discloses the following technical effects: 1. The present invention performs singular value decomposition on the covariance matrix of the traditional extended Kalman filter algorithm, and replaces the iterative update of the covariance matrix with the iterative update of the decomposition matrix of the covariance matrix, thereby avoiding the covariance matrix losing its positive definiteness due to the limited bytes of the single-chip computer during the calculation process, resulting in filter divergence. 2. The present invention uses the bias-compensated least squares method with forgetting factor (BCFFRLS) to identify the parameters of the battery model, effectively solving the problem of a large amount of measurement noise accompanying data multiplication, and the problem that the identification model is no longer unbiased due to the presence of data packets and uncertainty noise in the conventional least squares method, thereby ensuring the high-precision characteristics of the battery model. 3. The present invention adopts the multi-time-scale dual Kalman filter algorithm of SVDAEKF-AEKF to jointly estimate the SOC and SOH of the power battery, effectively solving the changes in the characteristics of the battery during operation and the influence of the real-time SOC value on the SOH value, improving the accuracy of the power battery SOH estimation, and performing calculations at multiple time scales, effectively reducing the amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] In order to more clearly illustrate the embodiments of the present invention or solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments.

[0088] Figure 1 A schematic flow chart of a battery state joint estimation method disclosed in the present invention;

[0089] Figure 2 is the second-order RC equivalent circuit model of lithium-ion battery;

[0090] Figure 3 This is a flow chart of the adaptive extended Kalman filter algorithm based on singular value decomposition;

[0091] Figure 4 The flowchart of the improved multi-time-scale dual extended Kalman filter algorithm is shown;

[0092] Figure 5 Demonstrated preliminary validation of the algorithm under dynamic stress test conditions;

[0093] Figure 6 The estimation error of SOC under this working condition is shown;

[0094] Figure 7 This is the estimated result of capacity. DETAILED DESCRIPTION

[0095] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited thereto.

[0096] See also Figure 1 , Figure 1 The method for jointly estimating the state of a lithium-ion battery according to an embodiment of the present invention includes the following steps:

[0097] Step 1: Read the initial SOC and capacity values ​​of the battery.

[0098] Step 2: The second-order equivalent circuit model of lithium-ion battery is as follows: Figure 2 As shown, a second-order equivalent circuit model of the lithium-ion battery is established, and the state space equation of the model is obtained based on Kirchhoff's voltage law.

[0099] The second-order RC equivalent circuit model for the lithium-ion battery in step 2 consists of a controlled voltage source, two RC links in series, and a capacitor. The controlled voltage source represents the battery's open-circuit voltage, representing the voltage difference between the two electrodes when the battery is open circuit. The RC links, the polarization capacitance and polarization internal resistance, describe the battery polarization process. The battery capacity is used to simulate the battery's ohmic polarization process.

[0100] The established model state space equation, including the state equation and observation equation, is as follows:

[0101]

[0102] Where t is the sampling time, R0 is the ohmic internal resistance of the battery, R1, R2 and C1, C2 are the polarization resistance and polarization capacitance of the battery respectively, τ1, τ2 are the polarization time constants and τ1=R1C1, τ2=R2C2, U1, U2 are the terminal voltages of the two RC links, C max is the rated capacity of the battery, U oc is the open circuit voltage of the battery, i is the operating current of the battery, U t is the battery terminal voltage, ω is the process noise, ν is the measurement noise, and SOC is the state of charge of the battery. The dual time scales k and l describe the macroscopic time scale and the microscopic time scale respectively, which can be regarded as: k,l t k,l =t k,0 +l×Δt(1≤l≤L z ) The state of the system at the moment, L z is the scale conversion limit, that is, a macro scale equals L z A microscopic time scale.

[0103] Step 3: Collect open circuit voltage data and state of charge data to obtain the relationship between the two. Based on the model, discretize the model equation and rewrite the discretized equation into least squares form. Then, use the bias-compensated least squares method with forgetting factor (BCFFRLS) and combine it with the relationship between open circuit voltage and state of charge. Identify the model parameters through the input battery current, voltage and other data.

[0104] Step 3 is implemented as follows:

[0105] The static method uses a fully charged battery to perform interval discharges, and then obtains the relationship between the battery's open circuit voltage (OCV) and state of charge (SOC) during the static method. The battery's open circuit voltage can be considered the terminal voltage of the battery after a long period of static storage.

[0106] The Matlab fitting tool is used to perform polynomial fitting on the relationship between battery OCV and SOC, using a ninth-order polynomial:

[0107]

[0108] Let y = U oc -U t , then the transfer function of the system is:

[0109]

[0110] By impulse response invariance method The discretized system difference equation can be obtained:

[0111] y(k)=y(k)=U oc (k)-U t (k)=a1y(k-1)+a2y(k-2)+a3I(k)+a4I(k-1)+a5I(k-2),k≥3

[0112] Convert to least squares form: e(k) is the measurement noise

[0113] Where the measurement data vector

[0114] The parameter vector to be identified is θ(k) = [a1(k)a2(k)a3(k)a4(k)a5(k)] T

[0115] The bias-compensated least squares method with forgetting factor is used for online model parameter identification. The main steps of the algorithm are as follows:

[0116] Parameter initialization:

[0117] Among them, θ BC (0) is the initial value of the least squares method for deviation compensation, θ LS (0) is the initial value of the least squares identification with forgetting factor, J(0) is the initial value of the cost function, and P(0) is the initial value of the covariance matrix.

[0118] Calculate the estimated error:

[0119] Update the system gain matrix:

[0120] Parameter estimation without considering noise: θ LS (k+1)=θ LS (k)+K(k+1)e(k+1)

[0121] Error criterion function calculation:

[0122] Average weighted variance estimation of voltage signal noise:

[0123] Update the system error covariance:

[0124] Update the parameter estimates after bias compensation:

[0125] Output the parameter result θ of the least squares method with the forgetting factor. BC (k+1), then according to the following formula:

[0126]

[0127] Calculate the model parameters R0, R1, C1, R2, and C2.

[0128] Step 4: Improve the extended Kalman, perform singular value decomposition on the error covariance matrix, and adaptively update the noise error covariance matrix. The improved algorithm flow is as follows Figure 3 shown.

[0129] The specific steps are as follows:

[0130] Introduction theorem: Let A be an m×n matrix, then there exists an m×n orthogonal matrix U and an n×n orthogonal matrix V such that:

[0131] A=UΛV T ,in

[0132] Where Λ is an m×n matrix, S=diag(σ1,...,σ r ) and there is:

[0133] σ1>...>σ r >0;σ r+1 =0,...,σ n =0

[0134] in is called the singular value of matrix A, λ i is the matrix A T The eigenvalues ​​of A. The column vector of U is AA TThe orthogonal eigenvectors of V are A T The orthogonal eigenvectors of A.

[0135] In particular, when A is a symmetric positive definite matrix, then A can be decomposed into a symmetric singular value:

[0136] A=USU T =UD 2 U T

[0137] In the Kalman filter algorithm, the covariance matrix is ​​symmetric and positive definite, so the covariance matrix can be decomposed into the symmetric singular value in the above formula.

[0138] Furthermore, the specific steps of singular value decomposition of the covariance matrix in step 4 are as follows:

[0139] In the Kalman recursion formula, the error covariance matrix P k Perform singular value decomposition:

[0140]

[0141] Therefore, the covariance matrix time update can be expressed as:

[0142]

[0143] Define the following matrix and perform singular value decomposition:

[0144]

[0145] Multiply both sides by their own transposed matrix:

[0146]

[0147] From this we can get:

[0148]

[0149] According to the known formula:

[0150] P k+1 =(IK k+1 C)P k+1|k =P k+1|k -P k+1|k C T (CP k+1|k C T +R k ) -1 CP k+1|k

[0151] According to the formula: (A+BCB T ) -1 =A-1 -A -1 B(B T A -1 B+C -1 ) -1 B T A -1

[0152] You can get:

[0153]

[0154] Will and Perform singular value decomposition:

[0155]

[0156] make Suppose the following matrix and perform singular value decomposition on it:

[0157]

[0158] Multiply both sides of the equation by its own transpose:

[0159]

[0160] Then the formula It can be expressed as:

[0161]

[0162] Therefore, we can solve:

[0163]

[0164] Then we have:

[0165] From the known formula K k+1 =P k+1|k C T (CP k+1|k C T +R k+1 ) -1 , add on the right side of the equation and The gain value does not change, so it can be concluded that:

[0166]

[0167] From the above formula, we can get:

[0168] Further, perform state estimation: x k+1 =x k+1|k +Kk+1 (y k+1 -g(x k+1|k ,u k ))

[0169] Furthermore, the improved extended Kalman filter algorithm avoids the iterative solution of the covariance matrix and instead iteratively solves the decomposition matrix of the covariance matrix, effectively avoiding the covariance matrix losing its positive definiteness during the iteration process and causing filter divergence.

[0170] Furthermore, the improved Sage-Husa adaptive filtering algorithm is used to update the covariance of process noise and measurement noise:

[0171]

[0172]

[0173] in, b is the forgetting factor.

[0174] Step 5: Based on the obtained initial values ​​and model parameters, the multi-scale calculation formulas for joint estimation of battery SOC and SOH are established using the Adaptive Extended Kalman Matrix (SVDAEKF) based on singular value decomposition and the Adaptive Extended Kalman Matrix (AEKF). SOH can be expressed as the maximum available capacity of the battery at this moment. Therefore, the battery SOH can be estimated by estimating the maximum available capacity of the battery at this moment, which can be expressed as: First, the capacity estimation module runs, passing the estimated capacity value and the collected current and voltage values ​​to the SOC estimation module to calculate the SOC value. Simultaneously, the observed values ​​obtained during the SOC estimation process are passed to the capacity estimation module to participate in the calculation and estimate the capacity. Because capacity changes slowly while SOC changes constantly, a multi-timescale approach is adopted, estimating capacity at a macroscale and SOC at a microscale. The capacity is updated every 60 seconds, while the SOC value is updated every 1 second.

[0175] Step 5 is implemented according to the following steps:

[0176] Set the capacity observer AEKF respectively θ and state observer SVDAEKF χ Initial value:

[0177]

[0178] Where θ 0,0 , Capacity observer AEKF θ The initial capacity value, error covariance matrix initial value and system noise covariance matrix initial value; χ0,0 , They are state observers SVDIEKF χ The initial value of the state, the initial value of the error covariance matrix and the initial value of the system noise covariance matrix, is the decomposition matrix of the initial error covariance matrix; is the observation noise covariance, and satisfies but When the estimation starts, the value at time (0) is converted to the value at time (k-1), and the value at time (0, 0) is converted to the value at time (k-1, l-1).

[0179] Capacity observer AEKF based on macroscopic time scale θ Time update:

[0180]

[0181] For microscopic time scale series, l=1,2,...,L z , when l reaches the scale conversion limit L z , that is, completing the cyclic calculation of the micro time scale under a macro time scale and entering the next macro time scale, that is, the conversion of k→k+1.

[0182] SVDAEKF state observer based on microscopic time scale χ Time update:

[0183] χ k,l+1|l =A k,l χ k,l +B k,l u k,l

[0184] State estimation innovation matrix update: e k,l =y k,l -g(x k,l+1|l ,θ k+1|k ,u k,l )

[0185] in,

[0186] Make matrix M1 and perform singular value decomposition:

[0187] Get the decomposition matrix of the prediction error covariance matrix:

[0188] Observation error covariance matrix update:

[0189] Make the matrix M2 and perform singular value decomposition: in

[0190] The updated singular value decomposition matrix of the error covariance matrix is:

[0191] Kalman filter gain:

[0192] Process noise covariance matrix update:

[0193] State Estimation:

[0194] Microscopic time scale cycle calculation (l=1:L z ) and scale conversion (when l=L z hour):

[0195]

[0196] At this point, a micro time scale cycle calculation under a macro time scale is completed. The next step is to return to the macro time scale to perform measurement updates of capacity estimation.

[0197] Capacity estimation innovation matrix update:

[0198]

[0199] Measurement error covariance matrix update:

[0200] Kalman filter gain update:

[0201] in,

[0202]

[0203] Capacity Estimate Revisions:

[0204] Error covariance matrix update:

[0205] At this point, the multi-time-scale estimation of the state and capacity at time k is completed, and we are ready to enter the estimation at time k+1.

[0206] Figure 4 The flowchart of the improved multi-time-scale dual extended Kalman filter algorithm is shown.

[0207] Figure 5 The preliminary verification of the algorithm under dynamic stress test conditions is demonstrated. Figure 6 The estimation error of SOC under this condition is shown. Figure 7The capacity estimation result is shown in Figure 2. As can be seen, the improved dual Kalman filter algorithm provides relatively accurate estimation results, with a maximum absolute error within 2%. Furthermore, even with an incorrect initial capacity value, the algorithm can quickly converge to the true value.

[0208] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the 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 in the claims of the present invention.

Claims

1. A method for jointly estimating the state of a lithium-ion battery, characterized in that: The following steps are involved: Step 1: Read the battery initial value and capacity initial value; Step 2: Establish a second-order equivalent circuit model of the lithium-ion battery and derive the state space equation of the model based on Kirchhoff's voltage law; Step 3: Collect open-circuit voltage data and state-of-charge data to determine the relationship between the two. Based on a second-order equivalent circuit model, discretize the state-space equation of the model and rewrite the discretized equation into a least-squares form. Then, apply the bias-compensated least-squares method with a forgetting factor and combine it with the relationship between open-circuit voltage and state-of-charge to identify the model parameters using the input battery current and voltage data. Step 4: Improve the ordinary extended Kalman, perform singular value decomposition on the error covariance matrix and update the noise error covariance matrix in real time; Step 5: Based on the obtained initial values ​​and model parameters, the adaptive extended Kalman algorithm based on singular value decomposition and the adaptive extended Kalman algorithm are used to establish multi-scale calculation formulas for joint estimation of battery state of charge and SOH respectively; SOH can be expressed by the maximum available capacity of the battery at this moment, so the battery SOH can be estimated by estimating the maximum available capacity of the battery at this moment, which can be expressed as: First, the capacity estimation module runs, and the estimated capacity value and the collected current and voltage values ​​are passed to the state-of-charge estimation module to calculate the state-of-charge value. At the same time, the observed values ​​obtained during the state-of-charge estimation process are passed to the capacity estimation module to participate in the calculation and estimate the capacity. Because the capacity changes slowly and the state-of-charge changes constantly, a multi-timescale approach is adopted to estimate the capacity on a macroscale and the state-of-charge on a microscale. The capacity is updated every 60 seconds, and the state-of-charge value is updated every 1 second. The state space equation in step 2 includes the state equation and the observation equation, which can be expressed as: Where k represents the kth sampling moment, t is the sampling time, R0 is the ohmic internal resistance of the battery, R1, R2 and C1, C2 are the polarization resistance and polarization capacitance of the battery respectively, τ1, τ2 are the polarization time constants and τ1=R1C1, τ2=R2C2, U1, U2 are the terminal voltages of the two RC links, C max is the rated capacity of the battery, U oc is the open circuit voltage of the battery, i is the operating current of the battery, U t is the battery terminal voltage, ω is the process noise, ν is the measurement noise, and SOC is the state of charge of the battery; the dual time scales k and l describe the macroscopic time scale and the microscopic time scale respectively, which can be regarded as: k,l t k,l =t k,0 +l×Δt(1≤l≤L z ) The state of the system at the moment, L z is the scale conversion limit, that is, a macro scale equals L z microscopic time scales; The relationship between the open circuit voltage and state of charge of the battery in step 3 is determined by a static method, where the battery is discharged intermittently from a full charge, and the open circuit voltage of the battery is obtained by static method. Furthermore, the open circuit voltage and state of charge were polynomially fitted using the Matlab fitting tool to obtain the relationship between the open circuit voltage and state of charge: The model parameters described in step 3 include battery capacity, battery polarization internal resistance, polarization capacitance, concentration polarization internal resistance, and concentration polarization capacitance. Data is collected through battery dynamic stress testing, and the parameters are identified using the least squares method with deviation compensation and forgetting factor. The parameter identification process of the bias-compensated least squares method with forgetting factor is as follows: Parameter initialization: Among them, θ BC (0) is the initial value of the least squares method for deviation compensation, θ LS (0) is the initial value of the least squares identification with the forgetting factor, J(0) is the initial value of the cost function, and P(0) is the initial value of the covariance matrix; Calculate the estimated error: Update the system gain matrix: Parameter estimation without considering noise: θ LS (k+1)=θ LS (k)+K(k+1)e(k+1) Error criterion function calculation: Average weighted variance estimation of voltage signal noise: Update the system error covariance: Update the parameter estimates after bias compensation: Output the parameter result θ of the least squares method with the forgetting factor. BC (k+1) ， Then according to the following formula: Calculate the model parameters R0, R1, C1, R2, and C2; The improvement to the ordinary extended Kalman in step 4 includes SVD decomposition of the covariance matrix. The specific process of the improved algorithm is as follows: x k+1|k =Ax k +Bu k U k+1|k =V k '、D k+1|k =D' k K k+1 =U k+1 (D k+1 ) 2 (U k+1 ) T C T L k+1 L k+1 T x k+1 =x k+1k +K k+1 e k In step 5, the SOH estimation is characterized by the battery capacity, and the capacity is estimated using the adaptive extended Kalman filter algorithm. In actual battery operation, the SOH changes very slowly relative to the state of charge. Therefore, a multi-scale approach is used to estimate the state of charge from a macro time scale and the capacity from a micro time scale. The adaptive extended Kalman filter algorithm described in step 5 is as follows: Initialization: x0, P0, R0, Q0 Time update: x k+1|k =Ax k +Bu k Error covariance matrix prediction: P k+1|k =AP k A T +Q k Noise matrix update: Calculate the Kalman filter gain: K k+1 =P k+1|k C T (CP k+1|k C T +R k+1 ) -1 Observation update: x k+1 =x k+1|k +K k+1 (y k+1 -g(x k+1|k ,u k )) Error covariance matrix update: P k+1 =(IK k+1 C)P k+1|k Noise matrix update: Furthermore, in parameter estimation, the state space equation of the system is: The collaborative estimation framework of state of charge and SOH described in step 5 is: Set the capacity observer AEKF respectively θ and state observer SVDAEKF χ Initial value: Where θ 0,0 , Capacity observer AEKF θ The initial capacity value, error covariance matrix initial value and system noise covariance matrix initial value; χ 0,0 , They are state observers SVDIEKF χ The initial value of the state, the initial value of the error covariance matrix and the initial value of the system noise covariance matrix, is the decomposition matrix of the initial error covariance matrix; is the observation noise covariance, and satisfies but When the estimation starts, the value at time (0) is converted to the value at time (k-1), and the value at time (0, 0) is converted to the value at time (k-1, l-1); Capacity observer AEKF based on macroscopic time scale θ Time update: For microscopic time scale series, l=1,2,...,L z , when l reaches the scale conversion limit L z , that is, completing the micro time scale cycle calculation under a macro time scale and entering the next macro time scale, that is, the conversion from k to k+1; SVDAEKF state observer based on microscopic time scale χ Time update: x k,l+1|l =A k,l x k,l +B k,l you k,l State estimation innovation matrix update: e k,l =y k,l -g(x k,l+1|l ,θ k+1|k ,u k,l ) in, Make matrix M1 and perform singular value decomposition: Get the decomposition matrix of the prediction error covariance matrix: Observation error covariance matrix update: Make the matrix M2 and perform singular value decomposition: in The updated singular value decomposition matrix of the error covariance matrix is: Kalman filter gain: Process noise covariance matrix update: State Estimation: Microscopic time scale cycle calculation (l=1:L z ) and scale conversion (when l=L z hour): This completes a micro-time scale cycle calculation under a macro-time scale. The next step is to return to the macro-time scale to perform measurement updates of capacity estimation. Capacity estimation innovation matrix update: Measurement error covariance matrix update: Kalman filter gain update: in, Capacity Estimate Revisions: Error covariance matrix update: At this point, the multi-time-scale estimation of the state and capacity at time k is completed, and we are ready to enter the estimation at time k+1.

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