CN114217234B - IDE-ASRCKF-based lithium ion battery parameter identification and SOC estimation method - Google Patents

Abstract

The invention provides a lithium ion battery parameter identification and SOC estimation method based on IDE-ASRCKF, which belongs to the technical field of lithium ion batteries and comprises the following technical scheme: the method comprises the following steps: step 1), determining an OCV-SOC relation through intermittent constant current discharging measurement of load current and terminal voltage data of a battery; step 2) establishing a second-order RC model of the lithium ion battery; step 3) constructing an identification flow of an IDE algorithm, and identifying parameters of a battery model; step 4) constructing an estimation flow of an ASRCKF algorithm; and 5) determining each parameter in the lithium battery model by utilizing an IDE algorithm, and estimating the battery SOC by utilizing ASRCKF. The beneficial effects of the invention are as follows: the invention improves the convergence speed and precision of the algorithm; and the SOC estimation is carried out by combining the parameter result obtained by identification with an ASRCKF algorithm, so that the accuracy is high, the robustness is good, and the effect is better than CKF.

Description

A lithium-ion battery parameter identification and SOC estimation method based on IDE-ASRCKF

Technical Field

The present invention relates to the technical field of lithium-ion batteries, and in particular to a lithium-ion battery parameter identification and SOC estimation method based on IDE-ASRCKF.

Background Art

The state of charge (SOC) of lithium-ion batteries is one of the important parameters in the battery management system (BMS), which provides a basis for the control strategy of the vehicle battery pack. Usually, the SOC is estimated by real-time monitoring of the terminal voltage, load current and ambient temperature of the lithium-ion battery, and then the battery pack is controlled. Accurate SOC estimation results can ensure the safe and reliable operation of the battery system.

Establishing an appropriate and accurate battery model is crucial to the SOC estimation effect. According to the different parameter processing methods in the battery model, the lithium-ion battery model can be divided into an electrochemical model, a neural network model and an equivalent circuit model, among which the equivalent circuit model is a more widely studied model. Model identification methods are mainly divided into online identification and offline identification. Traditional online identification methods can modify parameters according to the battery environment and the current battery status, but in some cases the parameter error is large. In contrast, offline identification can call a large amount of data, and the parameter accuracy is higher, which has certain advantages. Various types of group intelligent optimization algorithms are widely used in the field of offline identification. How to ensure high algorithm accuracy and fast convergence speed is an important research topic.

On the basis of a high-precision battery model, it is equally important to choose the SOC estimation method. Currently, there are two commonly used estimation methods: one is to directly calculate using the ampere-hour integration method, but this type of method is overly dependent on the initial SOC value. When the initial value error is large, the estimation error is large and does not meet actual needs; the other is to estimate based on the battery model and state quantity prediction results, such as support vector machines, neural networks, and Kalman filtering algorithms. The first two methods have high requirements on data volume and data quality, and their applications are limited. The Kalman filtering algorithm is relatively mature and can solve the SOC estimation problem well, but it still faces problems such as low accuracy and poor robustness.

How to solve the above technical problems is the subject faced by the present invention.

Summary of the invention

The purpose of the present invention is to provide a lithium-ion battery parameter identification and SOC estimation method based on IDE-ASRCKF. An adaptive factor is added to the original differential evolution algorithm (DE), and the mutation and crossover process is improved. An improved differential evolution algorithm (IDE) is proposed, which effectively solves the problems that the traditional heuristic identification algorithm is easy to fall into the local optimum and the convergence speed is slow, and the identification parameter accuracy is high. Considering that the positive definiteness of the error covariance matrix of the traditional cubature Kalman filter (CKF) algorithm is difficult to guarantee, a square root filter is introduced to directly calculate the square root factor of the state quantity error covariance prediction value and the state quantity error covariance estimation value, avoiding the square root of the matrix; at the same time, a residual sequence and an adaptive factor are introduced to adaptively update the process noise and the measurement noise, thereby improving the accuracy of the process noise and the measurement noise. The two improvements are combined to propose an adaptive cubature Kalman filter (ASRCKF) algorithm and used to estimate the SOC of lithium-ion batteries. The estimation result is accurate and the algorithm has high robustness.

The present invention is achieved by the following measures: a lithium-ion battery parameter identification and SOC estimation method based on IDE-ASRCKF, which specifically includes the following steps:

Step 1) measuring the load current and terminal voltage data of the battery by intermittent constant current discharge to determine the OCV-SOC relationship;

Step 2) establishing a second-order RC model of a lithium-ion battery;

Step 3) constructing an identification process of the IDE algorithm to identify the battery model parameters;

Step 4) Construct the estimation process of ASRCKF algorithm;

Step 5) Using the IDE algorithm to determine the parameters in the lithium battery model, and using ASRCKF to estimate the battery SOC;

As a further optimization scheme of the lithium-ion battery parameter identification and SOC estimation method based on IDE-ASRCKF of the present invention, the step 2) specifically includes the following steps:

Considering the dual polarization characteristics of lithium-ion batteries, a second-order RC model of lithium-ion batteries is established:

U _oc and U correspond to the open circuit voltage and terminal voltage of the battery. The voltages across capacitors C ₁ and C ₂ are represented by U ₁ and U _2, respectively, and R ₀ represents the ohmic internal resistance. The lithium-ion battery model has two RC parallel links, which represent the two polarization effects inside the battery: the electrochemical polarization effect represented by R ₁ and C ₁ and the concentration difference polarization effect represented by R ₂ and C ₂ ;

SOC represents the state of charge of a lithium-ion battery, which is expressed as:

Where _Qn is the rated capacity, and SOC( _t0 ) represents the SOC value at time t.

As a further optimization scheme of the lithium-ion battery parameter identification and SOC estimation method based on IDE-ASRCKF of the present invention, the step 3) specifically includes the following steps:

Step 3-1) Differential evolution algorithm:

The differential evolution algorithm is based on the genetic evolution algorithm and is used to solve the overall optimal solution in multidimensional space. Its core steps include mutation, crossover and selection;

The steps of differential evolution algorithm include:

a. Initialization

Set the population size to M, the individual dimension to N, the maximum number of iterations to G _m and the crossover factor to w, and randomly generate individuals in the population:

Where: rand _i,j (0,1) represents a random decimal in [0,1], represents the upper and lower limits of the jth dimension of the ith individual;

b. Individual variation

Where: and are three individuals randomly selected from the population, is the difference vector of two individuals, F is the mutation factor, G is the current iteration number, and individual mutation refers to the generation of mutant individuals by weighting the vector difference of any two individuals and summing them with the third individual according to the rules;

c. Crossover operation

The crossover operation can effectively increase the diversity of the population. By comparing the variant individuals with a predetermined target, the variant individuals are obtained. The specific formula is as follows:

Where: randl _i,j is a random decimal between [0,1], A mutant individual The j-th dimension vector of Is an individual The j-th dimension vector of , the crossover factor ω can control the degree of participation of each dimension of the individual parameter in the crossover and the balance between global and local search capabilities, between [0,1];

d. Select an operation

The fitness values of the target individual and the test individual are judged, and the individual with good fitness is selected using the greedy method:

Step 3-1) Improve the differential evolution algorithm:

The mutation factor F and crossover factor w in the basic DE algorithm determine the diversity of the population, thus affecting the convergence of the algorithm. By improving the mutation and crossover process in the basic DE algorithm, an improved differential evolution algorithm is proposed to enhance the algorithm optimization process and accelerate the convergence speed. The specific steps are as follows:

a. Adaptive mutation factor

Mutation is a step in the DE algorithm to increase the diversity of the population and achieve the optimization performance of the algorithm. The mutation factor in the original algorithm is a constant. The randomness is large during the mutation process, and it is difficult to determine the optimal value. By introducing an adaptive operator, the mutation factor becomes a dynamic value that changes periodically, so that the search range of the mutation factor is within a reasonable range. With the increase in the number of iterations, the mutation factor is also looking for the optimal value, so that the algorithm effectively approaches the optimal solution and ensures the diversity of the population. The specific improvement strategies are as follows:

F＝F ₀ ×2 ^α (8)

b. Improved crossover strategy

Based on the adaptive principle, the crossover factor in the crossover operation of the original algorithm is improved:

ω＝0.6×(1+rand()) (10)

Through adaptive adjustment of cross factors, the global and local search capabilities of the algorithm are balanced to quickly obtain the optimal solution.

As a further optimization scheme of the lithium-ion battery parameter identification and SOC estimation method based on IDE-ASRCKF of the present invention, the step 4) specifically includes the following steps:

On the basis of the cubature Kalman filter algorithm, in order to ensure the symmetry and positive definiteness of the error covariance matrix in the iterative process, the square root filter is introduced to directly calculate the square root factors of the state quantity error covariance prediction value and the state quantity error covariance estimation value to avoid taking the square root of the matrix; and considering that the process noise and measurement noise in CKF are constant, while in actual situations, both are constantly changing during the charging and discharging process of lithium-ion batteries, in order to improve the accuracy of the two errors, the residual sequence is introduced and combined with the iterative idea in the swarm intelligence algorithm, the process and measurement noise covariances are adaptively updated, and an adaptive square root cubature Kalman filter algorithm is proposed;

The state equation and observation equation of the nonlinear system are:

x(k)＝f(x(k-1),u(k-1))+w(k-1) (11)

y(k)＝g(x(k),u(k))+v(k) (12)

Where: x(k) is the system state variable at time k, u(k) is the input data, y(k) is the output data, g is the nonlinear function of the observation equation, f is the nonlinear function of the state equation, w(k) is the input noise, and v(k) is the observation noise;

The algorithm steps are as follows:

Step 4-1) Parameter initialization:

Initialize the state variable to its initial value State error covariance P ₀ , process noise Q and measurement noise R;

Step 4-2) Time update:

a. Calculate volume points

Decompose the error covariance matrix through Cholesky and calculate the volume points:

P _k-1 ＝S _k-1 S _k-1 ^T (13)

Where i = 1, 2, 3, ..., 2n, n is the dimension of the state quantity, ξ _i is the volume point set, as shown below:

Where [1] is the unit matrix;

b. Propagation volume point

c. Estimate the state prediction value at time k

d. Calculate the square root of the predicted value of the state error covariance at time k

Where S _Q = Chol(Q _k ), Tria(…) represents the triangularization of the matrix. The definition is as follows:

Step 4-3) Measurement update:

a. Using the state prediction value at time k and the square root of the state error covariance prediction Update Volume Points

b. Calculate the predicted value of the observed value

Where:

c. Calculate the square root of the innovation covariance matrix and the square root of the error covariance matrix

Where:

S _R = chol(R _k-1 ) (25)

R _k-1 is the measurement noise covariance at time k-1;

d. Update Kalman gain

e. Calculate the estimated value of the system state quantity

f. Calculate the square root of the system state error covariance matrix

S _k =Tria([μ _k -K _k r _k K _k S _R ]) (30)

g. Update the measurement noise covariance _Rk and system noise covariance _Qk

The approximate value of the voltage residual covariance at time K is:

In the formula represents the deviation between the measured value and the estimated value at time k; L is the new information length, the adaptive operator α is introduced and the weight n is defined as follows:

n＝n ₀ ×2 ^α (33)

Where G is the total length of the data set, H is the current data position, and the expression of the measurement noise covariance R _k and the system noise covariance Q _k at time k is established as follows:

R _k =(1-n _k )R _k-1 +n _k F _k (34)

Step 4-4) ASRCKF algorithm estimates SOC:

According to equations (11) and (12), [SOC, U ₁ , U ₂ ] is used as the system state quantity to establish the discrete state space expression of the second-order RC model of lithium-ion battery:

Wherein the current I is the input, the terminal voltage U is the output, [SOC, U ₁ , U ₂ ] is the state variable, Δt is the system sampling time, which is 1s. In the ASRCKF algorithm, the observation quantity y(k)=U(k), the state quantity x _k =[SOC(k),U ₁ (k),U ₂ (k)], and the input quantity u(k)=I(k) are set. The lithium-ion battery is a nonlinear system, and its state equation and observation equation are as follows:

Through iteration, the algorithm can estimate the SOC value of the lithium-ion battery at each moment.

As a further optimization scheme of the lithium-ion battery parameter identification and SOC estimation method based on IDE-ASRCKF of the present invention, the step 5) specifically includes the following steps:

Step 5-1) Parameter identification:

Under different SOC conditions, the identification results of lithium-ion battery parameters will be biased, so the entire discharge process is divided into 10 stages for identification. In each stage, the battery undergoes static, pulse discharge, and static again. The SOC before discharge is defined as the initial SOC. The IDE algorithm is used to identify each battery discharge process, and then the results of each identification are polynomially fitted with the corresponding initial SOC to obtain the change curve of the battery model parameters under different SOCs.

Step 5-2) SOC estimation:

The identified parameters are substituted into the state equation and observation equation, and combined with the experimentally measured terminal voltage and current data, the ASRCKF algorithm is used to predict and update the lithium-ion battery state variables to obtain the SOC estimation result.

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

(1) The present invention establishes a second-order RC model of a lithium-ion battery based on Kirchhoff's law, and obtains a set of intermittent constant current discharge data through experiments to fit the OCV-SOC relationship.

(2) The present invention proposes an adaptive improvement method based on the original differential evolution algorithm to improve the mutation and crossover steps in the original algorithm, effectively solving the problem that the original algorithm is prone to fall into local optimality and slow convergence speed during the battery model parameter identification process. The identification effect is better than that of the traditional heuristic algorithm.

(3) Compared with the traditional CKF algorithm, the present invention has certain effects in the SOC estimation process. However, during the algorithm iteration process, the symmetry and positive definiteness of the covariance matrix are easily destroyed, which will lead to the termination of the algorithm. The present invention introduces square root filtering on the basis of the original algorithm, directly calculates the square root factor of the state quantity error covariance prediction value and the error covariance estimation value, avoids the square root operation of the matrix, and effectively avoids the destruction of the covariance symmetry and positive definiteness. At the same time, during the CKF algorithm iteration process, the process noise and the measurement noise are constant by default, but in actual situations, the two are constantly changing during the charging and discharging process of the lithium-ion battery, which will cause large errors in the estimation results of the algorithm. In order to improve the accuracy of the two errors, the present invention introduces the covariance residual sequence and combines the adaptive idea to adaptively update the process and measurement noise covariance, effectively improving the error accuracy, thereby improving the algorithm estimation accuracy.

(4) The accuracy of the SOC estimation result of the present invention depends on the accuracy of the model parameters and the effectiveness of the estimation algorithm. The present invention effectively utilizes the high accuracy and fast convergence characteristics of the IDE algorithm, and combines it with ASRCKF to accurately and quickly estimate the battery SOC, and the algorithm is highly robust. The combination of the two algorithms has great engineering value and broad prospects for practical application.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

FIG. 1 is a schematic diagram of a second-order RC model of a lithium-ion battery of the present invention.

FIG. 2 is a voltage-current curve of the intermittent constant current discharge experiment of the present invention.

FIG. 3 is an OCV-SOC fitting curve used in the intermittent constant current experiment of the present invention.

FIG. 4 is a curve showing the change of the fitness function during the iteration process of the IDE algorithm, the DE algorithm and the PSO algorithm of the present invention.

FIG. 5 is a fitting curve of the IDE algorithm parameter identification result of the present invention.

FIG. 6 is a terminal voltage prediction curve of the IDE algorithm and the DE algorithm of the present invention under an intermittent constant current discharge test.

FIG. 7 is a terminal voltage prediction error curve of the IDE algorithm and the DE algorithm of the present invention under an intermittent constant current discharge test.

FIG. 8 is an SOC estimation curve and an SOC estimation error curve of the present invention.

FIG. 9 is an SOC estimation curve and an SOC estimation error curve of the present invention when there is a deviation in the initial value.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

The present invention uses Panasonic lithium-ion battery NCR-18650B as the research object. The rated voltage of the battery is 3.7V and the capacity is 3400mAh. The battery is charged in a constant current charging mode (0.5C) until the cut-off voltage is reached. After standing for a period of time, the battery reaches a fully charged state.

Referring to FIG. 1 to FIG. 9 , the present invention provides a lithium battery parameter identification and SOC estimation method based on the coyote optimization algorithm, which includes the following steps:

Step 1) Perform an intermittent constant current discharge experiment on the battery at a constant temperature of 25°C, discharge for 5 minutes, stand for 30 minutes, the current is 3400mA, the discharge rate is 1C, repeat multiple times and record relevant data. According to the experiment, 21211 groups of terminal voltage and current data are measured, and the data change curve is shown in Figure 2. The battery SOC theoretical value is calculated using the ampere-hour integration method, and multiple groups of terminal voltage and corresponding SOC data are selected. The polyfit function in MATLAB is used for fitting to determine the battery OCV-SOC coefficient:

f(x)＝P ₁ x ⁹ +P ₂ x ⁸ +P ₃ x ⁷ +P ₄ x ⁶ +P ₅ x ⁵ +P ₆ x ⁴ +P ₇ x ³ +P ₈ x ² +P ₉ x ¹ + P ₁₀ x ⁰ (1)

The OCV-SOC fitting curve is shown in Figure 3.

Step 2) establishing a second-order RC model of a lithium-ion battery;

Step 3) constructing an identification process of the IDE algorithm to identify the battery model parameters;

Step 4) Construct the estimation process of ASRCKF algorithm;

Step 5) Using the IDE algorithm to determine the parameters in the lithium battery model, and using ASRCKF to estimate the battery SOC;

As a further optimization scheme of the lithium-ion battery parameter identification and SOC estimation method based on IDE-ASRCKF of the present invention, the step 2) specifically includes the following steps:

Considering the dual polarization characteristics of lithium-ion batteries, a second-order RC model of lithium-ion batteries is established:

_Uoc and U correspond to the open circuit voltage and terminal voltage of the battery. The voltages across capacitors _C1 and _C2 are represented by _U1 and _U2 , respectively, and _R0 represents the ohmic internal resistance. The lithium-ion battery model has two RC parallel links, which represent the two polarization effects inside the battery: the electrochemical polarization effect represented by _R1 and _C1 and the concentration difference polarization effect represented by _R2 and _C2 .

SOC represents the state of charge of a lithium-ion battery, which is expressed as:

Where _Qn is the rated capacity, and SOC( _t0 ) represents the SOC value at time t.

As a further optimization scheme of the lithium-ion battery parameter identification and SOC estimation method based on IDE-ASRCKF of the present invention, the step 3) specifically includes the following steps:

Step 3-1) Differential evolution algorithm:

The differential evolution algorithm is based on the genetic evolution algorithm and is used to solve the overall optimal solution in multidimensional space. Its core steps include mutation, crossover and selection;

The steps of differential evolution algorithm include:

a. Initialization

Set the population size to M, the individual dimension to N, the maximum number of iterations to G _m and the crossover factor to w, and randomly generate individuals in the population:

Where: rand _i,j (0,1) represents a random decimal in [0,1], represents the upper and lower limits of the jth dimension of the ith individual;

b. Individual variation

Where: and are three individuals randomly selected from the population, is the difference vector of two individuals, F is the mutation factor, G is the current iteration number, and individual mutation refers to the generation of mutant individuals by weighting the vector difference of any two individuals and summing them with the third individual according to the rules;

c. Crossover operation

The crossover operation can effectively increase the diversity of the population. By comparing the variant individuals with a predetermined target, the variant individuals are obtained. The specific formula is as follows:

Where: randl _i,j is a random decimal between [0,1], A mutant individual The j-th dimension vector of Is an individual The j-th dimension vector of , the crossover factor ω can control the degree of participation of each dimension of the individual parameter in the crossover and the balance between global and local search capabilities, between [0,1];

d. Select an operation

The fitness values of the target individual and the test individual are judged, and the individual with good fitness is selected using the greedy method:

Step 3-1) Improve the differential evolution algorithm:

The mutation factor F and crossover factor w in the basic DE algorithm determine the diversity of the population, thus affecting the convergence of the algorithm. By improving the mutation and crossover process in the basic DE algorithm, an improved differential evolution algorithm is proposed to enhance the algorithm optimization process and accelerate the convergence speed. The specific steps are as follows:

a. Adaptive mutation factor

Mutation is a step in the DE algorithm to increase the diversity of the population and achieve the optimization performance of the algorithm. The mutation factor in the original algorithm is a constant. The randomness is large during the mutation process, and it is difficult to determine the optimal value. By introducing an adaptive operator, the mutation factor becomes a dynamic value that changes periodically, so that the search range of the mutation factor is within a reasonable range. With the increase in the number of iterations, the mutation factor is also looking for the optimal value, so that the algorithm effectively approaches the optimal solution and ensures the diversity of the population. The specific improvement strategies are as follows:

F＝F ₀ ×2 ^α (9)

b. Improved crossover strategy

Based on the adaptive principle, the crossover factor in the crossover operation of the original algorithm is improved:

ω＝0.6×(1+rand()) (11)

Through adaptive adjustment of cross factors, the global and local search capabilities of the algorithm are balanced to quickly obtain the optimal solution.

As a further optimization scheme of the lithium-ion battery parameter identification and SOC estimation method based on IDE-ASRCKF of the present invention, the step 4) specifically includes the following steps:

On the basis of the cubature Kalman filter algorithm, in order to ensure the symmetry and positive definiteness of the error covariance matrix in the iterative process, the square root filter is introduced to directly calculate the square root factors of the state quantity error covariance prediction value and the state quantity error covariance estimation value to avoid taking the square root of the matrix; and considering that the process noise and measurement noise in CKF are constant, while in actual situations, both are constantly changing during the charging and discharging process of lithium-ion batteries, in order to improve the accuracy of the two errors, the residual sequence is introduced and combined with the iterative idea in the swarm intelligence algorithm, the process and measurement noise covariances are adaptively updated, and an adaptive square root cubature Kalman filter algorithm is proposed;

The state equation and observation equation of the nonlinear system are:

x(k)＝f(x(k-1),u(k-1))+w(k-1) (12)

y(k)＝g(x(k),u(k))+v(k) (13)

Where: x(k) is the system state variable at time k, u(k) is the input data, y(k) is the output data, g is the nonlinear function of the observation equation, f is the nonlinear function of the state equation, w(k) is the input noise, and v(k) is the observation noise;

The algorithm steps are as follows:

Step 4-1) Parameter initialization:

Initialize the state variable to its initial value State error covariance P ₀ , process noise Q and measurement noise R;

Step 4-2) Time update:

a. Calculate volume points

Decompose the error covariance matrix through Cholesky and calculate the volume points:

P _k-1 ＝S _k-1 S _k-1 ^T (14)

Where i = 1, 2, 3, ..., 2n, n is the dimension of the state quantity, ξ _i is the volume point set, as shown below:

Where [1] is the unit matrix;

b. Propagation volume point

c. Estimate the state prediction value at time k

d. Calculate the square root of the predicted value of the state error covariance at time k

Where S _Q = Chol(Q _k ), Tria(…) represents the triangularization of the matrix. The definition is as follows:

Step 4-3) Measurement update:

a. Using the state prediction value at time k and the square root of the state error covariance prediction Update Volume Points

b. Calculate the predicted value of the observed value

Where:

c. Calculate the square root of the innovation covariance matrix and the square root of the error covariance matrix

Where:

S _R = chol(R _k-1 ) (26)

R _k-1 is the measurement noise covariance at time k-1;

d. Update Kalman gain

e. Calculate the estimated value of the system state quantity

f. Calculate the square root of the system state error covariance matrix

S _k =Tria([μ _k -K _k r _k K _k S _R ]) (31)

g. Update the measurement noise covariance _Rk and system noise covariance _Qk

The approximate value of the voltage residual covariance at time K is:

In the formula represents the deviation between the measured value and the estimated value at time k; L is the new information length, the adaptive operator α is introduced and the weight n is defined as follows:

n＝n ₀ ×2 ^α (34)

Where G is the total length of the data set, H is the current data position, and the expression of the measurement noise covariance R _k and the system noise covariance Q _k at time k is established as follows:

R _k =(1-n _k )R _k-1 +n _k F _k (35)

Step 4-4) ASRCKF algorithm estimates SOC:

According to equations (11) and (12), [SOC, U ₁ , U ₂ ] is used as the system state quantity to establish the discrete state space expression of the second-order RC model of lithium-ion battery:

Wherein the current I is the input, the terminal voltage U is the output, [SOC, U ₁ , U ₂ ] is the state variable, Δt is the system sampling time, which is 1s. In the ASRCKF algorithm, the observation quantity y(k)=U(k), the state quantity x _k =[SOC(k),U ₁ (k),U ₂ (k)], and the input quantity u(k)=I(k) are set. The lithium-ion battery is a nonlinear system, and its state equation and observation equation are as follows:

Through iteration, the algorithm can estimate the SOC value of the lithium-ion battery at each moment.

As a further optimization scheme of the lithium-ion battery parameter identification and SOC estimation method based on IDE-ASRCKF of the present invention, the step 5) specifically includes the following steps:

Step 5-1) Parameter identification:

Under different SOC conditions, the lithium-ion battery parameter identification results will be biased, so the entire discharge process is divided into 10 stages for identification. In each stage, the battery undergoes static, pulse discharge, and static again. The SOC before discharge is defined as the initial SOC. Establish the fitness function:

Wherein x＝[R ₀ ,R ₁ ,R ₂ ,C ₁ ,C ₂ ]; is the estimated value of the terminal voltage; u(k) is the actual value of the terminal voltage; k is the discrete time. The number of iterations is set to 1000, and the parameters of the second-order RC model of lithium-ion batteries are identified using IDE, DE, and particle swarm optimization (PSO) algorithms. The fitness function change curve during the iteration process is shown in Figure 4. By comparison, it is found that the IDE algorithm has certain advantages in convergence speed and accuracy. By improving the crossover and mutation operations of the original algorithm, the algorithm can be effectively prevented from falling into the local optimum and converge faster. The IDE algorithm is used to identify each battery discharge process, and the identification results are shown in the following table:

Then, the polynomial fitting of the result obtained from each segment of identification and the corresponding initial SOC can be performed to obtain the variation curve of the battery model parameters under different SOCs, as shown in Figure 5. Using the obtained parameters, the predicted value of the battery terminal voltage can be calculated, and the accuracy of the identification algorithm can be evaluated by comparing it with the actual value. The comparison results are shown in Figures 6 and 7. The results show that the parameters identified by the IDE algorithm are more accurate, and the error between the predicted value of the terminal voltage and the actual value is smaller.

Step 5-2) SOC estimation:

The high-precision model parameter identification results are conducive to the accurate estimation of SOC by ASRCKF. The identified parameters are substituted into the state equation and observation equation, and combined with the experimentally measured terminal voltage and current data, the ASRCKF algorithm is used to predict and update the lithium-ion battery state variables, and then the SOC estimation results can be obtained and compared with CKF. As shown in Figure 8, the results show that ASRCKF has a faster tracking speed and the error is significantly smaller than CKF. When the initial SOC is set to 0.8 and 0.6, ASRCKF is used to estimate the SOC. The results are shown in Figure 9. When the initial error is 20% and 40%, the estimation results are still accurate, indicating that the algorithm has good robustness.

In summary, it can be seen that the improved differential evolution algorithm and adaptive volumetric Kalman filter algorithm have a good effect on lithium-ion battery parameter identification and SOC estimation. The model parameter identification results are accurate, the SOC estimation accuracy is high, and it has engineering value.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A lithium-ion battery parameter identification and SOC estimation method based on IDE-ASRCKF, characterized in that it comprises the following steps: Step 1) measuring the load current and terminal voltage data of the battery by intermittent constant current discharge to determine the OCV-SOC relationship; Step 2) establishing a second-order RC model of a lithium-ion battery; Step 3) constructing an identification process of the IDE algorithm to identify the battery model parameters; Step 4) Construct the estimation process of ASRCKF algorithm; Step 5) Using the IDE algorithm to determine the parameters in the lithium battery model, and using ASRCKF to estimate the battery SOC; The step 2) specifically comprises the following steps: Considering the dual polarization characteristics of lithium-ion batteries, a second-order RC model of lithium-ion batteries is established: U _oc and U correspond to the open circuit voltage and terminal voltage of the battery. The voltages across capacitors C ₁ and C ₂ are represented by U ₁ and U _2, respectively. R ₀ represents the ohmic internal resistance. The lithium-ion battery model has two RC parallel links, which represent the two polarization effects inside the battery: the electrochemical polarization effect represented by R ₁ and C ₁ and the concentration difference polarization effect represented by R ₂ and C ₂ . SOC represents the state of charge of a lithium-ion battery, which is expressed as: Where Q _n is the rated capacity, SOC(t ₀ ) represents the SOC value at time t; The step 3) specifically comprises the following steps: Step 3-1) Improve the differential evolution algorithm: The mutation factor F and the crossover factor w in the basic DE algorithm determine the diversity of the population, thus affecting the convergence of the algorithm. By improving the mutation and crossover processes in the basic DE algorithm, an improved differential evolution algorithm is proposed to enhance the algorithm optimization process and accelerate the convergence speed. The specific steps are as follows: a. Adaptive mutation factor Mutation is a step in the DE algorithm to increase the diversity of the population and achieve the optimization performance of the algorithm. The mutation factor in the original algorithm is a constant. The randomness is large during the mutation process, and it is difficult to determine the optimal value. By introducing an adaptive operator, the mutation factor becomes a dynamic value that changes periodically, so that the search range of the mutation factor is within a reasonable range. With the increase in the number of iterations, the mutation factor is also looking for the optimal value, so that the algorithm effectively approaches the optimal solution and ensures the diversity of the population. The specific improvement strategies are as follows: F＝F ₀ ×2 ^α (8) b. Improved crossover strategy Based on the adaptive principle, the crossover factor in the crossover operation of the original algorithm is improved: ω＝0.6×(1+rand()) (10) Where: randl _i,j is a random decimal between [0,1], A mutant individual The j-th dimension vector of Is an individual The j-th dimension vector of , the crossover factor ω can control the degree of participation of each dimension of the individual parameter in the crossover and the balance between global and local search capabilities, between [0,1]; Through adaptive adjustment of cross factors, the global and local search capabilities of the algorithm are balanced to quickly obtain the optimal solution; The step 4) specifically comprises the following steps: On the basis of the cubature Kalman filter algorithm, in order to ensure the symmetry and positive definiteness of the error covariance matrix in the iterative process, the square root filter is introduced to directly calculate the square root factors of the state quantity error covariance prediction value and the state quantity error covariance estimation value to avoid taking the square root of the matrix; and considering that the process noise and measurement noise in CKF are constant, while in actual situations, both are constantly changing during the charging and discharging process of lithium-ion batteries, in order to improve the accuracy of the two errors, the residual sequence is introduced and combined with the iterative idea in the swarm intelligence algorithm, the process and measurement noise covariances are adaptively updated, and an adaptive square root cubature Kalman filter algorithm is proposed; The state equation and observation equation of the nonlinear system are: x(k)＝f(x(k-1),u(k-1))+w(k-1) (11) y(k)＝g(x(k),u(k))+v(k) (12) Where: x(k) is the system state variable at time k, u(k) is the input data, y(k) is the output data, g is the nonlinear function of the observation equation, f is the nonlinear function of the state equation, w(k) is the input noise, and v(k) is the observation noise; The algorithm steps are as follows: Step 4-1) Parameter initialization: Initialize the state variable to its initial value State error covariance P ₀ , process noise Q and measurement noise R; Step 4-2) Time update: a. Calculate volume points Decompose the error covariance matrix through Cholesky and calculate the volume points: P _k-1 ＝S _k-1 S _k-1 ^T (13) Where i = 1, 2, 3, ..., 2n, n is the dimension of the state quantity, ξ _i is the volume point set, as shown below: Where [1] is the unit matrix; b. Propagation volume point c. Estimate the state prediction value at time k d. Calculate the square root of the predicted value of the state error covariance at time k Where S _Q = Chol(Q _k ), Tria(…) represents the triangularization of the matrix. The definition is as follows: Step 4-3) Measurement update: a. Using the state prediction value at time k and the square root of the state error covariance prediction Update Volume Points b. Calculate the predicted value of the observed value Where: c. Calculate the square root of the innovation covariance matrix and the square root of the error covariance matrix Where: S _R = chol(R _k-1 ) (25) R _k-1 is the measurement noise covariance at time k-1; d. Update Kalman gain e. Calculate the estimated value of the system state quantity f. Calculate the square root of the system state error covariance matrix S _k =Tria([μ _k -K _k r _k K _k S _R ]) (30) g. Update the measurement noise covariance _Rk and system noise covariance _Qk The approximate value of the voltage residual covariance at time K is: In the formula represents the deviation between the measured value and the estimated value at time k; L is the new information length, the adaptive operator β is introduced and the weight n is defined as follows: n＝n ₀ ×2 ^β (33) Where P is the total length of the data set, H is the current data position, n ₀ is the initial weight value, and the expression of the measurement noise covariance R _k and the system noise covariance Q _k at time k is established as follows R _k =(1-n _k )R _k-1 +n _k F _k (34) Step 4-4) ASRCKF algorithm estimates SOC: According to equations (11) and (12), [SOC, U ₁ , U ₂ ] is used as the system state quantity to establish the discrete state space expression of the second-order RC model of lithium-ion battery: Wherein the current I is the input, the terminal voltage U is the output, [SOC, U ₁ , U ₂ ] is the state variable, Δt is the system sampling time, which is 1s. In the ASRCKF algorithm, the observation quantity y(k)=U(k), the state quantity x _k =[SOC(k),U ₁ (k),U ₂ (k)], and the input quantity u(k)=I(k) are set. The lithium-ion battery is a nonlinear system, and its state equation and observation equation are as follows: Through iteration, the algorithm can estimate the SOC value of the lithium-ion battery at each moment; The step 5) specifically comprises the following steps: Step 5-1) Parameter identification: Under different SOC conditions, the lithium-ion battery parameter identification results will have deviations, so the entire discharge process is divided into 10 stages for identification. In each stage, the battery undergoes static, pulse discharge, and static again. The SOC before discharge is defined as the initial SOC. The IDE algorithm is used to identify each battery discharge process, and then the results of each identification are polynomially fitted with the corresponding initial SOC to obtain the change curve of the battery model parameters under different SOCs. Step 5-2) SOC estimation: The identified parameters are substituted into the state equation and observation equation, and combined with the terminal voltage and current data measured experimentally, the ASRCKF algorithm is used to predict and update the lithium-ion battery state variables to obtain the SOC estimation result.