A method for lithium battery model parameter identification and state of charge estimation

Abstract

The application provides a lithium battery model parameter identification and state of charge estimation method, establishes a fractional order equivalent circuit model by analyzing the electrochemical impedance spectrum of a lithium battery; proposes a multi-strategy and mean factor differential evolution algorithm NMMDE based on a neighborhood to identify model parameters; in the developed NMMDE algorithm, the application proposes a new mutation strategy, which first defines a dynamic neighborhood called the top domain, and then replaces the current individual with the mean of all individuals in the top domain; in addition, the application introduces an additional mutation strategy in the mutation process, which adjusts the proportion of the two different strategies in the population adaptively, and makes up for the imbalance between exploration and utilization; then, the fractional order extended Kalman filter algorithm is used to estimate SOC, and the obtained SOC and the actual value are compared, and the absolute error average is 1%. The experimental results show that the algorithm provided by the application can more accurately identify the model parameters and obtain accurate SOC estimation results.

Description

Technical Field

[0001] The invention relates to the field of parameter identification and state of charge estimation for lithium battery models, and specifically to a method for parameter identification and state of charge estimation for lithium battery models. Background Technology

[0002] Today, lithium batteries are widely used in electric vehicles, hybrid vehicles, and renewable energy storage systems. Accurately estimating lithium battery parameters is crucial for the safety, performance, and lifespan of battery management systems. Designing battery model parameter identification methods and state-of-charge (SOC) estimation methods can help monitor battery charge, diagnose faults, and guide battery charging and discharging behavior. However, due to the complex chemical processes and nonlinear characteristics of lithium batteries, accurately identifying parameters and estimating the SOC remains a challenging problem.

[0003] Currently, lithium battery model parameter identification and state of charge estimation have the following shortcomings:

[0004] 1. The behavior of lithium batteries is affected by a variety of factors, such as temperature, charge / discharge rate, and capacity decay. Therefore, the model not only needs to have good adaptability and robustness to accurately predict battery behavior, but also needs to balance the relationship between model accuracy and computational cost. More complex models may require higher computational resources and time, making them unsuitable for practical applications, which greatly increases the difficulty of modeling.

[0005] 2. The parameters of lithium battery models are typically multidimensional, including the battery's internal physical and chemical properties. When using evolutionary algorithms to identify these parameters, the algorithms may get stuck in local optima, potentially preventing the acquisition of the optimal parameter solution. To overcome this problem, appropriate heuristic strategies and mutation operations need to be designed to enhance the global search capability. Therefore, accurately identifying these parameters is challenging in practice.

[0006] 3. The charging and discharging behavior of lithium batteries is typically nonlinear, leading to a complex relationship between the state of charge and battery voltage, current, and other parameters. Therefore, appropriate state estimation algorithms are needed to address this nonlinearity. Summary of the Invention

[0007] To address the aforementioned problems, this invention provides a method for identifying lithium battery model parameters and estimating the state of charge. This method can accurately estimate the model parameters and state of charge of the lithium battery, and effectively manage and control the battery system, which is crucial for optimizing the operation and control of the lithium battery system.

[0008] The technical solution adopted in this invention is as follows:

[0009] A method for lithium battery model parameter identification and state of charge estimation includes the following steps:

[0010] Step 1: Test the battery and collect data using battery testing equipment: Obtain the battery's current maximum usable capacity through static capacity testing, then use hybrid power pulse characteristic testing to obtain offline data of the battery's OCV, and conduct cyclic dynamic discharge testing under federal city driving conditions.

[0011] Step 2, Model Establishment: A fractional-order equivalent circuit model is established by analyzing the electrochemical impedance spectroscopy of lithium batteries;

[0012] Step 3: Identify the model parameters using the neighborhood-based multi-strategy and mean factor difference evolutionary algorithm (NMMDE).

[0013] Step 4: Based on the identified parameters, estimate the battery state of charge using the fractional extended Kalman filter algorithm.

[0014] Furthermore, in step 2, the specific steps for fractional-order modeling of the lithium battery include:

[0015] Step 2-1, the transfer function of the fractional-order model is represented by equation (1).

[0016]

[0017] In the formula, U d For terminal voltage, U OCV R is the open-circuit voltage, R0 is the ohmic internal resistance, R1 is the electrochemical polarization resistance, and R2 is the concentration polarization resistance; C1, C2, and W represent the parameters of the phase constant elements CPE1, CPE2, and the Warburg impedance, respectively; v, k, and r represent the fractional order.

[0018] Step 2-2: Use the hybrid power pulse characteristic test to obtain the correspondence between SOC and OCV, and then use the eighth-order polynomial shown in equation (2) for fitting;

[0019]

[0020] Steps 2-3: The system model of the fractional differential equation in the time domain is represented by equation (3); where y(t)=U d (t)-U OCV u(t) = I(t);

[0021]

[0022] Steps 2-4: The fractional derivative terms are discretized using the DL definition, as shown in equation (4):

[0023]

[0024] Steps 2-5: Define the relevant parameters:

[0025]

[0026] According to the parameter definition, equation (3) can be expressed as:

[0027]

[0028] Steps 2-6, for the sake of simplicity, use equation (6) to define parameters A(i) and B(i):

[0029]

[0030] Steps 2-7: In order to meet the accuracy standards of the lithium battery model while adhering to the "short-time memory principle", the data length needs to be truncated to an appropriate size; when N=1, the system model equation (3) can be transformed into a first-order difference equation, represented by equation (7):

[0031]

[0032] Steps 2-8: A fractional-order equivalent circuit model of the lithium battery was established using equation (7), and the parameter θ to be identified is expressed as equation (8):

[0033]

[0034] Furthermore, the specific steps of step 3 are as follows:

[0035] Step 3-1, the objective function utilizes the root mean square error between the actual voltage and the predicted voltage, as expressed by equation (9).

[0036]

[0037] In the formula: U d (j) represents the terminal voltage at the j-th sampling point, U(I j , ) represents the output voltage of the fractional-order model, and N represents the number of sampling points;

[0038] Step 3-2: Generate a randomly initialized population;

[0039] Step 3-3: Generate a new population according to the reverse learning strategy of equation (10), sort the individuals in the new population with the individuals in the initial population by fitness, and take the top NP individuals as the current population, where NP represents the population size and D represents the dimension.

[0040]

[0041]

[0042] In the formula: x i j Let x represent the j-th generation of the i-th particle. i 0, j The corresponding antiparticle of the current particle is calculated using equation (11); a j and b j a represents the boundary range of the j-th dimension variable of the particle. j b is the lower bound. j The upper bound is defined by w; w represents the inertia factor, and r represents the upper bound. 1, i and r 2, i A random number between 0 and 1;

[0043] Steps 3-4: Generate the crossover factor CR according to the JADE algorithm. i and mutation factor F i ;

[0044] Steps 3-5 involve setting up a dynamic neighborhood, which dynamically considers the number of high-quality individuals to guide the search process; during mutation, its value is calculated using equation (12).

[0045]

[0046] In the formula: f represents the smallest subpopulation size. best f represents the individual with the best fitness. i G represents the fitness value of individual i. m Indicates the maximum number of iterations;

[0047] Steps 3-6 introduce a mean factor based on the JADE algorithm. Equation (13) represents the mutation strategy.

[0048]

[0049] In the formula: X j top _ best X represents the best individual in the top domain. j top_avgX represents the average value of all individuals in the top domain. j r1 and X j r2 A random individual within the population; Indicates the mutation rate factor; This represents the j-th dimension of the i-th individual in the population.

[0050] Steps 3-7: To avoid the limitations of a single strategy, the "DE / rand / 1" mutation strategy is introduced. Equation (14) is an adaptive strategy selection mechanism that performs mutation operations on the population.

[0051]

[0052] In the formula, FES represents the total number of function evaluations performed; MaxFES represents the maximum allowed number of function evaluations.

[0053] Steps 3-8 involve performing crossover and selection operations on the population;

[0054] Steps 3-9: Apply the JADE algorithm to S CR S F Update with outdated population A;

[0055] Steps 3-10: Iterate and update until the termination condition is met, and output the optimal solution.

[0056] Furthermore, in step 4, the fractional extended Kalman filter algorithm is used to estimate the SOC. The specific steps are as follows:

[0057] Step 4-1: Initialize the state, state covariance matrix, and noise. Set the covariance matrix as a diagonal matrix, with the elements on the diagonal representing the variance of each state variable.

[0058] Step 4-2: Update the parameters online according to equation (15);

[0059] .

[0060] Compared with the prior art, the advantages of the present invention are as follows:

[0061] (1) A fractional-order modeling method was selected, and the internal electrochemical kinetics of lithium batteries can be accurately described by analyzing electrochemical impedance spectroscopy.

[0062] (2) The NMMDE algorithm is used to identify the model parameters. This algorithm has high identification accuracy and can avoid the particles from missing the optimal solution due to deviation from the optimal search space during the search process.

[0063] (3) The fractional extended Kalman filter algorithm is used for SOC estimation. By introducing fractional calculus, the dynamic characteristics of the nonlinear system can be better described, and the accuracy of the estimation is improved. Attached Figure Description

[0064] Figure 1 The schematic diagram of the fractional-order equivalent circuit model of a lithium battery;

[0065] Figure 2 The flowchart shows the algorithm for parameter identification of the model.

[0066] Figure 3 Voltage curves for each algorithm;

[0067] Figure 4 This is the SOC estimation result. Detailed Implementation

[0068] The invention will now be further described with reference to the accompanying drawings.

[0069] This invention provides a method for lithium battery model parameter identification and state of charge estimation, comprising the following steps:

[0070] Step 1: Test the battery and collect data using battery testing equipment: Obtain the battery's current maximum usable capacity through static capacity testing, then use hybrid power pulse characteristic testing to obtain offline data of the battery's OCV, and conduct cyclic dynamic discharge testing under federal city driving conditions.

[0071] Step 2, Model Establishment: A fractional-order equivalent circuit model is established through analysis of the electrochemical impedance spectroscopy of the lithium battery, such as... Figure 1 As shown.

[0072] The specific steps for fractional-order modeling of lithium batteries include:

[0073] Step 2-1, the transfer function of the fractional-order model is represented by equation (1).

[0074]

[0075] In the formula, U d For terminal voltage, U OCV R is the open-circuit voltage, R0 is the ohmic internal resistance, R1 is the electrochemical polarization resistance, and R2 is the concentration polarization resistance; C1, C2, and W represent the parameters of the phase constant elements CPE1, CPE2, and the Warburg impedance, respectively; v, k, and r represent the fractional order.

[0076] Step 2-2: Use the hybrid power pulse characteristic test to obtain the correspondence between SOC and OCV, and then use the eighth-order polynomial shown in equation (2) for fitting;

[0077]

[0078] Steps 2-3: The system model of the fractional differential equation in the time domain is represented by equation (3); where y(t)=U d (t)-U OCV u(t) = I(t);

[0079]

[0080] Steps 2-4: The fractional derivative terms are discretized using the DL definition, as shown in equation (4):

[0081]

[0082] Steps 2-5: Define the relevant parameters:

[0083]

[0084] According to the parameter definition, equation (3) can be expressed as:

[0085]

[0086] Steps 2-6, for the sake of simplicity, use equation (6) to define parameters A(i) and B(i):

[0087]

[0088] Steps 2-7: In order to meet the accuracy standards of the lithium battery model while adhering to the "short-time memory principle", the data length needs to be truncated to an appropriate size; when N=1, the system model equation (3) can be transformed into a first-order difference equation, represented by equation (7):

[0089]

[0090] Steps 2-8: A fractional-order equivalent circuit model of the lithium battery was established using equation (7), and the parameter θ to be identified is expressed as equation (8):

[0091]

[0092] Step 3: Identify the model parameters using the neighborhood-based multi-strategy and mean factor difference evolutionary algorithm (NMMDE), such as... Figure 2 As shown, the specific steps are as follows:

[0093] Step 3-1, the objective function utilizes the root mean square error between the actual voltage and the predicted voltage, as expressed by equation (9).

[0094]

[0095] In the formula: U d (j) represents the terminal voltage at the j-th sampling point, U(I j , ) represents the output voltage of the fractional-order model, and N represents the number of sampling points;

[0096] Step 3-2: Generate a randomly initialized population;

[0097] Step 3-3: Generate a new population according to the reverse learning strategy of equation (10), sort the individuals in the new population with the individuals in the initial population by fitness, and take the top NP individuals as the current population, where NP represents the population size and D represents the dimension.

[0098]

[0099]

[0100] In the formula: x i j Let x represent the j-th generation of the i-th particle. i 0, j The corresponding antiparticle of the current particle is calculated using equation (11); a j and b j a represents the boundary range of the j-th dimension variable of the particle. j b is the lower bound. j The upper bound is defined by w; w represents the inertia factor, and r represents the upper bound. 1, i and r 2, i A random number between 0 and 1;

[0101] Steps 3-4: Generate the crossover factor CR according to the JADE algorithm. i and mutation factor F i ;

[0102] Steps 3-5 involve setting up a dynamic neighborhood, which dynamically considers the number of high-quality individuals to guide the search process; during mutation, its value is calculated using equation (12).

[0103]

[0104] In the formula: f represents the smallest subpopulation size. bestf represents the individual with the best fitness. i G represents the fitness value of individual i. m Indicates the maximum number of iterations;

[0105] Steps 3-6 introduce a mean factor based on the JADE algorithm. Equation (13) represents the mutation strategy.

[0106]

[0107] In the formula: X j top _ best X represents the best individual in the top domain. j top_avg X represents the average value of all individuals in the top domain. j r1 and X j r2 A random individual within the population; Indicates the mutation rate factor; Let j represent the j-th dimension of the i-th individual in the population;

[0108] Steps 3-7: To avoid the limitations of a single strategy, the "DE / rand / 1" mutation strategy is introduced. Equation (14) is an adaptive strategy selection mechanism that performs mutation operations on the population.

[0109]

[0110] In the formula, FES represents the total number of function evaluations performed; MaxFES represents the maximum allowed number of function evaluations.

[0111] Steps 3-8 involve performing crossover and selection operations on the population;

[0112] Steps 3-9: Apply the JADE algorithm to S CR S F Update with outdated population A;

[0113] Steps 3-10: Iterate and update until the termination condition is met, and output the optimal solution.

[0114] Step 4: Based on the identified parameters, estimate the battery state of charge using the fractional extended Kalman filter algorithm. The specific steps are as follows:

[0115] Step 4-1: Initialize the state, state covariance matrix, and noise. Set the covariance matrix as a diagonal matrix, with the elements on the diagonal representing the variance of each state variable.

[0116] Step 4-2: Update the parameters online according to equation (15);

[0117] .

[0118] Regarding the evaluation of the test results, the accuracy of parameter identification results of this invention was compared with that of other algorithms in the field. Figure 3 The paper presents voltage curves showing the parameter identification results of several advanced evolutionary algorithms (SEDE, PGJAYA, DOLJADE, JAD, LBLDE). Tables 1 and 2 show the corresponding parameter identification results and root mean square errors.

[0119] Table 1. Parameter identification results for each algorithm

[0120]

[0121] Table 2 Root Mean Square Error Results for Each Algorithm

[0122]

[0123] The results show that the algorithm designed in this invention can provide more accurate parameter results and obtain more accurate fitting results with the actual voltage, thus enabling better monitoring of battery safety and health status. After obtaining the parameter identification results, this invention uses a fractional extended Kalman filter algorithm to estimate the battery's SOC, and the results are shown in... Figure 4 To verify the fast convergence of the fractional extended Kalman filter algorithm, this invention provides an incorrect initial value. It can be seen that the SOC estimate quickly converges to near the correct value, and the SOC value predicted by the fractional extended Kalman filter algorithm matches the actual SOC value very well, with an average absolute error of 1%. Therefore, this invention can provide real-time SOC estimation data for the BMS, helping the BMS optimize its charging and discharging strategy and further improve battery performance and lifespan.

Claims

1. A method for identifying lithium battery model parameters and estimating state of charge, characterized in that, Includes the following steps: Step 1: Test the battery and collect data using battery testing equipment: Obtain the battery's current maximum usable capacity through static capacity testing, then use hybrid power pulse characteristic testing to obtain offline data of the battery's OCV, and conduct cyclic dynamic discharge testing under federal city driving conditions. Step 2, Model Establishment: A fractional-order equivalent circuit model is established by analyzing the electrochemical impedance spectroscopy of lithium batteries; Step 3: Identify the model parameters using the neighborhood-based multi-strategy and mean factor difference evolutionary algorithm (NMMDE); the specific steps are as follows: Step 3-1, the objective function utilizes the root mean square error between the actual voltage and the predicted voltage, as expressed by equation (9). In the formula: U d (j) represents the terminal voltage at the j-th sampling point, U(I j , () represents the output voltage of the fractional-order model, and N represents the number of sampling points; Step 3-2: Generate a randomly initialized population; Step 3-3: Generate a new population according to the reverse learning strategy of equation (10), sort the individuals in the new population with the individuals in the initial population by fitness, and take the top NP individuals as the current population, where NP represents the population size and D represents the dimension. In the formula: x i j Let x represent the j-th generation of the i-th particle. i 0, j The corresponding antiparticle of the current particle is calculated using equation (11); a j and b j a represents the boundary range of the j-th dimension variable of the particle. j b is the lower bound. j The upper bound is defined by w; w represents the inertia factor, and r represents the upper bound. 1, i and r 2, i A random number between 0 and 1; Steps 3-4: Generate the crossover factor CR according to the JADE algorithm. i and mutation factor F i ; Steps 3-5 involve setting up a dynamic neighborhood, which dynamically considers the number of high-quality individuals to guide the search process; during mutation, its value is calculated using equation (12). In the formula: f represents the smallest subpopulation size. best f represents the individual with the best fitness. i G represents the fitness value of individual i. m Indicates the maximum number of iterations; Steps 3-6 introduce a mean factor based on the JADE algorithm. Equation (13) represents the mutation strategy. In the formula: X j top _ best X represents the best individual in the top domain. j top_avg X represents the average value of all individuals in the top domain. j r1 and X j r2 A random individual within the population; Indicates the mutation rate factor; Let j represent the j-th dimension of the i-th individual in the population; Steps 3-7: To avoid the limitations of a single strategy, the "DE / rand / 1" mutation strategy is introduced. Equation (14) is an adaptive strategy selection mechanism that performs mutation operations on the population. In the formula, FES represents the total number of function evaluations performed; MaxFES represents the maximum allowed number of function evaluations. Steps 3-8 involve performing crossover and selection operations on the population; Steps 3-9: Apply the JADE algorithm to S CR S F Update with outdated population A; Steps 3-10: Iterate and update until the termination condition is met, and output the optimal solution; Step 4: Based on the identified parameters, estimate the battery state of charge using the fractional extended Kalman filter algorithm.

2. The method for lithium battery model parameter identification and state of charge estimation according to claim 1, characterized in that: In step 2, the specific steps for fractional-order modeling of the lithium battery include: Step 2-1, the transfer function of the fractional-order model is represented by equation (1). In the formula, U d For terminal voltage, U OCV R is the open-circuit voltage, R0 is the ohmic internal resistance, R1 is the electrochemical polarization resistance, and R2 is the concentration polarization resistance; C1, C2, and W represent the parameters of the phase constant elements CPE1, CPE2, and the Warburg impedance, respectively; v, k, and r represent the fractional order. Step 2-2: Use the hybrid power pulse characteristic test to obtain the correspondence between SOC and OCV, and then use the eighth-order polynomial shown in equation (2) for fitting; Steps 2-3: The system model of the fractional differential equation in the time domain is represented by equation (3); where y(t)=U d (t)-U OCV u(t) = I(t); Steps 2-4: The fractional derivative terms are discretized using the DL definition, as shown in equation (4): Steps 2-5: Define the relevant parameters: According to the parameter definition, equation (3) can be expressed as: Steps 2-6, for the sake of simplicity, use equation (6) to define parameters A(i) and B(i): Steps 2-7: In order to meet the accuracy standards of the lithium battery model while adhering to the "short-time memory principle", the data length needs to be truncated to an appropriate size; when N=1, the system model equation (3) can be transformed into a first-order difference equation, represented by equation (7): Steps 2-8: A fractional-order equivalent circuit model of the lithium battery was established using equation (7), and the parameter θ to be identified is expressed as equation (8): 。 3. The method for lithium battery model parameter identification and state of charge estimation according to claim 1, characterized in that, In step 4, the specific steps for estimating the SOC using the fractional extended Kalman filter algorithm are as follows: Step 4-1: Initialize the state, state covariance matrix, and noise. Set the covariance matrix as a diagonal matrix, with the diagonal elements representing the variance of each state variable. Step 4-2: Update the parameters online according to equation (15); 。

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