Lithium ion battery state of charge estimation method under multiple working conditions and wide temperature based on f-fomiaekf

Abstract

The application discloses a lithium ion battery state of charge estimation method under wide temperature in multiple working conditions based on F-FOMIAEKF, and the method comprises the following steps: calculating a SOC reference value according to a capacity value under wide temperature in a first working condition; after the experiment under wide temperature in the first working condition, a data set containing W groups of data points is constructed, and a relationship formula of OCV-SOC is derived by using a polynomial fitting method; a fractional order 2 order equivalent circuit model of a lithium ion battery and a state space equation are established; parameters to be identified in the model are identified; under wide temperature in different working conditions, state variables and observation variables in the state space equation of the fractional order 2 order equivalent circuit model are estimated by using a SOC estimation algorithm according to the identified parameters, and a SOC estimation value is obtained. The application introduces a fractional order model on one hand, introduces a multi-innovation theory to optimize the filter updating process in the whole estimation process on the other hand, in addition, an adaptive theory is introduced, the statistical characteristics of process noise and measurement noise are updated in real time to optimize the estimation algorithm, so that the accuracy and stability of SOC estimation are improved.

Description

Technical Field

[0001] This invention relates to a method for estimating the state of charge of lithium-ion batteries under multiple operating conditions and wide temperature ranges based on F-FOMIAEKF, belonging to the field of lithium-ion battery technology. Background Technology

[0002] Faced with the challenges of energy crisis and environmental degradation, low-pollution, high-efficiency new energy vehicles are gradually becoming the mainstream direction of future transportation development. Lithium-ion batteries, with their advantages of high safety performance, wide operating temperature range, high operating voltage, and no memory effect, have become the main battery type for current new energy vehicles. In the Battery Management System (BMS), the state of charge (SOC) estimation of lithium-ion batteries is an extremely critical link, comparable in importance to the fuel level indicator in traditional gasoline vehicles. It plays a pivotal role in improving the vehicle's energy distribution strategy, increasing the capacity utilization efficiency and energy efficiency of the power battery, effectively preventing overcharging and over-discharging, ensuring the safety of the power battery, and extending its lifespan.

[0003] As a highly complex time-varying nonlinear system, the state of charge (SOC) of a lithium-ion battery cannot be directly measured and must be estimated using measured physical quantities such as current and voltage. SOC estimation methods include: ampere-hour integration method, open-circuit voltage method, discharge testing method, filtering method, model-based method, and data-driven method. Model-based methods require building a lithium-ion battery model and treating the battery SOC as the state to be estimated within the model. Then, an algorithm is designed to estimate it. Compared to other methods, this approach has advantages such as low computational complexity and good real-time performance, making it the primary choice for SOC estimation.

[0004] Currently, the mainstream models are equivalent circuit models, which are mostly integer orders. The ideal capacitor elements in integer-order models cannot fully reflect the complex dynamic behavior of lithium-ion batteries during actual charging and discharging. The internal processes of lithium-ion batteries, such as charge diffusion, insertion, and deinsertion, exhibit more complex fractional-order characteristics, which are difficult to accurately represent in integer-order models. Furthermore, traditional hyperparameter optimization algorithms require multiple iterations, which not only prolongs the convergence time but also increases the computational load during further research and in-depth analysis. In addition, the estimation of the SOC of lithium-ion batteries under extremely low temperatures and abnormal charging and discharging conditions has not yet been verified.

[0005] How to solve the above-mentioned technical problems is the challenge facing this invention. Summary of the Invention

[0006] The purpose of this invention is to provide a method for estimating the state of charge (SOC) of lithium-ion batteries under multiple operating conditions and wide temperatures based on F-FOMIAEKF. This method introduces a fractional-order model on the one hand, and multi-innovation theory on the other hand to optimize the filter update process in the entire estimation process. In addition, adaptive theory is introduced to optimize the estimation algorithm by updating the statistical characteristics of process noise and measurement noise in real time, thereby improving the accuracy and stability of SOC estimation.

[0007] The technical solution of this invention is:

[0008] According to a first aspect of the present invention, a method for estimating the state of charge of a lithium-ion battery under multiple operating conditions and wide temperature range based on F-FOMIAEKF is provided, comprising the following steps:

[0009] Step 1: Build an experimental platform and obtain the current, voltage, and capacity values ​​under multiple operating conditions and wide temperature ranges through experiments; the multiple operating conditions include at least the first operating condition and the second operating condition.

[0010] Step 2: Calculate the SOC reference value based on the capacity value under the first operating condition wide temperature range; after the first operating condition wide temperature range experiment, select the voltage value at the moment the lithium-ion battery is put into storage, and obtain a total of W voltage values, and select the corresponding SOC reference value to construct a dataset containing W sets of data points; then, based on the dataset of W sets of data points, derive the OCV-SOC relationship using the polynomial fitting method.

[0011] Step 3: Establish a fractional-order second-order equivalent circuit model of a lithium-ion battery; based on the fractional-order second-order equivalent circuit model of a lithium-ion battery, establish the state-space equations of the fractional-order second-order equivalent circuit model of a lithium-ion battery.

[0012] Step 4: Identify the parameters to be identified in the fractional-order second-order equivalent circuit model of the lithium-ion battery.

[0013] Step 5: Construct the SOC estimation algorithm; under different operating conditions and wide temperature ranges, the SOC estimation algorithm is used to estimate the state variables and observation variables in the state space equation of the fractional-order second-order equivalent circuit model based on the identified parameters, and the SOC estimate is obtained.

[0014] Furthermore, the multi-condition system also includes a third condition.

[0015] Furthermore, the relationship between OCV and SOC is as follows:

[0016] U OCV (SOC)=p8SOC 8 +p7SOC 7 +p6SOC 6 +p5SOC 5 +p4SOC4 +p3SOC 3 +p2SOC 2 +p1SOC 1 +p0

[0017] Among them, U OCV (SOC) represents the open-circuit voltage; SOC represents the battery state of charge; p0-p8 are the fitting coefficients.

[0018] Furthermore, step 3 specifically includes:

[0019] Based on circuit principles, a fractional-order second-order equivalent circuit model of a lithium-ion battery is established using the definition of fractional-order calculus in GL. The fractional-order second-order equivalent circuit model of the lithium-ion battery includes loop state equations and observation equations.

[0020] Based on the fractional-order second-order equivalent circuit model of a lithium-ion battery, the state-space equation of the fractional-order second-order equivalent circuit model of a lithium-ion battery is established, and the expression is:

[0021]

[0022] Where: state variables intermediate variables D = -R0; U1(k) is the voltage across resistor R1 and capacitor C1 in the fractional-order second-order equivalent circuit model; U2(k) is the voltage across resistor R2 and capacitor C2 in the fractional-order second-order equivalent circuit model; SOC k The state of charge of the battery at time k; T s is the sampling interval; m and n are the fractional order, respectively; R1 and C1 are the polarization resistor and capacitor, R2 and C2 are the diffusion resistor and capacitor; R0 is the ohmic internal resistance; u(k-1) represents the model input; y(k) represents the observed variable value of the state at time k; a = [m,n,0] represents the differential order vector; when a>0, It is a fractional differential; when a = 0, When a<0, For fractional integrals; U OCV (SOC) represents the open-circuit voltage.

[0023] Furthermore, step 4 specifically includes the following steps:

[0024] Step 4.1 After the first operating condition wide temperature range, calculate the ohmic internal resistance for each pulse discharge under the first operating condition, and average the ohmic internal resistance calculated under all pulse discharges to obtain the identified ohmic internal resistance R0.

[0025] Step 4.2: Based on the adaptive genetic algorithm, identify the polarization resistor R1, polarization capacitor C1, diffusion resistor R2, diffusion capacitor C2, and fractional order m and n in the fractional order 2 equivalent circuit model to obtain the identified polarization resistor R1, polarization capacitor C1, diffusion resistor R2, diffusion capacitor C2, and fractional order m and n.

[0026] Furthermore, step 5 specifically includes the following steps:

[0027] Step 5.1: Initialize the initial values ​​of the actual values ​​of the state variables, the initial values ​​of the process noise covariance, and the initial values ​​of the error covariance matrix, k = 1:

[0028] Step 5.2: Based on the identified parameters, estimate the state variables and observation variables in the state space equation of the fractional-order second-order equivalent circuit model to obtain the prior estimates of the state variables and observation variables at time k.

[0029] Step 5.3: Based on the state variable estimation error at time k, estimate the error covariance matrix to obtain the prior estimate of the error covariance matrix at time k; where the difference between the actual value of the state variable at time k and the prior estimate of the state variable is the state variable estimation error.

[0030] Step 5.4: Determine the Kalman gain at time k based on the prior estimate of the error covariance matrix at time k;

[0031] Step 5.5: Determine the multiple innovation gain matrix based on the Kalman gain at time k;

[0032] Step 5.6: Determine the multiple innovation matrix based on the estimation error of the observed variable at time k; where the difference between the actual value of the observed variable at time k and the prior estimate of the observed variable is the estimation error of the observed variable.

[0033] Step 5.7: Based on the multiple innovation gain matrix and the multiple innovation matrix, update the prior estimates of the state variables, observation variables, and error covariance matrix to obtain the posterior estimates:

[0034] Step 5.8: Adaptively adjust the measurement noise covariance R k With process noise covariance Q k :

[0035] Step 5.9: Let k = k + 1, repeat steps 5.2-5.8 until k equals the data length, and output all posterior estimates.

[0036] According to a second aspect of the present invention, a lithium-ion battery state-of-charge estimation system based on F-FOMIAEKF multi-condition wide-temperature is provided, comprising a module of the lithium-ion battery state-of-charge estimation method based on F-FOMIAEKF multi-condition wide-temperature as described in any one of the above.

[0037] The beneficial effects of this invention are as follows:

[0038] (1) Based on the characteristics of lithium-ion batteries, this invention establishes a fractional-order second-order RC equivalent circuit model, which can not only more accurately describe the nonlinearity and hysteresis effect of lithium-ion batteries, but also make full use of the observation information at multiple time points to improve the estimation performance, thereby greatly improving the model's prediction accuracy of battery dynamic behavior.

[0039] (2) Based on the original Kalman filter algorithm, this invention proposes an adaptive adjustment method for process noise and measurement noise, which enables the model to better adapt to the uncertainty in the battery charging and discharging process and improves the robustness of state estimation. At the same time, it incorporates multiple innovation theory and improves the accuracy and stability of state estimation by optimizing the filter update process.

[0040] (3) This invention innovatively introduces a forgetting factor into the estimation algorithm to improve data utilization. By adjusting the value of the forgetting factor, the influence of historical information on state estimation can be controlled. In the modeling and state estimation of lithium-ion batteries, the battery performance gradually deteriorates with increasing usage time, thus the importance of historical information gradually decreases. By introducing a forgetting factor, the algorithm can focus more on recent observation information, thereby improving the real-time performance and accuracy of state estimation.

[0041] (4) The SOC estimation algorithm of the present invention not only has superior estimation accuracy under normal temperature and normal charging and discharging conditions, but also can effectively estimate SOC under low temperature, high temperature and abnormal charging and discharging conditions. The algorithm is robust and has great engineering value and broad application prospects. Attached Figure Description

[0042] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0043] Figure 1 This invention provides a lithium-ion battery charge-discharge experimental platform.

[0044] Figure 2 This invention illustrates the battery discharge conditions under different temperature conditions.

[0045] Figure 3 This is a schematic diagram of the fractional-order second-order RC model of the lithium-ion battery of the present invention;

[0046] Figure 4 This is a locally magnified curve of the terminal voltage in the pulse discharge experiment at 24℃ of this invention;

[0047] Figure 5 This is the basic flow of the adaptive genetic algorithm of this invention;

[0048] Figure 6 This refers to the lithium-ion battery terminal voltage predicted by this invention.

[0049] Figure 7 This invention provides the F-FOMIAEKF process for estimating SOC.

[0050] Figure 8 These are the prediction results of the present invention under different operating conditions at 1℃;

[0051] Figure 9 These are the prediction results of this invention under different operating conditions at 24℃;

[0052] Figure 10 The results are the predictions for different operating conditions at 43°C according to the present invention. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily combined with each other.

[0054] Considering that integer-order models cannot fully reflect the internal state of the battery, a fractional-order model is established by replacing the ideal capacitor with a constant-phase element (CPE). The fractional-order model more accurately describes the dynamic behavior and performance characteristics of lithium-ion batteries while enhancing the storage capacity of historical data. Multiple innovation theory is introduced to optimize the filter update process throughout the estimation process. Furthermore, adaptive theory is introduced to optimize the estimation algorithm by updating the statistical characteristics of process noise and measurement noise in real time, thereby improving the accuracy and stability of SOC estimation. To ensure efficient data utilization, a forgetting factor is added to the estimation algorithm. This factor can improve the accuracy of the algorithm by adjusting the ratio of new and old data. Combining these three improvements, a multiple innovation adaptive extended Kalman filter algorithm based on a fractional-order second-order model with a forgetting factor is proposed. This algorithm provides accurate estimation results under various operating conditions and wide temperature ranges, and exhibits high robustness. The embodiments of this invention are described below with reference to the accompanying drawings.

[0055] like Figures 1-10As shown, according to a first aspect of the present invention, a method for estimating the state of charge of a lithium-ion battery under multiple operating conditions and wide temperature range based on F-FOMIAEKF is provided, comprising the following steps:

[0056] Step 1: Build an experimental platform and obtain the current, voltage, and capacity values ​​under multiple operating conditions and wide temperature range through experiments; wherein the multiple operating conditions include at least the first operating condition and the second operating condition; further, the multiple operating conditions also include the third operating condition.

[0057] Step 2: Calculate the SOC reference value based on the capacity value under the first operating condition wide temperature range; after the first operating condition wide temperature range experiment, select the voltage value at the moment the lithium-ion battery is put into storage, and obtain a total of W voltage values, and select the corresponding SOC reference value to construct a dataset containing W sets of data points; then, based on the dataset of W sets of data points, derive the OCV-SOC relationship using the polynomial fitting method.

[0058] Step 3: Establish a fractional-order second-order equivalent circuit model of a lithium-ion battery; based on the fractional-order second-order equivalent circuit model of a lithium-ion battery, establish the state-space equations of the fractional-order second-order equivalent circuit model of a lithium-ion battery.

[0059] Step 4: Identify the parameters to be identified in the fractional-order second-order equivalent circuit model of the lithium-ion battery.

[0060] Step 5: Construct a SOC estimation algorithm using a multi-innovation adaptive extended Kalman filter (F-FOMIAEKF) with a forgetting factor; under different operating conditions and wide temperatures, the SOC estimation algorithm of F-FOMIAEKF is used to estimate the state variables and observation variables in the state space equation of the fractional second-order equivalent circuit model based on the identified parameters, and obtain the SOC estimate.

[0061] Further, step 1 specifically includes:

[0062] Step 1.1: Set up the experimental platform;

[0063] Specifically: This invention utilizes a BTS battery testing system, a high and low temperature change test chamber, a main unit, and a lithium-ion battery to construct a system as follows: Figure 1 The experimental platform shown uses an 18650 lithium-ion battery with a rated capacity of 2000mAh. During operation, three temperature settings are used in the high and low temperature variation test chamber (1℃, 24℃, and 43℃; however, the actual temperature displayed on the chamber's screen will fluctuate within the set error range during the experiment).

[0064] Step 1.2: Conduct a constant-capacity test on the battery under wide temperature conditions to verify that the battery capacity meets the rated capacity.

[0065] For example, a constant-capacity test was conducted on the battery under a wide temperature range while it was in a discharged state to obtain the following results: Figure 2 The relationship between battery terminal voltage and capacity under the three temperature conditions shown in the figure can be seen from the figure. The capacity of the battery under the three temperature conditions meets the rated capacity. The constant capacity test shows that the experimental platform built by this invention is reliable.

[0066] Step 1.3: After verifying that the battery capacity meets the rated capacity, conduct experiments under different operating conditions in a wide temperature range to obtain the current, voltage, and capacity values ​​under multiple operating conditions and wide temperature ranges.

[0067] In this embodiment of the invention, the battery in the experimental platform is subjected to HPPC, D-ynamic Stress Test (DST), and Federal Urban Driving Schedule (FUDS) tests at 1°C, 24°C, and 43°C respectively, to obtain different current and voltage values ​​under wide temperature and multiple operating conditions.

[0068] The HPPC operating condition is the first operating condition, the D-ynamic Stress Test (DST) operating condition is the second operating condition, and the Federal Urban Driving Schedule (FUDS) operating condition is the third operating condition.

[0069] Further, step 2 specifically involves: calculating the SOC reference value using the ampere-hour integration method based on the capacity value under the first operating condition wide temperature range; after the first operating condition wide temperature range experiment, selecting the voltage value at the moment the lithium-ion battery is placed to end, obtaining a total of W voltage values, and selecting the corresponding SOC reference values, thereby constructing a dataset containing W sets of data points; then, based on the dataset of W sets of data points, using the polynomial fitting method to derive the OCV-SOC relationship.

[0070] Specifically, during the HPPC experiment under the first operating condition, the lithium-ion battery, in the resting stage after constant current charging and discharging, experiences a slow increase in terminal voltage due to the combined effects of internal polarization and hysteresis. Therefore, the voltage value at the moment the resting period ends was selected, resulting in 11 voltage values. Corresponding SOC reference values ​​were also selected, thus constructing a dataset containing 11 data points. Subsequently, the relationship between OCV and SOC was derived using a polynomial fitting method:

[0071] U OCV (SOC)=p8SOC 8 +p7SOC 7 +p6SOC 6+p5SOC 5 +p4SOC 4 +p3SOC 3 +p2SOC 2 +p1SOC 1 +p0

[0072] Among them, U OCV (SOC) represents the open-circuit voltage; SOC represents the battery state of charge; p0-p8 are the fitting coefficients.

[0073] The open-circuit voltage (OCV) of a battery changes monotonically with its state of charge (SOC). When the ambient temperature remains constant, the OCV-SOC relationship curves of the same type of battery under different operating conditions remain essentially unchanged. In this embodiment of the invention, the same relationship curve is used for different operating conditions at the same temperature. Table 1 below shows the specific fitting coefficients for different temperatures:

[0074] Table 1

[0075]

[0076] Furthermore, step 3 specifically includes:

[0077] Based on circuit principles, a second-order fractional equivalent circuit model of a lithium-ion battery is established using the definition of fractional calculus in GL. A schematic diagram of the model is shown below. Figure 3 As shown, the equivalent circuit model includes loop state equations and observation equations;

[0078] The state equation of the loop is expressed as follows:

[0079]

[0080] The expression for the observation equation is:

[0081] U r =U OCV (SOC)-R0I(k)-U1(k)-U2(k)

[0082] Among them, SOC k The state of charge of the battery at time k; T s Q is the sampling interval; r U is the rated capacity of the battery; m and n are the fractional order, respectively; I(k) is the current at time k; U1(k) is the voltage across resistor R1 and capacitor C1 in the fractional second-order equivalent circuit model; U2(k) is the voltage across resistor R2 and capacitor C2 in the fractional second-order equivalent circuit model; U r R1 is the power supply voltage; R1 and C1 are polarization resistors and capacitors, respectively; R2 and C2 are diffusion resistors and capacitors, respectively; R0 is the internal resistance in ohms; U OCV (SOC) represents the open-circuit voltage.

[0083] For a discrete stochastic system, representing the state and observation equations based on Kalman filtering in matrix form can solve the problem of simultaneous estimation of multiple variables. Therefore, the state-space equation of the fractional-order second-order equivalent circuit model of a lithium-ion battery can be expressed as:

[0084]

[0085] Where: state variables intermediate variables D = -R0; u(k-1) represents the model input, and u(k-1) = I(k-1) is selected; y(k) represents the observed variable value of the state at time k; a = [m,n,0] represents the differential order vector; when a>0, It is a fractional differential; when a = 0, When a<0, It is a fractional integral.

[0086] It should be noted that this invention establishes a fractional-order second-order equivalent circuit model of a lithium-ion battery based on the definition of fractional-order calculus in the GL framework. The discrete-continuous fractional-order equations under the definition of fractional-order calculus in the GL framework are as follows:

[0087]

[0088] Where n>0, It is a fractional differential; when n = 0, D t n =1; when n<0, For fractional integrals; Δt is the sampling interval, and [t / Δt] represents the integer part of t / Δt; Here, represents the Newton's binomial coefficients. When i = 0, the Newton's binomial coefficients are 1; when i > 0, the Newton's binomial coefficients are specifically expressed as:

[0089]

[0090] Where Γ(x) is the gamma equation, specifically expressed as:

[0091]

[0092] The dynamic equation for a capacitor CPE connected in parallel with a resistor is:

[0093]

[0094] Where, when i = 1, a = m; when i = 2, a = n; m and n are the fractional order; I(k) is the current at time k; U1(k) is the voltage across resistor R1 and capacitor C1 in the fractional second-order equivalent circuit model; U2(k) is the voltage across resistor R2 and capacitor C2 in the fractional second-order equivalent circuit model; U r R1 is the power supply voltage; R1 and C1 are polarization resistors and capacitors, R2 and C2 are diffusion resistors and capacitors; R0 is the internal resistance in ohms.

[0095] Furthermore, step 4 specifically includes the following steps:

[0096] Step 4.1 After the first operating condition wide temperature range, calculate the ohmic internal resistance for each pulse discharge under the first operating condition, and average the ohmic internal resistance calculated under all pulse discharges to obtain the identified ohmic internal resistance R0.

[0097] Specifically: By conducting Hybrid Power Pulse Characteristics (HPPC) experiments on the battery, specific discharge data can be obtained, such as... Figure 4 This is a magnified curve of the terminal voltage during a single pulse discharge experiment at 24℃. The OA segment represents the resting phase. When the battery begins to discharge, the terminal voltage drops instantaneously from point A to point B. Discharge begins at point B. The period from point B to point C represents the battery discharge phase, during which the terminal voltage drops instantaneously from point U... A Descending to U B When the battery stops discharging, the terminal voltage changes from U... C Instantly upgraded to U D Points D to E represent the battery storage period. The ohmic internal resistance was calculated for each pulse discharge under HPPC conditions at 24℃, with the following expression:

[0098]

[0099] The continuous discharge current I = 2A; the HPPC operating condition of this invention has 10 pulse discharges, and the average value of the 10 results calculated according to the above formula is taken as the identified ohmic internal resistance value.

[0100] Step 4.2, based on as follows Figure 5 An adaptive genetic algorithm identifies the polarization resistor R1, polarization capacitor C1, diffusion resistor R2, diffusion capacitor C2, and fractional order m and n in the fractional order 2 equivalent circuit model, and obtains the identified polarization resistor R1, polarization capacitor C1, diffusion resistor R2, diffusion capacitor C2, and fractional order m and n.

[0101] Furthermore, the adaptive genetic algorithm specifically comprises:

[0102] The initial population size is determined, the fitness of individuals is evaluated, and it is determined whether they meet the set fitness function. If the condition is met, the optimal solution for the parameters to be identified is obtained. If not, the crossover and mutation probabilities of individuals that are close to the set conditions are adaptively adjusted. Then, individuals with higher fitness are selected, and these individuals are used to form a new population through crossover and mutation operations. Their fitness is re-evaluated, and the iteration continues until the fitness function is met, thus obtaining the optimal solution for the parameters.

[0103] In this embodiment of the invention, the adaptive genetic algorithm is configured as follows: the initial population size is 200, the crossover probability is 0.5, and the mutation probability is 0.05. This invention uses the adaptive genetic algorithm to identify parameters of the constructed fractional-order second-order equivalent circuit model. The aim is to find an optimal solution that minimizes the difference between the model's predicted terminal voltage and the experimentally measured terminal voltage while meeting the requirements. For this optimization problem, an optimization objective and a fitness function are constructed, which are as follows:

[0104]

[0105]

[0106] Where VJ(i) is the sum of squared terminal voltage errors of the current individual across N data points; N is the length of the data used; M is the current population size; U o The terminal voltage measured in the experiment; U r VJ is the terminal voltage predicted by the equivalent circuit model. max is the maximum value of VJ in the population; J(i) is the fitness of the i-th sample.

[0107] The model established in this experiment was used to predict the terminal voltage, and the results are as follows: Figure 6 As shown, the true value is U. o The estimated value is U r .

[0108] Furthermore, step 5 specifically includes the following steps:

[0109] Step 5.1 Initialization: Set the initial values ​​of the actual values ​​of the state variables x0, the initial values ​​of the process noise covariance Q0, and the initial values ​​of the error covariance matrix P0, k=1:

[0110] For illustrative purposes and not for limitation, the following is further provided: The initial value can be adjusted as needed;

[0111] Step 5.2: Based on the identified parameters, estimate the state variables and observed variables in the state-space equations of the fractional-order second-order equivalent circuit model, as shown in the following expressions:

[0112]

[0113] in, Represents the prior estimates of the state and observed variables at time k; intermediate variables R1 and C1 are polarization resistors and capacitors, R2 and C2 are diffusion resistors and capacitors, and T... s Q is the sampling interval. r Let m and n be the rated capacity of the battery, respectively; I(k-1) and I(k) be the currents at times k-1 and k, respectively. N is the length of the data used; R represents the coefficients of the Newton-Binomial equation; R0 is the internal resistance of the Ohm.

[0114] Step 5.3: Estimate the error covariance matrix:

[0115] The difference between the actual value of the state variable at time k and the prior estimate of the state variable is the state variable estimation error.

[0116]

[0117] In the formula, x k The actual value of the state variable at time k; The difference between the actual value of the state variable at time k and the prior estimate of the state variable is called the state variable estimation error.

[0118] Based on the estimation error of the state variables, the error covariance matrix is ​​estimated:

[0119]

[0120] In the formula, P kk-1 P is the prior estimate of the error covariance matrix at time k; k-1 Q is the error covariance matrix at time k-1; k-1 The process noise covariance at time k-1; T represents the expected operation; T represents the transpose.

[0121] Step 5.4: Determine the Kalman gain based on the prior estimate of the error covariance matrix.

[0122] K k =P kk-1 C T (CP kk-1 C T +R k-1 ) -1

[0123] In the formula, K k R is the Kalman gain at time k;k Let k be the measurement noise covariance at time k;

[0124] Step 5.5: Determine the multiple innovation gain matrix based on the Kalman gain:

[0125] K(p,k)=[K k K k-1 …K k+1-p ] T

[0126] In the formula, K(p,k) is the multiple innovation gain matrix; p is the innovation length;

[0127] Step 5.6: Determine the multi-innovation matrix:

[0128] The difference between the actual value of the observed variable at time k and the prior estimate of the observed variable is the estimation error of the observed variable.

[0129]

[0130] In the formula, y k Let k be the actual value of the observed variable at time k; The difference between the actual value of the observed variable at time k and the prior estimate of the observed variable is called the estimation error of the observed variable.

[0131] Based on the estimation error of the observed variables, the multiple innovation matrix is ​​determined as follows:

[0132]

[0133] In the formula, E(p,k) is the multi-innovation matrix.

[0134] Step 5.7: Based on the multiple innovation gain matrix and the multiple innovation matrix, update the prior estimates of the state variables, observation variables, and error covariance matrix to obtain the posterior estimates:

[0135]

[0136] in, P represents the posterior estimates of the state and observed variables at time k; k is the posterior estimate of the error covariance matrix; is the forgetting factor matrix, defined as:

[0137] a = diag(λ1, λ2, ..., λ p )

[0138]

[0139] in, This represents the historical data forgetting rate, which ranges from 0 to 1.

[0140] Step 5.8: Based on the prior estimates of the Kalman gain and error covariance matrix, adaptively adjust the measurement noise covariance R. k With process noise covariance Q k :

[0141]

[0142] Among them, F k The variance is used to estimate the real-time information; G is the length of the sliding data window; Q is the variance. k R is the process noise covariance at time k; k Let k be the measurement noise covariance at time k;

[0143] Step 5.9: Let k = k + 1, repeat steps 5.2-5.8 until k equals the data length, and output all posterior estimates.

[0144] The overall process of the F-FOMIAEKF algorithm for predicting the state of charge of lithium-ion batteries is as follows: Figure 7 As shown.

[0145] Furthermore, it also includes S6, which includes: accurately estimating the SOC under various operating conditions and wide temperature ranges.

[0146] Step 6 specifically includes the following steps:

[0147] Step 6.1: Conduct HPPC, DST, and FUDS tests under low-temperature conditions (1℃). The SOC prediction results obtained using the F-FOMIAEKF proposed in this invention, compared with traditional EKF, AEKF, and FOEKF, are as follows: Figure 8 As shown in (a), (b), and (c), the SOC prediction error is as follows: Figure 8 As shown in (d), (e), and (f).

[0148] Step 6.2: Under normal temperature conditions (24℃), HPPC, DST, and FUDS operating conditions were tested respectively. The SOC prediction results obtained by comparing the F-FOMIAEKF proposed in this invention with the traditional EKF, AEKF, and FOEKF are as follows: Figure 9 As shown in (a), (b), and (c), the SOC prediction error is as follows: Figure 9 As shown in (d), (e), and (f).

[0149] Step 6.3: Under high temperature conditions (43℃), HPPC, DST, and FUDS tests were conducted respectively. The SOC prediction results obtained by comparing the F-FOMIAEKF proposed in this invention with those of the traditional EKF, AEKF, and FOEKF are as follows: Figure 10As shown in (a), (b), and (c), the SOC prediction error is as follows: Figure 10 As shown in (d), (e), and (f).

[0150] Step 6.4: Conduct experimental analysis on the prediction results:

[0151] Compared to the EKF algorithm, the SOC predicted by FOEKF is closer to the reference value (true value). The fractional-order model demonstrates better historical data utilization than the integer-order model, thus improving the accuracy of its SOC prediction. Under wide temperature and multi-condition working conditions, the SOC predicted by the AEKF algorithm shows better accuracy, with its maximum error being smaller than that predicted by the basic EKF algorithm. The AEKF algorithm allows noise statistics to adaptively adjust as the estimation results change, thereby reducing the impact of noise information on the entire prediction process. After introducing multiple innovation theory, the accuracy of the algorithm is further improved. The proposed F-FOMIAEKF algorithm shows better convergence than other algorithms. The forgetting factor reduces the impact of data accumulation interference on the prediction results by automatically adjusting the weights of new and old historical data.

[0152] In summary, although temperature and operating conditions can affect the accuracy of SOC estimation for lithium-ion batteries, the algorithm proposed in this invention still demonstrates high accuracy in the SOC estimation process. Compared with the other three basic algorithms, this algorithm is more accurate in predicting the SOC of lithium-ion batteries over a wide temperature range and under multiple operating conditions, and the error value is always stable within a certain range, fully verifying its excellent adaptability to a wide temperature range and multiple operating conditions.

[0153] According to a second aspect of the present invention, a lithium-ion battery state-of-charge (SOC) estimation system based on F-FOMIAEKF multi-condition wide-temperature model is provided, comprising modules of the lithium-ion battery SOC estimation method based on F-FOMIAEKF multi-condition wide-temperature model described in any one of the above embodiments, specifically comprising: a first module, used to obtain current, voltage, and capacity values ​​under multi-condition wide-temperature model through experiments; wherein the multi-condition model includes at least a first condition and a second condition; a second module, used in step 2, to calculate a SOC reference value based on the capacity value under the first condition wide-temperature model; after the first condition wide-temperature experiment, selecting the voltage value at the instant the lithium-ion battery is placed, obtaining a total of W voltage values, and correspondingly selecting the corresponding SOC reference value, and then... This constructs a dataset containing W sets of data points; then, based on the dataset of W sets of data points, a polynomial fitting method is used to derive the OCV-SOC relationship; the third module is used to establish a fractional-order second-order equivalent circuit model of the lithium-ion battery; based on the fractional-order second-order equivalent circuit model of the lithium-ion battery, the state-space equation of the fractional-order second-order equivalent circuit model of the lithium-ion battery is established; the fourth module is used to identify the parameters to be identified in the fractional-order second-order equivalent circuit model of the lithium-ion battery; the fifth module is used to construct a SOC estimation algorithm; under different operating conditions and wide temperatures, based on the identified parameters, the SOC estimation algorithm is used to estimate the state variables and observed variables in the state-space equation of the fractional-order second-order equivalent circuit model to obtain the SOC estimate. As used above, the term "module" can be a combination of software and / or hardware that implements a predetermined function. For parts of each module not described in detail, please refer to the relevant descriptions in this embodiment.

[0154] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for estimating the state of charge of lithium-ion batteries under multiple operating conditions and wide temperature ranges based on F-FOMIAEKF, characterized in that, Includes the following steps: Step 1: Build an experimental platform and obtain current, voltage, and capacity values ​​under multiple operating conditions and wide temperatures through experiments; The multiple operating conditions include at least the first operating condition and the second operating condition; Step 2: Calculate the SOC reference value based on the capacity value under the first operating condition with a wide temperature range; After the first operating condition wide temperature test, the voltage value of the lithium-ion battery at the moment of the end of the storage was selected, and a total of W voltage values ​​were obtained. Corresponding SOC reference values ​​were selected to construct a dataset containing W sets of data points. Then, based on the dataset of W sets of data points, the relationship between OCV and SOC was derived using the polynomial fitting method. Step 3: Establish a fractional-order second-order equivalent circuit model of a lithium-ion battery; based on the fractional-order second-order equivalent circuit model of a lithium-ion battery, establish the state-space equations of the fractional-order second-order equivalent circuit model of a lithium-ion battery. Step 4: Identify the parameters to be identified in the fractional-order second-order equivalent circuit model of the lithium-ion battery. Step 5: Construct the SOC estimation algorithm; Under different operating conditions and wide temperatures, based on the identified parameters, use the SOC estimation algorithm to estimate the state variables and observed variables in the state space equation of the fractional-order second-order equivalent circuit model to obtain the SOC estimate. Step 4 specifically includes the following steps: Step 4.1: After the first operating condition with a wide temperature range, calculate the ohmic internal resistance for each pulse discharge under the first operating condition. Average the calculated ohmic internal resistances for all pulse discharges to obtain the identified ohmic internal resistance. ; Step 4.2: Based on the adaptive genetic algorithm, analyze the polarization resistor in the fractional-order second-order equivalent circuit model. Polarized capacitors diffusion resistance diffusion capacitance Fractional order and Identification is performed to obtain the identified polarization resistance. Polarized capacitors diffusion resistance diffusion capacitance Fractional order and ; Step 5 specifically includes the following steps: Step 5.1: Initialize the initial values ​​of the actual values ​​of the state variables, the initial values ​​of the process noise covariance, and the initial values ​​of the error covariance matrix. =1: Step 5.2: Based on the identified parameters, estimate the state variables and observation variables in the state space equation of the fractional-order second-order equivalent circuit model to obtain the prior estimates of the state variables and observation variables at time k. Step 5.3, based on The state variable estimation error at time step is obtained by estimating the error covariance matrix. The prior estimate of the error covariance matrix at time t; where, The difference between the actual value of the state variable at time t is the state variable estimation error; Step 5.4, based on The prior estimate of the error covariance matrix at time t is determined. Kalman gain at time step; Step 5.5, based on The Kalman gain at time 1 determines the multiple innovation gain matrix; Step 5.6, based on The estimation error of the observed variables at time t is used to determine the multiple innovation matrix; where, The difference between the actual value of the observed variable at time t is the estimation error of the observed variable. Step 5.7: Based on the multiple innovation gain matrix and the multiple innovation matrix, update the prior estimates of the state variables, observation variables, and error covariance matrix to obtain the posterior estimates: Step 5.8: Adaptive adjustment of measurement noise covariance Covariance of process noise : Step 5.9, let Repeat steps 5.2-5.8 until... Given a data length equal to the given length, output all posterior estimates.

2. The method for estimating the state of charge of lithium-ion batteries under multiple operating conditions and wide temperature ranges based on F-FOMIAEKF as described in claim 1, characterized in that, The multi-condition system also includes a third condition.

3. The method for estimating the state of charge of lithium-ion batteries under multiple operating conditions and wide temperature ranges based on F-FOMIAEKF as described in claim 1, characterized in that, The relationship between OCV and SOC is as follows: ； in, Indicates open-circuit voltage; This represents the battery state of charge value; p0-p8 are the fitting coefficients.

4. The method for estimating the state of charge of lithium-ion batteries under multiple operating conditions and wide temperature ranges based on F-FOMIAEKF according to claim 1, characterized in that, Step 3 specifically involves: Based on circuit principles, a fractional-order second-order equivalent circuit model of a lithium-ion battery is established using the definition of fractional-order calculus in GL. The fractional-order second-order equivalent circuit model of the lithium-ion battery includes loop state equations and observation equations. Based on the fractional-order second-order equivalent circuit model of a lithium-ion battery, the state-space equation of the fractional-order second-order equivalent circuit model of a lithium-ion battery is established, and the expression is: ； Where: state variables ; intermediate variables ; For the resistor in the fractional second-order equivalent circuit model and capacitor The voltage across the two ends; For the resistor in the fractional second-order equivalent circuit model and capacitor The voltage across the two ends; The state of charge of the battery at time k; The sampling interval; These are the fractional order and the order of the product. , For polarization resistors and capacitors, , For diffusion resistors and capacitors; The internal resistance is ohmic; Represents the input to the model; express The observed variable values ​​corresponding to the state at any given time; Represents the vector of differential order; hour, It is a fractional derivative; hour, ; hour, It is a fractional integral; This indicates the open-circuit voltage.

5. A lithium-ion battery state-of-charge estimation system based on F-FOMIAEKF under multiple operating conditions and wide temperature range, characterized in that, The system includes a module that implements the lithium-ion battery state-of-charge estimation method based on F-FOMIAEKF under multiple operating conditions and wide temperature range as described in any one of claims 1-4.

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