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

Abstract

The invention discloses a lithium ion battery state-of-charge estimation method based on F-FOMIAEKF multi-working-condition wide temperature, and the method comprises the steps: calculating an SOC reference value according to a capacity value at a first working condition wide temperature; after the first working condition wide temperature experiment, constructing a data set containing W groups of data points, and deducing an OCV-SOC relational expression by using a polynomial fitting method; establishing a lithium ion battery fractional order second-order equivalent circuit model and a state-space equation; identifying parameters to be identified in the model; and under different working condition wide temperatures, state variables and observation variables in a state-space equation of the fractional-order second-order equivalent circuit model are estimated by adopting an SOC estimation algorithm according to the identified parameters, and an SOC estimation value is obtained. On one hand, a fractional order model is introduced; on the other hand, a filter updating process in the whole estimation process is optimized by introducing a multi-information theory, and in addition, an estimation algorithm is optimized by updating statistical characteristics of process noise and measurement noise in real time by introducing an adaptive theory, so that the accuracy and the stability of SOC estimation are improved.

Description

Technical Field

[0001] The invention relates to a method for estimating the state of charge of a lithium ion battery under multiple working conditions and wide temperatures based on F-FOMIAEKF, and belongs to the technical field of lithium ion batteries. Background Art

[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 have become the main battery type for new energy vehicles due to their high safety performance, wide temperature adaptability, high operating voltage and no memory effect. In the battery management system (BMS), the state of charge (SOC) estimation of lithium-ion batteries is an extremely critical link, and its importance is comparable to the oil level indicator in traditional fuel vehicles. It plays a pivotal role in improving the energy distribution strategy of the whole vehicle, improving the capacity utilization efficiency and energy utilization efficiency of the power battery, effectively preventing the battery from being overcharged and over-discharged, ensuring the safety of the power battery and extending the service life of the power battery.

[0003] As a highly complex time-varying nonlinear system, the SOC of lithium-ion batteries cannot be measured directly, and it needs to be estimated through the measured current, voltage and other physical quantities. SOC estimation methods include: ampere-hour integration method, open circuit voltage method, discharge test method, filtering method, model method and data-driven method. The model-based method requires building a lithium-ion battery model, and taking the battery SOC as the state to be estimated in the model, and then designing an algorithm to estimate it. Compared with other methods, it has the advantages of low computational complexity and good real-time performance, and is the first choice for SOC estimation.

[0004] The current mainstream model is the equivalent circuit model, whose order is mostly integer. The ideal capacitor elements in the integer-order model cannot fully reflect the complex dynamic behavior of lithium-ion batteries in the actual charging and discharging process. The internal processes of lithium-ion batteries, such as charge diffusion, embedding and de-embedding, all show more complex fractional-order characteristics, which are difficult to accurately reflect in integer-order models. At the same time, traditional hyperparameter optimization algorithms require multiple iterations, which not only prolongs the convergence time but also increases the amount of calculation in the process of further research and in-depth analysis. In addition, the estimation of the SOC of lithium-ion batteries under abnormal temperature and abnormal charging and discharging conditions has not been verified.

[0005] How to solve the above technical problems is the subject faced by the present invention. Summary of the invention

[0006] The purpose of the present invention is to provide a lithium-ion battery state of charge estimation method under multiple working conditions and wide temperatures based on F-FOMIAEKF. On the one hand, the method introduces a fractional order model; on the other hand, it introduces multi-innovation theory to optimize the filter update process in the entire estimation process. In addition, the 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 the present 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 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 temperatures through experiments; wherein the multiple operating conditions include at least the first operating condition and the second operating condition;

[0010] Step 2, according to the capacity value under the first wide temperature condition, calculate the SOC reference value; after the first wide temperature condition experiment, select the voltage value of the lithium-ion battery at the moment of the end of the shelf life, obtain a total of W voltage values, and select the corresponding SOC reference value, thereby constructing a data set containing W groups of data points; then, based on the data set of W groups of data points, use the polynomial fitting method to derive the OCV-SOC relationship;

[0011] Step 3, establishing a fractional second-order equivalent circuit model of a lithium-ion battery; based on the fractional second-order equivalent circuit model of a lithium-ion battery, establishing a state space equation of the fractional second-order equivalent circuit model of a lithium-ion battery;

[0012] Step 4, identifying the parameters to be identified in the fractional second-order equivalent circuit model of the lithium-ion battery;

[0013] Step 5, construct an SOC estimation algorithm; under different operating conditions and wide temperatures, use the SOC estimation algorithm 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 to obtain the SOC estimation value.

[0014] Furthermore, the multiple operating conditions also include a third operating condition.

[0015] Furthermore, the OCV-SOC relationship 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 open circuit voltage; SOC represents the battery state of charge; p0-p8 are fitting coefficients.

[0018] Furthermore, the step 3 is specifically as follows:

[0019] According to the circuit principle, a fractional second-order equivalent circuit model of a lithium-ion battery is established by using the GL fractional calculus definition, wherein the fractional second-order equivalent circuit model of a lithium-ion battery includes a loop state equation and an observation equation;

[0020] According to the fractional second-order equivalent circuit model of lithium-ion batteries, the state space equation of the fractional second-order equivalent circuit model of lithium-ion batteries is established, and the expression is:

[0021]

[0022] Where: state variable Intermediate variables D = -R0; U1(k) is the voltage across the resistor R1 and capacitor C1 in the fractional 2nd order equivalent circuit model; U2(k) is the voltage across the resistor R2 and capacitor C2 in the fractional 2nd order equivalent circuit model; SOC k is the battery charge state at time k; T s is the sampling interval; m and n are fractional orders respectively; R1 and C1 are polarization resistance and capacitance, R2 and C2 are diffusion resistance and capacitance; R0 is the ohmic internal resistance; u(k-1) represents the input of the model; y(k) represents the observed variable value of the state corresponding to time k; a=[m,n,0] represents the differential order vector; when a>0, is a fractional differential; when a=0, When a<0, is the fractional integral; U OCV (SOC) stands for open circuit voltage.

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

[0024] Step 4.1, after the first operating condition reaches a wide temperature, the ohmic internal resistance is calculated for each pulse discharge under the first operating condition, and the ohmic internal resistance calculated under all pulse discharges is averaged to obtain the identified ohmic internal resistance R0;

[0025] Step 4.2, according to the adaptive genetic algorithm, the polarization resistance R1, polarization capacitance C1, diffusion resistance R2, diffusion capacitance C2, fractional order m and n in the fractional-order 2nd-order equivalent circuit model are identified to obtain the identified polarization resistance R1, polarization capacitance C1, diffusion resistance R2, diffusion capacitance C2, fractional order m and n.

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

[0027] Step 5.1, initialize the actual value of the state variable, the initial value of the process noise covariance and the initial value 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 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 estimation value of the error covariance matrix at time k; wherein, the difference between the actual value of the state variable at time k and the prior estimation value 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 multi-innovation gain matrix based on the Kalman gain at time k;

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

[0033] Step 5.7: Update the prior estimates of the state variables, observation variables, and error covariance matrix based on the multi-innovation gain matrix and the multi-innovation matrix to obtain the posterior estimates:

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

[0035] Step 5.9, let k = k + 1, repeat steps 5.2-5.8 until k is equal to the data length, and output all posterior estimation values.

[0036] According to a second aspect of the present invention, a lithium-ion battery state of charge estimation system based on F-FOMIAEKF multi-operating conditions and wide temperature is provided, comprising a module of any one of the above-mentioned lithium-ion battery state of charge estimation methods based on F-FOMIAEKF multi-operating conditions and wide temperature.

[0037] The beneficial effects of the present invention are:

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

[0039] (2) Based on the original Kalman filter algorithm, the present invention proposes a method for adaptively adjusting process noise and measurement noise, so that the model can better adapt to the uncertainty in the battery charging and discharging process and improve the robustness of state estimation. At the same time, it incorporates the multi-innovation theory and improves the accuracy and stability of state estimation by optimizing the update process of the filter.

[0040] (3) The present invention innovatively introduces a forgetting factor into the estimation algorithm to achieve the purpose of improving data utilization. By adjusting the value of the forgetting factor, the influence of historical information in state estimation is controlled. In the modeling and state estimation of lithium-ion batteries, since battery performance gradually declines with the increase of usage time, the importance of historical information will gradually decrease. By introducing the forgetting factor, the algorithm can pay more attention to recent observation information, thereby improving the real-time and accuracy of state estimation.

[0041] (4) The SOC estimation algorithm of the present invention not only has excellent estimation accuracy under normal temperature and normal charging and discharging conditions, but can also effectively estimate the SOC under low temperature, high temperature and abnormal charging and discharging conditions. The algorithm is highly robust, has great engineering value, and has broad practical application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] 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.

[0043] Figure 1 It is a lithium-ion battery charging and discharging experimental platform of the present invention;

[0044] Figure 2 The battery discharge conditions under different temperature conditions of the present invention;

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

[0046] Figure 4 It is the local amplification curve of the terminal voltage of the pulse discharge experiment at 24°C of the present invention;

[0047] Figure 5 This is the basic process of the adaptive genetic algorithm of the present invention;

[0048] Figure 6 The terminal voltage of the lithium-ion battery predicted by the present invention;

[0049] Figure 7 The SOC estimation process of F-FOMIAEKF of the present invention;

[0050] Figure 8 This is the prediction result of the present invention under different working conditions at 1°C;

[0051] Fig. 9 The prediction results of the present invention under different working conditions at 24°C;

[0052] Fig.10 These are the prediction results of the present invention under different working conditions at 43°C. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. It should be noted that the embodiments in this application and the features in the embodiments can be combined with each other arbitrarily without conflict.

[0054] Considering that the integer-order model cannot fully reflect the internal state of the battery, the constant phase element CPE is used instead of the ideal capacitor to establish a fractional-order model. The fractional-order model can more accurately describe the dynamic behavior and performance characteristics of the lithium-ion battery while enhancing the storage capacity of historical data; the multi-new information theory is introduced to optimize the filter update process in the entire estimation process. In addition, the adaptive theory is introduced to optimize the estimation algorithm by updating the statistical characteristics of the process noise and the measurement noise in real time, thereby improving the accuracy and stability of the SOC estimation; to ensure efficient use of data, a forgetting factor is added to the estimation algorithm, which can improve the accuracy of the algorithm by adjusting the ratio of new and old data. The three improvements are combined to propose a multi-new information adaptive extended Kalman filter algorithm based on a fractional-order second-order model with a forgetting factor. The estimation results are accurate under multiple working conditions and a wide temperature range, and the algorithm has high robustness. The embodiments of the present invention are described below in conjunction with the accompanying drawings:

[0055] like Figure 1-Figure 10As shown, according to a first aspect of an embodiment of the present invention, a method for estimating the state of charge of a lithium-ion battery under multiple operating conditions and wide temperature 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 a wide temperature through experiments; wherein the multiple operating conditions include at least a first operating condition and a second operating condition; further, the multiple operating conditions also include a third operating condition.

[0057] Step 2, according to the capacity value under the first wide temperature condition, calculate the SOC reference value; after the first wide temperature condition experiment, select the voltage value of the lithium-ion battery at the moment of the end of the shelf life, obtain a total of W voltage values, and select the corresponding SOC reference value, thereby constructing a data set containing W groups of data points; then, based on the data set of W groups of data points, use the polynomial fitting method to derive the OCV-SOC relationship;

[0058] Step 3, establishing a fractional second-order equivalent circuit model of a lithium-ion battery; based on the fractional second-order equivalent circuit model of a lithium-ion battery, establishing a state space equation of the fractional second-order equivalent circuit model of a lithium-ion battery;

[0059] Step 4, identifying the parameters to be identified in the fractional second-order equivalent circuit model of the lithium-ion battery;

[0060] Step 5. Construct a SOC estimation algorithm of a multi-information adaptive extended Kalman filter (F-FOMIAEKF) with forgetting factor. Under different operating conditions and wide temperatures, use the SOC estimation algorithm of F-FOMIAEKF to estimate the state variables and observation variables in the state space equation of the fractional second-order equivalent circuit model according to the identified parameters to obtain the SOC estimation value.

[0061] Furthermore, the step 1 is specifically as follows:

[0062] Step 1.1, build the experimental platform;

[0063] Specifically: The present invention is constructed by a BTS battery detection system, a high and low temperature change test box, a host and a lithium ion battery. Figure 1 The experimental platform shown uses 18650 lithium-ion batteries with a rated capacity of 2000mAh. In specific operations, three groups of temperatures are set through the high and low temperature test box (three groups of temperatures are set at 1°C, 24°C, and 43°C during specific operations. During the actual experiment, the temperature displayed on the display screen of the high and low temperature test box will fluctuate within the set numerical error range).

[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 experiment is performed on the battery under a wide temperature condition in a discharge state to obtain the following Figure 2 The relationship between the battery terminal voltage and capacity under the three sets of temperature conditions is shown in the figure. It can be seen from the figure that the capacity of the battery under the three sets of temperature conditions meets the rated capacity. The constant capacity experiment shows that the experimental platform constructed by the present invention is reliable.

[0066] Step 1.3: When it is verified that the capacity of the battery meets the rated capacity, different operating conditions are selected for experiments under wide temperature conditions to obtain the current, voltage and capacity values ​​under multiple operating conditions and wide temperature.

[0067] In an embodiment of the present invention, the battery in the experimental platform is subjected to HPPC working conditions, cyclic dynamic stress test (DST) working conditions and Federal Urban Driving Schedule (FUDS) working conditions at 1°C, 24°C and 43°C respectively, and different current and voltage values ​​under wide temperature and multi-working conditions are obtained through experiments.

[0068] The HPPC operating condition is the first operating condition, the cyclic dynamic stress test (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] Furthermore, the step 2 is specifically as follows: according to the capacity value under the first operating condition wide temperature, the SOC reference value is calculated by the ampere-hour integration method; after the first operating condition wide temperature experiment, the voltage value of the lithium-ion battery at the moment of the end of the shelving is selected, a total of W voltage values ​​are obtained, and the corresponding SOC reference value is selected accordingly, thereby constructing a data set containing W groups of data points; then, based on the data set of W groups of data points, the OCV-SOC relationship is derived using a polynomial fitting method.

[0070] Specifically: During the first working condition HPPC experiment, the terminal voltage of lithium-ion batteries will slowly rise during the standby stage after constant current charging and discharging due to the dual effects of internal polarization effect and hysteresis effect. For this reason, the voltage value at the moment of standby is specially selected, a total of 11 voltage values ​​are obtained, and the corresponding SOC reference value is selected accordingly, thereby constructing a data set containing 11 groups of data points; then, the polynomial fitting method is used to derive the OCV-SOC relationship:

[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 open circuit voltage; SOC represents the battery state of charge; p0-p8 are fitting coefficients.

[0073] The open circuit voltage OCV of the battery changes monotonically with the SOC. When the ambient temperature remains unchanged, the OCV-SOC relationship curve of the same type of battery under different working conditions remains basically unchanged. In the embodiment of the present invention, the same relationship curve is used for different working conditions at the same temperature. The specific fitting coefficients at different temperatures are given in Table 1 below:

[0074] Table 1

[0075]

[0076] Furthermore, the step 3 is specifically as follows:

[0077] According to the circuit principle, the GL fractional calculus definition is used to establish a fractional second-order equivalent circuit model for lithium-ion batteries. The model schematic diagram is shown in the figure. Figure 3 As shown, the equivalent circuit model includes a loop state equation and an observation equation;

[0078] The loop state equation expression is:

[0079]

[0080] The observation equation expression is:

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

[0082] Among them, SOC k is the battery charge state at time k; T s is the sampling interval; Q r is the rated capacity of the battery; m and n are the fractional order numbers respectively; I(k) is the current at time k; U1(k) is the voltage across the resistor R1 and the capacitor C1 in the fractional 2nd order equivalent circuit model; U2(k) is the voltage across the resistor R2 and the capacitor C2 in the fractional 2nd order equivalent circuit model; U r is the voltage at the power supply end; R1 and C1 are polarization resistance and capacitance, R2 and C2 are diffusion resistance and capacitance; R0 is the ohmic internal resistance; U OCV (SOC) stands for open circuit voltage.

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

[0084]

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

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

[0087]

[0088] Among them, when n>0, is the fractional differential; when n=0, D t n =1; when n<0, is the fractional integral; Δt is the sampling interval, and [t / Δt] means rounding t / Δt; is the Newton binomial coefficient. When i=0, the Newton binomial coefficient is 1. When i>0, the Newton binomial coefficient is specifically expressed as:

[0089]

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

[0091]

[0092] The dynamic equation of the capacitor CPE in parallel with the resistor is:

[0093]

[0094] Wherein, when i=1, a=m; when i=2, a=n; m and n are the fractional order numbers respectively; I(k) is the current at time k; U1(k) is the voltage across the resistor R1 and the capacitor C1 in the fractional 2nd order equivalent circuit model; U2(k) is the voltage across the resistor R2 and the capacitor C2 in the fractional 2nd order equivalent circuit model; U r is the voltage at the power supply end; R1 and C1 are polarization resistance and capacitance, R2 and C2 are diffusion resistance and capacitance; R0 is the ohmic internal resistance.

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

[0096] Step 4.1, after the first operating condition reaches a wide temperature, the ohmic internal resistance is calculated for each pulse discharge under the first operating condition, and the ohmic internal resistance calculated under all pulse discharges is averaged to obtain the identified ohmic internal resistance R0;

[0097] Specifically: By conducting a hybrid power pulse characteristics (HPPC) experiment on the battery, specific discharge data can be obtained, such as Figure 4 This is the local amplification curve of the terminal voltage of a pulse discharge experiment at 24°C. Among them, the OA segment is the static stage. When the battery starts to discharge, the terminal voltage drops from point A to point B instantly. The discharge starts at time B. Point B to point C is the battery discharge stage. The terminal voltage drops from U to C instantly. A Descend to U B ; When the battery stops discharging, the terminal voltage changes from U C Instantly rise to U D , point D to point E is the battery storage stage; for each pulse discharge at 24°C and HPPC conditions, the ohmic internal resistance is calculated separately, and the expression is as follows:

[0098]

[0099] Wherein, the continuous discharge current I=2A; the HPPC working condition of the present invention has 10 pulse discharges, and the average value of the 10 calculation results according to the above formula is taken as the ohmic internal resistance value after identification.

[0100] Step 4.2: According to Figure 5 The adaptive genetic algorithm identifies the polarization resistance R1, polarization capacitance C1, diffusion resistance R2, diffusion capacitance C2, fractional order m and n in the fractional second-order equivalent circuit model to obtain the identified polarization resistance R1, polarization capacitance C1, diffusion resistance R2, diffusion capacitance C2, fractional order m and n.

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

[0102] Determine the initial population size, evaluate the fitness of the individuals, and determine whether they meet the set fitness function. If the conditions are met, the optimal solution for the parameters to be identified is obtained. If not, the hybridization and mutation probabilities of individuals close to the set conditions are adaptively adjusted, and then individuals with higher fitness are selected. These individuals are then formed into a new population through operations such as crossover and mutation, and their fitness is re-evaluated. Continue to iterate until the fitness function is met, thereby obtaining the optimal solution for the parameters.

[0103] In the embodiment of the present invention, the adaptive genetic algorithm is set as follows: the initial population size is 200, the crossover probability is 0.5, and the mutation probability is 0.05; the present invention uses the adaptive genetic algorithm to perform parameter identification on the constructed fractional-order second-order equivalent circuit model, with the aim of finding a set of optimal solutions that minimize the difference between the model prediction terminal voltage and the experimental measurement terminal voltage and meet the requirements, and constructs an optimization objective and a fitness function for this optimization problem, and the optimization problem and the fitness function are respectively:

[0104]

[0105]

[0106] Where VJ(i) is the sum of squares of the terminal voltage errors of the current individual within N data points; N is the length of the adopted data, M is the current population size; U o is the terminal voltage measured in the experiment; U r The terminal voltage predicted by the equivalent circuit model; VJ 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 is 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, the step 5 specifically includes the following steps:

[0109] Step 5.1, initialization: set the initial value x0 of the actual value of the state variable, the initial value Q0 of the process noise covariance and the initial value P0 of the error covariance matrix, k = 1:

[0110] For the purpose of illustration and not limitation, it is further given that: The initial value can be adjusted as needed;

[0111] Step 5.2: Based on the identified parameters, estimate the state variables and observation variables in the state space equation of the fractional second-order equivalent circuit model. The expression is as follows:

[0112]

[0113] in, Represents the prior estimates of state variables and observed variables at time k; intermediate variables R1 and C1 are polarization resistance and capacitance, R2 and C2 are diffusion resistance and capacitance, T s is the sampling interval, Q r is the rated capacity of the battery, m and n are the fractional order numbers respectively; I(k-1) and I(k) are the currents at time k-1 and k respectively; N is the length of the data used; represents the Newton binomial coefficient; R0 is the ohmic internal resistance;

[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 estimated value of the state variable is the state variable estimation error

[0116]

[0117] In the formula, x k is 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 estimated value of the state variable is called the state variable estimation error;

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

[0119]

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

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

[0125] K(p,k)=[K k K k-1 …K k+1-p ] T

[0126] Where K(p,k) is the multi-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 estimated value of the observed variable is the observed variable estimation error.

[0129]

[0130] In the formula, y k is 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 estimated value of the observed variable is called the observed variable estimation error;

[0131] According to the estimation error of the observed variables, the multi-innovation matrix is ​​determined as:

[0132]

[0133] Where E(p,k) is the multi-information matrix.

[0134] Step 5.7: Update the prior estimates of the state variables, observation variables, and error covariance matrix based on the multi-innovation gain matrix and the multi-innovation matrix to obtain the posterior estimates:

[0135]

[0136] in, represents the posterior estimated value of the state variable and observation variable at time k; P k is the posterior estimate of the error covariance matrix; a is the forgetting factor matrix, defined as:

[0137] a=diag(λ1,λ2,…,λ p )

[0138]

[0139] in, is the historical data forgetting rate, which takes a value between 0 and 1;

[0140] Step 5.8: Adaptively adjust the measurement noise covariance R according to the prior estimate of the Kalman gain and the error covariance matrix k and process noise covariance Q k :

[0141]

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

[0143] Step 5.9, let k = k + 1, repeat steps 5.2-5.8 until k is equal to the data length, and output all posterior estimation values.

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

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

[0146] The step 6 specifically includes the following steps:

[0147] Step 6.1: HPPC, DST and FUDS working conditions are tested under low temperature (1°C). The SOC prediction results obtained by the F-FOMIAEKF proposed in the present invention and the traditional EKF, AEKF and FOEKF are as follows: Figure 8 As shown in (a), (b), and (c), the SOC prediction error is Figure 8 As shown in (d), (e) and (f).

[0148] Step 6.2: HPPC, DST and FUDS working conditions are tested under normal temperature (24°C). The SOC prediction results obtained by the F-FOMIAEKF proposed in the present invention and the traditional EKF, AEKF and FOEKF are as follows: Fig. 9 As shown in (a), (b), and (c), the SOC prediction error is Fig. 9 As shown in (d), (e) and (f).

[0149] Step 6.3: HPPC, DST and FUDS working conditions are tested under high temperature (43°C). The SOC prediction results obtained by the F-FOMIAEKF proposed in the present invention and the traditional EKF, AEKF and FOEKF are as follows: Fig.10As shown in (a), (b), and (c), the SOC prediction error is Fig.10 As shown in (d), (e) and (f).

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

[0151] Compared with the EKF algorithm, the SOC predicted by FOOKF is closer to the reference value (true value), and the fractional-order model has better historical data utilization capabilities than the integer-order model, thereby improving the accuracy of its estimated SOC. The SOC predicted by the AEKF algorithm under wide temperature and multi-operating conditions shows better accuracy, and its maximum error is smaller than the SOC predicted by the basic EKF algorithm. The AEKF algorithm allows the noise statistical characteristics to be adaptively adjusted as the estimation results change, thereby reducing the impact of noise information on the entire prediction process. After introducing the multi-new information theory, the accuracy of the algorithm is further improved. The F-FOMIAEKF proposed in the present invention shows better convergence than other algorithms. The forgetting factor reduces the impact of data accumulation interference problems on the prediction results by automatically adjusting the weights of new and old historical data.

[0152] In summary, although temperature conditions and operating conditions will have a certain impact on the SOC estimation accuracy of lithium-ion batteries, the algorithm proposed in the present invention still shows a high accuracy in the SOC estimation process. Compared with the other three basic algorithms, this algorithm is more accurate in estimating the SOC of lithium-ion batteries under a wide temperature range and multiple operating conditions, and the error value is always stable within a certain range, which fully verifies its excellent wide temperature and multi-operating condition adaptability.

[0153] According to a second aspect of an embodiment of the present invention, a lithium-ion battery state of charge estimation system based on F-FOMIAEKF multi-conditions and wide temperature is provided, including a module of the lithium-ion battery state of charge estimation method based on F-FOMIAEKF multi-conditions and wide temperature as described in any one of the above, specifically including: a first module, used to obtain current, voltage, and capacity values ​​under multi-conditions and wide temperature through experiments; wherein the multi-conditions include at least the first condition and the second condition; a second module, used for step 2, calculating the SOC reference value according to the capacity value under the first condition and wide temperature; after the first condition and wide temperature experiment, selecting the voltage value of the lithium-ion battery at the moment of termination of the shelving, obtaining a total of W voltage values, and selecting the corresponding SOC reference value accordingly, by A data set containing W groups of data points is constructed; then, based on the data set of W groups of data points, the polynomial fitting method is used to derive the OCV-SOC relationship; the third module is used to establish a fractional second-order equivalent circuit model of a lithium-ion battery; based on the fractional second-order equivalent circuit model of a lithium-ion battery, the state space equation of the fractional second-order equivalent circuit model of a lithium-ion battery is established; the fourth module is used to identify the parameters to be identified in the fractional second-order equivalent circuit model of a lithium-ion battery; the fifth module is used to construct an SOC estimation algorithm; under different operating conditions and wide temperatures, the state variables and observation variables in the state space equation of the fractional second-order equivalent circuit model are estimated using the SOC estimation algorithm based on the identified parameters to obtain the SOC estimation value. As used above, the term "module" may be a combination of software and / or hardware that implements a predetermined function. For the parts not described in detail in each module, please refer to the relevant description of this embodiment.

[0154] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A method for estimating the state of charge of a lithium-ion battery under multiple operating conditions and wide temperature based on F-FOMIAEKF, characterized in that: The following steps are involved: Step 1: Build an experimental platform and obtain the current, voltage and capacity values ​​under multiple working conditions and wide temperatures through experiments; The multiple working conditions include at least a first working condition and a second working condition; Step 2, calculating the SOC reference value according to the capacity value under the first operating condition wide temperature; After the first wide temperature experiment, the voltage value of the lithium-ion battery at the moment of the end of the shelf life is selected, and a total of W voltage values ​​are obtained, and the corresponding SOC reference value is selected accordingly, thereby constructing a data set containing W groups of data points; then, based on the data set of W groups of data points, the polynomial fitting method is used to derive the OCV-SOC relationship; Step 3, establishing a fractional second-order equivalent circuit model of a lithium-ion battery; based on the fractional second-order equivalent circuit model of a lithium-ion battery, establishing a state space equation of the fractional second-order equivalent circuit model of a lithium-ion battery; Step 4, identifying the parameters to be identified in the fractional second-order equivalent circuit model of the lithium-ion battery; Step 5, construct an SOC estimation algorithm; under different operating conditions and wide temperatures, use the SOC estimation algorithm 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 to obtain the SOC estimation value.

2. The method for estimating the state of charge of a lithium-ion battery under multiple operating conditions and wide temperature based on F-FOMIAEKF according to claim 1, characterized in that: The multiple operating conditions also include a third operating condition.

3. The method for estimating the state of charge of a lithium-ion battery under multiple operating conditions and wide temperature based on F-FOMIAEKF according to claim 1, characterized in that: The OCV-SOC relationship is as follows: U OCV (SOC)=p8SOC 8 +p7SOC 7 +p6SOC 6 +p5SOC 5 +p4SOC 4 +p3SOC 3 +p2SOC 2 +p1SOC 1 +p0 Among them, U OCV (SOC) represents open circuit voltage; SOC represents the battery state of charge; p0-p8 are fitting coefficients.

4. The method for estimating the state of charge of a lithium-ion battery under multiple operating conditions and wide temperature based on F-FOMIAEKF according to claim 1, characterized in that: The step 3 is specifically as follows: According to the circuit principle, a fractional second-order equivalent circuit model of a lithium-ion battery is established by using the GL fractional calculus definition, wherein the fractional second-order equivalent circuit model of a lithium-ion battery includes a loop state equation and an observation equation; According to the fractional second-order equivalent circuit model of lithium-ion batteries, the state space equation of the fractional second-order equivalent circuit model of lithium-ion batteries is established, and the expression is: Where: state variable Intermediate variables D = -R0; U1(k) is the voltage across the resistor R1 and capacitor C1 in the fractional 2nd order equivalent circuit model; U2(k) is the voltage across the resistor R2 and capacitor C2 in the fractional 2nd order equivalent circuit model; SOC k is the battery charge state at time k; T s is the sampling interval; m and n are fractional orders respectively; R1 and C1 are polarization resistance and capacitance, R2 and C2 are diffusion resistance and capacitance; R0 is the ohmic internal resistance; u(k-1) represents the input of the model; y(k) represents the observed variable value of the state corresponding to time k; a=[m,n,0] represents the differential order vector; when a>0, is the fractional differential; when a=0, D k a =1; when a<0, is the fractional integral; U OCV (SOC) stands for open circuit voltage.

5. The method for estimating the state of charge of a lithium-ion battery under multiple operating conditions and wide temperature based on F-FOMIAEKF according to claim 1, characterized in that: The step 4 specifically includes the following steps: Step 4.1, after the first operating condition reaches a wide temperature, the ohmic internal resistance is calculated for each pulse discharge under the first operating condition, and the ohmic internal resistance calculated under all pulse discharges is averaged to obtain the identified ohmic internal resistance R0; Step 4.2, according to the adaptive genetic algorithm, the polarization resistance R1, polarization capacitance C1, diffusion resistance R2, diffusion capacitance C2, fractional order m and n in the fractional-order 2nd-order equivalent circuit model are identified to obtain the identified polarization resistance R1, polarization capacitance C1, diffusion resistance R2, diffusion capacitance C2, fractional order m and n.

6. The method for estimating the state of charge of a lithium-ion battery under multiple operating conditions and wide temperature based on F-FOMIAEKF according to claim 1, characterized in that: The step 5 specifically includes the following steps: Step 5.1, initialize the actual value of the state variable, the initial value of the process noise covariance and the initial value of the error covariance matrix, k = 1: Step 5.2, based on the identified parameters, estimate the state variables and observation variables in the state space equation of the fractional 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 k, estimate the error covariance matrix to obtain the prior estimation value of the error covariance matrix at time k; wherein, the difference between the actual value of the state variable at time k and the prior estimation value of the state variable is the state variable estimation error; Step 5.4, determine the Kalman gain at time k based on the prior estimate of the error covariance matrix at time k; Step 5.5, determine the multi-innovation gain matrix based on the Kalman gain at time k; Step 5.6: Determine the multi-innovation matrix based on the estimation error of the observed variable at time k; the difference between the actual value of the observed variable at time k and the prior estimated value of the observed variable is the estimation error of the observed variable; Step 5.7: Update the prior estimates of the state variables, observation variables, and error covariance matrix based on the multi-innovation gain matrix and the multi-innovation matrix to obtain the posterior estimates: Step 5.8: Adaptively adjust the measurement noise covariance R k and process noise covariance Q k : Step 5.9, let k = k + 1, repeat steps 5.2-5.8 until k is equal to the data length, and output all posterior estimation values.

7. A lithium-ion battery state of charge estimation system based on F-FOMIAEKF under multiple working conditions and wide temperature, characterized in that: A module comprising the method for estimating the state of charge of a lithium-ion battery under multiple operating conditions and wide temperatures based on F-FOMIAEKF as described in any one of claims 1 to 5.

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