A SOC-SOH joint estimation method based on lithium battery model and fractional order theory

Abstract

The invention discloses a SOC-SOH joint estimation method based on a lithium battery model and fractional-order theory, the method comprising: first, establishing a lithium battery ECM, and adaptively optimizing the error covariance of an EKF, constructing an AEKF algorithm, and providing a lithium battery SOC estimation process; then using fractional-order calculus theory to realize the conversion of the RC series module of the ECM to a fractional-order module, establishing a lithium battery fractional-order model, proposing the time from 20% SOC to the end of constant-current charging and the lithium battery fractional-order model parameters as health factors, designing a fuzzy controller to identify the fractional-order model parameters, and using a sparrow search algorithm (SSA) to optimize a back propagation neural network (BPNN), and establishing a lithium battery SOH estimation model based on SSA-BPNN. The invention has the beneficial effects of small error and good accuracy.

Description

Technical Field

[0001] The invention relates to the technical field of lithium battery formation prediction, and in particular to a SOC-SOH joint estimation method based on a lithium battery model and fractional order theory. Background Art

[0002] The state of charge (SOC) and state of health (SOH) of lithium batteries are key state variables that reflect the operating characteristics of the system. SOC is defined as the ratio of the current capacity of the battery to the maximum capacity, reflecting the amount of charge currently stored in the battery. Accurate estimation of the SOC of lithium batteries helps to improve energy utilization and prevent overcharging and over-discharging; SOH is usually defined by the current maximum capacity or internal resistance, reflecting the aging state of the battery over its entire life cycle. Accurate estimation of the SOH of lithium batteries is conducive to timely warning of the system and ensuring long-term safe operation.

[0003] There is a coupling relationship between the SOH and SOC of lithium batteries. When the capacity defines SOH, as the SOH decreases, the maximum capacity of the lithium battery changes. If the capacity parameters are not corrected, the SOC estimation result will be biased. At present, the estimation of lithium battery SOC based on the equivalent circuit model (ECM) and KF algorithm has been well applied, but the AC impedance analysis under offline conditions and the insufficient fitting accuracy limit the application of ECM in the online estimation method of lithium battery SOH. Summary of the invention

[0004] The purpose of the present invention is to solve the above problems and to design a SOC-SOH joint estimation method based on a lithium battery model and fractional order theory.

[0005] A SOC-SOH joint estimation method based on a lithium battery model and fractional order theory, the method comprising the following steps:

[0006] Step 1: Construct a lithium battery equivalent circuit model (ECM). In the lithium battery equivalent circuit model, U oc is the battery open circuit voltage, I is the battery charge and discharge current, R L , C L are the electrochemical polarization resistance and polarization capacitance, R S , C S are concentration polarization resistance and polarization capacitance respectively, U is the battery terminal voltage, R o is the equivalent internal resistance of the battery; according to the lithium battery equivalent circuit model, the state equation is constructed as formula (1) and the measurement equation is constructed as formula (2):

[0007]

[0008] U=Uoc (SOC)-U S -U L -R o I(k) (2)

[0009] Where: U S and U L R S and R L Terminal voltage, τ s and τ l The time constants R S C S and R L C L , Q c is the battery capacity, Δt is the sampling time, k is the discrete time,

[0010] The recursive least squares method with forgetting factor (FFRLS) is used to online identify the state equation and the resistance and capacitance parameters of the measurement equation, obtain the dynamic values ​​of the resistance and capacitance parameters, and improve the fitting accuracy of the ECM. The recursive formula of FFRLS is shown in formula (3):

[0011]

[0012] In the formula, θ is the coefficient vector to be determined, I e is the same type unit matrix, λ is the forgetting factor, is I and U from k-2 to k, K LS is the gain coefficient, P LS is the covariance matrix:

[0013] Step 2: Use the extended Kalman filter (EKF) algorithm to estimate the SOC of the lithium battery, and add the error covariance adaptive calculation to the recursive formula of the EKF algorithm. Use the battery terminal voltage measurement value and the model prediction value to calculate the mean square error, and calculate the dynamic error covariance according to the Kalman gain to construct an adaptive extended Kalman filter algorithm (AEKF) to estimate the SOC of the lithium battery, as follows:

[0014] Transform equations (1) and (2):

[0015] x k+1 =A k x k +B k u k +w (5)

[0016] y k =H k x k +C k u k +v (6)

[0017]

[0018] Among them: A k , B k , H k , C k are the state transfer matrix, input matrix, output matrix and feedforward matrix of the system respectively; x k ,y k are the state vector and measurement value of the system respectively; w and Q are the process noise and its covariance of the system; v and R are the measurement noise and its covariance of the system;

[0019] Step 3: The fractional calculus theory is introduced to improve the lithium battery equivalent circuit model (ECM), and the RC module is expanded to the nth order to obtain an equivalent circuit model with 2n+1 parameters to be identified. Under the condition of short-time constant current charge / discharge, the nth order RC module can be regarded as a linear steady-state system, which can be described by transfer function and simplified as shown in Equation (17):

[0020]

[0021] Among them U rc is the voltage at the terminals of the RC series module, a i and b are the coefficients of the denominator term after the transfer function is simplified;

[0022] The integer-order transfer function shown in formula (17) is equivalent to the fractional-order transfer function shown in formula (20), and a high-precision, low-parameter-dimensional fractional-order model of lithium batteries is obtained:

[0023]

[0024] Among them U RC is the terminal voltage of the fractional-order transfer function module, a and c are the coefficients of the denominator of the fractional-order transfer function;

[0025] Step 4: Select the time t from the nominal capacity 20% SOC to the end of constant current charging c The parameters a and c in the fractional-order model of lithium batteries are used as health factors. The sampling windows of a and c are set to 0 seconds to N seconds of constant current discharge of lithium batteries in full charge state. In order to quantify the selected t c The correlation between the three health factors a, a, c and SOH is calculated using the Spearman formula, as shown in formula (21):

[0026]

[0027] where x i and i is the sample individual;

[0028] For the fractional-order model parameters a and c, a time-domain identification method based on a fuzzy controller under DC excitation is proposed to introduce the definition of fractional-order calculus:

[0029]

[0030] The fractional Laplace inverse transform formula is:

[0031]

[0032] The Mittag-Leffler function has the general form:

[0033]

[0034] The Gamma function is:

[0035]

[0036] When the input is a step response, the inverse transformation of equation (20) is performed using equations (22) to (25), and the time domain expression of the fractional-order module is obtained as follows:

[0037]

[0038] Where t is the sampling time, the first sampling point is recorded as time 0, and a and c reflect U RC The time domain change rate of the terminal voltage is established within the sampling window:

[0039]

[0040] in is the model output voltage, and the SOC estimation value is obtained by AEKF. is the difference between the estimated value and the true value of the terminal voltage at t = 1, R o Obtained from the output of FFRLS; Equation (28) represents the voltage fitting error within the window.

[0041]

[0042] Step 5: Construct a fully connected neural network with 3 input layer nodes, 1 output layer node, 2 hidden layers, and 5 and 3 hidden layer nodes respectively. Use the connection weights of each layer of BPNN to form the sparrow population matrix W = [W 1,ij W 2,ij W 3,ij ], the initial value of each element is a random number, and the fitness function is constructed as shown in formula (29):

[0043] F(W)=BPNN(W,input)-output (29)

[0044] The input is the health factor of the lithium battery, and the output is the SOH of the lithium battery;

[0045] The sparrow population finder iterates according to formula (30), W m,n Represents the row and column position of the sparrow individual in the population matrix, R w is the population warning value, a random number in [0,1], ST is the proportion of individuals in the population except the discoverer, rand is a random number that obeys the normal distribution, L is a matrix whose elements of the same dimension are all 1, Iter max is the maximum number of population evolutions, is the population evolution parameter, with a value range of [0, 1]. w When <ST, the weight is searched exponentially. w When ≥ST, change the weight search range,

[0046]

[0047] The follower iterates according to formula (31), W worst is the individual with the worst fitness in the tth generation, W best is the individual with the best fitness in the tth generation. A is a matrix of the same dimension in which each element is randomly preset to 1 or -1. n is the total number of individuals. When m>n / 2, it means that the fitness of the mth weight is poor and the search interval needs to be changed. When m≤n / 2, the search will continue near the current optimal weight.

[0048]

[0049] The vigilant iterates according to formula (32), W P represents the individual with the best global fitness, θ is the control step size, obeys the standard normal distribution, k∈[-1,1], q is a constant to avoid the denominator of the term being 0, F i is the current individual fitness, F w is the global worst individual fitness, F g is the global individual optimal fitness, when F i ≠F g When F i =F g When , it means that the fitness of the current weight is very close to the global optimal fitness, and it will continue to approach the optimal weight.

[0050]

[0051] SSA-BPNN algorithm is based on t c, a, c estimate the SOH of the lithium battery, and finally use the SOH estimation result and formula (20) to inversely solve Q c , correct Q in AEKF c The value of SOC and SOH is updated alternately.

[0052] The open circuit voltage U in the lithium battery equivalent circuit model in step 1 oc The nonlinear relationship between U and SOC can be fitted using a high-order polynomial, as shown in formula (3), where U oc Take the average of the open circuit voltage during the charge and discharge phases.

[0053] U OC =a5SOC 5 -a4SOC 4 +a3SOC 3 -a2SOC 2 + a1SOC+a0 (3).

[0054] The recursive process of AEKF estimating SOC in step 2 is:

[0055] 1) Time update

[0056] x k+1|k =A k+1 x k +B k+1 u k (8)

[0057]

[0058] 2) Measurement update, y 测 Indicates the actual measured value.

[0059]

[0060]

[0061] x k+1 =x k+1|k +K k+1 [y 测 -y k+1|k ] (12)

[0062] P k+1 =(I e -K k+1 J H ) k+1|k (13)

[0063] 3) Perform adaptive calculation of error covariance

[0064]

[0065]

[0066] Formula (17) in step 3 is obtained by converting the high-order integer transfer function into a fractional transfer function according to the Oustaloup filter principle. The mathematical model of the Oustaloup filter is shown in Formula (18):

[0067]

[0068] Where p and q are weighted parameters, and the zero poles and gain are:

[0069]

[0070] α is the order of the fractional operator, which can be a rational number in (0, 1). In this paper, 0.4 is taken, ω1 and ω h The upper and lower limits of the selected frequency band: 10 -8 -10 8 (rad / s), the model order n is used as the filter order.

[0071] In step 4, the sampling window The vector ΔU that is different from the actual measured voltage U of the lithium battery is used as the input, and the parameters a and c are used as the output; the domain of ΔU is divided into five levels: N + Indicates a large negative value, N indicates a negative value, ZS indicates a small value, P indicates a positive value, P + Represents a large positive value; the sampling window domain is divided into two levels: A represents the adjustment parameter a, and C represents the adjustment parameter c; the a and c iteration step domains are divided into five levels: BN represents a large step size decrease, MN represents a medium step size decrease, Z represents a random increase or decrease of a small step size, and MP represents a medium step size increase; BP represents a large step size increase.

[0072] The SOH of a lithium battery is the ratio of the current maximum capacity to the rated capacity:

[0073]

[0074] Beneficial Effects

[0075] A SOC-SOH joint estimation method based on a lithium battery model and fractional order theory is prepared using the technical solution of the present invention, which has the following advantages:

[0076] 1. This method establishes the second-order ECM of lithium battery and uses AEKF to realize SOC estimation; proposes a fractional-order model of lithium battery, and uses the fractional-order model parameters and the time from 20% SOC to the end of constant current charging as health factors, and designs a fuzzy controller to identify the fractional-order model parameters;

[0077] 2. This method constructs a SOH estimation model based on SSA-BPNN. In the experimental stage, the AEKF algorithm is compared with the EKF. The maximum error of SOC estimation of AEKF is 1.13%, which has good accuracy. The SOH of lithium batteries is estimated by SSA-BPNN, and the absolute error is less than 2.5%. By comparing the SOC estimation of lithium batteries under 95%, 90%, 85%, and 80% SOH and the SOC-SOH joint estimation, the effectiveness of the proposed lithium battery SOC-SOH joint estimation system is verified. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 It is a flow chart of a SOC-SOH joint estimation method based on a lithium battery model and fractional order theory according to the present invention;

[0079] Figure 2 is a diagram of an equivalent circuit model of the lithium battery of the present invention;

[0080] Figure 3 is the parameter identification flow chart of the present invention;

[0081] Figure 4 is the n-order equivalent circuit model of the present invention;

[0082] Figure 5 It is the structural principle diagram of the fuzzy controller of the present invention;

[0083] Figure 6 is the input-output membership function diagram of the present invention;

[0084] Figure 7 is the back propagation neural network graph of the present invention;

[0085] Figure 8 It is the SSA-BPNN offline training flow chart of the present invention;

[0086] Fig. 9 is the SOC estimation curve diagram of the present invention;

[0087] Fig.10 is a charging voltage curve diagram of the battery aging process of the present invention;

[0088] Fig.11 is a charging voltage curve diagram of the battery aging process of the present invention;

[0089] Fig.12 is a discharge voltage curve diagram of the battery aging process of the present invention;

[0090] Fig.13 is the model fitting error diagram of the present invention;

[0091] Fig.14is the population fitness curve diagram of the present invention;

[0092] Fig.15 is a graph of the SOH estimation result of the present invention;

[0093] Fig.16 is a diagram of SOC estimation results under different SOH states according to the present invention;

[0094] Fig.17 This is the SOC-SOH combined estimation result table described in the present invention. DETAILED DESCRIPTION

[0095] The characteristic of this technical solution is to combine the SOC estimation method with the SOH estimation method to build a lithium battery SOC-SOH joint estimation system framework, such as Figure 1 After the sensor collects the battery voltage and current data, it is input into FFRLS to identify the parameters of ECM; then the ECM parameters are imported into equations (1) and (2) to implement AEKF to estimate the lithium battery SOC; the SOC estimation result is used to calibrate t c Initial moment; when the system is determined to be within the sampling window, the fuzzy controller identifies the parameters a and c of the lithium battery fractional model; the SSA-BPNN algorithm is based on t c , a, c estimate the SOH of lithium battery; finally, use the SOH estimation result and formula (20) to inversely solve Q c , correct Q in AEKF c The value of SOC and SOH is updated alternately.

[0096] according to Figure 2 Construct the state equation and measurement equation:

[0097]

[0098] U=U oc (SOC)-U S -U L -R o I(k) (2)

[0099] Where: U S and U L R S and R L Terminal voltage, τ s and τ l The time constants R S C S and R L C L , Q c is the battery capacity, Δt is the sampling time, and k is the discrete time.

[0100] Based on the open circuit voltage U in ECMoc The nonlinear relationship between U and SOC can be fitted using a high-order polynomial, as shown in formula (3), where U oc Take the average of the open circuit voltage during the charge and discharge phases.

[0101] U OC =a5SOC 5 -a4SOC 4 +a3SOC 3 -a2SOC 2 + a1SOC+a0 (3)

[0102] The values ​​of resistance and capacitance in ECM change dynamically with the different excitations applied to the battery terminals. The recursive least squares method with forgetting factor (FFRLS) is used to identify the resistance and capacitance parameters online, obtain the dynamic values ​​of the resistance and capacitance parameters, and improve the fitting accuracy of ECM. The recursive formula of FFRLS is shown in formula (4).

[0103]

[0104] In the formula, θ is the coefficient vector to be determined, I e is the same type unit matrix, λ is the forgetting factor, is I and U from k-2 to k, K LS is the gain coefficient, P LS is the covariance matrix. The parameter identification process of FFRLS is as follows: Figure 3 As shown:

[0105] When the EKF algorithm estimates the SOC of lithium batteries, the error covariance is set to a fixed value, but during the convergence of the algorithm, the actual error covariance changes dynamically. To address the above problems, it is proposed to add error covariance adaptive calculation to the recursive formula of EKF, calculate the mean square error using the battery terminal voltage measurement value and the model prediction value, and calculate the dynamic error covariance based on the Kalman gain to construct AEKF to estimate the SOC of lithium batteries, as follows:

[0106] Transform equations (1) and (2):

[0107] x k+1 =A k x k +B k u k +w (5)

[0108] y k =H k x k +C k u k +v (6)

[0109]

[0110] Among them: A k , B k , H k , C k are the state transfer matrix, input matrix, output matrix and feedforward matrix of the system respectively; x k ,y k are the state vector and measurement value of the system respectively; w and Q are the process noise and its covariance of the system; v and R are the measurement noise and its covariance of the system. The recursive process of AEKF estimating SOC is:

[0111] 1) Time update

[0112] x k+1|k =A k+1 x k +B k+1 u k (8)

[0113]

[0114] 2) Measurement update, y 测 Indicates the actual measured value.

[0115]

[0116]

[0117] x k+1 =x k+1|k +K k+1 [y 测 -y k+1|k ] (12)

[0118] P k+1 =(I e -K k+1 J H ) k+1|k (13)

[0119] 3) Perform adaptive calculation of error covariance

[0120]

[0121]

[0122] The SOH of a lithium battery is defined as the ratio of the current maximum capacity to the rated capacity.

[0123]

[0124] In SOH estimation, according to the capacity increment analysis method, the accuracy of ECM is difficult to reflect the impact of SOH on the external characteristics of lithium batteries. In order to provide theoretical support for solving the above problems, fractional calculus theory is introduced to improve ECM. Figure 2 The lithium battery ECM is extended to n-order RC modules to obtain an ECM with 2n+1 parameters to be identified, such as Figure 4 In the case of short-time constant current charge / discharge, the n-order RC module can be regarded as a linear steady-state system, which can be described by transfer function and simplified as shown in equation (17).

[0125]

[0126] Among them U rc is the voltage at the terminals of the RC series module, a i and b are the coefficients of the denominator term after the simplification of the transfer function.

[0127] According to the Oustaloup filter principle, a high-order integer transfer function can be equivalent to a fractional-order transfer function. The mathematical model of the Oustaloup filter is shown in equation (18).

[0128]

[0129] Where p and q are weighted parameters, and the zero poles and gain are:

[0130]

[0131] α is the order of the fractional operator, which can be a rational number in (0, 1). In this paper, 0.4 is taken, ω1 and ω h The upper and lower limits of the selected frequency band: 10 -8 -10 8 (rad / s), the model order n is used as the filter order.

[0132] The integer-order transfer function shown in equation (17) is equivalent to the fractional-order transfer function shown in equation (20), resulting in a high-precision, low-parameter-dimensional fractional-order model of lithium batteries.

[0133]

[0134] Among them U RC is the terminal voltage of the fractional-order transfer function module, and a and c are the coefficients of the denominator of the fractional-order transfer function.

[0135] There is a coupling relationship between the SOC and SOH of lithium batteries. As the battery SOH decreases, the capacity Q cGradually decreases, resulting in a high actual value of the discharge rate, affecting the accuracy of SOC estimation. Accurately estimating the SOH of lithium batteries can ensure the accuracy of SOC estimation during the life cycle of lithium batteries, but battery SOH is difficult to measure directly. It is necessary to extract a health factor that has a strong correlation with SOH to indirectly estimate the SOH of lithium batteries. Lithium batteries use a constant current-constant voltage charging mode. The integral of the charging current and time can intuitively reflect the change in lithium battery capacity. The charging time can be used as a health factor to estimate SOH. Considering that the initial charging SOC of lithium batteries in actual applications is not fixed and the complete constant current charging time is not easy to measure, the time t from the nominal capacity 20% SOC to the end of constant current charging is selected. c As one of the health factors. In the fractional-order model of lithium batteries, equation (20) reflects the polarization characteristics of lithium batteries, and the parameters a and c are selected as health factors. The sampling windows of a and c are set to 0 seconds to N seconds for constant current discharge of lithium batteries in a fully charged state. In order to quantify the selected t c The correlation coefficient between the three health factors a, a, and c and SOH was calculated using the Spearman formula, as shown in formula (21).

[0136] where x i and i For sample individuals.

[0137] For the fractional-order model parameters a and c, a time-domain identification method based on fuzzy controller under DC excitation is proposed. The definition of fractional-order calculus is introduced:

[0138]

[0139] The fractional Laplace inverse transform formula is:

[0140]

[0141] The Mittag-Leffler function has the general form:

[0142]

[0143] The Gamma function is:

[0144]

[0145] When the input is a step response, equation (20) is transformed by using equations (22) to (25) to obtain the time domain expression of the fractional-order module, as shown in equation (26).

[0146]

[0147] Where t is the sampling time, the first sampling point is recorded as time 0, and a and c reflect U RCThe time domain change rate of the terminal voltage is established within the sampling window.

[0148]

[0149] in is the model output voltage, and the SOC estimation value is obtained by AEKF. is the difference between the estimated value and the true value of the terminal voltage at t = 1, R o Obtained from the output of FFRLS. Equation (28) represents the voltage fitting error within the window.

[0150]

[0151] Design the fuzzy controller to identify the parameters a and c. The schematic diagram is as follows: Figure 5 As shown, within the sampling window The vector ΔU that is different from the measured voltage U of the lithium battery is used as the input, and the parameters a and c are used as the output. The domain of ΔU is divided into five levels: N + Indicates a larger negative value; N indicates a negative value; ZS indicates a small value; P indicates a positive value; P + Indicates a large positive value. The sampling window domain is divided into two levels: A represents the adjustment parameter a; C represents the adjustment parameter c. The domain of a and c iteration steps is divided into five levels: BN represents large step size decrease; MN represents medium step size decrease; Z represents random increase or decrease of small step size; MP represents medium step size increase; BP represents large step size increase. The input and output membership functions are shown in Figure 6. SSA is used to optimize the weights between the nodes of each connection layer of BPNN, and then the nonlinear mapping relationship between health factor and SOH is established based on the obtained SSA-BPNN model to realize the SOH estimation of lithium battery.

[0152] First, construct Figure 7 The fully connected neural network shown has 3 input layer nodes, 1 output layer node, 2 hidden layers, and 5 and 3 hidden layer nodes respectively.

[0153] The sparrow population matrix W = [W 1,ij W 2,ij W 3,ij ], the initial value of each element is a random number. Construct the fitness function as shown in formula (29).

[0154] F(W)=BPNN(W,input)-output (29)

[0155] The input is the lithium battery health factor, and the output is the lithium battery SOH.

[0156] The sparrow population finder iterates according to formula (30), W m,nRepresents the row and column position of the sparrow individual in the population matrix. w is the population warning value, which is a random number in [0,1]. ST is the proportion of individuals in the population other than the discoverer, which is 0.8. rand is a random number that follows a normal distribution, and L is a matrix whose elements of the same dimension are all 1. max is the maximum number of population evolutions, is the population evolution parameter, with a value range of [0, 1]. w When <ST, the weight is searched exponentially. w ≥ ST, change the weight search range.

[0157]

[0158] The follower iterates according to formula (31), W worst is the individual with the worst fitness in the tth generation, W best is the individual with the best fitness in the tth generation, A is a matrix of the same dimension with each element randomly preset to 1 or -1, and n is the total number of individuals. When m>n / 2, it means that the fitness of the mth weight is poor and the search interval needs to be changed. When m≤n / 2, the search will continue near the current optimal weight.

[0159]

[0160] The vigilant iterates according to formula (32), W P represents the individual with the best global fitness, θ is the control step size, and it obeys the standard normal distribution. k∈[-1, 1], q is a constant to avoid the denominator of the term being 0, F i is the current individual fitness, F w is the global worst individual fitness, F g is the global individual optimal fitness. i ≠F g When , it means that the fitness of the current weight is far from the global optimal fitness, and an extensive search is needed. i =F g When , it means that the fitness of the current weight is very close to the global optimal fitness, and it will continue to approach the optimal weight.

[0161]

[0162] The training process of SSA-BPNN for estimating SOH of lithium batteries is as follows Figure 8 shown.

[0163] Example

[0164] Eliminating the influence of battery capacity attenuation on the SOC estimation result, a lithium battery with a SOH state of 100% is selected to perform SOC estimation during constant current-constant voltage charging, and the proposed AEKF algorithm is compared with the EKF algorithm, as shown in Fig. 9 As shown in the figure, the maximum error (ME) of AEKF in estimating SOC is 1.13%, and the maximum error of EKF in estimating SOC is 4.98%. The results show that the AEKF algorithm with the addition of error covariance adaptive calculation has higher accuracy in estimating lithium battery SOC.

[0165] Regarding the three health factors mentioned in this article c , a, c to verify the correlation of SOH.

[0166] Taking No. 1 battery as an example, the relationship between the charging curve and the number of cycles is as follows: Fig.10 As shown, constant current charging is adopted first. When the battery terminal voltage reaches 4.2V, it is switched to constant voltage charging. The white grid part indicates that the battery SOC is in the range of 0% to 20%. In actual application, the battery can be charged at any position in this range. The constant current charging time t c The counting point is set at 20% SOC, which is easier to measure and has strong practicality. As the number of cycles increases, t c According to formula (21), t of 8 experimental batteries is calculated c The Spearman correlation coefficients with SOH all reached above 0.97, showing a strong correlation.

[0167] The voltage data of the constant current discharge terminal of lithium battery under different cycle times is as follows Fig.11 As shown in the figure. As the number of cycles increases, the incremental change in the capacity of the lithium battery (ΔQ / ΔU) causes the terminal voltage characteristics to change. The curvature of the terminal voltage curve gradually decreases within [0s, 100s], and the absolute value of the slope increases within [100s, 300s]. Setting the upper limit of the sampling window of a and c to N = 300s has the advantages of shorter sampling time and more convenient calculation, which meets the actual application requirements.

[0168] In the sampling window, the fuzzy controller is used to identify the parameters a and c of the lithium battery fractional-order model. The initial values ​​can be rational numbers between [30, 100] and [5, 10]. The fitting effect of the proposed lithium battery fractional-order model and the second-order ECM is compared. Fig.12 As shown in the figure, the errors of each model are Fig.13 The ME, mean absolute error (MAE) and root mean square error (RMSE) of the lithium battery fractional-order model are 1.5×10 -4 , 1.3×10-4 , 0.16%, the fitting accuracy of the battery terminal voltage is much higher than that of the second-order ECM, which meets the accuracy requirement of fitting the changes in the external characteristics of the battery caused by the reduction of SOH. According to formula (21), the Spearman correlation coefficients of the fractional-order model parameters a, c and SOH of the 8 experimental batteries are all above 0.96, which has a strong correlation.

[0169] The eight batteries are divided into two groups, batteries 1 to 4 are used as the training group for estimating the SOH of lithium batteries, and batteries 5 to 8 are used as the validation group. The fitness function defined in formula (29) is used to compare the training effects of BPNN and SSA-BPNN. The smaller the fitness, the better the training effect. Fig.14 As shown in the figure, the maximum number of population evolutions is set to 30, and the fitness of BPNN without SSA optimization is greater than 0.8%. Using SSA to optimize BPNN, the population reaches the best fitness after 12 evolutions, and the fitness of SSA-BPNN is less than 0.1%. The results show that the training effect of SSA-BPNN is stronger than that of BPNN.

[0170] Using SSA-BPNN to estimate lithium battery SOH, the results are as follows Fig.15 As shown in the figure, the SOH estimation of lithium battery is performed once every 20 aging cycles, and the absolute error is less than 2.5%, which has high accuracy. The SOH-SOC joint estimation is compared with the SOC estimation alone to verify the effectiveness of the SOH-SOC joint estimation system.

[0171] Taking No. 5 battery as an example, SOC-SOH joint estimation is performed under the conditions that the battery SOH is actually at 95%, 90%, 85% and 80%. The starting state is 90% SOC and the discharge is 10% of the maximum capacity. The SOC estimation results are as follows: Fig.16 As shown in the figure, when SOH is 95%, the ME of the single estimated SOC is 0.33% and the ME of the joint estimated SOC is 0.23%; when SOH is 90%, the ME of the single estimated and joint estimated SOC are 0.20% and 0.98% respectively; when SOH is 85%, the ME of the single estimated and joint estimated SOC are 0.26% and 1.73% respectively; when SOH is 80%, the ME of the single estimated and joint estimated SOC are 0.25% and 2.6% respectively. The results show that due to the battery capacity Q c The reduction of c In the case of , the actual value of the discharge rate in formula (1) is greater than the theoretical value, and the error of estimating SOC alone increases with the decrease of SOH; when SOC-SOH is estimated jointly, the system corrects Q according to the SOH estimation result. c , ensuring that the maximum error of the SOC estimation result is always less than 0.3%.

[0172] When the actual SOH values ​​of batteries 5 to 8 are 95%, 90%, 85% and 80% respectively, the average values ​​of the errors of the SOC-SOH combined estimation and the SOC estimation alone are as follows: Fig.17 As shown in the figure, the average values ​​of various errors in SOC estimation using the joint method are lower than those in SOC estimation alone, and the effectiveness of the SOC-SOH joint estimation system is verified.

[0173] In summary, the AEKF algorithm is compared with the EKF. The maximum error of SOC estimation of AEKF is 1.13%, which has good accuracy. The effectiveness of the fractional-order model and health factor of lithium batteries is verified, and the Spearman correlation coefficient is above 0.96. The SOH of lithium batteries is estimated using SSA-BPNN, and the absolute error is less than 2.5%. By comparing the separate SOC estimation and SOC-SOH joint estimation of lithium batteries under 95%, 90%, 85%, and 80% SOH, the effectiveness of the proposed lithium battery SOC-SOH joint estimation system is verified.

[0174] The above technical solutions only reflect the preferred technical solutions of the technical solutions of the present invention. Some changes that may be made to certain parts thereof by technicians in this technical field all reflect the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. A SOC-SOH joint estimation method based on lithium battery model and fractional order theory, characterized in that: The method comprises the following steps: Step 1: Construct a lithium battery equivalent circuit model, where U oc is the battery open circuit voltage, I is the battery charge and discharge current, R L , C L are the electrochemical polarization resistance and polarization capacitance, R S , C S are concentration polarization resistance and polarization capacitance respectively, U is the battery terminal voltage, R o is the equivalent internal resistance of the battery; according to the lithium battery equivalent circuit model, the state equation is constructed as formula (1) and the measurement equation is constructed as formula (2): U=U oc (SOC)-U S -U L -R o I(k) (2) Where: U S and U L R S and R L Terminal voltage, τ s and τ l The time constants R S C S and R L C L , Q c is the battery capacity, Δt is the sampling time, k is the discrete time, The recursive least square method with forgetting factor is used to online identify the resistance and capacitance parameters of the state equation and the measurement equation, obtain the dynamic values ​​of the resistance and capacitance parameters, and improve the fitting accuracy of the ECM. The recursive least square method with forgetting factor is shown in formula (3): In the formula, θ is the coefficient vector to be determined, I e is the same type unit matrix, λ is the forgetting factor, is I and U from k-2 to k, K LS is the gain coefficient, P LS is the covariance matrix: Step 2: Use the extended Kalman filter algorithm to estimate the SOC of the lithium battery, and add the error covariance adaptive calculation to the recursive formula of the extended Kalman filter algorithm to construct an adaptive extended Kalman filter algorithm to estimate the SOC of the lithium battery, as follows: Transform equations (1) and (2): x k+1 =A k x k +B k u k +w (5) y k =H k x k +C k u k +v (6) Among them: A k , B k , H k , C k are the state transfer matrix, input matrix, output matrix and feedforward matrix of the system respectively; x k ,y k are the state vector and measurement value of the system respectively; w and Q are the process noise and its covariance of the system; v and R are the measurement noise and its covariance of the system; Step 3: Introduce fractional calculus theory to improve the lithium battery equivalent circuit model, expand the RC module to nth order, obtain an equivalent circuit model with 2n+1 parameters to be identified and describe it with a transfer function, which is simplified as shown in formula (17): Among them U rc is the voltage at the terminals of the RC series module, a i and b are the coefficients of the denominator term after the simplification of the transfer function; The integer-order transfer function shown in formula (17) is equivalent to the fractional-order transfer function shown in formula (20), and a high-precision, low-parameter-dimensional fractional-order model of lithium batteries is obtained: Among them U RC is the terminal voltage of the fractional-order transfer function module, a and c are the coefficients of the denominator of the fractional-order transfer function; Step 4: Select the time t from the nominal capacity 20% SOC to the end of constant current charging c and the parameters a and c in the fractional-order model of lithium batteries as health factors. In order to quantify the selected t c The correlation between the three health factors a, a, and c and SOH is calculated using the Spearman formula, as shown in formula (21): where x i and i is the sample individual; For the fractional-order model parameters a and c, the time-domain identification method based on the fuzzy controller introduces the fractional-order calculus definition: The fractional Laplace inverse transform formula is: The Mittag-Leffler function has the general form: The Gamma function is: When the input is a step response, the inverse transformation of equation (20) is performed using equations (22) to (25), and the time domain expression of the fractional-order module is obtained as follows: Where t is the sampling time, the first sampling point is recorded as time 0, and a and c reflect U RC The time domain change rate of the terminal voltage is established within the sampling window: in is the model output voltage, and the SOC estimation value is obtained by AEKF. is the difference between the estimated value and the true value of the terminal voltage at t = 1, R o Obtained from the output of FFRLS; Equation (28) represents the voltage fitting error within the window, Step 5: Construct a fully connected neural network with 3 input layer nodes, 1 output layer node, 2 hidden layers, and 5 and 3 hidden layer nodes respectively. Use the connection weights of each layer of BPNN to form the sparrow population matrix W = [W 1,ij W 2,ij W 3,ij ], the initial value of each element is a random number, and the fitness function is constructed as shown in formula (29): F(W)=BPNN(W,input)-output (29) The input is the health factor of the lithium battery, and the output is the SOH of the lithium battery; The sparrow population finder iterates according to formula (30), W m,n Represents the row and column position of the sparrow individual in the population matrix, R w is the population warning value, a random number in [0,1], ST is the proportion of individuals in the population except the discoverer, rand is a random number that obeys the normal distribution, L is a matrix whose elements of the same dimension are all 1, Iter max is the maximum number of population evolutions, is the population evolution parameter, with a value range of [0, 1]. w When <ST, the weight is searched exponentially. w When ≥ST, change the weight search range, The follower iterates according to formula (31), W worst is the individual with the worst fitness in the tth generation, W best is the individual with the best fitness in the tth generation. A is a matrix of the same dimension in which each element is randomly preset to 1 or -1. n is the total number of individuals. When m>n / 2, it means that the fitness of the mth weight is poor and the search interval needs to be changed. When m≤n / 2, the search will continue near the current optimal weight. The vigilant iterates according to formula (32), W P represents the individual with the best global fitness, θ is the control step size, obeys the standard normal distribution, k∈[-1,1], q is a constant to avoid the denominator of the term being 0, F i is the current individual fitness, F w is the global worst individual fitness, F g is the global individual optimal fitness, when F i ≠F g When F i =F g When , it means that the fitness of the current weight is very close to the global optimal fitness, and it will continue to approach the optimal weight. SSA-BPNN algorithm is based on t c , a, c estimate the SOH of the lithium battery, and finally use the SOH estimation result and formula (20) to inversely solve Q c , correct Q in AEKF c The value of SOC and SOH is updated alternately.

2. The SOC-SOH joint estimation method based on a lithium battery model and fractional order theory according to claim 1, characterized in that: Formula (17) in step 3 is obtained by converting the high-order integer transfer function into a fractional transfer function according to the Oustaloup filter principle. The mathematical model of the Oustaloup filter is shown in Formula (18): Where p and q are weighted parameters, and the zero poles and gain are: α is the order of the fractional operator, which can be a rational number in (0, 1). In this paper, 0.4 is taken, ω1 and ω h The upper and lower limits of the selected frequency band: 10 -8 -10 8 (rad / s), the model order n is used as the filter order.

3. The SOC-SOH joint estimation method based on a lithium battery model and fractional order theory according to claim 1 is characterized in that: In step 4, the sampling window The vector ΔU that is different from the actual measured voltage U of the lithium battery is used as the input, and the parameters a and c are used as the output; the domain of ΔU is divided into five levels: N + Indicates a large negative value, N indicates a negative value, ZS indicates a small value, P indicates a positive value, P + Represents a large positive value; the sampling window domain is divided into two levels: A represents the adjustment parameter a, and C represents the adjustment parameter c; the a and c iteration step domains are divided into five levels: BN represents a large step size decrease, MN represents a medium step size decrease, Z represents a random increase or decrease of a small step size, and MP represents a medium step size increase; BP represents a large step size increase.

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