Four-step method for parameter identification of lithium battery equivalent circuit model based on differential-algebraic equation

Abstract

A four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations is disclosed. In the method, an equivalent circuit model of a lithium battery is selected and a differential algebraic equation is established. A loss function is constructed according to the equation and the voltage and current values at the terminals of the battery, and relevant constraint conditions and initial values of the identification parameters are determined. A system of ordinary differential equations is solved, the loss function is calculated according to the solution and the voltage and current values at the terminals of the battery, the partial derivatives of each independent variable of the loss function are calculated, and the identification parameter values of the next iteration are obtained by substituting the partial derivatives into the gradient descent method. The iteration is repeated until the minimum value of the loss function is obtained, and the volt-ampere characteristics and state of charge of the lithium battery are predicted according to the identification parameter values. This method establishes a mathematical model, constructs a loss function, and uses a gradient descent optimization method and a numerical solution method to identify the parameters of the lithium battery equivalent circuit model, which can fit the entire charging and discharging process, has a faster convergence speed, and has high accuracy in predicting battery performance.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of lithium batteries, and particularly relates to a four-step method for identifying parameters of a lithium battery equivalent circuit model based on a differential algebraic equation. BACKGROUND

[0002] Lithium batteries have the advantages of small volume, large capacity and high discharge rate, and are widely used in the fields of electronic devices, aerospace technology and the like. Current lithium battery performance prediction depends on a battery model, and model selection determines the accuracy of subsequent parameter identification and state evaluation. As a widely used lithium battery model, an equivalent circuit model is usually composed of a circuit network of circuit elements, so as to simulate the dynamic voltage response characteristics of the battery.

[0003] Based on the established lithium battery model, parameter identification needs to be performed to predict the performance of the lithium battery such as the volt-ampere characteristic and the state of charge. The parameter identification methods mainly include a particle swarm optimization algorithm, a Kalman filter algorithm and a least square method. The particle swarm optimization algorithm is troublesome in selecting genetic operators, and cannot effectively solve discrete and combination optimization problems, and is prone to fall into local optimal processing. The Kalman filter algorithm is an algorithm for developing optimal estimation of a platform output observation data information system through a state equation of a modern control theory, but the parameter identification of the lithium battery involves nonlinear operation, and the Kalman filter cannot well handle the nonlinear operation. The least square method has low requirements for the system, and the result has quite good statistical analysis characteristics, but researchers need to design a corresponding parameter identification method according to the actual equivalent circuit model, and the parameter identification method based on the least square method does not have universality. Therefore, it is necessary to develop an identification method with universality and high precision.

[0004] The above information disclosed in the background section is only intended to enhance the understanding of the background of the application, and therefore can contain information that is not prior art known to those of ordinary skill in the art. SUMMARY

[0005] In view of the problems in the prior art, the application provides a four-step method for identifying parameters of a lithium battery equivalent circuit model based on a differential algebraic equation, improves the parameter identification efficiency and precision of the lithium battery model, and thus achieves the purposes of reducing model error, improving system efficiency and optimizing operation of an energy storage system.

[0006] The application aims to realize the following technical scheme, a four-step method for identifying parameters of a lithium battery equivalent circuit model based on a differential algebraic equation comprises the following steps.

[0007] Step 1: selecting a lithium battery equivalent circuit model and establishing a differential algebraic equation, the differential algebraic equation is expressed in the form of formula (1):

[0008] Ax'(t) + Bx(t) = F (1)

[0009] wherein t is an independent variable representing time, A and B are matrix functions of the independent variable t, F is a vector function of t, x(t) is a vector of unknowns, the matrix function A of the differential algebraic equation is non-singular, a system of ordinary differential equations is obtained based on the differential algebraic equation, and the system of ordinary differential equations is in the form of equation (6):

[0010] F(t, u, u', u'',... u (n) ) = 0 (6),

[0011] wherein F is a vector function, t is an independent variable, u is a dependent variable, and the superscript n represents an n-th derivative of u;

[0012] Step 2: obtaining battery terminal voltage and current values and initial state values of the lithium battery from lithium battery testing or simulation, and constructing a loss function according to the differential algebraic equation and establishing relevant constraint conditions, the loss function being in the form of equation (2):

[0013]

[0014] wherein X represents an input parameter, y represents an observation result, distance represents a spatial distance between an observation sample and a simulation result, f(X, ω) represents a mathematical model corresponding to an equivalent circuit model, ω represents a model parameter, and p represents a probability, the loss function being represented by equation (2), and the relevant constraint conditions being represented by equations (3)-(4):

[0015] c i (x) = 0, i ∈ ε1 = {1, 2,..., l} (3)

[0016] c i (x) ≤ 0, i ∈ ε2 = {l+1, l+2,..., l+m} (4)

[0017] Equation (3) is an equality constraint, and equation (4) is an inequality constraint, wherein c represents a constraint relationship, the subscript i represents an order of a constraint condition, and ε represents a set of constraint conditions;

[0018] Step 3: obtaining a minimum value of the loss function by using a gradient descent method and a numerical solution method, the gradient descent method being in the form of equation (5):

[0019]

[0020] wherein x on the right side represents a recognized parameter value of a current iteration, x on the left side represents a recognized parameter value of a next iteration, eta represents a learning rate, and L represents the loss function;

[0021] Step 3-1, solving the ordinary differential equations with the identification parameter value of the current iteration; Step 3-2, calculating the loss function according to the solving result of the ordinary differential equations and the experimental result; Step 3-3, calculating the identification parameter value of the next iteration by taking partial derivatives of the loss function with respect to each of its arguments to obtain a vector consisting of the partial derivatives, and repeating steps 3-1 to 3-3 until the minimum value of the loss function is obtained as the identification parameter value through iteration;

[0022] Step 4: predicting the lithium battery volt-ampere characteristic and state of charge according to the identification parameter value.

[0023] In the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential-algebraic equations, the ordinary differential equations are constraint conditions of an optimization problem, and the loss function is an objective function of the optimization problem, and the minimum value of the loss function is obtained by solving the optimization problem, and the optimization problem is shown in equations (7)-(9):

[0024]

[0025] s.t.c i (x)=0,i∈ε1={1,2,...,l}(8)

[0026] c i (x)≤0,i∈ε2={l+1,l+2,...,l+m} (9)。

[0027] In the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential-algebraic equations, when the values of the battery terminal voltage and current include the charging stage, the discharging stage, and the standing stage at the same time, the parameters of the lithium battery are identified for the entire charging and discharging stage; when the values of the battery terminal voltage and current include only one of the charging stage, the discharging stage, and the standing stage, the parameters of the lithium battery are identified for each charging and discharging stage.

[0028] In the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential-algebraic equations, when all equivalent circuit model parameters are unknown, all model parameters of the equivalent circuit model are identified; when some parameters of the equivalent circuit model are known, the remaining model parameters are identified by regarding the known model parameters as constants.

[0029] In the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential-algebraic equations, the lithium battery equivalent circuit model is the Rint model, the Thevenin model, the DP model, and the PNGV model.

[0030] In the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential-algebraic equations, the lithium battery is replaced by a lead-acid battery, a sodium-sulfur battery, a flow battery, and a supercapacitor.

[0031] In the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations, the loss function is constructed as an absolute value loss function, a log loss function, or a square loss function.

[0032] In the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations, the gradient descent method is replaced by a stochastic gradient descent method, a Momentum gradient descent method, or an AdaGrad gradient descent method.

[0033] In the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations, the numerical solution method of the equivalent circuit model includes Euler method, improved Euler method, and Runge-Kutta method.

[0034] Compared with the prior art, the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations has the following advantages: The method is applicable to Rint model, Thevenin model, DP model, and more complex PNGV model, and does not need to design a corresponding parameter identification method for each equivalent circuit model, and has universality. The method can be used for parameter identification in the whole charging and discharging stage of the lithium battery, and the fitted model parameters are more consistent with the overall charging and discharging curve. The method can also divide the whole charging and discharging stage into several sub-stages, and then perform parameter identification, so that the fitted model parameters have higher precision, and the method is beneficial to realize operation optimization of the lithium battery, and has flexibility. The method can also be used for parameter identification of batteries with equivalent circuit models, such as lead-acid batteries, sodium-sulfur batteries, flow batteries, and supercapacitors, and therefore the method has generalization. BRIEF DESCRIPTION OF DRAWINGS

[0035] Various other advantages and benefits of the present application will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The accompanying drawings are intended to only illustrate preferred embodiments of the application and are consequently not to be considered limiting of its scope. Obviously, other embodiments can be derived from the drawings without paying creative labor, which will be understood by those of ordinary skill in the art. Moreover, the same reference numbers are used throughout the drawings for the same or similar components.

[0036] In the drawings:

[0037] Figure 1 is a flowchart of a four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations proposed by the present application;

[0038] Figure 2 is a schematic diagram of a Thevenin second-order RC equivalent circuit model provided by an embodiment of the present application;

[0039] Figure 3 is a fitting curve of the terminal voltage response of the lithium battery model provided by an embodiment of the present application and an experimental curve graph;

[0040] Figure 4 is an error graph of the fitting curve of the terminal voltage response of the lithium battery model and the actual terminal voltage response curve provided by an embodiment of the present application.

[0041] The present application will be further explained with reference to the accompanying drawings and embodiments. DETAILED DESCRIPTION

[0042] The specific embodiments of the present application will be described below in detail with reference to the accompanying drawings. Although specific embodiments of the present application are shown in the drawings, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present application and to fully convey the scope of the present application to those skilled in the art.

[0043] It should be noted that certain terms are used in the specification and claims to refer to certain components. Those skilled in the art will understand that the same component can be referred to by different names. The present specification and claims do not distinguish components based on the difference in names, but rather on the difference in function. As used throughout the specification and claims, "comprise" or "include" is an open term, which should be interpreted as "including but not limited to". The subsequent description describes preferred embodiments of implementing the present application, but the description is for the purpose of illustrating the general principles of the specification, and is not intended to limit the scope of the present application. The scope of protection of the present application is defined by the appended claims.

[0044] For the sake of understanding the embodiments of the present application, the following will be further explained and described with specific embodiments as examples in conjunction with the accompanying drawings, and each drawing does not constitute a limitation on the embodiments of the present application.

[0045] As shown in the formula (1), the four-step method for identifying the parameters of the lithium battery equivalent circuit model based on the differential algebraic equation comprises, Figures 1 to 4

[0046] Step 1: Establish the lithium battery equivalent circuit model and the differential algebraic equation, the form of the differential algebraic equation is represented by formula (1): Ax'(t)+Bx(t)=F (1);

[0047] Where t is the independent variable, representing time, A and B are matrix functions of the independent variable t, F is a vector function of t, x(t) is a vector of unknown numbers, the matrix function A of the differential algebraic equation is non-singular, the constant differential equation set is obtained based on the differential algebraic equation, and the form of the constant differential equation set is represented by formula (6): ​

[0048] F(t, u, u', u''...u (n) ) = 0 (6) ;

[0049] Where F is a vector function, t is the independent variable, u is the dependent variable, and n represents the n-th derivative of u;

[0050] Further, according to the model prediction accuracy and the calculation speed requirement, the Thevenin second-order RC equivalent circuit model is selected, which has higher prediction accuracy and faster calculation speed compared with other equivalent circuit models. The differential algebraic equation is established according to the lithium battery equivalent circuit model, and the form of the differential algebraic equation is represented by formula (1):

[0051] U OC = IR0+I1R1+I2R2+U T (1)

[0052]

[0053]

[0054] Where t is the independent variable, I represents the current, I1 and I2 represent the current flowing through R1 and R2, and C1 and C2 represent the capacitance of the capacitors in the two RC circuits. The algebraic equations in the equation set are converted into related ordinary differential equations. The ordinary differential equations are represented by formula (4) to formula (5):

[0055]

[0056]

[0057] Step 2: Obtain the battery terminal voltage value and current value from the lithium battery test or simulation, and the initial state value of the lithium battery, and construct a loss function according to the differential algebraic equation, and establish related constraints, the form of the loss function is represented by formula (2):

[0058]

[0059] In the formula, X represents the input parameter, y represents the observation result, f(X, ω) represents the mathematical model corresponding to the equivalent circuit model, ω represents the model parameter, p represents the probability, The loss function is represented by formula (2), and the related constraints are represented by formula (3) to formula (4):

[0060] c i (x) = 0, i ∈ ε1 = {1, 2,..., l} (3)

[0061] c i (x) ≤ 0, i ∈ ε2 = {l+1, l+2,..., l+m} (4)

[0062] Equation (3) is an equality constraint, and equation (4) is an inequality constraint, wherein c represents a constraint relationship, subscript i represents the order of a constraint condition, and ε represents a set of constraint conditions;

[0063] Step 3: obtaining the minimum value of the loss function by using a gradient descent method and a numerical solution method, and the gradient descent method is in the form of equation (5):

[0064]

[0065] wherein x on the right side represents the recognized parameter value of the current iteration, x on the left side represents the recognized parameter value of the next iteration, eta represents a learning rate, and L represents a loss function;

[0066] Step 3-1: solving the system of ordinary differential equations by using the recognized parameter value of the current iteration; Step 3-2: calculating the loss function according to the solving result of the system of ordinary differential equations and the experimental result; Step 3-3: calculating the recognized parameter value of the next iteration by calculating the partial derivatives of the loss function with respect to each independent variable and obtaining a vector composed of the partial derivatives, and repeating steps 3-1 to 3-3 until the minimum value of the loss function is obtained as the recognized parameter value through iteration;

[0067] Step 4: predicting the volt-ampere characteristic and the state of charge of the lithium battery according to the recognized parameter value.

[0068] In the preferred embodiment of the four-step method for identifying the parameters of the lithium battery equivalent circuit model based on differential-algebraic equations, the system of ordinary differential equations is a constraint condition of an optimization problem, and the loss function is an objective function of the optimization problem, and the minimum value of the loss function is obtained by solving the optimization problem, and the optimization problem is shown in equations (7)-(9):

[0069]

[0070] s.t.c i (x)=0,i∈ε1={1,2,...,l}(8)

[0071] c i (x)≤0,i∈ε2={l+1,l+2,...,l+m} (9)。

[0072] In the preferred embodiment of the four-step method for identifying the parameters of the lithium battery equivalent circuit model based on differential-algebraic equations, when the values of the battery terminal voltage and the current include the charging stage, the discharging stage and the standing stage at the same time, the parameters of the lithium battery are identified in the whole charging and discharging stage; when the values of the battery terminal voltage and the current include only one of the charging stage, the discharging stage and the standing stage, the parameters of the lithium battery are identified in each charging and discharging stage.

[0073] In the preferred embodiment of the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations, when all the equivalent circuit model parameters are unknown, all the model parameters of the equivalent circuit model are identified; when some of the equivalent circuit model parameters are known, the remaining model parameters are identified by regarding the known model parameters as constants.

[0074] In the preferred embodiment of the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations, the lithium battery equivalent circuit model is an Rint model, a Thevenin model, a DP model, and a PNGV model.

[0075] In the preferred embodiment of the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations, the lithium battery is replaced by a lead-acid battery, a sodium-sulfur battery, a flow battery, and a supercapacitor.

[0076] In the preferred embodiment of the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations, the loss function is constructed as an absolute value loss function, a log loss function, and a square loss function.

[0077] In the preferred embodiment of the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations, the gradient descent method is replaced by a stochastic gradient descent method, a Momentum gradient descent method, and an AdaGrad gradient descent method.

[0078] In the preferred embodiment of the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations, the numerical solution method of the equivalent circuit model includes Euler method, improved Euler method, and Runge-Kutta method.

[0079] In one embodiment, the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations includes selecting an equivalent circuit model, establishing a differential algebraic equation corresponding to the equivalent circuit model and converting it into a system of ordinary differential equations, constructing a loss function, determining a gradient descent method, selecting a suitable numerical solution method, and identifying the model parameters of the lithium battery equivalent circuit model.

[0080] In a specific example, a Samsung 18650 lithium battery is used as an example to identify the model parameters of the lithium battery.

[0081] As shown in Figure 1 , the four-step method for identifying parameters of a lithium battery equivalent circuit model based on differential algebraic equations proposed by the present application is performed as follows:

[0082] Step 1: In the specific example, a Thevenin second-order RC equivalent circuit model is selected, as shown in Figure 2 .

[0083] The equivalent circuit model is composed of an open-circuit voltage Uoc , Ohm resistance R0 and two RC network structure, U1, U2 are R1, R2 terminal voltage, U T represents the terminal voltage of the battery.

[0084] The differential algebraic equation of the lithium battery is established according to the Thevenin second-order RC equivalent circuit model. The differential algebraic equation is represented by equations (1)-(3):

[0085] U OC = IR0+I1R1+I2R2+U T (1)

[0086]

[0087]

[0088] Where t is the independent variable, I represents the current, I1, I2 represents the current flowing through R1, R2, C1, C2 represents the capacitance of the capacitor in the two RC circuits. The algebraic equation in the equation group is converted into the related ordinary differential equation. The ordinary differential equation is represented by equations (4)-(5):

[0089]

[0090]

[0091] Step 2: Obtain the battery terminal voltage value and current value from the battery test system or simulation software, and the initial state value of the battery terminal, such as the state of charge (SOC) of the battery, temperature, etc. In this specific example, the hybrid power pulse characteristic (HPPC) experimental method is used for parameter identification. By inputting the given battery and the output of the battery response into the battery model, the battery parameters can be identified. Divide the SOC into ten equal parts, which are 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0, respectively. Perform a pulse discharge experiment at each equal point. At room temperature, use HPPC to perform the following experiments:

[0092] (1) The battery is fully charged, and is left for 1 hour. Discharge completely at 1C current, record the time required, repeat 3 times, calculate the average value of the battery capacity; (requirement: the error of three times capacity is less than 2%)

[0093] (2) After the battery is fully charged, discharge to 90% SOC at 1C current, stand for 1 hour, discharge at 5C current for 10s, stand for 30s, charge for 10s;

[0094] (3) Again, the battery is fully charged, and discharged at 1C to reduce the state of charge (SOC) by 10%, repeat step (2), and end the experiment when SOC = 0.

[0095] The lithium battery capacity (Q) obtained by three capacity tests is 3.3553 Ah, 3.3532 Ah, and 3.3448 Ah, respectively. The average of the three results is Q = 3.3511 Ah. According to the calculation, the maximum capacity error in the three capacity tests is 1.88%, which is less than 2%, so this test meets the experimental requirements and can proceed to the next test.

[0096] According to the ordinary differential equation and the obtained battery terminal voltage and current values, a loss function is constructed, and relevant constraint conditions are established. In this specific example, a square loss function is used to establish the loss function, and is represented by equation (6):

[0097]

[0098] In equation (6), y represents the voltage experimental value, represents the voltage simulation value, and represents the square loss function. The relevant constraint conditions are represented by equation (7):

[0099]

[0100] In equation (7), U oc represents the open-circuit voltage, R0 represents the ohmic resistance, U1 and U2 are the terminal voltages of R1 and R2, respectively, represents the terminal voltage of the battery in the equivalent circuit model.

[0101] After constructing the loss function and the constraint conditions, the optimization problem can be established, which is shown in equations (8) and (9):

[0102]

[0103]

[0104] Step 3: Select an appropriate optimization method such as gradient descent, stochastic gradient descent, Momentum gradient descent, etc. In this specific example, the gradient descent method is selected as the optimization method to identify the model parameters R0, R1, R2, C1, and C2. The equation is shown in equation (10):

[0105]

[0106] where the model parameters R0 i , R1 i , R2 i , C1 i , and C2 iR0 represents the identified parameter value of the current iteration, R0 represents the model parameter of the left formula i+1 R1 i+1 R2 i+1 C1 i+1 C2 i+1 R1 represents the identified parameter value of the next iteration, eta represents the learning rate, and L represents the loss function

[0107] The ordinary differential equation system formula (4)-formula (5) is solved by the identified parameter value of the current iteration, and the Runge-Kutta numerical solution method is used to solve the ordinary differential equation system in this embodiment. After formula (4)-formula (5) is solved, the loss function formula (6) is calculated according to the solving result and the experimental result, then the partial derivatives of the loss function formula (6) with respect to each independent variable are obtained, a vector composed of the partial derivatives is substituted into formula (10), and the identified parameter value of the next iteration can be obtained. Repeat the iteration until the minimum value of the loss function is obtained.

[0108] Step 4: Taking the working point near the state of charge SOC of 0.8 as an example, the battery parameters identified in the charging and discharging process are respectively brought into the lithium battery model, and the pulse charging and discharging simulation curve is obtained by solving the mathematical model of the equivalent circuit. As shown in Figure 3 , the pulse charging and discharging fitting curve and the experimental curve are shown. The battery parameters identified are shown in Table 1.

[0109] Table 1: Lithium battery model parameters when the state of charge SOC is 0.8

[0110]

[0111] By comparing the experimental data and the simulation data of the lithium battery, the error between the fitting curve of the terminal voltage response of the lithium battery model and the actual terminal voltage response curve can be obtained, as shown in Figure 4 .

[0112] It can be seen that the fitting voltage curve error range of each point is within about ±0.006V, i.e. 0.19%, which has a very high precision. For the second-order RC model identified this time, the maximum voltage error is 0.0059V, and the average error is 0.0021V. The voltage error is much smaller than the change range of the lithium battery platform voltage. Therefore, from the accuracy point of view, the model error is still within an acceptable range.

[0113] The results show that the four-step method for identifying the parameters of the lithium battery equivalent circuit model based on differential algebraic equations proposed in the present application can better fit the relationship between the measured and simulated terminal voltages in different intervals, and has good precision.

[0114] In one embodiment, the four-step method for identifying parameters of the lithium battery equivalent circuit model of the differential algebraic equation comprises the following steps: 1. selecting the equivalent circuit model of the lithium battery and establishing the differential algebraic equation; 2. constructing a loss function according to the equation and the battery terminal voltage and current values, and determining the relevant constraint conditions and initial values of the identified parameters; 3. solving the ordinary differential equation set, calculating the loss function according to the solving result and the battery terminal voltage and current values, and obtaining the identified parameter values of the next iteration by substituting the partial derivatives of each independent variable of the loss function into the gradient descent method; repeating the iteration until the minimum value of the loss function is obtained; and 4. predicting the volt-ampere characteristics and state of charge of the lithium battery according to the identified parameter values. The method can realize the parameter identification of the lithium battery equivalent circuit model by establishing a mathematical model, constructing a loss function, using a gradient descent optimization method and a numerical solution method, can fit the entire charging and discharging process, has a faster convergence speed, and has high battery performance prediction accuracy.

[0115] Although the embodiments of the present application are described above in conjunction with the drawings, the present application is not limited to the above-described specific embodiments and application fields, and the above-described specific embodiments are merely illustrative and instructive, but not restrictive. Those skilled in the art can make many forms under the guidance of the present specification and without departing from the scope protected by the claims of the present application, which all belong to the protection scope of the present application.

Claims

1. A four-step method for parameter identification of lithium battery equivalent circuit model based on differential-algebraic equations, characterized in that, It comprises the following steps, Step 1: selecting a lithium battery equivalent circuit model and establishing a differential algebraic equation, the form of the differential algebraic equation is expressed by formula (1): (1)， Where t is the independent variable, representing time, A and B are matrix functions of the independent variable t, F is a vector function of t, x(t) is a vector of unknown numbers, the matrix function A of the differential algebraic equation is non-singular, a system of ordinary differential equations is obtained based on the differential algebraic equation, and the form of the system of ordinary differential equations is expressed by formula (6): (6)， Where F is a vector function, t is an independent variable, u is a dependent variable, and the superscript n represents the n-th derivative of u; Step 2: obtaining the battery terminal voltage and current values and the initial state values of the lithium battery from the lithium battery test or simulation, constructing a loss function according to the differential algebraic equation, and establishing relevant constraint conditions, the form of the loss function is expressed by formula (2): (2)， In the formula, X represents an input parameter, y represents an observation result, distance represents a spatial distance between an observation sample and a simulation result, In the formula, X represents an input parameter, y represents an observation result, distance represents a spatial distance between an observation sample and a simulation result, In the formula, X represents an input parameter, y represents an observation result, distance represents a spatial distance between an observation sample and a simulation result, In the formula, X represents an input parameter, y represents an observation result, distance represents a spatial distance between an observation sample and a simulation result, In the formula, X represents an input parameter, y represents an observation result, distance represents a spatial distance between an observation (3)， (4)， Formula (3) is an equality constraint, and formula (4) is an inequality constraint, wherein x represents a state quantity, including the terminal voltage, terminal current and current and voltage values of each branch of the equivalent circuit model, l represents the number of equality constraints, m represents the number of inequality constraints, c represents a constraint relationship, the subscript i represents the order of the constraint condition, and ε represents a set of constraint conditions; Step 3: obtaining the minimum value of the loss function by using the gradient descent method and the numerical solution method, and the form of the gradient descent method is shown in formula (5): (5)， Where x on the right side represents the identification parameter value of the current iteration, x on the left side represents the identification parameter value of the next iteration, i represents the number of iterations, eta represents the learning rate, and L represents the loss function; Step 3-1, solving the system of ordinary differential equations represented by formula (6) by using the identification parameter value of the current iteration; step 3-2, calculating the loss function according to the solving result of the system of ordinary differential equations and the experimental result; step 3-3, calculating the identification parameter value of the next iteration by taking the partial derivative of the loss function with respect to each independent variable and obtaining a vector composed of the partial derivatives, and repeating steps 3-1 to 3-3 until the minimum value of the loss function is obtained as the identification parameter value through iteration; Step 4: predicting the lithium battery volt-ampere characteristic and state of charge according to the identification parameter value, the system of ordinary differential equations is a constraint condition of the optimization problem, and the loss function is an objective function of the optimization problem, and the minimum value of the loss function is obtained by solving the optimization problem, and the optimization problem is shown in formula (7)-(9): (7)， (8)， (9), parameter identification is performed during the whole charging and discharging stage of the lithium battery, the model parameters fitted are more consistent with the overall charging and discharging curve, and the whole charging and discharging stage can be divided into several sub-stages, and then parameter identification is performed.

2. The four-step method for parameter identification of lithium battery equivalent circuit model based on differential algebraic equations according to claim 1, wherein, When the values of the battery terminal voltage and current include the charging stage, the discharging stage and the standing stage at the same time, the parameters of the lithium battery in the whole charging stage, the discharging stage and the standing stage are identified; when the values of the battery terminal voltage and current only include one of the charging stage, the discharging stage and the standing stage, the parameters of the lithium battery in each charging stage, discharging stage and standing stage are identified respectively.

3. The four-step method for parameter identification of lithium battery equivalent circuit model based on differential algebraic equations according to claim 1, wherein, When all the equivalent circuit model parameters are unknown, all the model parameters of the equivalent circuit model are identified; when part of the equivalent circuit model parameters are known, the remaining model parameters are identified by regarding the known model parameters as constants.

4. The four-step method for parameter identification of lithium battery equivalent circuit model based on differential algebraic equations according to claim 1, wherein, The lithium battery equivalent circuit model is Rint model, Thevenin model, DP model and PNGV model.

5. The four-step method for parameter identification of lithium battery equivalent circuit model based on differential algebraic equations according to claim 1, wherein, The lithium battery is replaced by a lead-acid battery, a sodium-sulfur battery, a flow battery and a super capacitor.

6. The four-step method for parameter identification of lithium battery equivalent circuit model based on differential algebraic equations according to claim 1, wherein, The loss function is constructed as an absolute value loss function, a log loss function, and a square loss function.

7. The four-step method for parameter identification of lithium battery equivalent circuit model based on differential algebraic equations according to claim 1, wherein, The gradient descent method is replaced by a stochastic gradient descent method, a Momentum gradient descent method, and an AdaGrad gradient descent method.

8. The four-step method for parameter identification of lithium battery equivalent circuit model based on differential algebraic equations according to claim 1, wherein, The numerical solution of the equivalent circuit model includes Euler method, improved Euler method, and Runge-Kutta method.

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