CN116660758A - Method for identifying parameters and estimating state of charge of lithium battery model - Google Patents

Abstract

The invention provides a method for identifying parameters and estimating the state of charge of a lithium battery model, which establishes a fractional equivalent circuit model by analyzing electrochemical impedance spectrums of the lithium battery; providing a neighborhood-based multi-strategy and mean factor differential evolution algorithm NMMDE to identify model parameters; in the developed NMMDE algorithm, the invention provides a new mutation strategy, which firstly defines a dynamic neighborhood called a top domain, and then replaces the current individual with the average value of all individuals in the top domain; in addition, an extra mutation strategy is introduced in the mutation process, and the problems of exploration and unbalance utilization are overcome by adaptively adjusting the proportion of two different strategies in the population; and then estimating the SOC by using a fractional order extended Kalman filtering algorithm, and comparing the obtained SOC with an actual value, wherein the absolute error is 1 percent on average. Experimental results show that the algorithm provided by the invention can identify model parameters more accurately and obtain accurate SOC estimation results.

Description

Method for identifying parameters and estimating state of charge of lithium battery model

Technical Field

The invention relates to the technical field of parameter identification and state of charge estimation of a lithium battery model, in particular to a method for identifying parameters and estimating the state of charge of the lithium battery model.

Background

Nowadays, lithium batteries have been widely used in the fields of electric vehicles, hybrid vehicles, renewable energy storage systems, and the like, and accurate estimation of parameters of lithium batteries is critical to the safety, performance, and life of battery management systems. The battery model parameter identification method and the state of charge (SOC) estimation method are designed, so that the battery model parameter identification method and the SOC estimation method can help to monitor the battery electricity quantity, perform fault diagnosis and guide the charge and discharge behaviors of the battery. However, accurate identification of parameters and estimation of state of charge has been a challenging problem due to the complex chemistry and non-linear nature of lithium batteries.

At present, the following disadvantages exist in the identification of the parameters of the lithium battery model and the estimation of the state of charge:

1. the behavior of lithium batteries is affected by a variety of factors, such as temperature, charge-discharge rate, capacity fade, etc. Therefore, the model not only needs to have good adaptability and robustness to accurately predict the behavior of the battery, but also needs to balance the relationship between the accuracy of the model and the calculation cost, and a more complex model may need higher calculation resources and time and is not suitable for practical application, so that the modeling difficulty is greatly improved.

2. The parameters of the lithium battery model are usually multidimensional, including physical and chemical characteristics inside the battery, and when the parameters are identified by using an evolutionary algorithm, the evolutionary algorithm may fall into a problem of a locally optimal solution, and may result in that the optimal parameter solution cannot be obtained. To overcome this problem, appropriate heuristic strategies and mutation operations need to be designed to increase the ability of global searching. Thus, in practice, it is challenging to accurately identify these parameters.

3. The charge-discharge behavior of lithium batteries is typically nonlinear, resulting in a complex relationship between state of charge and battery voltage, current, etc. Therefore, an appropriate state estimation algorithm is required to solve the non-linearity problem.

Disclosure of Invention

In order to solve the problems, the invention provides a method for identifying the model parameters and estimating the state of charge of a lithium battery, which can accurately estimate the model parameters and the state of charge of the lithium battery, effectively manage and control a battery system and is important for optimizing the operation and the control of the lithium battery system.

The invention adopts the technical scheme that:

a method for identifying parameters and estimating state of charge of a lithium battery model comprises the following steps:

step 1, testing a battery through battery testing equipment and collecting data: obtaining the current maximum available capacity of the battery through a static capacity test, then adopting a hybrid power pulse characteristic test to obtain off-line data of the OCV of the battery, and carrying out a cyclic dynamic discharge test by using the federal city driving condition;

step 2, building a model: establishing a fractional equivalent circuit model through analysis of electrochemical impedance spectrum of the lithium battery;

step 3, identifying model parameters by using a neighborhood-based multi-strategy and mean factor differential evolution algorithm NMMDE;

and 4, estimating the state of charge of the battery by using a fractional order extended Kalman filtering algorithm according to the identified parameters.

Further, in step 2, the specific step of fractional modeling of the lithium battery includes:

step 2-1, the transfer function of the fractional order model is represented by equation (1),

in U _d Is the terminal voltage, U _OCV Is open circuit voltage, R ₀ Is ohmic internal resistance, R ₁ For electrochemically polarizing resistance, R ₂ Is concentration polarization resistance; c (C) ₁ 、C ₂ And W respectively represent constant phase element CPE ₁ 、CPE ₂ And a parameter of the wobbe impedance; v, k, r represent fractional order;

step 2-2, obtaining a corresponding relation between the SOC and the OCV by using a mixed power pulse characteristic test, and then fitting by using an eighth-order polynomial shown in an equation (2);

step 2-3, the system model of the fractional differential equation in the time domain is represented by equation (3); wherein y (t) =u _d (t)-U _OCV (t)，u(t)＝I(t)；

Step 2-4, discretizing the fractional derivative term using the DL definition, as shown in equation (4):

step 2-5, defining relevant parameters:

[a ₁ a ₂ a ₃ a ₄ ]＝[r v+r k+r v+k+r]

[b ₁ b ₂ b ₃ b ₄ ]＝[W WR ₁ C ₁ WR ₂ C ₂ WR ₁ C ₁ R ₂ C ₂ ]

[c ₁ c ₂ c ₃ c ₄ c ₅ c ₆ c ₇ ]＝[v k r v+k v+r k+r v+k+r]

[d ₁ d ₂ d ₃ d ₄ d ₅ d ₆ d ₇ ]＝[R ₁ C ₁ R ₂ C ₂ (R ₀ +R ₁ +R ₂ )W R ₁ C ₁ R ₂ C ₂ (R ₀ +R ₂ )WR ₁ C ₁ (R ₀ +R ₁ )WR ₂ C ₂ R ₀ WR ₁ C ₁ R ₂ C ₂ ]

equation (3) can be expressed according to the parameter definition as:

step 2-6, parameters a (i) and B (i) are defined using equation (6) for simplicity of description:

step 2-7, in order to meet the accuracy standard of the lithium battery model and simultaneously follow the short-time memory principle, the data length is required to be cut off to a proper size; when n=1, the system model equation (3) can be converted into a first order differential equation, represented by equation (7):

step 2-8, establishing a fractional equivalent circuit model of the lithium battery through an equation (7), wherein the parameter to be identified theta is expressed as an equation (8):

θ＝[R ₀ R ₁ C ₁ R ₂ C ₂ W v k r] (23)

further, the specific steps of the step 3 are as follows:

in step 3-1, the objective function uses the root mean square error between the actual voltage and the predicted voltage, represented by equation (9),

wherein: u (U) _d (j) Representing the terminal voltage of the jth sample point,the output voltage of the fractional order model is represented, and N represents the number of sampling points;

step 3-2, generating a randomly initialized population;

step 3-3, generating a new population according to a reverse learning strategy of the equation (10), adaptively sequencing the individuals of the new population and the individuals of the initialized population, wherein the individuals with the top NP are used as the current population, NP represents the size of the population, and D represents the dimension;

x _i ^D0,j ＝x _i ^j +w*r _1,i *(r _2,i *x _i ^0,j -x _i ^j ) (25)

x _i ^0,j ＝a _j +b _j -x _i ^j ,j＝1:D (26)

wherein: x is x _i ^j The jth generation, x, representing the ith particle _i ^0,j The corresponding inverse particle, representing the current particle, is calculated by equation (11); a, a _j And b _j Represents the boundary range, a, of the j-th dimensional variable of the particle _j Is lower bound, b _j Is an upper bound; w represents an inertial factor, r _1,i And r _2,i A random number between 0 and 1;

step 3-4, generating a crossing factor CR according to the JADE algorithm _i And mutant factor F _i ；

Step 3-5, setting a dynamic neighborhood, dynamically considering the number of high-quality individuals, and enabling the high-quality individuals to be used for guiding the searching process; in the mutation process, the value is calculated by equation (12),

wherein: _min representing the minimum sub-population size, f _best Represents the individual with the best fitness, f _i Indicating fitness value of individual i, G _m Representing a maximum number of iterations;

step 3-6, introducing a mean factor based on JADE algorithm, wherein equation (13) is a mutation strategy,

wherein: x is X ^j _{top_best} Represents the best individual in the top domain, X ^j _{top_avg} Mean value of all individuals in top domain, X ^j _r1 And X ^j _r2 Is a random individual in the population;

step 3-7, to avoid the limitation of a single strategy, introducing a 'DE/rand/1' mutation strategy, wherein equation (14) is an adaptive strategy selection mechanism, and carrying out mutation operation on the population;

step 3-8, intersecting and selecting the population;

step 3-9, S is compared with the JADE algorithm _CR 、S _F Updating the outdated population A;

and 3-10, iteratively updating until reaching a termination condition, and outputting an optimal solution.

Further, in step 4, the SOC is estimated by using a fractional order extended kalman filter algorithm, which specifically includes the following steps:

step 4-1, initializing a state, a state covariance matrix and noise, setting the covariance matrix as a diagonal matrix, and enabling elements on the diagonal to represent variances of all state quantities;

step 4-2, online updating parameters according to equation (15);

compared with the prior art, the invention has the advantages that:

(1) The fractional order modeling method is selected, and electrochemical dynamic behaviors inside the lithium battery can be accurately described through analysis of electrochemical impedance spectra;

(2) The NMMDE algorithm is adopted to identify the model parameters, and has higher identification precision, so that the problem that the particles deviate from an optimal search space in the search process to miss an optimal solution can be avoided;

(3) The SOC estimation is carried out by adopting a fractional order extended Kalman filtering algorithm, and the dynamic characteristics of a nonlinear system can be better described by introducing fractional order calculus, so that the estimation accuracy is improved.

Drawings

FIG. 1 is a schematic diagram of a fractional equivalent circuit model of a lithium battery;

FIG. 2 is a flow chart of a parameter identification algorithm for a model;

FIG. 3 is a graph of the voltage curves of the algorithms;

fig. 4 is a SOC estimation result.

Detailed Description

The invention is further described below with reference to the accompanying drawings.

The invention relates to a method for identifying parameters and estimating the state of charge of a lithium battery model, which comprises the following steps:

step 1, testing a battery through battery testing equipment and collecting data: and obtaining the current maximum available capacity of the battery through a static capacity test, then obtaining off-line data of the OCV of the battery by adopting a hybrid power pulse characteristic test, and carrying out a cyclic dynamic discharge test by using the federal city driving condition.

Step 2, building a model: a fractional equivalent circuit model was created by analysis of the electrochemical impedance spectrum of the lithium battery as shown in fig. 1.

The specific steps of fractional modeling of the lithium battery comprise:

step 2-1, the transfer function of the fractional order model is represented by equation (1),

in U _d Is the terminal voltage, U _OCV Is open circuit voltage, R ₀ Is ohmic internal resistance, R ₁ For electrochemically polarizing resistance, R ₂ Is concentration polarization resistance; c (C) ₁ 、C ₂ And W respectively represent constant phase element CPE ₁ 、CPE ₂ And a parameter of the wobbe impedance; v, k, r denote fractional order.

Step 2-2, obtaining a corresponding relation between the SOC and the OCV by using a mixed power pulse characteristic test, and then fitting by using an eighth-order polynomial shown in an equation (2);

step 2-3, the system model of the fractional differential equation in the time domain is represented by equation (3); wherein y (t) =u _d (t)-U _OCV (t)，u(t)＝I(t)；

Step 2-4, discretizing the fractional derivative term using the DL definition, as shown in equation (4):

step 2-5, defining relevant parameters:

[a ₁ a ₂ a ₃ a ₄ ]＝[r v+r k+r v+k+r]

[b ₁ b ₂ b ₃ b ₄ ]＝[W WR ₁ C ₁ WR ₂ C ₂ WR ₁ C ₁ R ₂ C ₂ ]

[c ₁ c ₂ c ₃ c ₄ c ₅ c ₆ c ₇ ]＝[v k r v+k v+r k+r v+k+r]

[d ₁ d ₂ d ₃ d ₄ d ₅ d ₆ d ₇ ]＝[R ₁ C ₁ R ₂ C ₂ (R ₀ +R ₁ +R ₂ )W R ₁ C ₁ R ₂ C ₂ (R ₀ +R ₂ )WR ₁ C ₁ (R ₀ +R ₁ )WR ₂ C ₂ R ₀ WR ₁ C ₁ R ₂ C ₂ ]

equation (3) can be expressed according to the parameter definition as:

step 2-6, parameters a (i) and B (i) are defined using equation (6) for simplicity of description:

step 2-7, in order to meet the accuracy standard of the lithium battery model and simultaneously follow the short-time memory principle, the data length is required to be cut off to a proper size; when n=1, the system model equation (3) can be converted into a first order differential equation, represented by equation (7):

step 2-8, establishing a fractional equivalent circuit model of the lithium battery through an equation (7), wherein the parameter to be identified theta is expressed as an equation (8):

θ＝[R ₀ R ₁ C ₁ R ₂ C ₂ W v k r] (38)

step 3, identifying model parameters by using a neighborhood-based multi-strategy and mean factor differential evolution algorithm NMMDE, as shown in fig. 2, specifically comprising the following steps:

in step 3-1, the objective function uses the root mean square error between the actual voltage and the predicted voltage, represented by equation (9),

wherein: u (U) _d (j) Representing the terminal voltage of the jth sample point,the output voltage of the fractional order model is represented, and N represents the number of sampling points;

step 3-2, generating a randomly initialized population;

step 3-3, generating a new population according to a reverse learning strategy of the equation (10), adaptively sequencing the individuals of the new population and the individuals of the initialized population, wherein the individuals with the top NP are used as the current population, NP represents the size of the population, and D represents the dimension;

x _i ^D0,j ＝x _i ^j +w*r _1,i *(r _2,i *x _i ^0,j -x _i ^j ) (40)

x _i ^0,j ＝a _j +b _j -x _i ^j ,j＝1:D (41)

wherein: x is x _i ^j The jth generation, x, representing the ith particle _i ^0,j The corresponding inverse particle, representing the current particle, is calculated by equation (11); a, a _j And b _j Represents the boundary range, a, of the j-th dimensional variable of the particle _j Is lower bound, b _j Is an upper bound; w represents an inertial factor, r _1,i And r _2,i A random number between 0 and 1;

step 3-4, generating a crossing factor CR according to the JADE algorithm _i And mutant factor F _i ；

Step 3-5, setting a dynamic neighborhood, dynamically considering the number of high-quality individuals, and enabling the high-quality individuals to be used for guiding the searching process; in the mutation process, the value is calculated by equation (12),

wherein: _min representing the minimum sub-population size, f _best Represents the individual with the best fitness, f _i Indicating fitness value of individual i, G _m Representing a maximum number of iterations;

step 3-6, introducing a mean factor based on JADE algorithm, wherein equation (13) is a mutation strategy,

wherein: x is X ^j _top _ _best Represents the best individual in the top domain, X ^j _{top_avg} Mean value of all individuals in top domain, X ^j _r1 And X ^j _r2 Is a random individual in the population;

step 3-7, to avoid the limitation of a single strategy, introducing a 'DE/rand/1' mutation strategy, wherein equation (14) is an adaptive strategy selection mechanism, and carrying out mutation operation on the population;

step 3-8, intersecting and selecting the population;

step 3-9, S is compared with the JADE algorithm _CR 、S _F Updating the outdated population A;

and 3-10, iteratively updating until reaching a termination condition, and outputting an optimal solution.

And 4, estimating the state of charge of the battery by using a fractional order extended Kalman filtering algorithm according to the identified parameters, wherein the specific steps are as follows:

step 4-1, initializing a state, a state covariance matrix and noise, setting the covariance matrix as a diagonal matrix, and enabling elements on the diagonal to represent variances of all state quantities;

step 4-2, online updating parameters according to equation (15);

regarding the evaluation of the test result, the invention compares with the accuracy of the parameter identification result of other algorithms in the field. In fig. 3, voltage curves of several advanced evolutionary algorithm (SEDE, PGJAYA, DOLJADE, JAD, LBLDE) parameter identification results are shown. The corresponding parameter identification results and root mean square errors are shown in tables 1 and 2.

Table 1 results of the identification of the algorithm parameters

Table 2 root mean square error results for each algorithm

The result shows that the algorithm designed in the invention can provide more accurate parameter results and obtain more accurate fitting results with real voltage, so that the monitoring of battery safety, health state and the like can be better realized. After the parameter identification result is obtained, the invention uses fractional order extended Kalman filtering algorithm to estimate the SOC of the battery, and the result is shown in figure 4. In order to verify the rapid convergence of the fractional order extended Kalman filtering algorithm, the invention gives an incorrect initial value, the SOC estimation value can be seen to rapidly converge to the vicinity of the correct value, the SOC value predicted by the fractional order extended Kalman filtering algorithm is matched with the actual SOC value, and the absolute error is 1% on average. Therefore, the invention can provide real-time SOC estimation data for the BMS, help the BMS optimize the charge and discharge strategy, and further improve the performance and service life of the battery.

Claims (4)

1. The method for identifying the parameters of the lithium battery model and estimating the state of charge is characterized by comprising the following steps:

step 1, testing a battery through battery testing equipment and collecting data: obtaining the current maximum available capacity of the battery through a static capacity test, then adopting a hybrid power pulse characteristic test to obtain off-line data of the OCV of the battery, and carrying out a cyclic dynamic discharge test by using the federal city driving condition;

step 2, building a model: establishing a fractional equivalent circuit model through analysis of electrochemical impedance spectrum of the lithium battery;

step 3, identifying model parameters by using a neighborhood-based multi-strategy and mean factor differential evolution algorithm NMMDE;

and 4, estimating the state of charge of the battery by using a fractional order extended Kalman filtering algorithm according to the identified parameters.

2. The method for identifying parameters and estimating state of charge of a lithium battery model according to claim 1, wherein the method comprises the following steps: in step 2, the specific steps of fractional modeling of the lithium battery include:

step 2-1, the transfer function of the fractional order model is represented by equation (1),

in U _d Is the terminal voltage, U _OCV Is open circuit voltage, R ₀ Is ohmic internal resistance, R ₁ For electrochemically polarizing resistance, R ₂ Is concentration polarization resistance; c (C) ₁ 、C ₂ And W respectively represent constant phase element CPE ₁ 、CPE ₂ And a parameter of the wobbe impedance; v, k, r represent fractional order;

step 2-2, obtaining a corresponding relation between the SOC and the OCV by using a mixed power pulse characteristic test, and then fitting by using an eighth-order polynomial shown in an equation (2);

step 2-3, the system model of the fractional differential equation in the time domain is represented by equation (3); wherein the method comprises the steps of

y(t)＝U _d (t)-U _OCV (t)，u(t)＝I(t)；

Step 2-4, discretizing the fractional derivative term using the DL definition, as shown in equation (4):

step 2-5, defining relevant parameters:

[a ₁ a ₂ a ₃ a ₄ ]＝[r v+r k+r v+k+r]

[b ₁ b ₂ b ₃ b ₄ ]＝[W WR ₁ C ₁ WR ₂ C ₂ WR ₁ C ₁ R ₂ C ₂ ]

[c ₁ c ₂ c ₃ c ₄ c ₅ c ₆ c ₇ ]＝[v k r v+k v+r k+r v+k+r]

[d ₁ d ₂ d ₃ d ₄ d ₅ d ₆ d ₇ ]＝[R ₁ C ₁ R ₂ C ₂ (R ₀ +R ₁ +R ₂ )W R ₁ C ₁ R ₂ C ₂ (R ₀ +R ₂ )WR ₁ C ₁ (R ₀ +R ₁ )WR ₂ C ₂ R ₀ WR ₁ C ₁ R ₂ C ₂ ]equation (3) can be expressed according to the parameter definition as:

step 2-6, parameters a (i) and B (i) are defined using equation (6) for simplicity of description:

step 2-7, in order to meet the accuracy standard of the lithium battery model and simultaneously follow the short-time memory principle, the data length is required to be cut off to a proper size; when n=1, the system model equation (3) can be converted into a first order differential equation, represented by equation (7):

step 2-8, establishing a fractional equivalent circuit model of the lithium battery through an equation (7), wherein the parameter to be identified theta is expressed as an equation (8):

θ＝[R ₀ R ₁ C ₁ R ₂ C ₂ W v k r] (8)。

3. the method for identifying parameters and estimating state of charge of a lithium battery model according to claim 1, wherein the specific steps of step 3 are as follows:

in step 3-1, the objective function uses the root mean square error between the actual voltage and the predicted voltage, represented by equation (9),

wherein: u (U) _d (j) Representing the terminal voltage of the jth sample point,the output voltage of the fractional order model is represented, and N represents the number of sampling points;

step 3-2, generating a randomly initialized population;

step 3-3, generating a new population according to a reverse learning strategy of the equation (10), adaptively sequencing the individuals of the new population and the individuals of the initialized population, wherein the individuals with the top NP are used as the current population, NP represents the size of the population, and D represents the dimension;

x _i ^D0,j ＝x _i ^j +w*r _1,i *(r _2,i *x _i ^0,j -x _i ^j ) (10)

x _i ^0,j ＝a _j +b _j -x _i ^j ,j＝1:D (11)

wherein: x is x _i ^j The jth generation, x, representing the ith particle _i ^0,j The corresponding inverse particle, representing the current particle, is calculated by equation (11); a, a _j And b _j Represents the boundary range, a, of the j-th dimensional variable of the particle _j Is lower bound, b _j Is an upper bound; w represents an inertial factor, r _1,i And r _2,i A random number between 0 and 1;

step 3-4, generating a crossing factor CR according to the JADE algorithm _i And mutant factor F _i ；

Step 3-5, setting a dynamic neighborhood, dynamically considering the number of high-quality individuals, and enabling the high-quality individuals to be used for guiding the searching process; in the mutation process, the value is calculated by equation (12),

wherein: _min representing the minimum sub-population size, f _best Represents the individual with the best fitness, f _i Indicating fitness value of individual i, G _m Representing a maximum number of iterations;

step 3-6, introducing a mean factor based on JADE algorithm, wherein equation (13) is a mutation strategy,

wherein: x is X ^j _top _ _best Represents the best individual in the top domain, X ^j _{top_avg} Mean value of all individuals in top domain, X ^j _r1 And X ^j _r2 Is a random individual in the population;

step 3-7, to avoid the limitation of a single strategy, introducing a 'DE/rand/1' mutation strategy, wherein equation (14) is an adaptive strategy selection mechanism, and carrying out mutation operation on the population;

step 3-8, intersecting and selecting the population;

step 3-9, S is compared with the JADE algorithm _CR 、S _F Updating the outdated population A;

and 3-10, iteratively updating until reaching a termination condition, and outputting an optimal solution.

4. The method for identifying parameters and estimating state of charge of a lithium battery model according to claim 1, wherein in step 4, the specific step of estimating SOC by using fractional order extended kalman filter algorithm is as follows:

step 4-1, initializing a state, a state covariance matrix and noise, setting the covariance matrix as a diagonal matrix, and enabling elements on the diagonal to represent variances of all state quantities;

step 4-2, online updating parameters according to equation (15);