CN114740385A - Self-adaptive lithium ion battery state of charge estimation method - Google Patents

Abstract

The invention discloses a self-adaptive lithium ion battery state of charge estimation method, which comprises the following steps: establishing a second-order RC equivalent circuit model of the lithium ion battery, and identifying parameters of the second-order RC equivalent circuit model in an off-line manner; fitting a correlation curve between the open-circuit voltage and the state of charge of the lithium ion battery; verifying the accuracy of the model through a dynamic stress test; performing online identification on the model parameters according to a recursive least square method containing forgetting factors; and determining an estimated value of the state of charge of the lithium ion battery by using an adaptive extended Kalman particle filter algorithm. According to the method, the stability and the accuracy of the charge state estimation result are improved by outputting the weighted average value of a plurality of particles; the importance of the particles is sampled through the adaptive extended Kalman filtering algorithm, so that the operation efficiency of the algorithm is improved while the charge state of the lithium ion battery is accurately estimated.

Description

An Adaptive Method for Estimating the State of Charge of Li-ion Batteries

technical field

The invention belongs to the technical field of lithium ion batteries, and in particular relates to an adaptive method for estimating the state of charge of lithium ion batteries.

Background technique

Lithium batteries have the advantages of high energy density, high operating voltage, low self-discharge rate and long service life, and are widely used in new energy vehicles, mobile robots, new energy and other fields. However, lithium batteries also have many disadvantages, such as high internal resistance resulting in high temperature under high charge-discharge rates. At the same time, overcharge and overdischarge will damage the battery, shorten the battery life, and even cause accidents such as explosion. Therefore, detecting the working state of the lithium battery can significantly improve the performance and life of the lithium battery.

The state of charge (SOC) of a lithium battery is an important indicator to measure the state of a lithium battery, and it directly represents the remaining power of the battery. SOC is defined as the percentage of charge remaining after a lithium battery is fully charged. Accurate SOC estimation can prevent battery overcharge and discharge, improve battery performance and prolong battery life. Due to the nonlinear characteristics of Li-ion batteries, SOC cannot be directly measured by sensors. At present, the commonly used methods in the field of SOC estimation include data-driven methods, direct estimation methods and model-based estimation methods.

The SOC estimation method based on the equivalent circuit model simulates battery dynamics by establishing an equivalent circuit model, which has strong robustness and is therefore very suitable for SOC estimation of lithium-ion batteries. In addition, the method based on the equivalent circuit model also needs to be combined with a filtering algorithm to estimate the battery SOC. In the invention patent with the patent application number of CN201910567240.2, "Power Lithium Battery SOC Estimation Method Based on Adaptive Kalman Filtering Method", the adaptive extended Kalman filtering algorithm is used to estimate the battery SOC. Although the computational complexity of the adaptive extended Kalman filter algorithm is not high, the algorithm cannot deal with non-Gaussian noise, and there is a model linearization error when the system is strongly nonlinear. In the invention patent with the patent application number CN201910567240.2, "State of Charge Estimation Method and Battery Management System Based on Adaptive Particle Filtering", the particle filter algorithm is used to estimate the battery SOC. Although the particle filter algorithm can deal with the nonlinearity of the system and the non-Gaussian noise, there is a problem that the particle degradation leads to a high computational complexity of the algorithm.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide an adaptive lithium-ion battery state-of-charge estimation method to solve the problems existing in particle filtering and adaptive extended Kalman filtering: it can not only deal with the situation of system nonlinearity and non-Gaussian noise, It can also ensure the operation efficiency of the algorithm.

For realizing the above-mentioned technical purpose, the present invention adopts following technical scheme:

An adaptive lithium-ion battery state of charge estimation method, comprising the following steps:

Step S1, establishing a second-order RC equivalent circuit model of the lithium-ion battery, performing an HPPC cycle working condition experiment, and using an exponential fitting method to perform offline identification of the parameters of the equivalent circuit model;

Step S2, obtaining the correlation curve between the battery open circuit voltage and the state of charge according to the result of the HPPC cycle working condition experiment;

Step S3, input the correlation curve of the current, open circuit voltage and state of charge of the battery dynamic stress test and the equivalent circuit model parameters identified offline into the battery equivalent circuit model to obtain the corresponding output voltage of the equivalent circuit model; compare The error between the output voltage of the equivalent circuit model and the actual dynamic stress test voltage verifies the accuracy of the equivalent circuit model;

Step S4, using the recursive least squares method with forgetting factor to update the parameters of the equivalent circuit model online;

Step S5, derive the state space equation and the observation equation of the battery according to the mathematical expression of the equivalent circuit model, and use the adaptive extended Kalman particle filter to estimate the state of charge of the lithium-ion battery.

In a better technical solution, the mathematical expression of the equivalent circuit model in step S1 is:

Among them, U _oc is the open circuit voltage of the battery; R ₀ is the ohmic internal resistance of the battery; R ₁ and C ₁ are the resistance and capacitance of the electrochemical polarization reaction of the battery; R ₂ and C ₂ are the concentration polarization reaction of the battery. Resistance and capacitance; U _t is the terminal voltage of the battery.

In a better technical solution, the specific process of the HPPC experiment in step S1 is as follows: after the battery is allowed to stand for 5 minutes, when the battery voltage is charged to 4.2V with a constant current of 0.5C, it is converted into a constant voltage charging mode; After charging the battery current to less than 0.05C in pressure charging mode, stop charging and let the battery stand for 2 hours; then discharge it at 3C, let the battery stand for 1 hour every time the state of charge drops by 10%, and measure the corresponding Open circuit voltage, repeat the above steps until the battery state of charge is 0%.

In a more optimal technical solution, the offline identification process of the parameters described in step S1 is:

(1) According to the terminal voltage V ₁ 1 second before the loading of the HPPC pulse, the terminal voltage V ₂ at the moment of loading the HPPC pulse, the terminal voltage V ₃ at the end of the loading HPPC pulse and the terminal voltage 1 second after the end of the loading HPPC pulse V ₄ , the ohmic resistance R ₀ in the lithium-ion equivalent circuit is calculated, and the calculation formula is as follows:

(2) The zero input voltage response of the battery during the stationary process of the HPPC pulse charge-discharge experiment is:

Among them, U ₁ (0) and U ₂ (0) are the terminal voltages of the two RC networks respectively, τ ₁ =R ₁ C ₁ , τ ₂ =R ₂ C ₂ ; using the matlab fitting toolbox, the above formula Perform fitting, and calculate the specific values of the two time constants τ ₁ and τ ₂ ;

(3) The zero-state response of the RC network during the HPPC pulse charge-discharge experiment of the battery is:

Similarly, fit the above formula in the matlab fitting toolbox to obtain the specific values of R ₁ and R ₂ ;

(4) According to the relational expressions τ ₁ =R ₁ C ₁ , τ ₂ =R ₂ C ₂ , and the obtained R ₁ and R ₂ , the specific values of C ₁ and C ₂ are obtained.

In a better technical solution, the specific model of the correlation curve between the open circuit voltage and the state of charge in step S2 is:

U _oc =k ₁ SOC ⁶ -k ₂ SOC ³ +k ₃ SOC ⁴ -k ₄ SOC ³ +k ₅ SOC ² +k ₆ SOC+k ₇

Among them, k ₁ , k ₂ . . . k ₇ are coefficients to be fitted, which are obtained by fitting the open-circuit voltage points under 10 states of charge.

In a better technical solution, the dynamic stress test in step S3 refers to: cyclically testing the battery under a dynamic stress condition until the voltage is less than 3V; wherein one dynamic stress condition contains multiple charge-discharge pulses , it will take 360 seconds for each dynamic stress condition test, and the battery needs to stand for 120 seconds before the next dynamic stress condition test is performed; the shortest duration of a single discharge pulse in the dynamic stress condition is 8 seconds, and the longest It can reach 40 seconds for a long time, the maximum discharge current is 2C, and the maximum charging current is 0.5C.

In a better technical solution, the specific steps of step S4 include:

(1) Calculate the error between the parameter identification result at the last moment and the actual battery voltage measured by the sensor:

为当前时刻测量向量，

为上一时刻估计出的模型参数向量，e(k)上一时刻通过参数辨识结果得到的模型输出电压与实际电池输出电压的误差；Among them, y(k) is the real voltage of the battery at the current moment,

measure the vector for the current moment,

is the model parameter vector estimated at the last moment, e(k) the error between the model output voltage obtained through the parameter identification result at the last moment and the actual battery output voltage;

(2) Update the gain matrix

Among them, P(k-1) is the covariance matrix at the previous moment, λ is the forgetting factor, and K(k) is the gain matrix at the current moment;

(3) Update the covariance matrix to calculate the gain matrix at the next moment

(4) Use the gain matrix and the error to update the parameter identification result at the current moment

In a better technical solution, the state space equation and the observation equation of the battery described in step S5 are respectively:

U _t,k =U _oc,k -U _1,k -U _2,k -I _k R ₀

Among them, T is the sampling time, k is the discrete time variable, and Q is the rated capacity of the battery.

In a more optimal technical solution, the particles of the adaptive extended Kalman particle filter described in step S5 are a series of random samples with weights, and the specific steps are:

以及粒子权重设为

(1) Initialize the particle set

and particle weights set to

(2) The adaptive extended Kalman filter is used as the importance sampling function

(3) Update the particle weight according to the following formula:

(4) Normalize the weights:

(5) Calculate the effective number of particles according to the following formula:

Among them, N _eff is the effective number of particles. If N _eff is less than 0.7N, resampling is required;

(6) Obtain the estimation result of the current moment:

(7) Go back to step (2) and set k=k+1 until the loop ends.

The beneficial effects of the invention are as follows: the invention establishes a second-order RC equivalent circuit model of the lithium ion battery, and uses the exponential fitting method to identify the model parameters offline; The model parameters were identified online by recursive least squares method with forgetting factor. Based on the model parameters identified online, combined with the adaptive extended Kalman particle filter algorithm, the state of charge estimation of the lithium-ion battery was realized. The invention combines the adaptive extended Kalman filter algorithm with the particle filter algorithm, and improves the stability and accuracy of the SOC estimation result by outputting the weighted average value of multiple particles; the adaptive extended Kalman filter is used as the importance sampling function, The operation efficiency of the algorithm is improved.

Description of drawings

Figure 1 is a flow chart of the present invention.

FIG. 2 is a schematic diagram of a second-order RC equivalent circuit model in the present invention.

Detailed ways

The present invention is described in detail below in conjunction with the examples. The present example is carried out based on the technical solutions of the present invention, and provides detailed implementation modes and specific operation processes, and further explains the technical solutions of the present invention.

As shown in FIG. 1 , a method for estimating state of charge based on adaptive extended Kalman particle filter of the present invention includes the following steps:

In step S1, firstly, a second-order RC equivalent circuit model of the lithium-ion battery is established, and the equivalent circuit model is shown in FIG. 2 . where R ₀ represents the ohmic internal resistance; the first RC network, R ₁ and C ₁ , is used to describe the electrochemical polarization reaction of the battery; the second RC network, R ₂ and C ₂ , is used to describe the concentration polarization of the battery reaction; U _t is the battery terminal voltage; U _oc is the battery open circuit voltage; I is the battery load current. According to Kirchhoff's current-voltage law, the mathematical expression of the second-order RC equivalent circuit model can be obtained:

In order to identify the initial values of the unknown parameters R ₀ , R ₁ , R ₂ , C ₁ , and C ₂ in the model, the present invention adopts an offline parameter identification method. Using the terminal voltage data of HPPC cycle conditions, combined with the fitting toolbox of matlab, the above parameters can be identified.

Before the parameter identification, the HPPC pulse charge and discharge experiment needs to be carried out. The process is: first, let the battery stand for 5 minutes, then charge the battery voltage to 4.2V with a constant current of 0.5C, and then change to the constant voltage charging mode. After charging the battery current to less than 0.05C in constant voltage charging mode, stop charging and let the battery stand for 2 hours. After that, it was discharged at 3C, and the battery was allowed to stand for 1 hour for every 10% drop in the state of charge, and the corresponding open circuit voltage was measured. Repeat this step until the battery state of charge is 0%.

After that, the initial values of the model parameters are identified offline. According to the terminal voltage V ₁ 1 second before the loading of the HPPC pulse, the terminal voltage V ₂ at the moment of loading the HPPC pulse, the terminal voltage V ₃ at the end of the loading HPPC pulse, and the terminal voltage V ₄ 1 second after the loading of the HPPC pulse, it can be calculated The ohmic resistance R ₀ in the lithium-ion equivalent circuit is obtained, and the calculation formula is as follows:

Then, by fitting the zero-input voltage response of the battery during the stationary process of the HPPC pulse charge-discharge experiment, the specific values of the two time constants τ ₁ and τ ₂ can be calculated:

By fitting the zero-state response of the RC network, the values of R ₁ and R ₂ can be obtained:

Since τ ₁ =R ₁ C ₁ , τ ₂ =R ₂ C ₂ , and R ₁ and R ₂ are known at this time, C ₁ and C ₂ can be solved to complete the second-order RC equivalent circuit model Parameter initial value identification.

Step S2, fitting the correlation curve between the open circuit voltage and the state of charge. First, 10 data points were calibrated using the HPPC cycle experiment, namely the open circuit voltage corresponding to 100% state of charge, the open circuit voltage corresponding to 90% state of charge...the open circuit voltage corresponding to 0% state of charge. Then use a sixth-order polynomial model to fit the above 10 data points. The expression of the sixth-order polynomial model is:

U _oc =k ₁ SOC ⁶ -k ₂ SOC ³ +k ₃ SOC ⁴ -k ₄ SOC ³ +k ₅ SOC ² +k ₆ SOC+k ₇

After completing the fitting of the open-circuit voltage and the state of charge calibration points, the values of k ₁ , k ₂ . . . k ₇ can be obtained. This polynomial is also the correlation curve between the open circuit voltage and the state of charge.

In step S3, the battery is tested cyclically using the dynamic stress test condition to verify the accuracy of the established model. First of all, the dynamic stress test should be carried out, that is, in the time of 360 seconds, the applied pulse currents are of different durations and sizes. The shortest duration of a single discharge pulse is 8 seconds, the longest time can reach 40 seconds, the maximum discharge current is 2C, and the maximum charging current is 0.5C. Then the next dynamic stress condition test is performed after an interval of 120 seconds, until the terminal voltage of the battery is lower than 3V.

The expression for the voltage at the output of the battery model is:

U _t =U _oc -U ₁ -U ₂ -IR ₀

Among them, U _oc can be obtained by the correlation curve between the state of charge and open circuit voltage, and U ₁ and U ₂ can be obtained by calculating the identified R ₁ , R ₂ , C ₁ , and C ₂ . Therefore, by inputting the current of the battery dynamic stress test into the battery model, the corresponding model output voltage can be obtained. Then, the accuracy of the model is verified by comparing the error between the output voltage of the model and the actual dynamic stress test voltage.

In step S4, using recursive least squares with forgetting factor to identify the model parameters online, the main steps include:

(1) Calculate the error between the parameter identification result at the last moment and the actual battery voltage measured by the sensor

为当前时刻测量向量，

为上一时刻估计出的模型参数向量，e(k)上一时刻通过参数辨识结果得到的模型输出电压与实际电池输出电压的误差。Among them, y(k) is the real voltage of the battery at the current moment,

measure the vector for the current moment,

is the model parameter vector estimated at the last moment, e(k) the error between the model output voltage obtained through the parameter identification result at the last moment and the actual battery output voltage.

(2) Update the gain matrix

Among them, P(k-1) is the covariance matrix at the previous moment, λ is the forgetting factor, and K(k) is the gain matrix at the current moment.

(3) Update the covariance matrix to calculate the gain matrix at the next moment

(4) Use the gain matrix and the error to update the parameter identification result at the current moment

In step S5, the state of charge of the lithium-ion battery is estimated based on the adaptive extended Kalman particle filter. Before carrying out the specific filtering algorithm, it is necessary to establish the relevant state equation and measurement equation. For a discrete control system, its state equation and observation equation can be expressed as:

x _k =A _k-1 x _k-1 +B _k-1 u _k-1 +w _k-1

y _k =C _k x _k +D _k u _k +v _k

Among them, x _k is the system state vector at the k-th time; y _k is the measurement vector at the _k -th time; uk is the input vector at the k-th time; w and v are the process noise and measurement noise of the system, respectively; A, B, The C and D matrices are the parameter matrices of the system. The present invention uses SOC(k+1) U ₁ (k+1) U ₂ (k+1) ^T as the state vector of the system, U _t as the output of the system, and I as the input of the system. According to the mathematical expression of the second-order RC equivalent circuit model and the definition of SOC, write the state equation and the observation equation:

U _t,k =U _oc,k -U _1,k -U _2,k -I _k R ₀

D_k＝-R₀。Among them, T is the sampling time, k is the discrete time variable, Q is the rated capacity of the battery,

D _k = -R ₀ .

Then, the state of charge of the lithium-ion battery is estimated by using the adaptive extended Kalman particle filter, where the particles are a group of random samples with weights. The specific steps are as follows:

以及粒子权重设为

(1) Initialize the particle set

and particle weights set to

需要用到上述推导出的ABCD矩阵。因为自适应扩展卡尔曼滤波为现有技术，因此在本发明中不进行重复的阐述；(2) Use adaptive extended Kalman filter to generate importance sampling function

The ABCD matrix derived above needs to be used. Because the adaptive extended Kalman filter is the prior art, it will not be repeated in the present invention;

(3) Update the particle weight according to the following formula:

(4) Normalize the weights:

(5) Calculate the effective number of particles according to the following formula:

Among them, N _eff is the effective number of particles. If N _eff is less than 0.7N, resampling is required;

(6) Obtain the estimation result of the current moment:

(7) Go back to step (2) and set k=k+1 until the loop ends.

The above embodiments are the preferred embodiments of the application, and those of ordinary skill in the art can also carry out various transformations or improvements on this basis. Without departing from the general concept of the application, these transformations or improvements should belong to the present application. within the scope of the application for protection.

Claims (9)

1. A self-adaptive lithium ion battery state of charge estimation method is characterized by comprising the following steps:

s1, establishing a second-order RC equivalent circuit model of the lithium ion battery, performing an HPPC cycle condition experiment, and performing off-line identification on parameters of the equivalent circuit model by using an exponential fitting method;

step S2, obtaining a correlation curve of the open-circuit voltage and the state of charge of the battery according to the result of the HPPC cycle condition experiment;

step S3, inputting the correlation curves of current, open-circuit voltage and state of charge of the battery dynamic stress test and the equivalent circuit model parameters of off-line identification into the battery equivalent circuit model to obtain the corresponding equivalent circuit model output voltage; comparing the error between the output voltage of the equivalent circuit model and the actual dynamic stress test voltage, and verifying the accuracy of the equivalent circuit model;

step S4, updating the equivalent circuit model parameters on line by using a recursive least square method containing forgetting factors;

and step S5, deducing a state space equation and an observation equation of the battery according to the mathematical expression of the equivalent circuit model, and estimating the state of charge of the lithium ion battery by using the adaptive extended Kalman particle filter.

2. The adaptive lithium ion battery state of charge estimation method of claim 1, wherein the mathematical expression of the equivalent circuit model in step S1 is as follows:

wherein, U_ocIs the open circuit voltage of the battery; r₀Ohmic internal resistance of the battery; r is₁And C₁Is the resistance and capacitance representing the electrochemical polarization reaction of the cell; r₂And C₂Is the resistance and capacitance representing the concentration polarization reaction of the cell; u shape_tIs the terminal voltage of the battery.

3. The adaptive lithium ion battery state of charge estimation method according to claim 1, wherein the specific process of the HPPC experiment in step S1 is as follows: after the battery is kept stand for 5 minutes, when the voltage of the battery is charged to 4.2V by the current with the constant current of 0.5C, the battery is converted into a constant voltage charging mode; in the constant voltage charging mode, after the current of the battery is charged to be lower than 0.05C, the charging is stopped, and the battery is kept stand for 2 hours; discharging at 3C, standing the battery for 1 hour when the charge state is reduced by 10%, measuring the corresponding open-circuit voltage, and repeating the steps until the charge state of the battery is 0%.

4. The adaptive lithium ion battery state of charge estimation method according to claim 1, wherein the offline identification process of the parameters in step S1 is as follows:

(1) according to the terminal voltage V1 second before the lithium ion battery is loaded with the HPPC pulse₁Terminal voltage V at moment of loading HPPC pulse₂End voltage V at the moment of finishing of loading HPPC pulse₃And terminal voltage V1 second after the end of the HPPC pulse loading₄Calculating ohmic resistance R in the lithium ion equivalent circuit₀The calculation formula is as follows:

(2) the zero input voltage response of the battery in the standing process of the HPPC pulse charge-discharge experiment is as follows:

wherein, U₁(0) And U₂(0) Terminal voltages, τ, of two RC networks, respectively₁＝R₁C₁，τ₂＝R₂C₂(ii) a Fitting the above formula by using a fitting tool box of matlab, and calculating two time constants tau₁And τ₂The specific value of (a);

(3) the zero state response of the RC network in the HPPC pulse charging and discharging experiment process of the battery is as follows:

likewise, the above equation was fit in the matlab fitting toolsetTo obtain a specific R₁And R₂Taking the value of (A);

(4) according to the relation₁＝R₁C₁，τ₂＝R₂C₂And R already obtained₁And R₂Solve for C₁And C₂The specific value of (a).

5. The adaptive lithium ion battery state of charge estimation method according to claim 1, wherein the specific model of the open-circuit voltage and state of charge correlation curve in step S2 is:

U_oc＝k₁SOC⁶-k₂SOC³+k₃SOC⁴-k₄SOC³+k₅SOC²+k₆SOC+k₇

wherein k is₁，k₂…k₇The coefficient to be fitted is obtained by fitting the open circuit voltage points at 10 states of charge.

6. The adaptive lithium ion battery state of charge estimation method of claim 1, wherein the dynamic stress test in step S3 refers to: carrying out a cyclic test on the battery under the dynamic stress working condition until the voltage is less than 3V; the dynamic stress working condition test method comprises the following steps that (1) one dynamic stress working condition comprises a plurality of charging and discharging pulses, 360 seconds are consumed when each dynamic stress working condition test is carried out, and the battery still needs to stand for 120 seconds before the next dynamic stress working condition test is carried out; the shortest duration time of a single discharge pulse in the dynamic stress working condition is 8 seconds, the longest duration time can reach 40 seconds, the maximum discharge current is 2C, and the maximum charge current is 0.5C.

7. The adaptive lithium ion battery state of charge estimation method according to claim 1, wherein the specific step of step S4 includes:

(1) calculating the error between the parameter identification result at the last moment and the actual battery voltage measured by the sensor:

wherein y (k) is the real battery voltage at the current moment,

the vector is measured for the current time instant,

e (k) the error between the model output voltage and the actual battery output voltage obtained by the parameter identification result at the last moment;

(2) updating a gain matrix

Wherein, P (k-1) is a covariance matrix at the last moment, lambda is a forgetting factor, and K (k) is a gain matrix at the current moment;

(3) updating the covariance matrix for calculating the gain matrix at the next time instant

(4) Updating the current time parameter identification result by using the gain matrix and the error

8. The adaptive lithium ion battery state-of-charge estimation method of claim 1, wherein the state space equation and the observation equation of the battery in step S5 are respectively:

U_t,k＝U_oc,k-U_1,k-U_2,k-I_kR₀

wherein T is sampling time, k is discrete time variable, and Q is battery rated capacity.

9. The adaptive lithium ion battery state of charge estimation method of claim 1, wherein the particles of the adaptive extended kalman particle filter of step S5 are a series of random samples with weights, and the specific steps are as follows:

(1) initializing a set of particles

And the particle weight is set to

(2) Adaptive extended Kalman filtering as an importance sampling function

(3) The particle weights are updated according to:

(4) normalizing the weights:

(5) the effective number of particles was calculated according to the following formula:

wherein N is_effIs the effective number of particles, if N_effIf the sampling rate is less than 0.7N, resampling is needed;

(6) obtaining a current time estimation result:

(7) returning to step (2), setting k to k +1 until the loop is ended.

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