CN109839599B - Lithium-ion battery SOC estimation method based on second-order EKF algorithm - Google Patents

Abstract

The invention discloses a method for estimating the SOC of a lithium ion battery based on a second-order EKF algorithm. The voltage curve and the charging and discharging static voltage curve characterizing the rebound characteristics of the battery; 2. Establish the equivalent circuit model of the battery; 3. Identify the parameters of the equivalent circuit model of the battery; 4. Use the second-order EKF algorithm to The SOC of the battery is estimated to obtain a prediction result of the SOC of the battery. The method of the invention has novel and reasonable design, convenient implementation, good adaptability to the dynamic and static characteristics of the battery, high estimation accuracy, strong practicability, and high popularization and application value.

Description

Lithium-ion battery SOC estimation method based on second-order EKF algorithm

technical field

The invention belongs to the technical field of battery SOC estimation, and in particular relates to a lithium-ion battery SOC estimation method based on a second-order EKF algorithm.

Background technique

In the current era of advocating green economy and advocating sustainable development, pure electric vehicles have become the main direction of current research due to their low noise, no pollution, and high energy efficiency. As the main power supply system and power carrier of electric vehicles, power battery is very important to the whole electric vehicle.

Due to the advantages of high cell voltage, high energy density and long cycle life, lithium-ion power batteries have become the first choice of many domestic and foreign automobile manufacturers. However, due to the immature lithium-ion power battery technology, there are disadvantages such as short mileage on one-time charging, poor safety performance and short battery life. Therefore, it is particularly important to effectively manage and control it through a battery management system (Battery Management System, BMS). In BMS, it is of great significance to accurately estimate the SOC working state of the battery pack, both for the BMS system itself and for electric vehicles. However, due to the influence of surrounding factors on the operation of electric vehicles, the SOC cannot be directly measured. Therefore, selecting the SOC estimation method suitable for the actual operation of the power battery is the main research direction of current scholars in the industry. The invention relates to the estimation of the remaining power (SOC) of a power battery, in particular to a method for estimating the SOC of a lithium ion battery based on a second-order EKF.

In recent years, domestic and foreign scholars' research methods on battery SOC are mainly divided into three categories.

The first category is the SOC estimation method based on the electrochemical properties of the battery, and the representative methods are: the ampere-hour integration (AH) method and the open circuit voltage (OCV) method. The battery dynamic model combined with the AH method is used to estimate the battery SOC, which can still be effectively estimated under the conditions of temperature and current changes. The experimental results show that the error range of the SOC is within 2.5%; based on the first-order equivalent Circuit model, the OCV method is improved and combined with the EKF algorithm to estimate the battery capacity and SOC respectively. The final result shows that the SOC estimation accuracy is controlled within ±5%. The advantage of this method is that the principle is simple and easy to implement, but it does not have the ability to correct in real time, and the SOC estimation error will increase significantly when the vehicle is in a strongly changing working condition.

The second category is mainly the emerging intelligent prediction algorithm based on artificial neural network. This algorithm uses the neural network estimation method of input time delay, and adopts the multilayer perceptron structure of back-propagation learning rules to adjust the weights between neurons to achieve accurate estimation. The simulation results show that the root mean square error of SOC estimation is: less than 0.35%. However, this method is based on a large amount of sample data, which is greatly affected by the scale of the sample data and the rules of the training algorithm, and the calculation amount is large, which increases the online cost.

The third type of method is mainly the Kalman Filter algorithm based on the battery model. Since the KF algorithm is for linear systems, and the algorithm for the nonlinear system of power batteries is mainly the first-order EKF algorithm, the SOC of the battery is estimated based on the electrochemical model of the battery combined with the extended Kalman filter. The experimental results show that the error is not large. More than 5%; considering the influence of the discharge rate change on the battery capacity, a dual power supply model was established, and the extended Kalman filter algorithm was used to estimate the SOC of the battery. The error is within 8% and the average error remains within 5%. Compared with other SOC estimation methods, the first-order EKF algorithm not only has the ability of online estimation, but also is suitable for various types of batteries, and has become a commonly used estimation method. question.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a lithium-ion battery SOC estimation method based on the second-order EKF algorithm, which is novel and reasonable in design, convenient in implementation, and adaptable to the dynamic and static characteristics of the battery, aiming at the deficiencies in the above-mentioned prior art. It has high estimation accuracy, strong practicability, and high promotion and application value.

In order to solve the above-mentioned technical problems, the technical solution adopted in the present invention is: a lithium-ion battery SOC estimation method based on a second-order EKF algorithm, the method comprises the following steps:

Step 1, analysis of the external characteristics of the battery, the specific process is: performing an intermittent charge-discharge experiment on the battery to obtain an open-circuit voltage curve representing the hysteresis characteristic of the battery and a charge-discharge static voltage curve representing the rebound characteristic of the battery;

Step 2, establish the equivalent circuit model of the battery, the specific process is as follows:

Step 201 , establishing an SOC calculation model of the battery, establishing an equivalent voltage source model according to an open circuit voltage curve of the battery, and establishing an equivalent impedance model according to a charging and discharging static voltage curve of the battery;

Step 202 , combining the three parts of the SOC calculation model, the equivalent voltage source model and the equivalent impedance model to establish an equivalent circuit model of the battery;

Step 3: Perform parameter identification on the parameters of the equivalent circuit model of the battery;

Step 4: Use the second-order EKF algorithm to estimate the SOC of the battery, and obtain the prediction result of the SOC of the battery.

In the above-mentioned method for estimating the SOC of a lithium-ion battery based on the second-order EKF algorithm, the specific process of performing an intermittent charge-discharge experiment on the battery described in step 1 is as follows:

Step 101, emptying the battery;

Step 102, charge at 1/3C discharge rate for 20min, when the battery voltage reaches 3.65V within 20min, go to Step 104, otherwise go to Step 103;

Step 103, let the battery stand for 30 minutes, and then return to step 102;

Step 104, fully charge the battery;

Step 105, discharge at 1/3C discharge rate for 20min, if the battery voltage is lower than 2.0V within 20min, go to step 107, otherwise go to step 106;

Step 106, let the battery stand for 30 minutes, and then return to step 105;

Step 107: Empty the battery with a small current of 0.02C.

In the above-mentioned method for estimating the SOC of a lithium-ion battery based on the second-order EKF algorithm, the SOC calculation model in step 202 includes a capacitor _CN and an equivalent battery B, and one end of the capacitor _CN is connected to the positive electrode of the equivalent battery B, so The other end of the capacitor _CN is connected to the negative electrode of the equivalent battery B; the equivalent voltage source model in step 202 includes a current source M, an inductance L _h , a voltage source U ₁ and a voltage source U ₂ , the current source M The positive electrode of U is connected to one end of the inductor L _h , the negative electrode of the current source M is connected to the other end of the inductor L _h , and the negative electrode of the voltage source U ₁ and the voltage source U ₂ connected in series is connected to the negative electrode of the current source M; step The equivalent impedance model in 202 includes a resistor R ₀ , a resistor R ₁ , a resistor R ₂ , a capacitor C ₁ and a capacitor C ₂ , the resistor R ₀ , the resistor R ₁ and the resistor R ₂ are connected in series, and the capacitor C ₁ is connected to the The resistor R ₁ is connected in parallel, the capacitor C ₂ is connected in parallel with the resistor R ₂ ; the negative electrode of the equivalent battery B is connected to the negative electrode of the voltage source U ₂ , the resistor R ₀ , the resistor R ₁ and the resistor R ₂ are connected in series after the resistor R _One end of ₀ is connected to the positive pole after the voltage source U1 and the voltage source _U2 are connected in series.

In the above-mentioned lithium-ion battery SOC estimation method based on the second-order EKF algorithm, the specific process of performing parameter identification on the parameters of the equivalent circuit model of the battery described in step 3 is as follows:

Step 301, parameter identification of the equivalent voltage source model: the equilibrium potential EMF of the battery is expressed as

EMF=0.5(EMF _c +EMF _d ) (F1)

The hysteresis voltage V _h of the battery is expressed as

V _h =0.5(EMF _c -EMF _d ) (F2)

Among them, EMF _c is the charge balance potential, and EMF _d is the discharge balance potential;

Step 302, parameter identification of the equivalent impedance model: the voltage U at any time is expressed as

R₂为电阻R₂的阻值，τ₂为与电阻R₂对应的时间常数且

t为时间；Among them, OCV _D is the voltage at time D of the charging and discharging static voltage curve, and time D is the time when the voltage does not change after the battery is discharged after the rebound stage; I is the current value flowing through the battery, and R ₁ is the resistance of the resistor R ₁ value, _τ1 is the time constant corresponding to resistor _R1 and

R2 is the resistance value of the resistor _R2 , _τ2 is the time _{constant corresponding} to the resistor R2 and

t is time;

Denote the fitting function as

f(x)=A-B·exp(-ax)-C·exp(-bx) (F4)

Fit the C-D stage of the charge-discharge static voltage curve to obtain the values of the parameters A, B, C, a and b in the fitting function; among them, the C-D stage of the charge-discharge static voltage curve refers to the moment when the battery is discharged The voltage mutation starts to the stage where the voltage does not change after the battery is discharged through the rebound stage; according to formula (F3) and formula (F4) correspondingly equal, the parameters of the equivalent impedance model are obtained as follows:

Among them, C ₁ is the capacitance value of the capacitor C ₁ , and C ₂ is the capacitance value of the capacitor C ₂ .

In the above-mentioned method for estimating the SOC of a lithium-ion battery based on the second-order EKF algorithm, the second-order EKF algorithm is used to estimate the SOC of the battery as described in step 4, and the specific process of obtaining the prediction result of the SOC of the battery is as follows:

Step 401 , establish a state space model of the battery system: according to the equivalent circuit model of the battery established in step 2, the SOC of the battery, the voltage V _{1 across the capacitor C 1 and} the voltage V ₂ across the capacitor C ₂ are used as the state of the system variable, the current value I flowing through the battery is the input quantity, and the terminal voltage V is the output quantity. According to the circuit equation, the state space model equation of the battery system is derived as:

The output equation is:

V(t)=V _OCV (SOC(t))-V ₁ (t)-V ₂ (t)-R ₀ I(t) (F7)

Among them, C _n is the rated capacity of the battery, V _OCV is the total voltage of the voltage source U ₁ and the voltage source U ₂ ;

Step 402: Linearize the nonlinear state space model equation of the battery system through a second-order Taylor expansion, and the specific process is as follows:

Step 4021: Perform the second-order Taylor expansion of the state space model equation (F6) of the battery system at the state estimation point to obtain:

为x_k的估计值；Among them, f(x _k , u _k ) is the state transition function, g(x _k , u _k ) is the measurement function, x _k is the state variable at time _k , uk is the control input of the system at time k,

is the estimated value of x _k ;

将公式(F8)代入非线性离散系统的状态空间模型方程

中，得到电池系统的线性化方程为：Step 4022, define

Substitute Equation (F8) into the state-space model equation of the nonlinear discrete system

, the linearized equation of the battery system is obtained as:

D_k＝R₀；R₀为电阻R₀的阻值，Δt为时间的变化量，ω_k为均值为零的过程噪声，v_k为均值为零的测量噪声，且ω_k与v_k互不相关，ω_k～N(0,Q_k)，v_k～N(0,R_k)；即ω_k和v_k均服从均值为0的高斯分布；in,

D _k =R ₀ ; R ₀ is the resistance value of the resistor R ₀ , Δt is the change in time, ω _k is the process noise with zero mean, v _k is the measurement noise with zero mean, and ω _k and v _k mutually Irrelevant, ω _k ～N(0, Q _k ), v _k ～N(0, R _k ); that is, both ω _k and v _k obey the Gaussian distribution with mean 0;

Step 403, using the second-order EKF algorithm to estimate the SOC of the lithium-ion battery, the specific process is:

Step 4031, initialization phase:

为x₀的估计值，P₀为状态变量预测估计的误差协方差矩阵的初始化值；Among them, x ₀ is the initialization value of the state variable,

is the estimated value of x ₀ , and P ₀ is the initialization value of the error covariance matrix of the state variable prediction estimation;

Step 4032, the prediction stage:

Predictive estimates of state variables:

为x_k-1的估计值，x_k-1为k-1时刻的状态变量，u_k-1为k-1时刻系统的控制输入量；in,

is the estimated value of x k- ₁ , x _k-1 is the state variable at time k-1, and u _k-1 is the control input of the system at time k-1;

Error covariance matrix for state variable prediction estimates:

Wherein, Q _k-1 is the covariance matrix of process noise at time k-1 and Q _k-1 =Q _k , Q _k is the covariance matrix of process noise at time k;

Step 4033, the correction stage:

Kalman filter gain:

where R is the covariance matrix of the observation noise;

Corrected estimates of state variables:

The error covariance matrix of the state variable correction estimate:

P _k =(IK _k C _k )P _k|k-1 (F15)

Step 4034: Repeat steps 4032 and 4033 until the number of iterations reaches a preset iteration termination value.

In the above-mentioned lithium-ion battery SOC estimation method based on the second-order EKF algorithm, the value of Q _k-1 described in step 4032 is

In the above-mentioned method for estimating the SOC of a lithium-ion battery based on the second-order EKF algorithm, the value of R in step 4033 is 0.1.

In the above-mentioned method for estimating the SOC of a lithium-ion battery based on the second-order EKF algorithm, the preset iteration termination value in step 4034 is 150.

Compared with the prior art, the present invention has the following advantages:

1. Aiming at the problem of inaccurate SOC estimation in the power battery management system, the present invention takes lithium batteries as the main research object, and the current first-order Extended Kalman Filter (EKF) algorithm has low precision and poor stability. On the basis of the first order, a second-order EKF algorithm based on the battery model is proposed to estimate the SOC of the battery. Experiments show that the second-order EKF algorithm has higher performance than the first-order EKF algorithm when estimating the SOC of the battery. The estimation accuracy is good, and it has good adaptability to the dynamic and static characteristics of the battery.

2. The present invention considers the hysteresis voltage phenomenon of the battery on the one hand, and fits the rebound voltage characteristics of the battery through RC circuits of different orders on the other hand. The second-order RC circuit model with hysteresis voltage characteristics can more accurately simulate the dynamic and static working characteristics of the battery, which is convenient to obtain more accurate SOC estimation results.

3. Since the power battery has a high degree of nonlinearity in the actual use process, and the first-order EKF algorithm ignores the high-order terms above the second order, its nonlinearity is weak and the estimation accuracy is not high. The second-order Taylor expansion of the state space equation of the system at the state estimation point can maintain the non-linearity of the battery and improve the estimation accuracy. The tracked true value of .

4. Experiments show that the error of the first-order EKF algorithm is within 5.5% and the error of the second-order EKF algorithm is not more than 3% in the whole discharge stage, which shows that the second-order EKF algorithm has better estimation accuracy than the first-order EKF algorithm. .

To sum up, the method of the present invention has novel and reasonable design, convenient implementation, good adaptability to the dynamic and static characteristics of the battery, high estimation accuracy, strong practicability, and high popularization and application value.

The technical solutions of the present invention will be further described in detail below through the accompanying drawings and embodiments.

Description of drawings

FIG. 1 is a flow chart of the method of the present invention.

FIG. 2 is an equivalent circuit model diagram of the battery established by the present invention.

FIG. 3 is a flow chart of the present invention using the second-order EKF algorithm to estimate the SOC of the battery.

Detailed ways

As shown in FIG. 1 , the method for estimating the SOC of a lithium-ion battery based on the second-order EKF algorithm of the present invention includes the following steps:

Step 1, analysis of the external characteristics of the battery, the specific process is: performing an intermittent charge-discharge experiment on the battery to obtain an open-circuit voltage curve representing the hysteresis characteristic of the battery and a charge-discharge static voltage curve representing the rebound characteristic of the battery;

In this embodiment, the specific process of performing the intermittent charge-discharge experiment on the battery described in step one is as follows:

Step 101, emptying the battery;

Step 102, charge at 1/3C discharge rate for 20min, when the battery voltage reaches 3.65V within 20min, go to Step 104, otherwise go to Step 103;

Step 103, let the battery stand for 30 minutes, and then return to step 102;

Step 104, fully charge the battery;

Step 105, discharge at 1/3C discharge rate for 20min, if the battery voltage is lower than 2.0V within 20min, go to step 107, otherwise go to step 106;

Step 106, let the battery stand for 30 minutes, and then return to step 105;

Step 107: Empty the battery with a small current of 0.02C.

In step 103 and step 106, the continuity of the experiment can be ensured by setting the resting time of the battery to 30 minutes.

To use the EKF algorithm to estimate the SOC of the battery, an accurate battery model must be established for the battery, and the establishment of the battery model is based on the analysis of the external characteristics of the battery. Therefore, the primary work is to analyze the external characteristics of the battery. The charge-discharge balance potential of the battery at different SOC points is different. This phenomenon is called the hysteresis characteristic of the battery. The hysteresis characteristic exists not only in lithium iron phosphate power batteries, but also in other types of lithium-ion batteries. When the battery is discharging and standing, the voltage gradually rises, and during the charging and standing period, the voltage gradually decreases. This phenomenon is called the rebound characteristic of the battery, which is mainly affected by the polarization resistance and polarization capacitance inside the battery.

Step 2, establish the equivalent circuit model of the battery, the specific process is as follows:

Step 201 , establishing an SOC calculation model of the battery, establishing an equivalent voltage source model according to an open circuit voltage curve of the battery, and establishing an equivalent impedance model according to a charging and discharging static voltage curve of the battery;

Step 202 , combining the three parts of the SOC calculation model, the equivalent voltage source model and the equivalent impedance model to establish an equivalent circuit model of the battery;

In this embodiment, as shown in FIG. 2 , the SOC calculation model in step 202 includes a capacitor _CN and an equivalent battery B, one end of the capacitor _CN is connected to the positive electrode of the equivalent battery B, and the capacitor _CN The other end of the battery is connected to the negative pole of the equivalent battery B; the equivalent voltage source model in step 202 includes a current source M, an inductance L _h , a voltage source U ₁ and a voltage source U ₂ , the positive pole of the current source M is connected to the inductance One end of L _h is connected, the negative electrode of the current source M is connected to the other end of the inductor L _h , and the negative electrode of the voltage source U ₁ and the voltage source U ₂ connected in series is connected to the negative electrode of the current source M; as described in step 202 The equivalent impedance model includes a resistor R ₀ , a resistor R ₁ , a resistor R ₂ , a capacitor C ₁ and a capacitor C ₂ , the resistor R ₀ , the resistor R ₁ and the resistor R ₂ are connected in series, and the capacitor C ₁ is connected in parallel with the resistor R ₁ , the capacitor C ₂ is connected in parallel with the resistor R ₂ ; the negative electrode of the equivalent battery B is connected to the negative electrode of the voltage source U ₂ , and one end of the resistor R ₀ is connected to the resistor R ₀ , the resistor R ₁ and the resistor R ₂ in series. _The positive poles _of the voltage source U1 and the voltage source U2 are connected in series.

The equivalent circuit model of the battery established by the invention can not only describe the relationship between the hysteresis voltage and the open circuit voltage of the battery and the battery SOC, but also directly estimate the battery SOC through the ampere-hour integration method.

Step 3: Perform parameter identification on the parameters of the equivalent circuit model of the battery;

In this embodiment, the specific process of performing parameter identification on the parameters of the equivalent circuit model of the battery described in step 3 is as follows:

Step 301, parameter identification of the equivalent voltage source model: the equilibrium potential EMF of the battery is expressed as

EMF=0.5(EMF _c +EMF _d ) (F1)

The hysteresis voltage V _h of the battery is expressed as

V _h =0.5(EMF _c -EMF _d ) (F2)

Among them, EMF _c is the charge balance potential, and EMF _d is the discharge balance potential;

Step 302, parameter identification of the equivalent impedance model: the voltage U at any time is expressed as

R₂为电阻R₂的阻值，τ₂为与电阻R₂对应的时间常数且

t为时间；Among them, OCV _D is the voltage at time D of the charging and discharging static voltage curve, and time D is the time when the voltage does not change after the battery is discharged after the rebound stage; I is the current value flowing through the battery, and R ₁ is the resistance of the resistor R ₁ value, _τ1 is the time constant corresponding to resistor _R1 and

R2 is the resistance value of the resistor _R2 , _τ2 is the time _{constant corresponding} to the resistor R2 and

t is time;

Denote the fitting function as

f(x)=A-B·exp(-ax)-C·exp(-bx) (F4)

Fit the C-D stage of the charge-discharge static voltage curve to obtain the values of the parameters A, B, C, a and b in the fitting function; among them, the C-D stage of the charge-discharge static voltage curve refers to the moment when the battery is discharged The voltage mutation starts to the stage where the voltage does not change after the battery is discharged through the rebound stage; according to formula (F3) and formula (F4) correspondingly equal, the parameters of the equivalent impedance model are obtained as follows:

Among them, C ₁ is the capacitance value of the capacitor C ₁ , and C ₂ is the capacitance value of the capacitor C ₂ .

Step 4: Use the second-order EKF algorithm to estimate the SOC of the battery, and obtain the prediction result of the SOC of the battery.

In this embodiment, as shown in FIG. 3 , the second-order EKF algorithm is used in step 4 to estimate the SOC of the battery, and the specific process of obtaining the prediction result of the SOC of the battery is as follows:

Step 401 , establish a state space model of the battery system (non-linear discrete system): according to the equivalent circuit model of the battery established in step 2, the SOC of the battery, the voltage V ₁ across the capacitor C ₁ and the voltage across the capacitor C ₂ are V ₂ is used as the state variable of the system, the current value I flowing through the battery (discharge is negative, charging is positive) is the input quantity, and the terminal voltage V is the output quantity. According to the circuit equation, the state space model equation of the battery system is deduced as:

The output equation is:

V(t)=V _OCV (SOC(t))-V ₁ (t)-V ₂ (t)-R ₀ I(t) (F7)

Among them, C _n is the rated capacity of the battery, V _OCV is the total voltage of the voltage source U ₁ and the voltage source U ₂ ;

Step 402: Linearize the nonlinear state space model equation of the battery system through a second-order Taylor expansion, and the specific process is as follows:

Step 4021: Perform the second-order Taylor expansion of the state space model equation (F6) of the battery system at the state estimation point to obtain:

为x_k的估计值；Among them, f(x _k , u _k ) is the state transition function, g(x _k , u _k ) is the measurement function, x _k is the state variable at time _k , uk is the control input of the system at time k,

is the estimated value of x _k ;

将公式(F8)代入非线性离散系统的状态空间模型方程

中，得到电池系统的线性化方程为：Step 4022, define

Substitute Equation (F8) into the state-space model equation of the nonlinear discrete system

, the linearized equation of the battery system is obtained as:

D_k＝R₀；R₀为电阻R₀的阻值，Δt为时间的变化量，ω_k为均值为零的过程噪声，v_k为均值为零的测量噪声，且ω_k与v_k互不相关，ω_k～N(0,Q_k)，v_k～N(0,R_k)；即ω_k和v_k均服从均值为0的高斯分布；in,

D _k =R ₀ ; R ₀ is the resistance value of the resistor R ₀ , Δt is the change in time, ω _k is the process noise with zero mean, v _k is the measurement noise with zero mean, and ω _k and v _k mutually Irrelevant, ω _k ～N(0, Q _k ), v _k ～N(0, R _k ); that is, both ω _k and v _k obey the Gaussian distribution with mean 0;

Step 403, using the second-order EKF algorithm to estimate the SOC of the lithium-ion battery, the specific process is:

Step 4031, initialization phase:

为x₀的估计值，P₀为状态变量预测估计的误差协方差矩阵的初始化值；Among them, x ₀ is the initialization value of the state variable,

is the estimated value of x ₀ , and P ₀ is the initialization value of the error covariance matrix of the state variable prediction estimation;

Step 4032, the prediction stage:

Predictive estimates of state variables:

为x_k-1的估计值，x_k-1为k-1时刻的状态变量，u_k-1为k-1时刻系统的控制输入量；in,

is the estimated value of x k- ₁ , x _k-1 is the state variable at time k-1, and u _k-1 is the control input of the system at time k-1;

Error covariance matrix for state variable prediction estimates:

Wherein, Q _k-1 is the covariance matrix of process noise at time k-1 and Q _k-1 =Q _k , Q _k is the covariance matrix of process noise at time k;

In this embodiment, the value of Q _k-1 in step 4032 is

Step 4033, the correction stage:

Kalman filter gain:

where R is the covariance matrix of the observation noise;

Corrected estimates of state variables:

The error covariance matrix of the state variable correction estimate:

P _k =(IK _k C _k )P _k|k-1 (F15)

In this embodiment, the value of R in step 4033 is 0.1.

Step 4034: Repeat steps 4032 and 4033 until the number of iterations reaches a preset iteration termination value.

In this embodiment, the preset iteration termination value in step 4034 is 150.

In order to verify the technical effect that the present invention can produce, the 18650 lithium iron phosphate battery produced by Tianjin Lishen Battery Co., Ltd. is used as the experimental object. The main performance parameters of the battery are shown in Table 1.

Table 1 The main performance parameters of the battery

In order to study the external characteristics of the battery, intermittent charging and discharging experiments were carried out on the battery. For the continuity of the experiment, the resting time of the battery was set to 30min. The experimental steps are shown in Table 2.

Table 2 Experimental steps of intermittent charge and discharge

The open-circuit voltage curve, which characterizes the hysteresis characteristics of the battery, and the charge-discharge static voltage curve, which characterizes the rebound characteristics of the battery, are obtained from the battery charge-discharge experiment. The SOC calculation model of the battery is established, and the equivalent voltage source model is established according to the hysteresis characteristics of the battery, and the equivalent impedance model is established according to the rebound characteristics of the battery; when the parameters of the equivalent impedance model are identified, different orders of RC network fitting A comparison table of the results is shown in Table 3.

Table 3 Comparison of fitting results of RC networks of different orders

According to the comparison of the fitting results in Table 3, the fitting errors of the second-order RC network and the third-order RC network are not much different, and the first-order fitting results are worse than the second-order and third-order fitting results. Since the second-order RC network is simpler than the third-order RC network, it is convenient for later parameter identification and algorithm estimation, and can better describe the external characteristics of the battery than the first-order RC network. Therefore, the present invention selects the second-order RC network.

In this embodiment, the established equivalent circuit model diagram of the battery is shown in FIG. 2 .

Using the second-order EKF algorithm to estimate the SOC of the battery, the state variables of the system are: x _k =[SOC(k), V ₁ (k), V ₂ (k)] ^T , and the input of the system is: u _k =I( k). The state space model equation of the system is linearized by the second-order Taylor formula to obtain the linearized matrix parameters of the second-order EKF algorithm. The SOC is estimated based on the second-order EKF algorithm. Table 4 shows the comparison of the SOC estimation results of the first-order EKF algorithm and the second-order EKF algorithm under different simulation conditions.

Table 4 Comparison of algorithm errors in different simulation conditions

By analyzing the characteristics of the lithium iron phosphate battery, a second-order equivalent circuit model with hysteresis voltage is established and parameters are identified; on the basis of the equivalent model, the first-order and second-order EKF algorithms are used to estimate the battery SOC , the estimation accuracy of the algorithm is verified by simulating different working conditions of the battery, and the final experimental results show that the estimation error accuracy of the second-order EKF algorithm for battery SOC under different simulation conditions is better than that of the first-order EKF algorithm, and the dynamic adaptation of the battery is better than that of the first-order EKF algorithm. Good performance and high precision.

As will be appreciated by those skilled in the art, the embodiments of the present application may be provided as a method, a system, or a computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It will be understood that each flow and/or block in the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to the processor of a general purpose computer, special purpose computer, embedded processor or other programmable data processing device to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing device produce Means for implementing the functions specified in a flow or flow of a flowchart and/or a block or blocks of a block diagram.

These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory result in an article of manufacture comprising instruction means, the instructions The apparatus implements the functions specified in the flow or flow of the flowcharts and/or the block or blocks of the block diagrams.

These computer program instructions can also be loaded on a computer or other programmable data processing device to cause a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process such that The instructions provide steps for implementing the functions specified in the flow or blocks of the flowcharts and/or the block or blocks of the block diagrams.

The foregoing descriptions of specific exemplary embodiments of the present invention have been presented for purposes of illustration and description. These descriptions are not intended to limit the invention to the precise form disclosed, and obviously many changes and modifications are possible in light of the above teachings. The exemplary embodiments were chosen and described for the purpose of explaining certain principles of the invention and their practical applications, to thereby enable one skilled in the art to make and utilize various exemplary embodiments and various different aspects of the invention. Choose and change. The scope of the invention is intended to be defined by the claims and their equivalents.

Claims (6)

1. A lithium ion battery SOC estimation method based on a second-order EKF algorithm is characterized in that: the method comprises the following steps:

the method comprises the following steps of firstly, analyzing the external characteristics of the battery, and specifically comprising the following steps: carrying out intermittent charge and discharge experiments on the battery to obtain an open-circuit voltage curve representing the hysteresis characteristic of the battery and a charge and discharge standing voltage curve representing the rebound characteristic of the battery;

step two, establishing an equivalent circuit model of the battery, and the specific process is as follows:

step 201, establishing an SOC calculation model of a battery, establishing an equivalent voltage source model according to an open-circuit voltage curve of the battery, and establishing an equivalent impedance model according to a charge-discharge standing voltage curve of the battery;

202, combining an SOC calculation model, an equivalent voltage source model and an equivalent impedance model to establish an equivalent circuit model of the battery;

the SOC calculation model comprises a capacitance C_NAnd an equivalent battery B, the capacitor C_NIs connected with the positive pole of the equivalent battery B, and the capacitor C_NThe other end of the anode is connected with the cathode of the equivalent battery B; the equivalent voltage source model comprises a current source M and an inductor L_hVoltage source U₁And a voltage source U₂Positive pole of the current source M and the inductor L_hIs connected with the negative pole of the current source M and the inductance L_hIs connected to the other end of the voltage source U₁And a voltage source U₂The cathode after series connection is connected with the cathode of the current source M; the equivalent impedance model includes a resistance R₀Resistance R₁Resistance R₂Capacitor C₁And a capacitor C₂Said resistance R₀Resistance R₁And a resistance R₂In series, said capacitor C₁And a resistor R₁In parallel, the capacitor C₂And a resistor R₂Parallel connection; the cathode of the equivalent battery B and a voltage source U₂The negative pole of (2) is connected, the resistor R₀Resistance R₁And a resistance R₂Series rear resistor R₀One end of (1) and a voltage source U₁And a voltage source U₂Connecting the anodes after series connection;

thirdly, identifying parameters of an equivalent circuit model of the battery;

estimating the SOC of the battery by adopting a second-order EKF algorithm to obtain a prediction result of the SOC of the battery;

step 401, establishing a state space model of the battery system: according to the cell established in step twoEquivalent circuit model based on SOC and capacitance C of battery₁Voltage V across₁And a capacitor C₂Voltage V across₂As the state variable of the system, the current value I flowing through the battery is input quantity, the terminal voltage V is output quantity, and the state space model equation of the battery system is deduced according to the circuit equation as follows:

the output equation is:

V(t)＝V_OCV(SOC(t))-V₁(t)-V₂(t)-R₀I(t) (F7)

wherein, C_nIs the rated capacity of the battery, V_OCVIs a voltage source U₁And a voltage source U₂The total voltage of (c);

step 402, linearizing a nonlinear state space model equation of the battery system through second-order Taylor expansion, wherein the specific process is as follows:

step 4021, performing second-order Taylor expansion on a state space model equation (F6) of the battery system at a state estimation point to obtain:

wherein, f (x)_k,u_k) As a function of the state transition, g (x)_k,u_k) As a measurement function, x_kIs the state variable at time k, u_kFor the control input of the system at time k,

is x_kAn estimated value of (d);

step 4022, definition

Substituting formula (F8) into the state space model equation of the nonlinear discrete system

In the above, the linear equation of the battery system is obtained as follows:

wherein,

D_k＝R₀；R₀is a resistance R₀Δ t is the amount of change in time, ω_kProcess noise, v, with mean value of zero_kIs measurement noise with mean value of zero, and ω_kAnd v_kAre not related to each other, ω_k～N(0,Q_k)，v_k～N(0,R_k) (ii) a I.e. omega_kAnd v_kObey a gaussian distribution with a mean value of 0;

step 403, estimating the SOC of the lithium ion battery by using a second-order EKF algorithm, which comprises the following specific steps:

step 4031, initialization phase:

wherein x is₀In order to be the initial value of the state variable,

is x₀Estimated value of (P)₀Predicting an initialized value of an estimated error covariance matrix for the state variable;

step 4032, prediction phase:

predictive estimation of state variables:

wherein,

is x_k-1Estimate of (a), x_k-1Is a state variable at time k-1, u_k-1The control input quantity of the system at the moment k-1;

error covariance matrix of state variable prediction estimation:

wherein Q is_k-1Covariance matrix of process noise at time k-1 and Q_k-1＝Q_k，Q_kA covariance matrix of the process noise at time k;

step 4033, correction phase:

kalman filter gain:

wherein R is a covariance matrix of observation noise;

modified estimation of state variables:

error covariance matrix of state variable correction estimation:

P_k＝(I-K_kC_k)P_k|k-1 (F15)

and step 4034, repeating the step 4032 and the step 4033 until the iteration number reaches a preset iteration termination value.

2. The lithium ion battery SOC estimation method based on the second-order EKF algorithm of claim 1, wherein: the specific process of carrying out the intermittent charge-discharge experiment on the battery in the first step is as follows:

step 101, emptying a battery;

102, charging at 1/3C discharge rate for 20min, executing step 104 when the battery voltage reaches 3.65V within 20min, otherwise executing step 103;

step 103, standing the battery for 30min, and then returning to step 102;

step 104, fully charging the battery;

105, discharging at 1/3C discharge rate for 20min, if the battery voltage is lower than 2.0V within 20min, entering step 107, otherwise, entering step 106;

step 106, standing the battery for 30min, and then returning to the step 105;

step 107, the battery is discharged at a low current of 0.02C.

3. The lithium ion battery SOC estimation method based on the second-order EKF algorithm of claim 1, wherein: the specific process of identifying the parameters of the equivalent circuit model of the battery in the third step is as follows:

step 301, identifying parameters of the equivalent voltage source model: the equilibrium potential EMF of the battery is expressed as

EMF＝0.5(EMF_c+EMF_d) (F1)

Hysteresis voltage V of battery_hIs shown as

V_h＝0.5(EMF_c-EMF_d) (F2)

Wherein EMF_cFor charging a balanced potential, EMF_dBalancing the potential for discharge;

step 302, identifying parameters of the equivalent impedance model: the voltage U at any time is expressed as

Wherein the OCV_DThe voltage at the moment D of the charging and discharging standing voltage curve is the moment when the voltage does not change after the battery is discharged in the rebound stage; i is the value of the current flowing through the battery, R₁Is a resistance R₁Resistance value of₁Is equal to the resistance R₁Corresponding time constant and

R₂is a resistance R₂Resistance value of₂Is equal to the resistance R₂Corresponding time constant and

t is time;

expressing the fitting function as

f(x)＝A-B·exp(-ax)-C·exp(-bx) (F4)

Fitting the C-D stage of the charging and discharging standing voltage curve to obtain values of parameters A, B, C, a and b in a fitting function; the C-D stage of the charging and discharging standing voltage curve refers to a stage from sudden change of voltage at the moment of discharging the battery to the stage that the voltage is not changed after the battery is discharged and undergoes a rebound stage; and obtaining parameters of the equivalent impedance model according to the equation (F3) and the equation (F4) which are correspondingly equal to each other:

wherein, C₁Is a capacitor C₁Capacity value of C₂Is a capacitor C₂The capacity value of (c).

4. The lithium ion battery SOC estimation method based on the second-order EKF algorithm of claim 1, wherein: q in step 4032_k-1Is taken as

5. The lithium ion battery SOC estimation method based on the second-order EKF algorithm of claim 1, wherein: in step 4033, the value of R is 0.1.

6. The lithium ion battery SOC estimation method based on the second-order EKF algorithm of claim 1, wherein: the preset iteration end value in step 4034 is 150.

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