CN116559673A - Lithium battery SOC estimation method based on IGWO-EKF algorithm - Google Patents

Abstract

The invention discloses a lithium battery SOC estimation method based on an improved gray wolf algorithm and an optimized EKF algorithm, which comprises the following steps: establishing a first-order Thevenin equivalent circuit model, and carrying out parameter identification; fitting a correlation curve between the open-circuit voltage and the state of charge of the lithium battery based on an HHPC experiment; introducing a Levy flight strategy in a Tent chaotic map and a cuckoo algorithm, and improving a traditional gray wolf algorithm; optimizing a noise covariance matrix in a traditional EKF algorithm by using an improved gray wolf algorithm to obtain an optimal noise covariance matrix; and inputting the obtained optimal noise covariance matrix into an EKF algorithm to perform lithium battery SOC estimation. According to the improved gray-wolf algorithm-based lithium battery SOC estimation method for optimizing the EKF algorithm, disclosed by the invention, the accuracy of lithium battery SOC estimation is improved, and the accuracy and speed of the optimizing algorithm are improved while noise optimizing is completed through the improvement of the gray-wolf algorithm.

Description

A lithium battery SOC estimation method based on IGWO-EKF algorithm

technical field

The invention belongs to the technical field of lithium battery SOC estimation, in particular to an IGWO-EKF-based lithium battery SOC estimation method.

Background technique

In recent years, with the escalation of energy crisis and environmental pollution, the demand for renewable energy to replace traditional fossil energy has been increasing. Lithium batteries have become the first choice of energy storage devices for electric vehicles due to their advantages such as high energy ratio, low self-discharge rate, and environmental protection. Accurate estimation of battery state of charge (State of Charge, SOC) can not only provide information related to battery performance, but also improve reliability and safety during battery operation. Due to the complex, nonlinear and time-varying internal reactions of lithium batteries, the SOC cannot be directly measured, and a series of state estimations are required. Due to the existence of many factors such as charge and discharge rate, discharge process, temperature, etc., the accuracy and robustness of lithium battery SOC estimation are greatly affected.

At present, there are many methods for estimating the SOC of lithium batteries. Among them, the ampere-hour integration method is the most basic method to predict the remaining capacity of the battery. This method integrates the current when the battery is discharging, and subtracts the integral value from the rated capacity of the battery to obtain the remaining capacity of the battery. However, the ampere-hour integration method has an open-loop characteristic, and it is easy to diverge due to error accumulation when measuring current. In addition, there is an open-circuit voltage method to predict the remaining capacity of the battery. By collecting the terminal voltage of the battery after a long period of rest, and then performing a table lookup or mapping relationship to reverse the current remaining capacity of the battery. However, the open circuit voltage method can only be accurately measured and estimated after the battery has been left to stand for a long time to reach a stable state, and it is not suitable for batteries that are in continuous operation. The internal resistance measurement method predicts the remaining capacity by measuring the current internal resistance of the battery, but this method requires special measuring equipment, and the internal resistance measurement method will produce large errors when the battery is working. Compared with the previous three methods, the Extended Kalman Filter (EKF) algorithm has the advantages of high estimation accuracy and small calculation amount, and is currently a research hotspot in lithium battery SOC estimation.

The EKF algorithm needs to set the process noise covariance matrix Q and the measurement noise covariance matrix R in advance. At present, the usual practice is to select randomly after multiple attempts. However, random selection of the noise covariance matrix will not only affect the state variable correction rate and estimation accuracy, but even cause the EKF algorithm to fail to converge.

Contents of the invention

Aiming at the deficiencies of the prior art, the present invention provides a lithium battery SOC estimation method based on IGWO-EKF. The method is based on the improved gray wolf algorithm, and the process noise covariance matrix Q and the measurement noise covariance matrix R in the EKF algorithm are Online optimization, selecting the optimal noise matrix under the current working conditions, can improve the SOC estimation accuracy of lithium batteries.

The present invention provides a method for estimating the SOC of a lithium battery based on IGWO-EKF, comprising the following steps:

Step 1, establish the first-order Thevenin equivalent circuit model of the lithium battery, and its state equation model is:

Among them, R ₀ is the ohmic internal resistance, R ₁ is the polarization resistance, C ₁ is the polarization capacitance, U ₁ is the voltage across the capacitor C ₁ , U _L is the battery terminal voltage, U _ocv is the open circuit voltage;

Step 2: Carry out parameter identification on the first-order Thevenin equivalent circuit model of the lithium battery, and obtain the relationship function between open circuit voltage U _ocv and SOC, the relationship function between ohmic internal resistance R ₀ and SOC, and the relationship function between polarization resistance R ₁ and SOC And the relationship function between polarization capacitance C ₁ and SOC;

Step 3: On the basis of the Gray Wolf Optimization (GWO), introduce the Tent chaotic map to initialize the gray wolf population, and introduce the Levy flight strategy in the Cuckoo Search (CS) to enhance the global search of the Gray Wolf Algorithm Ability and search speed, get the improved gray wolf algorithm (IGWO);

Step 4, use the IGWO algorithm described in step 3 to optimize the process noise covariance matrix Q and the measurement noise covariance matrix R in the EKF algorithm online, and obtain the optimal process noise covariance matrix Q _k and the optimal measurement noise covariance matrix R _k ;

Step 5, update the first-order Thevenin equivalent circuit model of the lithium battery with the parameter identification results obtained in step 2, and input the optimal process noise covariance matrix Q _k and the optimal measurement noise covariance matrix R _k obtained in step 4 into the EKF algorithm, Estimate the SOC of the lithium battery to obtain the estimated value of the SOC of the lithium battery at different times. This step is specifically as follows:

Step 5.1, assuming that the system state quantity at time k is x _k , the system input is u _k , the system observation is y _k , f(x _k ,u _k ) is the system state equation, and g(x _k ,u _k ) is the measurement Equation, the discretization space equation of the model system is:

in, D _k ＝R _0,k I _k , x _k ＝[SOC _k U _1,k ] ^T , w _k is the system process noise, v _k is the system measurement noise;

Step 5.2, set the initial value, the optimal process noise covariance matrix Q _k and the optimal measurement noise covariance matrix R _k obtained in step 4 are used as initial values, and the state vector and error covariance are initialized as:

Step 5.3, start the EKF recursive algorithm according to the initial value set in step 5.2, and substitute the first-order discretization space equation of the lithium battery determined in step 5.1 to obtain the state variable prediction matrix at time k And the error covariance prediction matrix P _k|k-1 is:

Step 5.4, calculate the gain state matrix K _k of the EKF algorithm:

Step 5.5, according to the terminal voltage value y _k at time k and the gain state matrix K _k of the EKF algorithm, obtain the state variable output matrix updated at time k and the updated error covariance matrix P _k :

Among them, I is the identity matrix;

Thus, the lithium battery SOC value SOC _k at time k can be obtained;

In step 5.6, set k=k+1, and return to step 5.3 to start the next round of lithium battery SOC estimation, so that the lithium battery SOC value at each moment can be obtained through such iterations.

Preferably, the IGWO algorithm in step 3 specifically includes the following steps:

Step 3.1, in the gray wolf algorithm, first randomly generate a population of gray wolves with a size N, and determine the populations α, β, and δ wolves by calculating the fitness value of each individual, and the remaining gray wolves are called ω wolves. In the iterative process, α, β and δ wolves predict the position of the prey, and instruct the wolves to update their own position according to the position of the prey;

Preferably, in order to improve the effect of the initial population distribution, increase the diversity of the population, and speed up the optimization speed of the algorithm, the step 3.1 uses the chaotic mapping function to generate the chaotic sequence as the position of the initial population individual, and the chaotic sequence Tent mapping expression is as follows:

Among them, u=0.5, after the individual chaos initialization of the gray wolf population, there is approximately the same distribution density for different parameters;

In step 3.2, during the process of searching for prey, wolves will gradually form an encirclement to encircle the prey. The model of this behavior is as follows:

Among them, t represents the current iteration number, t _max is the maximum iteration number, Indicates the distance between a gray wolf and its prey, and /> are the location of the prey and the location of the gray wolf, respectively, /> and /> is a random number modulo [0,1], /> is the convergence factor, which decreases linearly from 2 to 0 with continuous iterations;

Step 3.3, after determining the location of the prey, the β and δ wolves encircle the prey under the command of the α wolf, introduce the CS algorithm, readjust the positions of the α, β and δ wolves, and other gray wolves move accordingly, and define ω The step size for the wolf to approach the α, β and δ wolves. The model of this behavior is as follows:

in, and /> are the position vectors of α, β, and δ wolves in the gray wolf population after updating with the Levy flight strategy, /> for the location of other gray wolves, /> and /> represent the distances between the current gray wolf and α, β and δ wolves, respectively;

Preferably, the gray wolf position update strategy using the CS algorithm in the step 3.3 is:

in, is the Levy random search path, λ is the step size adjustment coefficient, and L _v is the flight step size;

Step 3.4, during the process of chasing the prey, the gray wolf will continuously compress the range of activities of the prey, forcing it to stop moving. When the prey stops, the wolves start to attack. The process of attacking the prey can be expressed as: the convergence factor a gradually decreases , The value of changes in [-a, a], when /> When the value of is outside the interval [-1,1], it means that the wolves are searching for prey. When /> When the value of is in the interval [-1,1], it means that the wolves attack the prey;

Step 3.5: Update the position information of the wolves according to the formula (8) and formula (11). If the alpha wolf has reached the maximum number of iterations or meets the end condition of the iterative loop, stop the loop and output the coordinate information of the alpha wolf as the found Optimal solution;

Preferably, the specific steps for online optimization of the process noise covariance matrix Q and the measurement noise covariance matrix R in the EKF algorithm in the step 4 are:

Step 4.1, initially set the gray wolf population size N, the maximum number of iterations t _max , the optimization variable dimension Dim, the search range [lb, lu], and initialize the position of the gray wolf population;

Step 4.2, calculate the fitness value of each gray wolf individual, that is, the minimum value of the cumulative voltage error of the first-order Thevenin model of the lithium battery, and find out the optimal solution α wolf, suboptimal solution β wolf and The third optimal solution δ wolf;

Preferably, in the step 4.2, the fitness function is set to:

in, Represents the predicted value of the terminal voltage measurement equation, y _k represents the measured value of the terminal voltage, and L is the maximum number of sampling points at discrete frequency points;

In step 4.3, the values of Q and R corresponding to the optimal solution α wolf are substituted into the model to obtain the initial cumulative voltage error of the first-order Thevenin model of the lithium battery;

Step 4.4, using the CS algorithm to adjust the positions of α, β and δ wolves in each cycle;

Step 4.5, after each cycle, compare the cumulative voltage error of the lithium battery first-order Thevenin model obtained in this cycle with the minimum cumulative error obtained in the previous cycle, and take the smaller value as the current lithium battery first-order Thevenin model The minimum cumulative voltage error;

Step 4.6, repeat step 4.2 to step 4.5 until the set maximum number of iterations is reached. After the iteration, the values of Q and R corresponding to the current α wolf are the optimal process noise covariance matrix Q _k and the optimal measurement noise covariance matrix R _k ;

Compared with prior art, the beneficial effect of the present invention is:

1. Using the IGWO algorithm to optimize the process noise covariance matrix Q and measurement noise covariance matrix R of the EKF algorithm can overcome the adverse effects of randomly selecting the noise covariance matrix on the state variable correction rate and estimation accuracy, and accelerate the convergence of the EKF algorithm speed;

2. Introduce the Tent chaotic map to initialize the gray wolf population, so that the initial population position is more evenly distributed in the search space, and the population diversity is improved;

3. In view of the problem that the position update formula of the GWO algorithm is only affected by elite wolves, and the population is prone to fall into local optimum, the Levy flight strategy in the CS algorithm is introduced to reduce the risk of the population falling into local optimum;

4. The present invention adopts the IGWO algorithm to obtain the optimal solution of the noise covariance matrix, and then combines the EKF algorithm to improve the accuracy of lithium battery SOC estimation, which has broad application prospects.

Description of drawings

Fig. 1 is the flowchart of the lithium battery SOC estimation method based on IGWO-EKF algorithm proposed by the present invention;

Fig. 2 is a flow diagram of the IGWO algorithm in the specific embodiment of the present invention;

Fig. 3 is the random distribution diagram of initial population in [0,1] interval in the specific embodiment of the present invention;

Fig. 4 is the initial population in the specific embodiment of the present invention in [0,1] interval, utilizes the distribution diagram after Tent chaotic sequence mapping;

Fig. 5 is the fitness curve figure of GWO algorithm and IGWO algorithm when D=10 under the given test function in the specific embodiment of the present invention:

Fig. 6 is the fitness curve figure of GWO algorithm and IGWO algorithm when D=30 under the given test function in the specific embodiment of the present invention:

Fig. 7 is a comparison chart of the SOC estimation curve between the IGWO-EKF algorithm and the standard EKF algorithm under the DST working condition in the specific embodiment of the present invention;

Fig. 8 is the SOC estimation error figure of IGWO-EKF algorithm and standard EKF algorithm under the DST working condition in the specific embodiment of the present invention;

Fig. 9 is a comparison chart of the SOC estimation curve between the IGWO-EKF algorithm and the standard EKF algorithm under the UDDS working condition in the specific embodiment of the present invention;

Fig. 10 is the SOC estimation error diagram of the IGWO-EKF algorithm and the standard EKF algorithm under the UDDS working condition in the specific embodiment of the present invention;

Detailed ways

In order to make the technical problems, technical solutions and beneficial effects solved by the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

In one embodiment, as shown in Figure 1, the present invention proposes a lithium battery SOC estimation method based on the IGWO-EKF algorithm, comprising the following steps:

Step 1, establish the first-order Thevenin equivalent circuit model of the lithium battery, and its state equation model is:

Among them, R ₀ is the ohmic internal resistance, R ₁ is the polarization resistance, C ₁ is the polarization capacitance, U ₁ is the voltage across the capacitor C ₁ , _UL is the battery terminal voltage, and U _ocv is the open circuit voltage.

Step 2: Carry out parameter identification on the first-order Thevenin equivalent circuit model of the lithium battery, and obtain the relationship function between open circuit voltage U _ocv and SOC, the relationship function between ohmic internal resistance R ₀ and SOC, and the relationship function between polarization resistance R ₁ and SOC And the relationship function of polarization capacitance C ₁ and SOC.

This step is specifically:

The relationship between the open circuit voltage U _ocv and SOC is identified using the open circuit voltage charge and discharge experiment. The specific steps are:

1) After the battery is fully charged, let it stand for 12 hours, and measure the open circuit voltage of the battery in the fully charged state;

2) Discharge with a constant current of 1C. When the battery SOC drops by 0.1, let it stand for 3600s. The measured terminal voltage of the battery at this time is the open circuit voltage when SOC=0.9;

3) Return to step 2) until the battery is completely discharged, and the experiment ends.

Then carry out the battery charging experiment, the steps are basically the same as the discharging experiment. After obtaining the U _ocv data under the charging and discharging experiment, the final data of U _ocv can be obtained by taking the average value of the two. Use the cftool toolbox to fit the OCV curve to a quintic polynomial:

U _ocv ＝3.44003+1.71448soc-3.51247soc ² +5.70868soc ³ -5.06869soc ⁴ +1.86699soc ⁵ (2)

For the identification of the model impedance parameters R ₀ , R ₁ and C ₁ , the off-line parameter identification method is adopted, based on the current and voltage values of the HPPC pulse experiment, the specific voltage curve during the pulse process is fitted according to the most suitable function curve, and then The parameter values of the model are obtained, and the identification results are shown in Table 1:

Table 1 Off-line identification results of each parameter in HPPC pulse experiment

Step 3: On the basis of the Gray Wolf Optimizer (GWO), introduce the Tent chaotic map to initialize the gray wolf population, and introduce the Levy flight strategy in the Cuckoo Search (CS) to enhance the global search of the Gray Wolf Algorithm Ability and search speed, the improved gray wolf algorithm (IGWO) is obtained, and the algorithm flow chart is shown in Figure 2.

Step 3 is specifically:

Step 3.1, in the gray wolf algorithm, first randomly generate a population of gray wolves with a size N, and determine the populations α, β, and δ wolves by calculating the fitness value of each individual, and the remaining gray wolves are called ω wolves. α wolf determines the behavior of wolves to the greatest extent, corresponding to the position of optimal fitness, followed by β wolf and δ wolf, corresponding to the second optimal fitness position and the third optimal fitness position respectively. The first three elite wolves are responsible for tracking the prey and guiding the wolf pack, and the ω wolf is responsible for encircling and killing the prey. In each iteration, its position is updated according to the position information of the elite wolf in the previous iteration.

Specifically, in order to improve the effect of the initial population distribution, increase the diversity of the population, and speed up the optimization speed of the algorithm, the chaotic sequence generated by the chaotic mapping function is used as the position of the initial population individual. The Tent mapping expression of the chaotic sequence is as follows:

Among them, u=0.5, after the individual chaos initialization of the gray wolf population, there is approximately the same distribution density for different parameters.

Figure 3 is a random initialization of a population of 5000 in the interval [0,1], and Figure 4 is a distribution diagram after initialization using Tent mapping. It can be seen from Figure 3 and Figure 4 that after using Tent mapping The initial population is more evenly distributed in the [0,1] interval, which can enhance the ergodic uniformity of the initial solution and find the optimal solution faster.

In step 3.2, during the process of searching for prey, wolves will gradually form an encirclement to encircle the prey. The model of this behavior is as follows:

Among them, t represents the current iteration number, t _max is the maximum iteration number, Indicates the distance between a gray wolf and its prey, and /> are the location of the prey and the location of the gray wolf, respectively, /> and /> is a random number modulo [0,1], /> is the convergence factor, which decreases linearly from 2 to 0 with continuous iterations.

In the process of location updating, the GWO algorithm only considers the location information of the gray wolf individual and the location information of the optimal solution, the optimal solution, and the suboptimal solution of the population. less capable. Cuckoo algorithm is a new meta-heuristic search algorithm. The cuckoo searches for an optimal nest to incubate eggs by random walk, which can achieve an efficient optimization mode. The invention introduces the CS algorithm to improve the GWO algorithm, uses the Levy flight strategy in the CS algorithm to improve the GWO, improves the global search ability of the algorithm and enhances the ability to converge to the global optimum.

Step 3.3, after determining the location of the prey, the β and δ wolves encircle the prey under the command of the α wolf, introduce the CS algorithm, readjust the positions of the α, β and δ wolves, and other gray wolves move accordingly, and define ω The step size for the wolf to approach the α, β and δ wolves. The model of this behavior is as follows:

in, and /> are the position vectors of α, β, and δ wolves in the gray wolf population after updating with the Levy flight strategy, /> for the location of other gray wolves, /> and /> represent the distances between the current gray wolf and α, β, and δ wolves, respectively.

Specifically, the gray wolf position update strategy using the CS algorithm is:

in, is the Levy random search path, λ is the step size adjustment coefficient, and L _v is the flight step size.

Step 3.4, during the process of chasing the prey, the gray wolf will continuously compress the range of activities of the prey, forcing it to stop moving. When the prey stops, the wolves start to attack. The process of attacking the prey can be expressed as: the convergence factor a gradually decreases , The value of changes in [-a, a], when /> When the value of is outside the interval [-1,1], it means that the wolves are searching for prey. When /> When the value of is in the interval [-1,1], it means that the wolves are attacking the prey.

Step 3.5: Update the position information of the wolves according to the formula (4) and formula (7). If the alpha wolf has reached the maximum number of iterations or meets the end condition of the iterative loop, stop the loop and output the coordinate information of the alpha wolf as the found Optimal solution.

In order to test the performance of the IGWO algorithm proposed in step 3, relevant experiments were carried out on MATLAB, and the test function was selected as follows:

Comparing the traditional GWO algorithm with the IGWO algorithm proposed by the present invention, the gray wolf population size is uniformly set to 50, and the number of iterations is 500. The accuracy of the two algorithms is compared when the dimension D=10 and D=30 respectively. When dimensions D=10 and D=30, the fitness curves are shown in Figure 5 and Figure 6 respectively. It can be seen from Fig. 5 and Fig. 6 that the IGWO algorithm proposed by the present invention has a faster convergence speed, a smaller fitness value, and more excellent performance.

Step 4, use the IGWO algorithm described in step 3 to optimize the process noise covariance matrix Q and the measurement noise covariance matrix R in the EKF algorithm online, and obtain the optimal process noise covariance matrix Q _k and the optimal measurement noise Covariance matrix R _k .

Step 4 is specifically:

Step 4.1. Initially set the gray wolf population size N, the maximum number of iterations t _max , the optimization variable dimension Dim, and the search range [lb,lu], set the optimization variable matrix to F=[QR] ^T , and use Tent mapping to initialize Location of gray wolf populations.

Step 4.2, calculate the fitness value of each gray wolf individual, that is, the minimum value of the cumulative voltage error of the lithium battery first-order Thevenin model, and arrange them according to the fitness in the current gray wolf group to determine the optimal solution α wolf, second The optimal solution β wolf and the third optimal solution δ wolf.

Specifically, the fitness function of the IGWO-EKF algorithm is set as:

in, Represents the predicted value of the terminal voltage measurement equation, y _k represents the measured value of the terminal voltage, and L is the maximum number of sampling points at discrete frequency points.

In step 4.3, the values of Q and R corresponding to the optimal solution α wolf are substituted into the model to obtain the initial cumulative voltage error of the first-order Thevenin model of the lithium battery.

In step 4.4, the CS algorithm is used to adjust the positions of α, β and δ wolves in each cycle.

Step 4.5, after each cycle, compare the cumulative voltage error of the lithium battery first-order Thevenin model obtained in this cycle with the minimum cumulative error obtained in the previous cycle, and take the smaller value as the current lithium battery first-order Thevenin model The minimum accumulated voltage error.

Step 4.6, repeat step 4.2 to step 4.5 until the set maximum number of iterations is reached. After the iteration, the values of Q and R corresponding to the current α wolf are the optimal process noise covariance matrix Q _k and the optimal measurement noise Covariance matrix R _k .

Step 5, update the first-order Thevenin equivalent circuit model of the lithium battery with the parameter identification results obtained in step 2, and input the optimal process noise covariance matrix Q _k and the optimal measurement noise covariance matrix R _k obtained in step 4 into the EKF algorithm, Estimate the SOC of the lithium battery to obtain the estimated value of the SOC of the lithium battery at different times.

Step 5 is specifically:

Step 5.1, assuming that the system state variable x _k =[SOC _k U _1,k ] ^T at time k, the system input is u _k , the system observation is y _k , and f(x _k ,u _k ) is used as the system state equation, g( x _k ,u _k ) is the measurement equation, and the discretization space equation of the model system is:

in, D _k =R _0,k I _k , w _k is the system process noise, and v _k is the system measurement noise.

Step 5.2, set the initial value, the optimal process noise covariance matrix Q _k and the optimal measurement noise covariance matrix R _k obtained in step 4 are used as initial values, and the state vector and error covariance are initialized as:

Step 5.3, start the EKF recursive algorithm according to the initial value set in step 5.2, and substitute the first-order discretization space equation of the lithium battery determined in step 5.1 to obtain the state variable prediction matrix at time k And the error covariance prediction matrix P _k|k-1 is:

Step 5.4, calculate the gain state matrix K _k of the EKF algorithm:

Step 5.5, according to the terminal voltage value y _k at time k and the gain state matrix K _k of the EKF algorithm, obtain the state variable output matrix updated at time k and the updated error covariance matrix P _k is:

Among them, I is the identity matrix.

Since x _k =[SOC _k U _1,k ] ^T , the lithium battery SOC value SOC _k at time k can be obtained.

In step 5.6, set k=k+1, and return to step 5.3 to start the next round of lithium battery SOC estimation, so that the lithium battery SOC value at each moment can be obtained through such iterations.

Under the EKF algorithm, the battery SOC estimation process is a continuous recursive process. The initial value is continuously corrected through the estimated value, measured value and filter gain obtained in each iteration, and the noise is gradually removed to make the estimated value closer to the real value. Obtain the optimal estimate of the state variable, that is, obtain the optimal estimated value of the SOC.

Step 6, simulation experiment verification. In order to verify the accuracy of the SOC estimation by the IGWO-EKF algorithm proposed in the present invention, the battery DST cycle condition and the UDDS power condition are selected as the verification conditions, and the verification is carried out on the MATLAB/Simulink simulation platform. Compare the actual estimated SOC with the estimated SOC obtained by the traditional EKF algorithm and the IGWO-EKF algorithm.

First, under the DST cycle condition, the results of the traditional EKF algorithm and the IGWO-EKF algorithm to realize the online SOC estimation are shown in Figure 7, and the error of the estimation result is shown in Figure 8. The SOC estimation errors of the two algorithms are shown in Table 2 below:

Table 2 Error analysis of standard EKF algorithm and IGWO-EKF algorithm under DST working conditions

According to Figure 7 and Figure 8, under the DST cycle condition, the trend of IGWO-EKF algorithm, EKF algorithm and test SOC curve is basically the same. However, the estimation of SOC by IGWO-EKF algorithm is closer to the real value than that of EKF algorithm, and in the early stage of discharge, the SOC curve under IGWO-EKF algorithm can quickly converge to the real SOC value, which can better realize the accurate estimation of SOC. According to Table 2, under DST conditions, compared with the traditional EKF algorithm, the maximum error of the IGWO-EKF algorithm for lithium battery SOC estimation is reduced by 22.26%, the average error is reduced by 28.62%, and the root mean square error is reduced by 42.88%. %, showing a stronger accuracy.

Then, under the UDDS power condition, the results of the traditional EKF algorithm and the IGWO-EKF algorithm to realize the online SOC estimation are shown in Figure 9, and the error of the estimation result is shown in Figure 10. The SOC estimation errors of the two algorithms are shown in Table 3 below:

Table 3 Error analysis of standard EKF algorithm and IGWO-EKF algorithm under UDDS working conditions

It can be seen from Fig. 9 and Fig. 10 that under the UDDS working condition, although the overall trends of the IGWO-EKF algorithm, EKF algorithm and test SOC curve are similar, the estimation of SOC by the IGWO-EKF algorithm is closer to the real value than the EKF algorithm. It can be seen from the partial enlarged picture that the tracking ability of the EKF algorithm is poor, but the IGWO-EKF algorithm can accurately converge to the vicinity of the real SOC value, and can better realize the accurate estimation of SOC. According to Table 3, under the UDDS working condition, compared with the traditional EKF algorithm, the maximum error of the IGWO-EKF algorithm for lithium battery SOC estimation is reduced by 25.63%, the average error is reduced by 38.34%, and the root mean square error is reduced by 41.14%. %. On the whole, the optimized algorithm can better estimate the real-time SOC, and the error is small. Even if there is a point with a large error, it can quickly converge to the real value.

Based on the EKF algorithm and the IGWO algorithm, the present invention proposes a lithium battery SOC estimation method based on the IGWO-EKF algorithm in combination with the first-order Thevenin equivalent circuit model of the lithium battery, and verifies that the method has higher accuracy through simulation experiments and practicality.

The above is only a preferred embodiment of the present invention, it should be pointed out that, for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements and modifications can also be made, and these improvements and modifications can also be made. It should be regarded as the protection scope of the present invention.

Claims (6)

1. The lithium battery SOC estimation method based on the IGWO-EKF is characterized by comprising the following steps of:

step 1, a first-order Thevenin equivalent circuit model of a lithium battery is established, and a state equation model is as follows:

wherein ,R₀ Is ohm internal resistance, R ₁ For polarization resistance, C ₁ For polarizing capacitance, U ₁ Is a capacitor C ₁ Voltage at two ends, U _L For battery terminal voltage, U _ocv Is an open circuit voltage.

Step 2, carrying out parameter identification on a first-order Thevenin equivalent circuit model of the lithium battery to respectively obtain open-circuit voltage U _ocv Relation function with SOC, ohmic internal resistance R ₀ Relation function with SOC, polarization resistance R ₁ Relation function with SOC and polarization capacitance C ₁ Relationship function with SOC.

And 3, introducing a Tent chaotic map to initialize a wolf population on the basis of a wolf algorithm (Grey Wolf Optimization, GWO), introducing a Levy flight strategy in a Cuckoo Search (CS), and enhancing the global searching capability and searching speed of the wolf algorithm to obtain an improved wolf algorithm (IGWO).

Step 4, performing online optimization on the process noise covariance matrix Q and the measurement noise covariance matrix R in the EKF algorithm by using the IGWO algorithm in step 3 to obtain an optimal process noise covariance matrix Q _k And an optimal measurement noise covariance matrix R _k 。

Step 5, updating the first-order Thevenin equivalent circuit model of the lithium battery by the parameter identification result obtained in the step 2, and obtaining an optimal process noise covariance matrix Q in the step 4 _k And an optimal measurement noise covariance matrix R _k And (3) inputting an EKF algorithm, and carrying out lithium battery SOC estimation to obtain lithium battery SOC estimation values at different moments.

The step 5 is specifically as follows:

step 5.1, assume that the system state quantity at k time is x _k The system input is u _k The observed quantity of the system is y _k With f (x) _k ,u _k ) As a system state equation, g (x _k ,u _k ) For the measurement equation, the discretized space equation of the model system is obtained as follows:

wherein ,D _k ＝R _0,k I _k ，x _k ＝[SOC _k U _1,k ] ^T ，w _k v for system process noise _k Noise is measured for the system.

Step 5.2, setting an initial value, and obtaining an optimal process noise covariance matrix Q from the step 4 _k Optimum measurement noise covarianceMatrix R _k As an initial value, the state vector and the error covariance are initialized to:

step 5.3, starting an EKF recursive algorithm according to the initial value set in the step 5.2, substituting the initial value into the lithium battery first-order discretization space equation determined in the step 5.1 to obtain a k-moment state variable prediction matrixAnd error covariance prediction matrix P _k|k-1 The method comprises the following steps:

step 5.4, calculating the gain state matrix K of the EKF algorithm _k ：

Step 5.5, according to the terminal voltage value y at the moment k _k And the gain state matrix K of the EKF algorithm _k Obtaining a state variable output matrix updated at k momentAnd an updated error covariance matrix P _k The method comprises the following steps:

wherein I is an identity matrix.

From this, the SOC value SOC of the lithium battery at the k moment can be obtained _k 。

And 5.6, let k=k+1, return to step 5.3, start the next round of lithium battery SOC estimation, and iterate in this way to obtain the lithium battery SOC value at each moment.

2. The lithium battery SOC estimation method based on IGWO-EKF according to claim 1, wherein step 3 specifically comprises:

step 3.1, in the wolf algorithm, a wolf population with a scale of N is randomly generated, the population alpha, beta and delta wolf are determined by calculating the fitness value of each individual, the rest wolves are called omega wolves, and in the iteration process, the alpha, beta and delta wolves predict the position of a game, and command the wolf population to update the position of the wolf population according to the position of the game.

Step 3.2, the wolf group gradually forms a surrounding trapped hunting object in the hunting process, and the behavior model is as follows:

wherein t represents the current iteration number, t _max For the maximum number of iterations to be performed,indicating the distance between the wolf and the prey, < ->Andthe position of prey and the position of the wolf, respectively,> and />Is molded in [0,1]]Random number of->As a convergence factor, decreases linearly from 2 to 0 with successive iterations.

Step 3.3, after determining the position of the prey, surrounding the prey by beta and delta wolves under the command of alpha wolves, introducing a CS algorithm, readjusting the positions of the alpha, beta and delta wolves, moving other gray wolves along with the position of the alpha, beta and delta wolves, and defining the step length of approaching the alpha, beta and delta wolves by the omega wolves in the wolf cluster, wherein the behavior model is as follows:

wherein , and />The position vectors of alpha, beta and delta wolves in the wolf population after being updated by adopting the Levy flight strategy are respectively +.>For the position of other wolves +.> and />Representing the current distance between the wolf and alpha, beta and delta wolves, respectively.

Step 3.4, the wolf will not be in the process of chasing the preyThe movable range of the hunting body is compressed to force the hunting body to stop moving, when the hunting body stops, the wolf group starts to attack, and the process of attacking the hunting body can be expressed as follows: convergence factorGradually decrease (S) of (B)>The value of (a) is [ -a, a]Internal variation, when the value of A is [ -1,1]When the interval is out, the position of the wolf group in searching for hunting is shown as +.>The value of (2) is [ -1,1]Within the interval, it is shown that the wolf group is attacking the prey.

And 3.5, updating the wolf group position information according to the formula (7) and the formula (10), stopping the circulation if the alpha wolf reaches the maximum iteration times or meets the iteration circulation ending condition, and outputting alpha wolf coordinate information, namely the found optimal solution.

3. The lithium battery SOC estimation method based on IGWO-EKF according to claim 1, wherein step 4 is specifically:

step 4.1, initially setting the population scale N of the wolf and the maximum iteration number t _max Optimizing variable dimension Dim, search range [ lb, lu]The position of the wolf population is initialized.

And 4.2, calculating the fitness value of each gray wolf individual, namely, the minimum value of the accumulated voltage error of the first-order Thevenin model of the lithium battery, and finding out an optimal solution alpha wolf, a suboptimal solution beta wolf and a third optimal solution delta wolf in the current gray wolf group.

And 4.3, substituting the values of Q and R corresponding to the optimal solution alpha wolf into the model to obtain the initial accumulated voltage error of the first-order Thevenin model of the lithium battery.

And 4.4, adjusting the positions of alpha, beta and delta wolf by adopting a CS algorithm every time of circulation.

And 4.5, after each cycle is finished, comparing the accumulated voltage error of the first-order Thevenin model of the lithium battery obtained in the current cycle with the minimum accumulated error obtained in the last cycle, and taking a smaller value as the minimum accumulated voltage error of the first-order Thevenin model of the current lithium battery.

Step 4.6, repeatedly executing the steps 4.2 to 4.5 until the set maximum iteration number is reached, and after the iteration is finished, obtaining the values of Q and R corresponding to the current alpha wolf as the optimal process noise covariance matrix Q _k And an optimal measurement noise covariance matrix R _k 。

4. The lithium battery SOC estimation method based on the IGWO-EKF according to claim 2, wherein in order to improve the effect of initial population distribution, the diversity of the population is increased, the optimizing speed of an algorithm is accelerated, and step 3.1 adopts a chaotic mapping function to generate a chaotic sequence as the position of an initial population individual:

wherein u=0.5, and the wolf population individuals have approximately consistent distribution densities for different parameters after chaos initialization.

5. The IGWO-EKF based lithium battery SOC estimation method of claim 2, wherein the gray wolf position update strategy using CS algorithm in step 3.3 is:

wherein ,for Levy random search path, lambda is stepLong adjustment coefficient, L _v Is the flight step length.

6. The lithium battery SOC estimation method based on IGWO-EKF according to claim 3, wherein the fitness function in step 4.2 is set as follows:

wherein ,representing the predicted value, y, of the terminal voltage measurement equation _k Representing the terminal voltage measurement, L is the maximum number of samples at the discrete frequency point.