阅读说明：本技术 一种基于分数阶理论的锂离子电池建模及参数辨识方法 (Fractional order theory-based lithium ion battery modeling and parameter identification method ) 是由 李俊红 蒋泽宇 王娟 李磊 褚云琨 芮佳丽 李政 于 2021-07-12 设计创作，主要内容包括：本发明提供了一种基于分数阶理论的锂离子电池建模及参数辨识方法,属于离子电池技术领域。解决了整数阶等效电路模型描述电池的动态特征的能力弱,低阶模型不能满足精度要求,高阶模型又会增加了模型复杂度和计算量的技术问题。其技术方案为：包括以下步骤：步骤1)采用经验公式法确定OCV-SOC的关系；步骤2)推导系统辨识方程；步骤3)构建改进蚁群优化算法的辨识流程。本发明的有益效果为：本发明经过分数阶理论改进的PNGV模型虽然呈现非线性,更加精确,推导出基于分数阶的PNGV模型辨识表达式,并且采用改进的蚁群优化算法进行在线辨识,可以获得估计精度高的模型参数和分数阶阶数,可以准确、有效地反应锂电池的实时性能。(The invention provides a lithium ion battery modeling and parameter identification method based on a fractional order theory, and belongs to the technical field of ion batteries. The method solves the technical problems that the capability of an integer order equivalent circuit model for describing the dynamic characteristics of the battery is weak, a low order model cannot meet the precision requirement, and a high order model increases the complexity and the calculated amount of the model. The technical scheme is as follows: the method comprises the following steps: step 1) determining the relation between OCV and SOC by adopting an empirical formula method; step 2), deducing a system identification equation; and 3) constructing an identification process of the improved ant colony optimization algorithm. The invention has the beneficial effects that: although the PNGV model improved by the fractional order theory is nonlinear and more accurate, the identification expression of the PNGV model based on the fractional order is deduced, and the improved ant colony optimization algorithm is adopted for online identification, so that the model parameters with high estimation precision and the fractional order can be obtained, and the real-time performance of the lithium battery can be accurately and effectively reflected.)

1. A lithium ion battery modeling and parameter identification method based on a fractional order theory is characterized by comprising the following steps:

step 1) measuring the voltage of a lithium ion battery terminal with the SOC from 1 to 0 and load current data through an intermittent constant-current discharge standing experiment, and determining the relation between the OCV and the SOC by adopting an empirical formula method;

step 2) establishing a fractional order PNGV equivalent circuit model of the lithium ion battery, and deducing a system identification equation representing the relation between a battery parameter identification vector and system input and output;

and 3) constructing an identification process of an improved ant colony optimization algorithm, and carrying out online identification on the fractional order PNGV model parameters.

2. The fractional order theory-based lithium ion battery modeling and parameter identification method according to claim 1, wherein the step 2) specifically comprises the steps of:

step 2-1), a PNGV model of the lithium ion battery is established to obtain a parameter identification model, and according to kirchhoff's law, a transfer function of a system can be obtained:

wherein, U_OCVIs the open circuit voltage, U, of a lithium ion battery_dIs the terminal voltage of the lithium ion battery, I is the current of the lithium ion battery, R_p、C_pCharacterization of the electrochemical polarization reaction, C_bCharacterization of concentration polarization reaction, R₀Ohmic resistance of the lithium ion battery;

the discrete fraction equation of Grunwald-Letnikov is used for definition:

let Y(s) be U_OCV(s)-U_d(s), u(s) is i(s), then the time domain fractional calculus equation can be obtained from equation (1):

expanding and shifting equation (3) yields:

(R_pC_pC_bD^α+β+C_bD^α)y(t)＝(R₀R_pC_pC_bD^α+β+(R₀+R_p)C_bD^α+R_pC_pD^β)u(t)+u(t) (4)

the SOC of the system can also be written as a fractional model, according to the definition of the ampere-hour integration method, as follows:

wherein Q is_nIs the rated capacity of the battery, eta is the coulomb efficiency of the battery, and eta is equal to 1 when a discharge test is adopted;

the discretization of the terms in equation (4) according to the definition of equation (2) is as follows:

wherein N is the number of historical data points participating in calculation, and T is a sampling interval;

in equations (6) to (10), some variables are defined as follows:

[a₁ a₂]＝[R_pC_pC_b C_b] (11)

[b₁ b₂]＝[α+β α] (12)

[c₁ c₂ c₃]＝[R₀R_pC_pC_b (R₀+R_p)C_b R_pC_p] (13)

[d₁ d₂ d₃]＝[α+β α β] (14)

according to the definitions of equations (11) to (14), equation (4) can be simplified as follows:

defining intermediate variables ω (i) andthe following were used:

considering the accuracy requirement and the short-time memory principle of the lithium ion battery model, the data length can be appropriately truncated, and taking N to 3, the following formula can be obtained:

the formula (17) is obtained by arranging:

wherein

The right side of equations (19) - (24) can be represented with the parameters to be identified as follows:

a₁＝θ₂θ₃θ₄ (25)

a₂＝θ₄ (26)

b₁＝θ₅+θ₆ (27)

b₂＝θ₅ (28)

c₁＝θ₁θ₂θ₃θ₄ (29)

c₂＝(θ₁+θ₂)θ₃ (30)

wherein θ ═ θ₁θ₂θ₃θ₄θ₅θ₆]＝[R₀ R_p C_p C_b αβ](ii) a Equation (5) can also be discretized as:

the identification vector and the information vector are as follows:

the PNGV model based on the fractional order theory can be usedEstablishing, wherein theta is an expression of theta;

the difference between the open circuit voltage and the terminal voltage of the lithium battery is taken as the real output of the system, and then the estimated output can be obtained by the following formula:

finally, a system identification equation representing the battery parameter identification vector and the system input-output relationship can be obtained by the following equation:

where y (t) is the true output value at time t.

3. The fractional order theory-based lithium ion battery modeling and parameter identification method according to claim 1 or 2, wherein the step 3) specifically comprises the steps of:

step 3-1) deducing a basic ant colony optimization algorithm:

the core idea of the Ant colony optimization algorithm is that parameters to be estimated are regarded as a plurality of path nodes of an Ant colony for searching food, a path which reaches the food fastest is found after pheromone is accumulated, the estimation of the parameters is obtained, the Ant colony dimensionality and the Ant colony number N are initialized, an Ant colony position Ant _ P is initialized according to an upper bound and a lower bound, an pheromone matrix q and an pheromone weight w are set_aPheromone heuristic matrix delta q and pheromone heuristic weight w_bPheromone memory factor p, pheromone quality Q and iteration frequency NI;

then, the difference of the fitness function of the ith ant colony and the jth ant colony is calculated as follows:

Δf_ij＝f_i-f_j (35)

wherein, i is 1,2,3 … N, j is 1,2,3 … N;

according to the formula (35), when Δ f_ijWhen the value is more than 0, the fitness value representing the jth ant colony is smaller than that of the ith ant colony, and if the fitness function value of k ant colonies is lower than that of the ith ant colony, the probability Ps that the ith ant colony moves to the jth ant colony can be respectively calculated_ijThe following were used:

wherein j is 1,2, …, k;

after the ant colony with the maximum probability is selected, updating the position of the ant colony, and updating the pheromone heuristic matrix, the pheromone matrix and the iteration times:

step 3-2) constructing a fitness function F of the online optimization identification algorithm according to the system identification equation in the step 2)_i,t＝F(Θ)，F_i,tRepresenting the fitness function value of the ith ant colony at the time t;

step 3-3) deducing an improved ant colony online optimization algorithm:

firstly, initializing parameters, and introducing a search interval reduction factor r and online identification time t;

calculating the difference between the fitness function values of the ith ant colony and the jth ant colony at the time t, namely the difference value of the system identification equation is as follows:

ΔF_ij,t＝F_i,t-F_j,t (38)

where i is 1,2, …, N, j is 1,2, …, N, when Δ F_ij,tIf > 0, it means that the fitness function value of the jth ant colony is lower than that of the ith ant colony at time t, and if the fitness function values of k ant colonies are lower than that of the ith ant colony at time t, the probability that the ith ant colony moves to the k ant colonies is as follows:

wherein j is 1,2, …, k;

ant colony random variation coefficient R of ith ant colony at time t_i,tRand is a random number from 0 to 1, and the next ant colony m moved by the ith ant colony satisfies the following equation:

wherein m is less than k;

after the moving ant colony is selected, updating the position near the ant colony, and updating the pheromone heuristic matrix, the pheromone matrix and the iteration times:

when the ant colony of the searching fractional order exceeds the limit range (0,1), the position of the ant colony is assigned as rand again;

when the iteration number NI reaches the iteration maximum value, completing the online identification of the fractional order model parameters and the fractional order at the moment t, and when new data are collected, t is t + 1;

step 3-4) obtaining the SOC and the open-circuit voltage at the time t according to the OCV-SOC relation;

step 3-5) reading the terminal voltage and the working current data of the lithium ion battery at the t moment according to the acquired terminal voltage and the working current of the lithium ion battery, and carrying out information vector

Step 3-6) constructing an identification vector theta according to the initialized ant colony position to obtain a fitness function F of the online optimization identification algorithm_i,t＝F(Θ)；

Step 3-7) calculating the difference delta F of the fitness function values_ij,tUsing Δ F_ij,tCalculating the probability P of ant colony movement_ij,tSelecting the moving position of the ant colony according to the following formula;

step 3-8) updating the Ant colony position Ant _ P;

Ant_P_i＝Ant_P_m+(2rand-1)r^NI (43)

step 3-9) updating the pheromone q;

q＝pq+Δq (44)

step 3-10) judging whether the identification termination times are met, and if so, outputting an identification result; otherwise, returning to step 3-4) if NI is NI + 1;

and 3-10) outputting the identification result, returning to the step 3-2 when t is t + 1), and identifying the data at the new moment.

Technical Field

The invention relates to the technical field of ion batteries, in particular to a lithium ion battery modeling and parameter identification method based on a fractional order theory.

Background

The new energy automobile industry is rapidly developed, and batteries are used as a core part of new energy automobile energy supply and become a mainstream direction for research of various national scholars. Lithium batteries are the most important energy storage elements in batteries due to their advantages of long life, high specific energy, and the like. The battery management system in the new energy automobile is particularly important for safely and efficiently using the lithium battery, and in order to simulate the lithium battery in the battery management system, a model which is simple in structure and convenient to simulate needs to be established. In reality, it is still a challenging task to complete the above model building and online identification of model parameters.

In the existing lithium battery modeling method, an electrochemical model can accurately describe various electrochemical properties of a lithium ion battery, but the model has a complex structure and excessive parameters to be identified, and is not dominant in simulation of batteries of electric vehicles and mobile phones; the black box model has overlarge demand on data quantity, the relation between the precision and the training frequency and the training method is large, and the adaptability is poor; in the equivalent circuit model, the capability of the integer order equivalent circuit model for describing the dynamic characteristics of the battery is weak, the low order model cannot meet the precision requirement, and the high order model increases the complexity and the calculated amount of the model. In terms of battery model parameter identification algorithm, group intelligence algorithm is widely researched due to the capability of nonlinear and complex system identification. For example, particle swarm optimization and an improved algorithm thereof can be well suitable for different working conditions, but the problem that reliable estimation is difficult to obtain by online identification of a swarm intelligence algorithm becomes one.

How to solve the above technical problems is the subject of the present invention.

Disclosure of Invention

The invention aims to provide a lithium ion battery modeling and parameter identification method based on a fractional order theory, which introduces the fractional order theory into the construction of an equivalent circuit model of a lithium ion battery, and a PNGV model improved by the fractional order theory is nonlinear but more accurate than an integer order. A PNGV model identification expression based on fractional order is deduced, online identification is carried out by adopting an improved ant colony optimization algorithm, model parameters with high estimation precision and the fractional order can be obtained, and the real-time performance of the lithium battery can be accurately and effectively reflected in a battery management system.

The invention is realized by the following measures: a lithium ion battery modeling and parameter identification method based on a fractional order theory comprises the following steps:

step 1) measuring the terminal voltage and load current data of a lithium ion battery with the SOC from 1 to 0 through an intermittent constant-current discharge standing experiment, and determining the relation between the OCV and the SOC by adopting an empirical formula method;

step 2) establishing a fractional order PNGV equivalent circuit model of the lithium ion battery, and deducing a system identification equation representing the relation between a battery parameter identification vector and system input and output;

step 3) constructing an identification process of an improved ant colony optimization algorithm, and carrying out online identification on the parameters of the fractional order PNGV model;

as a further optimization scheme of the lithium ion battery modeling and parameter identification method based on the fractional order theory provided by the invention, the step 2) specifically comprises the following steps:

step 2-1), a PNGV model of the lithium ion battery is established to obtain a parameter identification model, and according to kirchhoff's law, a transfer function of a system can be obtained:

wherein, U_OCVIs the open circuit voltage, U, of a lithium ion battery_dIs the terminal voltage of the lithium ion battery, I is the current of the lithium ion battery, R_p、C_pCharacterization of the electrochemical polarization reaction, C_bCharacterization of concentration polarization reaction, R₀Is the ohmic resistance of a lithium ion battery.

The discrete fraction equation of Grunwald-Letnikov is used for definition:

let Y(s) be U_OCV(s)-U_d(s), u(s) is i(s), then the time domain fractional calculus equation can be obtained from equation (1):

expanding and shifting equation (3) yields:

(R_pC_pC_bD^α+β+C_bD^α)y(t)＝(R₀R_pC_pC_bD^α+β+(R₀+R_p)C_bD^α+R_pC_pD^β)u(t)+u(t) (4)

the SOC of the system can also be written as a fractional model, according to the definition of the ampere-hour integration method, as follows:

wherein Q_nIs the rated capacity of the battery, eta is the coulombic efficiency of the battery, and eta is equal to 1 in a discharge test.

The discretization of the terms in equation (4) according to the definition of equation (2) is as follows:

wherein N is the number of historical data points participating in calculation, and T is the sampling interval.

In equations (6) to (10), some variables are defined as follows:

[a₁ a₂]＝[R_pC_pC_b C_b] (11)

[b₁ b₂]＝[α+β α] (12)

[c₁ c₂ c₃]＝[R₀R_pC_pC_b (R₀+R_p)C_b R_pC_p] (13)

[d₁ d₂ d₃]＝[α+β α β] (14)

according to the definitions of equations (11) to (14), equation (4) can be simplified as follows:

defining intermediate variables ω (i) andthe following were used:

the data length can be appropriately truncated in consideration of the accuracy requirement of the lithium ion battery model and the short-time memory principle. When N is 3, the following formula can be obtained:

the formula (17) is obtained by arranging:

wherein

The right side of equations (19) - (24) can be represented with the parameters to be identified as follows:

a₁＝θ₂θ₃θ₄ (25)

a₂＝θ₄ (26)

b₁＝θ₅+θ₆ (27)

b₂＝θ₅ (28)

c₁＝θ₁θ₂θ₃θ₄ (29)

c₂＝(θ₁+θ₂)θ₃ (30)

wherein θ ═ θ₁ θ₂ θ₃ θ₄ θ₅ θ₆]＝[R₀ R_p C_p C_bα β]. Equation (5) can also be discretized as:

the identification vector and the information vector are as follows:

the PNGV model based on the fractional order theory can be usedEstablishing, wherein theta is an expression of theta.

The difference between the open circuit voltage and the terminal voltage of the lithium battery is taken as the real output of the system, and then the estimated output can be obtained by the following formula:

finally, a system identification equation representing the battery parameter identification vector and the system input-output relationship can be obtained by the following equation:

where y (t) is the true output value at time t.

As a further optimization scheme of the lithium ion battery modeling and parameter identification method based on the fractional order theory provided by the invention, the step 3) specifically comprises the following steps:

step 3-1) deducing a basic ant colony optimization algorithm:

the core idea of the ant colony optimization algorithm is that the parameters to be estimated are regarded as a plurality of path nodes for finding food by the ant colony, and after pheromone accumulation, the path which reaches the food fastest is found to obtain the estimation of the parameters. Firstly, initializing the Ant colony dimension, the number N of the Ant colonies, and initializing the Ant colony position Ant _ P according to an upper bound and a lower bound. Setting pheromone matrix q and pheromone weight w_aPheromone heuristic matrix delta q and pheromone heuristic weight w_bPheromone memory factor p, pheromone quality Q and iteration number NI.

Then, the difference of the fitness function of the ith ant colony and the jth ant colony is calculated as follows:

Δf_ij＝f_i-f_j (35)

wherein, i is 1,2,3 … N, j is 1,2,3 … N.

According to the formula (35), when Δ f_ij> 0, the fitness value for the jth ant colony is smaller than that for the ith ant colony. Assuming that the fitness function value of the k ant colonies is lower than that of the ith ant colony, the probability Ps of the ith ant colony moving to the jth ant colony can be calculated respectively_ijThe following were used:

where j is 1,2, …, k.

After the ant colony with the maximum probability is selected, updating the position of the ant colony, and updating the pheromone heuristic matrix, the pheromone matrix and the iteration times:

step 3-2) constructing a fitness function F of the online optimization identification algorithm according to the system identification equation in the step 2)_i,t＝F(Θ)，F_i,tAnd representing the fitness function value of the ith ant colony at the time t.

Step 3-3) deducing an improved ant colony online optimization algorithm:

firstly, initializing parameters, and introducing a search interval reduction factor r and online identification time t.

Calculating the difference between the fitness function values of the ith ant colony and the jth ant colony at the time t, namely the difference value of the system identification equation is as follows:

ΔF_ij,t＝F_i,t-F_j,t (38)

wherein, i is 1,2, …, N, j is 1,2, …, N. When Δ F_ij,tAnd when the value is more than 0, the fitness function value of the jth ant colony at the time t is lower than that of the ith ant colony. Assuming that the fitness function value of k ant colonies at time t is lower than that of the ith ant colony, the probability that the ith ant colony moves to the position of the k ant colonies is as follows:

where j is 1,2, …, k.

Ant colony random variation coefficient R of ith ant colony at time t_i,tRand, which is a random number from 0 to 1, the next ant colony m to which the ith ant colony moves satisfying the following formula:

wherein m is less than k.

After the moving ant colony is selected, updating the position near the ant colony, and updating the pheromone heuristic matrix, the pheromone matrix and the iteration times:

wherein, when the ant colony of the searching fractional order exceeds the limit range (0,1), the position is re-assigned as rand.

And when the iteration number NI reaches the iteration maximum value, completing the online identification of the fractional order model parameters and the fractional order at the moment t, and when new data are collected, t is t + 1.

Step 3-4) obtaining the SOC and the open-circuit voltage at the time t according to the OCV-SOC relation;

step 3-5) reading the terminal voltage and the working current data of the lithium ion battery at the t moment according to the acquired terminal voltage and the working current of the lithium ion battery, and carrying out information vector

Step 3-6) constructing an identification vector theta according to the initialized ant colony position to obtain a fitness function F of the online optimization identification algorithm_i,t＝F(Θ)；

Step 3-7) calculating the difference delta F of the fitness function values_ij,tUsing Δ F_ij,tCalculating the probability P of ant colony movement_ij,tSelecting the moving position of the ant colony according to the following formula;

step 3-8) updating the Ant colony position Ant _ P;

Ant_P_i＝Ant_P_m+(2rand-1)r^NI (43)

step 3-9) updating the pheromone q;

q＝pq+Δq (44)

step 3-10) judging whether the identification termination times are met, and if so, outputting an identification result; otherwise, NI ═ NI +1, return to step 3-4).

And 3-10) outputting the identification result, returning to the step 3-2 when t is t + 1), and identifying the data at the new moment.

Compared with the prior art, the invention has the beneficial effects that:

(1) the invention introduces a fractional order theory into the establishment of a lithium battery PNGV model. Compared with a common RC circuit, the PNGV model has the same physical significance as a second-order RC circuit in the aspect of describing an electrochemical impedance spectrum, but one circuit parameter is reduced compared with the second-order RC circuit, the number of the circuit parameters is reduced, and the structure is simpler; the fractional order PNGV model has two more fractional orders than the integer order PNGV model, which makes the model more accurate.

(2) The method deduces the system identification equation with the minimum information vector length based on the model according to the fractional order short-term memory, can adjust the length of the information vector according to the precision requirement of the external environment, and has adaptability and practicability. And the system identification equation can realize the online identification of the fractional order model parameters and the fractional order, and has real-time performance and application value.

(3) The improved ant colony optimization algorithm has higher identification precision, and the output estimated value is very close to the true value, thereby having engineering value; compared with other swarm intelligence algorithms such as a particle swarm optimization algorithm, the method has a smooth identification parameter curve and has practical physical significance.

Drawings

The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.

Fig. 1 is an overall framework flow diagram of the present invention.

FIG. 2 is a diagram of a fractional order PNGV model of a lithium ion battery according to the present invention.

FIG. 3 is a graph of the test voltage current of the present invention.

FIG. 4 is a graph of an empirical formula fit of OCV-SOC used in intermittent constant current experiments in accordance with the present invention.

Fig. 5 is a schematic diagram of the identification error of the improved ant colony optimization algorithm according to the present invention.

Fig. 6 is a graph of terminal voltage predictions obtained by the improved ant colony optimization algorithm of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative of the invention and are not intended to be limiting.

Example 1

Referring to fig. 1 to 6, the technical solution provided by the present invention is a lithium battery modeling and parameter online identification method based on a fractional order theory, in this embodiment, a research is performed with an under-the-pine lithium ion battery NCR-18650B as an object, a calibration voltage is 3.7V, and a battery capacity is 3400 mAh. The battery is charged to the cut-off voltage in a constant current charging mode (0.5C), and after standing for 1h, the battery is in a full charge state. The battery operates in an intermittent constant current discharge mode: discharging for 5min, standing for 30min, discharging current is 3400mA, and discharging rate is 1C. This process is repeated until the voltage drops to the discharge cutoff voltage. The test voltage curve versus current curve is shown in fig. 4.

In order to better achieve the object of the present invention, the present embodiment is a method for modeling and online parameter identification of a lithium ion battery based on a fractional order theory, comprising the following steps:

step 1) measuring the voltage of a lithium ion battery terminal with the SOC from 1 to 0 and load current data through an intermittent constant-current discharge standing experiment, wherein the sampling period is 1s, solving the SOC through a time-safety method, and fitting by an empirical formula method is to perform curve fitting in MATLAB by using a fitting function polyfit to determine the function relation of the OCV-SOC;

step 2) establishing a fractional order PNGV equivalent circuit model of the lithium ion battery, and deducing a system identification equation representing the relation between a battery parameter identification vector and system input and output;

step 3) constructing an identification process of an improved ant colony optimization algorithm, and carrying out online identification on the parameters of the fractional order PNGV model;

preferably, the step 2) specifically comprises the following steps:

step 2-1), a PNGV model of the lithium ion battery is established to obtain a parameter identification model, and according to kirchhoff's law, a transfer function of a system can be obtained:

wherein, U_OCVIs the open circuit voltage, U, of a lithium ion battery_dIs the terminal voltage of the lithium ion battery, I is the current of the lithium ion battery, R_p、C_pCharacterization of the electrochemical polarization reaction, C_bCharacterization of concentration polarization reaction, R₀Is the ohmic resistance of a lithium ion battery.

The discrete fraction equation of Grunwald-Letnikov is used for definition:

let Y(s) be U_OCV(s)-U_d(s), u(s) is i(s), then the time domain fractional calculus equation can be obtained from equation (1):

expanding and shifting equation (3) yields:

(R_pC_pC_bD^α+β+C_bD^α)y(t)＝(R₀R_pC_pC_bD^α+β+(R₀+R_p)C_bD^α+R_pC_pD^β)u(t)+u(t) (4)

the SOC of the system can also be written as a fractional model, according to the definition of the ampere-hour integration method, as follows:

wherein Q_nIs the rated capacity of the cell, eta is the coulomb efficiency of the cell, andeta is equal to 1 in the discharge test.

The discretization of the terms in equation (4) according to the definition of equation (2) is as follows:

wherein N is the number of historical data points participating in calculation, and T is the sampling interval.

In equations (6) to (10), some variables are defined as follows:

[a₁ a₂]＝[R_pC_pC_b C_b] (11)

[b₁ b₂]＝[α+β α] (12)

[c₁ c₂ c₃]＝[R₀R_pC_pC_b (R₀+R_p)C_b R_pC_p] (13)

[d₁ d₂ d₃]＝[α+β α β] (14)

according to the definitions of equations (11) to (14), equation (4) can be simplified as follows:

intermediate variables a (i) and b (i) are defined as follows:

the data length can be appropriately truncated in consideration of the accuracy requirement of the lithium ion battery model and the short-time memory principle. When N is 3, the following formula can be obtained:

the formula (17) is obtained by arranging:

wherein

The right side of equations (19) - (24) can be represented with the parameters to be identified as follows:

a₁＝θ₂θ₃θ₄ (25)

a₂＝θ₄ (26)

b₁＝θ₅+θ₆ (27)

b₂＝θ₅ (28)

c₁＝θ₁θ₂θ₃θ₄ (29)

c₂＝(θ₁+θ₂)θ₃ (30)

wherein θ ═ θ₁ θ₂ θ₃ θ₄ θ₅ θ₆]＝[R₀ R_p C_p C_bα β]. Equation (5) can also be discretized as:

the identification vector and the information vector are as follows:

the PNGV model based on the fractional order theory can be usedEstablishing, wherein theta is an expression of theta.

The difference between the open circuit voltage and the terminal voltage of the lithium battery is taken as the real output of the system, and then the estimated output can be obtained by the following formula:

finally, a system identification equation representing the battery parameter identification vector and the system input-output relationship can be obtained by the following equation:

where y (t) is the true output value at time t.

Specifically, the step 3) specifically includes the following steps:

step 3-1) deducing a basic ant colony optimization algorithm:

the core idea of the ant colony optimization algorithm is that the parameters to be estimated are regarded as a plurality of path nodes for finding food by the ant colony, and after pheromone accumulation, the path which reaches the food fastest is found to obtain the estimation of the parameters. Firstly, initializing the Ant colony dimension, the number N of the Ant colonies, and initializing the Ant colony position Ant _ P according to an upper bound and a lower bound. Setting pheromone matrix q and pheromone weight w_aPheromone heuristic matrix delta q and pheromone heuristic weight w_bPheromone memory factor p, pheromone quality Q and iteration number NI.

Then, the difference of the fitness function of the ith ant colony and the jth ant colony is calculated as follows:

Δf_ij＝f_i-f_j (35)

wherein, i is 1,2,3 … N, j is 1,2,3 … N.

According to the formula (35), when Δ f_ij> 0, the fitness value for the jth ant colony is smaller than that for the ith ant colony. Assuming that the fitness function value of the k ant colonies is lower than that of the ith ant colony, the probability Ps of the ith ant colony moving to the jth ant colony can be calculated respectively_ijThe following were used:

where j is 1,2, …, k.

After the ant colony with the maximum probability is selected, updating the position of the ant colony, and updating the pheromone heuristic matrix, the pheromone matrix and the iteration times:

step 3-2) constructing a fitness function F of the online optimization identification algorithm according to the system identification equation in the step 2)_i,t＝F(Θ)，F_i,tAnd representing the fitness function value of the ith ant colony at the time t.

Step 3-3) deducing an improved ant colony online optimization algorithm:

firstly, initializing parameters, and introducing a search interval reduction factor r and online identification time t.

Calculating the difference between the fitness function values of the ith ant colony and the jth ant colony at the time t, namely the difference value of the system identification equation is as follows:

ΔF_ij,t＝F_i,t-F_j,t (38)

wherein, i is 1,2, …, N, j is 1,2, …, N. When Δ F_ij,tAnd when the value is more than 0, the fitness function value of the jth ant colony at the time t is lower than that of the ith ant colony. Assuming that the fitness function value of k ant colonies at time t is lower than that of the ith ant colony, the probability that the ith ant colony moves to the position of the k ant colonies is as follows:

where j is 1,2, …, k.

Ant colony random variation coefficient R of ith ant colony at time t_i,tRand, which is a random number from 0 to 1, the next ant colony m to which the ith ant colony moves satisfying the following formula:

wherein m is less than k.

After the moving ant colony is selected, updating the position near the ant colony, and updating the pheromone heuristic matrix, the pheromone matrix and the iteration times:

wherein, when the ant colony of the searching fractional order exceeds the limit range (0,1), the position is re-assigned as rand.

And when the iteration number NI reaches the iteration maximum value, completing the online identification of the fractional order model parameters and the fractional order at the moment t, and when new data are collected, t is t + 1.

Step 3-4) obtaining the SOC and the open-circuit voltage at the time t according to the OCV-SOC relation;

step 3-5) reading the terminal voltage and the working current data of the lithium ion battery at the t moment according to the acquired terminal voltage and the working current of the lithium ion battery, and carrying out information vector

Step 3-6) constructing an identification vector theta according to the initialized ant colony position to obtain a fitness function F of the online optimization identification algorithm_i,t＝F(Θ)；

Step 3-7) calculating the difference delta F of the fitness function values_ij,tUsing Δ F_ij,tCalculating the probability P of ant colony movement_ij,tSelecting the moving position of the ant colony according to the following formula;

step 3-8) updating the Ant colony position Ant _ P;

Ant_P_i＝Ant_P_m+(2rand-1)r^NI (43)

step 3-9) updating the pheromone q;

q＝pq+Δq (44)

step 3-10) judging whether the identification termination times are met, and if so, outputting an identification result; otherwise, NI ═ NI +1, return to step 3-4).

And 3-10) outputting the identification result, returning to the step 3-2 when t is t + 1), and identifying the data at the new moment.

The OCV-SOC relationship curve used in this embodiment is shown in fig. 4, the terminal voltage of the fractional PNGV model is predicted by the parameter identified at each time and the operating current at the corresponding time, the error is shown in fig. 5, and the result is shown in fig. 6. The model parameter predicted voltage value is compared with the actual test value to evaluate the accuracy of parameter identification.

And introducing the fractional order theory into a lithium battery PNGV model to establish a fractional order model shown in figure 1. Compared with a common RC circuit, the PNGV model has the same physical significance as a second-order RC circuit in the aspect of describing an electrochemical impedance spectrum, but one circuit parameter is reduced compared with the second-order RC circuit, the number of the circuit parameters is reduced, and the structure is simpler; compared with an integer order PNGV model, the fractional order PNGV model has two more fractional order orders, so that the model is more accurate, and the simulation accuracy is improved.

According to the short-term memory of fractional order, a system identification equation with the minimum information vector length is deduced based on the model, the length of the information vector can be adjusted according to the precision requirement of the external environment, and the method has adaptability and practicability. And the system identification equation can realize the on-line identification of the fractional order model parameters and the fractional order, and has real-time performance and application value.

The experiment verifies that the improved ant colony optimization algorithm can well identify each model parameter, the identification precision of the algorithm is high, the output estimated value is very close to the true value, and the engineering value is achieved; compared with other group intelligent algorithms such as particle group optimization algorithm, the method has good identification parameter continuity, has a smooth identification parameter curve, and has practical physical significance.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.