Lithium battery parameter identification method based on speed pause particle swarm algorithm

Abstract

The invention discloses a lithium battery parameter identification method based on a speed pause particle swarm algorithm, and the method comprises the steps: 1, collecting the current data, terminal voltage data and open-circuit voltage data of a lithium battery according to a sampling time interval; 2, constructing a second-order fractional order equivalent circuit model of the lithium battery, and determining a to-be-identified parameter vector; step 3, constructing a VPPSO equivalent circuit model parameter identification algorithm; and 4, inputting the current data, the terminal voltage data, the open-circuit voltage data and the to-be-identified parameter vector of the lithium battery into a VPPSO equivalent circuit model parameter identification algorithm to obtain an identification parameter vector, a minimum fitness value, a terminal voltage prediction sequence and a convergence fitness sequence. The method has the characteristics that the global search capability is improved, and the search efficiency and the identification precision of the optimization process are improved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of lithium ion battery modeling, and more particularly to a lithium battery parameter identification method based on a speed pause particle swarm algorithm. BACKGROUND

[0002] Efficient and accurate estimation of lithium batteries is becoming a core challenge of battery management systems, and its estimation accuracy depends heavily on the parameter identification results of the battery model. Current mainstream estimation methods are based on three types of models: the electrochemical model can represent the aging mechanism, but it relies on high-dimensional partial differential equations for solving, which is computationally complex and has poor real-time performance; the data-driven model maps the characteristics through data without physical equations, but it lacks generalization and physical interpretation; the equivalent circuit model simplifies the dynamic response with an RC network, has low computational complexity, and has high accuracy (typically less than 3% error in state estimation achieved by combining Kalman filter algorithms). However, the non-linear time-varying characteristics of its parameters under discharge depth, rate, and aging lead to traditional identification easily falling into local optimal solution and slow convergence, causing cumulative voltage fitting deviation.

[0003] Particle swarm optimization (PSO) algorithm is a swarm intelligence optimization algorithm derived from the foraging behavior of natural group cooperation. Its core mechanism is to initialize a group of particles in the solution space of the problem to be optimized, each particle corresponds to a potential solution vector, and is assigned a position vector Xi and a velocity vector Vi. In the iterative search process, the particle updates its own speed and position by tracking and memorizing its individual historical optimal position and perceiving the current global optimal position of the group. This dual guidance mechanism, which combines individual historical optimal experience and global optimal information, drives the entire particle swarm to continuously adjust its trajectory and efficiently explore and develop the solution space. In the parameter identification of lithium ion battery equivalent circuit model, PSO algorithms are effective means to solve parameter coupling and sensitivity differences due to their lack of gradient information and adaptability to non-linear characteristics, but such algorithms are prone to premature convergence into local optimal solution and slow convergence speed in high-dimensional parameter identification of lithium ion batteries.

[0004] In order to better establish a lithium battery model, many PSO-based identification algorithms have been applied to the parameter identification of lithium ion battery equivalent circuit models, such as using PSO algorithm to identify the second-order RC equivalent circuit model, which to some extent achieves a balance between precision and timeliness, but the precision is limited in complex road conditions; for example, optimizing the PSO topology for Thevenin model, but it is prone to local optimum and has high parameter sensitivity; and a lithium ion battery full SOC range estimation method based on global PSO (GPSO) and improved extended Kalman filter, which improves the parameter accuracy of full SOC range by dividing multiple sub-regions, but faces the trade-off between computational complexity and convergence speed.

[0005] How to solve the above technical problems is a subject faced by the existing research. SUMMARY

[0006] The purpose of the present application is to design and develop a lithium battery parameter identification method based on a velocity pause particle swarm optimization algorithm, use the VPPSO algorithm to identify the parameters of the equivalent circuit model of the lithium battery, and feed back the optimal model parameters obtained by identification to the equivalent circuit model, thereby improving the identification accuracy and accelerating the convergence speed.

[0007] The technical scheme provided by the present application is:

[0008] A lithium battery parameter identification method based on a velocity pause particle swarm optimization algorithm, comprising the following steps:

[0009] Step one, collect the current data, terminal voltage data and open circuit voltage data of the lithium battery according to the sampling time interval;

[0010] Step two, construct a lithium battery second-order fractional-order equivalent circuit model and determine a to-be-identified parameter vector;

[0011] Step three, construct a VPPSO equivalent circuit model parameter identification algorithm;

[0012] Step four, input the current data, terminal voltage data, open circuit voltage data and to-be-identified parameter vector of the lithium battery into the VPPSO equivalent circuit model parameter identification algorithm to obtain an identification parameter vector, a minimum fitness value, a terminal voltage prediction sequence and a convergence fitness sequence.

[0013] Preferably, the step one specifically comprises:

[0014] Step 1, place the lithium battery on a charge-discharge platform for experiment, and the environmental temperature is constant at 25 DEG C;

[0015] Step 2, perform constant current pulse discharge on the battery;

[0016] Step 3, repeat step 2 until the terminal voltage of the lithium battery drops to the discharge cutoff voltage.

[0017] Preferably, the lithium battery second-order fractional-order equivalent circuit model comprises an ideal open circuit voltage source, an ohmic internal resistance, a first polarization branch and a second polarization branch, the first polarization branch is composed of a first constant phase element CPE1 and a first polarization resistance R1 in parallel, and the second polarization branch is composed of a second constant phase element CPE2 and a second polarization resistance R2 in parallel.

[0018] Preferably, the to-be-identified parameter vector comprises:

[0019] The ohmic internal resistance of the lithium battery second-order fractional-order equivalent circuit model;

[0020] A first polarization resistance of a first polarization branch in a second-order fractional-order equivalent circuit model of a lithium battery

[0021] A second polarization resistance of a second polarization branch in the second-order fractional-order equivalent circuit model of the lithium battery

[0022] A capacitance value of a first constant phase element in the second-order fractional-order equivalent circuit model of the lithium battery

[0023] A capacitance value of a second constant phase element in the second-order fractional-order equivalent circuit model of the lithium battery

[0024] A fractional-order order of the first constant phase element in the second-order fractional-order equivalent circuit model of the lithium battery

[0025] A fractional-order order of the second constant phase element in the second-order fractional-order equivalent circuit model of the lithium battery

[0026] Preferably, the VPPSO equivalent circuit model parameter identification algorithm comprises:

[0027] Step a, initializing a particle swarm;

[0028] wherein the particle swarm is equally divided into a first subgroup and a second subgroup;

[0029] Step b, calculating an adaptive value of each particle;

[0030] Step c, iteratively updating and optimizing the particle swarm;

[0031] wherein the first subgroup performs speed updating and position updating with a pause mechanism;

[0032] the second subgroup performs position updating based on global optimal position attenuation disturbance;

[0033] Step d, updating individual optimal and global optimal;

[0034] Step e, when t≥T or |f(Gbest(t))|<5×10 -3 V, iteration termination;

[0035] wherein t is a current iteration number, T is a maximum iteration number, Gbest(t) is a global optimal position after the tth iteration, and f(·) is an adaptive value.

[0036] Preferably, the adaptive value satisfies:

[0037]

[0038] wherein f(·) is an adaptive function, K is a sampling point number, U meas (k) represents a measured voltage value at a sampling time k, U est (k|Xi represents the use of the position vector X i The voltage estimate value at the sampling moment k is calculated.

[0039] Preferably, the velocity update of the first sub-group satisfies:

[0040] If rand < a, then V i,j (t+1) = V i,j (t) + C

[0041] If rand ≥ a, then

[0042] V i,j (t+1) = ω · V i,j (t) + C p · r1 · (Pbest i,j (t) - X i,j (t)) + C g · r2 · (Gbest j (t) - X i,j (t)) ;

[0043] In the formula, rand is a random number, V i,j (t+1) is the updated velocity of the i-th particle in the j-th dimension at the t+1-th iteration, ω is an inertia weight, V i,j (t) is the velocity of the i-th particle in the j-th dimension at the t-th iteration, C p is a local acceleration coefficient, r1 and r2 are two random numbers in the interval [0, 1], Pbest i,j (t) is the individual optimal position of the i-th particle in the j-th dimension at the t-th iteration, X i,j (t) is the current position of the i-th particle in the j-th dimension at the t-th iteration, C g is a global acceleration coefficient, Gbest j (t) is the global optimal position of all particles in the j-th dimension at the t-th iteration, a is a velocity pause parameter, a ∈ [0, 1], when a = 1, the particle does not pause the velocity update, when a = 0, the particle always maintains the same velocity and does not update the velocity.

[0044] Preferably, the position update of the second sub-group satisfies:

[0045] X i,j (t+1) = Gbest j (t) ± β(t) · rand · |Gbest j (t) | ;

[0046] In the formula, β(t) is a decreasing function.

[0047] Preferably, the terminal voltage prediction sequence satisfies:

[0048] U est (k) = U ocv (k) + I T (k) R0 + U1(k) + U2(k) ;

[0049] wherein U est (k) is an estimated value of the terminal voltage at sampling time k, U ocv (k) is an open-circuit voltage at sampling time k, I T (k) is a current at sampling time k, R0 is an ohmic internal resistance of a lithium battery second-order fractional-order equivalent circuit model, U1(k) is a first polarization branch voltage at sampling time k, and U2(k) is a second polarization branch voltage at sampling time k.

[0050] Preferably, the first polarization branch voltage satisfies:

[0051]

[0052] wherein U1(k) is a first polarization branch voltage at sampling time k, T s n is a first branch fractional-order discretization coefficient, and U1(k-1) is a first polarization branch voltage at sampling time k-1.

[0053] The present application has the following beneficial effects:

[0054] The present application discloses a lithium battery parameter identification method based on a speed pause particle swarm algorithm, which introduces a speed pause update mechanism and a double population strategy. The speed pause update mechanism can make some particles have a probability to pause the speed update of the particles, thereby enhancing the diversity of the particle population, avoiding falling into a local optimal solution, and improving the global search ability. The double population strategy balances the global optimization and local optimization abilities of the particle swarm through the cooperative work of the global population and the local population, improves the search efficiency and accuracy of the optimization process, and effectively avoids the premature convergence problem caused by the reduction of population diversity and the insufficient global search ability, thereby improving the precision and convergence speed of the lithium battery equivalent circuit model parameter identification. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 Fig. 1 is a flowchart of the lithium battery parameter identification method based on the speed pause particle swarm algorithm.

[0056] Figure 2 Fig. 2 is a schematic diagram of the lithium battery second-order fractional-order equivalent circuit model.

[0057] Figure 3A schematic diagram of the comparison between the estimated value and the true value of the terminal voltage of each model over time in the VPPSO parameter identification of the four equivalent circuit models under the HPPC condition described in the present application.

[0058] Figure 4 A schematic diagram of the comparison between the estimated error of the terminal voltage over time in the VPPSO parameter identification of the four equivalent circuit models under the HPPC condition described in the present application.

[0059] Figure 5 A schematic diagram of the convergence curve based on the number of iterations and RMSE as fitness value in the VPPSO parameter identification of the four equivalent circuit models under the HPPC condition described in the present application.

[0060] Figure 6 A schematic diagram of the comparison between the estimated value and the true value of the terminal voltage of each model over time in the PSO parameter identification of the four equivalent circuit models under the HPPC condition described in the present application.

[0061] Figure 7 A schematic diagram of the comparison between the estimated error of the terminal voltage over time in the PSO parameter identification of the four equivalent circuit models under the HPPC condition described in the present application.

[0062] Figure 8 A schematic diagram of the convergence curve based on the number of iterations and RMSE as fitness value in the PSO parameter identification of the four equivalent circuit models under the HPPC condition described in the present application.

[0063] Figure 9 A schematic diagram of the comparison between the estimated value and the true value of the terminal voltage of each model over time in the VPPSO parameter identification of the four equivalent circuit models under the FTP75 condition described in the present application.

[0064] Figure 10 A schematic diagram of the comparison between the estimated error of the terminal voltage over time in the VPPSO parameter identification of the four equivalent circuit models under the FTP75 condition described in the present application.

[0065] Figure 11 A schematic diagram of the convergence curve based on the number of iterations and RMSE as fitness value in the VPPSO parameter identification of the four equivalent circuit models under the FTP75 condition described in the present application.

[0066] Figure 12 A schematic diagram of the comparison between the estimated value and the true value of the terminal voltage of each model over time in the PSO parameter identification of the four equivalent circuit models under the FTP75 condition described in the present application.

[0067] Figure 13 A schematic diagram of the comparison between the estimated error of the terminal voltage over time in the PSO parameter identification of the four equivalent circuit models under the FTP75 condition described in the present application.

[0068] Figure 14 The convergence curve schematic diagram drawn based on the iteration number and the RMSE as the fitness value when identifying the four equivalent circuit models of the PSO parameters of the FTP75 working condition of the application is shown in the figure. DETAILED DESCRIPTION

[0069] The application will be further described in detail below with reference to the accompanying drawings of the specification, so that those skilled in the art can implement the application according to the description.

[0070] As Figure 1 shown, the lithium battery parameter identification method based on the speed pause particle swarm algorithm provided by the application comprises the following steps:

[0071] Step one, collect the working condition current data I T (k) of the lithium battery according to the sampling time interval, the open circuit voltage data U meas (k) and the terminal voltage data U ocv (k) of the lithium battery, specifically comprising the following steps:

[0072] Step 1, place the lithium battery on a charge-discharge platform for experiment, and the environmental temperature is constant at 25℃;

[0073] Step 2, perform constant current pulse discharge on the battery;

[0074] Wherein, after each discharge, the lithium battery is placed for 4 hours to eliminate the polarization effect of the battery;

[0075] Step 3, repeat step 2 until the terminal voltage of the lithium battery drops to the discharge cutoff voltage, at which time the lithium battery is discharged and the experiment is completed.

[0076] Step two, construct a second-order fractional-order equivalent circuit model of the lithium battery to determine the parameter vector to be identified;

[0077] As Figure 2 shown, the second-order fractional-order equivalent circuit model of the lithium battery comprises an ideal open circuit voltage source U oc , an ohmic internal resistance R0, a first polarization branch and a second polarization branch, the first polarization branch is composed of a first constant phase element CPE1 and a first polarization resistance R1 in parallel, and the second polarization branch is composed of a second constant phase element CPE2 and a second polarization resistance R2 in parallel;

[0078] Wherein, the impedance of the first constant phase element CPE1 is represented as:

[0079] Z CPE1 (jw)=1 / [C CPE1 (jw)] n ;

[0080] In the formula, n is a fractional order of the first constant phase element CPE1, n∈R, 0≤n≤1, and when n=1, C CPE1 is a capacitance value of the first constant phase element CPE1;

[0081] The impedance of the second constant phase element CPE2 is represented as:

[0082] Z CPE2 (jw)=1 / [C CPE2 (jw)] m ;

[0083] In the formula, m is a fractional order of the second constant phase element CPE2, m∈R, 0≤m≤1, and when m=1, C CPE2 is a capacitance value of the second constant phase element CPE2;

[0084] The to-be-identified parameters are R0, R1, R2, C CPE1 , C CPE2 , n, and m;

[0085] The observation equation of the lithium battery second-order fractional order equivalent circuit model is:

[0086] U est (k)=U ocv (k)+I T (k)R0+U1(k)+U2(k);

[0087] In the formula, U est (k) is an end voltage estimation value at a sampling time k, U ocv (k) is an open circuit voltage at the sampling time k, I T (k) is a current at the sampling time k, R0 is an ohmic internal resistance of the lithium battery second-order fractional order equivalent circuit model, U1(k) is a first polarization branch voltage at the sampling time k, and U2(k) is a second polarization branch voltage at the sampling time k;

[0088] The state space equation of the lithium battery second-order fractional order equivalent circuit model is represented as:

[0089]

[0090] In the formula, x=[U1,U2] T is a state vector, y=[U T -U OC ] is an observation output vector, a=[n,m] T is a fractional order differential operator order vector, A is a first intermediate parameter, B is a second intermediate parameter, C is a third intermediate parameter, and D is a fourth intermediate parameter, and the following conditions are satisfied:

[0091]

[0092] C = [-1 -1];

[0093] D = [-R0];

[0094] Step three, constructing the VPPSO equivalent circuit model parameter identification algorithm, specifically comprising:

[0095] Step a, initializing the particle swarm:

[0096] Set the population size N, and divide the particle swarm into a first sub-population N1 and a second sub-population N2, both of which have a size of N / 2, and set parameters, including: maximum number of iterations, local acceleration coefficient, global acceleration coefficient, velocity pause parameter, and inertia weight;

[0097] Initialize the particle positions and velocities in the first sub-population and the second sub-population:

[0098] Position initialization:

[0099] X i,j (0) = lb j + rand × (ub j -lb j );

[0100] In the formula, X i,j (0 is the initial position vector of the i-th particle in the j-th dimension, X i = [R0, R1, R2, C CPE1 , C CPE2 , n, m] T , the components of the position vector in each dimension are randomly initialized within the parameter search space, and the dimensions j correspond to: j = 1 → R0, j = 2 → R1, j = 3 → R2, …, j = 7 → m, lb j is the lower bound vector of the parameter in the j-th dimensional search space, and ub j is the upper bound vector of the parameter in the j-th dimensional search space, thereby ensuring that the particle parameters are generated within a physically reasonable range.

[0101] Velocity initialization:

[0102] Let the parameter dimension be j, then for the j-th dimensional velocity initialization, we have:

[0103] V i,j (0) = -d j + 2 × r i,j × d j ;

[0104] In the formula, V i,j (0) is the initial velocity of the i-th particle in the j-th dimension, d j is the intermediate parameter with respect to the j-th dimension, and d j= |ub j - lb j |, r i,j is a random number uniformly distributed on the interval [0, 1];

[0105] Thus, the initial velocity of each particle: V i (0) = [v i,1 (0), v i,2 (0), …, v i,2 (0)] is generated uniformly at random within the velocity clipping interval of its corresponding dimension.

[0106] For each parameter dimension j = 1, 2, …, D, the upper limit of the velocity of the j-th dimension parameter satisfies:

[0107]

[0108] wherein, is the upper limit of the velocity of the j-th dimension parameter, and 0.25 is a constraint factor, which ensures that the single-step displacement of the particle does not exceed 25% of the parameter range;

[0109] Step b, calculate the fitness value of each particle:

[0110] The root mean square error (RMSE) is used as the fitness evaluation function, and its mathematical expression is defined as:

[0111]

[0112] wherein, f(·) is the fitness function, K is the number of sampling points, U meas (k) represents the measured voltage value at sampling time k, U est (k | X i ) represents the voltage estimation value at sampling time k calculated using the position vector X i ;

[0113] Step c, iterative update optimization of the particle swarm:

[0114] 1) The particles in the first sub-swarm perform velocity update and position update with a pause mechanism:

[0115] A velocity pause mechanism is introduced for each particle i:

[0116] If rand < a, then V i,j (t+1) = V i,j (t);

[0117] If rand ≥ a, then:

[0118] V i,j (t+1) = ω·V i,j (t) + C p• r1 · (Pbest i,j (t) - X i,j (t) + C g • r2 · (Gbest j (t) - X i,j (t) + C

[0119] wherein, is a random number, indicating the randomness factor in the algorithm; V i,j (t+1) is the updated velocity of the i-th particle in the j-th dimension at the t+1-th iteration, ω is the inertia weight, V i,j (t) is the velocity of the i-th particle in the j-th dimension at the t-th iteration, C p is the local acceleration coefficient, r1 and r2 are two random numbers between the interval [0, 1], which are used to increase the randomness of the algorithm so that the particles will not move completely in a fixed direction, Pbest i,j (t) is the individual optimal position of the i-th particle in the j-th dimension at the t-th iteration, X i,j (t) is the current position of the i-th particle in the j-th dimension at the t-th iteration, C g is the global acceleration coefficient, Gbest j (t) is the global optimal position of all particles in the j-th dimension at the t-th iteration, t is the iteration number, and t = 1, 2, …, T, α is a probability parameter (i.e., velocity suspension parameter) that controls whether the particle suspends the velocity update, the value of α is between 0 and 1, α = 1 indicates that the particle will not suspend the velocity update, and VPPSO degenerates into PSO; α = 0 indicates that the particle always maintains the same velocity and does not update the velocity, this updating mechanism enables the particle to continue to explore along the current velocity direction in some iterations, rather than adjusting the velocity according to the individual and global optimum every time, thereby significantly enhancing the exploration ability.

[0120] After the velocity update of the particle swarm N1, its position is updated by the current velocity vector:

[0121] X i,j (t+1) = X i,j (t) + V i,j (t+1) + C

[0122] wherein, X i,j (t+1) is the position of the i-th particle in the j-th dimension after the t+1-th iteration;

[0123] 2) The particles in the second sub-swarm are not updated in position based on the velocity update vector, but are updated in position based on the global optimal position attenuation disturbance:

[0124] X i,j (t+1) = Gbest j(t) ± β(t) · rand · |Gbest j (t) · |Gbest

[0125] where β(t) is a decreasing function to control the second sub-population particles gradually approaching the global optimal position, and satisfies:

[0126]

[0127] This position updating method makes particles more concentrated in the neighborhood of the global optimal position for detailed development, rather than being limited by the individual optimal, so that VPPSO ensures that some particles can be widely explored, and some particles can be deeply developed, which fundamentally improves the defect of PSO easily falling into local optimal solution.

[0128] Step d, updating individual optimal and global optimal:

[0129] In the VPPSO parameter identification algorithm, each particle will track and record its own historical optimal position found in the iteration process. The update of the individual optimal position (Pbesti) is based on the following rules: if the fitness value of the current position of the particle is better than that of its individual historical optimal position, update the individual optimal position as the current position; otherwise, keep the original individual optimal position unchanged. This rule can be formally expressed as:

[0130]

[0131] where Pbest i,j (t+1) is the individual historical optimal position of the i-th particle after the end of the t+1 iteration;

[0132] The set of all particle individual optimal positions of the entire population at iteration time t+1 is:

[0133] {Pbest 1,1 (t+1),…,Pbest 1,D (t+1);…;Pbest N,1 (t+1),…,Pbest N,D (t+1)};

[0134] The algorithm will update the global optimal position (Gbest) after each iteration, and the global optimal position represents the best solution found by all particles in the entire population in historical search. Its update rule is: from the set of individual optimal positions of all particles at present, select the position with the optimal fitness value (i.e. the minimum RMSE value) as the global optimal position of the new generation, and the rule update expression is:

[0135]

[0136]

[0137] where Gbest j (t+1) is the jth parameter component of the global optimal position vector after the end of the t+1th iteration, is the jth parameter component of the individual optimal position vector of the particle (whose index is i * ) that makes the value of the fitness function f minimum, denotes the jth parameter component of the individual optimal position Pbest i (t+1), i = 1, 2, …, N, from which the index i of the particle that makes the value of the fitness function f minimum is found, * and each parameter component of the global optimal position is assigned the corresponding component of the optimal particle:

[0138]

[0139] Step e, termination condition judgment:

[0140] A double termination condition judgment is adopted:

[0141] When the iteration number t reaches the preset maximum value T or when the absolute value of the fitness function value f(Gbest(t)) of the global optimal solution is less than 0.005V, i.e., t≥T or |f(Gbest(t))|<5×10 -3 V, the iteration is terminated.

[0142] Step four, input the current data I T (k), the terminal voltage data U meas (k), the open-circuit voltage data U ocv (k), and the to-be-identified parameter vector VPPSO into the equivalent circuit model parameter identification algorithm to obtain the identified parameter vector, the minimum fitness value, the terminal voltage prediction sequence, and the convergence fitness sequence;

[0143] Set the boundary constraint condition of the to-be-identified parameter vector:

[0144] R0, R1, R2 ∈ [0.001, 0.1] Ω;

[0145] C CPE1 ,C CPE2 ∈ [500, 50000] F;

[0146] n, m ∈ [0, 1];

[0147] In actual applications, the values of n and m in the range of 0-0.1 are not reasonable to understand, so according to the actual situation, n, m ∈ [0.1, 1].

[0148] The model polarization branch voltage is calculated according to the observation equation and the state space equation of the lithium battery second-order fractional-order equivalent current model in step two:

[0149]

[0150] In the formula, U1(k) is the first polarization branch voltage at the sampling time k, T s n is the first branch fractional-order discretization coefficient, U1(k-1) is the first polarization branch voltage at the sampling time k-1, I T (k) is the current at the sampling time k, U2(k) is the second polarization branch voltage at the sampling time k, U2(k-1) is the second polarization branch voltage at the sampling time k-1, T s m is the second branch fractional-order discretization coefficient.

[0151] The terminal voltage estimation (combined with the open-circuit voltage U ocv The terminal voltage estimation value is calculated in real time):

[0152] U est (k)=U ocv (k)+I T (k)R0+U1(k)+U2(k);

[0153] The terminal voltage prediction sequence is obtained:

[0154] The identification parameter vector is the globally optimal parameter vector: The minimum fitness value is f(Gbest), and the convergence fitness sequence is:

[0155] In order to verify the effect of the application, a working condition simulation experiment is carried out, the lithium ion battery used in the simulation is a South Korean Samsung INR18650-25R power lithium battery, and the test working condition is HPPC working condition and FTP75 working condition.

[0156] The nominal capacity of the South Korean Samsung INR18650-25R power lithium battery is 2.5 Ah, the discharge current is 3 A per single, the duration of each constant current pulse discharge is 5 minutes, each discharge is 10% of the capacity, and after each discharge, the lithium battery is rested for 4 hours to eliminate the polarization effect of the battery.

[0157] The first-order, second-order, third-order and second-order fractional-order equivalent circuit model parameter identification of the lithium battery for HPPC and FTP75 working conditions is carried out by using the VPPSO algorithm and the PSO algorithm respectively, the iteration number and the RMSE are used as the fitness value to draw the convergence curve, and the performance of the identification algorithm in terms of accuracy and convergence performance is measured.

[0158] In the simulation experiment, the sampling time interval in the VPPSO algorithm is 1s, the population size is set to 100 particles to balance the search efficiency and the calculation complexity, the maximum iteration number T is 600 to balance the calculation complexity while meeting the identification accuracy, the local acceleration coefficient C p = 1.5, the global acceleration coefficient C g = 1.5 cooperates to guide the particle search direction, the velocity pause parameter a is 0.3 to balance the exploration and development of the particle group, and the inertia weight w is 0.5 to maintain the inertia of the particle motion.

[0159] The VPPSO algorithm identifies the HPPC working condition result as shown in Figures 3-5 The PSO algorithm identifies the HPPC working condition result as shown in Figures 6-8 The VPPSO algorithm identifies the FTP75 working condition result as shown in Figures 9-11 The PSO algorithm identifies the FTP75 working condition result as shown in Figures 12-14 The identification error of different algorithms and different model parameters under two working conditions is shown in Table 1.

[0160] As shown in Figures 3-8 Experiments show that the VPPSO algorithm is significantly better than the PSO in the HPPC working condition parameter identification, in terms of terminal voltage error, both algorithms show significant error pulses at the dynamic working condition switching point, and the VPPSO algorithm suppresses the pulse error to a certain extent, and the error curve shows a decay characteristic, which is more accurate than the periodic oscillation mode of the PSO algorithm, and the model accuracy (RMSE) is improved by more than 60%. The convergence curve shows that the fitness curve of the PSO algorithm appears obvious platform period in the middle of iteration, which further reveals the defect that the particle group is easy to fall into local optimum; and the VPPSO algorithm realizes the continuous monotone decreasing convergence trajectory by means of the population diversity maintenance strategy, which verifies the breakthrough of its global optimization ability.

[0161] As shown in Figures 9-14 In the FTP75 dynamic working condition parameter identification with more complex dynamic characteristics, the VPPSO algorithm shows more significant accuracy advantage than the PSO algorithm, and the terminal voltage estimation error of each model is improved by more than 68%, the error timing analysis shows that the VPPSO algorithm keeps narrow convergence in the error band in the high frequency fluctuation stage of the working condition, while the error amplitude of the PSO algorithm diffuses with the dynamic process, and the deviation accumulates obviously, and the difference is due to the better premature convergence suppression characteristic of the VPPSO algorithm in the high-dimensional parameter space, so as to avoid the optimization stagnation caused by local extreme oscillation, and in terms of convergence characteristics, similar to the HPPC working condition experiment, the VPPSO algorithm still maintains the continuous monotone convergence characteristic in the FTP75 working condition, and the convergence performance is significantly better than that of the PSO algorithm.

[0162] Table 1 Identification error of different algorithms and different model parameters under two working conditions

[0163]

[0164] The results in Table 1 show that, compared with the PSO algorithm, the VPPSO algorithm has a significant advantage in precision in identifying models of each order under two working conditions. Meanwhile, different models under dynamic conditions show a significant trade-off between precision and efficiency: high-order models have high precision but slow convergence, low-order models are the opposite, and the second-order fractional-order model can better represent the nonlinear characteristics of lithium batteries by introducing a fractional-order differential operator, achieving faster convergence speed with the precision of three orders, and showing unique advantages in precision-efficiency balance, verifying its adaptability to complex dynamic characteristics.

[0165] The lithium battery parameter identification method based on the speed pause particle swarm optimization algorithm is designed and developed, the speed pause updating mechanism and the double population strategy are introduced, the speed pause updating mechanism can make part of the particles have the probability to pause the speed update of the particles, thereby enhancing the diversity of the particle population, avoiding falling into the local optimal solution, and improving the global search ability, and the double population strategy balances the global optimization and local optimization ability of the particle swarm through the cooperative work of the global population and the local population, improves the search efficiency and precision of the optimization process, the combination of the two can effectively avoid the premature convergence problem caused by the reduction of population diversity and the insufficient global search ability, and improve the precision and convergence speed of the lithium battery equivalent circuit model parameter identification.

[0166] Although the embodiments of the present application have been disclosed as above, it is not limited to the application listed in the specification and the embodiments, and can be fully applied to various fields suitable for the present application, and other modifications can be easily realized by those skilled in the art, therefore, the present application is not limited to specific details and the examples shown and described herein, without departing from the general concept defined by the claims and the equivalent scope.

Claims

1. A method for identifying lithium battery parameters based on velocity-pause particle swarm optimization, characterized in that, Includes the following steps: Step 1: Collect the current data, terminal voltage data, and open-circuit voltage data of the lithium battery according to the sampling time interval; Step 2: Construct a second-order fractional-order equivalent circuit model of the lithium battery and determine the parameter vector to be identified; Step 3: Construct a parameter identification algorithm for the VPPSO equivalent circuit model; Step 4: Input the current data, terminal voltage data, open-circuit voltage data of the lithium battery and the parameter vector to be identified into the parameter identification algorithm of the VPPSO equivalent circuit model to obtain the identification parameter vector, minimum fitness value, terminal voltage prediction sequence and convergence fitness sequence.

2. The lithium battery parameter identification method based on velocity-pause particle swarm optimization algorithm as described in claim 1, characterized in that, Step one specifically includes: Step 1: Place the lithium battery on a charging and discharging platform for testing, with the ambient temperature kept constant at 25°C; Step 2: Perform constant current pulse discharge on the battery; Step 3: Repeat step 2 until the terminal voltage of the lithium battery drops to the discharge cutoff voltage.

3. The lithium battery parameter identification method based on velocity-pause particle swarm optimization algorithm as described in claim 2, characterized in that, The second-order fractional equivalent circuit model of the lithium battery includes an ideal open-circuit voltage source, an ohmic internal resistance, a first polarization branch, and a second polarization branch. The first polarization branch is formed by a first constant-phase element CPE1 connected in parallel with a first polarization resistor R1, and the second polarization branch is formed by a second constant-phase element CPE2 connected in parallel with a second polarization resistor R2.

4. The lithium battery parameter identification method based on velocity-pause particle swarm optimization algorithm as described in claim 3, characterized in that, The parameter vector to be identified includes: Ohmic internal resistance of a second-order fractional equivalent circuit model of a lithium battery. The first polarization resistor of the first polarization branch in the second-order fractional equivalent circuit model of a lithium battery; The second polarization resistance of the second polarization branch in the second-order fractional-order equivalent circuit model of a lithium battery; The capacitance value of the first constant-phase element in the second-order fractional-order equivalent circuit model of a lithium battery; The capacitance value of the second constant-phase element in the second-order fractional-order equivalent circuit model of a lithium battery; The fractional order of the first constant-phase element in the second-order fractional-order equivalent circuit model of a lithium battery; The fractional order of the second constant-phase element in the second-order fractional-order equivalent circuit model of a lithium battery.

5. The lithium battery parameter identification method based on velocity-pause particle swarm optimization algorithm as described in claim 4, characterized in that, The VPPSO equivalent circuit model parameter identification algorithm includes: Step a: Initialize the particle swarm; The particle swarm is divided into a first subgroup and a second subgroup. Step b: Calculate the fitness value for each particle; Step c: Particle swarm optimization through iterative updates; The first subgroup performs speed and position updates with a pause mechanism. The second subgroup performs position updates based on the globally optimal position decay perturbation; Step d: Update the individual optimal and global optimal; Step e, when t≥T or |f(Gbest(t))|<5×10 -3 V, iteration terminates; Where t is the current iteration number, T is the maximum iteration number, Gbest(t) is the global optimal position after the t-th iteration, and f(·) is the fitness value.

6. The lithium battery parameter identification method based on velocity-pause particle swarm optimization algorithm as described in claim 5, characterized in that, The fitness value satisfies: In the formula, f(·) is the fitness function, K is the number of sampling points, and U meas (k) represents the measured voltage value at sampling time k, U est (k∣X i ) indicates the use of position vector X i The voltage estimate at sampling time k is calculated.

7. The lithium battery parameter identification method based on velocity-pause particle swarm optimization algorithm as described in claim 6, characterized in that, The speed update of the first subgroup satisfies: If rand < α, then V i,j (t+1)=V i,j (t); If rand ≥ α, then V i,j (t+1)=ω·V i,j (t)+C p ·r1·(Pbest i,j (t)-X i,j (t))+C g ·r2·(Gbest j (t)-X i,j (t)); In the formula, V is a random number. i,j (t+1) represents the velocity of the i-th particle in the j-th dimension after the (t+1)-th iteration, ω is the inertia weight, and V i,j (t) represents the velocity of the i-th particle in the j-th dimension at the t-th iteration, C p R1 and R2 are local acceleration coefficients, and R2 are two random numbers in the interval [0,1]. Pbest i,j (t) represents the optimal position of the i-th particle in the j-th dimension at the t-th iteration, X i,j (t) represents the current position of the i-th particle in the j-th dimension at the t-th iteration, C g This is the global speedup factor, Gbest j (t) represents the global optimal position of all particles in the j-th dimension at the t-th iteration, and α is the velocity pause parameter, α∈[0,1]. When α=1, the particles will not pause velocity updates, and when α=0, the particles always maintain the same velocity and do not perform velocity updates.

8. The lithium battery parameter identification method based on velocity-pause particle swarm optimization algorithm as described in claim 7, characterized in that, The position update of the second subgroup satisfies: X i,j (t+1)=Gbest j (t)±β(t)·rand·|Gbest j (t)|; In the formula, β(t) is a decreasing function.

9. The lithium battery parameter identification method based on velocity-pause particle swarm optimization algorithm as described in claim 8, characterized in that, The terminal voltage prediction sequence satisfies: U est (k)=U ocv (k)+I T (k)R0+U1(k)+U2(k); In the formula, U est (k) is the estimated terminal voltage at sampling time k, U ocv (k) is the open-circuit voltage at sampling time k, I T (k) represents the current at sampling time k, R0 represents the ohmic internal resistance of the second-order fractional equivalent circuit model of the lithium battery, U1(k) represents the voltage of the first polarization branch at sampling time k, and U2(k) represents the voltage of the second polarization branch at sampling time k.

10. The lithium battery parameter identification method based on velocity-pause particle swarm optimization algorithm as described in claim 9, characterized in that, The voltage of the first polarization branch satisfies: In the formula, U1(k) is the voltage of the first polarization branch at sampling time k. U1(k-1) represents the fractional-order discretization coefficient of the first branch, and U1(k-1) represents the voltage of the first polarized branch at sampling time k-1.

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