A lithium battery balancing index optimization method based on NSGA-2 genetic algorithm

Abstract

This invention discloses a lithium battery balancing index optimization method based on the NSGA-2 genetic algorithm. The method first determines the objective function for optimizing the lithium battery balancing index. Then, empirical data on system operation under NEDC operating conditions is collected based on the range of the balancing threshold. This data is then fitted to obtain the relationship between the balancing threshold and the balancing index. The NSGA-2 genetic algorithm is then used to optimize the objective function and obtain a Pareto solution set. A multi-objective decision-making strategy is then designed to find the optimal solution within the Pareto solution set. This method addresses the problem of relying on manual experience to set the balancing system threshold and focusing on only one balancing objective, thereby obtaining the optimal threshold for the balancing system.

Description

Technical Field

[0001] The present invention relates to the technical field of lithium-ion battery applications, and in particular to a lithium battery balancing index optimization method based on the NSGA-2 genetic algorithm. Background Art

[0002] Lithium-ion batteries (referred to as lithium batteries) are widely used in various energy storage fields due to their advantages such as high energy density, low self-discharge rate, and zero memory. Since the voltage of lithium battery cells is generally between 2 and 4.2V, in order to meet the power supply requirements of high voltage and high current loads, hundreds or even thousands of cells need to be connected in series and parallel. However, factors such as raw materials, processes, and assembly in the manufacturing process of battery cells can lead to inconsistencies in internal characteristics such as internal resistance, capacity, and self-discharge rate; external factors such as ambient temperature, charge and discharge current, and depth of discharge during battery use will aggravate the inconsistency of battery packs. Therefore, inconsistency is inevitable after the batteries are grouped, and balancing technology is needed to detect the operating status of the cells in the battery pack and improve the differences between batteries.

[0003] The first step in designing a balancing system is to determine the balancing topology. Common balancing topologies fall into three categories: passive balancing, active balancing, and reconfigurable balancing. A key step in a balancing system is determining whether the battery pack currently requires balancing. Therefore, the balancing system must select balancing metrics and set corresponding thresholds to assess the current consistency of the battery pack. Common balancing metrics include voltage, state of charge (SOC), and capacity. To evaluate the balancing performance of the balancing system, corresponding metrics (balancing targets) should be set to assess the desired state of the system after balancing, such as battery pack voltage consistency, SOC consistency, and system balancing speed. Depending on the balancing topology selected, the system also considers other balancing targets. For example, active balancing topologies set multiple targets, such as the number of energy storage elements, the number of switches, and balancing cost. However, there are two problems in the current research on the threshold of the balancing system. First, the balancing threshold is set by manual experience and lacks a theoretical basis. This will lead to the balancing threshold selected by this method not necessarily achieving the optimal system goal, that is, the optimal threshold may not be obtained. On the other hand, most existing studies only focus on a single balancing goal, but the actual operating conditions of lithium batteries are complex and changeable, and systematic optimization of multiple goals is more in line with actual needs.

[0004] Non-dominated Sorting Genetic Algorithm-II (NSGA-2) is widely used in solving multi-objective problems because of its advantages such as unrestricted search range, ability to dynamically optimize multiple objectives and ensuring a balanced distribution of non-inferior optimal solutions. Summary of the Invention

[0005] To address the above issues, the present invention aims to provide a lithium battery balancing index optimization method based on the NSGA-2 genetic algorithm. This method uses the NSGA-2 genetic algorithm to obtain the Pareto solution set for optimizing lithium battery balancing indicators, and then formulates a corresponding target decision strategy to obtain the optimal threshold that takes into account multiple balancing objectives. This solves the problem of balancing system thresholds relying on manual experience and focusing on only one balancing objective. The technical solution is as follows:

[0006] A lithium battery balancing index optimization method based on NSGA-2 genetic algorithm includes the following steps:

[0007] Step 1: Determine the objective function for optimizing the lithium battery balancing index:

[0008]

[0009] Where, Δ V is the equilibrium threshold, N sw is the number of power electronic switch operations, T eq is the equilibrium speed, σ SOC Characterizes the consistency of the battery pack SOC after balancing, represented by the average value of the battery pack SOC standard deviation, σ SOC_max is the battery pack σ SOC The maximum value of

[0010] Step 2: According to the equalization threshold Δ V The value range of the system is to collect the empirical data of the system operation under NEDC conditions, perform data fitting on the collected empirical data, and solve the equilibrium threshold Δ V The relationship between it and the equilibrium indicator;

[0011] Step 3: Use the NSGA-2 genetic algorithm and the equilibrium threshold Δ V Calculate the data of each point based on the relationship between the equilibrium index, optimize the objective function, and obtain the Pareto solution set;

[0012] Step 4: Design a multi-objective decision-making strategy to find the optimal solution in the Pareto solution set.

[0013] Furthermore, the equalization threshold Δ in step 2 V The value range of is:

[0014] The minimum value of the equalization threshold is determined by the following formula:

[0015]

[0016] Where n is the number of battery cells in the battery pack, n1 is the voltage distribution in V c The number of battery cells, n2 is the voltage distribution in Vc +D_V battery cell number, V c is an assumed value, D_V is the ideal accuracy of the battery management system; Cell_V i Indicates the voltage of a battery cell. is the average value of the voltage of each battery cell;

[0017] When n2=n / 2, the minimum value of the equalization threshold is obtained

[0018] The maximum value of the equalization threshold is the difference in battery pack voltage at the initial moment Δ V_初始状态 ;

[0019] Equalization threshold Δ V The value range of is:

[0020]

[0021] Furthermore, in step 2, the data fitting uses cubic spline interpolation to obtain unknown data within the interval based on the obtained finite data.

[0022] Furthermore, the step 4 specifically includes:

[0023] Step 4.1: Normalization

[0024] The data of the three targets are respectively analyzed based on the standard that the minimum value of each target in the Pareto solution set is 10 points: the number of power electronic switch operations N sw , equilibrium speed T eq , the average value of the battery pack SOC standard deviation σ SOC Perform normalization to obtain the normalized scores of each solution under the three objectives. The calculation formula is as follows:

[0025]

[0026] Where Score_f(i) represents the normalized score of the i-th solution in target f, f_min is the minimum value of target f, and f(i) is the value of the i-th solution of target f;

[0027] Step 4.2: Weighting

[0028] The scores obtained by normalization are added with their respective weight coefficients to obtain the weighted total score of each solution; the calculation formula is as follows:

[0029]

[0030] Among them, Score i is the weighted total score of the i-th solution, ω jis the weight coefficient corresponding to the j-th target, j = 1, 2, ..., 3;

[0031] Step 4.3: Select the solution with the highest weighted total score as the optimal solution of the optimization algorithm.

[0032] The beneficial effects of the present invention are as follows: the present invention obtains the Pareto solution set through the NSGA-2 genetic algorithm and formulates a corresponding target decision strategy, thereby obtaining the optimal threshold that takes into account multiple equilibrium objectives, solving the problem that the threshold of the equilibrium system relies on manual experience to set and only focuses on one equilibrium objective, and obtaining the optimal threshold of the equilibrium system. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a reconfigurable two-switch balanced topology.

[0034] Figure 2(a) shows Δ V With N sw The fitting results of the relationship.

[0035] Figure 2(b) shows Δ V With T eq The fitting results of the relationship.

[0036] Figure 2(c) shows Δ V and σ SOC The fitting results of the relationship.

[0037] Figure 3 This is the flow chart of the NSGA-2 algorithm.

[0038] Figure 4(a) shows the optimization result: Pareto optimal solution set.

[0039] Figure 4(b) shows the optimization results: Δ V =0.0232 and Δ V =0.01Comparison of equilibrium results. DETAILED DESCRIPTION

[0040] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0041] In order to solve the problem that the threshold of the balancing system relies on manual experience and only focuses on one balancing target, the present invention optimizes the threshold of the lithium battery balancing system using the NSGA-2 algorithm.

[0042] In one embodiment of the present invention, for a reconfigurable two-switch balancing system (such as Figure 1 As shown), with Δ V As the balancing threshold, the number of times the power electronic switch operates N sw , equilibrium speed T eq And the consistency of SOC after battery pack balancing σ SOCThe minimum threshold of the balanced system is optimized as the balanced target.

[0043] The experiment sets the battery pack to operate under the New European Driving Cycle (NEDC) conditions, and the initial SOC of each cell is set to [SOC1, SOC2, SOC3, SOC4, SOC5, SOC6] = [95%, 96%, 92%, 90%, 85%, 85%].

[0044] The key steps of the optimization method of this embodiment include: determining the objective function for optimizing the lithium battery balancing index, solving the relationship between the balancing threshold and the balancing index under NEDC conditions, optimizing the objective function using the NSGA-2 algorithm, and designing a multi-objective decision-making strategy to obtain the optimal threshold.

[0045] The following will introduce each key link of the present invention one by one in the form of embodiments.

[0046] Step 1: Determine the objective function for optimizing the lithium battery balancing index.

[0047] During the balancing process, when the maximum SOC (SOC max ) and minimum SOC(SOC min ) First time meeting |SOC max -SOC min |<Δ SOC (This paper takes Δ SOC =0.05) when the time required is T eq It is the response time of the balancing system, that is, the balancing speed. The shorter the response time, the faster the balancing speed of the system, which is more beneficial to the operation of the battery pack.

[0048] Switching times N sw This is the number of times the high-frequency power electronic switch needs to operate during the balancing process of the system. If the value of this indicator is too large, it will not only affect the stability of the system but also increase additional energy loss. Therefore, the value of this indicator should be as small as possible.

[0049] In a single charge and discharge cycle, if the battery pack continuously and stably meets the SOC max -SOC min |<Δ SOC , then the average value of the battery pack SOC standard deviation during this period is σ SOC The smaller the index is, the better the consistency of the battery pack is. The maximum value should not exceed σ SOC_max .

[0050] Therefore, the objective function of the two-switch reconfigurable balanced topology is as follows:

[0051]

[0052] Among them, σ SOC_max Generally, 0.02 can be taken.

[0053] Step 2: Solve the relationship between the balance threshold and the balance index under NEDC conditions.

[0054] Step 2.1: Determine Δ V The value range of

[0055] Since the cell voltage is measured, the accuracy of the battery management system is generally 5mV, which is a very ideal state. Therefore, within the hardware allowable range, the ideal battery pack voltage consistency is when the voltage of all cells (V c ) are distributed in the range [V c ,V c +5mV]. Select the voltage distribution of the n1 block monomer to be between V c , n2 block single voltage distribution V c +5mV is analyzed as a special distribution of monomer voltage. According to formula (2), when n2=n / 2, the minimum value can be obtained. Δ V The maximum value is to hope that the voltage difference of the battery pack after the balancing operation is at least not greater than the difference of the battery pack voltage at the initial moment (Δ V_初始状态 ), that is, Δ V_max =Δ V_初始状态 .

[0056]

[0057] Where n represents the number of cells in the battery pack, Cell_V i Indicates the voltage of a battery cell, D_V = 5mV.

[0058] In summary, the threshold value range is:

[0059]

[0060] Step 2.2: Collect empirical data: Select as much data as possible within the determined threshold range and input the actual operating conditions of the system to obtain the actual value of the equilibrium target at different thresholds.

[0061] Step 2.3: Data Fitting: Using interpolation, we can determine the unknown data within the interval based on the limited data we have. For this article, we used cubic spline interpolation to fit the data we collected. Based on the collected empirical data and the interpolation method, we can derive the relationship between the threshold and the balance indicator.

[0062] According to formula (3) and the initial SOC of the battery pack, 0.0027≤Δ V ≤0.1. After determining the initial range of the threshold, we can collect empirical data on system operation under NEDC conditions based on the range. Then, based on the empirical data and the constraints in formula (1), we can further obtain 0.0027≤Δ V ≤0.0293, and then use MATLAB to fit the range of Δ V With N sw 、T eq , σ SOC The relationship formulas are as follows Figure 2(a)-Figure 2(c) shown.

[0063] The relationship between the equilibrium threshold and the equilibrium index is not a specific expression, but is obtained through interpolation, that is, Figure 2(a)-(c).

[0064] Step 3: Use the NSGA-2 algorithm to optimize the objective function.

[0065] Using the NSGA-2 genetic algorithm, the equilibrium threshold Δ V The relationship between the equilibrium index and the data of each point is calculated, the objective function is optimized, and the Pareto solution set is obtained.

[0066] The flowchart of the NSGA-2 algorithm is as follows Figure 3 As shown, the population POP is initialized, followed by non-dominated sorting and crowding calculation to obtain the evolutionary generation number Gen = 1. The population is then subjected to selection, crossover, and mutation to generate the offspring population POP_n. The parent population POP is then merged with the offspring population POP_n, followed by non-dominated sorting and crowding calculation. An elitist strategy is used to retain outstanding individuals to generate a new parent population POP. Finally, a check is performed to determine whether the genetic generation number meets the set value. If not, the selection, crossover, and mutation operations are repeated. If so, evolution is complete. The selection, crossover, and mutation method in the NSGA-2 algorithm is similar to that of traditional genetic algorithms. Its uniqueness lies in the introduction of a non-dominated sorting method to reduce the algorithm's computational complexity, the use of crowding to ensure individual diversity in the population, and the use of an elitist strategy to ensure that outstanding individuals are retained with a greater probability.

[0067] The population POP can be stratified by the non-dominated sorting method. First, the individual Δ Vi Each objective function value (ie, the number of power electronic switch actions N sw , equilibrium speed T eq And the consistency of SOC after battery pack balancing σ SOC ) is less than individual Δ VjEach objective function value of (i≠j) determines the dominance and domination of each individual, and obtains the dominated individual Δ Vi The set of dominated individuals S i and the dominant individual Δ Vi The individual set Wi; then determine the dominant individual Δ Vi Is the number of individuals Num_Wi 0? If it is 0, the Pareto level of the individual is 1. Finally, the individual Δ Vi Repeat the above steps after subtracting 1 from the number of dominated sets Wj. After completing the above operations, the Pareto level can be obtained.

[0068] To estimate the crowding of solutions around a specific solution in the population, the NSGA-2 algorithm calculates the average distance between the two points on either side of each objective function. The algorithm essentially sorts individuals within each Pareto level based on the size of each objective value, with individuals at the boundary having a crowding degree of ∞.

[0069] The elite retention strategy is to merge the offspring population and the parent population and retain the excellent individuals with higher Pareto levels and crowding to obtain a new generation of population.

[0070] The present invention uses Δ V is the equilibrium threshold, N sw 、T eq , σ SOC The NSGA-2 genetic algorithm is used to optimize the equilibrium system under NEDC conditions, with the minimum as the equilibrium objective. The algorithm population size is set to 1000 and the genetic scale is set to 200. The Pareto set results are shown in Figure 4(a).

[0071] Step 4: Design a multi-objective decision-making strategy to obtain the optimal threshold.

[0072] Using the NSGA-2 optimization algorithm yields a set of optimal Pareto solutions. However, none of the solutions in the set can simultaneously minimize the three objective functions. An optimal solution is one where no solution outside the set is completely superior to the solutions in the set. Therefore, after obtaining a Pareto optimal solution, a set of relatively optimal solutions should be determined based on application requirements. The target decision-making strategy of this invention is generally based on normalization and weighting.

[0073] Step 4.1: Normalization: Normalize the data of the three targets separately, taking the minimum value of each target in the solution set as 10 points, and obtain the normalized scores of each solution under the three targets. The calculation formula is as follows:

[0074]

[0075] Where Score_f(i) represents the normalized score of the i-th solution in target f, f_min is the minimum value of target f, and f(i) is the value of the i-th solution of target f.

[0076] Step 4.2: Weighted processing: Because the balancing system has different requirements for each balancing target in different application scenarios, for example, for large-scale energy storage systems, the system is expected to be as stable as possible (that is, the number of switching times is as small as possible), but the charging and discharging time of the energy storage system is relatively long, so the balancing speed is less critical than stability. For the consistency data in the solution set, the span is very small and the difference is not large, so the importance of consistency is slightly less than the number of switching times and balancing speed. Therefore, the scores obtained by normalization should also be added with their respective weight coefficients, and finally the weighted total score of each solution is obtained. The calculation formula is as follows:

[0077]

[0078] Among them, Score i is the weighted total score of the i-th solution, ω j (j=1,2,…,N) is the weight coefficient corresponding to each target.

[0079] Step 4.3: Select the solution with the highest weighted total score as the optimal solution of this optimization algorithm.

[0080] In this embodiment, according to formulas (4) and (5) and setting ω1 = 0.5, ω2 = 0.4, ω3 = 0.1, the decision is to obtain Δ V The top 5 solutions in the Pareto solution set when the equilibrium threshold is used are shown in Table 1. The solution ranked 1 in the table is used as the best solution for the equilibrium index optimization design. The solution is input into the actual operating conditions to obtain [Δ V ,N sw ,T eq ,σ SOC ]=[0.0232,2771,2035,0.0182].

[0081] Table 1Δ V As the equilibrium threshold decision, the top 5 solutions in the Pareto solution set are obtained.

[0082]

[0083] Assume that the equilibrium threshold is selected based on experience, Δ V =0.01, input the threshold into the system to get [Δ V ,N sw ,T eq ,σ SOC]=[0.01,3299,2022,0.011], Figure 4(b) is a comparison of the equalization results obtained by the two threshold input systems. V =0.01 and the optimal threshold Δ V =0.0232, we can see that the equilibrium speeds obtained by the two thresholds are similar, Δ V =0.0232 switching frequency is Δ V = 84% of 0.01, and the battery pack consistency is Δ V =1.65 times of 0.01. However, according to the weights set according to the requirements, it can be further found that Δ V =0.0232 switching frequency is Δ V = 42% of 0.01, and the battery pack consistency of the two thresholds is almost equal, so Δ is selected under this weight V =0.0232 as the equilibrium threshold can better meet the needs.

Claims

1. A lithium battery balancing index optimization method based on NSGA-2 genetic algorithm, characterized in that: The following steps are involved: Step 1: Determine the objective function for optimizing the lithium battery balancing index: Where, Δ V is the equilibrium threshold, N sw is the number of power electronic switch operations in the two-switch reconfigurable balanced topology, T eq is the equilibrium speed, σ SOC Characterizes the consistency of the SOC of the battery pack after balancing, which is represented by the average value of the battery pack SOC standard deviation. σ SOC_max is the maximum value of the average value of the battery pack SOC standard deviation; Step 2: According to the equalization threshold Δ V The value range of the system is to collect the empirical data of the system operation under NEDC conditions, perform data fitting on the collected empirical data, and solve the equilibrium threshold Δ V The relationship between it and the equilibrium indicator; Step 3: Use the NSGA-2 genetic algorithm and the equilibrium threshold Δ V Calculate the data of each point based on the relationship between the equilibrium index, optimize the objective function, and obtain the Pareto solution set; Step 4: Design a multi-objective decision-making strategy to find the optimal solution in the Pareto solution set.

2. The lithium battery balancing index optimization method based on the NSGA-2 genetic algorithm according to claim 1, characterized in that: The equalization threshold Δ in step 2 V The value range of is: The minimum value of the equalization threshold is determined by the following formula: Where n is the number of battery cells in the battery pack, n1 is the voltage distribution in V c The number of battery cells, n2 is the voltage distribution in V c +D_V battery cell number, V c is an assumed value, D_V is the ideal accuracy of the battery management system; Cell_V i Indicates the voltage of a battery cell. is the average value of the voltage of each battery cell; When n2=n / 2, the minimum value of the equalization threshold is obtained The maximum value of the equalization threshold is the difference in battery pack voltage at the initial moment Δ V_初始状态 ; Equalization threshold Δ V The value range of is:

3. The lithium battery balancing index optimization method based on the NSGA-2 genetic algorithm according to claim 1, characterized in that: In step 2, data fitting uses cubic spline interpolation to obtain unknown data within the interval based on the obtained finite data.

4. The lithium battery balancing index optimization method based on the NSGA-2 genetic algorithm according to claim 1, characterized in that: The step 4 specifically includes: Step 4.1: Normalization The data of the three targets are respectively analyzed based on the standard that the minimum value of each target in the Pareto solution set is 10 points: the number of power electronic switch operations N sw , equilibrium speed T eq , the average value of the battery pack SOC standard deviation σ SOC Perform normalization to obtain the normalized scores of each solution under the three objectives. The calculation formula is as follows: Where Score_f(i) represents the normalized score of the i-th solution in target f, f_min is the minimum value of target f, and f(i) is the value of the i-th solution of target f; Step 4.2: Weighting The scores obtained by normalization are added with their respective weight coefficients to obtain the weighted total score of each solution; the calculation formula is as follows: Among them, Score i is the weighted total score of the i-th solution, ω j is the weight coefficient corresponding to the j-th target, j = 1, 2, ..., 3; Step 4.3: Select the solution with the highest weighted total score as the optimal solution of the optimization algorithm.

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