A method, device and storage medium for modeling battery hysteresis characteristics

Abstract

The present invention discloses a method, device and storage medium for modeling battery hysteresis characteristics, belonging to the field of battery modeling. A method for modeling battery hysteresis characteristics, comprising: modeling battery hysteresis characteristics to obtain an initial model, and discretizing the initial model to obtain a discrete battery hysteresis characteristic model; measuring the OCV and SOC when the battery charge and discharge direction changes only once to obtain the battery first-order rotation curve; performing parameter identification on the discrete battery hysteresis characteristic model based on the battery first-order rotation curve to obtain a target battery hysteresis characteristic model. The constructed target battery hysteresis characteristic model can distinguish between the reversible component and the irreversible component of OCV, improve the OCV reconstruction accuracy and SOC estimation accuracy, and improve the accuracy of battery sorting and matching using OCV without increasing hardware costs.

Description

Technical Field

[0001] The present invention belongs to the field of battery modeling, and more specifically, relates to a method, device and storage medium for modeling battery hysteresis characteristics. Background Art

[0002] Due to the core advantages of lithium-ion batteries such as high energy density, long cycle life, low self-discharge rate, and no memory effect, they are currently widely used in industrial fields such as portable devices, electric vehicles, grid energy storage, and aerospace. Compared with ternary lithium batteries, lithium iron phosphate batteries have better thermal stability, which can effectively reduce the risk of safety accidents such as fire and explosion. At the same time, the manufacturing cost is relatively low, making them suitable for scenarios with high requirements for economy and safety. However, due to the combined influence of multiple factors such as stress accumulation during the phase transition of the lithium iron phosphate positive electrode and the mass transfer characteristics of the graphite negative electrode, the OCV-SOC curve of the lithium iron phosphate battery shows a hysteresis phenomenon, that is, at the same SOC, the OCV measured during the charging and discharging process do not coincide, which directly leads to the fact that there is no longer a one-to-one mapping relationship between SOC and OCV, increasing the difficulty of SOC estimation.

[0003] To address the above issues, the most commonly used solution is to obtain an average OCV-SOC curve by taking the average value, and then use it as an important basis for estimating SOC under dynamic conditions. For batteries with significant voltage platforms such as lithium iron phosphate batteries, liquid metal batteries, and lithium sulfur batteries, due to the existence of a persistent and flat voltage platform, the deviation and noise introduced during the battery voltage and current sampling process will lead to a serious deterioration in the accuracy of SOC estimation. At this time, the disadvantages of applying the average OCV-SOC curve will become apparent: taking the OCV of a lithium iron phosphate battery at 50% SOC as an example, the measured values ​​obtained during the charge and discharge process have a difference of about 24mV. If this difference is reflected in the average OCV-SOC curve, the corresponding SOC range is 33% to 66%. This means that if the hysteresis voltage is ignored, the SOC estimation error will be as high as more than 15%.

[0004] Chinese invention patent CN201510578190.X discloses a method for estimating the state of charge (SOC) based on the hysteresis characteristics of open-circuit voltage. This method determines the initial parameters of an adaptive model for the hysteresis characteristics of open-circuit voltage (OCV) using the Preisach operator based on hysteresis curve training. This model is then established and used to estimate the SOC of lithium-ion batteries online. Chinese invention patent CN200980105680.0 discloses a method for calculating the SOC of batteries using a Preisach model. However, both methods simply use the classic Preisach model to fit experimental data and, after parameter identification, use it to predict the battery's hysteresis voltage in real time. These methods are insufficient to accurately describe the true physical laws governing how OCV varies with SOC. In fact, the physical mechanisms driving the dynamic changes in OCV during charge and discharge can be categorized into two types: First, changes in lithium concentration cause changes in electrode potential. This change is fully reversible, and there is a well-defined functional relationship between the ideal electrode equilibrium potential and lithium concentration. The ideal OCV is determined solely by the current SOC and is unrelated to the historical trajectory of SOC changes. Secondly, due to the hysteresis effect, the measured OCV at a given SOC will always deviate from the ideal OCV, and this deviation is closely related to the charge and discharge history. This results in OCV differences when the battery reaches the same SOC under different charge and discharge paths, and this change is irreversible.

[0005] From the perspective of model accuracy, the classic Preisach model can only accurately reflect the irreversible component of OCV changes, without incorporating the reversible component into the modeling scope. It cannot fully reflect the two different mechanisms that drive OCV changes, thereby reducing the accuracy of the model. From the perspective of model application, directly using the classic Preisach model can only obtain the actual value of the open circuit voltage after integrating the two factors. In some application scenarios, it is also necessary to obtain a theoretical OCV value that is only related to the lithium concentration in order to analyze the relevant characteristics of the battery. For example, when performing battery sorting and matching through OCV testing, the measured OCV includes the influence of historical SOC, which reduces the accuracy of battery sorting and matching.

[0006] Therefore, existing methods cannot accurately describe the true law of OCV changes with SOC, the accuracy of OCV curve reconstruction is low, and the battery SOC cannot be estimated with high precision. In application scenarios that rely on OCV for battery electrochemical characteristics analysis, the relevant characteristics of the battery cannot be accurately analyzed. Summary of the Invention

[0007] In response to the defects of the related art, the purpose of the present invention is to provide a method, device and storage medium for modeling the hysteresis characteristics of a battery, aiming to solve the problems of being unable to accurately describe the true law of the change of OCV with SOC, the low accuracy of OCV curve reconstruction, the inability to estimate SOC with high precision, and the inability to accurately analyze the relevant characteristics of the battery in application scenarios that rely on OCV for battery electrochemical characteristic analysis.

[0008] To achieve the above object, the present invention provides a method for modeling battery hysteresis characteristics, comprising:

[0009] S1. Modeling the battery hysteresis characteristics to obtain an initial model, and discretizing the initial model to obtain a discrete battery hysteresis characteristic model; the initial model is:

[0010]

[0011] OCV1t=∫∫ 0≤α＜β≤1 μα,βγ αβ [SoC t|dαdβ

[0012]

[0013] Among them, OCV max and OCV min are the maximum and minimum values ​​of OCV, the battery SOC is the model input, and the battery OCV is the model output. OCV1t and OCV2t represent the irreversible component and reversible component of OCV change, respectively. The irreversible component represents the OCV change caused by the hysteresis effect, and the reversible component represents the OCV change caused by the change of lithium concentration. γ αβ and γ αα is the hysteresis operator, γ αβ is finite width, γ αα is zero width, μα, β and να are weight functions used to measure the contribution of each hysteresis operator to the output, α and β are the thresholds of the input in the descending and ascending directions respectively;

[0014] S2, measure the OCV and SOC when the battery charge and discharge direction changes only once, and obtain the battery first-order rotation curve;

[0015] S3. Perform parameter identification on a discrete battery hysteresis characteristic model based on the battery first-order rotation curve to obtain a target battery hysteresis characteristic model.

[0016] Optionally, discretizing the initial model to obtain a discrete battery hysteresis characteristic model includes:

[0017] After discretizing the irreversible component OCV1t of the initial model, the expression is:

[0018]

[0019] Among them, α n ,β n and α n-1 ,β n For two adjacent charge and discharge turning points, Fα n-1 ,β n -Fα n ,β n is the contribution of two adjacent charge-discharge turning points to the total hysteresis effect, k is the total number of charge-discharge conversion orders, each order of charge-discharge conversion includes one charge-to-discharge and one discharge-to-charge, C1 is a constant term;

[0020] The reversible component OCV2t of the initial model is converted into a linear combination of weight functions by the trapezoidal method, which is expressed as follows:

[0021]

[0022] Where C2 is a constant term, p is the number of equal divisions of the complete SOC interval (i.e., 0 ≤ SOC ≤ 1), i is the nearest equal division point when SOC t is rounded down, i.e., the closest i-th equal division point when SOC t is rounded down;

[0023] The discrete battery hysteresis characteristic model is:

[0024]

[0025] Here, C represents a constant term.

[0026] Optionally, discretizing the irreversible component OCV1 t of the initial model includes:

[0027] The irreversible component OCV1t of the initial model is converted into the sum of integrals on a right trapezoid through geometric relationships, and then converted into a linear combination of integrals on a right triangle with the charge and discharge turning point as the right-angle vertex and the straight line α=β as the hypotenuse;

[0028] Among them, α n ,β n is the coordinate of the corresponding rectangular vertex in the Preisach triangle during the nth-order charge-discharge conversion, Fα n-1 ,β n The charge and discharge turning point α n-1 ,β n is the integral of the weight function on the right triangle with the right vertex and the straight line α=β as the hypotenuse, Fα n ,β n The charge and discharge turning point α n ,βn It is the integral of the weight function on the right triangle with the right vertex and the straight line α=β as the hypotenuse.

[0029] Optionally, S3 specifically includes:

[0030] S31, discretizing the weight functions μα,β in the discrete battery hysteresis characteristic model;

[0031] S32. Based on the experimental data obtained from the first-order rotation curve test of the battery, the constrained linear least squares method is used to perform parameter identification on the discretized weight function μα, β, and the weight function is solved to obtain the target battery hysteresis characteristic model.

[0032] Optionally, S32 specifically includes:

[0033] S321, setting the objective function to the sum of squares of the errors between the measured OCV in the first-order rotation curve and the OCV predicted by the discrete battery hysteresis characteristic model;

[0034] S322. Set constraints including boundary constraints and inequality constraints; wherein the boundary constraint is: vα≥0; the inequality constraint is: ∫∫ Tαβ μ,βdαd≥0; where Tα,β is a right triangle with α,β as right-angled vertices and the line α=β as the hypotenuse;

[0035] S323 . Solve the discretized weight function in the discrete battery hysteresis characteristic model based on the objective function and the constraint conditions to obtain a target battery hysteresis characteristic model.

[0036] In a second aspect, the present invention further provides a battery SOC estimation method, comprising:

[0037] Establishing an equivalent circuit model of the battery to be tested and identifying model parameters, wherein the OCV in the equivalent circuit model is divided into a reversible component OCV2 and an irreversible component OCV1; wherein OCV1 is obtained from the historical charge and discharge turning points of the battery to be tested and a target battery hysteresis characteristic model, wherein the target battery hysteresis characteristic model is constructed using the method for modeling battery hysteresis characteristics as described in any one of the first aspects;

[0038] Obtaining an OCV2-SOC relationship of the battery to be tested according to the target battery hysteresis characteristic model;

[0039] A spatial state equation is established based on the equivalent circuit model, and the OCV2-SOC relationship OCV2=f(SOC) is used as the observation equation. The SOC of the battery to be tested is estimated by combining the state space equation and the observation equation through a filtering algorithm.

[0040] In a third aspect, the present invention further provides a battery matching method, comprising:

[0041] Obtaining an OCV2-SOC relationship of the battery to be tested according to the target battery hysteresis characteristic model; the target battery hysteresis characteristic model is constructed using the method for modeling battery hysteresis characteristics as described in any one of the first aspects;

[0042] The difference in OCV2 between different batteries under test at the same SOC is calculated according to the OCV2-SOC relationship of the battery under test. Different batteries under test with the difference less than a threshold are determined to have consistent performance and are matched.

[0043] In a fourth aspect, the present invention further provides a device for modeling battery hysteresis characteristics, comprising:

[0044] The model building module is used to model the battery hysteresis characteristics to obtain an initial model, and discretize the initial model to obtain a discrete battery hysteresis characteristic model; the initial model is:

[0045]

[0046] OCV1 t=∫∫ 0≤α≤β≤1 μ,α,β,γ αβ SoC t|dαdβ

[0047]

[0048] Among them, OCV max and OCV min are the maximum and minimum values ​​of OCV, the battery SOC is the model input, and the battery OCV is the model output. OCV1t and OCV2t represent the irreversible component and reversible component of OCV change, respectively. The irreversible component represents the OCV change caused by the hysteresis effect, and the reversible component represents the OCV change caused by the change of lithium concentration. γ αβ and γ αα is the hysteresis operator, γ αβ is finite width, γ αα is zero width, μα, β and vα are weight functions used to measure the contribution of each hysteresis operator to the output, α and β are the thresholds of the input in the descending and ascending directions respectively;

[0049] The curve acquisition module is used to measure the OCV and SOC when the battery charge and discharge direction changes only once, and obtain the battery's first-order rotation curve;

[0050] The parameter identification module is used to perform parameter identification on the discrete battery hysteresis characteristic model based on the battery first-order rotation curve to obtain a target battery hysteresis characteristic model.

[0051] In a fifth aspect, the present invention further provides a computer-readable storage medium storing computer instructions, wherein the computer instructions are used to enable a processor to implement the method for modeling battery hysteresis characteristics as described in any one of the first aspects when executed.

[0052] Compared with the prior art, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

[0053] 1. The present invention provides a method for modeling battery hysteresis characteristics. Before the classic Preisach model is used to model the OCV hysteresis phenomenon, necessary corrections are made to it, and an item is added to the model that is only related to the input at the current moment and has nothing to do with the historical path, namely the reversible component. The battery hysteresis characteristic model based on the improved Preisach model can fully reflect the two different mechanisms (reversible component and irreversible component) that drive OCV changes, and can accurately describe the true law of OCV changes with SOC. At the same time, a reversible OCV value that is only related to the lithium concentration and an irreversible OCV value that is only related to the historical path of charge and discharge are obtained, thereby improving the reconstruction accuracy of OCV.

[0054] 2. This invention provides a method for modeling battery hysteresis characteristics and a specific method for discretizing the battery hysteresis characteristic model, laying the foundation for integrating the model into the core algorithm system of existing battery management systems. Continuous battery hysteresis characteristic models cannot be directly deployed in embedded systems. Discretizing the battery hysteresis characteristic model not only significantly reduces computational overhead but also simplifies the model parameter identification process, facilitating the model's deployment in embedded systems.

[0055] 3. The present invention provides a battery SOC estimation method. The target battery hysteresis characteristic model constructed by the method for modeling battery hysteresis characteristics provided by the present invention can obtain the OCV2-SOC relationship of the battery to be tested, and the OCV in the equivalent circuit model of the battery to be tested is divided into a reversible component OCV2 and an irreversible component OCV1, wherein OCV1 is obtained by the historical charge and discharge turning points of the battery to be tested and the target battery hysteresis characteristic model. A spatial state equation is established according to the equivalent circuit model, and the OCV2-SOC relationship OCV2=f(SOC) is used as the observation equation. Then, the SOC estimation is completed by combining the state space equation and the observation equation through a filtering algorithm. The reversible OCV (OCV2) eliminates the influence of the hysteresis effect. Under different charge and discharge paths, OCV2 corresponds one-to-one with the SOC, making the SOC estimation of batteries with serious hysteresis characteristics that cannot be ignored (such as iron phosphate batteries) more accurate and reliable, while not increasing hardware costs.

[0056] 4. Utilizing the battery hysteresis characteristics model provided by this invention, the OCV2 of the battery can be obtained on the battery production line using the target battery hysteresis characteristics model to screen out cells with consistent performance for forming a highly balanced battery pack. This helps ensure the consistency and reliability of the battery pack, improving its overall performance and safety. Reversible OCV (OCV2) eliminates the influence of historical behavior and better reflects the intrinsic electrochemical characteristics of the battery, making battery sorting and matching based on OCV2 more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 1 is a flow chart of a method for modeling battery hysteresis characteristics provided by the present invention;

[0058] Figure 2 (a) is a schematic diagram of the main hysteresis loop of the lithium iron phosphate battery. Figure 2 (b) is a schematic diagram of the small hysteresis loop of the lithium iron phosphate battery;

[0059] Figure 3 It is a schematic diagram of the smallest unit that represents the hysteresis phenomenon in the Preisach model;

[0060] Figure 4 It is a schematic diagram of the Preisach triangle;

[0061] Figure 5 It is a schematic diagram of the Preisach triangle step memory curve;

[0062] Figure 6 It is a schematic diagram of the integral domain decomposition during the discretization process of the initial model;

[0063] Figure 7 is a schematic diagram of a first-order rotation curve;

[0064] Figure 8 This is a first-order rotation curve diagram obtained from the experiment. (a) and (b) in the figure correspond to the first-order rotation curve of charge to discharge and the first-order rotation curve of discharge to charge.

[0065] Figure 9 This is a diagram of the first-order rotation curve reconstructed using the parameter identification results. (a) and (b) in the figure respectively represent the first-order rotation curve reconstruction results of charge-to-discharge and discharge-to-charge. The solid line is the first-order rotation curve obtained by battery testing, and the single mark is the OCV predicted by the hysteresis characteristic model of the target battery. DETAILED DESCRIPTION

[0066] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0067] The contents involved in the above embodiment are described below in conjunction with a preferred embodiment.

[0068] Example 1

[0069] like Figure 1 As shown, a method for modeling battery hysteresis characteristics includes:

[0070] S1. Modeling the battery hysteresis characteristics to obtain an initial model, and discretizing the initial model to obtain a discrete battery hysteresis characteristic model; the initial model is:

[0071]

[0072] OCV1 t=∫∫ 0≤α≤β≤1 μ,α,β,γ αβ SoC t|dαdβ

[0073]

[0074] Among them, OCV max and OCV min are the maximum and minimum values ​​of OCV, the battery SOC is the model input, and the battery OCV is the model output. OCV1t and OCV2t represent the irreversible component and reversible component of OCV change, respectively. The irreversible component represents the OCV change caused by the hysteresis effect, and the reversible component represents the OCV change caused by the change of lithium concentration. γ αβ and γ αα is the hysteresis operator, γ αβ is finite width, γ αα is zero width, μα, β and α are weight functions used to measure the contribution of each hysteresis operator to the output, α and β are the thresholds of the input in the descending and ascending directions respectively;

[0075] S2, measure the OCV and SOC when the battery charge and discharge direction changes only once, and obtain the battery first-order rotation curve;

[0076] S3. Perform parameter identification on a discrete battery hysteresis characteristic model based on the battery first-order rotation curve to obtain a target battery hysteresis characteristic model.

[0077] Figure 2(a) shows the main hysteresis loop of the lithium iron phosphate battery tested in the laboratory. It can be clearly seen from the figure that the hysteresis effect causes the OCV-SOC relationship to become a multi-valued function. Figure 2 Figure (b) shows the small hysteresis loop of a lithium iron phosphate battery. The solid line is the main hysteresis loop curve, which delineates the outer boundary of the small hysteresis loop. Under current conditions with frequent charge and discharge, due to the hysteresis effect, the OCV-SOC relationship will also form a reciprocating motion trajectory within the main hysteresis loop, tending to the upper and lower boundaries during charging and discharging, respectively.

[0078] The principle of the classic Preisach model commonly used in existing methods is as follows: Figure 3 The hysteresis operator shown is the smallest unit in the Preisach model that represents the hysteresis phenomenon. The horizontal axis represents the system input, and the vertical axis represents the system output. The output of the hysteresis operator has only two states, "1" and "-1". α and β are the thresholds of the input in the falling and rising directions, respectively. The output state will only switch when the input crosses the threshold. αβ The input-output relationship can be expressed as

[0079]

[0080] Macroscopic hysteresis can be considered the result of an infinite number of hysteresis operators with different thresholds. The threshold of each hysteresis operator can be arbitrarily selected within a specific range, as long as it does not exceed the theoretically allowed maximum value and α < β. For OCV hysteresis, the input is SOC, which theoretically ranges from 0 ≤ SoC ≤ 1. The two thresholds must satisfy 0 ≤ α < β ≤ 1.

[0081] Figure 4 The isosceles right triangle shown is the Preisach triangle. For each coordinate point within the Preisach triangle, there is a corresponding hysteresis operator. If the contribution of each hysteresis operator to the output is measured by a weight function μα,β, the output at any time can be obtained by solving a double integral within the Preisach triangle:

[0082] yt=∫∫ 0≤α＜β≤1 μ,βγ αβ [xt]dαdβ

[0083] Figure 5This is a schematic diagram of the Preisach triangle step memory curve. Assume that the battery starts charging from a fully discharged state. When the SOC increases to xt1, all hysteresis operators that satisfy β≤xt1 take the value of "1", while other hysteresis operators still take the value of "-1". At this time, the Preisach triangle is divided into two parts, upper and lower, by a straight line β=xt1 parallel to the α-axis. The hysteresis operators take the values ​​of "1" and "-1". As the charging process progresses, the upper and lower boundaries will continue to move upward. If at a certain point in the future the battery is not fully charged and is discharged, the SOC gradually drops to xt2. At this time, all hysteresis operators that satisfy xt2≤α take the value of "-1". A straight line α=xt2 parallel to the β-axis appears in the Preisach triangle as the left and right boundaries, forming Figure 5 Boundary lines shown.

[0084] As the discharge process continues, the left and right boundaries will continue to shift to the left. After the next charge-discharge transition, the battery begins charging: 1) If the SOC never exceeds the historical extreme value xt1 during the charging process, the boundary will be stepped; 2) If the SOC exceeds the historical extreme value xt1 during the charging process, the historical boundary will be erased and a new straight boundary will be formed.

[0085] For some physical systems, the underlying principle of the input-output relationship consists of two components: the output magnitude is directly related to the current input magnitude. Furthermore, due to factors such as different reaction pathways, the output magnitude exhibits historical input dependence. This means that the output magnitude is related not only to the current input magnitude but also to historical input. While directly using the Preisach model can yield relatively accurate output results, the resulting output encompasses both aspects, preventing further analysis from distinguishing them. Therefore, the Preisach model is modified to ensure that it fully reflects the two distinct mechanisms driving output changes.

[0086] The improved Preisach model is:

[0087] yt=y1t+y2t

[0088] y1 t=∫∫ 0≤α＜β≤1 μ,βγ αβ [xt]dαdβ

[0089]

[0090] Among them, γ αβ and γ αα is the hysteresis operator, γ αβ is finite width, γ ααis zero width, μα, β and vα are weight functions used to measure the contribution of each hysteresis operator to the output, α and β are the thresholds of the input in the descending and ascending directions respectively, xt is the model input, yt is the model output, y1t is the first output item, which describes the part of the output that is only related to the historical input, and y2t is the second output item, which describes the component of the output that is only related to the input.

[0091] Compared with the classic Preisach model, the improved Preisach model only adds an integral term to describe the component of the output that is independent of the historical input. At the same time, the basic structure and physical meaning of the second term and the first term remain the same, but the integral dimension is degenerated from two dimensions to one dimension. From the perspective of the hysteresis operator, the finite width hysteresis operator γ αβ Degenerates into a zero-width hysteresis operator γ αα , when the input xt exceeds the threshold α, γ αα The output state will mutate. From the perspective of weight function, the two-dimensional weight function μα,β degenerates into a one-dimensional weight function να, and the zero-width hysteresis operator γ αα Continuously distributed in the range of 0≤α≤1.

[0092] In the above model, y1 t is the first output term, representing the traditional Preisach model. Due to the Preisach model's memory mechanism, when the two-dimensional weight functions μα,β on the hypotenuse of the Preisach triangle are zero, the output magnitude only includes hysteresis effects—that is, the portion related to historical inputs. y2 t is the second output term, and the second integral describes the component of the output that is solely related to the current input. Therefore, in the modified improved Preisach model, the first and second integrals respectively model the irreversible and reversible components of the output change, fundamentally resolving the problem of the classic Preisach model's inability to accurately match the output evolution mechanism.

[0093] The battery hysteresis characteristic is modeled based on the improved Preisach model, resulting in an initial model. This model includes the irreversible component of OCV variation, OCV1t, and the reversible component, OCV2t. The irreversible component, OCV1t, represents the OCV variation caused by the hysteresis effect and its magnitude depends only on the historical SOC, not the current SOC. The reversible component, OCV2t, represents the OCV variation caused by changes in lithium concentration and its magnitude depends only on the current SOC, not the historical SOC. To facilitate subsequent calculations, the initial model is discretized and simplified to obtain a discrete battery hysteresis characteristic model. The OCV and SOC are measured when the battery undergoes a single change in charge and discharge direction, generating the first-order battery rotation curve. Parameter identification of the discrete battery hysteresis characteristic model is performed based on the obtained first-order battery rotation curve to confirm the unknown parameters in the model and ultimately obtain the target battery hysteresis characteristic model.

[0094] In the initial model above, the first integral term is based on the classic Preisach model, where the output value OCV1t is used to describe the component of OCV variation that is only related to the charge and discharge path. The second integral term is used to describe the component of OCV variation that is only related to the input value. It maintains the same basic structure and physical meaning as the first term, but the integral dimension is degenerated from two dimensions to one dimension. From the perspective of the hysteresis operator, the finite width hysteresis operator γ αβ Degenerates into a zero-width hysteresis operator γ αα , when the input SOC t exceeds the threshold α, γ αα The output state will suddenly change. According to the memory mechanism of the improved Preisach model, during the charging and discharging process, the second integral is only related to the SOC at the current moment.

[0095] The continuous battery hysteresis characteristic model cannot be directly deployed into the embedded system. Discretizing the model will not only significantly reduce the computational overhead, but also help simplify the model parameter identification process.

[0096] The Preisach triangle is divided into two parts, where the output states of the two-dimensional hysteresis operator are "1" and "-1", respectively denoted as S + t and S - t, T represents the area covered by the Preisach triangle, then T=S + t∪S - t. It can be obtained that the term that changes with time in the model is the integral of the part of the output state of the two-dimensional hysteresis operator that is "1", that is, S + The integral on t, the boundary of the region is stepped, such as Figure 6 As shown, the integral on this area is simplified into several trapezoidal areas Q through geometric relations. nThe sum of the integrals on each trapezoid is converted into the difference of the integrals on two right triangles through geometric relationships. Each right triangle can be uniquely determined by its right-angle vertex, which is also the turning point of charge and discharge. Therefore, α n ,β n The integral on the right triangle with vertices is expressed as:

[0097]

[0098] Therefore, after discretizing the irreversible component OCV1t in the initial model, the expression is:

[0099]

[0100] Among them, C1 is a constant term.

[0101] Whether the last step of the battery operating condition is discharge or charge will determine whether the last segment of the step boundary is vertical or horizontal. In the above derivation, it is assumed that the current condition ends in discharge. At this time, α k =SOC t. On the contrary, when the current condition ends in charging, α k =β k =SOC t.

[0102] The complete SOC interval (i.e. 0≤SOC≤1) is divided into two parts, where the output states of the one-dimensional hysteresis operator are “1” and “-1”, respectively denoted as L + t and L - t, [0, SOC t] range is L + t, [SOC t, 1] is Lt. It can be obtained that the term that changes with time in the model is the integral of the part of the output state of the one-dimensional hysteresis operator that is "1", that is, L + The integral over t.

[0103] Furthermore, L + The integral discretization on t can be achieved by the trapezoidal method. Divide the complete SOC interval (i.e., 0≤SOC≤1) into p equal parts. Assuming that when SOC t is rounded down, the closest equal division point is the i-th equal division point in the interval (i.e., i / p), then the expression after discretizing the reversible component in the initial model is:

[0104]

[0105] Among them, C2 is a constant term.

[0106] The discrete battery hysteresis characteristic model is:

[0107]

[0108] Here, C represents a constant term.

[0109] Figure 7 This is a schematic diagram of a first-order conversion curve. "First-order" refers to the fact that the direction of the model input changes only once, meaning only one charge-discharge transition occurs. The battery starts at full charge and continues charging until the state of charge reaches SOC1. It then switches to discharging until the state of charge reaches SOC2. The open-circuit voltages corresponding to SOC1 and SOC2 are denoted as OCV1 and OCV2, respectively.

[0110] During the charge-discharge conversion process, the hysteresis operator in the triangle T SOC2,SOC1 will change the output, and we can get:

[0111]

[0112] In the above formula, the left side of the equation can be obtained through experiments, while the right side of the equation is a linear function of the discrete battery hysteresis characteristic model parameters.

[0113] Figure 8 This is the first-order charge-discharge conversion curve obtained in the laboratory. The test method is to first charge to a full charge state with constant current and constant voltage and let it stand, and then pulse discharge to a full discharge state. The ΔSOC of a single pulse discharge process is 5%. The cycle is repeated 20 times, and the SOC threshold of each constant current and constant voltage charging process is lowered by 5%.

[0114] The experimental steps to obtain the first-order rotation curve of the battery are as follows:

[0115] Charge to discharge process:

[0116] 1. Constant current and constant voltage charging to full charge state: charging current is 8A, cut-off voltage is 3.65V, cut-off current is 0.8A, and standing time is 1h;

[0117] 2. Pulse discharge to full discharge state: discharge current is 8A, cut-off voltage is 2V, ΔSOC of a single pulse discharge process is 5%, rest time is 1h, and cycled 20 times;

[0118] 3. Charge at constant current and constant voltage until SOC=95%, then pulse discharge to full discharge state after standing for 1 hour;

[0119] 4. The SOC threshold of the constant current constant voltage charging process is lowered by 5%, and step 3 is repeated for 19 times.

[0120] Discharge to charge process:

[0121] 1. Constant current discharge to full discharge state: discharge current is 8A, cut-off voltage is 2V, and standstill time is 1h;

[0122] 2. Pulse charging to full charge: charging current 8A, cut-off voltage 3.65V, ΔSOC of a single pulse charging process is 5%, rest time is 1h, and cycled 20 times;

[0123] 3. Constant current discharge to SOC = 5%, then pulse charge to full charge after standing for 1 hour;

[0124] 4. Increase the SOC threshold of the constant current discharge process by 5%, repeat step 3, and cycle 19 times.

[0125] Based on the experimental data obtained from the above charging and discharging processes, the first-order rotation curve of the battery is calculated.

[0126] Optionally, S3 specifically includes:

[0127] S31, discretizing the weight functions μα,β in the discrete battery hysteresis characteristic model;

[0128] S32. Based on the experimental data obtained from the first-order rotation curve test of the battery, the constrained linear least squares method is used to perform parameter identification on the discretized weight function μα, β, and the weight function is solved to obtain the target battery hysteresis characteristic model.

[0129] In S31, the continuous weight function μα,β is discretized, specifically including: taking a discrete step length L = 0.05, dividing the horizontal axis and the vertical axis into 20 equal parts, drawing a uniform grid in the Preisach triangle, and placing the grid point α i ,β j The weight function at is denoted as μα i ,β j , so as to convert the continuous integral in the above formula into a numerical integral, the voltage difference of different data points in the OCV first-order rotation curve is expressed as a linear weighted superposition of discrete weight functions.

[0130] Optionally, S32 specifically includes:

[0131] S321, setting the objective function to the sum of squares of the errors between the measured OCV in the first-order rotation curve and the OCV predicted by the discrete battery hysteresis characteristic model;

[0132] S322. Set constraint conditions including boundary constraints and inequality constraints; wherein the boundary constraint is: 0; the inequality constraint is: ∫∫ Tα,β μ,α,βdαdβ≥0;

[0133] S323 . Solve the discretized weight function in the discrete battery hysteresis characteristic model based on the objective function and the constraint conditions to obtain a target battery hysteresis characteristic model.

[0134] The constraints for constrained linear least squares are divided into two parts:

[0135] 1) Boundary constraints. The functional relationship between the ideal OCV and SOC is a monotonically increasing function, so να≥00 always holds.

[0136] 2) Inequality constraints. The OCV in the charging path is higher than the OCV in the discharging path, that is, at any SOC, the hysteresis voltage is positive during charging and negative during discharging. For any α and β in the definition domain, the integral ∫∫ Tα,β ,μ,α,βdαdβ≥0 always holds true; where Tα,β is a right triangle with α,β as right-angled vertices and the straight line α=β as the hypotenuse.

[0137] The solution can be completed using MATLAB's lsqlin function to obtain the target battery hysteresis characteristic model.

[0138] In this embodiment, the first-order rotation curve of discharge-to-charge is reconstructed by using the parameter identification results of the first-order rotation curve of charge-to-discharge; the first-order rotation curve of charge-to-discharge is reconstructed by using the parameter identification results of the first-order rotation curve of discharge-to-charge. Figure 9 In the figure, the solid line represents the first-order rotation curve obtained from battery testing, and the single marker represents the OCV predicted by the target battery hysteresis model. It can be seen that the two have a high degree of overlap. The root mean square error (RMSE) and mean absolute error (MAE) of the OCV prediction are shown in Table 1, demonstrating the high accuracy of the model.

[0139] Table 1 OCV prediction accuracy in first-order rotation curve

[0140]

[0141] Furthermore, based on the above embodiment, the application of the battery hysteresis characteristic model based on the improved Preisach model includes two aspects: 1. Battery SOC estimation, 2. Battery sorting and matching. When estimating the battery SOC, the OCV2-SOC relationship is obtained in advance through the target battery hysteresis characteristic model, and an equivalent circuit model is established to estimate the battery SOC in combination with the OCV2-SOC relationship. When sorting and matching batteries, the OCV2 is accurately obtained to analyze the relevant electrochemical characteristics of the battery, and the OCV2 of the battery is obtained through the target battery hysteresis characteristic model to screen out cells with consistent performance, thereby performing battery sorting and matching.

[0142] The present invention also provides a battery SOC estimation method, which uses the target battery hysteresis characteristic model constructed by the above-mentioned method for modeling battery hysteresis characteristics, including:

[0143] Obtaining an OCV2-SOC relationship of the battery to be tested according to the target battery hysteresis characteristic model;

[0144] Establishing an equivalent circuit model of the battery under test and identifying model parameters, wherein the OCV in the equivalent circuit model is divided into a reversible component OCV2 and an irreversible component OCV1; wherein OCV1 is obtained from the historical charge and discharge turning points of the battery under test and the hysteresis characteristic model of the target battery;

[0145] A spatial state equation is established based on the equivalent circuit model, and the OCV2-SOC relationship OCV2=F(SOC) is used as the observation equation. The SOC estimation is completed by combining the state space equation and the observation equation through a filtering algorithm.

[0146] Depending on the accuracy and complexity of the model, a first-order Thevenin equivalent circuit model can be selected and processed to transform it into a form that facilitates model identification. Depending on the speed and accuracy of the parameter identification algorithm, a recursive least squares algorithm with a forgetting factor can be used to identify model parameters.

[0147] The reversible component OCV2 eliminates the influence of the hysteresis effect. Under different paths, OCV2 corresponds to SOC one-to-one, thereby improving the accuracy of SOC estimation.

[0148] The present invention also provides a battery matching method, comprising:

[0149] Obtaining an OCV2-SOC relationship of the battery to be tested according to the target battery hysteresis characteristic model; the target battery hysteresis characteristic model is constructed using the method for modeling battery hysteresis characteristics as described in any one of the above embodiments;

[0150] The difference in OCV2 between different batteries under test at the same SOC is calculated according to the OCV2-SOC relationship of the battery under test. Different batteries under test with the difference less than a threshold are determined to have consistent performance and are matched.

[0151] The target battery hysteresis characteristic model constructed by the method of modeling battery hysteresis characteristics can be used on the battery production line to obtain the OCV2 of the battery to be tested at a certain SOC value. The degree of closeness of OCV2 at the same SOC is used as a screening criterion or one of the screening criteria. When other conditions are the same, the closer the OCV2 of the batteries at the same SOC, the higher the consistency of the two batteries. This is to screen out cells with consistent performance to form a battery pack with a higher degree of balance. This helps to ensure the consistency and reliability of the battery pack and improve the overall performance and safety of the battery pack. Reversible OCV (OCV2) eliminates the influence of historical behavior and can better reflect the intrinsic electrochemical characteristics of the battery. Battery sorting and matching based on OCV2 is more accurate.

[0152] In this embodiment, a modified Preisach model is used to model battery hysteresis characteristics. This model addresses the inability to accurately describe the true pattern of OCV variation with SOC, resulting in low accuracy in OCV curve reconstruction, the inability to accurately estimate battery SOC, and the inability to accurately analyze relevant battery characteristics in applications that rely on OCV for battery electrochemical characterization. By incorporating a term that is only related to the current SOC and not to the historical path, the model comprehensively reflects the two different mechanisms driving OCV variation, improving the accuracy of the battery hysteresis model. When reconstructing the OCV curve, both the reversible and irreversible OCV components can be obtained. The reversible OCV component is only related to SOC and is used for SOC estimation, making SOC estimation more accurate and reliable for batteries with severe hysteresis that cannot be ignored. In applications such as battery sorting and matching, the reversible OCV component (OCV2) more accurately reflects the intrinsic electrochemical characteristics of the battery, thereby enhancing the accuracy of battery sorting and matching based on OCV2.

[0153] Example 2

[0154] The present invention also provides a device for modeling battery hysteresis characteristics, comprising:

[0155] The model building module is used to model the battery hysteresis characteristics to obtain an initial model, and discretize the initial model to obtain a discrete battery hysteresis characteristic model; the initial model is:

[0156]

[0157] OCV1 t=∫∫ 0≤α≤β≤1 μ,α,βγ αβ [SOC t]dαdβ

[0158]

[0159] Among them, OCV max and OCV min are the maximum and minimum values ​​of OCV, the battery SOC is the model input, and the battery OCV is the model output. OCV1t and OCV2t represent the irreversible component and reversible component of OCV change, respectively. The irreversible component represents the OCV change caused by the hysteresis effect, and the reversible component represents the OCV change caused by the change of lithium concentration. γ αβ and γ αα is the hysteresis operator, γ αβ is finite width, γ αα is zero width, μα, β and vα are weight functions used to measure the contribution of each hysteresis operator to the output, α and β are the thresholds of the input in the descending and ascending directions respectively;

[0160] The curve acquisition module is used to measure the OCV and SOC when the battery charge and discharge direction changes only once, and obtain the battery's first-order rotation curve;

[0161] The parameter identification module is used to perform parameter identification on the discrete battery hysteresis characteristic model based on the battery first-order rotation curve to obtain a target battery hysteresis characteristic model.

[0162] An apparatus for modeling battery hysteresis characteristics provided by an embodiment of the present invention is used to execute a method for modeling battery hysteresis characteristics provided by any embodiment of the present invention, and has corresponding beneficial effects.

[0163] Example 3

[0164] The present invention further provides a computer-readable storage medium storing computer instructions, wherein the computer instructions are used to enable a processor to implement the method for modeling battery hysteresis characteristics as described in any one of the first embodiments when executed.

[0165] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for modeling battery hysteresis characteristics, characterized in that: include: S1. Modeling the battery hysteresis characteristics to obtain an initial model, and discretizing the initial model to obtain a discrete battery hysteresis characteristic model; the initial model is: OCV1(t)∫∫ 0≤α＜β≤1 μ(a,b)γ αβ [SOC(t)]dαdβ Among them, OCV max and OCV min are the maximum and minimum values ​​of OCV, the battery SOC is the model input, and the battery OCV is the model output. OCV1(t) and OCV2(t) represent the irreversible and reversible components of OCV change, respectively. The irreversible component represents the OCV change caused by the hysteresis effect, and the reversible component represents the OCV change caused by the change in lithium concentration. γ αβ and γ αα is the hysteresis operator, γ αβ is finite width, γ αα is zero width, μ(α,β) and ν(α) are weight functions used to measure the contribution of each hysteresis operator to the output, and α and β are the thresholds of the input in the descending and ascending directions respectively; S2, measure the OCV and SOC when the battery charge and discharge direction changes only once, and obtain the battery first-order rotation curve; S3. Perform parameter identification on a discrete battery hysteresis characteristic model based on the battery first-order rotation curve to obtain a target battery hysteresis characteristic model.

2. The method according to claim 1, wherein The discretization of the initial model to obtain a discrete battery hysteresis characteristic model includes: After discretizing the irreversible component OCV1(t) of the initial model, the expression is: Among them, (α n ,β n ) and (α n-1 ,β n ) are two adjacent charge and discharge turning points, F(α n-1 ,β n )-F(α n ,β n ) is the contribution of two adjacent charge-discharge turning points to the total hysteresis effect, k is the total number of charge-discharge conversion orders, each order of charge-discharge conversion includes one charge-to-discharge and one discharge-to-charge, C1 is a constant term; The reversible component OCV2(t) of the initial model is converted into a linear combination of weight functions by the trapezoidal method, which is expressed as follows: Where C2 is a constant term, p is the number of equal divisions of the complete SOC interval, that is, the interval 0≤SOC≤1 is divided into p equal divisions, and i is the nearest equal division point when SOC(t) is rounded down, that is, the closest i-th equal division point when SOC(t) is rounded down; The discrete battery hysteresis characteristic model is: Here, C represents a constant term.

3. The method according to claim 2, wherein The discretizing of the irreversible component OCV1(t) of the initial model includes: The irreversible component OCV1(t) of the initial model is converted into a sum of integrals on a right trapezoid through geometric relationships, and then converted into a linear combination of integrals on a right triangle with the charge and discharge turning point as a right-angle vertex and the straight line α=β as the hypotenuse; Among them, (α n ,β n ) is the coordinate of the corresponding right-angle vertex in the Preisach triangle during the n-th order charge-discharge conversion, F(α n-1 ,β n ) is the charge and discharge turning point (α n-1 ,β n ) is the integral of the weight function on the right triangle with the right vertex and the straight line α=β as the hypotenuse, F(α n ,β n ) is the charge and discharge turning point) n ,β n ) is the integral of the weight function on the right triangle with the right vertex and the straight line α=β as the hypotenuse.

4. The method according to claim 1, wherein S3 specifically includes: S31, discretizing the weight function μ(α, β) in the discrete battery hysteresis characteristic model; S32. Based on the experimental data obtained from the first-order rotation curve test of the battery, the constrained linear least squares method is used to perform parameter identification on the discretized weight function μ(α, β), and the discretized weight function is solved to obtain the target battery hysteresis characteristic model.

5. The method according to claim 4, wherein S32 specifically includes: S321, setting the objective function to the sum of squares of the errors between the measured OCV in the first-order rotation curve and the OCV predicted by the discrete battery hysteresis characteristic model; S322. Set constraints including boundary constraints and inequality constraints; wherein the boundary constraint is: v(α)≥0; the inequality constraint is: ∫∫ T(α,β) μ(α,β)dαdβ≥0; where T(α,β) is a right triangle with (α,β) as its vertex and the line α=β as its hypotenuse; S323 . Solve the discretized weight function in the discrete battery hysteresis characteristic model based on the objective function and the constraint conditions to obtain a target battery hysteresis characteristic model.

6. A battery SOC estimation method, characterized in that: include: Establishing an equivalent circuit model of the battery to be tested and identifying model parameters, wherein the OCV in the equivalent circuit model is divided into a reversible component OCV2 and an irreversible component OCV1; wherein OCV1 is obtained from the historical charge and discharge turning points of the battery to be tested and a target battery hysteresis characteristic model, wherein the target battery hysteresis characteristic model is constructed using the method for battery hysteresis characteristic modeling according to any one of claims 1 to 5; Obtaining an OCV2-SOC relationship of the battery to be tested according to the target battery hysteresis characteristic model; A spatial state equation is established based on the equivalent circuit model, and the OCV2-SOC relationship OCV2=f(SOC) is used as the observation equation. The SOC of the battery to be tested is estimated by combining the state space equation and the observation equation through a filtering algorithm.

7. A battery matching method, characterized in that: include: Obtaining an OCV2-SOC relationship of the battery to be tested according to the target battery hysteresis characteristic model; The target battery hysteresis characteristic model is constructed by using the method for modeling battery hysteresis characteristics according to any one of claims 1 to 5; The difference in OCV2 between different batteries under test at the same SOC is calculated according to the OCV2-SOC relationship of the battery under test. Different batteries under test with the difference less than a threshold are determined to have consistent performance and are matched.

8. A device for modeling battery hysteresis characteristics, characterized in that: include: The model building module is used to model the battery hysteresis characteristics to obtain an initial model, and discretize the initial model to obtain a discrete battery hysteresis characteristic model; the initial model is: OCV1(t)=∫∫ 0≤α＜β≤1 μ(a,b)γ αβ [SOC(t)]dαdβ OCV2(t)=∫0 1 v(a)c αα [SOC(t)]dα Among them, OCV max and OCV min are the maximum and minimum values ​​of OCV, the battery SOC is the model input, and the battery OCV is the model output. OCV1(t) and OCV2(t) represent the irreversible and reversible components of OCV change, respectively. The irreversible component represents the OCV change caused by the hysteresis effect, and the reversible component represents the OCV change caused by the change in lithium concentration. γ αβ and γ αα is the hysteresis operator, γ αβ is finite width, γ αα is zero width, μ(α,β) and ν(α) are weight functions used to measure the contribution of each hysteresis operator to the output, and α and β are the thresholds of the input in the descending and ascending directions respectively; The curve acquisition module is used to measure the OCV and SOC when the battery charge and discharge direction changes only once, and obtain the battery's first-order rotation curve; The parameter identification module is used to perform parameter identification on the discrete battery hysteresis characteristic model based on the battery first-order rotation curve to obtain a target battery hysteresis characteristic model.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to implement the method for modeling battery hysteresis characteristics according to any one of claims 1 to 5 when executed.

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