Lithium iron phosphate battery soc estimation method, storage medium and program product

Abstract

The present application relates to the field of new energy, especially to a lithium iron phosphate battery SOC estimation method, a storage medium and a program product, wherein the method comprises the following steps: step S1, building an electric force coupling model under the influence of multiple factors, and obtaining the electric force coupling model under the influence of multiple factors in the charging and discharging conditions of the battery cell; step S2, analyzing the stress condition of the battery module during operation, establishing a module mechanical model, and obtaining the expansion force Fms of the single battery cell; step S3, obtaining the battery SOC estimation model, and correspondingly obtaining the battery SOC estimation model under the charging and discharging conditions; step S4, dynamically estimating the battery SOC in real time according to the battery SOC estimation model. The present application has the advantages of effectively improving the estimation accuracy of the battery cell state of charge, and is efficient in calculation, low in data demand, and high in estimation accuracy.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of new energy, in particular to a lithium iron phosphate battery SOC estimation method, a storage medium and a program product. BACKGROUND

[0002] In the prior art, there are four mainstream methods for battery SOC estimation, including traditional ampere-hour integration method, cell OCV lookup table method, filtering estimation method and big data neural network method. Among them, the traditional ampere-hour integration method has low estimation accuracy due to inaccurate current sampling and unpredictable initial state of the cell; the cell OCV lookup table method needs to keep the cell for a long enough time to obtain the open circuit voltage, and cannot realize dynamic estimation of the SOC value; the filtering estimation method depends on the accuracy of the cell model, and needs to repeatedly iterate and optimize the model accuracy, so the calculation space is large and the robustness is poor; and the big data neural network method depends on the amount of input data, and when the input data has errors, it cannot be directly diagnosed, so the development cost is high, the cycle is long, and the reliability is poor. SUMMARY

[0003] To overcome the shortcomings of the prior art, the present application provides a lithium iron phosphate battery SOC estimation method, a storage medium and a program product, which can effectively improve the estimation accuracy of the cell state of charge, and is efficient in calculation, low in data demand and high in estimation accuracy.

[0004] Firstly, the present application also discloses a lithium iron phosphate battery SOC estimation method, a lithium iron phosphate battery module comprising a plurality of lithium iron phosphate cells, referred to as cells, the method comprising the following steps S1 to S3:

[0005] Step S1, build a cell electro-mechanical coupling model under the influence of multiple factors as shown in the following formula (9), wherein the multiple factors include temperature t, cycle number cyc and expansion force change amount AF; and obtain the electro-mechanical coupling model of the cell under the influence of multiple factors under charging and discharging conditions accordingly;

[0006] AF(cyc,t,SOC)=[∫(a2∙cyc 2 +b2∙cyc+c2)d(cyc)]*[∫(a1∙t+b1)dt]*f(SOC 3 ) (9);

[0007] Wherein, SOC is the state of charge of the battery, i.e. the remaining capacity; a1, b1, a2, b2 and c2 are model parameters;

[0008] Step S2, analyze the stress condition of the battery module during operation, establish a mechanical model of the module, and obtain a single cell swelling force Fms as follows: Fms=Fm-Fy-a3*ln(x) (14), wherein the battery module includes a plurality of cells, and the battery module is referred to as a module; wherein Fm is the stress of the cell in the module, Fy is the initial pre-tightening force, a3 is a fitting coefficient, and x is the number of cells in the module;

[0009] Fms=Fm-Fy-a3*ln(x) (14);

[0010] Step S3, obtain a battery SOC estimation model, and correspondingly obtain a battery SOC estimation model under charging and discharging conditions;

[0011] Step S4, obtain the single cell swelling force variation in the battery module according to the single cell swelling force Fms in the battery module, correct the initial value of the single cell swelling force variation in the battery module online, and thus dynamically estimate the battery SOC in real time.

[0012] 2. Further, the step S4 includes:

[0013] Step S41, obtain an initial value for calculating the swelling force variation at the current time according to the charging and discharging state of the cell in the module;

[0014] Step S42, obtain the cell swelling force variation at the current time according to the initial value of the swelling force obtained in step S41;

[0015] S43, obtain the battery SOC at the current time according to the battery SOC estimation model at the current time;

[0016] Step S44, obtain an initial value for calculating the swelling force variation at the next time according to the charging and discharging state of the cell in the module, thereby obtaining the cell swelling force variation at the next time, and further obtaining the battery SOC at the next time.

[0017] Further, the electro-mechanical coupling model under the charging and discharging conditions of the cell under the influence of multiple factors is shown as formulas (9-1) and (9-2) respectively:

[0018] ΔF_char(cyc,t,SOC)=[∫(a21∙cyc 2 +b21∙cyc+c21)d(cyc)]*[∫(a11∙t+b11)dt]*f(SOC 3 ) (9-1);

[0019] ΔF_disc(cyc,t,SOC)=[∫(a22∙cyc 2 +b22∙cyc+c22)d(cyc)]*[∫(a12∙t+b12)dt]*f(SOC3 ) (9-2);

[0020] Wherein, a21, b21, c21, a11, b11 are characteristic parameters of the electric core charging electro-mechanical coupling model based on multi-factor influence; a22, b22, c22, a12, b12 are characteristic parameters of the electric core discharging electro-mechanical coupling model based on multi-factor influence.

[0021] 3, further, the step S1 includes: by the electric core positive electrode phase change is monotonized, take the electric core positive electrode phase change scalar and the electric core negative electrode phase change scalar and obtains the electric core expansion force change amount by the weighted coupling calculation as shown in formula (3):

[0022] (3);

[0023] As shown in formula (3) above can be changed into formula (4) as follows:

[0024] (4);

[0025] Wherein, a, b, c, d are the relationship fitting coefficients of the electric core expansion force change amount ΔF about SOC; the electric core expansion force change amount ΔF and the temperature t, the battery SOC exist relationship as shown in formula (7):

[0026] (7);

[0027] Wherein, a1, b1 are fitting coefficients, ΔT is the temperature change amount, t is the temperature;

[0028] The electric core expansion force change amount ΔF and the temperature t, the SOC exist relationship as shown in formula (8):

[0029] (8);

[0030] Wherein, a2, b2, c2 are the relationship fitting coefficients of the expansion force change amount about the cycle number;

[0031] Considering the influence of temperature, cycle number, electric core expansion force change amount on SOC, the formula (9) can be obtained, the right side of the formula (9) is the product of the right side of the formula (7) and the right side of the formula (8).

[0032] Further, the electric core charging electro-mechanical coupling model under the influence of multiple factors is shown in formula (10):

[0033] ​​​​ΔF_char(SOC, t, cyc) = (100 + 0.6519 * cyc - 0.0013 * cyc 2 + 3.002 * 10 -5 *cyc 3 )*(22.23 - 0.7811 * t + 1.268 * 10 -14 *t 2 )*(40.45 + 641.9 * SOC - 1055.7 * SOC 2 + 533.96 * SOC 3 ) (10).

[0034] Further, the electric-mechanical coupling model of the cell discharge under the influence of multiple factors is shown in formula (11):

[0035] ΔF_disc(SOC, t, cyc) = (100 + 0.02366 * cyc - 2.42 * 10 -5 *cyc 2 + 8.039 * 10 -7 *cyc 3 )*(86.22 - 0.72319 * t + 2.023 * 10 -14 *t 2 )*(57.55 + 117.14 * SOC - 165.15 * SOC 2 + 95.67 * SOC 3 ) (11).

[0036] Further, the expansion force variation ΔF can be obtained by testing the cell expansion force F under different SOC, and then obtained by formula (5) as follows:

[0037] (5).

[0038] 4、Further, the step S2 comprises:

[0039] Step S21, considering the influence of the initial pre-tightening force on the cells in the module, the relationship between Fcs and Fm and Fy is obtained as formula (12) as follows:

[0040] (12);

[0041] Wherein, Fcs is the expansion force of the cells in the module during the cycle process;

[0042] Step S22, considering the superposition effect of the expansion forces of the multiple cells in the module, the expansion force of the cells in the module increases in a logarithmic function, and the relationship between the expansion force Fcs of the cells in the module during the cycle process and the single cell expansion force Fms is shown in formula (13) as follows:

[0043] (13);

[0044] Step S23, considering the initial pre-tightening force and the superimposed influence of the expansion forces of multiple cells in the module, the single-cell expansion force Fms is obtained according to formula (12) and (13) as shown in the following formula (14);

[0045] Fms (14).

[0046] Secondly, the application further discloses a storage medium, which has a computer program stored thereon, and the computer program is executed by a processor to realize the method.

[0047] Furthermore, the application further discloses a program product, which is executed by a processor to realize the method.

[0048] The application has the following beneficial effects:

[0049] Firstly, the influences of different temperatures and different cycle numbers on the expansion force of the cell are considered, and the two influence factors are coupled, and a cell electric-force coupling model considering multiple factors is established, that is, a general expansion force change-SOC model, which improves the transferability of the model and the accuracy of the battery SOC estimation in the long life cycle.

[0050] Secondly, the concept of cell expansion force change is introduced to linearize the nonlinear expansion force-SOC curve. And since the expansion force change is more sensitive to the change of SOC, it has higher accuracy for estimating SOC. At the same time, the strategy of real-time correction of the initial value of the expansion force change is adopted, which improves the adaptability to complex working conditions and the accuracy of the model.

[0051] Furthermore, the differences between multiple-cell grouping (battery module) and single-cell expansion force are considered, and the module mechanical model is established to analyze the stress and force superposition, so as to decompose the single-cell expansion force from the collected module stress, provide correct input for the battery SOC estimation model, and improve the practicability of the expansion force change estimation of the battery SOC in the module or system.

[0052] These features and advantages of the application will be disclosed in detail in the following specific embodiments and drawings. BRIEF DESCRIPTION OF DRAWINGS

[0053] The application will be further described below in combination with the drawings:

[0054] Figure 1 The flow chart for lithium iron phosphate (LFP) battery SOC estimation;

[0055] Figure 2A schematic diagram of the relationship between the expansion force of the LFP battery and the SOC;

[0056] Figure 3 A schematic diagram of the relationship between the expansion force change amount AF of the LFP battery and the SOC;

[0057] Figure 4 A schematic diagram of the relationship between the expansion force change amount of the LFP battery cell and the SOC at different temperatures during charging;

[0058] Figure 5 A schematic diagram of the relationship between the expansion force change amount of the LFP battery cell and the SOC at different temperatures during discharging;

[0059] Figure 6 A schematic diagram of the relationship between the expansion force of the LFP battery cell and the SOC at different cycle times during charging;

[0060] Figure 7 A schematic diagram of the relationship between the expansion force of the LFP battery cell and the SOC at different cycle times during discharging;

[0061] Figure 8 A schematic diagram of the relationship between the cycle times and the peak value of the expansion force of the LFP battery cell;

[0062] Figure 9 A schematic diagram of the relationship between the expansion force change amount of the LFP battery cell and the SOC at different cycle times during discharging;

[0063] Figure 10 A schematic diagram of the relationship between the expansion force change amount of the LFP battery cell and the SOC at different cycle times during charging;

[0064] Figure 11 A schematic diagram of the mechanical analysis of the module;

[0065] Figure 12 A schematic diagram of the relationship between the number of battery cells and the expansion force of the module;

[0066] Figure 13 A flowchart of the online correction of the initial value of the expansion force change amount for the SOC estimation of the LFP battery;

[0067] Figure 14 A schematic diagram of the real value and the estimated value of the SOC of the LFP battery under full charging and discharging conditions;

[0068] Figure 15 A schematic diagram of the absolute value of the error of the SOC of the LFP battery under full charging and discharging conditions;

[0069] Figure 16 A schematic diagram of the real value and the estimated value of the SOC of the LFP battery under intermittent charging and discharging conditions;

[0070] Figure 17 A schematic diagram of the error of the SOC of the LFP battery under intermittent charging and discharging conditions. DETAILED DESCRIPTION

[0071] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application.

[0072] Unless otherwise specified, the battery cell in the present application is a lithium iron phosphate battery cell, i.e., an LFP battery cell.

[0073] The SOC estimation method of the lithium iron phosphate battery module of the present application comprises the following steps S1-S3.

[0074] Step S1: Build an electric-mechanical coupling model of the battery cell under the influence of multiple factors as shown in the following formula (9), wherein the multiple factors include temperature t, cycle number cyc, and expansion force change amount ΔF; and obtain the electric-mechanical coupling model of the battery cell under the influence of multiple factors under charging and the electric-mechanical coupling model of the battery cell under the influence of multiple factors under discharging.

[0075] As can be understood, during the charging and discharging process of the battery cell, the expansion volume of the battery cell will change with the change of lithium ion concentration due to the increase of the interlayer spacing of the negative electrode material and the phase change of the positive and negative electrode material structure of the battery cell. The reaction is manifested in the macroscopic performance, i.e., the expansion volume of the battery cell and the battery SOC are related. However, due to the non-monotonicity of the phase change of the positive electrode material of the lithium iron phosphate battery cell (LFP battery cell), the expansion force and the battery SOC are nonlinear, and directly applying the expansion force to the SOC estimation field has great challenges. The present application linearizes the nonlinear characteristics of the expansion force-SOC of the battery cell by using the concept of expansion force change amount, i.e., the numerical value of the change of the expansion force of the battery cell with the change of SOC. At the same time, considering the influence of environmental temperature and cycle number on the expansion force of the battery cell, the electric-mechanical coupling model of the battery cell considering the influence of multiple factors is built to improve the environmental adaptability and transferability of the model.

[0076] For the establishment of the mechanical model of the battery module (referred to as module), considering the actual application scene of the battery cell, the battery cell in the module will increase the expansion force detected by the sensor due to the effect of the pre-tightening force and the increase of the current density and volume. Therefore, the present application establishes a mechanical model of the module by analyzing the mechanics of the module and considering the space and heat generation effect of the superposition of multiple battery cells.

[0077] As Figure 1The battery SOC estimation with online correction of the initial value of the expansion force change amount is shown. The present application realizes battery SOC estimation based on the above-mentioned analysis of the single cell expansion force and the cell expansion force-SOC model under different environments (temperature) and cycle times. Due to the difference between the charge and discharge expansion force change amount-SOC model, it is necessary to judge the state of the cell in real time, otherwise a large estimation error will be caused. Therefore, the present application adopts the online initial value correction method to correct the cell expansion force change amount in real time, obtain the initial value of the cell expansion force change amount at each moment, and improve the adaptability of the estimation model under complex working conditions. Finally, the corrected expansion force change amount at each moment is taken as the input of the cell electro-mechanical coupling model considering multiple factors to obtain a more accurate SOC estimation value at each moment.

[0078] The operation process of the battery SOC estimation with online correction of the initial value of the expansion force change amount is as follows: based on the electro-mechanical coupling model and the SOC at the last moment, the initial value of the expansion force change amount is calculated; based on the current cell expansion force, the current cell expansion force change amount is calculated; based on the current charge and discharge state and the electro-mechanical coupling model, the current SOC is obtained; the initial value of the expansion force change amount is updated in a loop to obtain the SOC at each moment until the expansion force change amount record is complete.

[0079] Considering the diffusion-induced stress caused by the lithium concentration of electrode particles during the electrochemical reaction process, the following formula (1) can be obtained from the stress-strain relationship:

[0080] (1);

[0081] wherein, represents the normal expansion stress of the cell, and represents the radial expansion stress of the cell, represents the Poisson ratio, represents the Dirac delta function, and E represents the elastic modulus of the cell, represents the relationship between the expansion volume change rate of the cell and the solid-phase lithium ion concentration The mechanism of the cell diffusion-induced stress is shown here. The present application mainly explores the relationship between the battery SOC and the expansion force, and therefore only the effect of the cell diffusion-induced stress is considered here.

[0082] Related to the change of the lithium ion concentration of the cell, when the cell is charged, the lithium ions in the positive electrode material are released and embedded in the interlayer gap, and the concentration difference between the positive and negative electrodes causes the increase of the interlayer spacing of the negative electrode material; when the cell is discharged, the lithium ions move to the positive electrode, and the volume of the cell shrinks. At the same time, the positive electrode material of the lithium iron phosphate cell also undergoes a phase change from a crystalline state to a non-crystalline state. The phase change of the positive and negative electrode materials together causes the change of the expansion volume of the cell.

[0083] The above mechanism belongs to the working property of the battery cell. From a macroscopic point of view, the battery cell expansion volume and SOC have a constant changing trend. According to formula (1), the battery cell expansion force and battery SOC have a stable changing trend, such as Figure 2 As shown in the figure, the overall change trend is as follows: when the battery SOC increases from 0 to 30% SOC_R, the cell expansion force increases rapidly from 1600N to 5500N; when the battery SOC increases from 30% SOC_R to 60% SOC_R, the cell expansion force decreases from 5500N to 4500N; when the battery SOC increases from 60% SOC_R to 100% SOC_R, the cell expansion force increases slowly again from 4500N to about 5400N; where SOC_R is the rated value of the battery SOC; In addition, it should be noted that, if Figure 2 As shown in the figure, the cell expansion force has a small peak when the battery SOC is about 85% SOC_R. This is because the load here becomes smaller under actual working conditions, and it should not be considered to affect the overall change trend.

[0084] According to the mechanism of expansion force formation, the change in cell expansion volume is caused by the combined effect of phase transitions in the positive and negative electrode materials. Due to the differences in phase transitions between the positive and negative electrode materials: the positive electrode material of lithium iron phosphate cells has an olivine structure. In the battery SOC range of 30% SOC_R to 60% SOC_R, the volume of the positive electrode material of lithium iron phosphate cells shows a significant contraction trend, while the volume change of the negative electrode material of lithium iron phosphate cells is smaller, but still a monotonically increasing trend. Therefore, when the battery SOC is between 30% SOC_R and 60% SOC_R, the cell expansion force shows a downward trend, or in other words, as the battery SOC increases, the cell expansion force decreases. In contrast, in the battery SOC ranges of 0% to 30% SOC_R and 60SOC_R to 100% SOC_R, the negative electrode of lithium iron phosphate cells expands more significantly, while the positive electrode expands slightly. Therefore, the cell expansion force shows an upward trend, that is, as the battery SOC increases, the cell expansion force increases. It can be seen that when the battery SOC is in the range of 0% to 100% SOC_R, the combined effect of the positive and negative electrode materials of the lithium iron phosphate battery (or the combined effect of the positive and negative electrode phase changes) forms a unique nonlinear and non-monotonic expansion force change curve for the lithium iron phosphate battery. Therefore, the relationship between the nonlinear and non-monotonic cell expansion force and the battery SOC can be described as formula (2):

[0085] (2);

[0086] in, and are the weights of the positive and negative electrodes of the cell in the expansion force formation as the SOC changes, F, 、 They are the expansion force of the battery cell, the expansion force of the positive electrode of the battery cell, and the expansion force of the negative electrode of the battery cell. , i.e. a function of, , i.e. a function of, the positive electrode phase transition and the battery SOC present a non-monotonic relationship; the negative electrode phase transition and the battery SOC present a monotonic increasing relationship.

[0087] Due to the non-monotonic relationship of the positive electrode phase transition of the battery cell, the battery cell expansion force finally presents a non-monotonic nonlinear change, which increases the application difficulty of the battery cell expansion force. The present application processes the positive electrode phase transition of the battery cell to be monotonic, and obtains the battery cell expansion force change amount by weighting and coupling calculation of the positive electrode phase transition scalar of the battery cell and the negative electrode phase transition scalar of the battery cell, i.e. as follows formula (3):

[0088] (3);

[0089] As shown in the above formula (3), it can be transformed into the following formula (4):

[0090] (4);

[0091] Wherein, a, b, c, d are the relationship fitting coefficients of the battery cell expansion force change amount ΔF about SOC, which are model parameters, that is, characteristic parameters, or called model characteristic parameters (abbreviation parameters). When the model is established, the battery cell expansion force change amount ΔF is obtained by testing the battery cell expansion force F, the characteristics reflected by the battery cell expansion force F are learned, the battery cell expansion force change amount ΔF is linearly fitted with the measured corresponding battery SOC value, the parameter identification and confirmation are realized, that is, the specific values of a, b, c, d are obtained.

[0092] As shown in the above formula (3), it can be transformed into the following formula (4): Figure 3 The relationship curve of the battery cell expansion force change amount ΔF and the battery SOC is shown in the figure, the battery cell expansion force change amount and the battery SOC are one-to-one corresponding, and present a monotonic increasing relationship. The expression of the battery cell expansion force change amount ΔF is:

[0093] (5);

[0094] ​​​​As the above formula (5) reflects the cell expansion force variation amount ΔF is the scalar value of the cell expansion force F changes with SOC, since the cell expansion force variation amount ΔF cannot be directly measured, can be obtained by testing the cell expansion force F under different SOC, then according to formula (5) to get the cell expansion force variation amount ΔF, the cell expansion force variation amount ΔF and the measured SOC together to fit the a, b, c, d in formula (4). In addition, since the differentiation of F is carried out, the test error of the cell expansion force sensor can be ignored. As can be seen from the above description, the introduction of the cell expansion force variation amount ΔF not only linearizes the cell expansion force F, but also reduces the risk of inaccurate SOC estimation due to sensor acquisition error.

[0095] To enhance the environmental adaptability of the model and improve the accuracy of the model, the present application further considers the change trend of the cell expansion force and its variation amount under the influence of environmental temperature (referred to as temperature) and aging (cycle number), and builds a cell electro-mechanical coupling model based on multiple factors. By collecting the data of the cell expansion force under different temperatures (for example, 25℃, 35℃ and 45℃), it is found that the cell expansion force and the cell expansion force variation amount increase with the increase of the environmental temperature. The reason for this phenomenon is that the increase of temperature leads to the expansion of the cell material, and at the same time, the increase of temperature reduces the internal resistance of the cell, which increases the discharge current of the cell and further increases the internal pressure.

[0096] First, consider the effect of temperature on the cell expansion force. The test results of the cell expansion force under different temperatures (for example, 25℃, 35℃ and 45℃) are shown in Figure 4 、 Figure 5 From the test data of the cell expansion force under different temperatures, it can be seen that the temperature and the cell expansion force variation amount-SOC show a monotonically increasing and linear trend, or in other words, the cell expansion force variation amount under the same SOC shows a monotonically increasing and linear trend with temperature (for example, under the same SOC, the higher the temperature, the greater the cell expansion force variation amount), therefore the cell expansion force variation amount ΔF and the temperature variation amount ΔT, the battery SOC exist relationship as shown in formula (6):

[0097] (6) ;

[0098] From formula (6), the relationship between the cell expansion force variation amount ΔF and the temperature t, the battery SOC is shown in formula (7):

[0099] (7) ;

[0100] Wherein, a1, b1 are fitting coefficients, ΔT is the temperature variation amount, t is the temperature.

[0101] Secondly, as the cycle number of the battery cell increases, the aging degree of the battery cell deepens. The aging degree of the battery cell and the expansion force of the battery cell are positively correlated. This is because, on the one hand, the battery cell accumulates a certain thickness of SEI (Solid Electrolyte Interface) film on the electrode surface after aging, which increases the expansion volume, and on the other hand, as the aging degree increases, the heat and gas production of the chemical reaction inside the battery cell increases, causing the internal pressure of the battery cell to increase.

[0102] Therefore, in order to adapt to the changes of the battery cell in the long life cycle and increase the accuracy of the battery SOC estimation, the influence of the aging of the battery cell on the expansion force of the battery cell and the change amount thereof is crucial. Through testing, the change trend of the expansion force of the battery cell with the cycle number during the long life cycle of the battery cell can be obtained. Figure 6 / Figure 7 The change of the expansion force of the battery cell at 200 cycles, 300 cycles, 600 cycles and 1000 cycles under the charging / discharging condition is shown, Figure 8 The change of the peak value of the expansion force of the battery cell with the cycle number is shown every 50 cycles until about 2500 cycles. From Figure 6 、 Figure 7 、 Figure 8 It can be seen that the expansion force of the battery cell increases with the cycle number, the change trend of the entire expansion force-SOC curve is roughly unchanged, and the overall translation is upward, the peak protrusion is more serious, and the peak value of the expansion force of the battery cell is about 30% SOC_R of the battery SOC. For example, Figure 9 and Figure 10 , respectively show the relationship between the change amount of the expansion force of the battery cell and the battery SOC at different cycle numbers in the charging and discharging processes of the battery cell. According to Figure 8 It can be seen that the relationship between the peak value of the expansion force of the battery cell and the cycle number satisfies a quadratic polynomial model, therefore, the relationship curve between the change amount of the expansion force of the battery cell and the SOC at different cycle numbers can be expressed as formula (8), or in other words, the relationship between the change amount of the expansion force of the battery cell ΔF and the temperature t, the SOC is as shown in formula (8): wherein the three parameters a2, b2, c2 in formula (8) can be fitted by testing the cycle number, the expansion force (the change amount of the expansion force is obtained according to formula (5)), and the SOC.

[0103] (8);

[0104] In formula (8), a2, b2, c2 are fitting coefficients of the relationship between the change amount of the expansion force and the cycle number, are model parameters, or in other words, characteristic parameters, and are simply referred to as parameters; cyc is the cycle number; and Δcyc is the change amount of the cycle number. When the model is established, the characteristics reflected by the expansion force of the battery cell need to be learned through the measurement of the change amount of the expansion force of the battery cell, that is, the linear fitting of the cycle number and the actual measurement data is realized to achieve parameter identification and confirmation.

[0105] The SOC-variation-in-expansion-force-temperature-cyc relationship curve and the SOC-variation-in-expansion-force-cyc relationship curve are combined to build an electric-force coupling model of the battery cell considering the influence of multiple factors (temperature, cycle number, etc.), as shown in the following formula (9):

[0106] ΔF(cyc,t,SOC)=[∫(a2∙cyc 2 +b2∙cyc+c2)d(cyc)]*[∫(a1∙t+b1)dt]*f(SOC 3 ) (9);

[0107] In the formula, t is the temperature, and cyc is the cycle number.

[0108] Due to the difference in lithium ion concentration inside the battery cell under different charging and discharging conditions and the difference in structure phase change of the positive and negative electrode materials, the expansion force of the charging and discharging battery cells is different, so the electric-force coupling model of the battery cell needs to be divided into charging and discharging for separate calculation.

[0109] In one embodiment, the electric-force coupling model of the battery cell charging based on multiple factors is formula (9-1):

[0110] ΔF_char(cyc,t,SOC)=[∫(a21∙cyc 2 +b21∙cyc+c21)d(cyc)]*[∫(a11∙t+b11)dt]*f(SOC 3 ) (9-1);

[0111] Wherein a21, b21, c21, a11, b11 are characteristic parameters of the electric-force coupling model of the battery cell charging based on multiple factors.

[0112] In one embodiment, the electric-force coupling model of the battery cell discharging based on multiple factors is formula (9-2):

[0113] ΔF_disc(cyc,t,SOC)=[∫(a22∙cyc 2 +b22∙cyc+c22)d(cyc)]*[∫(a12∙t+b12)dt]*f(SOC 3 ) (9-2);

[0114] Wherein a22, b22, c22, a12, b12 are characteristic parameters of the electric-force coupling model of the battery cell discharging based on multiple factors.

[0115] The change of the expansion force of the battery cell under several typical temperature conditions (25 DEG C, 45 DEG C, 35 DEG C) and different cycle times can be measured to build the battery cell electric-force coupling model considering temperature and aging degree. The model is built based on the expansion mechanism of the battery cell, the temperature influence and the aging influence, is stable and reliable compared with the neural network large model, has fewer model calculation parameters, is different from the defects that the large model requires more parameters and depends on more input data, has less data requirement of the physical model, reduces the research and development cost, and is suitable for application in the project with short research and development cycle.

[0116] In one embodiment, the expansion force data under different temperature (25 DEG C, 35 DEG C and 45 DEG C) conditions obtained by testing and the expansion force data of the battery cell in the long-life cycle test and the above electric-force coupling model can be used to calculate the relationship between the change amount of the expansion force of the battery cell, the temperature, the cycle number and the SOC as shown in the following formula (10) and formula (11):

[0117] The battery cell charging electric-force coupling model based on multiple factors is formula (10):

[0118] Delta F_char (SOC, t, cyc) = (100 + 0.6519 * cyc - 0.0013 * cyc 2 + 3.002 * 10 -5 *cyc 3 ) * (22.23 - 0.7811 * t + 1.268 * 10 -14 *t 2 ) * (40.45 + 641.9 * SOC - 1055.7 * SOC 2 + 533.96 * SOC 3 ) (10) ;

[0119] The battery cell discharging electric-force coupling model based on multiple factors is formula (11):

[0120] Delta F_disc (SOC, t, cyc) = (100 + 0.02366 * cyc - 2.42 * 10 -5 *cyc 2 + 8.039 * 10 -7 *cyc 3 ) * (86.22 - 0.72319 * t + 2.023 * 10 -14 *t 2 ) * (57.55 + 117.14 * SOC - 165.15 * SOC 2 + 95.67 * SOC 3 ) (11) ;

[0121] The temperature, the cycle number and the expansion force change amount are taken as input conditions, and the battery SOC can be reversely output according to the established cell electro-mechanical coupling model, that is, the battery SOC is obtained. Therefore, the battery SOC is estimated by the method. In addition, the temperature, the cycle number and the current SOC are taken as inputs, and the cell expansion force change amount is forward searched (that is, it is judged whether the expansion force change amount is increased or decreased, if it is increased, the battery is in a charging state, and if it is decreased, the battery is in a discharging state), which is used for correcting the initial value and providing conditions for the subsequently proposed battery SOC estimation strategy based on the initial value correction of the expansion force. The establishment of the cell electro-mechanical coupling model under the influence of multiple factors improves the model transferability and the accuracy of the battery SOC estimation in the long life cycle.

[0122] Step S2: analyzing the stress condition of the battery module during operation, establishing a module mechanical model, and obtaining the single cell expansion force Fms.

[0123] As shown in Figure 11 , the battery module mechanical analysis needs to consider two aspects of influence, one is the pre-tightening force applied to the battery module, and the other is the superposition of the expansion force of the multiple cells in the battery module after being affected by the space and current density.

[0124] From Figure 11 the module mechanical analysis diagram, it can be known that the cells in the module are mainly affected by the pre-tightening force and the expansion force. If the module has not worked, the cells in the module do not perform electrochemical reaction, and thus do not expand and deform. Assuming that the pre-tightening force Fy is uniformly transmitted, the output value of the pressure sensor is Fy. If the module is in a cycle, assuming that the 3# cell (3# Cell in Figure 11 ) and the 5# cell (5# Cell in Figure 11 ) all expand and deform to different degrees, the cell expansion deformation generates an expansion force and transmits it to the adjacent two sides, the end plate, the steel belt and other buffer structures in the module slowly deform under the action of the cell expansion force and absorb part of the expansion force, and the cells finally reach force balance in the process. Therefore, at this time, the force Fm of the 4# cell (4# Cell in Figure 11 ) is Fy+Fcs; wherein Fy is the initial pre-tightening force of the battery module, that is, the pre-tightening force applied to the battery module, simply referred to as the initial pre-tightening force, Fcs is the expansion force of the cells in the module in the cycle process, and Fm is the force of the cells in the module when the force is balanced, that is, the detection value of the pressure sensor, that is, the stress of the cells in the module, or in other words, the stress of the cells in the module can be detected by the sensor. Here, the superposition of the multiple cells is not considered, and only the influence of the initial pre-tightening force Fy on the cells in the module is considered, and the relationship among the expansion force Fcs of the cells in the module in the cycle process, the force Fm of the cells in the module when the force is balanced and the initial pre-tightening force Fy is as follows:

[0125] (12);

[0126] Since the initial preload force Fy of the battery module is applied according to a fixed value when the battery cells are grouped, under normal circumstances, the applied preload force (i.e., the initial preload force of the battery module) Fy is 2000N. It is understandable that the applied preload force Fy may also be other values, which can be determined by referring to the corresponding specifications.

[0127] Next, consider the superposition effect of the expansion force of multiple cells in the module. The experimental test results show that the change of the expansion force of multiple cells is mainly affected by the number of cells and has nothing to do with the series and parallel connection of the cells. Figure 12 As shown in Figure 1, the relationship curve between the expansion force of the cells in the module and the number of cells in the group increases. As the number of cells in the group increases, the total volume of the cells increases, and the heat and expansion generated inside the cells also increase. Therefore, as the number of cells increases, the expansion force of the cells in the module increases in a logarithmic function. The relationship between the expansion force Fcs of the cells in the module (single cell) during the cycle and the expansion force Fms of the cells in the battery module (i.e., the expansion force of the single cell) is shown in Formula (13):

[0128] (13);

[0129] Among them, a3 is the fitting coefficient, x is the number of battery cells in the module, and Fms is the expansion force of a single battery cell in the battery module, referred to as single-cell expansion force, which can be obtained by testing.

[0130] Based on the force analysis of the cells in the above two modules (i.e., the battery modules corresponding to formulas (12) and (13) respectively), the expansion force Fms of a single cell in the battery module can be calculated by the following formula:

[0131] Fms=Fm-Fy-a3*ln(x) (14);

[0132] By accounting for the effects of preload and multi-cell expansion force, the cell stress Fm within the module, as detected by the pressure sensor, can be converted into the single-cell expansion force Fms within the module. This facilitates the estimation of battery SOC at the battery module application level by leveraging the relationship between single-cell expansion force Fms and battery SOC measured in the laboratory. Furthermore, since the increased expansion force after grouping multiple cells is primarily due to increased internal thermal effects and is unrelated to the cell's lithium ion concentration, the relationship between cell expansion force and SOC remains unchanged, with the cell expansion force increasing uniformly across the entire SOC range.

[0133] The step S2 considers the difference between the module expansion force and the single cell expansion force. By analyzing the stress condition of the module during operation, a mechanical model of the module is established. By subdividing the stress of the cell and superimposing the force of multiple cells, a mechanical model from the cell to the module is constructed, realizing the collection and application of the cell expansion force, and providing conditions for the application of the present application in the module. Meanwhile, the difference between the multiple cell grouping and the single cell expansion force is considered, and by establishing a mechanical model of the module, stress analysis and force superposition analysis are carried out, the single cell expansion force is decomposed from the collected module stress, the correct input is provided for the battery SOC estimation model, and the practicability of estimating the battery SOC by the expansion force change in the module is improved.

[0134] Step S3, obtaining a battery SOC estimation model, and respectively obtaining a battery SOC estimation model under charging and a battery SOC estimation model under discharging.

[0135] Step S31, replacing ΔF in the foregoing formula (9) with the single cell expansion force change ΔFms in the battery module to obtain a battery SOC estimation model as follows formula (15):

[0136] (15);

[0137] Step S32, replacing ΔF_char in the foregoing formula (9-1) with ΔFms_char to obtain a battery SOC estimation model under charging as follows formula (15-1):

[0138] (15-1);

[0139] Wherein, ΔFms_char is the single cell expansion force change in the battery module under charging.

[0140] Step S33, replacing ΔF_disc in the foregoing formula (9-2) with ΔFms_disc to obtain a battery SOC estimation model under discharging as follows formula (15-2):

[0141] (15-2);

[0142] Wherein, ΔFms_disc is the single cell expansion force change in the battery module under discharging.

[0143] Correspondingly, ΔF_char and ΔF_disc in formula (10) and (11) are replaced by ΔFms_char and ΔFms_disc respectively, and the battery SOC estimation model under charging and the battery SOC estimation model under discharging with the determined parameters are as shown in the following formula (16) and (17).

[0144] AFms_char(SOC, t, cyc) = (100 + 0.6519 * cyc - 0.0013 * cyc 2 + 3.002 * 10 -5 *cyc 3 ) * (22.23 - 0.7811 * t + 1.268 * 10 -14 *t 2 ) * (40.45 + 641.9 * SOC - 1055.7 * SOC 2 + 533.96 * SOC 3 ) (16);

[0145] The discharge electro-mechanical coupling model of the battery cell based on multiple factors is formula (17):

[0146] AFms_disc(SOC, t, cyc) = (100 + 0.02366 * cyc - 2.42 * 10 -5 *cyc 2 + 8.039 * 10 -7 *cyc 3 ) * (86.22 - 0.72319 * t + 2.023 * 10 -14 *t 2 ) * (57.55 + 117.14 * SOC - 165.15 * SOC 2 + 95.67 * SOC 3 ) (17);

[0147] It should be noted that the order of steps S31, S32 and S33 can be changed, or in other words, the order of the three can be arranged at will.

[0148] Step S4: Obtain the single battery cell expansion force change amount AFms according to the single battery cell expansion force Fms in the battery module, correct the initial value AFms of the single battery cell expansion force change amount, and thus real-time dynamic estimate the battery SOC.

[0149] Due to the lithium iron phosphate battery cell in the charging process, the positive electrode releases electrons, lithium ions on the negative electrode gradually insert into the positive material, and oxygen is discharged, and at the same time, hydrogen and water are generated in the electrolyte reaction, thereby causing internal gas production, so that the expansion force is larger during charging; however, during discharging, the lithium iron phosphate battery cell undergoes an oxidation-reduction reaction, and no gas is generated, so the expansion force is smaller during discharging. Assuming that the battery cell is in a constant current charging or constant current discharging condition, different expansion force change amount-SOC models can be selected according to the charging and discharging state for estimation; however, in actual application, the battery cell cannot always maintain a constant current full charging or constant current full discharging state, but rather a more complex and variable intermittent charging and discharging condition. Therefore, the large difference in the expansion force of the battery cell during charging and discharging under complex and variable conditions poses a certain challenge to the application of the battery SOC estimation algorithm. To solve this problem, the initial value of the expansion force change amount is corrected in real time online to meet the demand for high-precision battery SOC estimation under complex and variable conditions.

[0150] The battery SOC estimation flowchart based on the initial value correction of the expansion force change amount is as shown in Figure 13

[0151] Step S41, according to the charging and discharging state of the battery cell in the module, the initial value for calculating the expansion force change amount at the current time is obtained.

[0152] Specifically, by judging whether the charging and discharging state of the battery cell in the module at the current time and at the last time is consistent. If the current time and the last time remain consistent (i.e., the battery cell is in a charging state at the last time, and is also in a charging state at the current time; or the battery cell is in a discharging state at the last time, and is also in a discharging state at the current time), the expansion force change amount at the last time is used as the initial value for calculating the expansion force change amount at the current time; if not consistent (i.e., the battery cell is in a charging state at the last time, and is in a discharging state at the current time; or the battery cell is in a discharging state at the last time, and is in a charging state at the current time), the current charging and discharging state of the battery cell (i.e., whether the battery cell is in a charging state or a discharging state) needs to be further judged, and the battery state of charge (SOC) at the last time, the cycle number cyc and the temperature t updated in real time are used as the input of the battery SOC estimation model at the current time (if the battery module is in a charging state at the current time, the battery SOC estimation model at the current time is the battery SOC estimation model under the charging condition; if the battery module is in a discharging state at the current time, the battery SOC estimation model at the current time is the battery SOC estimation model under the discharging condition), and the initial value for calculating the expansion force change amount at the current time is output.

[0153] Step S42, the initial value of the expansion force obtained in step S41 is used to obtain the expansion force change amount of the battery cell at the current time.

[0154] ​Specifically, the initial value confirmed in step S41 and the unit time SOC corresponding expansion force change amount are added to calculate the current time cell expansion force change amount, wherein the unit time SOC corresponding expansion force change amount is ΔFmss= current time single cell expansion force Fms2- last time single cell expansion force Fms1, and the single cell expansion force at any time can be measured.

[0155] S43, obtaining the current time battery SOC according to the current time battery SOC estimation model.

[0156] Specifically, the current time temperature t, the current time cycle number cyc and the current time cell expansion force change amount obtained in step S42 are substituted into the current time battery SOC estimation model to obtain the current time battery SOC.

[0157] Step S44, obtaining the initial value for calculating the expansion force change amount at the next time according to the charge and discharge state of the cells in the module, thereby obtaining the cell expansion force change amount at the next time, and further obtaining the battery SOC at the next time.

[0158] It can be understood that the last time in steps S41, S42 and S43 is replaced by the current time, and the current time in steps S41, S42 and S43 is replaced by the next time, which is the specific step of step S44.

[0159] The foregoing battery SOC estimation method can dynamically and accurately estimate the battery SOC at any time according to the charge and discharge state of the cells in the module, and has high real-time performance and high accuracy.

[0160] As Figure 14 , Figure 15 , the error between the estimated battery SOC and the true SOC obtained by the battery SOC estimation method of the present application under a complete charge and discharge cycle condition is shown, from Figure 15 It can be seen that the error between the two obtained by the method is less than 4.5%, and the accuracy is high. Among them, the complete charge and discharge cycle refers to charging the battery from 0 to 100% SOC_R first, and then discharging to 0.

[0161] As Figure 16 , Figure 17 shown, the effect of the SOC estimation method proposed in the present application is verified under the intermittent charge and discharge complex condition of 0% ~ 50% SOC_R-40% SOC_R-50% SOC_R. From Figure 17It can be seen that the maximum error between the battery estimated SOC and the real SOC is 2.5%. Therefore, the present application can be used to solve the battery SOC estimation under complex and variable working conditions, and has strong adaptability and better accuracy. Among them, the intermittent charging and discharging between 0-50% SOC_R-40% SOC_R-50% SOC_R means charging the battery from 0 to 50% SOC_R first, then discharging to 40% SOC_R, and then charging to 50% SOC_R.

[0162] The method of the present application introduces the concept of the change amount of the cell expansion force, linearizes the nonlinear expansion force-SOC curve. And since the change amount of the expansion force is more sensitive to the change of SOC, it has higher accuracy for estimating SOC, at the same time, the strategy of real-time correction using the initial value of the change amount of the expansion force improves the adaptability and model accuracy under complex working conditions.

[0163] In one embodiment, the method of the present application further comprises:

[0164] The battery SOC obtained in step S4 and the battery SOC obtained by the ampere-hour integration method or / and the OCV lookup table method are dynamically weighted by two or three to obtain a weighted battery SOC; for example, in one embodiment, the weighted battery SOC=M1*SOC1+M2*SOC2; in another embodiment, the weighted battery SOC=N1*SOC1+N2*SOC3; in another embodiment, the weighted battery SOC=P1*SOC1+P2*SOC2+P3*SOC3; wherein M1, M2, N1, N2, P1, P2, P3 are weighting coefficients, M1+M2=N1+N2=P1+P2+P3=1; SOC1 is the battery SOC obtained in step S4, SOC2 is the battery SOC obtained by the ampere-hour integration method; SOC3 is the battery SOC obtained by the OCV lookup table method.

[0165] In one embodiment, the method of the present application further comprises:

[0166] The battery SOC output in S4 is used as the input of the battery equivalent circuit model to obtain a first voltage V1, the error E between the first voltage V1 and the cell terminal voltage V2 obtained by testing is obtained, i.e. E=V1-V2, the gain K is dynamically adjusted by using the filter estimation algorithm, the battery SOC is dynamically optimized by the error E and the gain K, and the optimized battery SOC is SOC10, i.e. SOC10=E*K+SOC1, SOC1 is the battery SOC obtained in step S4.

[0167] In one embodiment, the temperature, the cycle number, the battery swelling force change amount and the battery SOC under the battery charging condition and the battery discharging condition are respectively corresponded to each other (obtained by formula (16) and formula (17)) to draw a first table (a battery charging condition SOC table) and a second table (a battery discharging condition SOC table), and the battery SOC is obtained by inquiring the first table or the second table.

[0168] The application further discloses a storage medium, which stores a computer program, and the computer program is executed by a processor to realize the method.

[0169] The application further discloses a program product, which is executed by a processor to realize the method.

[0170] The above embodiments are only used to illustrate the technical solutions of the present application, rather than limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application.

Claims

1. A method for estimating the SOC of a lithium iron phosphate battery, wherein the lithium iron phosphate battery module includes a plurality of lithium iron phosphate cells, referred to as cells, characterized in that: The method comprises the following steps S1 to S3: Step S1, constructing an electric-mechanical coupling model of a battery cell under the influence of multiple factors as shown in the following formula (9), wherein the multiple factors include temperature t, cycle number cyc, and expansion force change ΔF; and correspondingly obtaining an electric-mechanical coupling model of the battery cell under the influence of multiple factors in the case of charging and discharging; ΔF(cyc,t,SOC)=[∫(a2∙cyc 2 +b2∙cyc+c2)d(cyc)]*[∫(a1∙t+b1)dt]*f(SOC 3 ) (9); Wherein, SOC is the state of charge of the battery, that is, the remaining power; the step S1 includes: by monotonizing the phase change of the positive electrode of the battery cell, taking the phase change scalar of the positive electrode of the battery cell and the phase change scalar of the negative electrode of the battery cell for weighted coupling calculation to obtain the change of the battery cell expansion force as shown in formula (3), wherein, ɑ(SOC) 、 β(SOC) is the weighting coefficient: * + * (3)； The above formula (3) can be transformed into the following formula (4): = (4)； Among them, a, b, c, and d are the fitting coefficients of the relationship between the change in the cell expansion force ΔF and the SOC; The relationship between the change in cell expansion force ΔF, temperature t, and battery SOC is shown in formula (7): （7）； Among them, a1 and b1 are fitting coefficients, and t is temperature; The relationship between the change in cell expansion force and cyc and SOC is shown in formula (8): （8）； Among them, a2, b2, and c2 are the fitting coefficients of the relationship between the change in expansion force and the number of cycles; Taking into account the influence of temperature, number of cycles, and change in cell expansion force on SOC, the formula (9) can be obtained. The right side of the equal sign of the formula (9) is the product of the right sides of the equal signs of the formula (7) and the formula (8). Step S2: Analyze the stress conditions of the battery module during operation, establish a module mechanical model, and obtain the single-cell expansion force Fms as follows (14), wherein the battery module includes multiple cells, and the battery module is referred to as a module; wherein Fm is the cell stress in the module, Fy is the initial preload force, a3 is the fitting coefficient, and x is the number of cells in the module; Fms=Fm-Fy-a3*ln(x) (14); Step S3: Obtain a battery SOC estimation model, and correspondingly obtain battery SOC estimation models under charging and discharging conditions; Step S4: obtaining the change in the expansion force of the single cell in the battery module according to the expansion force Fms of the single cell in the battery module, and performing online correction on the initial value of the change in the expansion force of the single cell in the battery module, thereby performing real-time dynamic estimation of the battery SOC.

2. The method for estimating SOC of a lithium iron phosphate battery according to claim 1, wherein: The step S4 comprises: Step S41: obtaining an initial value for calculating the current expansion force variation based on the charge and discharge status of the battery cells in the module; Step S42: Obtain the current cell expansion force variation based on the initial expansion force value obtained in step S41; Step S43: Obtain the current battery SOC according to the current battery SOC estimation model; Step S44: Obtain an initial value for calculating the expansion force change at the next moment according to the charge and discharge status of the battery cells in the module, thereby obtaining the expansion force change of the battery cells at the next moment, and further obtaining the battery SOC at the next moment.

3. The method for estimating SOC of a lithium iron phosphate battery according to claim 1, wherein: The electric-mechanical coupling models for cell charging and discharging under the influence of multiple factors are shown in equations (9-1) and (9-2) respectively: ΔF_char(cyc,t,SOC)=[∫(a21∙cyc 2 +b21∙cyc+c21)d(cyc)]*[∫(a11∙t+b11)dt]*f(SOC 3 ) (9-1); ΔF_disc(cyc,t,SOC)=[∫(a22∙cyc 2 +b22∙cyc+c22)d(cyc)]*[∫(a12∙t+b12)dt]*f(SOC 3 ) (9-2); Among them, a21, b21, c21, a11, and b11 are characteristic parameters of the battery cell charging electro-mechanical coupling model based on the influence of multiple factors; a22, b22, c22, a12, and b12 are characteristic parameters of the battery cell discharging electro-mechanical coupling model based on the influence of multiple factors.

4. A method for estimating SOC of a lithium iron phosphate battery according to any one of claims 1 to 3, characterized in that: The electric-mechanical coupling model of the battery cell charging under the influence of multiple factors is shown in formula (10): ΔF_char(SOC,t,cyc)=(100+0.6519*cyc-0.0013*cyc 2 +3.002*10 -5 *cyc 3 )*(22.23-0.7811*t+1.268·10 -14 *t 2 )*(40.45+641.9*SOC-1055.7*SOC 2 +533.96*SOC 3 ) (10)。 5. The method for estimating SOC of a lithium iron phosphate battery according to any one of claims 1 to 3, characterized in that: The electric-mechanical coupling model of the cell discharge under the influence of multiple factors is shown in formula (11): ΔF_disc(SOC,t,cyc)=(100+0.02366*cyc-2.42*10 -5 *cyc 2 +8.039*10 -7 *cyc 3 )*(86.22-0.72319*t+2.023*10 -14 *t 2 )*(57.55+117.14*SOC-165.15*SOC 2 +95.67*SOC 3 ) (11)。 6. The method for estimating SOC of a lithium iron phosphate battery according to claim 1, wherein: The expansion force variation ΔF can be obtained by testing the cell expansion force F at different SOCs and then using the following formula (5): （5）。 7. The method for estimating SOC of a lithium iron phosphate battery according to claim 1, wherein: The step S2 comprises: Step S21: Considering the influence of the initial preload force on the cells in the module, the relationship between Fcs, Fm and Fy is obtained as follows (12): Fcs=Fm-Fy (12); Among them, Fcs is the expansion force of the battery cells in the module during the cycle; Step S22: Considering the superposition effect of the expansion forces of multiple cells in the module, the expansion forces of the cells in the module increase in a logarithmic function. The relationship between the expansion force Fcs of the cells in the module during the cycle and the expansion force Fms of a single cell is as follows (13): Fcs=a3*ln(x)+Fms (13); Step S23, comprehensively considering the superposition effect of the initial preload force and the expansion force of multiple cells in the module, according to equations (12) and (13), the expansion force Fms of a single cell is obtained as shown in the following equation (14); Fms=Fm-Fy-a3*ln(x) (14).

8. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

9. A program product, characterized in that When the program product is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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