A method and system for online estimation of state of charge (SOC) of lithium-ion batteries based on force-electric coupling measurement.

Abstract

This invention provides a method and system for online SOC estimation of lithium-ion batteries based on force-electric coupling measurement. The method includes: establishing a second-order RC equivalent circuit model of the lithium-ion battery and obtaining a master estimate of the continuous electrical SOC; identifying the load switching moment based on the current change amplitude and duration, and selecting a recovery window after the load switching moment; performing relaxation fitting on the expansion force response within the recovery window and extracting the relaxation time constant characterizing the speed of the recovery process; generating a SOC correction reference value and determining the validity of the SOC correction reference value to obtain the corrected online SOC estimation result. This invention is applicable to solving the problems of decreased SOC estimation accuracy in the voltage plateau region of lithium iron phosphate batteries, accumulation of electrical estimation deviations under complex dynamic conditions, and insufficient utilization of mechanical response information of large-size cells.

Description

Technical Field

[0001] This invention belongs to the field of battery management technology for energy storage systems, specifically relating to an online SOC estimation method and system for lithium-ion batteries based on force-electric coupling measurement. Background Technology

[0002] State of Charge (SOC) is a crucial state parameter characterizing the remaining usable capacity of lithium-ion batteries. Its estimation accuracy directly impacts energy dispatch, safety management, and lifetime assessment during the operation of energy storage systems. For high-capacity lithium iron phosphate batteries, due to their wide voltage plateau region, the terminal voltage is less sensitive to SOC changes within a large SOC range. This leads to SOC estimation methods relying solely on electrical signals such as voltage and current exhibiting problems like decreased observability, error accumulation, and slower convergence in the plateau region.

[0003] While existing methods based on ampere-hour integration are simple to implement, they are highly dependent on initial values ​​and easily affected by the accumulation of current measurement errors, making it difficult to maintain high estimation accuracy over the long term. Methods based on equivalent circuit models and Kalman filtering can achieve closed-loop SOC estimation to some extent, but when the battery is in the voltage plateau region, the terminal voltage is not sensitive to changes in SOC, leading to a weakened observation correction effect. This causes the SOC estimation results to drift more heavily due to model predictions. These problems are particularly pronounced under complex dynamic operating conditions, temperature fluctuations, and parameter mismatches.

[0004] With the deepening research on the mechanism of force-electric coupling, it has been found that lithium-ion batteries not only exhibit electrical responses such as voltage and current during charging and discharging, but also measurable deformation or expansion force changes. Compared with the terminal voltage signal, the expansion force signal can provide additional state characterization information in certain SOC ranges, especially in the voltage plateau region. Therefore, using expansion force information to assist in SOC estimation has significant application value. However, most existing force-electric fusion methods directly use expansion force as a continuous observation in the filtering update, or simply input expansion force characteristics and electrical quantities in parallel into the estimation algorithm, without fully considering the dynamic characteristics of the expansion force signal during the recovery process after load switching and its intrinsic correlation with SOC.

[0005] Furthermore, the battery expansion force signal under dynamic operating conditions is typically superimposed with load disturbances, transient responses, and measurement noise, and its instantaneous value is easily affected by changes in operating conditions, resulting in fluctuations. Directly using the full-time expansion force signal for SOC correction may reduce the stability and reliability of the estimation results. Therefore, how to extract stable and reliable characteristic parameters with strong indicative significance for SOC from the expansion force response during complex operation and effectively integrate them with the main electrical estimation results has become a problem to be solved in current technology.

[0006] Based on this, it is necessary to propose a new online SOC estimation method for lithium-ion batteries. While maintaining the continuous online estimation capability of the electrical model, it utilizes the relaxation characteristics during the expansion force recovery process after load switching to construct SOC correction reference information. Furthermore, it performs constrained correction on the main electrical estimation results when the validity judgment conditions are met, thereby improving the accuracy, stability, and robustness of online SOC estimation. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention proposes an online SOC estimation method and system for lithium-ion batteries based on force-electric coupling measurement. This method uses a second-order RC equivalent circuit model and an adaptive unscented Kalman filter algorithm to obtain a master estimate of the continuous electrical SOC. After detecting a load switch, a local time period with small current fluctuations and a monotonically recovering or asymptotically stable expansion force signal is selected as a recovery window. The expansion force response within the recovery window is relaxed and fitted to extract the relaxation time constant. Further, based on the pre-calibrated correspondence between the relaxation time constant and SOC, and combined with the temperature and operating parameters corresponding to the current operating state, a SOC correction reference value is generated. When the SOC correction reference value meets the validity criteria such as goodness of fit, fitting residual, reasonable range of relaxation time constant, and the current operating temperature and operating conditions being within the preset calibration range, the deviation term in the master estimate of the continuous electrical SOC is recursively updated according to a preset update weight, satisfying the single correction amplitude constraint and the SOC change rate constraint, thereby obtaining the corrected online SOC estimation result.

[0008] This invention does not directly use the instantaneous value of the expansion force signal as a continuous filtering observation. Instead, it utilizes the dynamic characteristics of the expansion force recovery process after load switching as auxiliary correction information. By constructing a recovery window, extracting the relaxation time constant, establishing a calibration mapping relationship between the relaxation time constant and SOC, and combining it with an effectiveness gating judgment and a deviation term constraint update mechanism, it can improve the SOC estimation accuracy under complex working conditions, suppress error accumulation, and enhance the estimation stability and robustness in the plateau region and under dynamic working conditions.

[0009] To achieve the above objectives, the present invention provides the following solution: An online SOC estimation method for lithium-ion batteries based on force-electric coupling measurement, comprising: Collect current, voltage, temperature, and expansion force signals of lithium-ion batteries during operation; Based on the current signal, voltage signal and temperature signal, a second-order RC equivalent circuit model of lithium-ion battery is established, and an adaptive unscented Kalman filter algorithm is used to obtain the main estimate of continuous electrical SOC. The load switching moment is identified based on the current change amplitude and duration, and after the load switching moment, the recovery window is selected based on the current fluctuation condition and the expansion force recovery trend condition. An exponential relaxation fit is performed on the expansion force response within the recovery window to extract the relaxation time constant characterizing the speed of the recovery process; Based on the pre-calibrated correspondence between the relaxation time constant and SOC, and combined with the temperature and operating parameters corresponding to the current operating state, a SOC correction reference value is generated, and the effectiveness of the SOC correction reference value is determined according to the fitting quality and the preset applicable range. When the SOC correction reference value meets the validity determination condition, the deviation term in the continuous electrical SOC master estimate is recursively updated according to the preset update weight. In this process, a single correction magnitude constraint is applied to the recursive update of the deviation term, and a SOC change rate constraint is applied to the online SOC estimate result obtained based on the updated deviation term, so as to obtain the corrected online SOC estimate result of the lithium-ion battery.

[0010] Preferably, the main estimate of the continuous electrical SOC is obtained through an adaptive unscented Kalman filter framework based on a second-order RC equivalent circuit model, specifically including: A state-space model of a lithium-ion battery is constructed using a second-order RC equivalent circuit model. The state variables include the state of charge (SOC) and the voltages of the two polarization branches, as follows: in, Indicates the first k State of charge at time t, and They represent the first k The polarization voltages of the two polarization branches at any given time; The state transition equation of the second-order RC equivalent circuit model is expressed as: in, Indicates the working current and temperature The state transition function of the driver, Representing process noise; the terminal voltage output equation of the second-order RC equivalent circuit model is: in, Indicates the first k Terminal voltage at time 10:00 Indicates open-circuit voltage. Indicates the operating current. Indicates the internal resistance of the ohm; Based on the state-space model, an adaptive unscented Kalman filter algorithm is used to perform online recursive estimation of the state variables, obtaining the first... Master estimate of continuous electrical SOC at time t This serves as the primary estimation basis for subsequent expansion force auxiliary correction.

[0011] Preferably, the method for identifying load switching moments and constructing a recovery window includes: In the k At each time point, calculate the change in current between the current time and the previous time point: in, Indicates the first k The current value at time [time]. Indicates the first k-1 The current value at that moment; When the current change greater than the preset current change threshold When the change in current continuously meets the threshold condition within a preset continuous determination interval, the first determination is made. A load switching occurs at a specific time; after the load switching time, a local time period is selected as a candidate recovery window, and the current values ​​of each sampling point within the candidate recovery window satisfy the following: in, Indicates the first [item] in the restore window. i Current values ​​at each sampling point This represents the average current within the recovery window. Indicates the current fluctuation threshold; A local time period that meets the current fluctuation threshold condition and where the expansion force signal exhibits a monotonically recovering or asymptotically stable trend is selected as the recovery window; wherein, the preset current fluctuation threshold... The current fluctuation threshold The recovery window length is determined through statistical analysis and parameter calibration of offline experimental data of the target lithium-ion battery under preset temperature and operating conditions.

[0012] Preferably, the method for relaxing and fitting the expansion force response within the recovery window and extracting the relaxation time constant includes: Record the start time of the recovery window as The expansion force response within the recovery window is fitted using the following exponential relaxation model: in, Indicates the time within the restored window t The expansion force value, This indicates that the expansion force approaches its stable value. This represents the offset from the relatively stable value at the start of the recovery process. The relaxation time constant represents the response to the expansion force. Represents the fitting residuals; Based on the fitting results of the exponential relaxation model, the asymptotically stable value of the expansion force is obtained. The offset and the relaxation time constant Extract the relaxation time constant. The relaxation characteristic parameter is used to characterize the speed of the expansion force recovery process.

[0013] Preferably, the method for generating SOC correction reference values ​​based on relaxation time constants and determining their effectiveness includes: Based on the correspondence between the relaxation time constant and the state of charge (SOC) established through offline calibration of the target lithium-ion battery under preset temperature and operating conditions, and based on the relaxation time constant... Generate SOC calibration reference value , represented as: in This represents the calibration mapping relationship between the relaxation time constant and the state of charge (SOC). This indicates the temperature and operating parameters corresponding to the current operating status; Based on the goodness of fit of the expansion force response within the recovery window, the fitting residual, and the relaxation time constant Whether it is within the preset reasonable range, and the temperature and operating parameters corresponding to the current operating status. Whether it falls within the preset applicable range of the calibration mapping relationship, and the SOC correction reference value. Determine the validity of the application; When the SOC correction reference value When the validity criteria are met, the SOC correction reference value is retained as an auxiliary correction reference for the main estimate of the continuous electrical SOC; when the SOC correction reference value... If the validity determination criteria are not met, the SOC correction reference value is discarded and the SOC correction update is not triggered.

[0014] Preferably, the method for recursively updating the deviation term in the master estimate of continuous electrical SOC includes: In the k At time t, define the master estimate of continuous electrical SOC. With SOC calibration reference value The deviation between them is: Update weights according to preset settings The deviation term is updated recursively: in, Indicates the first k-1 The deviation term in time, Indicates the first k The deviation term after constant updates This represents the update weight used to control the degree of influence of the current SOC correction reference value on the deviation term update; The master estimate of continuous electrical SOC is corrected based on the updated deviation term to obtain the first... k Online SOC estimate at time: The update process for the deviation term is constrained to satisfy the single deviation correction magnitude constraint: And SOC rate of change constraint: in, This indicates the maximum allowable range of change for a single deviation correction. This represents the maximum allowable change in the SOC estimate between adjacent time points.

[0015] This invention also provides an online SOC estimation system for lithium-ion batteries based on force-electric coupling measurement, used to implement the method, comprising: The data acquisition module is used to collect current signals, voltage signals, temperature signals, and expansion force signals during the operation of lithium-ion batteries. The electrical SOC master estimation module is connected to the data acquisition module and is used to establish a second-order RC equivalent circuit model of the lithium-ion battery based on the current signal, voltage signal and temperature signal, and to output a continuous electrical SOC master estimate value using an adaptive unscented Kalman filter algorithm. The load switching and recovery window identification module is connected to the data acquisition module. It is used to identify the load switching time based on the current change amplitude and duration, and after the load switching time, to filter the recovery window based on the current fluctuation conditions and the expansion force recovery trend conditions. The relaxation feature extraction module, connected to the load switching and recovery window identification module, is used to perform exponential relaxation fitting on the expansion force response within the recovery window and extract the relaxation time constant characterizing the dynamic speed of the recovery process. The SOC reference correction module is connected to the relaxation feature extraction module and the data acquisition module. It is used to generate a SOC correction reference value based on the pre-calibrated correspondence between the relaxation time constant and SOC, combined with the temperature and operating parameters corresponding to the current operating state, and to determine the validity of the SOC correction reference value based on the fitting quality and the preset applicable range. The deviation update module, connected to the electrical SOC master estimation module and the SOC reference correction module, is used to recursively update the deviation term in the continuous electrical SOC master estimation value when the SOC correction reference value meets the validity judgment condition, and output the corrected lithium-ion battery SOC online estimation result.

[0016] Preferably, the SOC reference calibration module includes: The calibration management unit is used to establish, store, or recall the calibration mapping relationship between the relaxation time constant and SOC corresponding to the current operating state based on the offline experimental data of the target lithium-ion battery under preset temperature range and preset operating condition range. A mapping generation unit, connected to the calibration management unit, is used to generate a SOC correction reference value based on the relaxation time constant and the calibration mapping relationship; The validity determination unit, connected to the mapping generation unit, is used to filter the SOC correction reference value based on the goodness of fit of the expansion force response within the recovery window, the fitting residual, the reasonable range of the relaxation time constant, and whether the current operating temperature and operating conditions are within the applicable range of the calibration mapping relationship, and outputs a valid SOC correction reference value only when the validity determination conditions are met.

[0017] Preferably, the deviation update module includes: The deviation calculation unit, connected to the validity determination unit and the electrical SOC master estimation module, is used to calculate the current deviation based on the difference between the SOC correction reference value and the continuous electrical SOC master estimation value. The constraint update unit, connected to the deviation calculation unit, is used to recursively update the deviation item according to the preset update weight when the SOC correction reference value is valid, apply a single correction magnitude constraint to the recursive update of the deviation item, and apply a SOC change rate constraint to the online SOC estimation result obtained based on the updated deviation item. The result output unit is connected to the constraint update unit and the electrical SOC master estimation module. It is used to correct the continuous electrical SOC master estimate based on the updated deviation term and output the final online SOC estimation result.

[0018] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention adopts a collaborative estimation mechanism of "continuous electrical master estimation + expansion force recovery feature correction". It obtains the continuous electrical SOC master estimate using a second-order RC equivalent circuit model and an adaptive unscented Kalman filter algorithm. While ensuring the continuity and real-time performance of online estimation, it introduces relaxation features during the expansion force recovery process after load switching as auxiliary correction information. This solves the problem that traditional electrical methods suffer from weakened correction capability and easy error accumulation due to insensitivity to voltage changes in the wide voltage plateau region of lithium iron phosphate batteries. This invention does not directly use the instantaneous value of expansion force for continuous filtering updates. Instead, it extracts a relaxation time constant with stronger physical meaning and stability from the expansion force response under dynamic operating conditions, and generates an SOC correction reference value based on the pre-calibrated correspondence between the relaxation time constant and SOC. This effectively improves the reliability and accuracy of SOC estimation under complex operating conditions.

[0019] This invention establishes a phased correction mechanism for dynamic operation processes through load switching identification, recovery window construction, relaxation fitting, validity determination, and constraint-based updating of deviation terms. Compared with existing methods that directly utilize instantaneous observations for correction, this invention only triggers the correction of the continuous electrical SOC master estimate by the SOC correction reference value when current fluctuations are small, expansion force shows a recovery trend, the fitting result meets accuracy requirements, and the current temperature and operating conditions are within the preset calibration range. Therefore, it can effectively suppress the adverse effects of noise disturbances, abnormal operating conditions, and invalid fitting on the estimation results, and avoid problems such as SOC estimation oscillation, incorrect correction, or even instability caused by unreliable auxiliary information. By setting update weights and correction magnitude constraints for the deviation terms, this invention further enhances the smoothness, robustness, and engineering usability of the SOC estimation process.

[0020] This invention fully utilizes supplementary state information in the electromechanical coupling response of lithium-ion batteries, making it particularly suitable for online SOC estimation scenarios of large-capacity lithium iron phosphate energy storage batteries under complex operating conditions and long-term operation. In the voltage plateau region, the correction effect of traditional voltage observation-based methods is significantly weakened. This invention, however, leverages the internal state evolution characteristics reflected in the expansion force recovery process after load switching to provide additional reference for SOC estimation, thereby improving the state identification capability in the plateau region. In dynamic load switching scenarios, this invention distinguishes between transient disturbances and the stable recovery process through recovery window filtering and relaxation feature extraction, making the extracted auxiliary correction information more targeted and reliable. Therefore, this invention not only improves the accuracy of SOC estimation but also significantly enhances the consistency and stability of the estimation results under complex operating conditions.

[0021] This invention does not require changing the basic architecture of existing battery management systems that rely on continuous state estimation based on current, voltage, and temperature signals. It only introduces an expansion force measurement channel and corresponding feature extraction and correction mechanisms, thus exhibiting good engineering compatibility and feasibility. By improving the accuracy of SOC estimation and suppressing error drift during long-term operation, this invention enhances the energy storage system's ability to accurately perceive available capacity, reducing the conservative capacity usage caused by SOC estimation errors. Simultaneously, more accurate SOC information helps optimize charge and discharge control strategies, reducing the risk of overcharging and over-discharging due to estimation errors, thereby mitigating battery degradation, extending battery system lifespan, and reducing the overall operation and maintenance costs of the energy storage system throughout its lifecycle.

[0022] This invention also improves the safety and reliability of energy storage systems during operation. For applications such as grid-side energy storage, power source-side energy storage, and industrial and commercial energy storage, high-precision and robust online SOC estimation results help reduce the risks of energy dispatch imbalance, misjudgment of available capacity, and abnormal shutdowns caused by severe SOC deviations, and provide more reliable state-based information for battery safety management and operational decisions. Especially under the long-term operation conditions of large-scale energy storage battery clusters, this invention can enhance the system's ability to perceive key state parameters, which is of great significance for ensuring the safe and stable operation of energy storage systems, improving the capacity for new energy absorption, and promoting the construction of a green and low-carbon energy system.

[0023] In summary, the technical solution of this invention organically combines continuous electrical SOC master estimation with SOC reference correction based on expansion force recovery relaxation characteristics, which significantly improves the accuracy, stability and robustness of online SOC estimation of lithium-ion batteries, while also possessing good real-time performance, engineering adaptability and application prospects. Attached Figure Description

[0024] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a flowchart of a method according to an embodiment of the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0028] Example 1: like Figure 1 As shown, an online SOC estimation method for lithium-ion batteries based on force-electric coupling measurement includes: S1: Collects current, voltage, temperature, and expansion force signals during the operation of lithium-ion batteries.

[0029] In this embodiment, a current sensor acquires the operating current signal of the lithium-ion battery, a voltage acquisition module acquires the battery terminal voltage signal, a temperature sensor acquires the battery operating temperature, and a force sensor installed in the battery constraint structure acquires the expansion force signal during the battery charging and discharging process. The acquired current, voltage, temperature, and expansion force signals are synchronously recorded using a uniform sampling period to ensure the temporal consistency of subsequent load switching identification, recovery window construction, and expansion force relaxation fitting.

[0030] A further implementation method is to assume that the first The multi-source measurement information collected at all times is as follows: (1) in, Indicates the first k The current value at time [time]. Indicates the first k The terminal voltage value at time 10:00. Indicates the first k Temperature value at time, Indicates the first k The value of the expansion force at any given moment.

[0031] The purpose of step S1 is to provide an electrical input signal for the main estimation of continuous electrical SOC, and at the same time provide mechanical observation input for subsequent auxiliary correction based on the expansion force recovery characteristics.

[0032] S2: Based on current, voltage and temperature signals, a second-order RC equivalent circuit model of a lithium-ion battery is established, and an adaptive unscented Kalman filter algorithm is used to obtain the main estimate of the continuous electrical SOC.

[0033] Step S2 uses a second-order RC equivalent circuit model to describe the dynamic electrical characteristics of the lithium-ion battery, and constructs a state-space model based on the current, voltage, and temperature signals. On this basis, an adaptive unscented Kalman filter algorithm is used to perform online recursive estimation of the battery state, thereby obtaining the main estimate of the continuous electrical SOC.

[0034] Specifically, a second-order RC equivalent circuit model is used to construct the state-space model of the lithium-ion battery. The state variables include SOC and the voltages of the two polarization branches, expressed as: (2) in, Indicates the first k State of charge at time t, and They represent the first k The polarization voltage of the two polarization branches at any given time.

[0035] The state transition equation of the second-order RC equivalent circuit model is expressed as: (3) in, Represents the state transition function. This indicates process noise.

[0036] The terminal voltage output equation of the second-order RC equivalent circuit model is expressed as: (4) in This represents the functional relationship between open-circuit voltage and state of charge (SOC). This represents the internal resistance of the Ohm.

[0037] The system observation equation is expressed as: (5) in, Represents the observation function, This indicates observation noise.

[0038] Based on the state-space model, an adaptive unscented Kalman filter algorithm is used to perform online recursive estimation of the state variables, obtaining the first... The principal estimate of the continuous electrical SOC at time t is denoted as: (6) in, Indicates the first The master estimate of the continuous electrical SOC at time step is obtained by the electrical model and the adaptive unscented Kalman filter algorithm.

[0039] In some implementations, the adaptive unscented Kalman filter algorithm can adjust the process noise covariance and measurement noise covariance online based on the statistical characteristics of the voltage residual, thereby improving the stability and robustness of the master estimate of the continuous electrical SOC under complex operating conditions. This master estimate of the continuous electrical SOC is continuously output throughout the entire operation, serving as the basis for subsequent auxiliary corrections based on the expansion force recovery relaxation characteristics.

[0040] The purpose of step S2 is to continuously output the main electrical estimation results of SOC throughout the entire operation, providing the main estimation basis for subsequent expansion force auxiliary correction.

[0041] S3: Identify the load switching moment based on the current change amplitude and duration, and after the load switching moment, filter the recovery window based on the current fluctuation condition and the expansion force recovery trend condition.

[0042] In step S3, in order to extract recovery features with strong physical meaning and stability from the expansion force signal under complex dynamic working conditions, it is first necessary to identify the load switching time and then construct the recovery window.

[0043] A further implementation method is that, in the first... At each time point, calculate the change in current between the current time and the previous time point: (7) in, Indicates the first k The current value at time [time]. Indicates the first k-1 The current value at a given time.

[0044] Preferably, to avoid misjudgment caused by single-point noise, a duration criterion can be used for joint identification of load switching. Let the length of the continuous judgment interval be... When the following conditions are met: (8) At that time, it was determined that in the first k Load switching occurs constantly, among which, This indicates the preset current change threshold.

[0045] When the current change greater than the preset current change threshold When the change in current continuously meets the threshold condition within a preset continuous determination interval, the first determination is made. A load switching occurs at a specific time; after the load switching time, a local time period is selected as a candidate recovery window, and the current values ​​of each sampling point within the candidate recovery window satisfy the following: in, Indicates the first [item] in the restore window. i Current values ​​at each sampling point This represents the average current within the recovery window. Indicates the current fluctuation threshold; A local time period that meets the current fluctuation threshold condition and where the expansion force signal exhibits a monotonically recovering or asymptotically stable trend is selected as the recovery window; wherein, the preset current fluctuation threshold... The current fluctuation threshold The recovery window length is determined through statistical analysis and parameter calibration of offline experimental data of the target lithium-ion battery under preset temperature and operating conditions.

[0046] Furthermore, define the first k c If the identified load switching time is the time interval, then a time interval is selected after the identified load switching time. As candidate recovery windows, among them And the candidate recovery window satisfies the following current stability condition: (9) in, (10) This represents the average current within the candidate recovery window. This indicates the current fluctuation threshold.

[0047] To further ensure the fitability of the expansion force response within the recovery window, the trend of expansion force variation can be constrained. Preferably, the first-order difference of the expansion force within the candidate recovery window satisfies: (11) When the expansion force response is a recovery decay process, the following is required: (12) in, This represents the tolerance threshold for changes in expansion force.

[0048] In another preferred embodiment, the asymptotically stable recovery trend can also be characterized by a gradual decrease in the local slope of the expansion force curve, i.e., satisfying: (13) in, This indicates the slope convergence tolerance.

[0049] Furthermore, restoring the window length satisfies: (14) in, Indicates the restoration of the window length. This indicates the minimum effective window length.

[0050] Based on satisfying the current fluctuation constraint condition within the candidate recovery window, the monotonic recovery change or asymptotically stable change trend of the expansion force signal is further combined for screening, and the recovery window is finally determined.

[0051] A further implementation involves setting a preset current change threshold. Current fluctuation threshold Expansion force variation tolerance threshold Slope convergence tolerance and minimum effective window length The parameters are determined through statistical analysis and parameter calibration of offline experimental data. Specifically, based on the operating data of the target lithium-ion battery under different SOC ranges, different temperature conditions, and different operating conditions, the distribution of current changes before and after load switching, the distribution of current fluctuations during the stable phase after switching, the distribution of expansion force difference changes, and the stability of fitting results under different window lengths are statistically analyzed to determine the parameter thresholds suitable for online estimation.

[0052] The purpose of step S3 is to distinguish the strong transient disturbance stage after load switching from the subsequent relatively stable recovery stage, so as to provide an effective data range for subsequent expansion force relaxation fitting.

[0053] S4: Perform exponential relaxation fitting on the expansion force response within the recovery window, and extract the relaxation time constant that characterizes the speed of the recovery process; based on the pre-calibrated correspondence between the relaxation time constant and SOC, and combined with the temperature and operating parameters corresponding to the current operating state, generate a SOC correction reference value, and determine the validity of the SOC correction reference value according to the fitting quality and the preset applicable range.

[0054] In step S4, after constructing the recovery window, the expansion force response within the recovery window is relaxed and fitted to extract the relaxation time constant characterizing the speed of the recovery process; subsequently, the relaxation time constant is converted into a SOC correction reference value and its effectiveness is determined.

[0055] A further implementation method is to set the recovery window start time as... The expansion force response within the recovery window can then be described by the following exponential relaxation model: (15) in, Indicates the time within the restored window t The expansion force value, This indicates that the expansion force approaches its stable value. This represents the offset from the relatively stable value at the start of the recovery process. The relaxation time constant represents the response to the expansion force. This represents the fitting residual.

[0056] For discrete sampling sequences, the above equation can be written as: (16) in, Indicates the first i The expansion force value at each sampling point Indicates the first i The sampling time corresponding to each sampling point This represents the fitting error for the corresponding sampling point.

[0057] Furthermore, the parameters can be adjusted using the least squares method. , and The estimation is performed, and the optimization objective is: (17) in, (18) This represents the sum of squared residuals between the measured and fitted values ​​of the expansion force within the recovery window.

[0058] After fitting, the optimal estimated parameters are obtained: in, This is the relaxation time constant corresponding to the current recovery window.

[0059] Furthermore, the fitted value can be expressed as: (19) Accordingly, the fitted residual sequence is: (20) The root mean square index of the fitting residuals can be expressed as: (twenty one) in, This indicates the window length to be restored.

[0060] Furthermore, the goodness of fit can be expressed as: (twenty two) in, (twenty three) This indicates the restoration of the average expansion force within the window.

[0061] After obtaining the relaxation time constant, the correspondence between the relaxation time constant and the state of charge (SOC) is established through offline calibration experiments. Specifically, charge-discharge experiments are conducted on the target lithium-ion battery within a preset temperature range and a preset operating condition range to collect the expansion force recovery response during multiple load switching processes under different SOC states; multiple recovery windows are extracted, and relaxation fitting is performed on each recovery window to obtain the corresponding relaxation time constant. Extract the relaxation time constant The relaxation feature parameter is used to characterize the dynamic speed of the expansion force recovery process; it is then correlated with the reference SOC at the corresponding time to construct a calibration sample set: (twenty four) in, Indicates the number of calibration samples. Indicates the first n The relaxation time constant for each sample. Indicates the corresponding reference SOC, This indicates the corresponding temperature range parameters and operating condition range parameters.

[0062] Based on the calibration sample set, a mapping relationship between the relaxation time constant and SOC can be established: (25) in, Indicates the first k The SOC correction reference value generated at each time point, This represents the calibration mapping relationship between the relaxation time constant and the state of charge (SOC). This indicates the temperature range parameters, operating condition range parameters, or other calibration constraint parameters corresponding to the current operating status.

[0063] Furthermore, in the segmented lookup table implementation, the mapping relationship can be represented as: (26) in, Indicates the first m Temperature-operating condition zones This indicates the mapping function for the corresponding partition.

[0064] In the polynomial fitting implementation, the mapping relationship can also be expressed as: (27) in, These are the polynomial fitting coefficients. The fitting order is denoted as .

[0065] If piecewise linear interpolation is used, then in When, it can be represented as: (28) in, and To find adjacent labeled nodes in the table.

[0066] A further implementation involves extracting the relaxation time constant corresponding to the current recovery window during online operation. Then, based on the current temperature and the operating condition range, the corresponding mapping relationship is invoked to generate the SOC correction reference value for the current moment: (29) in, Indicates the first k The current temperature-operating condition range parameters corresponding to the current moment.

[0067] To ensure sufficient reliability of the SOC correction reference values ​​generated from the relaxation time constant, not all correction reference values ​​are directly used in subsequent corrections; instead, their validity needs to be determined first. This determination is based on the goodness of fit of the expansion force response within the recovery window, the fitting residuals, and the relaxation time constant. Whether it is within the preset reasonable range, and the temperature and operating parameters corresponding to the current operating status. Whether it falls within the preset applicable range of the calibration mapping relationship, and the SOC correction reference value. Determine the validity of the application; When the SOC correction reference value When the validity criteria are met, the SOC correction reference value is retained as an auxiliary correction reference for the main estimate of the continuous electrical SOC; when the SOC correction reference value... If the validity determination criteria are not met, the SOC correction reference value is discarded and the SOC correction update is not triggered.

[0068] Specifically, the SOC correction reference value is determined to be a valid correction reference value only if the following validity criteria are met simultaneously: Goodness of fit satisfies: (30) The fitted residuals satisfy: (31) The relaxation time constant is within a preset reasonable range: (32) The current operating temperature and operating conditions are within the preset calibration range. Among them, This represents the set of temperature-operating condition parameters corresponding to the preset calibration range.

[0069] Furthermore, a validity determination function can be defined: (33) in, This indicates that the current SOC calibration reference value is valid. This indicates that the current SOC calibration reference value is invalid.

[0070] A further implementation involves setting a goodness-of-fit threshold. Fitting residual threshold and the reasonable range of relaxation time constant The following method was used to determine the goodness-of-fit threshold for online estimation: Based on offline experimental data obtained from the target lithium-ion battery under preset SOC, temperature, and operating condition ranges, statistical analysis was performed on the relaxation fitting results of the expansion force response within the recovery window to obtain the distribution characteristics of goodness-of-fit, fitting residuals, and relaxation time constants; corresponding candidate threshold intervals were determined based on these distribution characteristics; and the candidate threshold intervals were screened through repeated experiments and cross-validation to determine the final goodness-of-fit threshold for online estimation. Fitting residual threshold And the reasonable range of relaxation time constant.

[0071] To quantify the reliability of the current SOC calibration reference value, a normalized reliability index can also be defined: (34) in, This represents a reliability index calculated by combining goodness of fit and fitting residuals, assuming the fit is deemed valid. For example, it can be defined as: (35) If any of the above validity criteria are not met, the current SOC correction reference value is deemed invalid, and the current correction update will not be performed.

[0072] The purpose of step S4 is to extract recovery feature parameters that have strong indicative significance for SOC from the expansion force signal in the complex dynamic operation process, and convert them into reliable SOC correction reference information that has been screened.

[0073] S5: When the SOC correction reference value meets the validity determination condition, the deviation term in the main estimate of the continuous electrical SOC is recursively updated according to the preset update weight. The recursive update of the deviation term is subject to a single correction magnitude constraint, and the SOC change rate constraint is applied to the online SOC estimate result obtained based on the updated deviation term, so as to obtain the corrected online SOC estimate result of the lithium-ion battery.

[0074] In step S5, the main estimate of continuous electrical SOC and the final online SOC estimate satisfy the following relationship: (36) in, Indicates the first k Online SOC estimation results after time correction Indicates the first k The master estimate of the continuous electrical SOC at time t. Indicates the first k The deviation term in time.

[0075] Define the reference deviation at the current moment as: (37) Once the current SOC correction reference value passes the validity determination, the deviation term is recursively updated according to the following relationship: (38) Right now: (39) in, Indicates the first k-1 The deviation term in time, Indicates the first k The weights are updated at each moment, satisfying: A further implementation method is that the updated weights The determination is based on the reliability of the current SOC correction reference value. Preferably, it can be set as follows: (40) in, This indicates the preset maximum update weight. The credibility index is defined by expression (34).

[0076] In another implementation, a weighted expression with upper and lower limits can also be used: (41) in, This represents the minimum update weight. This represents the weight scaling factor.

[0077] To avoid abrupt changes in SOC estimation due to excessively large single corrections, further constraints can be imposed on the change in the bias term. The increment of the bias term is defined as: (42) Then we have: Right now (43) If equation (43) is not satisfied, then the deviation term is subject to amplitude limiting: (44) in The saturation limiting function is defined as follows: (45) Furthermore, constraints can be imposed on the rate of change of the final online SOC estimation result, namely, satisfying: (46) in, This represents the upper limit of the SOC change rate constraint between adjacent time points. The final online SOC estimation result can also be limited to a physically feasible range. When the current SOC correction reference value fails the validity determination, let Therefore, At this point, the final online SOC estimation result degenerates into: (47) If the initial deviation term is set to zero, that is... Then, if the correction is not triggered, we have: (48) The purpose of step S5 is to integrate reliable expansion force recovery feature reference information into the SOC estimation result in a constrained manner while maintaining the continuity of the main electrical estimate, thereby improving the estimation accuracy and avoiding over-correction that could cause estimation oscillations or instability.

[0078] This embodiment addresses the issues of lithium iron phosphate batteries' insensitivity to SOC changes within a wide voltage plateau region and the tendency of traditional electrical estimation methods to suffer from weakened correction capabilities and error accumulation under dynamic operating conditions. It proposes an online SOC estimation method based on "continuous electrical master estimation + expansion force recovery characteristic correction." This method does not directly use the instantaneous value of expansion force as a continuous filtering observation. Instead, after identifying load switching, it extracts the relaxation time constant from the expansion force recovery process and generates an SOC correction reference value based on the pre-calibrated correspondence between the relaxation time constant and SOC. Then, through validity judgment and a constraint-based update mechanism for the deviation term, it achieves auxiliary correction of the continuous electrical SOC master estimate, thereby improving the accuracy, stability, and robustness of online SOC estimation under complex operating conditions.

[0079] To verify the effectiveness of this invention, 120 sets of voltage, current, temperature, and expansion force data were collected on a 280Ah lithium iron phosphate battery platform, and SOC estimation comparison experiments were conducted under multiple temperature (10℃, 25℃, 40℃) and multiple operating conditions. The comparison methods included unscented Kalman filtering (UKF), adaptive unscented Kalman filtering (AUKF), and the method of this invention. Since this invention is mainly aimed at energy storage system applications, the peak-shaving and frequency-modulation condition at 25℃ was selected as the focus of analysis. The root mean square error (RMSE) results of SOC estimation for each method under different temperatures and operating conditions are shown in Table 1.

[0080] Table 1 As can be seen from the table above, the present invention is significantly superior to existing methods in key performance indicators such as the average error of SOC estimation, the ability to reduce plateau period error, and the speed of filtering convergence, and can meet the stringent requirements of energy storage systems for high-precision status monitoring.

[0081] From a technical perspective, this invention innovatively introduces relaxation characteristics during the expansion force recovery process after load switching as auxiliary correction information, based on the continuous electrical SOC master estimation. This effectively compensates for the weakened observation correction capability of lithium iron phosphate energy storage batteries in the voltage plateau region due to the insensitivity of terminal voltage to SOC changes. Instead of directly using the instantaneous expansion force value as a continuous observation for filter updates, this invention identifies the load switching moment and constructs a recovery window. It then performs relaxation fitting on the expansion force response within the recovery window, extracting a relaxation time constant with strong physical meaning and stability. Based on the pre-calibrated correspondence between the relaxation time constant and SOC, it generates a SOC correction reference value. Furthermore, this invention rigorously screens the SOC correction reference value through multiple validity criteria, including goodness of fit, fitting residuals, reasonable range of relaxation time constants, and temperature condition matching range. A constraint-based update mechanism for the deviation term is used to smoothly correct the continuous electrical SOC master estimate, thereby effectively suppressing the technical problems of error accumulation, weakened correction capability, and decreased estimation stability that traditional filtering algorithms easily encounter under long-term operation, complex conditions, and wide voltage plateau regions.

[0082] From an economic perspective, this invention, based on the existing battery management system state estimation architecture based on current, voltage, and temperature signals, introduces an expansion force measurement and recovery feature extraction mechanism, exhibiting good engineering compatibility and low deployment costs. By improving the accuracy of online SOC estimation and suppressing error drift during long-term operation, this invention can more accurately characterize the available capacity state of the energy storage system, reducing capacity waste caused by conservative SOC estimation. Simultaneously, more accurate SOC state awareness helps optimize peak shaving and valley filling and frequency regulation operation strategies, reducing unnecessary energy loss during charging and discharging; and it can reduce the risk of overcharging and over-discharging caused by misjudgment of SOC, thereby slowing battery aging, extending the service life of energy storage battery clusters under long-term operating conditions, and ultimately reducing the operation and maintenance costs and overall energy costs of the energy storage power station throughout its entire lifecycle.

[0083] From a social benefit perspective, this invention improves the safety, reliability, and state awareness capabilities of large-scale energy storage power stations during operation. In applications such as grid-side energy storage, power source-side energy storage, and industrial and commercial energy storage, this invention can reduce the risks of energy dispatch imbalances, misjudgments of available capacity, and abnormal shutdowns caused by severe deviations in SOC estimation, and provides more reliable state data for battery safety monitoring and operation control. Especially for the long-term continuous operation of new energy storage clusters, this invention helps improve the stable operation capability of energy storage systems and their adaptability to the volatility of renewable energy, which is of positive significance for ensuring the safe operation of new energy storage systems, enhancing the grid's capacity to absorb renewable energy, and promoting the construction of a green and low-carbon energy system.

[0084] In summary, the technical solution of this invention significantly improves the accuracy, stability, and robustness of online SOC estimation for lithium-ion batteries by combining continuous electrical SOC master estimation with SOC reference correction based on expansion force recovery relaxation characteristics. It also has good real-time performance, engineering adaptability, and application prospects.

[0085] Example 2 This invention also provides an online SOC estimation system for lithium-ion batteries based on force-electric coupling measurement, used to implement the method of Embodiment 1, comprising: The data acquisition module is used to collect current, voltage, temperature, and expansion force signals during the operation of the lithium-ion battery. In a static configuration, the data acquisition module is connected to the current sensor, voltage acquisition unit, temperature sensor, and expansion force measurement unit to obtain multi-source measurement information required for online SOC estimation. During dynamic operation, the data acquisition module synchronously acquires and aligns the various signals according to a unified sampling period, providing raw input data for subsequent electrical master estimation, load switching identification, and expansion force recovery feature extraction. The effect is to ensure the consistency of multi-source measurement information in the time dimension, improving the accuracy and reliability of subsequent state estimation and feature extraction results.

[0086] The electrical SOC master estimation module, connected to the data acquisition module, is used to establish a second-order RC equivalent circuit model of the lithium-ion battery based on the current, voltage, and temperature signals, and output a continuous electrical SOC master estimate using an adaptive unscented Kalman filter algorithm. Specifically, the electrical master estimation module uses SOC and the voltages of the two polarization branches as state variables, combines the battery terminal voltage output equation to construct a state-space model, and uses the adaptive unscented Kalman filter algorithm for online recursive estimation. In static terms, the electrical master estimation module is connected to the data acquisition module to receive real-time current, voltage, and temperature signals. During dynamic operation, the electrical master estimation module continuously outputs a continuous electrical SOC master estimate, providing a master estimation basis for subsequent auxiliary corrections. The effect is to achieve continuous, real-time electrical SOC estimation throughout the entire operation.

[0087] A load switching and recovery window identification module, connected to the data acquisition module, identifies the load switching time based on the current change amplitude and duration. After the load switching time, it filters the recovery window based on current fluctuation conditions and expansion force recovery trend conditions. Specifically, the module identifies load switching events based on the current change at adjacent times and, combined with the current fluctuation threshold after switching, the minimum length of the recovery window, and the expansion force recovery trend, filters candidate time periods to determine a recovery window suitable for relaxation fitting. Statically, the module connects to the data acquisition module and outputs recovery window boundary information to the relaxation feature extraction module. Dynamically, after detecting a current step change or a significant operating condition switch, the module automatically identifies the recovery phase that meets the conditions from subsequent sampled data. The effect is to distinguish the strong transient disturbance phase after load switching from the relatively stable recovery phase, providing an effective data range for subsequent expansion force feature extraction.

[0088] The relaxation feature extraction module, connected to the load switching and recovery window identification module, performs exponential relaxation fitting on the expansion force response within the recovery window to extract the relaxation time constant, which characterizes the speed of the recovery process's dynamics. Specifically, the relaxation feature extraction module uses an exponential relaxation model to fit the expansion force response within the recovery window, obtaining fitting parameters such as the asymptotically stable value of the expansion force, the initial offset, and the relaxation time constant, and calculates the fitting residual and goodness-of-fit index. In static terms, the relaxation feature extraction module is connected to the load switching and recovery window identification module and outputs the extracted relaxation time constant and fitting evaluation index to the SOC reference correction module. During dynamic operation, after each valid recovery window is identified, the module performs a local relaxation fitting operation to extract the relaxation features corresponding to the current recovery process. The effect is to extract recovery feature parameters with strong physical meaning and stability from the expansion force signal under complex dynamic conditions.

[0089] The SOC reference correction module, connected to the relaxation feature extraction module and the data acquisition module, generates a SOC correction reference value based on a pre-calibrated correspondence between the relaxation time constant and SOC, combined with the temperature and operating parameters corresponding to the current operating state. It then determines the validity of the SOC correction reference value based on the fitting quality and a preset applicable range. Specifically, the SOC reference correction module uses the extracted relaxation time constant and the current temperature and operating condition range parameters to call the corresponding pre-calibrated mapping relationship to generate the SOC correction reference value. Simultaneously, it determines the validity of the SOC correction reference value based on conditions such as a goodness-of-fit threshold, a fitting residual threshold, a reasonable range for the relaxation time constant, and whether the current operating temperature and operating conditions are within a preset calibration range. Statically, this module is connected to both the relaxation feature extraction module and the deviation update module. Dynamically, the module outputs a valid SOC correction reference value only when all validity determination conditions are simultaneously met. The effect is to convert the expansion force recovery features into reliable SOC auxiliary correction information and avoid invalid or unreliable features from intervening in the subsequent state update process.

[0090] The deviation update module, connected to the main electrical SOC estimation module and the SOC reference correction module, is used to recursively update the deviation term in the continuous main electrical SOC estimate when the SOC correction reference value meets the validity determination condition, and output the corrected online SOC estimation result of the lithium-ion battery. Specifically, the deviation update module establishes the deviation term relationship between the final SOC estimation result and the continuous main electrical SOC estimate, recursively updates the deviation term based on the difference between the current SOC correction reference value and the continuous main electrical SOC estimate, and performs amplitude limiting and smoothing processing on the update process by combining update weights, single correction amplitude constraints of deviation terms, and SOC change rate constraints. In a static relationship, the deviation update module simultaneously receives the continuous main electrical SOC estimate output by the main electrical estimation module and the valid correction reference value output by the SOC reference correction module. In dynamic operation, the deviation update module performs deviation updates when a valid correction reference value exists, and keeps the deviation term unupdated or sets the update weight to zero when no valid correction reference value exists. The effect is that, while maintaining the continuity of the main electrical estimation, reliable expansion force recovery feature auxiliary information is incorporated into the final online SOC estimation result in a constrained manner, thereby improving the estimation accuracy and suppressing abrupt changes and oscillations.

[0091] A further embodiment is that the SOC reference correction module includes: The calibration management unit is used to establish, store, or recall the calibration mapping relationship between the relaxation time constant and SOC corresponding to the current operating state based on the offline experimental data of the target lithium-ion battery under preset temperature range and preset operating condition range. A mapping generation unit, connected to the calibration management unit, is used to generate a SOC correction reference value based on the relaxation time constant and the calibration mapping relationship; The validity determination unit, connected to the mapping generation unit, is used to filter the SOC correction reference value based on the goodness of fit of the expansion force response within the recovery window, the fitting residual, the reasonable range of the relaxation time constant, and whether the current operating temperature and operating conditions are within the applicable range of the calibration mapping relationship, and outputs a valid SOC correction reference value only when the validity determination conditions are met.

[0092] A further implementation method includes a deviation update module comprising: The deviation calculation unit, connected to the validity determination unit and the electrical SOC master estimation module, is used to calculate the current deviation based on the difference between the SOC correction reference value and the continuous electrical SOC master estimation value. The constraint update unit, connected to the deviation calculation unit, is used to recursively update the deviation item according to the preset update weight when the SOC correction reference value is valid, apply a single correction magnitude constraint to the recursive update of the deviation item, and apply a SOC change rate constraint to the online SOC estimation result obtained based on the updated deviation item. The result output unit is connected to the constraint update unit and the electrical SOC master estimation module. It is used to correct the continuous electrical SOC master estimate based on the updated deviation term and output the final online SOC estimation result.

[0093] To verify the effectiveness of the method of this invention, this embodiment collected 120 sets of voltage, current, temperature, and expansion force data on a 280Ah lithium iron phosphate battery platform, and conducted online SOC estimation experiments under three temperatures (10℃, 25℃, and 40℃) and multiple operating conditions. Comparison methods included unscented Kalman filtering (UKF), adaptive unscented Kalman filtering (AUKF), and the method of this invention. Since this invention is primarily aimed at energy storage system applications, the peak-shaving and frequency-modulating condition at 25℃ was selected as the key verification object. Experimental results show that the SOC estimation error of the method of this invention in the voltage plateau region is significantly lower than that of the comparison methods, and no significant divergence or drastic jumps occurred during operation, demonstrating good estimation accuracy, stability, and robustness. Engineering application projections show that the method of this invention can improve the effective utilization rate of battery energy by approximately 6%–9% in energy storage system applications, and can extend the battery system life by approximately 8%–12% by reducing the risk of over-discharge caused by SOC estimation errors, thereby effectively improving the operational reliability and economic benefits of energy storage battery systems.

Claims

1. A method for online estimation of SOC of lithium-ion battery based on force-electric coupling measurement driven, characterized in that, include: Collect current, voltage, temperature, and expansion force signals of lithium-ion batteries during operation; Based on the current signal, voltage signal and temperature signal, a second-order RC equivalent circuit model of lithium-ion battery is established, and an adaptive unscented Kalman filter algorithm is used to obtain the main estimate of continuous electrical SOC. The load switching moment is identified based on the current change amplitude and duration, and after the load switching moment, the recovery window is selected based on the current fluctuation condition and the expansion force recovery trend condition. An exponential relaxation fit is performed on the expansion force response within the recovery window to extract the relaxation time constant characterizing the speed of the recovery process; Based on the pre-calibrated correspondence between the relaxation time constant and SOC, and combined with the temperature and operating parameters corresponding to the current operating state, a SOC correction reference value is generated, and the effectiveness of the SOC correction reference value is determined according to the fitting quality and the preset applicable range. When the SOC correction reference value meets the validity determination condition, the deviation term in the continuous electrical SOC master estimate is recursively updated according to the preset update weight. In this process, a single correction magnitude constraint is applied to the recursive update of the deviation term, and a SOC change rate constraint is applied to the online SOC estimate result obtained based on the updated deviation term, so as to obtain the corrected online SOC estimate result of the lithium-ion battery.

2. The method of claim 1, wherein, The master estimate of the continuous electrical SOC is obtained through an adaptive unscented Kalman filter framework based on a second-order RC equivalent circuit model, specifically including: A state-space model of a lithium-ion battery is constructed using a second-order RC equivalent circuit model. The state variables include the state of charge (SOC) and the voltages of the two polarization branches, as follows: wherein, denotes the state of charge at the time k and denotes the polarization voltage of the two polarization branches at the time k t0.​ The state transition equation of the second-order RC equivalent circuit model is expressed as: wherein, represents a state transition function driven by the operating current and the temperature , represents the process noise; the end voltage output equation of the second-order RC equivalent circuit model is: wherein, represents the end voltage at the time k represents the open circuit voltage, represents the working current, represents the working current, represents the ohmic internal resistance; Based on the state-space model, an adaptive unscented Kalman filter algorithm is used to perform online recursive estimation of the state variables, obtaining the first... Master estimate of continuous electrical SOC at time t This serves as the primary estimation basis for subsequent expansion force auxiliary correction.

3. The method of claim 1, wherein, Methods for identifying load switching moments and constructing recovery windows include: At the first k At the current time, the current change amount from the previous time is calculated: wherein, represents the current value at the k time point, represents the current value at the k-1 time point; when the current variation amount is greater than a preset current variation threshold , and the current variation amount continuously satisfies the threshold condition in a preset continuous determination interval, determining that load switching occurs at a first time; after the load switching time, selecting a local time period as a candidate recovery window, and the current values of the sampling points in the candidate recovery window satisfy: wherein, represents the current value of the i-th sample point within the recovery window, i represents the current value of the i-th sample point within the recovery window, represents the average current value within the recovery window, represents the current fluctuation threshold value; The local time period satisfying the current fluctuation threshold condition and the inflation force signal showing a monotonic recovery change or an asymptotic stable change trend is selected as the recovery window; wherein the preset current change threshold , the current fluctuation threshold and the recovery window length are determined by statistical analysis and parameter calibration of offline experimental data of the target lithium ion battery under a preset temperature interval and a preset working condition interval.

4. The method of claim 1, wherein, Methods for relaxing and fitting the expansion force response within the recovery window and extracting the relaxation time constant include: Let the recovery window start time be denoted as The inflation force response within the recovery window was fitted with an exponential relaxation model as follows: wherein, represents the inflation force value at time t within the recovery window, represents the asymptotic inflation force value, represents the offset of the recovery start time relative to the asymptotic value, represents the relaxation time constant of the inflation force response, represents the fitting residual; obtaining the asymptotic stable value of the swelling force based on the fitting result of the exponential relaxation model , the offset , and the relaxation time constant ; extracting the relaxation time constant as a relaxation characteristic parameter representing the fast or slow feature of the kinetics of the swelling force recovery process.

5. The method of claim 1, wherein, Methods for generating SOC correction reference values ​​and determining their effectiveness based on relaxation time constants include: According to the corresponding relationship between the relaxation time constant and the SOC of the target lithium ion battery established by offline calibration of the target lithium ion battery under a preset temperature range and a preset working condition range, based on the relaxation time constant The SOC correction reference value is generated , which is represented as: wherein represents a calibrated mapping relationship between the relaxation time constant and the SOC, represents the temperature and the operating condition parameters corresponding to the current operating state; According to the fitting degree, fitting residual of the inflation force response in the recovery window, the relaxation time constant Whether located in a preset reasonable interval, and the temperature and working condition parameters corresponding to the current operating state Whether located in a preset applicable range of the calibration mapping relationship, the SOC correction reference value Perform validity determination; When the SOC correction reference value When the validity criteria are met, the SOC correction reference value is retained as an auxiliary correction reference for the main estimate of the continuous electrical SOC; when the SOC correction reference value... If the validity determination criteria are not met, the SOC correction reference value is discarded and the SOC correction update is not triggered.

6. The method according to claim 1, characterized in that, Methods for recursively updating the deviation term in the master estimate of continuous electrical SOC include: In the k At time t, define the master estimate of continuous electrical SOC. With SOC calibration reference value The deviation between them is: Update weights according to preset settings The deviation term is updated recursively: in, Indicates the first k-1 The deviation term in time, Indicates the first k The deviation term after constant updates This represents the update weight used to control the degree of influence of the current SOC correction reference value on the deviation term update; The master estimate of continuous electrical SOC is corrected based on the updated deviation term to obtain the first... k Online SOC estimate at time: The update process for the deviation term is constrained to satisfy the single deviation correction magnitude constraint: And SOC rate of change constraint: in, This indicates the maximum allowable range of change for a single deviation correction. This represents the maximum allowable change in the SOC estimate between adjacent time points.

7. A lithium-ion battery SOC online estimation system based on force-electric coupling measurement, used to implement the method described in any one of claims 1-6, characterized in that, include: The data acquisition module is used to collect current signals, voltage signals, temperature signals, and expansion force signals during the operation of lithium-ion batteries. The electrical SOC master estimation module is connected to the data acquisition module and is used to establish a second-order RC equivalent circuit model of the lithium-ion battery based on the current signal, voltage signal and temperature signal, and to output a continuous electrical SOC master estimate value using an adaptive unscented Kalman filter algorithm. The load switching and recovery window identification module is connected to the data acquisition module. It is used to identify the load switching time based on the current change amplitude and duration, and after the load switching time, to filter the recovery window based on the current fluctuation conditions and the expansion force recovery trend conditions. The relaxation feature extraction module, connected to the load switching and recovery window identification module, is used to perform exponential relaxation fitting on the expansion force response within the recovery window and extract the relaxation time constant characterizing the dynamic speed of the recovery process. The SOC reference correction module is connected to the relaxation feature extraction module and the data acquisition module. It is used to generate a SOC correction reference value based on the pre-calibrated correspondence between the relaxation time constant and SOC, combined with the temperature and operating parameters corresponding to the current operating state, and to determine the validity of the SOC correction reference value based on the fitting quality and the preset applicable range. The deviation update module, connected to the electrical SOC master estimation module and the SOC reference correction module, is used to recursively update the deviation term in the continuous electrical SOC master estimation value when the SOC correction reference value meets the validity judgment condition, and output the corrected lithium-ion battery SOC online estimation result.

8. The system according to claim 7, characterized in that, The SOC reference correction module includes: The calibration management unit is used to establish, store, or recall the calibration mapping relationship between the relaxation time constant and SOC corresponding to the current operating state based on the offline experimental data of the target lithium-ion battery under preset temperature range and preset operating condition range. A mapping generation unit, connected to the calibration management unit, is used to generate a SOC correction reference value based on the relaxation time constant and the calibration mapping relationship; The validity determination unit, connected to the mapping generation unit, is used to filter the SOC correction reference value based on the goodness of fit of the expansion force response within the recovery window, the fitting residual, the reasonable range of the relaxation time constant, and whether the current operating temperature and operating conditions are within the applicable range of the calibration mapping relationship, and outputs a valid SOC correction reference value only when the validity determination conditions are met.

9. The system according to claim 7, characterized in that, The deviation update module includes: The deviation calculation unit, connected to the validity determination unit and the electrical SOC master estimation module, is used to calculate the current deviation based on the difference between the SOC correction reference value and the continuous electrical SOC master estimation value. The constraint update unit, connected to the deviation calculation unit, is used to recursively update the deviation item according to the preset update weight when the SOC correction reference value is valid, apply a single correction magnitude constraint to the recursive update of the deviation item, and apply a SOC change rate constraint to the online SOC estimation result obtained based on the updated deviation item. The result output unit is connected to the constraint update unit and the electrical SOC master estimation module. It is used to correct the continuous electrical SOC master estimate based on the updated deviation term and output the final online SOC estimation result.

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