A high-precision method for joint electric-power estimation of lithium iron phosphate battery SOC

Abstract

This invention relates to a high-precision method for estimating the state of charge (SOC) of lithium iron phosphate (LFP) batteries using a combined electro-mechanical approach. The innovation lies in combining an electro-mechanical dual-signal collaborative mechanism with a two-stage unscented Kalman filter architecture. By simultaneously acquiring voltage, current, and expansion force signals, a dual-polarization equivalent circuit model and a Gaussian process regression expansion force model are established. The expansion force model employs global offset compensation to overcome mechanical relaxation drift. A primary SOC estimation is first performed based on the voltage model, followed by a secondary correction using expansion force as an independent observation. A dynamic triggering mechanism is introduced, triggering OCV (Optical Characteristic Value) inverse calibration when the voltage fitting error remains below a threshold. This patent overcomes the bottleneck in estimating the voltage flat region of LFP batteries, reducing the SOC error from 2.29-4.16% of traditional methods to 0.58-1.00%. The expansion force compensation mechanism improves robustness under different preload conditions, achieving an initial SOC error tolerance of ±20%, effectively preventing the risk of overcharging / over-discharging.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of battery management system, and particularly relates to a high-precision method for estimating SOC of lithium iron phosphate battery by combining electricity and force. BACKGROUND

[0002] With the transformation of global energy structure, electric vehicles as the core carrier of clean energy transportation are experiencing popular growth. In this transportation energy revolution, the power battery system is like the "heart" of the electric vehicle, and its performance directly determines the vehicle's range, safety reliability and power output characteristics. Among them, lithium ion battery has the advantages of high energy density, long cycle life and low self-discharge rate, and has become the mainstream in the field of power battery. However, safety is always a key problem that cannot be avoided in the development of battery technology. Therefore, in order to ensure the safety and efficient operation of the battery, it is essential to develop a battery management system that can accurately monitor the battery state and develop corresponding safety strategies.

[0003] In order to solve this problem, the SOC estimation technology has become the key to the large-scale commercial application of electric vehicles.

[0004] The state of charge (SOC) of the battery is one of the core monitoring parameters in the battery management system, which represents the real-time available capacity of the battery, and its accuracy directly affects the battery energy management optimization level, the control of the safe boundary of charging and discharging, and the reliability of the battery endurance. As a typical complex time-varying system, the battery SOC has a high nonlinear coupling relationship with directly measurable quantities such as terminal voltage and current. In order to describe this nonlinear relationship, researchers have explored various methods, which can be mainly summarized into four categories: methods based on characteristic parameters, ampere-hour integral, model-based and data-driven methods.

[0005] In the past research, the above estimation methods and their combinations are mainly focused on ternary lithium batteries and lithium cobalt oxide batteries, and their effectiveness has been verified on these battery types. Unlike the steep voltage curve of ternary lithium batteries and lithium cobalt oxide batteries, lithium iron phosphate batteries have a long and flat voltage platform, which makes it necessary to verify whether the above methods are applicable. Due to the flat characteristics of the OCV-SOC curve, it is difficult to accurately estimate the SOC by open-circuit voltage, which also leads to great challenges in SOC estimation based on the OCV-SOC curve method, and even possible failure. In summary, at present, there is still a lack of a SOC estimation method that can avoid complex curve modification and updating strategies to compensate for the lack of SOC estimation accuracy of lithium iron phosphate batteries based on electrical signals. SUMMARY

[0006] In order to overcome the deficiency of the current voltage-based lithium iron phosphate battery SOC estimation accuracy, the purpose of the present application is to provide a lithium iron phosphate battery SOC high-precision estimation method and system based on electrical signals and mechanical signals. The electric-power dual signal coordination mechanism is combined with the two-stage unscented Kalman filter architecture, the voltage, current and expansion force signals are synchronously collected, the dual polarization equivalent circuit model and the Gaussian process regression expansion force model are established, wherein the global offset compensation is adopted in the expansion force model to overcome the mechanical relaxation drift; the preliminary SOC estimation is carried out based on the voltage model, and the secondary correction is carried out by taking the expansion force as an independent observation; and the dynamic trigger mechanism is introduced, and when the voltage fitting error continuously falls below the threshold value, the OCV inverse solution calibration is triggered.

[0007] In order to achieve the above-mentioned purpose, the present application provides the following technical scheme: a high-precision method for electric-power combined estimation of lithium iron phosphate battery SOC, comprising the following steps:

[0008] Step S1, synchronously collecting the battery voltage, current and expansion force signals on an experimental platform;

[0009] Step S2, establishing a dual polarization equivalent circuit model according to the collected voltage and current signals, and using a dynamic forgetting factor least square method to identify parameters, and establishing a SOC-OCV relationship curve;

[0010] Step S3, inversely solving the SOC-OCV relationship curve to obtain an initial SOC, and using an unscented Kalman filter to perform a first-order correction on the initial SOC by combining the dual polarization equivalent circuit model;

[0011] Step S4, establishing an expansion force model by using a Gaussian process regression according to the collected expansion force signals, and performing a second-order correction on the first-order corrected SOC by using the expansion force model and recalculating the Kalman gain.

[0012] Further, the expression of the dual polarization equivalent circuit model is as follows:

[0013] ;

[0014] Among them, is the input current of the dual polarization equivalent circuit model, represents the measured battery terminal voltage, represents the open circuit voltage, represents the battery ohmic resistance, the parallel branch is used for simulating the electrochemical polarization of the battery, and the electrochemical polarization voltage generated is , the parallel branch is used for simulating the concentration polarization of the battery, and the concentration polarization voltage generated is .

[0015] Further, the swelling force model in S4 is established by Gaussian process regression, and the Gaussian process regression expression is as follows:

[0016] ;

[0017] Wherein is a random function, is a mean function, is a covariance function (or kernel function), represents a Gaussian process, which is used to describe the similarity of function values between input points.

[0018] Further, the transfer function is obtained by Laplace transform on the dual polarization equivalent circuit model as follows:

[0019] ;

[0020] In order to simplify the calculation, the intermediate variable is introduced, and the following equation is obtained:

[0021] ;

[0022] Wherein:

[0023] .

[0024] Further, the transfer function is discretized by using the bilinear transformation method, and the mapping relationship between s domain and z domain is established by , wherein T is the sampling time, the value is 1, represents the unit delay, and the following equation is obtained by substituting the transfer function equation:

[0025] ;

[0026] Simplifying the following equation can be obtained:

[0027] ;

[0028] Wherein:

[0029] represents the discrete time step, is the parameter matrix to be identified, denoted as ,

[0030] ;

[0031] Further, the SOC is estimated by using unscented Kalman filter, and the unscented Kalman filter process is as follows:

[0032] Initialize the state vector and covariance matrix:

[0033] ;

[0034] Calculate the Sigma point weights:

[0035] ;

[0036] in Let be the dimension of the state vector. and These are the weighting coefficients for the mean and the error covariance, respectively. This is a scaling factor used to control the dispersion of the Sigma points relative to the mean. This is a scaling correction factor used to further adjust the distribution of Sigma points; its value is 0. The mean weight parameter has a value of 2. Used to control the generation rules of Sigma points;

[0037] Calculate the Sigma point:

[0038] ;

[0039] in and The first The state mean and covariance matrix of the order This represents the Sigma point, where the mean shifts towards the positive or negative.

[0040] Prior estimates and covariance updates

[0041] ;

[0042] in This represents the value of each Sigma point obtained through model recursion. This represents the predicted state mean. The predicted state covariance is represented by Q, and the process noise in the model recursion is represented by Q.

[0043] Posterior estimation and covariance update:

[0044] ;

[0045] in This represents the predicted measurement value calculated using the observation equation for each Sigma point. To calculate the predicted measurement mean, This represents the predicted measurement covariance. This represents the measurement noise covariance.

[0046] Kalman gain calculation

[0047] ;

[0048] in This represents the cross-covariance between the state and the measurement. Indicates Kalman gain,

[0049] SOC status update:

[0050] ;

[0051] in This represents the measured value of the actual observed quantity.

[0052] Furthermore, the estimation method in S3 first obtains parameters, including the battery OCV, through real-time parameter identification. The obtained parameters are then fed into the model, and the implementation process is as follows:

[0053] S3.1. Order ,in This is a vector-form set of battery system parameters. This refers to the battery's OCV, or open-circuit voltage.

[0054] S3.2. Real-time estimation of battery terminal voltage ,in The terminal voltage estimated by the model. This is a voltage calculation function based on a dual-polarization equivalent circuit model. These are the parameter set estimates obtained through a real-time parameter identification algorithm. This is the estimated SOC value. This refers to the charging and discharging current measured in real time.

[0055] S3.3. Order ,in For model voltage fitting error, This is the measured battery terminal voltage;

[0056] S3.4. Order and ,in This is a preset voltage error threshold, used to determine whether the error is small enough. The rate of change of error over time is used to reflect whether the error is stable. The preset error change rate threshold is used to determine whether the change is gradual;

[0057] S3.5, obtained from the SOC-OCV experiment Inverse solution obtained ,in This is the fitting function for OCV and SOC. for The inverse function;

[0058] S3.6、 ,in The initial corrected SOC value is obtained based on the OCV inverse solution. To identify the obtained open-circuit voltage estimate.

[0059] Furthermore, by combining the dual-polarization equivalent circuit model and the unscented Kalman filtering method, the first-level correction of the SOC is performed, and its implementation process is as follows:

[0060] S3.7 ,in The state vector for the unscented Kalman filter. This refers to the electrochemical polarization voltage in the dual-polarization equivalent circuit model. This represents the concentration polarization voltage in the dual-polarization equivalent circuit model. The voltage is the internal resistance in ohms.

[0061] S3.8 ,in The terminal voltage predicted by the dual-polarization equivalent circuit model. The voltage prediction function for the dual-polarization equivalent circuit model is based on the state prediction values ​​and the current. The state predictions in the UKF (Unscented Kalman Filter) include the SOC (State of Charge) prediction, the ohmic internal resistance voltage prediction, and the polarization voltage prediction.

[0062] S3.9 ,in It is the voltage residual in the first-level correction, that is, the difference between the measured voltage and the predicted voltage, reflecting the prediction deviation.

[0063] S3.10 ,in The Kalman gain of the first-order UKF is used to determine the weight of the residual on the state correction. This is the cross-covariance matrix of the state and residuals in the first-level correction, used to reflect the correlation between the state and the residuals. This is the inverse of the covariance matrix of the residuals in the first-order correction, reflecting the uncertainty of the residuals.

[0064] S3.11 ,in This is the SOC value after UKF correction at level one. This is the predicted value of SOC in UKF.

[0065] Furthermore, in S4, the Kalman gain is calculated to complete the second-order correction of the SOC. The specific implementation process is as follows:

[0066] S4.1. Using the SOC of voltage observation as the initial value of expansion force observation, calculate the positive and negative offset Sigma points directly based on the SOC value estimated by the upper-level UKF and the updated state covariance.

[0067] make ;

[0068] in It is the state covariance matrix of the previous time step in the first-level UKF. It is the state covariance matrix at the current time in the first-level UKF. The matrix norm is used to quantify matrix differences. The preset covariance convergence threshold is used to determine whether the state estimation has reached stability.

[0069] make , ;

[0070] in This is the initial SOC value for the second-level UKF, which inherits the first-level correction result. Let the initial covariance matrix of the second-order UKF be the covariance matrix inherited from the first-order correction. ,in These are the sigma points generated in UKF, used to approximate the probability distribution of the state. This is the scaling factor for UKF. The dimension of the state vector;

[0071] S4.2 Calculate the mean of the state and the predicted state covariance, substitute the Sigma point of the mean into the expansion force model, and calculate the predicted measurement mean and covariance.

[0072] make ;

[0073] in For the expansion force predicted based on sigma points, This is a mapping function from SOC to expansion force, calibrated experimentally, reflecting the correlation between SOC and battery expansion force.

[0074] make , ;

[0075] in This represents the mean of the predicted expansion force. These are the mean weights of the sigma points, used for weighted calculation of the predicted mean. These are the covariance weights at the sigma points, used for weighted calculation of the predicted covariance. The covariance of the expansion force prediction reflects the uncertainty in the expansion force prediction. This represents summing over all sigma points; let ,in This is the cross-covariance matrix of SOC state and expansion force, used to reflect the correlation between the two;

[0076] S4.3 Calculate the cross covariance based on the state and measured values, and finally recalculate the Kalman gain to complete the second-level correction of the SOC:

[0077] make ;

[0078] in The Kalman gain of the second-order UKF is used to determine the weight of the expansion force residual on the SOC correction; the final SOC value ,in This is the final SOC value after UKF correction at level two. This is the measured battery expansion force. This is the expansion force residual, which is the difference between the measured expansion force and the predicted expansion force.

[0079] Beneficial Effects: To address the issue of insufficient accuracy in traditional SOC estimation methods for lithium iron phosphate (LFP) batteries due to the flat voltage plateau region, a collaborative estimation framework integrating electric and force signals is proposed. Its core is to achieve high-precision SOC correction by simultaneously acquiring voltage, current, and expansion force signals, combined with a two-stage unscented Kalman filter (UKF) architecture.

[0080] A dual-polarization equivalent circuit model is established to describe the electrochemical characteristics, and the parameters (such as ohmic internal resistance and polarization parameters) are identified in real time using the dynamic forgetting factor least squares method.

[0081] A Gaussian process regression (GPR) expansion force model is established, and a global offset compensation mechanism is introduced to suppress mechanical relaxation drift, thus nonlinearly linking the expansion force with the state of expansion (SOC).

[0082] Level 1 (Voltage Correction): Based on the equivalent circuit model and UKF, the initial SOC (from the SOC-OCV curve) is corrected using voltage observations.

[0083] Second stage (expansion force correction): Using the SOC output from the first stage as the initial value, the expansion force is directly used as an independent observation, and the SOC is corrected twice by UKF (skipping state recursion and directly calculating the Sigma point).

[0084] Dynamic calibration triggering: When the voltage fitting error remains below a threshold, OCV inverse calibration is triggered, accelerating convergence under large initial errors. This significantly improves SOC estimation accuracy and overcomes the bottleneck in the voltage flat region. It also enhances system robustness and safety. Attached Figure Description

[0085] Figure 1 This is a dual-polarization equivalent circuit model diagram of the lithium iron phosphate (LFP) battery of the present invention.

[0086] Figure 2 This is a comparison chart of the measured voltage and the model output voltage under UDDS conditions with a preload of 1000N.

[0087] Figure 3 This is a comparison chart between the predicted and actual expansion force values ​​under UDDS conditions according to the present invention.

[0088] Figure 4 This invention compares the SOC estimation with and without expansion force under a preload of 1000N and the ampere-hour integral method as the reference value for the true SOC. The SOC prediction results under the UDDS condition are shown in the figure.

[0089] Figure 5 This invention compares the SOC estimation with and without expansion force under a preload of 2000N and the ampere-hour integral method as the reference value for the true SOC. The SOC prediction results under the UDDS condition are shown in the figure.

[0090] Figure 6 This is a schematic diagram of the entire SOC estimation process of the present invention. Detailed Implementation

[0091] 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.

[0092] Please refer to Figures 1-6 The technical solution adopted by this invention to solve its technical problem is: a high-precision method for jointly estimating the state of charge (SOC) of a lithium iron phosphate battery using both electric and mechanical methods, comprising the following steps:

[0093] Step S1: Synchronously acquire voltage, current, and expansion force signals on the experimental platform;

[0094] Step S2: Establish a dual-polarization equivalent circuit model, identify parameters using the least squares method with dynamic forgetting factor, establish the SOC-OCV relationship, and establish an expansion force model using Gaussian process regression.

[0095] Step S3: Perform a primary SOC estimation based on the SOC-OCV curve, and then perform a first-level correction of the SOC by combining the equivalent circuit model and unscented Kalman filtering.

[0096] Step S4: Using the voltage observation SOC as the initial value of the expansion force observation, directly calculate the positive and negative offset Sigma points based on the SOC value estimated by the upper-level UKF and the updated state covariance. Then calculate the mean of the state and the predicted state covariance. Substitute the Sigma points of the mean into the expansion force model and calculate the predicted mean and covariance of the measured quantities. Calculate the cross covariance based on the state and measured values. Finally, calculate the Kalman gain again to complete the second-level correction of the SOC after the first-level correction.

[0097] The signals mentioned in step S1 include voltage signals, current signals, and expansion force signals.

[0098] The circuit model described in step S2 is a dual-polarization equivalent circuit model, and its expression is as follows:

[0099] ;

[0100] ;

[0101] ;

[0102] in, It is the input current in the dual-polarization equivalent circuit model. This indicates the measured battery terminal voltage. Indicates open-circuit voltage. This indicates the ohmic internal resistance of the battery. The parallel branch is used to simulate the electrochemical polarization of a battery, and the voltage it generates is , The parallel branch is used to simulate the concentration polarization of the battery, and the voltage it generates is .

[0103] The expansion force model established using Gaussian process regression mentioned in step S2 above has the following process expression:

[0104] ;

[0105] in, It is a mean function. It is the covariance function (or kernel function) used to characterize the similarity of function values ​​between input points.

[0106] ;

[0107] in Indicates the dimension of the input data. For amplitude parameters, and Represents the input vector and The dimensional components, Assign an independent length scale parameter to each feature.

[0108] For the training dataset Observed values We can assume it to be the objective function. Add independent Gaussian noise :

[0109] ;

[0110] in The variance of the noise is a hyperparameter, and the distribution of the observed vector is simultaneously subjected to a Gaussian process (i.e., The combined effects of noise and other factors.

[0111] Model output vector Follows a multivariate Gaussian distribution . Let be the covariance matrix, and its elements Therefore, the prior distribution of the observed values ​​follows:

[0112] ;

[0113] For new test points With training set function values The joint distribution still follows a Gaussian distribution:

[0114] ;

[0115] in Based on the conditional distribution properties of the multivariate Gaussian distribution, Bayesian inference is used to determine the conditional distribution of the input training data. and observation and test input Under the conditions, predicted value The distribution is as follows:

[0116] ;

[0117] The predicted mean and predicted variance are respectively:

[0118] ;

[0119] ;

[0120] The predicted mean provides the best point estimate, while the variance provides the uncertainty of the prediction.

[0121] The parameter identification method described in step S2 is the least squares method with a dynamic forgetting factor, and its process is as follows:

[0122] First, the established continuous battery model is discretized to accommodate the sensor's sampling data. The resulting transfer function is:

[0123] ;

[0124] ;

[0125] ;

[0126] To simplify the calculation, intermediate parameters are introduced. ,get:

[0127] ;

[0128] in, ;

[0129] The transfer function is discretized using the bilinear transform method, through... Establish a mapping relationship between the s-domain and the z-domain, where T is the sampling time and its value is 1. Representing a unit delay, substituting it into the transfer function equation yields:

[0130] ;

[0131] Simplifying, we get:

[0132] ;

[0133] in:

[0134] ;

[0135] ;

[0136] ;

[0137] Represents the discrete time step. Let be the parameter matrix to be identified, denoted as .

[0138] The unscented Kalman filtering process described in step S3 is as follows:

[0139] Step 1. Initialize the state vector and covariance matrix

[0140] ;

[0141] Step 2. Calculate the weights of the Sigma points.

[0142] ;

[0143] ;

[0144] in Let be the dimension of the state vector. and These are the weighting coefficients for the mean and the error covariance, respectively. This is a scaling factor used to control the dispersion of Sigma points relative to the mean. This is a scaling correction factor used to further adjust the distribution of Sigma points, and its value is 0. The mean weight parameter has a value of 2. Rules used to control the generation of Sigma points.

[0145] Step 3. Calculate the Sigma point

[0146] ;

[0147] ;

[0148] ;

[0149] in and The first The state mean and covariance matrix of the order This represents the Sigma point where the mean is shifted towards the positive or negative.

[0150] Step 4. Prior Estimation and Covariance Update

[0151] ;

[0152] ;

[0153] ;

[0154] in This represents the value of each Sigma point obtained through model recursion. This represents the predicted state mean. denoted by , where represents the predicted state covariance, and Q represents the process noise in the model recursion.

[0155] Step 5. Update of posterior estimates and covariance

[0156] ;

[0157] ;

[0158] ;

[0159] in This represents the predicted measurement value calculated using the observation equation for each Sigma point. To calculate the predicted measurement mean, This represents the predicted measurement covariance. This represents the measurement noise covariance.

[0160] Step 6. Calculation of Kalman Gain

[0161] ;

[0162] in This represents the cross-covariance between the state and the measurement. This represents the Kalman gain.

[0163] Step 7. Status Update

[0164] ;

[0165] in This represents the measured value of the actual observed quantity.

[0166] Furthermore, the secondary correction described in step S4 mainly includes the following process:

[0167] First, parameters, including the battery OCV, are acquired through real-time parameter identification. These acquired parameters are then incorporated into the model. The implementation process is as follows:

[0168] STEP 1. Order ,in This is a vector-form set of battery system parameters. This refers to the battery's OCV, or open-circuit voltage.

[0169] STEP 2. Real-time estimation of battery terminal voltage ,in The terminal voltage estimated by the model. This is a voltage calculation function based on an equivalent circuit model. These are the parameter set estimates obtained through a real-time parameter identification algorithm. This is the estimated SOC value. This refers to the charging and discharging current measured in real time.

[0170] STEP 3. Order ,in For model voltage fitting error, This is the measured battery terminal voltage.

[0171] STEP 4. Order and ,in This is a preset voltage error threshold, used to determine whether the error is small enough. The rate of change of error over time is used to reflect whether the error is stable. The preset error change rate threshold is used to determine whether the change is sufficiently gradual.

[0172] A high-precision method for jointly estimating the state of charge (SOC) of a lithium iron phosphate battery, as described in step S4, is characterized by assigning the SOC obtained by inversely solving the relationship between the identified operational variable (OCV) and the SOC to the current estimated value. Even if this SOC is not an accurate value, it can, to some extent, correct the original SOC, which may have a large initial error, thus accelerating the model correction. Based on this, a first-level correction of the SOC is performed by combining an equivalent circuit model and an unscented Kalman filter method. The implementation process is as follows:

[0173] STEP 1. Obtained from the SOC-OCV experiment Inverse solution obtained ,in This is the fitting function for OCV and SOC. for The inverse function of .

[0174] STEP2. ,in The initial corrected SOC value is obtained based on the OCV inverse solution. To identify the obtained open-circuit voltage estimate.

[0175] STEP3. ,in The state vector for the unscented Kalman filter. This refers to the electrochemical polarization voltage in the equivalent circuit model. This represents the concentration polarization voltage in the equivalent circuit model. The voltage is the internal resistance of the ohm.

[0176] STEP4. ,in The terminal voltage predicted by the equivalent circuit model. The voltage prediction function is based on the state prediction values ​​and current for the equivalent circuit model. These are the state prediction values ​​in the UKF, including the SOC prediction value, the ohmic internal resistance voltage prediction value, and the polarization voltage prediction value.

[0177] STEP 5. ,in It is the voltage residual in the first-level correction, that is, the difference between the measured voltage and the predicted voltage, reflecting the prediction deviation.

[0178] STEP 6. ,in The Kalman gain of the first-order UKF is used to determine the weight of the residual on the state correction. This is the cross-covariance matrix of the state and residuals in the first-level correction, used to reflect the correlation between the state and the residuals. It is the inverse of the covariance matrix of the residuals in the first-order correction, reflecting the uncertainty of the residuals.

[0179] STEP 7. ,in This is the SOC value after UKF correction at level one. This is the predicted value of SOC in UKF.

[0180] When the observed and measured values ​​are close and stable, the state covariance matrix gradually converges as the state estimation stabilizes. The SOC value estimated by the UKF based on voltage observations will be used as the initial value for the next level of SOC based on expansion force observations. At this point, instead of performing a recursive SOC calculation, the Sigma points for positive and negative offsets are directly calculated based on the SOC value estimated by the previous UKF and the updated state covariance. Then, the mean of the state and the predicted state covariance are calculated. The Sigma points of the mean are substituted into the expansion force model, and the mean and covariance of the predicted measured quantities are calculated. The cross covariance is calculated based on the state and measured values, and finally, the Kalman gain is calculated again to complete the second-level correction of the SOC. The specific implementation process is as follows:

[0181] STEP 1. Order ,in It is the state covariance matrix of the previous time step in the first-level UKF. It is the state covariance matrix at the current time in the first-level UKF. The matrix norm is used to quantify matrix differences. The preset covariance convergence threshold is used to determine whether the state estimation has reached stability.

[0182] STEP 2. Order , ,in This is the initial SOC value of the second-level UKF, which inherits the first-level correction result. This is the initial covariance matrix of the second-level UKF, which inherits the covariance of the first-level correction.

[0183] STEP 3. Order ,in These are the sigma points generated in UKF, used to approximate the probability distribution of the state. This is the scaling factor for UKF. The dimension is the state vector.

[0184] STEP 4. Order ,in For the expansion force predicted based on sigma points, This is a mapping function from SOC to expansion force, calibrated experimentally, reflecting the correlation between SOC and battery expansion force.

[0185] STEP 5. Order , ,in This represents the mean of the predicted expansion force. The mean weights of the sigma points are used to calculate the predicted mean using weighted averages. These are the covariance weights for the sigma points, used for weighted calculation of the predicted covariance. The covariance of the expansion force prediction reflects the uncertainty in the expansion force prediction. This represents summing over all sigma points.

[0186] STEP 6. Order ,in This is the cross-covariance matrix of the SOC state and the expansion force, used to reflect the correlation between the two.

[0187] STEP 7. Order ,in The Kalman gain of the second-order UKF is used to determine the weight of the expansion force residual on the SOC correction.

[0188] STEP 8. Final SOC value ,in This is the final SOC value after UKF correction at level two. This is the measured battery expansion force. This is the expansion force residual, which is the difference between the measured expansion force and the predicted expansion force.

[0189] like Figure 1 The circuit diagram described above is used to implement the SOC correction of this solution. It includes a power supply connected to an ohmic resistor. This ohmic resistor is used to simulate ohmic losses during charge transfer within a battery, and it is connected to an electrochemically polarized resistor. and electrochemical polarization capacitor It is used to simulate the electrochemical polarization of a battery, and the voltage it generates is The electrochemical polarization resistor and electrochemical polarization capacitor are connected to a concentration polarization resistor. and concentration polarization capacitance This model is used to simulate concentration polarization inside a battery; the input to the model is current. The model output is the terminal voltage. .

[0190] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A high-precision method for estimating the state of charge (SOC) of a lithium iron phosphate battery by combining electrical and mechanical parameters, characterized in that, The method comprises the following steps: Step S1, synchronously collecting the battery voltage, current and swelling force signals on an experimental platform; Step S2, establishing a dual polarization equivalent circuit model according to the collected voltage and current signals, and performing parameter identification by using a dynamic forgetting factor least square method to establish an SOC-OCV relationship curve; Step S3, inversely solving the SOC-OCV relationship curve to obtain an initial SOC, and performing first-order correction on the initial SOC by combining the dual polarization equivalent circuit model and using an unscented Kalman filter; The estimation method in the S3 first obtains parameters including the battery OCV through real-time parameter identification, and the obtained parameters are brought into the dual polarization equivalent circuit model, and the implementation process is as follows: S3.

1. Let wherein is the vector-form battery system parameter collection, is the battery OCV, i.e. open circuit voltage; S3.

2. Real-time estimation of the battery terminal voltage wherein is the model estimated terminal voltage, is the voltage calculation function based on the dual polarization equivalent circuit model, is the parameter set estimate obtained by the real-time parameter identification algorithm, is the SOC estimate, is the real-time measured charge and discharge current; S3.

3. Let where is the model voltage fitting error, is the measured battery terminal voltage; S3.

4. Let and wherein is a preset voltage error threshold value for determining whether the error is small enough, is a rate of change of the error over time for reflecting whether the error is stable, is a preset error rate threshold value for determining whether the change is smooth. S3.5, obtained from SOC-OCV experiment Solving the equation, we get where is the fitting function of OCV and SOC, is the inverse function of ​ S3.6、 , wherein is the initial SOC value obtained from the inverse OCV solution, is the identified open circuit voltage estimate; The first-order correction of the SOC is performed by combining the dual polarization equivalent circuit model and the unscented Kalman filter method, and the implementation process is as follows: S3.7、 wherein is the state vector of the unscented Kalman filter, is the electrochemical polarization voltage in the dual-polarization equivalent circuit model, is the concentration polarization voltage in the dual-polarization equivalent circuit model, is the voltage of the ohmic internal resistance; S3.8、 , wherein is the terminal voltage predicted by the dual-polarization equivalent circuit model, is a voltage prediction function of the dual-polarization equivalent circuit model based on state prediction values and current, is a state prediction value in the unscented Kalman filter (UKF) containing a SOC prediction value, an ohmic internal resistance voltage prediction value, and a polarization voltage prediction value; S3.9、 wherein is the voltage residual in the primary correction, i.e. the difference between the measured voltage and the predicted voltage, reflecting the prediction bias; S3.10、 wherein K1is the Kalman gain of the first order UKF, used to determine the weight of the residual to the state correction, P1is the cross-covariance matrix of the state and the residual in the first order correction, used to reflect the correlation between the state and the residual, R1is the inverse matrix of the covariance matrix of the residual in the first order correction, reflecting the uncertainty of the residual; S3.11、 wherein is the SOC value after the first order UKF correction, is the predicted value of SOC in the UKF; Step S4, establishing a swelling force model by using a Gaussian process regression according to the collected swelling force signals, and performing second-order correction on the first-order corrected SOC by the swelling force model and the recalculated Kalman gain; The second-order correction of the SOC is completed by calculating the Kalman gain in the S4, and the specific implementation process is as follows: S4.1, taking the SOC observed by the voltage as the initial value observed by the swelling force, directly calculating the Sigma points of positive and negative offsets based on the SOC value estimated by the upper UKF and the updated state covariance; Let ; wherein is the state covariance matrix at the previous time step in the primary UKF, is the state covariance matrix at the current time step in the primary UKF, denotes the matrix norm, which is used to quantify the matrix difference, is a pre-defined covariance convergence threshold, which is used to determine whether the state estimation has reached stability. Let , ; wherein is the initial SOC value of the secondary UKF, i.e. inherited from the primary correction, is the initial covariance matrix of the secondary UKF, i.e. inherited from the covariance of the primary correction, let wherein is the sigma point generated in the UKF, used to approximate the probability distribution of the state, is the scaling factor of the UKF, is the dimension of the state vector; S4.2, calculating the mean value of the state and the predicted state covariance, bringing the Sigma point of the mean value into the swelling force model, and calculating the predicted measurement mean value and covariance; Let ; wherein is the swelling force based on the sigma point prediction, is a mapping function from SOC to swelling force, calibrated from experiments, reflecting the correlation between SOC and battery swelling force; Let , ; wherein is the mean of the expansion force prediction, is the mean weight of the sigma points used for the weighted calculation of the prediction mean, is the covariance weight of the sigma points used for the weighted calculation of the prediction covariance, is the covariance of the expansion force prediction, reflecting the uncertainty of the expansion force prediction, denotes the summation over all sigma points; let wherein is the cross-covariance matrix of the SOC state and the expansion force, used to reflect the correlation of both. S4.3, calculating the cross covariance according to the state and the measurement value, and finally recalculating the Kalman gain to complete the second-order correction of the SOC: Let ; wherein K is the Kalman gain of the secondary UKF, which is used to determine the weight of the swelling force residual to the SOC correction; the final SOC value wherein is the final SOC value after the secondary UKF correction, is the measured battery swelling force, is the swelling force residual, i.e., the difference between the measured swelling force and the predicted swelling force.

2. The high-precision method for estimating the SOC of a lithium iron phosphate battery by combining electrical and mechanical methods according to claim 1, characterized in that, The expression of the dual polarization equivalent circuit model is as follows: ； wherein, is the input current of the dual-polarized equivalent circuit model, denotes the measured battery terminal voltage, denotes the open circuit voltage, denotes the battery ohmic internal resistance, The parallel branch is used to simulate the electrochemical polarization of the battery, and the electrochemical polarization voltage generated is , The parallel branch is used to simulate the concentration polarization of the battery, and the concentration polarization voltage generated is .

3. The high-precision method for electric-mechanical combined estimation of SOC of a lithium iron phosphate battery according to claim 1, characterized in that, The Gaussian process regression expression of the swelling force model in the S4 is as follows: ； where is a random function, is a mean function, is a covariance function, denotes a Gaussian process, which is used to characterize the similarity of function values between input points.

4. The high-precision method for electric-mechanical combined estimation of SOC of a lithium iron phosphate battery according to claim 2, characterized in that, The dual polarization equivalent circuit model is subjected to Laplace transformation to obtain a transfer function as follows: ； For simplicity of calculation, an intermediate variable is introduced and we get: ； Wherein: 。 5. The high-precision method for electric-mechanical combined estimation of SOC of a lithium iron phosphate battery according to claim 4, characterized in that, The transfer function is discretized by using the bilinear transformation method, and the transfer function is expressed as The mapping relationship between the s domain and the z domain is established, where T is the sampling time, and the value is 1, The unit delay is represented, and the transfer function equation can be obtained by substituting the unit delay. ； Simplifying can obtain: ； Wherein: denotes the discrete time steps, is the parameter matrix to be identified, denoted by , 。 6. The high-precision method for electric-mechanical combined estimation of SOC of a lithium iron phosphate battery according to claim 1, characterized in that, The unscented Kalman filter is used for SOC estimation, and the unscented Kalman filter process is as follows: Initializing the state vector and the covariance matrix: ； Calculating the Sigma point weight: ； wherein is the dimension of the state vector, and are the weight coefficients of the mean and error covariance, respectively, is a scaling factor for controlling the degree of dispersion of the Sigma points relative to the mean, is a scaling correction factor for further adjusting the distribution of the Sigma points, taking a value of 0, is a mean weight parameter, taking a value of 2, is used to control the generation rule of the Sigma points; Calculating the Sigma point: ； wherein and are the first order state mean and covariance matrix, respectively, denotes the Sigma points at the mean plus and minus the Sigma. Updating the prior estimate and covariance ； wherein denotes the value of each Sigma point obtained by model recursion, denotes the predicted state mean, denotes the predicted state covariance, Q denotes the process noise in model recursion, Updating the posterior estimate and covariance: ； wherein represents the predicted measurement value of each Sigma point calculated by the observation equation, for calculating the predicted measurement mean, represents the predicted measurement covariance, represents the measurement noise covariance, Calculating the Kalman gain: ； wherein denotes the cross covariance between states and measurements, denotes the Kalman gain, Updating the SOC state: ； wherein the measured value representing the actual observed quantity.

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