Method and system for online correction of lithium-ion battery capacity estimation error

Abstract

The application provides a lithium ion battery capacity estimation error online correction method and system, and relates to the technical field of state estimation. The method comprises the following steps: constructing a current and voltage measurement model by introducing sensor fixed deviation and random noise; based on the ampere-hour integral method, an estimated state of charge model is established by taking the measured current and the estimated capacity as variables, and combined with the measurement model by introducing the sensor error, an expression of the state of charge estimation error is derived; the capacity reciprocal is taken as the state to be estimated, the observation gradient is determined by using the state of charge estimation error, and the capacity estimation is updated according to the innovation and the observation gradient in the Kalman filtering; based on the state of charge estimation error and the observation gradient, the closed-loop transfer relationship of the capacity estimation error is derived, and the general solution of the capacity estimation error is obtained; according to the general solution of the capacity estimation error, the capacity estimation value is compensated and corrected at the output end of the Kalman filtering, so that the online correction of the battery capacity estimation is realized, and the operation reliability and adaptability of the BMS are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of state estimation technology, and in particular to an online correction method and system for capacity estimation errors of lithium-ion batteries. Background Technology

[0002] Lithium-ion batteries are widely used in electric vehicles, energy storage, and portable devices due to their high energy density, lightweight design, and long cycle life. Accurate estimation of their State of Health (SOH) is a core task of the Battery Management System (BMS). The Extended Kalman Filter (EKF) method, which uses capacity as a state variable, is widely applied and can integrate electrical parameter information to achieve dynamic tracking.

[0003] However, in practical applications, the complex errors of current and voltage sensors severely restrict estimation accuracy: the ampere-hour integral error accumulates linearly with operating time, resulting in significant deviations after long-term use; the voltage sensor's fixed bias interference terminal voltage residual causes steady-state deviations in the closed-loop feedback; and the observability of the OCV-SOC curve plateau region is weak, making it easy for random noise in the voltage residual to be amplified, causing fluctuations in the estimation results. Existing technologies mostly provide qualitative descriptions of errors or open-loop analysis, lacking systematic modeling and engineering correction methods for capacity error propagation in closed-loop systems, thus failing to meet the long-term high-precision estimation requirements of the new energy field. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes an online correction method and system for lithium-ion battery capacity estimation errors, enabling high-precision, high-stability long-term online estimation of lithium-ion battery capacity and effectively improving the operational reliability and adaptability of the battery management system.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] In a first aspect, the present invention provides an online correction method for lithium-ion battery capacity estimation errors, comprising:

[0007] Construct current and voltage measurement models that incorporate fixed sensor bias and random noise;

[0008] Based on the ampere-hour integral method, an estimated state of charge model is established with measured current and estimated capacity as variables. Combined with the measurement model that introduces sensor error, the expression for the estimated state of charge error is derived.

[0009] The reciprocal of the capacity is used as the state to be estimated. The observation gradient is determined using the state of charge estimation error. The capacity estimate is then updated in the Kalman filter based on the new information and the observation gradient.

[0010] Based on the state of charge estimation error and the observation gradient, the closed-loop propagation relationship of the capacity estimation error is derived, and the general solution of the capacity estimation error is obtained.

[0011] Based on the general solution of the capacity estimation error, the capacity estimate is compensated and corrected at the output of the Kalman filter to achieve online correction of the battery capacity estimate.

[0012] In a second aspect, the present invention provides an online correction system for lithium-ion battery capacity estimation errors, comprising:

[0013] The modeling module is configured to build current and voltage measurement models that incorporate fixed sensor biases and random noise.

[0014] The error module is configured to establish an estimated state of charge model with measured current and estimated capacity as variables based on the ampere-hour integration method, and derive the expression for the estimated state of charge error by combining the measurement model that incorporates sensor error.

[0015] The gradient module is configured to take the inverse of the capacity as the state to be estimated, determine the observation gradient using the state of charge estimation error, and update the capacity estimate in the Kalman filter based on the information and the observation gradient.

[0016] The derivation module is configured to derive the closed-loop propagation relationship of the capacity estimation error based on the state of charge estimation error and the observation gradient, and obtain the general solution of the capacity estimation error.

[0017] The correction module is configured to compensate and correct the capacity estimate at the output of the Kalman filter according to the general solution of the capacity estimation error, so as to realize online correction of the battery capacity estimate.

[0018] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the online correction method for capacity estimation error of a lithium-ion battery as described in the first aspect.

[0019] Fourthly, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the online correction method for capacity estimation error of a lithium-ion battery described in the first aspect.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0021] This invention addresses the industry pain points of traditional Kalman filter estimation—namely, the accumulation of ampere-hour integration errors, steady-state deviations caused by voltage bias, and noise amplification in the plateau region—by explicitly modeling sensor errors and systematically characterizing the propagation law of state-of-charge errors. Simultaneously, the correction strategy designed based on the error propagation mechanism can dynamically adjust filter parameters, suppressing long-term drift of current deviations, maintaining estimation stability under weakly observable conditions, and matching noise variations in actual operating conditions. Compared to traditional methods, this invention significantly improves the accuracy and stability of battery capacity estimation, achieving high-precision online estimation throughout the entire lifecycle, and providing reliable technical support for the safe and efficient operation of new energy vehicles and energy storage systems.

[0022] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0023] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute a limitation thereof.

[0024] Figure 1 A main flowchart of an online correction method for capacity estimation error of lithium-ion batteries provided in an embodiment of the present invention;

[0025] Figure 2 The following is a diagram showing the uncorrected capacity estimation and its error analysis provided in an embodiment of the present invention; wherein, (a) is a comparison diagram of the capacity estimation value and the true value under the uncorrected condition; and (b) is a comparison diagram of the theoretical confidence interval and the actual error of the capacity estimation error under the uncorrected condition.

[0026] Figure 3 This is a schematic diagram of the corrected capacity estimation provided for an embodiment of the present invention. Detailed Implementation

[0027] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0028] Example 1

[0029] like Figure 1 As shown in the figure, this embodiment discloses an online correction method for lithium-ion battery capacity estimation error, including the following steps:

[0030] S1: Construct current and voltage measurement models that incorporate fixed sensor bias and random noise;

[0031] S2: Based on the ampere-hour integral method, an estimated state of charge model is established with the measured current and estimated capacity as variables. Combined with the measurement model that introduces sensor error, the expression for the estimated state of charge error is derived.

[0032] S3: Take the reciprocal of the capacity as the state to be estimated, use the state of charge estimation error to determine the observation gradient, and update the capacity estimate in the Kalman filter based on the information and the observation gradient.

[0033] S4: Based on the state of charge estimation error and the observation gradient, derive the closed-loop propagation relationship of the capacity estimation error to obtain the general solution of the capacity estimation error;

[0034] S5: Based on the general solution of the capacity estimation error, the capacity estimation value is compensated and corrected at the output of the Kalman filter to achieve online correction of the battery capacity estimation.

[0035] Next, combined Figure 2 This embodiment provides a detailed description of an online correction method for capacity estimation errors in lithium-ion batteries.

[0036] (I) Measurement Equations and Error Source Modeling

[0037] First, based on the nth-order RC equivalent circuit model, a discrete-time system is defined with time steps k = 0, 1, 2, ...

[0038] Based on the discrepancy and noise between sensor readings and the true value, the measurement model is modeled as follows:

[0039] True value = Measured value + Error;

[0040] In this model, the measured value is defined as the difference between the true value and the error to clearly distinguish the physical direction of the sensor bias: here, "error" specifically refers to the negative deviation component of the measured value relative to the true value, that is, when the sensor has a fixed bias or noise, the measured value will be systematically smaller than the true value. This definition directly leads to the formula "true value = measured value + error," which is more convenient for introducing the sensor error as a state variable to be estimated into the observation equation within the subsequent Kalman filter framework, thus achieving explicit modeling and correction of bias and noise.

[0041] Furthermore, to achieve explicit modeling and closed-loop correction of current and voltage sensor errors, current measurement models and voltage measurement models are established.

[0042] 1. Current measurement model:

[0043] ;

[0044] in, For current sensor readings; This represents the actual current, in amperes (A), with discharge being positive. >0), indicating a negative charge; The fixed bias of the current sensor originates from sensor zero drift, hardware aging, or calibration error, and manifests as a systematic deviation from the true value. The random noise of the current sensor follows a Gaussian distribution. These disturbances originate from electronic thermal noise, electromagnetic interference, etc., and manifest as measurement perturbations with zero mean and random fluctuations. This indicates current noise.

[0045] 2. Voltage measurement model:

[0046] First, define the physical terminal voltage equation (discharge model):

[0047] ;

[0048] in, This represents the actual terminal voltage, in volts (V). This indicates the open-circuit voltage of the battery. Indicates the true state of charge. Represents the true state of charge At that time, the corresponding open-circuit voltage value of the battery; Let represent the ohmic internal resistance of the battery, assumed to be a known constant.

[0049] It should be noted that polarization is temporarily ignored in this embodiment because the polarization voltage is considered to be without deviation in the error analysis. When the measured value and the estimated value are subtracted, the polarization voltage is directly eliminated, and the polarization voltage is not used in the subsequent formula derivation.

[0050] Voltage measurement value Including sensor errors:

[0051] ;

[0052] in, This indicates the fixed deviation of the voltage sensor. Indicates random noise of voltage sensor , This is voltage noise.

[0053] In existing technologies, SOC error analysis using the ampere-hour integration method typically only considers ideal current or introduces a single "current measurement error" as a global disturbance term, without distinguishing the statistical characteristics of the error. In this embodiment, however, the current sensor error is explicitly decomposed into systematic deviations for the first time. and random noise Two categories are identified, and SOC error models are introduced for each category. This decomposition is not a simple sign substitution, but is based on the actual sensor measurement model. The precise error propagation relationship is derived. By modeling bias and noise as state variables, sensor errors can be estimated and dynamically compensated online in real time during the later filtering process, thereby significantly improving the estimation accuracy of SOC and SOH and eliminating steady-state estimation bias caused by fixed bias.

[0054] (II) Calculus Model of State Observer and Gradient

[0055] After modeling the errors of the current and voltage sensors, the impact of these errors needs to be incorporated into the dynamic process of SOC estimation. Since SOC estimation relies on current integration, sensor bias and noise accumulate through ampere-hour integration, causing the estimation error to increase over time; simultaneously, capacity estimation errors also directly affect SOC updates. Therefore, a propagation model for SOC estimation errors needs to be established, incorporating the aforementioned error sources into a unified expression, laying the foundation for subsequent joint estimation based on Kalman filtering.

[0056] Specifically, State of Charge (SOC) cannot be directly measured and needs to be dynamically calculated through current integration. The ampere-hour integration method estimates the change in SOC by integrating the current over time, and is the most fundamental dynamic update method for SOC estimation. (True State of Charge) Calculated based on the ampere-hour integration method:

[0057] ;

[0058] in, This is the initial state of charge; This represents the reciprocal of the Coulomb efficiency, and represents the change in SOC per ampere-hour of current. This represents the actual battery capacity, in units of... Assuming the capacity is constant over a short period of time, the reciprocal of the capacity is used as a state variable for estimation in order to maintain the linear form of the equation during modeling and analysis, thus facilitating solution and processing. This method is a mathematical technique, and the true capacity can ultimately be obtained by inverse transformation. The time (in seconds) for the kth sampling moment is the absolute time point corresponding to the current calculation moment. Indicates the current in time Instantaneous value at time (unit: A, ampere); Indicates the first The actual current at any given moment; Indicates the sampling time step.

[0059] Estimating the state of charge Using current measurement The reciprocal of the estimated capacity at the previous time step The calculation yielded:

[0060] ;

[0061] in, express Time-based estimated reciprocal of capacity, in units of , ， This is a capacity estimate; Indicates the first The current sensor reading at any given time.

[0062] exist The formula directly uses Known , This indicates the error in the reciprocal estimation. ; This indicates a definition.

[0063] By explicitly incorporating the fixed bias, random noise, and capacity estimation error of the current sensor into the SOC error expression, a systematic model of the error propagation process is achieved, rather than relying solely on empirical correction or qualitative analysis.

[0064] Define the state of charge estimation error :

[0065] ;

[0066] Calculated:

[0067] ;

[0068] in, This indicates the fixed bias of the current sensor. Let represent the random noise at time j.

[0069] Existing technologies often attribute SOC error solely to "ampere-hour integral drift" or "inaccurate capacity parameters," while this embodiment attributes it to the reciprocal capacity estimation error. With accumulated ampere Explicit coupling is presented for the first time with a quantitative expression for the cross-coupling of the two factors, and it is simultaneously reflected in the same SOC error expression along with the integral effect of the current error. Two key sources of error appear in the formula:

[0070] First item, The reciprocal error of the capacity is amplified by accumulating ampere-hours;

[0071] The second item, (The cumulative integral effect of current measurement error).

[0072] This reveals that the SOC error is the result of the combined effects of the reciprocal capacity error and the current measurement error, both of which are significantly amplified through time accumulation (integration). Simultaneously, this lays the foundation for the linearization of the subsequent Extended Kalman Filter (EKF) observation equations. The matrix and closed-loop error propagation analysis provide a precise mathematical basis.

[0073] This SOC error formula is a direct prerequisite for the subsequent derivation of the observation Jacobian matrix, the innovation expansion, and the recursive general solution of the state error in this embodiment. Without this precise SOC error decomposition, the analytical expressions for the expected value and variance of the subsequent capacity inverse error cannot be obtained.

[0074] This embodiment can more accurately reveal the physical nature and propagation mechanism of the error, and clarify the current deviation. It will cause over time Linearly growing SOC drift, random noise After integration, it exhibits random walk characteristics, thus providing a solid theoretical basis for formulating targeted compensation strategies; at the same time, it has significant engineering guiding significance, as the obtained formula can directly guide BMS engineers to balance the calibration accuracy of current sensors in online capacity estimation to reduce [the impact of current sensor calibration]. And reasonably select the cumulative amperage window to control Size, avoids capacity estimation in OCV platform areas or under conditions of insufficient ampere-hour throughput, effectively improving engineering practicality and estimation reliability.

[0075] By deriving the expression for the State of Charge (SOC) estimation error, the impact of current deviation, random noise, and capacity estimation error on SOC is clarified. However, within the Extended Kalman Filter (EKF) framework, to achieve online capacity correction, it is also necessary to establish a linearized relationship between the observed values ​​and the state to be estimated, i.e., the observation matrix (gradient). This matrix reflects the sensitivity of the terminal voltage to the reciprocal of the capacity and is the core of the Kalman gain calculation, directly affecting the direction and magnitude of the state update. Therefore, this embodiment starts from the voltage model and derives the matrix using the chain rule. The physical expression provides a theoretical basis for the subsequent implementation of filters.

[0076] First, in EKF, the observation matrix is ​​defined as the partial derivative of the observation with respect to the state vector (Jacobi matrix). This embodiment uses the inverse of the capacity... As a state to be estimated:

[0077] ;

[0078] in, This represents the reciprocal of the estimated capacity.

[0079] Since the expression for terminal voltage includes an ohmic internal resistance term. However, this term does not directly depend on the capacity, so its effect on the partial derivative can be ignored. The contribution is only considered in relation to the open-circuit voltage portion of the SOC:

[0080] ;

[0081] in, Indicates the estimated terminal voltage. This represents the estimated open-circuit voltage corresponding to the state of charge.

[0082] According to the chain rule:

[0083] ;

[0084] The first term represents the slope of the OCV curve, denoted as . The slope reflects the sensitivity of the current SOC point voltage to changes in SOC.

[0085] For the second term, the formula for calculating the estimated SOC, as known above, is:

[0086] ;

[0087] For ease of differentiation, the cumulative ampere-hour term is denoted as a constant (relative to the time factor). ):

[0088] ;

[0089] When calculating the Jacobian, the actual current or the known cumulative value from the previous time step is typically used to ensure... Certainty.

[0090] The estimation of SOC can then be simplified to:

[0091] ;

[0092] Now regarding the state variables Taking the partial derivative, we obtain the second term:

[0093] ;

[0094] Therefore, observe gradient Simplified to:

[0095] ;

[0096] The numerator represents the cumulative discharge ampere-hours. The longer the discharge lasts, the higher the ampere-hours The larger, The greater the amplitude.

[0097] In this embodiment, the reciprocal of the capacity is calculated using precise chain rule differentiation. right The impact is explicitly quantified as cumulative ampere-hours. In existing technologies, it is common to... Typically, only the OCV slope is taken, or a rough approximation is made, without performing this precise coupling. This clearly reveals... The physical amplitude is determined by the "cumulative discharge ampere-hours" and serves as the core basis for observability analysis. This embodiment specifically points out that the numerator is the cumulative discharge ampere-hours. The longer the discharge, the greater the amplitude. The larger, The larger the amplitude, the better. Existing technologies often only qualitatively describe "a certain throughput per ampere-hour is needed to estimate capacity," while this embodiment provides a quantitative, computable expression and directly uses it for system observability assessment:

[0098] ;

[0099] Traditional methods struggle to explain why capacity estimation is only effective in the non-plateau region with sufficient discharge. This embodiment addresses this by... Accurately reveals the physical nature and observability conditions of capacity estimation: avoiding the OCV plateau region and having a sufficiently large cumulative ampere-hour. Only when the value increases significantly can the observation information be sufficiently strong. This provides a clear engineering guideline for practical BMS, avoiding invalid estimations in static or plateau regions. Furthermore, the proposed observation matrix is ​​a direct prerequisite for subsequent innovation expansion, state error recursive equations, and error general solutions; without this precise... Therefore, it is impossible to derive the expressions for the expected value (Bias) and variance (Variance) of the capacity estimation error, nor is it possible to quantify the current deviation. The linear cumulative effect provides a precise mathematical basis for error analysis.

[0100] (III) Calculation of Capacity Error in Kalman Filtering

[0101] Next, we will deduce how to feed the observation error (residual) back to the system.

[0102] New calculate:

[0103] ;

[0104] in, The voltage measurement value at time k is... This is a voltage estimate. Indicates voltage sensor deviation. This indicates voltage sensor noise.

[0105] Linearized OCV error:

[0106] ;

[0107] Substituting the linearized OCV error into :

[0108] ;

[0109] The update formula for the reciprocal of the capacity in Kalman filtering is:

[0110] ;

[0111] For Kalman gain.

[0112] Define capacity error ,but:

[0113] ;

[0114] Will Substitute:

[0115] ;

[0116] Using mathematical induction:

[0117] when ;

[0118] when ;

[0119] when ;

[0120] Therefore, the above equation can be written as a standard first-order difference equation:

[0121] ;

[0122] Among them, the state transition coefficient ,because The design purpose is to make the system converge, usually .

[0123] Comprehensive input items: This fully demonstrates the driving effect of various sensor biases and noise on capacity estimation errors, which is the root cause of steady-state errors.

[0124] (iv) General solution for capacity error

[0125] Analogous to linear system theory, a state transition matrix is ​​introduced. It represents the error propagation coefficient from time j to time k. Define the state transition matrix. :

[0126] ;

[0127] ;

[0128] Wherein, the initial term coefficient .

[0129] General solution for capacity error:

[0130] ;

[0131] expect:

[0132] ;

[0133] Its physical meaning is current deviation. This error is amplified by integration, which is the main source of error during long-term operation. The sign of the symbol reflects the direction of the estimation bias.

[0134] Initial error decay term: The algorithm for eliminating initial guess error is described. The ability. As long as the system is observable. Furthermore, the gain K is designed reasonably, and this term converges exponentially to 0 over time.

[0135] Instantaneous deviation term (voltage and ohms): by and Composition. These deviations at each time step are transmitted through the gain. Entering the system. If the filter is in a steady state, this part will form a fixed steady-state error.

[0136] Integral deviation term (fundamental deviation): This term is attributed to the current deviation. The cumulative effect. The formula includes a factor. j (At the current moment), this means that the input bias increases linearly with time. Even with the Kalman gain... It decays over time; if the decay rate is slower than the growth rate of time j, the term will not converge.

[0137] variance: ;

[0138] Voltage noise contribution: by the item The decision. This directly reflects the Kalman gain. The magnitude of the gain. The higher the gain, the lower the voltage noise. The greater the fluctuations introduced.

[0139] Current noise contribution: determined by weights The decision consists of two parts:

[0140] Integral pathway: Once current noise enters the state of charge (SOC), it will persist for a long time, affecting the estimation of all subsequent time points.

[0141] Ohm Path: Current noise directly causes voltage jumps through internal resistance.

[0142] As can be seen, Kalman filtering suppresses the cumulative effect of historical noise by using closed-loop feedback coefficients.

[0143] (v) Output correction method based on explicit error expression

[0144] The preceding sections have fully derived the general solution for the reciprocal capacity error, its statistical properties, and explicit expressions for its expectation (systematic bias) and variance. Based on this, this embodiment proposes an effective output correction strategy, the core idea of ​​which is:

[0145] Existing correction techniques often involve directly modifying the filter's internal state or gain, introducing the deviation as an augmented state into the closed-loop filter, or using indirect methods such as empirical / residual feedback. These methods alter the filter's covariance propagation and dynamic characteristics, potentially introducing instability. This embodiment, however, performs output compensation entirely based on the explicit analytical expression of the error propagation model, without interfering with the EKF's internal prediction-update loop and covariance matrix update, thus maintaining the filter's theoretical consistency and original convergence characteristics.

[0146] Thus, without changing the closed-loop dynamics of the extended Kalman filter, the capacity estimate at each moment (or every fixed time window) is compensated post-hocly using the explicit results of the error propagation model, thereby significantly reducing the impact of systematic bias on the final output.

[0147] Suppose that EKF obtains the posterior estimate after completing the update at time k. .

[0148] 1. Calculate the estimated value of the current error. :

[0149] Based on the aforementioned general solution for the error, the following method can be used to estimate it. :

[0150] Using known sensor bias priors (such as those obtained from calibration) , Substituting into the expected value formula:

[0151] ;

[0152] Among them, the initial error It can be set to 0 or determined based on historical convergence data.

[0153] In engineering implementation, a more accurate error recalculation can also be performed periodically (e.g., every 10% change in SOC or every 50 Ah of accumulated ampere-hours).

[0154] 2. Obtain the corrected capacity value

[0155] ;

[0156] Or equivalent:

[0157] (Approximate with small error);

[0158] 3. Strictly distinguish between internal states and output values.

[0159] The most crucial principle is the correction value. or For external output only, including: capacity / SOH values ​​displayed to users or host computers; the prior state of the EKF at the next moment for upper-level decisions such as energy management, lifetime prediction, and balance control (used for prediction). and calculation The original, uncorrected values ​​must continue to be used:

[0160] ;

[0161] In this embodiment, the error expectation expression explicitly provides the deviation term, allowing the calculation of the error using known or calibrated prior sensor deviations or historical information trends. The specific values ​​are determined to achieve targeted and quantitative post-event compensation. This allows for precise quantification and compensation of current deviations. This reduces long-term linear drift without sacrificing filter stability. It is more accurate than existing empirical corrections or residual feedback, and significantly suppresses capacity estimation drift caused by the accumulation of fixed biases in the current sensor during long-term operation.

[0162] Since EKF does not modify the internal state, covariance and gain The propagation law remains unchanged, avoiding the suboptimal or divergence risks introduced by additional corrections. Simultaneously, the output value directly benefits from the analytical results of the error model, achieving higher long-term absolute accuracy, making it particularly suitable for scenarios requiring reliable capacity SOH output, such as electric vehicles or energy storage systems. Furthermore, correction is performed only at the output end (per step or periodically), without altering the original BMS algorithm framework, facilitating integration into existing systems.

[0163] As one implementation method, the steps of the online correction method for lithium-ion battery capacity estimation error include:

[0164] Step 1: System initialization;

[0165] When the battery management system (BMS) is powered on or the reinitialization conditions are met, perform the following operations:

[0166] Set the initial value of the reciprocal of the capacity. (Usually, the reciprocal of the nominal capacity is taken, or a statistical average based on historical data is used);

[0167] Set the initial error covariance P 0, process noise covariance Q 0, Measurement noise covariance R 0;

[0168] Step 2: Real-time data acquisition and cumulative ampere-hour calculation;

[0169] In each sampling period k:

[0170] Collect battery terminal voltage and current measurement value ;

[0171] Calculate the cumulative discharge ampere-hours .

[0172] Step 3: SOC state prediction;

[0173] Based on the reciprocal estimate of the capacity from the previous moment, predict the current state of charge:

[0174] ;

[0175] Step 4: Terminal voltage prediction;

[0176] Based on the predicted SOC and measured current, calculate the predicted terminal voltage (ignoring polarization or with compensated polarization terms):

[0177] ;

[0178] in, For ohmic internal resistance, sampling can be performed for offline identification or online identification and calibration.

[0179] Step 5: Calculate the new interest;

[0180]

[0181]

[0182] ;

[0183] Step 6: Calculate the observation matrix (Jacobi matrix);

[0184] Calculate the observation matrix based on the cumulative ampere-hours and the current operating point OCV slope:

[0185] ;

[0186] in, Obtained in real time through OCV-SOC curve lookup table and interpolation.

[0187] Step 7: Kalman filtering;

[0188] Calculate the Kalman gain:

[0189] ;

[0190] Updated reciprocal capacity estimate:

[0191] ;

[0192] Update error covariance:

[0193] ;

[0194] in, This represents the prior error covariance;

[0195] Output capacity estimate:

[0196] ;

[0197] Step 8: Correct the output capacity value:

[0198] use :

[0199] ;

[0200] get:

[0201] ;

[0202] Will Substitute:

[0203] ;

[0204] ;

[0205] Output the final capacity estimate: ;

[0206] Calculate SOH: The ratio of the current estimated capacity to the nominal capacity is the current output SOH.

[0207] To verify the correctness of the above method and error propagation model, the following experiments were conducted in a simulation environment:

[0208] Experimental conditions: A ternary lithium battery with a nominal capacity of 2.453819558 Ah was used, and the test was conducted at 25℃ under mixed pulse power characteristic (HPPC) conditions.

[0209] A fixed bias of 0.5A was added to the actual current measurement value, and a fixed bias of 100mV was added to the actual terminal voltage measurement value. Gaussian white noise (standard deviation of current noise 0.5A, standard deviation of voltage noise 10mV) was then superimposed on the actual current measurement value.

[0210] The standard EKF and the correction strategy of this invention are used for online capacity estimation, while theoretical predictions are made based on the calculated expected error and variance.

[0211] The main experimental results are as follows:

[0212] After adding a fixed bias and noise, such as Figure 2 :from Figure 2 As can be seen in (a), the capacity estimation of the traditional fixed-parameter EKF exhibits a significant linear drift, due to... Figure 2 As can be seen in (b), the estimation error fluctuates greatly in the initial stage, but it is still within the theoretical limit of three times the variance (the estimation error is a dimensionless error value).

[0213] After adopting the correction strategy of this invention, long-term drift is significantly suppressed, such as Figure 3 Although it cannot completely eliminate the error caused by the sensor, it can be controlled within 2% to 5%.

[0214] Experimental results show that:

[0215] 1. The capacity estimation error analysis (including expectation and variance expressions) derived in this invention based on measurable battery data shows good agreement with actual statistical characteristics and has high theoretical accuracy;

[0216] 2. The correction strategy designed based on this model can effectively suppress long-term integral drift caused by fixed current bias, maintain high estimation accuracy and stability in noisy environments, and has extremely low computational overhead, making it easy to embed into existing BMS software;

[0217] 3. The error characteristics obtained by this invention can provide guidance for the selection of practical sensors;

[0218] 4. Based on the analysis of experimental results, the impact of model error and sensor noise on capacity estimation can be observed intuitively.

[0219] Example 2

[0220] This embodiment provides an online correction system for lithium-ion battery capacity estimation errors, including:

[0221] The modeling module is configured to build current and voltage measurement models that incorporate fixed sensor biases and random noise.

[0222] The error module is configured to establish an estimated state of charge model with measured current and estimated capacity as variables based on the ampere-hour integration method, and derive the expression for the estimated state of charge error by combining the measurement model that incorporates sensor error.

[0223] The gradient module is configured to take the inverse of the capacity as the state to be estimated, determine the observation gradient using the state of charge estimation error, and update the capacity estimate in the Kalman filter based on the information and the observation gradient.

[0224] The derivation module is configured to derive the closed-loop propagation relationship of the capacity estimation error based on the state of charge estimation error and the observation gradient, and obtain the general solution of the capacity estimation error.

[0225] The correction module is configured to compensate and correct the capacity estimate at the output of the Kalman filter according to the general solution of the capacity estimation error, so as to realize online correction of the battery capacity estimate.

[0226] Example 3

[0227] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps in the online correction method for lithium-ion battery capacity estimation error as described in Embodiment 1 above.

[0228] Example 4

[0229] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the online correction method for lithium-ion battery capacity estimation error as described in Embodiment 1 above.

[0230] The steps or modules involved in Embodiments 2 to 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0231] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for online correction of capacity estimation error in lithium-ion batteries, characterized in that, include: Construct current and voltage measurement models that incorporate fixed sensor bias and random noise; Specifically, a current measurement model is constructed based on real current, fixed deviation of current sensor, and random noise of current sensor; a voltage measurement model is constructed based on terminal voltage, fixed deviation of voltage sensor, and random noise of voltage sensor. Based on the ampere-hour integral method, an estimated state of charge model is established with measured current and estimated capacity as variables. Combined with the measurement model that introduces sensor error, the expression for the estimated state of charge error is derived. Specifically, a theoretical evolution model of the true state of charge is established based on the initial state of charge, the actual current variable, and the actual capacity variable; and an estimated state of charge calculation model is established using the ampere-hour integral method based on the initial state of charge, the measured current, and the reciprocal of the estimated capacity at the previous moment. The expression for the state of charge estimation error is derived from the difference between the actual state of charge and the estimated state of charge. The reciprocal of the capacity is used as the state to be estimated. The observation gradient is determined using the state of charge estimation error. The capacity estimate is updated in the Kalman filter based on the innovation and the observation gradient. Specifically, the open-circuit voltage slope corresponding to the current state of charge is obtained according to the mapping relationship between open-circuit voltage and state of charge. The ampere-hour integral is calculated based on the accumulated current measurement value. The negative product of the open-circuit voltage slope and the ampere-hour integral is used as the observation gradient. Based on the state of charge estimation error and the observation gradient, the closed-loop propagation relationship of the capacity estimation error is derived, and the general solution of the capacity estimation error is obtained. Based on the general solution of the capacity estimation error, the capacity estimate is compensated and corrected at the output of the Kalman filter to achieve online correction of the battery capacity estimate. Specifically, the expected expression of the general solution of the capacity estimation error is used, combined with known prior information on sensor bias, to estimate the reciprocal capacity estimation error at the current moment. The estimated error is then superimposed on the reciprocal capacity estimate output by the Kalman filter to obtain the corrected reciprocal capacity. The corrected reciprocal capacity is converted into a capacity value and output externally, while keeping the internal state and covariance of the filter unchanged, thus achieving online correction of the battery capacity estimate.

2. The online correction method for lithium-ion battery capacity estimation error as described in claim 1, characterized in that, The process of updating the capacity estimate based on the innovation and the observed gradient in the Kalman filter specifically includes: The information is obtained by subtracting the measured terminal voltage from the predicted terminal voltage based on the current state of charge. The Kalman gain is calculated using the observed gradient; The new information is multiplied by the Kalman gain and then superimposed onto the previous time step's reciprocal capacity estimate to obtain the updated reciprocal capacity estimate.

3. The online correction method for lithium-ion battery capacity estimation error as described in claim 1, characterized in that, The process of deriving the closed-loop propagation relationship of the capacity estimation error based on the state of charge estimation error and the observation gradient to obtain the general solution of the capacity estimation error specifically includes: A first-order linear recursive relationship is established for the capacity inverse estimation error from the previous time step to the current time step, where the recursive coefficient is determined by the product of the Kalman gain and the observation gradient; Expanding the recursive relation from the initial time to the current time yields an analytical expression for the capacity reciprocal estimation error, which serves as the general solution for the capacity estimation error. This expression includes a decay term for the initial error and a cumulative contribution term for sensor bias and noise.

4. An online correction system for lithium-ion battery capacity estimation error, based on the online correction method for lithium-ion battery capacity estimation error as described in claim 1, characterized in that, include: The modeling module is configured to build current and voltage measurement models that incorporate fixed sensor biases and random noise. The error module is configured to establish an estimated state of charge model based on the ampere-hour integration method, with the measured current and estimated capacity as variables, and derive an expression for the estimated state of charge error by combining the measurement model that incorporates sensor errors. The gradient module is configured to take the inverse of the capacity as the state to be estimated, determine the observation gradient using the state of charge estimation error, and update the capacity estimate in the Kalman filter based on the information and the observation gradient. The derivation module is configured to derive the closed-loop propagation relationship of the capacity estimation error based on the state of charge estimation error and the observation gradient, and obtain the general solution of the capacity estimation error. The correction module is configured to compensate and correct the capacity estimate at the output of the Kalman filter according to the general solution of the capacity estimation error, so as to realize online correction of the battery capacity estimate.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the online correction method for lithium-ion battery capacity estimation error as described in any one of claims 1-3.

6. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the online correction method for lithium-ion battery capacity estimation error as described in any one of claims 1-3.

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