Internal resistance estimation method and device, computer program product and computer readable storage medium

Abstract

The invention provides an internal resistance estimation method, device and equipment, a computer program product and a computer readable storage medium. The method comprises the following steps: synchronously acquiring voltages and currents of a plurality of batteries according to a target sampling period; for each battery, converting the second-order equivalent circuit model of the battery based on the terminal voltage and the terminal current collected at the current sampling moment and the historical sampling moment to obtain a linear regression model; performing iterative estimation on the to-be-estimated parameter vector in the linear regression model by adopting a recursive least square method with a forgetting factor to obtain a target parameter vector at the current sampling moment; determining the to-be-processed DC internal resistance of the battery at the current sampling moment based on the target parameter vector and the determined target mapping relation; the target mapping relation is determined based on a second-order equivalent circuit model and a linear regression model, and represents the corresponding relation between the parameter vector and the direct current internal resistance.

Description

Technical Field

[0001] This application relates to battery management and state estimation technology, and more particularly to an internal resistance estimation method, apparatus, device, computer program product, and computer-readable storage medium. Background Technology

[0002] Currently, online estimation of battery direct current resistance (DCR) faces the following main technical challenges: First, traditional precise measurement methods (such as HPPC testing) rely on applying specific excitation pulses under specific operating conditions, which cannot adapt to the real-time estimation requirements of batteries during complex dynamic operations, exhibiting intrusiveness and offline limitations. Second, although online parameter identification methods based on battery models and recursive algorithms exist (such as combining the ARX model with RLS and embedding a dual extended Kalman filter), these methods are usually coupled into a complex joint state estimation framework, resulting in huge computational overhead and making it difficult to achieve efficient, real-time, independent internal resistance estimation in resource-constrained vehicle battery management systems. Third, the internal resistance estimation results are easily confused with other polarization parameters, resulting in insufficient accuracy and physical certainty. Therefore, there is an urgent need for an online estimation method that can directly and accurately analyze the DC internal resistance using only the regular operating data of the battery management system, with lightweight computation. Summary of the Invention

[0003] This application provides an internal resistance estimation method, apparatus, computer program product, and computer-readable storage medium, which can not only reduce computational complexity but also improve the accuracy of internal resistance estimation.

[0004] The technical solution of this application embodiment is implemented as follows: This application provides an internal resistance estimation method, the method comprising: The voltage and current of multiple batteries are collected simultaneously according to the target sampling period; For each battery, based on the terminal voltage and terminal current collected at the current sampling time and the historical sampling time, the second-order equivalent circuit model of the battery is transformed to obtain a linear regression model; The recursive least squares method with a forgetting factor is used to iteratively estimate the parameter vector to be estimated in the linear regression model to obtain the target parameter vector at the current sampling time. Based on the target parameter vector and the determined target mapping relationship, the DC internal resistance of the battery at the current sampling time is calculated; wherein, the target mapping relationship is determined based on the second-order equivalent circuit model and the linear regression model, and characterizes the correspondence between the parameter vector and the DC internal resistance.

[0005] In the above scheme, the transformation of the second-order equivalent circuit model of the battery based on the voltage and current collected at the current sampling time and historical sampling times to obtain a linear regression model includes: The second-order equivalent circuit model is discretized based on the voltage and the current to obtain the first equation; The first equation at adjacent sampling times is subjected to a difference operation to obtain the second equation; wherein, the second equation includes the voltage, the current and the parameter vector to be estimated; The second equation is rearranged to obtain the linear regression model.

[0006] In the above scheme, the recursive least squares method with a forgetting factor is used to iteratively estimate the parameter vector to be identified in the linear regression model to obtain the target parameter vector at the current sampling time, including: Initialize the parameter vector in the linear regression model and the covariance matrix corresponding to the linear regression model; For each sampling time, the recursive least squares method with forgetting factor is used to iteratively update the parameter vector and the covariance matrix based on the regression vector and output value in the linear regression model, and the updated parameter vector is determined as the target parameter vector.

[0007] In the above scheme, determining the target mapping relationship includes: Based on the coefficients of the corresponding terms of terminal voltage and terminal current in the second equation and the linear regression model, the target mapping relationship is obtained.

[0008] In the above scheme, obtaining the target mapping relationship based on the coefficients of the corresponding terms of terminal voltage and terminal current in the second equation and the linear regression model includes: The coefficients of the second equation and the corresponding terms of terminal voltage and terminal current in the linear regression model are compared to establish a set of equations between the parameter vector of the linear regression model and the physical parameters of the second-order equivalent circuit model. The DC internal resistance is analyzed from the system of equations to obtain a functional relationship with respect to at least one parameter in the parameter vector, and the functional relationship is determined as the target mapping relationship.

[0009] In the above scheme, after determining the DC internal resistance to be processed of the battery at the current sampling time based on the target parameter vector and the determined target mapping relationship, the scheme further includes: For each battery, the initial DC internal resistance sequence corresponding to the battery is post-processed to obtain the target DC internal resistance sequence; wherein, the post-processing includes anomaly processing and smoothing filtering; the initial DC internal resistance sequence is constructed by the DC internal resistance to be processed at each sampling time.

[0010] In the above scheme, the post-processing of the initial DC internal resistance sequence corresponding to the battery to obtain the target DC internal resistance sequence includes: Determine the mean and standard deviation of the initial DC internal resistance sequence within the sliding window; Abnormal DC resistances in the initial DC resistance sequence are invalidated to obtain a processed DC resistance sequence. The processed DC internal resistance sequence is smoothed and filtered to obtain the target DC internal resistance sequence.

[0011] This application provides an internal resistance estimation device, the device comprising: The data acquisition unit is used to synchronously acquire the voltage and current of multiple batteries according to the target sampling period; The processing unit is used to transform the second-order equivalent circuit model of each battery based on the terminal voltage and terminal current collected at the current sampling time and the historical sampling time, to obtain a linear regression model. The processing unit is further configured to use a recursive least squares method with a forgetting factor to iteratively estimate the parameter vector to be estimated in the linear regression model, so as to obtain the target parameter vector at the current sampling time. The determining unit is used to determine the DC internal resistance of the battery at the current sampling time based on the target parameter vector and the determined target mapping relationship; wherein the target mapping relationship is determined based on the second-order equivalent circuit model and the linear regression model, and characterizes the correspondence between the parameter vector and the DC internal resistance.

[0012] This application provides an internal resistance estimation device, the device comprising: Memory is used to store executable instructions or computer programs. The processor, when executing computer-executable instructions or computer programs stored in the memory, implements the method provided in the embodiments of this application.

[0013] This application provides a computer program product, including a computer program or computer executable instructions, which, when executed by a processor, implement the method provided in this application.

[0014] This application provides a computer-readable storage medium storing a computer program or computer-executable instructions for implementing the method provided in this application when executed by a processor.

[0015] The embodiments of this application have the following beneficial effects: This application relies solely on voltage and current data synchronously collected by the battery management system during normal operation, without applying any special test pulses, achieving truly "non-intrusive" online estimation. This greatly improves the applicability and engineering convenience of the method in actual dynamic operating conditions. Furthermore, by transforming the second-order equivalent circuit model into a linear regression model and employing a recursive least squares method with a forgetting factor for iterative parameter vector estimation, an independent and lightweight dedicated estimation algorithm framework is constructed. Its computational complexity is low, requiring only limited historical data for each iteration, greatly reducing computational overhead. Simultaneously, based on the target mapping relationship determined by the model derivation, which characterizes the direct correspondence between the parameter vector and the DC internal resistance, the physical value of the DC internal resistance can be directly and accurately parsed from the updated parameter vector, avoiding the problem of fuzzy identification of internal resistance and other parameters. This provides accurate and reliable direct input for battery power state assessment, health status tracking, and early fault diagnosis. Attached Figure Description

[0016] Figure 1 This is a first flowchart illustrating the internal resistance estimation method provided in the embodiments of this application; Figure 2 This is a second flowchart illustrating the internal resistance estimation method provided in the embodiments of this application; Figure 3 This is a schematic diagram of the internal resistance estimation device provided in the embodiments of this application; Figure 4 This is a schematic diagram of the internal resistance estimation device provided in the embodiments of this application.

[0017] It should be noted that the terms "first" and "second" mentioned above are only used to distinguish between different options and do not represent the degree of superiority or inferiority of the options or their priority in the implementation process. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. The described embodiments should not be regarded as limitations on this application. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] It is important to note that in a Battery Management System (BMS), internal resistance, as a comprehensive parameter reflecting the electrochemical and transport processes at the battery ports, directly affects the model accuracy and control boundaries of the State of Charge (SOC) and State of Power (SOP). Deviations in internal resistance estimation can propagate to voltage prediction and available power constraints, thereby impacting the tracking capability of energy storage frequency regulation and the response quality and safety margin under dynamic conditions such as electric vehicle acceleration and energy recovery. Simultaneously, internal resistance is closely related to the State of Health (SOH): as cycling and calendar aging progress, mechanisms such as decreased electrode activity, thickened interfacial films, and limited ion transport cause internal resistance to gradually increase; its long-term changes can serve as important evidence for life assessment and replacement decisions. On a short timescale, abrupt changes in internal resistance may also indicate potential problems such as micro-short circuits, contact degradation, or abnormal polarization. Therefore, online and robust sensing of internal resistance is practically necessary to improve the reliability of state estimation and to identify fault symptoms early.

[0020] Taking the lithium iron phosphate system as an example, the internal resistance exhibits a range-bound characteristic with SOC: it is relatively high in the low / high range and relatively low in the medium range with a slower rate of change. In the low SOC range (usually below 30%), the internal resistance is relatively high and fluctuates greatly due to the availability of active materials and concentration polarization. In the high SOC range (usually above 90%), the internal resistance also increases as the electrode approaches full load and polarization intensifies. In the medium SOC range (approximately 30%-90%), especially when approaching 50% SOC, the reaction kinetics are more balanced and the ion conduction resistance is smaller. As a result, the internal resistance is not only lower in value but also changes more gradually with SOC. Based on this, the internal resistance near 50% SOC can be used as the "nominal internal resistance" for consistency calibration across SOC operating conditions, reducing the interference of operating condition differences on measurement results. At the same time, tracking the slow evolution of internal resistance in this stable range is more conducive to highlighting the intrinsic changes in health degradation and improving the reliability of SOH assessment and threshold maintenance. In summary, the real-time sensing of internal resistance and its SOC-related characteristics, especially the key characterization of the 50% SOC stable range, are of great engineering significance for optimizing battery management strategies, improving dynamic control performance, and extending system life.

[0021] To achieve accurate online estimation of internal resistance, a method for online parameter estimation has been disclosed in related technologies. Its core idea is to combine the battery model (ARX model) with recursive least squares (RLS) with a forgetting factor, that is, to incorporate ARX-RLS parameter identification as part of a dual extended Kalman filter (DEKF), constructing a complex joint SOC / SOH estimation algorithm. However, this method has the following limitations: First, its overall computational overhead is high, relying on a complex dual Kalman filter framework, making it difficult to achieve efficient real-time operation in computationally limited automotive BMS. Second, this method does not directly and explicitly parse the physical value of DC internal resistance (DCR) from the identified parameters, which may lead to confusion with other polarization parameters, affecting its direct usability in condition assessment and fault diagnosis.

[0022] Based on this, embodiments of this application provide an internal resistance estimation method, referring to... Figure 1 As shown, when applied to an internal resistance estimation device, the specific steps may include: Step 101: Collect the voltage and current of multiple batteries simultaneously according to the target sampling period.

[0023] In this embodiment of the application, the target sampling period ( The sampling period can be a pre-set time interval for data acquisition; voltage refers to the voltage across the positive and negative terminals of the battery, which can be directly measured by the battery management system; current refers to the current flowing into or out of the battery, with positive values ​​usually indicating charging and negative values ​​indicating discharging, and it can also be measured by the BMS; in one feasible implementation, the target sampling period can be set to 1 second; the battery specifically refers to a lithium iron phosphate battery.

[0024] In the embodiments of this application, during normal operation of the vehicle or energy storage system, the voltage and current of each battery in each battery cell or battery module can be synchronously collected by the BMS at fixed time intervals (e.g., 1 second). The collected data can be packaged in chronological order (e.g., packaged in matrix form). In this way, without applying special test pulses (e.g., Hybrid Pulse Power Characterization (HPPC)), the input for internal resistance estimation can be provided solely by the voltage and current data routinely collected by the BMS during normal battery operation, thus achieving non-invasive internal resistance estimation.

[0025] It should be noted that steps 102-104 can be performed for each of the multiple batteries, and multiple batteries can be processed in parallel.

[0026] Step 102: For each battery, based on the voltage and current collected at the current sampling time and the historical sampling time, the second-order equivalent circuit model of the battery is transformed to obtain a linear regression model.

[0027] In this application embodiment, the second-order equivalent circuit model is a circuit model used to simulate the dynamic characteristics of a battery. It typically includes a resistor representing the internal resistance (DCR) and two RC networks consisting of resistors and capacitors connected in parallel to describe the battery's polarization effect. The linear regression model is a mathematical model, typically in the form of... ,in, It is the output. It is a regression vector. It is the vector of parameters to be estimated. It is an error. In the embodiments of this application, the time-domain equations of the second-order equivalent circuit model can be discretized, differential elimination and data processing can be performed to obtain an equation of the form shown below. The linear regression model is thus transformed, through rigorous mathematical transformation, from a complex nonlinear battery model containing internal states to a standard linear regression form suitable for online parameter estimation using recursive least squares (RLS).

[0028] Step 103: Use the recursive least squares method with forgetting factor to iteratively estimate the parameter vector to be estimated in the linear regression model to obtain the target parameter vector at the current sampling time.

[0029] In this embodiment, the Forgetting Factor-based Recursive Least Squares (FFRLS) is an improved recursive least squares algorithm that introduces a forgetting factor between 0 and 1. This allows the algorithm to assign higher weights to new data during updates, thus enabling it to track the slow time-varying nature of parameters; the parameter vector to be estimated ( In a linear regression model, is a set of unknown constants that need to be estimated. It can be a four-dimensional vector, such as... In one feasible implementation, =0.999.

[0030] In this embodiment, for each battery, the parameter vector and covariance matrix corresponding to the linear regression model are first initialized. Then, the parameter vector and covariance matrix are iteratively updated using a recursive least squares method with a forgetting factor, thereby outputting a real-time target parameter vector for each sampling time k. .

[0031] Step 104: Based on the target parameter vector and the determined target mapping relationship, determine the DC internal resistance of the battery at the current sampling time.

[0032] The target mapping relationship is determined based on the second-order equivalent circuit model and the linear regression model, and it represents the correspondence between the parameter vector and the DC internal resistance.

[0033] In this embodiment, the target mapping relationship refers to the analytical conversion formula established through mathematical derivation from the parameter vector of the linear regression model to the battery physical parameters (specifically, the DC internal resistance R); the DC internal resistance to be processed refers to the original estimated value of the internal resistance directly calculated through the mapping relationship, without subsequent anomaly processing and smoothing processing; at each sampling time, the target parameter vector of the current sampling time obtained in step 103 is substituted into the target mapping relationship, and the estimated value of the battery's DC internal resistance at the current time can be directly calculated; it should be noted that, unlike the method of fuzzy identification of ohmic internal resistance and polarization internal resistance in related technologies, this application can accurately parse the physical value representing the ohmic internal resistance (DCR) from the estimated parameters through explicit algebraic mapping, thereby providing a direct and accurate physical internal resistance value.

[0034] The internal resistance estimation method provided in this application relies solely on voltage and current data synchronously collected by the battery management system during normal operation, without applying any special test pulses. This achieves truly "non-intrusive" online estimation, greatly improving the applicability and engineering convenience of the method in actual dynamic operating conditions. Furthermore, by transforming the second-order equivalent circuit model into a linear regression model and employing a recursive least squares method with a forgetting factor for iterative parameter vector estimation, an independent and lightweight dedicated estimation algorithm framework is constructed. This framework has low computational complexity, requiring only limited historical data for each iteration, significantly reducing computational overhead. Simultaneously, based on the target mapping relationship determined by the model derivation, which characterizes the direct correspondence between the parameter vector and the DC internal resistance, the physical value of the DC internal resistance can be directly and accurately parsed from the updated parameter vector, avoiding the problem of fuzzy identification of internal resistance and other parameters. This provides accurate and reliable direct input for battery power state assessment, health status tracking, and early fault diagnosis.

[0035] Based on the foregoing embodiments, this application provides yet another method for estimating internal resistance, referring to... Figure 2 As shown, when applied to an internal resistance estimation device, the specific steps may include: Step 201: Collect the voltage and current of multiple batteries simultaneously according to the target sampling period.

[0036] Step 202: For each battery, the second-order equivalent circuit model is discretized based on voltage and current to obtain the first equation.

[0037] Discretization refers to transforming continuous-time differential equations (or systems of equations) into discrete-time difference equations. Discretization methods include forward Euler method, backward Euler method, or bilinear transformation. The first equation is the discrete-time equation obtained by discretizing the continuous-time state-space equation of the second-order equivalent circuit model.

[0038] In this embodiment of the application, if the continuous-time state-space equation of the second-order equivalent circuit model is: Formula (1) in, and Let be the polarization voltages of the two RC networks. For current, For voltage, The open-circuit voltage of the battery is The function; For ohmic internal resistance, , and , These are the resistors and capacitors of two RC networks, respectively.

[0039] Therefore, discretizing the above continuous-time state-space equation using the backward Euler method yields the first equation as shown below: Formula (2) in, , , and It can also be obtained in a similar way; k represents the sampled value at sample time k.

[0040] Step 203: Perform a difference operation on the first equation at adjacent sampling times to obtain the second equation.

[0041] The second equation includes voltage, current, and a vector of parameters to be estimated.

[0042] In this embodiment, the difference operation refers to subtracting the equations at two adjacent time points, with the aim of eliminating certain state variables that are difficult to measure directly (such as polarization voltage). and This yields equations that contain only observables (voltage, current) and the vector of parameters to be estimated.

[0043] In one feasible implementation, the first equation at the sampling time ( )and The first equation at the sampling time ( By performing difference operations, we obtain the second equation. .

[0044] Step 204: Rearrange the second equation to obtain the linear regression model.

[0045] In the embodiments of this application, after obtaining the second time, it can be combined with The first equation at the sampling time ( The second equation is rearranged to obtain the linear regression model.

[0046] It should be noted that by transforming the battery internal resistance estimation problem into a standard linear regression problem, the mature and efficient recursive least squares method can be directly applied for online parameter estimation. This transformation makes the algorithm computationally intensive and easy to implement, while ensuring the convergence of parameter estimation.

[0047] Step 205: Initialize the parameter vector in the linear regression model and the covariance matrix corresponding to the linear regression model.

[0048] In this embodiment, parameter vector initialization refers to setting the parameter vector to an initial value. Specifically, it can be initialized using prior knowledge or default values, such as setting it to a zero vector or an initial value calculated based on typical battery parameters; the initialization of the covariance matrix can be achieved by setting the covariance matrix ( Initialize to ,in, It is the identity matrix. It is a very large positive number, which means that the uncertainty of the initial parameter estimation is large. In the initial stage, the algorithm will give high weight to the new data, thereby accelerating convergence.

[0049] Step 206: For each sampling time, the recursive least squares method with forgetting factor is used to iteratively update the parameter vector and covariance matrix based on the regression vector and output value in the linear regression model, and the updated parameter vector is determined as the target parameter vector.

[0050] In this embodiment, a recursive update loop is first performed: starting from the third sampling time (k=3), for each new sampling time k, the following recursive least squares iteration with a forgetting factor is executed: 1. Calculate the gain vector: 1. The gain vector determines the weight of the new observation data at the current moment on the parameter correction; 2. Update the parameter vector: That is, the prediction error can be utilized. and gain ( ) parameters of the previous time step ( The estimate is then corrected to obtain the updated parameter vector. 3. Update the covariance matrix: The covariance matrix reflects the uncertainty of the updated parameter estimates, and the forgetting factor ( The influence of older data is gradually diminished in the denominator; then the target parameter vector is output, which is the result of each iteration update. This serves as the target parameter vector at the current sampling time; it should be noted that the expression for the regression vector is: .

[0051] It should be noted that: 1. The recursive form means the algorithm only needs to perform a fixed number of matrix operations in each sampling period, resulting in low computational burden. This allows it to be embedded in a BMS microcontroller for real-time operation, providing constantly updated parameter estimates; 2. The introduction of a forgetting factor gives the algorithm memory decay characteristics, enabling it to continuously track the slow time-varying changes in battery internal resistance caused by aging, temperature variations, etc., improving the adaptability and long-term accuracy of the estimation; 3. The algorithm only needs to retain the state variables from the previous time step (i.e., ... It requires no storage of historical data, has extremely low memory usage, and has fixed computational complexity, making it very suitable for long-term stable operation in automotive embedded systems.

[0052] Step 207: Based on the coefficients of the corresponding terms of terminal voltage and terminal current in the second equation and the linear regression model, obtain the target mapping relationship.

[0053] In this embodiment of the application, after the linear regression model is determined, the regression vector and parameter vector are abstract numbers. In order to give the parameter vector physical meaning, it is necessary to associate it with the second equation representing the physical characteristics of the battery. By comparing the coefficients of the same observed variables (voltage, current and their difference terms) in the two equations, a set of equations can be established, thereby revealing the mathematical relationship between each element (i.e. parameter) of the parameter vector and the battery physical parameters (such as ohmic internal resistance, polarization time constant, polarization resistance, etc.).

[0054] It should be noted that step 207 can be achieved in the following way: Step 207A1: Compare the coefficients of the corresponding terms of terminal voltage and terminal current in the second equation and the linear regression model to establish a set of equations between the parameter vector of the linear regression model and the physical parameters of the second-order equivalent circuit model.

[0055] In this embodiment of the application, the second equation (containing physical parameters) and the rearranged linear regression model (containing parameter vectors) can be used. Place them side by side, and then observe the same measurable terms in the two equations (such as...). , , , , Then, by making the coefficients of these corresponding terms equal, and then through the matching described above, a set of equations is obtained. Each equation will have a parameter vector. One or more elements, expressed as battery physical parameters ( , , , , , , Functions such as (etc.).

[0056] Step 207A2: Extract the functional relationship between the DC internal resistance and at least one parameter in the parameter vector from the system of equations, and determine the functional relationship as the target mapping relationship.

[0057] In this embodiment of the application, the multi-parameter equations established in step 207A1 focus on the relationship with DC internal resistance ( Then, using multiple equations in the system of equations, through algebraic methods such as simultaneous equations, substitution, and elimination, other physical parameters (such as...) are... , (etc.) are eliminated, and finally it is deduced Only by parameter vector The expression that represents, i.e. .

[0058] Step 208: Based on the target parameter vector and the determined target mapping relationship, determine the DC internal resistance of the battery at the current sampling time.

[0059] The target mapping relationship is determined based on the second-order equivalent circuit model and the linear regression model, and it represents the correspondence between the parameter vector and the DC internal resistance.

[0060] Step 209: For each battery, perform post-processing on the initial DC internal resistance sequence corresponding to the battery to obtain the target DC internal resistance sequence.

[0061] The post-processing includes anomaly handling and smoothing filtering; the initial DC internal resistance sequence is constructed from the DC internal resistance to be processed at each sampling time.

[0062] In this embodiment of the application, the initial DC internal resistance sequence refers to the sequence of DC internal resistances of each battery obtained online by recursive least squares method and without any subsequent processing, arranged in chronological order; each battery will obtain an initial DC internal resistance sequence. Post-processing refers to further data cleaning and smoothing of the estimated internal resistance sequence; the target DC internal resistance sequence refers to the more stable and reliable DC internal resistance sequence obtained after post-processing. After obtaining the initial DC internal resistance sequence, due to noise, fluctuations in the early stages of convergence, or occasional anomalies that may exist during the estimation process, directly using the sequence may lead to misjudgment. Therefore, it is necessary to perform post-processing (including anomaly handling and smoothing filtering) on ​​the obtained initial DC internal resistance sequence to improve the continuity and robustness of the internal resistance curve.

[0063] It should be noted that step 209 can be achieved in the following way: Step 209B1: Determine the mean and standard deviation of the initial DC internal resistance sequence within the sliding window.

[0064] In this embodiment, a sliding window refers to a fixed-length data interval defined on a time series, which slides over time. The mean refers to the arithmetic mean of all DC internal resistances within the sliding window, reflecting the central tendency of the DC internal resistances within that window; the standard deviation is a measure of the dispersion of the DC internal resistances within the sliding window, reflecting the range of data fluctuation. Starting from a stable initial moment, a fixed-length sliding window (e.g., window length L = 30 sampling points) can be set for the initial DC internal resistance sequence. At each window position, the mean and standard deviation of all DC internal resistances within the window are calculated.

[0065] Step 209B2: Invalidate the abnormal DC internal resistance in the initial DC internal resistance sequence to obtain the processed DC internal resistance sequence.

[0066] In this embodiment, the processed DC resistance sequence refers to the DC resistance sequence obtained after invalidating the abnormal DC resistances in the initial DC resistance sequence. Invalidating the abnormal DC resistances means marking or replacing the abnormal DC resistances with invalid values; this can be achieved by... Principles (i.e.) The process involves filtering out abnormal DC resistances (outliers) from the initial DC resistance sequence. If the DC resistance at a certain sampling time exceeds this range, it is identified as an outlier. These outliers are then marked as invalid (e.g., marked as NaN), indicating that the data point is invalid and will not participate in subsequent smoothing calculations. This approach achieves the following: 1. Effectively filters out abnormal estimates caused by noise, sampling anomalies, or initial algorithm instability; 2. Retains most resistance data under normal operating conditions, improving the reliability of the sequence; 3. Uses NaN marking to prevent abnormal DC resistances from affecting the smoothing process and maintain sequence continuity.

[0067] Step 209B3: Smooth the processed DC internal resistance sequence to obtain the target DC internal resistance sequence.

[0068] In this embodiment, the target DC resistance sequence refers to the DC resistance sequence obtained after smoothing, which has better continuity and stability. For the sequence with abnormal DC resistance removed (i.e., the processed DC resistance sequence), a moving average method can be used to smooth the processed DC resistance sequence. Specifically, a sliding window of the same or another length (e.g., ...) can be used. The system performs a moving average calculation, employing a "NaN ignore" strategy when calculating the mean. This means that only valid values ​​within the window are averaged; if all values ​​are NaN, NaN is output. This results in a smoothed internal resistance sequence (i.e., the target DC internal resistance sequence). This approach achieves the following: 1. Further suppresses random noise and short-term fluctuations, highlighting the long-term trend of internal resistance; 2. Improves the smoothness and visual readability of the internal resistance curve, facilitating subsequent analysis and application; 3. Applicable to the input data requirements of upper-level functions such as battery state of health (SOH) tracking and power boundary management.

[0069] It should be noted that, through the above steps, this application achieves real-time online estimation of battery DCR based solely on voltage and current sequences routinely collected by the BMS under normal battery charging and discharging conditions. This method transforms the second-order equivalent circuit model into a linear regression form suitable for least squares through mathematical derivation, and uses recursive least squares with forgetting factor (FFRLS) for parameter estimation. This not only provides a method that can get rid of the dependence on offline measurements for specific test pulses (such as HPPC) in traditional methods, but also adaptively tracks the slow changes in DCR through the forgetting factor mechanism.

[0070] It should be noted that, when there are multiple batteries, after obtaining the target DC internal resistance sequence, multiple current and voltage curves can be plotted (one battery corresponds to one channel) to visually demonstrate the electrical behavior of each battery channel during operation; simultaneously, a comparison chart of multiple internal resistances can be plotted, where the DC internal resistance to be processed is represented by a dashed line, and the current and voltage curves after processing are shown in the figure. The DC internal resistance, after outlier removal and smoothing using a moving average method, is represented by a solid line, clearly showing the changes and optimization effects of the internal resistance curve before and after post-processing. Furthermore, the corresponding timestamps, multiple original internal resistances (i.e., the DC internal resistances to be processed), multiple smoothed internal resistances (i.e., the DC internal resistances in the target DC internal resistance sequence), and the battery's state of charge (SOC) are integrated and written into the results file to form a complete data record for subsequent performance analysis, health assessment, and historical traceability.

[0071] It should be noted that the descriptions of the same steps and contents as in other embodiments in this embodiment can be found in the descriptions in other embodiments, and will not be repeated here.

[0072] The internal resistance estimation method provided in this application relies solely on voltage and current data synchronously collected by the battery management system during normal operation, without applying any special test pulses. This achieves truly "non-intrusive" online estimation, greatly improving the applicability and engineering convenience of the method in actual dynamic operating conditions. Furthermore, by transforming the second-order equivalent circuit model into a linear regression model and employing a recursive least squares method with a forgetting factor for iterative parameter vector estimation, an independent and lightweight dedicated estimation algorithm framework is constructed. This framework has low computational complexity, requiring only limited historical data for each iteration, significantly reducing computational overhead. Simultaneously, based on the target mapping relationship determined by the model derivation, which characterizes the direct correspondence between the parameter vector and the DC internal resistance, the physical value of the DC internal resistance can be directly and accurately parsed from the updated parameter vector, avoiding the problem of fuzzy identification of internal resistance and other parameters. This provides accurate and reliable direct input for battery power state assessment, health status tracking, and early fault diagnosis.

[0073] Based on the foregoing embodiments, this application provides an internal resistance estimation device, which can be applied to... Figure 1 and Figure 2 In the internal resistance estimation method provided in the corresponding embodiment, refer to Figure 3 As shown, the internal resistance estimation device 3 may include: a data acquisition unit 31, a processing unit 32, and a determination unit 33, wherein: The data acquisition unit 31 is used to synchronously acquire the voltage and current of multiple batteries according to the target sampling period; The processing unit 32 is used to transform the second-order equivalent circuit model of each battery based on the terminal voltage and terminal current collected at the current sampling time and the historical sampling time, so as to obtain a linear regression model. The processing unit 32 is also used to iteratively estimate the parameter vector to be estimated in the linear regression model using the recursive least squares method with a forgetting factor, so as to obtain the target parameter vector at the current sampling time. The determination unit 33 is used to determine the DC internal resistance of the battery at the current sampling time based on the target parameter vector and the determined target mapping relationship; wherein, the target mapping relationship is determined based on the second-order equivalent circuit model and the linear regression model, and characterizes the correspondence between the parameter vector and the DC internal resistance.

[0074] In other embodiments of this application, the processing unit 32 is further configured to perform the following steps: The second-order equivalent circuit model is discretized based on voltage and current to obtain the first equation; The second equation is obtained by performing a difference operation on the first equation at adjacent sampling times; the second equation includes voltage, current and the vector of parameters to be estimated. The second equation is rearranged to obtain a linear regression model.

[0075] In other embodiments of this application, the processing unit 32 is further configured to perform the following steps: Initialize the parameter vector and the covariance matrix corresponding to the linear regression model; For each sampling time, the recursive least squares method with a forgetting factor is used to iteratively update the parameter vector and covariance matrix based on the regression vector and output value in the linear regression model, and the updated parameter vector is determined as the target parameter vector.

[0076] In other embodiments of this application, the determining unit 33 is further configured to perform the following steps: Based on the coefficients of the corresponding terms of terminal voltage and terminal current in the second equation and the linear regression model, the target mapping relationship is obtained.

[0077] In other embodiments of this application, the determining unit 33 is further configured to perform the following steps: By comparing the coefficients of the corresponding terms of terminal voltage and terminal current in the second equation and the linear regression model, a set of equations is established between the parameter vector of the linear regression model and the physical parameters of the second-order equivalent circuit model. The functional relationship between the DC internal resistance and at least one parameter in the parameter vector is analyzed from the system of equations, and the functional relationship is determined as the target mapping relationship.

[0078] In other embodiments of this application, the determining unit 33 is further configured to perform the following steps: For each battery, the initial DC internal resistance sequence corresponding to the battery is post-processed to obtain the target DC internal resistance sequence; the post-processing includes anomaly handling and smoothing filtering; the initial DC internal resistance sequence is constructed by the DC internal resistance to be processed at each sampling time.

[0079] In other embodiments of this application, the determining unit 33 is further configured to perform the following steps: Determine the mean and standard deviation of the initial DC internal resistance sequence within the sliding window; Abnormal DC resistances in the initial DC resistance sequence are invalidated to obtain a processed DC resistance sequence. The processed DC internal resistance sequence is smoothed and filtered to obtain the target DC internal resistance sequence.

[0080] It should be noted that the specific implementation process of the steps performed by each module in the embodiments of this application can be referred to Figure 1 and Figure 2 The implementation process of the internal resistance estimation method provided in the corresponding embodiment will not be described in detail here.

[0081] The internal resistance estimation device provided in this application relies solely on voltage and current data synchronously collected by the battery management system during normal operation, without applying any special test pulses. This achieves truly "non-intrusive" online estimation, greatly improving the applicability and engineering convenience of the method in actual dynamic operating conditions. Furthermore, by transforming the second-order equivalent circuit model into a linear regression model and employing a recursive least squares method with a forgetting factor for iterative parameter vector estimation, an independent and lightweight dedicated estimation algorithm framework is constructed. This framework has low computational complexity, requiring only limited historical data for each iteration, significantly reducing computational overhead. Simultaneously, based on the target mapping relationship determined by the model derivation, which characterizes the direct correspondence between the parameter vector and the DC internal resistance, the physical value of the DC internal resistance can be directly and accurately parsed from the updated parameter vector, avoiding the problem of fuzzy identification of internal resistance and other parameters. This provides accurate and reliable direct input for battery power state assessment, health status tracking, and early fault diagnosis.

[0082] Based on the foregoing embodiments, embodiments of this application provide an internal resistance estimation device, which can be applied to... Figure 1 and Figure 2 In the internal resistance estimation method provided in the corresponding embodiment, refer to Figure 4 As shown, the internal resistance estimation device 4 may include: a processor 41, a memory 42, and a communication bus 43, wherein: Communication bus 43 is used to realize the communication connection between processor 41 and memory 42; Processor 41 is used to execute the internal resistance estimation program in memory 42 to perform the following steps: The voltage and current of multiple batteries are collected simultaneously according to the target sampling period; For each battery, based on the terminal voltage and terminal current collected at the current sampling time and the historical sampling time, the second-order equivalent circuit model of the battery is transformed to obtain a linear regression model; The recursive least squares method with a forgetting factor is used to iteratively estimate the parameter vector to be estimated in the linear regression model, so as to obtain the target parameter vector at the current sampling time. Based on the target parameter vector and the determined target mapping relationship, the DC internal resistance of the battery at the current sampling time is determined; wherein, the target mapping relationship is determined based on the second-order equivalent circuit model and the linear regression model, and characterizes the correspondence between the parameter vector and the DC internal resistance.

[0083] In other embodiments of this application, processor 41 is used to execute the internal resistance estimation program in memory 42, based on the voltage and current collected at the current sampling time and historical sampling times, to transform the second-order equivalent circuit model of the battery to obtain a linear regression model, in order to achieve the following steps: The second-order equivalent circuit model is discretized based on voltage and current to obtain the first equation; The second equation is obtained by performing a difference operation on the first equation at adjacent sampling times; the second equation includes voltage, current and the vector of parameters to be estimated. The second equation is rearranged to obtain a linear regression model.

[0084] In other embodiments of this application, the processor 41 executes the internal resistance estimation program in the memory 42 using a recursive least squares method with a forgetting factor to iteratively estimate the parameter vector to be identified in the linear regression model, thereby obtaining the target parameter vector at the current sampling time, to achieve the following steps: Initialize the parameter vector and the covariance matrix corresponding to the linear regression model; For each sampling time, the recursive least squares method with a forgetting factor is used to iteratively update the parameter vector and covariance matrix based on the regression vector and output value in the linear regression model, and the updated parameter vector is determined as the target parameter vector.

[0085] In other embodiments of this application, processor 41 is used to execute the internal resistance estimation program in memory 42 to determine the target mapping relationship in order to implement the following steps: Based on the coefficients of the corresponding terms of terminal voltage and terminal current in the second equation and the linear regression model, the target mapping relationship is obtained.

[0086] In other embodiments of this application, processor 41 is used to execute the internal resistance estimation program in memory 42 based on the coefficients of the corresponding terms of terminal voltage and terminal current in the second equation and the linear regression model to obtain the target mapping relationship, so as to achieve the following steps: By comparing the coefficients of the corresponding terms of terminal voltage and terminal current in the second equation and the linear regression model, a set of equations is established between the parameter vector of the linear regression model and the physical parameters of the second-order equivalent circuit model. The functional relationship between the DC internal resistance and at least one parameter in the parameter vector is analyzed from the system of equations, and the functional relationship is determined as the target mapping relationship.

[0087] In other embodiments of this application, processor 41 is used to execute the internal resistance estimation method of the internal resistance estimation program in memory 42 to implement the following steps: For each battery, the initial DC internal resistance sequence corresponding to the battery is post-processed to obtain the target DC internal resistance sequence; the post-processing includes anomaly handling and smoothing filtering; the initial DC internal resistance sequence is constructed by the DC internal resistance to be processed at each sampling time.

[0088] In other embodiments of this application, the processor 41 is used to execute the internal resistance estimation program in the memory 42 to post-process the initial DC internal resistance sequence corresponding to the battery to obtain the target DC internal resistance sequence, so as to implement the following steps: Determine the mean and standard deviation of the initial DC internal resistance sequence within the sliding window; Abnormal DC resistances in the initial DC resistance sequence are invalidated to obtain a processed DC resistance sequence. The processed DC internal resistance sequence is smoothed and filtered to obtain the target DC internal resistance sequence.

[0089] It should be noted that a detailed description of the steps performed by the processor can be found in [reference needed]. Figure 1 and Figure 2 The implementation process of the internal resistance estimation method provided in the corresponding embodiment will not be described in detail here.

[0090] The internal resistance estimation device provided in this application relies solely on voltage and current data synchronously collected by the battery management system during normal operation, without applying any special test pulses. This achieves truly "non-intrusive" online estimation, greatly improving the applicability and engineering convenience of the method in actual dynamic operating conditions. Furthermore, by transforming the second-order equivalent circuit model into a linear regression model and employing a recursive least squares method with a forgetting factor for iterative parameter vector estimation, an independent and lightweight dedicated estimation algorithm framework is constructed. This framework has low computational complexity, requiring only limited historical data for each iteration, significantly reducing computational overhead. Simultaneously, based on the target mapping relationship determined by the model derivation, which characterizes the direct correspondence between the parameter vector and the DC internal resistance, the physical value of the DC internal resistance can be directly and accurately parsed from the updated parameter vector, avoiding the problem of fuzzy identification of internal resistance and other parameters. This provides accurate and reliable direct input for battery power state assessment, health status tracking, and early fault diagnosis.

[0091] Based on the foregoing embodiments, this application provides a computer program product, including a computer program, which implements [the following] when executed by a processor. Figure 1 and Figure 2 The steps in the internal resistance estimation method provided in the corresponding embodiment.

[0092] Based on the foregoing embodiments, this application provides a computer-readable storage medium storing one or more programs that can be executed by one or more processors to achieve... Figure 1 and Figure 2 The steps in the internal resistance estimation method provided in the corresponding embodiment.

[0093] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, and improvements made within the spirit and scope of this application are included within the scope of protection of this application.

Claims

1. A method for estimating internal resistance, characterized in that, The method includes: The voltage and current of multiple batteries are collected simultaneously according to the target sampling period; For each battery, based on the terminal voltage and terminal current collected at the current sampling time and the historical sampling time, the second-order equivalent circuit model of the battery is transformed to obtain a linear regression model; The recursive least squares method with a forgetting factor is used to iteratively estimate the parameter vector to be estimated in the linear regression model to obtain the target parameter vector at the current sampling time. Based on the target parameter vector and the determined target mapping relationship, the DC internal resistance of the battery at the current sampling time is determined; wherein, the target mapping relationship is determined based on the second-order equivalent circuit model and the linear regression model, and characterizes the correspondence between the parameter vector and the DC internal resistance.

2. The method according to claim 1, characterized in that, The second-order equivalent circuit model of the battery is transformed based on the voltage and current collected at the current sampling time and historical sampling times to obtain a linear regression model, including: The second-order equivalent circuit model is discretized based on the voltage and the current to obtain the first equation; The first equation at adjacent sampling times is subjected to a difference operation to obtain the second equation; wherein, the second equation includes the voltage, the current and the parameter vector to be estimated; The second equation is rearranged to obtain the linear regression model.

3. The method according to claim 1, characterized in that, The recursive least squares method with a forgetting factor is used to iteratively estimate the parameter vector to be identified in the linear regression model, obtaining the target parameter vector at the current sampling time, including: Initialize the parameter vector in the linear regression model and the covariance matrix corresponding to the linear regression model; For each sampling time, the recursive least squares method with forgetting factor is used to iteratively update the parameter vector and the covariance matrix based on the regression vector and output value in the linear regression model, and the updated parameter vector is determined as the target parameter vector.

4. The method according to claim 2, characterized in that, Determine the target mapping relationship, including: Based on the coefficients of the corresponding terms of terminal voltage and terminal current in the second equation and the linear regression model, the target mapping relationship is obtained.

5. The method according to claim 4, characterized in that, The process of obtaining the target mapping relationship based on the coefficients of the corresponding terms of terminal voltage and terminal current in the second equation and the linear regression model includes: The coefficients of the second equation and the corresponding terms of terminal voltage and terminal current in the linear regression model are compared to establish a set of equations between the parameter vector of the linear regression model and the physical parameters of the second-order equivalent circuit model. The DC internal resistance is analyzed from the system of equations to obtain a functional relationship with respect to at least one parameter in the parameter vector, and the functional relationship is determined as the target mapping relationship.

6. The method according to claim 1, characterized in that, After determining the DC internal resistance of the battery to be processed at the current sampling time based on the target parameter vector and the determined target mapping relationship, the method further includes: For each battery, the initial DC internal resistance sequence corresponding to the battery is post-processed to obtain the target DC internal resistance sequence; wherein, the post-processing includes anomaly processing and smoothing filtering; the initial DC internal resistance sequence is constructed by the DC internal resistance to be processed at each sampling time.

7. The method according to claim 6, characterized in that, The post-processing of the initial DC internal resistance sequence corresponding to the battery to obtain the target DC internal resistance sequence includes: Determine the mean and standard deviation of the initial DC internal resistance sequence within the sliding window; Abnormal DC resistances in the initial DC resistance sequence are invalidated to obtain a processed DC resistance sequence. The processed DC internal resistance sequence is smoothed and filtered to obtain the target DC internal resistance sequence.

8. An internal resistance estimation device, characterized in that, The internal resistance estimation device includes: Memory is used to store executable instructions or computer programs. A processor, when executing computer-executable instructions or computer programs stored in the memory, implements the method according to any one of claims 1 to 7.

9. A computer program product, comprising a computer program, characterized in that, The computer program, when executed by a processor, implements the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores one or more programs that can be executed by one or more processors to implement the method of any one of claims 1 to 7.

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