Nonlinear error calibration method and system for voltage sampling of energy storage battery cluster

Abstract

The invention belongs to the field of super capacitor management, and particularly relates to a nonlinear error calibration method and system for voltage sampling of an energy storage battery cluster. The method comprises the following steps: inputting an energy storage battery cluster sampling voltage value needing to be corrected into a constructed cubic polynomial model, and calculating to obtain a corrected voltage value; the cubic polynomial model takes a sampling voltage value as an independent variable and takes a corrected voltage value as a dependent variable; the initial value of the model constant term coefficient is determined according to a sampling voltage value obtained under the condition that the real voltage value of the energy storage battery cluster is equal to 0; an initial value of a model monomial coefficient is determined through linear fitting by taking the sampling voltage values as independent variables and taking the corrected voltage values as dependent variables according to each group of obtained sampling voltage values and corresponding real voltage values; initial values of a quadratic term coefficient and a cubic term coefficient of the model are determined through three-order polynomial fitting according to the acquired sampling voltage values of each group, the corresponding real voltage values and initial values of a monomial term coefficient and a constant term coefficient of the model.

Description

A nonlinear error calibration method and system for voltage sampling of energy storage battery clusters Technical Field

[0001] This invention belongs to the field of supercapacitor management, specifically relating to a nonlinear error calibration method and system for voltage sampling of energy storage battery clusters. Background Technology

[0002] In the voltage sampling process of an energy storage supercapacitor management system, the sampled voltage values ​​often contain errors due to non-ideal characteristics of the sampling circuit components (such as operational amplifier offset and resistor / capacitor tolerance), environmental factors (temperature, electromagnetic interference), and the nonlinearity of the analog-to-digital converter (ADC), failing to accurately reflect the true voltage. Existing technologies employ linear fitting for voltage sampling correction, with common methods such as two-point or three-point linear calibration. This involves first ensuring the hardware circuit is functioning correctly and providing a precisely known input voltage point, then averaging multiple samples to reduce noise. By measuring the ADC values ​​corresponding to the zero point and near the upper limit of the range, the offset error and gain error are calculated, leading to calibration coefficients and thus correcting the ADC measurement accuracy. However, when the voltage sampling system exhibits severe nonlinear errors, linear fitting struggles to achieve the desired correction effect. In existing technologies, linear calibration methods correct the total voltage by superimposing voltage calibration, which still relies on a linear model and does not solve the problem of global nonlinearity. On the other hand, the lookup table + interpolation method has a fixed calibration point spacing, and the error increases sharply in the nonlinear change region (such as 10%-20% of the range) (measured >1.2%). The piecewise linear lookup table method requires a large number of calibration points to be pre-stored (such as 20 intervals), occupying more than 100 bytes of EEPROM storage space.

[0003] Chinese invention patent application CN101905658A discloses a method and apparatus for obtaining voltage sampling. The method involves sampling a voltage reference source and comparing it with a preset reference voltage value to obtain a calibration value; acquiring the sampled voltage value collected by a voltage sampling circuit; and correcting the sampled voltage value based on the calibration value to obtain a corrected voltage value. Specifically, correcting the sampled voltage value includes: correcting the sampled voltage value x according to y = bx + a to obtain the corrected voltage value y, where a and b are calibration values. Summary of the Invention

[0004] The purpose of this invention is to provide a nonlinear error calibration method and system for voltage sampling of energy storage battery clusters, which solves the problem that existing voltage sampling correction methods are difficult to achieve ideal correction results when there are serious nonlinear errors in the voltage sampling of supercapacitors.

[0005] To achieve the above objectives, the present invention provides a nonlinear error calibration method for voltage sampling of energy storage battery clusters, comprising:

[0006] The sampled voltage values ​​of the energy storage battery clusters that need to be corrected are input into the constructed cubic polynomial model to calculate the corrected voltage values.

[0007] The constructed cubic polynomial model uses the sampled voltage value as the independent variable and the corrected voltage value as the dependent variable; the initial value of the coefficient of the constant term of the model is determined based on the sampled voltage value obtained when the actual voltage value of the energy storage battery cluster is equal to 0.

[0008] The initial values ​​of the coefficients of the first-order term of the model are determined by linear fitting with the sampled voltage values ​​as independent variables and the corrected voltage values ​​as dependent variables, based on the obtained sampled voltage values ​​and the corresponding true voltage values.

[0009] The initial values ​​of the coefficients of the quadratic and cubic terms of the model are determined by fitting a third-order polynomial based on the obtained sampled voltage values ​​and corresponding real voltage values, as well as the initial values ​​of the coefficients of the linear and constant terms of the model.

[0010] Furthermore, it also includes: when it is necessary to update the cubic polynomial model, substituting the real-time acquired sampled voltage values ​​and the corresponding true voltage values ​​into the error function; the error function is constructed based on the difference between the true voltage value corresponding to each sampled voltage value and the result of substituting the sampled voltage value into the cubic polynomial model.

[0011] Next, the error function is optimized by iteratively updating the coefficients of the constant term, linear term, quadratic term, and cubic term, starting from the initial value, until the set convergence condition is met. The cubic polynomial model is then updated based on the updated values ​​of each coefficient.

[0012] Furthermore, the Levenberg-Marquardt algorithm with a damping factor is used to optimize the error function.

[0013] Furthermore, the methods for determining whether the set convergence conditions are met include: if there is a case that satisfies any set convergence condition, then the set convergence conditions are determined to be met.

[0014] The convergence condition is set to include at least one of the first, second, and third convergence conditions;

[0015] The first convergence condition is that after this iteration, the changes in the coefficients of the constant term, the linear term, the quadratic term, and the cubic term are all less than the set coefficient change threshold; the second convergence condition is that after this iteration, the change in the error function is less than the set error change threshold; the third convergence condition is that the number of iterations reaches the set maximum number.

[0016] Furthermore, the method for determining whether the cubic polynomial model needs to be updated includes: when the change in the state of charge of the battery cluster exceeds a set ratio range, or when the voltage fluctuation exceeds the range by a set ratio, it is determined that the cubic polynomial model needs to be updated.

[0017] Furthermore, the methods for obtaining each group of sampled voltage values ​​and their corresponding true voltage values ​​include:

[0018] Within the range of the set lower voltage limit to the upper voltage limit of the energy storage battery cluster, at least two sets of raw sampled voltage values ​​and their corresponding real voltage values ​​are collected at each voltage point at intervals of a set voltage amount. The average of the raw sampled voltage values ​​at each voltage point is taken to obtain the sampled voltage value at that point. The average of the real voltage values ​​corresponding to the raw sampled voltage values ​​at each voltage point is taken to obtain the real voltage value corresponding to the sampled voltage value at that point.

[0019] Furthermore, based on the difference between the actual voltage value corresponding to each sampled voltage value and the result of substituting that sampled voltage value into the cubic polynomial model, the error function can be constructed in the following ways:

[0020] For each sampled voltage value, the difference between the actual voltage value and the result of substituting the sampled voltage value into the cubic polynomial model is squared. Then, the error function is obtained by summing the squared values ​​of each term.

[0021] Furthermore, the method of updating the cubic polynomial model based on the values ​​of each coefficient after iterative update includes: storing the values ​​of each coefficient after iterative update in EEPROM; and when calculating the corrected voltage value using the cubic polynomial model, substituting the latest values ​​of each coefficient in EEPROM into the cubic polynomial model for calculation.

[0022] Furthermore, the original value of the sampled voltage is obtained by sampling the target voltage using a voltage sampling circuit composed of a 16-bit ADC; the actual voltage value corresponding to the original value of the sampled voltage is obtained by measuring the actual value of the target voltage using a standard digital voltmeter.

[0023] The above-described technical solution of the present invention provides a novel nonlinear error calibration method for voltage sampling of energy storage battery clusters, the beneficial effects of which include:

[0024] Based on the characteristic that voltage sampling systems are prone to saturation nonlinearity under large signal input, a third-order polynomial model is used to fit and correct the sampled voltage value of the energy storage battery cluster. The constant term coefficients compensate for the zero-bias error of the sampling circuit, the first-order term coefficients correct the linear gain, and the second and third-order term coefficients further fit and correct the nonlinear error. Compared with linear or quadratic models, this method can more accurately fit the nonlinear distortion of voltage sampling, especially in the 1200V-1500V high-voltage range, particularly for high-voltage supercapacitor clusters, significantly improving voltage sampling accuracy. In other words, this model can effectively describe the nonlinear distortion of the ADC near full scale. Furthermore, this method does not require large-scale modifications to the existing voltage sampling hardware circuitry of the energy storage battery cluster; high-precision calibration can be achieved simply by upgrading the software algorithm and running a calibration program on the main control unit, reducing system modification costs and improving development efficiency. Moreover, the amount of data storage required for calibration is relatively small.

[0025] This invention also provides a nonlinear error calibration system for energy storage battery cluster voltage sampling, including a processor containing executable program instructions. These instructions are executed to implement a nonlinear error calibration method for energy storage battery cluster voltage sampling, specifically including:

[0026] The sampled voltage values ​​of the energy storage battery clusters that need to be corrected are input into the constructed cubic polynomial model to calculate the corrected voltage values.

[0027] The constructed cubic polynomial model uses the sampled voltage value as the independent variable and the corrected voltage value as the dependent variable; the initial value of the coefficient of the constant term of the model is determined based on the sampled voltage value obtained when the actual voltage value of the energy storage battery cluster is equal to 0.

[0028] The initial values ​​of the coefficients of the first-order term of the model are determined by linear fitting with the sampled voltage values ​​as independent variables and the corrected voltage values ​​as dependent variables, based on the obtained sampled voltage values ​​and the corresponding true voltage values.

[0029] The initial values ​​of the coefficients of the quadratic and cubic terms of the model are determined by fitting a third-order polynomial based on the obtained sampled voltage values ​​and corresponding real voltage values, as well as the initial values ​​of the coefficients of the linear and constant terms of the model.

[0030] Furthermore, it also includes: when it is necessary to update the cubic polynomial model, substituting the real-time acquired sampled voltage values ​​and the corresponding true voltage values ​​into the error function; the error function is constructed based on the difference between the true voltage value corresponding to each sampled voltage value and the result of substituting the sampled voltage value into the cubic polynomial model.

[0031] Next, the error function is optimized by iteratively updating the coefficients of the constant term, linear term, quadratic term, and cubic term, starting from the initial value, until the set convergence condition is met. The cubic polynomial model is then updated based on the updated values ​​of each coefficient.

[0032] Furthermore, the Levenberg-Marquardt algorithm with a damping factor is used to optimize the error function.

[0033] Furthermore, the methods for determining whether the set convergence conditions are met include: if there is a case that satisfies any set convergence condition, then the set convergence conditions are determined to be met.

[0034] The convergence condition is set to include at least one of the first, second, and third convergence conditions;

[0035] The first convergence condition is that after this iteration, the changes in the coefficients of the constant term, the linear term, the quadratic term, and the cubic term are all less than the set coefficient change threshold; the second convergence condition is that after this iteration, the change in the error function is less than the set error change threshold; the third convergence condition is that the number of iterations reaches the set maximum number.

[0036] Furthermore, the method for determining whether the cubic polynomial model needs to be updated includes: when the change in the state of charge of the battery cluster exceeds a set ratio range, or when the voltage fluctuation exceeds the range by a set ratio, it is determined that the cubic polynomial model needs to be updated.

[0037] Furthermore, the methods for obtaining each group of sampled voltage values ​​and their corresponding true voltage values ​​include:

[0038] Within the range of the set lower voltage limit to the upper voltage limit of the energy storage battery cluster, at least two sets of raw sampled voltage values ​​and their corresponding real voltage values ​​are collected at each voltage point at intervals of a set voltage amount. The average of the raw sampled voltage values ​​at each voltage point is taken to obtain the sampled voltage value at that point. The average of the real voltage values ​​corresponding to the raw sampled voltage values ​​at each voltage point is taken to obtain the real voltage value corresponding to the sampled voltage value at that point.

[0039] Furthermore, based on the difference between the actual voltage value corresponding to each sampled voltage value and the result of substituting that sampled voltage value into the cubic polynomial model, the error function can be constructed in the following ways:

[0040] For each sampled voltage value, the difference between the actual voltage value and the result of substituting the sampled voltage value into the cubic polynomial model is squared. Then, the error function is obtained by summing the squared values ​​of each term.

[0041] Furthermore, the method of updating the cubic polynomial model based on the values ​​of each coefficient after iterative update includes: storing the values ​​of each coefficient after iterative update in EEPROM; and when calculating the corrected voltage value using the cubic polynomial model, substituting the latest values ​​of each coefficient in EEPROM into the cubic polynomial model for calculation.

[0042] Furthermore, the original value of the sampled voltage is obtained by sampling the target voltage using a voltage sampling circuit composed of a 16-bit ADC; the actual voltage value corresponding to the original value of the sampled voltage is obtained by measuring the actual value of the target voltage using a standard digital voltmeter.

[0043] The technical solution of the nonlinear error calibration system for energy storage battery cluster voltage sampling described above can achieve the same beneficial effects as the nonlinear error calibration method for energy storage battery cluster voltage sampling described above. Attached Figure Description

[0044] Figure 1 is a flowchart illustrating the nonlinear error calibration method for energy storage battery cluster voltage sampling in the embodiment of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0046] Implementation of a Nonlinear Error Calibration Method for Energy Storage Battery Cluster Voltage Sampling

[0047] This embodiment presents a technical solution for nonlinear error calibration of voltage sampling in energy storage battery clusters. By combining third-order polynomial fitting with the least squares method, high-precision correction of voltage sampling is achieved, which is suitable for high-precision voltage sampling scenarios in supercapacitor energy storage power stations.

[0048] The method includes:

[0049] The sampled voltage values ​​of the energy storage battery clusters that need to be corrected are input into the constructed cubic polynomial model to calculate the corrected voltage values.

[0050] The constructed cubic polynomial model uses the sampled voltage value as the independent variable and the corrected voltage value as the dependent variable; the initial values ​​of the constant term coefficients of the model are determined based on the sampled voltage value obtained when the actual voltage value of the energy storage battery cluster is equal to 0.

[0051] The initial values ​​of the coefficients of the first term of the model are determined by linear fitting with the sampled voltage values ​​as independent variables and the corrected voltage values ​​as dependent variables, based on the obtained sampled voltage values ​​and the corresponding true voltage values.

[0052] The initial values ​​of the quadratic and cubic coefficients of the model are determined by fitting a third-order polynomial based on the obtained sampled voltage values ​​and corresponding real voltage values, as well as the initial values ​​of the linear and constant coefficients of the model.

[0053] Therefore, this method, based on the characteristic that voltage sampling systems are prone to saturation nonlinearity under large signal input, uses a third-order polynomial model to fit and correct the sampled voltage value of the energy storage battery cluster. The constant term coefficients compensate for the zero-bias error of the sampling circuit, the first-order term coefficients correct the linear gain, and the second and third-order term coefficients further fit and correct the nonlinear error. Compared with linear or quadratic models, this method can more accurately fit the nonlinear distortion of voltage sampling, especially in the 1200V-1500V high-voltage range (reducing the maximum sampling error from ±0.8% to ±0.2%, and controlling the full-range error within ±0.3%), significantly improving voltage sampling accuracy. In other words, this model can effectively describe the nonlinear distortion of the ADC near full scale. Furthermore, this method does not require large-scale modifications to the existing voltage sampling hardware circuit of the energy storage battery cluster; high-precision calibration can be achieved simply by upgrading the software algorithm and running a calibration program on the main control unit, reducing system modification costs and improving development efficiency. Moreover, the amount of data storage required for calibration is relatively small.

[0054] In one specific embodiment, the constructed cubic polynomial model is specifically expressed by the following formula:

[0055]

[0056] As a modified model, where V t For the actual voltage, V s The sampling voltage is represented by a0, a1, a2, and a3, which are nonlinear correction coefficients to be fitted. The constant term coefficient a0 is used to compensate for the zero bias error of the sampling circuit, the first term coefficient a1 is used for linear gain correction, and the second and third term coefficients a2 and a3 are used to correct nonlinear errors. This model can effectively describe the nonlinear distortion of the ADC when it is close to full scale. The measured data shows that the third-order model can cover 95% of the nonlinear error, while the fourth-order and above models improve the nonlinearity by less than 0.02% but the computational cost increases by a factor of two.

[0057] Furthermore, the nonlinear error calibration method also includes: when it is necessary to update the cubic polynomial model, substituting the real-time acquired sampled voltage values ​​and the corresponding true voltage values ​​into the error function; the error function is constructed based on the difference between the true voltage value corresponding to each sampled voltage value and the result of substituting the sampled voltage value into the cubic polynomial model.

[0058] Next, the error function is optimized by iteratively updating the coefficients of the constant term, linear term, quadratic term, and cubic term, starting from the initial value, until the set convergence condition is met. The cubic polynomial model is then updated based on the updated values ​​of each coefficient.

[0059] To facilitate updating the cubic polynomial model based on the values ​​of each coefficient after iterative updates, the following methods can be used: storing the updated values ​​of each coefficient in an EEPROM; and substituting the latest values ​​of each coefficient in the EEPROM into the cubic polynomial model when calculating the corrected voltage value using the cubic polynomial model.

[0060] In this embodiment, the Levenberg-Marquardt algorithm with a damping factor is used to optimize the error function. This algorithm is based on the least squares method and has relatively high accuracy.

[0061] Specifically, the error function can be constructed by comparing the difference between the actual voltage value corresponding to each sampled voltage value and the result of substituting that sampled voltage value into the cubic polynomial model. The methods include:

[0062] For each sampled voltage value, the difference between the actual voltage value and the result of substituting the sampled voltage value into the cubic polynomial model is squared. Then, the error function is obtained by summing the squared values ​​of each term.

[0063] Furthermore, in this embodiment, the method for determining whether the set convergence condition is met includes: as long as there is a situation that satisfies any set convergence condition, it is determined that the set convergence condition is met.

[0064] The convergence condition is set to include at least one of the first, second, and third convergence conditions;

[0065] The first convergence condition is that after this iteration, the changes in the coefficients of the constant term, the linear term, the quadratic term, and the cubic term are all less than the set coefficient change threshold; the second convergence condition is that after this iteration, the change in the error function is less than the set error change threshold; the third convergence condition is that the number of iterations reaches the set maximum number.

[0066] Referring to Figure 1, in one specific implementation, the error function is constructed as follows:

[0067]

[0068] The initial value of a0 is taken from V in the calibration dataset (constructed by sampling voltage values ​​and corresponding real voltage value data). siWhen the voltage is 0V, the average value of the difference between the sampled voltage and the true voltage is used as the initial zero bias estimate; the initial value of a1 is obtained by linear fitting of the calibration dataset. The initial estimated values ​​are generally set to 1. The initial values ​​of a2 and a3 are obtained by performing a preliminary fitting of the first 5 sets of sampled voltage values ​​and the corresponding real voltage values ​​in the calibration dataset using a third-order polynomial.

[0069] The Levenberg-Marquardt algorithm with damping factors is used to optimize the error function, and the parameter increments are calculated through matrix operations. In each iteration, the Jacobian matrix is ​​calculated. Where j = 0, 1, 2, 3, the correction coefficients a0, a1, a2, a3 are updated accordingly. The convergence condition is set as follows: the change in each coefficient is less than 1 / 2. or the change in the error function is less than If the maximum number of iterations reaches 30 (i.e., the maximum number of iterations is set to 30), the iteration stops when the condition is met first, thus obtaining the optimal correction coefficient. The optimal correction coefficient is then stored in the EEPROM.

[0070] Furthermore, in this embodiment, the method for determining whether the cubic polynomial model needs to be updated includes: when the change in the state of charge (SOC) of the battery cluster exceeds a set proportional range, or when the voltage fluctuation exceeds the range by a set proportion, it is determined that the cubic polynomial model needs to be updated. Therefore, this method uses the SOC change and voltage fluctuation of the supercapacitor cluster as triggering conditions, enabling dynamic updating of the correction coefficients and real-time tracking of the sampling error changes of the high-voltage supercapacitor cluster under different operating conditions, effectively solving the problem that traditional static calibration cannot adapt to changes in operating conditions.

[0071] In one embodiment, when the state of charge of the battery cluster changes by more than 15% or the voltage fluctuation exceeds 10% of the range, it is determined that the cubic polynomial model needs to be updated, and the coefficient update is initiated.

[0072] In this embodiment, to reduce the impact of random noise on the sampled voltage values ​​and their corresponding true voltage values, the methods for obtaining each group of sampled voltage values ​​and their corresponding true voltage values ​​include:

[0073] Within the range of the set lower voltage limit to the upper voltage limit of the energy storage battery cluster, at least two sets of raw sampled voltage values ​​and their corresponding real voltage values ​​are collected at each voltage point at intervals of a set voltage amount. The average of the raw sampled voltage values ​​at each voltage point is taken to obtain the sampled voltage value at that point. The average of the real voltage values ​​corresponding to the raw sampled voltage values ​​at each voltage point is taken to obtain the real voltage value corresponding to the sampled voltage value at that point.

[0074] In one specific embodiment, within a voltage range of 0-1500V (i.e., the lower voltage limit is set to 0, and the upper voltage limit of the energy storage battery cluster is set to 1500V), 10 sets of data are collected at 100V intervals (i.e., the set voltage value), for a total of 150 sets of raw sampled voltage values. and the corresponding actual voltage value Where i = 1, 2, ..., 150. To reduce the influence of random noise, the average of 10 sets of sampled raw voltage values ​​for each voltage point is taken to obtain the value for that point. The input voltage values ​​are sampled at 15 points. For each voltage point, the average of the actual voltage values ​​corresponding to 10 sets of original sampled voltage values ​​is taken to obtain the value for that point. There are 15 voltage points corresponding to the actual voltage values ​​of the input sampled voltage values.

[0075] When it is necessary to update the cubic polynomial model, the original voltage value and its corresponding real voltage value are collected at a period of 50ms. Following the above method of obtaining each group of sampled voltage values ​​and their corresponding real voltage values, each set of 150 data sets constitutes a calibration dataset, and the sampled voltage values ​​and real voltage values ​​are obtained accordingly.

[0076] When implementing voltage sampling correction, the sampled voltage value Vs acquired by the ADC is read in real time and substituted into a dynamically updated third-order polynomial model. The corrected voltage value Vt is calculated. The corrected voltage value can more accurately measure the cumulative charge and discharge, and is used for functions such as supercapacitor state estimation (state of energy SOE, state of health SOH), charge and discharge control, and overvoltage and undervoltage protection.

[0077] In addition, in this embodiment, to ensure the accuracy of obtaining the original sampled voltage value and its corresponding true voltage value, the original sampled voltage value is obtained by sampling the target voltage using a voltage sampling circuit composed of a 16-bit ADC; the true voltage value corresponding to the original sampled voltage value is obtained by measuring the true value of the target voltage using a standard digital voltmeter. In a preferred embodiment, the target voltage is sampled using a voltage sampling circuit composed of a 16-bit ADC, and the true value of the target voltage is measured using a standard digital voltmeter with an accuracy of 0.05% and a model number of FLUKE 8846A.

[0078] The aforementioned nonlinear error calibration method for voltage sampling of energy storage battery clusters addresses the nonlinear error problem in voltage sampling of 1000V-1500V high-voltage battery clusters (i.e., high-voltage energy storage battery clusters). It employs a third-order polynomial model and dynamically fits correction coefficients using the least squares method to achieve high-precision fitting of the nonlinear curve (overall error <0.1%), while reducing the amount of calibration data stored (≤4 coefficients). This method effectively fits the nonlinear distortion in the high-voltage section, controlling the sampling error within ±0.3%, improving the voltage sampling accuracy of high-voltage clusters and the safety and reliability of the supercapacitor management system. It is applicable to scenarios such as supercapacitor energy storage power stations and new energy vehicle battery packs. The corrected high-precision voltage sampling provides reliable data support for the supercapacitor management system, enabling more accurate estimation of the supercapacitor's state and charge / discharge control. This effectively avoids safety issues such as overcharging and over-discharging caused by sampling errors, improving the safety and reliability of energy storage power stations and new energy vehicle supercapacitor systems.

[0079] Implementation of a Nonlinear Error Calibration System for Energy Storage Battery Cluster Voltage Sampling

[0080] This embodiment provides a technical solution for a nonlinear error calibration system for energy storage battery cluster voltage sampling, including a processor containing executable program instructions. These instructions are executed to implement the following nonlinear error calibration method for energy storage battery cluster voltage sampling:

[0081] Therefore, this system, based on the characteristic that voltage sampling systems are prone to saturation nonlinearity under large signal input, uses a third-order polynomial model to fit and correct the sampled voltage value of the energy storage battery cluster. The constant term coefficients compensate for the zero-bias error of the sampling circuit, the first-order term coefficients correct the linear gain, and the second and third-order term coefficients further fit and correct the nonlinear error. Compared to linear or quadratic models, for the case of high-voltage supercapacitor clusters, this model can more accurately fit the nonlinear distortion of voltage sampling, especially in the 1200V-1500V high-voltage range (reducing the maximum sampling error from ±0.8% to ±0.2%, and controlling the full-range error within ±0.3%), significantly improving voltage sampling accuracy. In other words, this model can effectively describe the nonlinear distortion of the ADC near full scale. Furthermore, this system does not require large-scale modifications to the existing voltage sampling hardware circuit of the energy storage battery cluster; high-precision calibration can be achieved simply by upgrading the software algorithm and running a calibration program on the main control unit, reducing system modification costs and improving development efficiency. Moreover, the amount of data storage required for calibration is relatively small.

[0082] In one specific embodiment, the constructed cubic polynomial model is specifically expressed by the following formula:

[0083]

[0084] As a modified model, where V t For the actual voltage, V s The sampling voltage is represented by a0, a1, a2, and a3, which are nonlinear correction coefficients to be fitted. The constant term coefficient a0 is used to compensate for the zero bias error of the sampling circuit, the first term coefficient a1 is used for linear gain correction, and the second and third term coefficients a2 and a3 are used to correct nonlinear errors. This model can effectively describe the nonlinear distortion of the ADC when it is close to full scale. The measured data shows that the third-order model can cover 95% of the nonlinear error, while the fourth-order and above models improve the nonlinearity by less than 0.02% but the computational cost increases by a factor of two.

[0085] Furthermore, the nonlinear error calibration system also includes: when it is necessary to update the cubic polynomial model, substituting the real-time acquired sampled voltage values ​​and the corresponding true voltage values ​​into the error function; the error function is constructed based on the difference between the true voltage value corresponding to each sampled voltage value and the result of substituting the sampled voltage value into the cubic polynomial model.

[0086] Next, the error function is optimized by iteratively updating the coefficients of the constant term, linear term, quadratic term, and cubic term, starting from the initial value, until the set convergence condition is met. The cubic polynomial model is then updated based on the updated values ​​of each coefficient.

[0087] To facilitate updating the cubic polynomial model based on the values ​​of each coefficient after iterative updates, the following methods can be used: storing the updated values ​​of each coefficient in an EEPROM; and substituting the latest values ​​of each coefficient in the EEPROM into the cubic polynomial model when calculating the corrected voltage value using the cubic polynomial model.

[0088] In this embodiment, the Levenberg-Marquardt algorithm with a damping factor is used to optimize the error function. This algorithm is based on the least squares method and has relatively high accuracy.

[0089] Specifically, the error function can be constructed by comparing the difference between the actual voltage value corresponding to each sampled voltage value and the result of substituting that sampled voltage value into the cubic polynomial model. The methods include:

[0090] For each sampled voltage value, the difference between the actual voltage value and the result of substituting the sampled voltage value into the cubic polynomial model is squared. Then, the error function is obtained by summing the squared values ​​of each term.

[0091] Furthermore, in this embodiment, the method for determining whether the set convergence condition is met includes: as long as there is a situation that satisfies any set convergence condition, it is determined that the set convergence condition is met.

[0092] The convergence condition is set to include at least one of the first, second, and third convergence conditions;

[0093] The first convergence condition is that after this iteration, the changes in the coefficients of the constant term, the linear term, the quadratic term, and the cubic term are all less than the set coefficient change threshold; the second convergence condition is that after this iteration, the change in the error function is less than the set error change threshold; the third convergence condition is that the number of iterations reaches the set maximum number.

[0094] In one specific implementation, an error function is constructed:

[0095]

[0096] The initial value of a0 is taken from V in the calibration dataset (constructed by sampling voltage values ​​and corresponding real voltage value data). si When the voltage is 0V, the average value of the difference between the sampled voltage and the true voltage is used as the initial zero bias estimate; the initial value of a1 is obtained by linear fitting of the calibration dataset. The initial estimated values ​​are generally set to 1. The initial values ​​of a2 and a3 are obtained by performing a preliminary fitting of the first 5 sets of sampled voltage values ​​and the corresponding real voltage values ​​in the calibration dataset using a third-order polynomial.

[0097] The Levenberg-Marquardt algorithm with damping factors is used to optimize the error function, and the parameter increments are calculated through matrix operations. In each iteration, the Jacobian matrix is ​​calculated. Where j = 0, 1, 2, 3, the correction coefficients a0, a1, a2, a3 are updated accordingly. The convergence condition is set as follows: the change in each coefficient is less than 1 / 2. or the change in the error function is less than If the maximum number of iterations reaches 30 (i.e., the maximum number of iterations is set to 30), the iteration stops when the condition is met first, thus obtaining the optimal correction coefficient. The optimal correction coefficient is then stored in the EEPROM.

[0098] Furthermore, in this embodiment, the method for determining whether the cubic polynomial model needs to be updated includes: when the change in the state of charge (SOC) of the battery cluster exceeds a set proportional range, or when the voltage fluctuation exceeds the range by a set proportion, it is determined that the cubic polynomial model needs to be updated. Therefore, this system uses the SOC change and voltage fluctuation of the supercapacitor cluster as trigger conditions to achieve dynamic updates of the correction coefficients. It can track the sampling error changes of the high-voltage supercapacitor cluster under different operating conditions in real time, effectively solving the problem that traditional static calibration cannot adapt to changes in operating conditions.

[0099] In one embodiment, when the state of charge of the battery cluster changes by more than 15% or the voltage fluctuation exceeds 10% of the range, it is determined that the cubic polynomial model needs to be updated, and the coefficient update is initiated.

[0100] In this embodiment, to reduce the impact of random noise on the sampled voltage values ​​and their corresponding true voltage values, the methods for obtaining each group of sampled voltage values ​​and their corresponding true voltage values ​​include:

[0101] Within the range of the set lower voltage limit to the upper voltage limit of the energy storage battery cluster, at least two sets of raw sampled voltage values ​​and their corresponding real voltage values ​​are collected at each voltage point at intervals of a set voltage amount. The average of the raw sampled voltage values ​​at each voltage point is taken to obtain the sampled voltage value at that point. The average of the real voltage values ​​corresponding to the raw sampled voltage values ​​at each voltage point is taken to obtain the real voltage value corresponding to the sampled voltage value at that point.

[0102] In one specific embodiment, within a voltage range of 0-1500V (i.e., the lower voltage limit is set to 0, and the upper voltage limit of the energy storage battery cluster is set to 1500V), 10 sets of data are collected at 100V intervals (i.e., the set voltage value), for a total of 150 sets of raw sampled voltage values. and the corresponding actual voltage value Where i = 1, 2, ..., 150. To reduce the influence of random noise, the average of 10 sets of sampled raw voltage values ​​for each voltage point is taken to obtain the value for that point. The input voltage values ​​are sampled at 15 points. For each voltage point, the average of the actual voltage values ​​corresponding to 10 sets of original sampled voltage values ​​is taken to obtain the value for that point. There are 15 voltage points corresponding to the actual voltage values ​​of the input sampled voltage values.

[0103] When it is necessary to update the cubic polynomial model, the original voltage value and its corresponding real voltage value are collected at a period of 50ms. Following the above method of obtaining each group of sampled voltage values ​​and their corresponding real voltage values, each set of 150 data sets constitutes a calibration dataset, and the sampled voltage values ​​and real voltage values ​​are obtained accordingly.

[0104] When implementing voltage sampling correction, the sampled voltage value Vs acquired by the ADC is read in real time and substituted into a dynamically updated third-order polynomial model. The corrected voltage value Vt is calculated. The corrected voltage value can more accurately measure the cumulative charge and discharge, and is used for functions such as supercapacitor state estimation (state of energy SOE, state of health SOH), charge and discharge control, and overvoltage and undervoltage protection.

[0105] In addition, in this embodiment, to ensure the accuracy of obtaining the original sampled voltage value and its corresponding true voltage value, the original sampled voltage value is obtained by sampling the target voltage using a voltage sampling circuit composed of a 16-bit ADC; the true voltage value corresponding to the original sampled voltage value is obtained by measuring the true value of the target voltage using a standard digital voltmeter. In a preferred embodiment, the target voltage is sampled using a voltage sampling circuit composed of a 16-bit ADC, and the true value of the target voltage is measured using a standard digital voltmeter with an accuracy of 0.05% and a model number of FLUKE 8846A.

[0106] The aforementioned nonlinear error calibration system for energy storage battery cluster voltage sampling addresses the nonlinear error problem in voltage sampling of 1000V-1500V high-voltage battery clusters (i.e., high-voltage energy storage battery clusters). It employs a third-order polynomial model and dynamically fits correction coefficients using the least squares method to achieve high-precision fitting of the nonlinear curve (overall error <0.1%), while reducing the amount of calibration data stored (≤4 coefficients). This system effectively fits the nonlinear distortion in the high-voltage section, controlling the sampling error within ±0.3%, improving the high-voltage cluster voltage sampling accuracy and the safety and reliability of the supercapacitor management system. It is suitable for scenarios such as supercapacitor energy storage power stations and new energy vehicle battery packs. The corrected high-precision voltage sampling provides reliable data support for the supercapacitor management system, enabling more accurate supercapacitor state estimation and charge / discharge control, effectively avoiding safety issues such as overcharging and over-discharging caused by sampling errors, and improving the safety and reliability of energy storage power stations and new energy vehicle supercapacitor systems.

[0107] It should be understood that the above-described specific embodiments of the present invention are merely illustrative or explanatory of the principles of the present invention, and do not constitute a limitation thereof.

Claims

1. A nonlinear error calibration method for voltage sampling of energy storage battery clusters, characterized in that, include: The sampled voltage values ​​of the energy storage battery clusters that need to be corrected are input into the constructed cubic polynomial model to calculate the corrected voltage values. The constructed cubic polynomial model uses the sampled voltage value as the independent variable and the corrected voltage value as the dependent variable. The initial values ​​of the constant term coefficients of the model are determined based on the sampled voltage values ​​obtained when the actual voltage value of the energy storage battery cluster is equal to 0. The initial values ​​of the linear term coefficients of the model are determined by linear fitting with the sampled voltage value as the independent variable and the corrected voltage value as the dependent variable, based on the obtained sampled voltage values ​​and the corresponding actual voltage values. The initial values ​​of the quadratic and cubic term coefficients of the model are determined by third-order polynomial fitting based on the obtained sampled voltage values ​​and the corresponding actual voltage values, as well as the initial values ​​of the linear and constant term coefficients of the model.

2. The nonlinear error calibration method for energy storage battery cluster voltage sampling according to claim 1, characterized in that, Also includes: When it is necessary to update the cubic polynomial model, the real-time sampled voltage values ​​and the corresponding true voltage values ​​are substituted into the error function. The error function is constructed based on the difference between the actual voltage value corresponding to each sampled voltage value and the result of substituting the sampled voltage value into the cubic polynomial model. Then, the error function is optimized by iteratively updating the values ​​of the constant term coefficient, linear term coefficient, quadratic term coefficient, and cubic term coefficient starting from the initial value until the set convergence condition is met. The cubic polynomial model is updated based on the values ​​of each coefficient after iterative updates.

3. The nonlinear error calibration method for energy storage battery cluster voltage sampling according to claim 2, characterized in that, The Levenberg-Marquardt algorithm with damping factor is used to optimize the error function.

4. The nonlinear error calibration method for voltage sampling of energy storage battery clusters according to claim 2, characterized in that, The methods for determining whether the set convergence conditions are met include: as long as there is a case that satisfies any set convergence condition, the set convergence condition is determined to be satisfied; the set convergence conditions include at least one of the first, second, and third convergence conditions; the first convergence condition is that after this iteration, the changes in the coefficients of the constant term, the linear term, the quadratic term, and the cubic term are all less than the set coefficient change threshold; the second convergence condition is that after this iteration, the change in the error function is less than the set error change threshold; the third convergence condition is that the number of iterations reaches the set maximum number of iterations.

5. The nonlinear error calibration method for voltage sampling of energy storage battery clusters according to any one of claims 1-4, characterized in that, The methods for determining whether the cubic polynomial model needs to be updated include: when the change in the state of charge of the battery cluster exceeds a set ratio range, or when the voltage fluctuation exceeds the range by a set ratio, it is determined that the cubic polynomial model needs to be updated.

6. The nonlinear error calibration method for voltage sampling of energy storage battery clusters according to any one of claims 1-4, characterized in that, The methods for obtaining each set of sampled voltage values ​​and their corresponding true voltage values ​​include: within the range of a set lower voltage limit to the upper voltage limit of the energy storage battery cluster, at least two sets of raw sampled voltage values ​​and their corresponding true voltage values ​​are collected at each voltage point at intervals of a set voltage amount; the average of the raw sampled voltage values ​​at each voltage point is taken to obtain the sampled voltage value at that point; and the average of the true voltage values ​​corresponding to the raw sampled voltage values ​​at each voltage point is taken to obtain the true voltage value corresponding to the sampled voltage value at that point.

7. The nonlinear error calibration method for voltage sampling of energy storage battery clusters according to any one of claims 2-4, characterized in that, The error function is constructed based on the difference between the actual voltage value corresponding to each sampled voltage value and the result of substituting the sampled voltage value into the cubic polynomial model. The method includes: taking the square of the difference between the actual voltage value corresponding to each sampled voltage value and the result of substituting the sampled voltage value into the cubic polynomial model, and then obtaining the constructed error function based on the sum of the squares of each term.

8. The nonlinear error calibration method for voltage sampling of energy storage battery clusters according to any one of claims 2-4, characterized in that, The methods for updating the cubic polynomial model based on the values ​​of each coefficient after iterative updates include: storing the values ​​of each coefficient after iterative updates in EEPROM; and when calculating the corrected voltage value using the cubic polynomial model, substituting the latest values ​​of each coefficient in EEPROM into the cubic polynomial model for calculation.

9. The nonlinear error calibration method for voltage sampling of energy storage battery clusters according to claim 6, characterized in that, The original value of the sampled voltage is obtained by sampling the target voltage using a voltage sampling circuit composed of a 16-bit ADC; the actual voltage value corresponding to the original value of the sampled voltage is obtained by measuring the actual value of the target voltage using a standard digital voltmeter.

10. A nonlinear error calibration system for sampling the voltage of an energy storage battery cluster, comprising a processor, wherein the processor stores executable program instructions, characterized in that, The executable program instructions are to be executed to implement the nonlinear error calibration method for sampling the energy storage battery cluster voltage as described in any one of claims 1-9.

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