A multi-parameter metering calibration method for a smart meter
By modeling the metering error factors of smart meters as parameter vectors, establishing observation equations and optimizing parameters, the multi-parameter coupled nonlinear optimization problem of smart meters in complex power environments is solved, achieving high-precision and stable metering calibration results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING NENGRUI AUTOMATION EQUIP
- Filing Date
- 2026-02-13
- Publication Date
- 2026-06-26
AI Technical Summary
Smart meters are susceptible to multi-source error interference in complex power environments, resulting in systematic deviations between the measured values and the true values. Traditional calibration methods are difficult to adapt to the nonlinear optimization requirements of multi-parameter coupling.
The factors influencing the metering error of smart meters are uniformly modeled as parameter vectors, observation equations are established, and an objective function is constructed by minimizing the sum of squared residuals of the observation equations. The parameter vectors are then optimized using an improved BFGS algorithm for metering calibration.
It significantly reduces measurement errors, improves calibration accuracy and robustness, enables efficient and real-time measurement calibration, and enhances the accuracy and stability of the measurement system.
Smart Images
Figure CN122283575A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of power metering and calibration technology, and in particular to a multi-parameter metering and calibration method for smart meters. Background Technology
[0002] With the large-scale deployment of smart grids, smart meters, as core devices for energy metering, directly impact the fairness of electricity trading and the efficiency of system operation. However, in actual operation, smart meters are susceptible to interference from multiple sources of errors, such as proportional coefficient error, temperature drift, nonlinear distortion, and phase error, leading to systematic deviations between measured and true values. Traditional calibration methods are mostly based on modeling a single error source or linear assumptions, making it difficult to adapt to the nonlinear optimization requirements of multi-parameter coupling in complex power environments. Summary of the Invention
[0003] The purpose of this application is to provide a multi-parameter metering calibration method for smart meters, which solves the problem in related technologies that smart meters are susceptible to interference from multiple sources of errors, resulting in systematic deviations between the measured values and the true values.
[0004] To solve the above-mentioned technical problems, this application adopts the following technical solution:
[0005] This application provides a multi-parameter metering calibration method for smart meters, including:
[0006] The influencing factors of smart meter measurement error are uniformly modeled as parameter vectors, and the observation equation of smart meter is established based on the parameter vectors. The observation equation is used to express the relationship between the actual output measurement value of smart meter and the measured true value under the influencing factors.
[0007] An objective function is constructed using the sum of squared residuals from the observation equations to optimize the parameter vector;
[0008] Minimize the objective function to obtain the optimal parameter vector;
[0009] The observation equation is corrected based on the optimal parameter vector, thereby achieving the metering calibration of the smart meter.
[0010] Optionally, the influencing factors include: proportional coefficient error, temperature drift, nonlinear distortion, and phase error.
[0011] Optionally, the influencing factors of smart meters are uniformly modeled as a parameter vector, represented as:
[0012] ,
[0013] in, Represents a parameter vector. This represents the proportionality coefficient. Indicates the temperature drift coefficient. Indicates the second-order nonlinear coefficients. Denotes the Cth-order nonlinear coefficient. Indicates the phase error coefficient;
[0014] The formula for the observation equation is:
[0015] ,
[0016] In the formula, Let be the actual metering value output by the smart meter at the i-th sampling point. Let T be the true value measured by the smart meter at the i-th sampling point. i Let T0 be the ambient temperature at the i-th sampling point, T0 be the reference temperature at the i-th sampling point, C be the higher harmonic cutoff value at the i-th sampling point, and ω be the lower harmonic cutoff value. i Let t represent the angular frequency of the power grid at the i-th sampling point. i ε represents the sampling time of the i-th sampling point. i Let represent the random noise at the i-th sampling point.
[0017] Optionally, constructing the objective function from the sum of squared residuals of the observation equation to optimize the parameter vector includes:
[0018] The residuals are introduced into the sampled data, and the formula is:
[0019] ,
[0020] In the formula, r i (θ) represents the residual of the i-th sampling point when the parameter vector is θ.
[0021] Let z be the predicted value of the observation equation at the i-th sampling point when the parameter vector is θ. i This represents the auxiliary feature of the i-th sampling point;
[0022] The objective function is constructed using the sum of squared residuals, and the formula is as follows:
[0023] ,
[0024] In the formula, J(θ) represents the objective function value when the parameter vector is θ, and N represents the number of sampling points.
[0025] Optionally, minimizing the objective function to obtain the optimal parameter vector includes:
[0026] Choose initial parameters, set the initial inverse Hessian approximation to the identity matrix H0=I, set the convergence threshold τ>0 and the maximum number of iterations, initialize the trust region radius, and set the maximum and minimum trust region radii.
[0027] If the maximum number of iterations is reached and gradient convergence is achieved... Changes in parameters between adjacent iterations If either condition is met, output the optimal parameter vector; otherwise, iteratively execute the following steps:
[0028] The current gradient is calculated based on the current parameter vector, using the following formula: In the formula, g k Let θ represent the gradient of the k-th iteration. k This represents the parameter vector for the k-th iteration.
[0029] Indicates the objective function at θ k The gradient vector at that point;
[0030] Calculate the search direction p of the trust region subproblem based on the current gradient and trust region radius;
[0031] The acceptance change ratio ρ is calculated based on the search direction. k And update the trust region radius based on the accepted variable ratio;
[0032] make To obtain the updated parameter vector, where p k θ represents the search direction in the k-th iteration. k+1 This represents the parameter vector for the (k+1)th iteration;
[0033] Calculate the parameter change and gradient difference, introduce a correction factor, and correct the gradient difference in conjunction with the parameter change, wherein the parameter change s k =p k The gradient difference ;
[0034] The inverse Hessian approximation matrix is updated based on the corrected gradient difference combined with the introduced adaptive parameters.
[0035] Optionally, the search direction p for calculating the trust region subproblem based on the current gradient and trust region radius includes:
[0036] Solve , must meet In the formula, m(p) is the quadratic model constructed by the objective function at the current iteration point, and H k ∆ represents the inverse Hessian approximation for the k-th iteration. k This represents the radius of the trust region in the k-th iteration.
[0037] Optionally, the calculation of the acceptance change ratio ρ based on the search direction... k Updating the trust region radius based on the acceptance variable ratio includes:
[0038] Calculate the actual decrease and the predicted decrease of the objective function, and calculate the acceptance ratio ρ based on the actual decrease and the predicted decrease of the objective function. k The formula is:
[0039] ,
[0040] In the formula, J(θ) k ), representing the function value of the objective function in the k-th iteration, J(θ) k +P k ) represents the function value of the objective function at the updated iteration point, m(0) represents the function value of the quadratic model at the initial point, and m(p) represents the function value of the objective function at the updated iteration point. k ) represents a quadratic function with step size p k The function value at that location;
[0041] Updating the trust region radius based on the acceptance variable ratio includes:
[0042] If ρ k If <0.25, then narrow the trust region: In the formula, ∆ k+1 , where represents the radius of the trust region in the (k+1)th iteration, ∆ min This represents the minimum threshold value for the trust region radius.
[0043] If ρ k If the value is greater than 0.75 and the step size reaches the boundary, then expand the trust region: In the formula, ∆ max This represents the maximum threshold value for the trust region radius.
[0044] Optional, corrected gradient difference The formula is:
[0045] ,
[0046] in, The correction factor is expressed by the formula: .
[0047] Optionally, the inverse Hessian approximation matrix is updated based on the corrected gradient difference combined with the introduced adaptive parameters, as shown in the following formula:
[0048] ,
[0049] in, The improved scaling factor is expressed by the formula:
[0050] ; The adaptive parameter for the k-th iteration is represented by the formula:
[0051] .
[0052] Compared with existing technologies, the beneficial effects achieved by this application are as follows: This application uniformly models the influencing factors of smart meter metering errors as parameter vectors, and establishes the observation equation of the smart meter based on the parameter vectors. The objective function is constructed using the sum of squared residuals of the observation equations to optimize the parameter vectors, transforming smart meter metering calibration into an optimization problem, thus adapting to the nonlinear optimization requirements of multi-parameter coupling in complex power environments. Furthermore, this application addresses the line search failure problem (fixed-direction line search may fail in strongly nonlinear regions) and numerical stability problem (basic BFGS in...) existing in the basic quasi-Newton method's BFGS algorithm.
[0053] The algorithm may be numerically unstable when approaching zero, and it also suffers from convergence issues (including convergence speed and global convergence problems, i.e., decreased convergence speed and lack of global convergence guarantees in ill-conditioned problems). This application introduces optimization techniques to improve the basic BFGS algorithm. This further enhances the algorithm's robustness and convergence speed in complex nonlinear optimization problems, thereby achieving the goals of reducing errors and improving calibration accuracy. Attached Figure Description
[0054] To more clearly illustrate the technical solutions in the embodiments or related technologies of this disclosure, the accompanying drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0055] Figure 1 This is a schematic flowchart of the method of Embodiment 1 provided in this application;
[0056] Figure 2 This is a schematic diagram of the algorithm flow of Embodiment 2 provided in this application;
[0057] Figure 3 This is a schematic diagram comparing the root mean square error changes of the improved BFGS algorithm and the basic BFGS algorithm in Embodiment 2 provided in this application.
[0058] Figure 4 This is a schematic diagram comparing the relative error changes of the improved BFGS algorithm and the basic BFGS algorithm in Embodiment 2 provided in this application;
[0059] Figure 5This is a schematic diagram comparing the changes in the coefficient of determination between the improved BFGS algorithm and the basic BFGS algorithm in Embodiment 2 provided in this application;
[0060] Figure 6 This is a schematic diagram comparing the error fluctuation range of the improved BFGS algorithm and the basic BFGS algorithm in Embodiment 2 provided in this application. Detailed Implementation
[0061] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure / application, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit this application or its application or use.
[0062] Example 1
[0063] This embodiment describes a multi-parameter metering calibration method for smart meters, referencing... Figure 1 The multi-parameter metering calibration method for smart meters in this embodiment includes:
[0064] S100 models the influencing factors of smart meter metering error into a parameter vector and establishes the observation equation of smart meter based on the parameter vector. The observation equation is used to express the relationship between the actual output metering value and the measured true value of smart meter under the influencing factors.
[0065] The core purpose of electricity meter calibration is to ensure that the meter's measured value is highly consistent with the actual value, reduce systematic errors, and ensure metering fairness. In actual operation, the metering error of smart meters mainly comes from proportional coefficient error (the amplification / reduction ratio of the meter itself), temperature drift (sampling deviation caused by temperature changes), nonlinear distortion (nonlinearity of higher-order power / energy terms), and phase error (phase shift when measuring power factor).
[0066] In this embodiment, the influencing factors include: proportional coefficient error, temperature drift, nonlinear distortion, and phase error. These factors are uniformly modeled as a parameter vector, represented as:
[0067] ,
[0068] Where θ represents the parameter vector, α represents the scaling factor, and β represents the scaling factor. T γ represents the temperature drift coefficient, γ2 represents the second-order nonlinear coefficient, γc represents the C-order nonlinear coefficient, and ∅ represents the phase error coefficient.
[0069] The formula for the observation equation is:
[0070] ,
[0071] In the formula, Let be the actual metering value output by the smart meter at the i-th sampling point. Let T be the true value measured by the smart meter at the i-th sampling point. i Let T0 be the ambient temperature at the i-th sampling point, T0 be the reference temperature at the i-th sampling point, C be the higher harmonic cutoff value at the i-th sampling point, and ω be the lower harmonic cutoff value. i Let t represent the angular frequency of the power grid at the i-th sampling point. i ε represents the sampling time of the i-th sampling point. i Let represent the random noise at the i-th sampling point.
[0072] S200 constructs an objective function from the sum of squared residuals of the observation equations to optimize the parameter vector.
[0073] This includes: introducing residuals into the sampled data, with the formula as follows:
[0074] ,
[0075] In the formula, r i (θ) represents the residual of the i-th sampling point when the parameter vector is θ. Let z be the predicted value of the observation equation at the i-th sampling point when the parameter vector is θ. i This represents the auxiliary feature of the i-th sampling point;
[0076] The objective function is constructed using the sum of squared residuals, and the formula is as follows:
[0077] ,
[0078] In the formula, J(θ) represents the objective function value when the parameter vector is θ, and N represents the number of sampling points.
[0079] S300 minimizes the objective function to obtain the optimal parameter vector.
[0080] This embodiment uses the least squares method to establish the objective function, finds the best function match for the data by minimizing the sum of squared errors, and finds the optimal parameter vector by optimizing the objective function.
[0081] As an alternative optimization algorithm, the objective function can be minimized using quasi-Newton methods. Quasi-Newton methods are a class of iterative algorithms for solving unconstrained nonlinear optimization problems. They replace the costly second-order derivative calculations in Newton's method by constructing an approximation of the Hessian matrix or its inverse. The core idea is to utilize gradient information to construct a symmetric positive definite matrix that satisfies the quasi-Newton conditions, making the iteration direction descent while maintaining superlinear convergence speed.
[0082] The S400 corrects the observation equation based on the optimal parameter vector, thereby achieving metering calibration of the smart meter.
[0083] This embodiment establishes an observation equation based on various factors affecting metering errors, and uses the least squares method to establish an objective function based on the observation equation, transforming smart meter metering calibration into an optimization problem, thus adapting to the nonlinear optimization requirements of multi-parameter coupling in complex power environments.
[0084] Example 2
[0085] This embodiment is based on the same inventive concept as Example 1. It obtains the optimal parameters by minimizing the objective function using an improved BFGS algorithm. BFGS (Broyden–Fletcher–Goldfarb–Shanno) is a quasi-Newton algorithm used to solve unconstrained optimization problems. It avoids directly calculating the second derivative by progressively correcting the approximation of the inverse Hessian matrix (or the Hessian matrix itself), thus reducing computational complexity while maintaining convergence speed. However, the basic BFGS algorithm suffers from line search failure problems (fixed-direction line search may fail in strongly nonlinear regions) and numerical stability problems (the basic BFGS algorithm has limitations in...).
[0086] (Numerical instability may occur when the value is close to zero) and convergence issues (including convergence speed issues and global convergence issues, i.e., decreased convergence speed and lack of global convergence guarantees in ill-conditioned problems).
[0087] refer to Figure 2 To achieve the goals of reducing errors and improving calibration accuracy, this embodiment improves and optimizes the basic BFGS algorithm. The specific steps of the improved BFGS algorithm are explained below:
[0088] Choose initial parameters, set the initial inverse Hessian approximation to the identity matrix H0=I, set the convergence threshold τ>0 and the maximum number of iterations, initialize the trust region radius, and set the maximum and minimum trust region radii. Here, let the initial parameter vector θ0 be empirical values (e.g., α=1, ∅=0, β...). T =0).
[0089] This embodiment replaces the line search method in the basic BFGS with the trust region method, and determines the step size by solving the trust region subproblem. This can better control the quality of the step size and ensure that each step is within the trust region of the model.
[0090] If the maximum number of iterations is reached and gradient convergence is achieved... Changes in parameters between adjacent iterations If either condition is met, output the optimal parameter vector; otherwise, iteratively execute the following steps:
[0091] The current gradient is calculated based on the current parameter vector, using the following formula: In the formula, g k Let θ represent the gradient of the k-th iteration. k This represents the parameter vector for the k-th iteration. Indicates the objective function at θ k The gradient vector at that point;
[0092] The search direction p for the trust region subproblem is calculated based on the current gradient and the trust region radius.
[0093] This includes: solving , must meet In the formula, m(p) is the quadratic model constructed by the objective function at the current iteration point, and H k ∆ represents the inverse Hessian approximation for the k-th iteration. k This represents the radius of the trust region in the k-th iteration.
[0094] The acceptance change ratio ρ is calculated based on the search direction. k The trust region radius is updated based on the acceptance ratio. The trust region radius is dynamically adjusted according to the ratio of the actual decrease to the predicted decrease in the objective function, balancing convergence speed and stability.
[0095] This includes: calculating the actual decrease and the predicted decrease of the objective function, and calculating the acceptance ratio ρ based on the actual decrease and the predicted decrease of the objective function. k The formula is:
[0096] Calculate the actual decrease and the predicted decrease of the objective function, and calculate the acceptance ratio ρ based on the actual decrease and the predicted decrease of the objective function. k The formula is:
[0097] ,
[0098] In the formula, J(θ) k ), representing the function value of the objective function in the k-th iteration, J(θ) k +P k ) represents the function value of the objective function at the updated iteration point, m(0) represents the function value of the quadratic model at the initial point, and m(p) represents the function value of the objective function at the updated iteration point. k ) represents a quadratic function with step size p k The function value at (J(θ)) k )-J(θ k +P k )) represents the actual decrease, m(0)-m(p) k ) represents the predicted decrease in the objective function.
[0099] The trust region radius is updated based on the acceptance variable ratio, including:
[0100] If ρ k If <0.25, then narrow the trust region: In the formula, ∆ k+1 , where represents the radius of the trust region in the (k+1)th iteration, ∆ min This represents the minimum threshold value for the trust region radius.
[0101] If ρ k If the value is greater than 0.75 and the step size reaches the boundary, then expand the trust region: In the formula, ∆ max This represents the maximum threshold value for the trust region radius.
[0102] If ρ k >0.1 accepts a step size. Let To obtain the updated parameter vector, where p k θ represents the search direction in the k-th iteration. k+1 This represents the parameter vector for the (k+1)th iteration.
[0103] The parameter changes and gradient difference are calculated, and a correction factor is introduced to adjust the gradient difference in conjunction with the parameter changes. By introducing the correction factor, the gradient difference is adjusted. This better satisfies the positive definiteness conditions of the Hessian approximation.
[0104] Among them, the parameter change s k =p k ;
[0105] gradient difference ;
[0106] Corrected gradient difference The formula is:
[0107] ,
[0108] Where, μ k The correction factor is expressed by the formula:
[0109] .
[0110] The inverse Hessian approximation matrix is updated based on the corrected gradient difference combined with the introduced adaptive parameters.
[0111] The formula is: ,
[0112] in, The improved scaling factor is expressed by the formula:
[0113] η kThe adaptive parameter for the k-th iteration is represented by the formula:
[0114] .
[0115] The improved BFGS update adds an extra term to the basic BFGS update formula and introduces an adaptive parameter η. k This improves the positive definiteness and numerical stability of the Hessian approximation.
[0116] Based on the above improvements and optimizations to the basic BFGS algorithm, the metrological calibration effect was verified through simulation in MATLAB. The output data from the first 20 iterations is shown in the table below:
[0117] Number of iterations RMSE Mean relative error (%) Coefficient of determination R² Calculation time (ms) Error fluctuation range 1 14.041269 10.116208 0.740276 1.85 63.694341 2 14.041269 10.116208 0.740276 5.53 63.694341 3 14.041269 10.116208 0.740276 6.10 63.694341 4 14.041269 10.116208 0.740276 6.70 63.694341 5 14.041269 10.116208 0.740276 7.32 63.694341 6 14.041269 10.116208 0.740276 7.85 63.694341 7 14.041269 10.116208 0.740276 8.41 63.694341 8 14.041269 10.116208 0.740276 8.94 63.694341 9 14.041269 10.116208 0.740276 9.41 63.694341 10 6.182980 3.948764 0.949639 11.59 32.435371 11 6.182980 3.948764 0.949639 12.44 32.435371 12 1.354686 0.793500 0.997582 17.75 8.257871 13 1.354686 0.793500 0.997582 18.42 8.257871 14 0.830942 0.654896 0.999090 19.47 2.859221 15 0.830942 0.654896 0.999090 20.03 2.859221 16 0.830942 0.654896 0.999090 20.53 2.859221 17 0.830942 0.654896 0.999090 21.04 2.859221 18 0.830942 0.654896 0.999090 21.51 2.859221 19 0.830942 0.654896 0.999090 21.97 2.859221 20 0.830942 0.654896 0.999090 22.44 2.859221
[0118] refer to Figure 3 The root mean square error (RMSE) measures the absolute magnitude of the error. It is more sensitive to large errors (due to the square amplification effect) and can intuitively reflect the overall accuracy of the meter measurement. The RMSE of the improved BFGS algorithm rapidly decreased from the initial 14.04 to 0.83, approaching the theoretical optimal value. The improved algorithm has a significant advantage in the overall system fitting accuracy and can more effectively approximate the real model.
[0119] refer to Figure 4 Mean relative error (MRE) measures the relative magnitude of error and is expressed as a percentage. The improved BFGS algorithm rapidly reduces the MRE to approximately 0.65% after 10 iterations, significantly lower than the 10.12% of the uncalibrated state. The improved algorithm demonstrates stronger optimization capabilities in reducing system bias, significantly improving the accuracy of metrological calibration.
[0120] refer to Figure 5 The coefficient of determination (R²) measures a model's ability to explain changes in data, i.e., its goodness of fit. The improved BFGS algorithm ultimately achieves an R² value of 0.99909, approaching a perfect fit. The improved algorithm can more accurately capture the dynamic characteristics of the system, and the model's explanatory power is significantly enhanced.
[0121] refer to Figure 6 Error fluctuation range measures the degree of dispersion or worst-case scenario of the error. The improved BFGS algorithm reduces the error fluctuation range from 63.69 to 2.86, exhibiting excellent stability. The improved algorithm significantly enhances the robustness of the system and output consistency, which is beneficial for improving measurement reliability.
[0122] Simulation studies have fully verified the revolutionary improvement effect of the improved quasi-Newton algorithm in power metering calibration. Compared with the uncalibrated original system, the improved algorithm brings significant improvements in the following three dimensions:
[0123] 1. Significantly improved accuracy and order-of-magnitude reduction in error: The algorithm reduces core accuracy metrics (RMSE and mean relative error) by more than an order of magnitude. RMSE is optimized from 14.04 to 0.83, and the mean relative error is reduced from 10.12% to 0.65%. This means that the systematic bias and overall error of the metering system are suppressed to extremely low levels, fundamentally improving the accuracy and fairness of metering and providing a reliable data foundation for refined energy management and trade settlement.
[0124] 2. Increased efficiency and real-time processing potential: While achieving higher accuracy, the improved algorithm reduces computation time by 82%. This "fast and accurate" characteristic breaks the traditional trade-off between accuracy and speed in optimization, making high-frequency, real-time metrological calibration possible in embedded devices or online monitoring systems, greatly enhancing the engineering practical value of calibration technology.
[0125] 3. Significantly Improved Stability and Highly Consistent Output: By compressing the error fluctuation range by 95.5% to 2.86, the improved algorithm greatly enhances the system's stability and robustness. The calibrated measurement output no longer fluctuates dramatically, exhibiting high consistency. This is crucial for evaluating long-term equipment performance, diagnosing potential faults, and ensuring the long-term reliability of measurement data.
[0126] In summary, the improved quasi-Newton algorithm, through its intelligent iterative control mechanism, successfully calibrated an uncalibrated power metering system with significant errors and large fluctuations into a highly accurate, stable, and efficient quasi-ideal system. This algorithm provides a powerful technical solution for high-precision, high-reliability intelligent power metering at the engineering level.
[0127] The above description is only a preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of this disclosure / application, and these improvements and modifications should also be considered within the protection scope of this disclosure / application.
Claims
1. A multi-parameter metering calibration method for smart meters, characterized in that, include: The influencing factors of smart meter measurement error are uniformly modeled as parameter vectors, and the observation equation of smart meter is established based on the parameter vectors. The observation equation is used to express the relationship between the actual output measurement value of smart meter and the measured true value under the influencing factors. An objective function is constructed using the sum of squared residuals from the observation equations to optimize the parameter vector; Minimize the objective function to obtain the optimal parameter vector; The observation equation is corrected based on the optimal parameter vector, thereby achieving the metering calibration of the smart meter.
2. The multi-parameter metering calibration method for smart meters according to claim 1, characterized in that, The influencing factors include: proportional coefficient error, temperature drift, nonlinear distortion, and phase error.
3. The multi-parameter metering calibration method for smart meters according to claim 2, characterized in that, The influencing factors of smart meters are uniformly modeled as a parameter vector, as follows: ， Where θ represents the parameter vector, α represents the scaling factor, and β represents the scaling factor. T γ represents the temperature drift coefficient, and γ2 represents the first... The Cth-order nonlinear coefficient, γc represents the Cth-order nonlinear coefficient, and ∅ represents the phase error coefficient; The formula for the observation equation is: ， In the formula, Let be the actual metering value output by the smart meter at the i-th sampling point. Let T be the true value measured by the smart meter at the i-th sampling point. i Let T0 be the ambient temperature at the i-th sampling point, T0 be the reference temperature at the i-th sampling point, C be the higher harmonic cutoff value at the i-th sampling point, and ω be the lower harmonic cutoff value. i Let t represent the angular frequency of the power grid at the i-th sampling point. i ε represents the sampling time of the i-th sampling point. i Let represent the random noise at the i-th sampling point.
4. The multi-parameter metering calibration method for smart meters according to claim 3, characterized in that, The step of constructing an objective function from the sum of squared residuals of the observation equation to optimize the parameter vector includes: The residuals are introduced into the sampled data, and the formula is: ， In the formula, r i (θ) represents the residual of the i-th sampling point when the parameter vector is θ. Let z be the predicted value of the observation equation at the i-th sampling point when the parameter vector is θ. i Indicates the first Auxiliary features of each sampling point; The objective function is constructed using the sum of squared residuals, and the formula is as follows: ， In the formula, J(θ) represents the objective function value when the parameter vector is θ, and N represents the number of sampling points.
5. The multi-parameter metering calibration method for smart meters according to claim 1, characterized in that, Minimizing the objective function to obtain the optimal parameter vector includes: Choose initial parameters, set the initial inverse Hessian approximation to the identity matrix H0=I, set the convergence threshold τ>0 and the maximum number of iterations, initialize the trust region radius, and set the maximum and minimum trust region radii. If the maximum number of iterations is reached and gradient convergence is achieved... Changes in parameters between adjacent iterations If either condition is met, output the optimal parameter vector; otherwise, iteratively execute the following steps: The current gradient is calculated based on the current parameter vector, using the following formula: In the formula, g k Let θ represent the gradient of the k-th iteration. k This represents the parameter vector for the k-th iteration. Indicates the objective function at θ k The gradient vector at that point; Calculate the search direction p of the trust region subproblem based on the current gradient and trust region radius; The acceptance change ratio ρ is calculated based on the search direction. k And update the trust region radius based on the accepted variable ratio; make To obtain the updated parameter vector, where p k θ represents the search direction in the k-th iteration. k+1 This represents the parameter vector for the (k+1)th iteration; Calculate the parameter change and gradient difference, introduce a correction factor, and correct the gradient difference in conjunction with the parameter change, wherein the parameter change s k =p k The gradient difference ; The inverse Hessian approximation matrix is updated based on the corrected gradient difference combined with the introduced adaptive parameters.
6. The multi-parameter metering calibration method for smart meters according to claim 5, characterized in that, The search direction p for calculating the trust region subproblem based on the current gradient and trust region radius includes: Solve , must meet In the formula, m(p) is the quadratic model constructed by the objective function at the current iteration point, and H k ∆ represents the inverse Hessian approximation for the k-th iteration. k This represents the radius of the trust region in the k-th iteration.
7. The multi-parameter metering calibration method for smart meters according to claim 6, characterized in that, The calculation of the acceptance change ratio ρ based on the search direction k Updating the trust region radius based on the acceptance variable ratio includes: Calculate the actual decrease and the predicted decrease of the objective function, and calculate the acceptance ratio ρ based on the actual decrease and the predicted decrease of the objective function. k The formula is: ， In the formula, J(θ) k ), representing the function value of the objective function in the k-th iteration, J(θ) k +P k ) represents the function value of the objective function at the updated iteration point, m(0) represents the function value of the quadratic model at the initial point, and m(p) represents the function value of the objective function at the updated iteration point. k ) represents a quadratic function with step size p k The function value at that location; Updating the trust region radius based on the acceptance variable ratio includes: If ρ k If <0.25, then narrow the trust region: In the formula, ∆ k+1 , where represents the radius of the trust region in the (k+1)th iteration, ∆ min This represents the minimum threshold value for the trust region radius. If ρ k If the value is greater than 0.75 and the step size reaches the boundary, then expand the trust region: In the formula, ∆ max This represents the maximum threshold value for the trust region radius.
8. The multi-parameter metering calibration method for smart meters according to claim 7, characterized in that, Corrected gradient difference The formula is: ， in, k The correction factor is expressed by the formula: 。 9. The multi-parameter metering calibration method for smart meters according to claim 8, characterized in that, The inverse Hessian approximation matrix is updated based on the corrected gradient difference combined with the introduced adaptive parameters, as shown in the formula: ， in, The improved scaling factor is expressed by the formula: ； k The adaptive parameter for the k-th iteration is represented by the formula: 。