A CVT error calculation method and medium based on ALS-MLE

Abstract

This invention provides a CVT error calculation method and medium based on ALS-MLE, belonging to the field of power measurement technology. It aims to solve the problem of voltage measurement accuracy being affected by the non-steady-state characteristics of CVTs in power systems caused by temperature, humidity, and load changes, resulting in ratio and angle difference errors. This invention employs a hybrid algorithm combining ALS and MLE for online monitoring and calculation of CVT errors. First, secondary terminal voltage measurement data of the CVT at multiple time points are collected, and the amplitude and phase information are analyzed. Based on the log-likelihood function, maximum likelihood function estimation is used, combined with iterative optimization using ALS to solve for the CVT error parameters. Finally, based on the solution results, the amplitude and phase errors of the CVT are simultaneously corrected to adapt to dynamic error changes during operation. This invention can effectively estimate the error coefficients in capacitive voltage transformers and correct errors, thereby improving the accuracy of online voltage monitoring.

Description

Technical Field

[0001] This invention relates to the field of power measurement technology, specifically a method and medium for calculating CVT (capacitive voltage transformer) errors based on ALS (Adaptive Least Squares) and MLE (Maximum Likelihood Estimation). Background Technology

[0002] In modern power systems, CVTs, as key equipment, are widely used in important aspects such as voltage measurement, relay protection, and energy metering. Their measurement accuracy directly affects the safe and stable operation of the power system, economic dispatch, and the accuracy of energy metering. However, due to various factors, CVTs inevitably produce errors during actual operation.

[0003] On the one hand, the internal structure of a CVT is relatively complex, consisting of multiple components such as a capacitive voltage divider, an intermediate transformer, and a compensating reactor. The performance parameters of each component are prone to change during long-term operation, which can affect the overall measurement accuracy. For example, the capacitance value of the capacitive voltage divider may drift due to environmental factors such as temperature and humidity, and the core loss and winding resistance of the intermediate transformer will also change with the increase of operating time. All of these factors can cause deviations between the CVT output voltage and the actual input voltage.

[0004] On the other hand, the operating conditions of power systems are complex and variable. Frequent occurrences of load fluctuations, system short-circuit faults, and harmonic interference create an extremely harsh electromagnetic environment for CVTs. Under these complex electromagnetic conditions, CVTs are subject to various interferences such as electromagnetic coupling and electromagnetic induction, further increasing the likelihood of errors. For example, the presence of harmonics can distort CVT measurement results, making it impossible to accurately reflect the actual voltage value.

[0005] Traditional CVT error calculation methods are mostly based on simple models and fixed parameters, making it difficult to fully consider the influence of the aforementioned complex factors. This leads to significant deviations between the calculated error results and the actual error in practical applications, failing to meet the growing demand for high-precision operation of power systems. For example, traditional methods may not accurately capture CVT error changes under extreme operating conditions, thus affecting the correct operation of relay protection devices and threatening the safe and stable operation of the power system.

[0006] As power systems continue to evolve towards larger capacity, higher voltage, and greater intelligence, higher demands are being placed on the accuracy and real-time performance of CVT error calculation. Accurate error calculation not only helps in the timely detection of potential CVT faults, enabling early maintenance and replacement and preventing power outages caused by equipment failures, but also provides reliable data support for optimized power system scheduling, improving the operational efficiency and economic benefits of the power system. Therefore, developing a high-precision, real-time CVT error calculation method that can adapt to complex operating environments has become a crucial problem urgently needing to be solved in the power sector. Summary of the Invention

[0007] This invention provides a CVT error calculation method and medium based on ALS-MLE, aiming to solve the problem that the non-steady-state characteristics of CVT in power systems caused by temperature, humidity and load changes lead to the impact of ratio difference error and angle difference error on voltage measurement accuracy.

[0008] The technical solution adopted by this invention to solve its technical problem is: a CVT error calculation method based on ALS-MLE, applied to at least three in-phase CVTs on the same bus, which calculates CVT error parameters including ratio difference and angle difference through the following steps:

[0009] S1. Data Acquisition and Model Building: Acquire secondary voltage data of the CVT at multiple time points, including amplitude and phase information; Based on the secondary voltage data, estimate the initial value of the true voltage at each time point and the initial value of the noise variance of each CVT.

[0010] S2. Joint Parameter Iterative Optimization: Starting from the initial estimated value, an objective function based on maximum likelihood estimation is constructed using the log-likelihood function, and an alternating optimization framework is used to iteratively solve the ratio difference, angle difference, and the true voltage estimate at each time point of the CVT; the alternating optimization framework includes: a step of updating the ratio difference and angle difference in at least one round based on the current noise variance estimate, and a step of updating the true voltage estimate in at least one round;

[0011] S3. Iterative Convergence and Output: Calculate the change in CVT error parameters after each iteration, determine whether to terminate the iteration based on the change, and output the final ratio difference and angle difference.

[0012] S4. Error Correction: Using the final ratio difference and angle difference, the amplitude and phase errors of the subsequent voltage measurement results of the corresponding CVT are compensated.

[0013] By collecting secondary voltage data of the CVT at multiple time points, the amplitude and phase information are analyzed. Based on the log-likelihood function, maximum likelihood estimation (MLE) is used, combined with alternating least squares (ALS) for iterative optimization to solve for the CVT error parameters. Finally, based on the solution results, the amplitude and phase errors of the CVT are simultaneously corrected to adapt to dynamic error changes during operation. This invention can simultaneously consider and correct the amplitude and phase errors of the CVT, adapt to the dynamic error changes of the voltage transformer during operation, significantly improve the accuracy of voltage measurement, avoid system deviations caused by calibration errors, and effectively improve the accuracy of CVT error calculation by using the above process for angle difference calculation.

[0014] As a further improvement of the present invention: step S1 includes the following steps:

[0015] S1.1 Collect secondary voltage data of CVT at multiple time points, including amplitude and phase information, and use the truncated averaging method to calculate the initial estimate of the true voltage at each time point;

[0016] S1.2 Calculate the initial residual based on the initial estimate of the actual voltage, and estimate the initial estimate of the noise variance of each CVT based on the median absolute deviation of the initial residual;

[0017] By employing the truncated averaging method to calculate the initial estimate of the true voltage, extreme values ​​in the measurement data can be automatically filtered out, providing a reliable starting point for iteration against interference. Secondly, the initial noise variance is estimated using a method based on the median absolute deviation (MAD), making the initial assessment of the measurement noise level more robust.

[0018] As a further improvement of the present invention: the specific steps of the truncated averaging method in step S1.1 are as follows:

[0019] Assuming the measurement at time t indivual( ≥3) The voltage amplitudes of in-phase CVTs are arranged in ascending order as follows: Set the truncation ratio The initial estimate of the actual voltage at time t is obtained. ,in The voltage amplitude at time t is the actual value. The voltage phase at time t;

[0020] By setting a fixed 10% truncation ratio, outliers that may exist at both ends of the sorted data can be automatically and quantitatively removed, such as extreme measurement values ​​caused by momentary CVT failures or strong interference. This ensures that the sample used to calculate the initial estimate of the real voltage is relatively stable and reliable, significantly improving the anti-interference capability of the initial estimate of the real voltage, making it less susceptible to distortion by a few outlier data points, and exhibiting outstanding robustness and practicality.

[0021] As a further improvement of the present invention: step S1.2 specifically includes:

[0022] Based on the initial estimate of the actual voltage at time t, the initial residual of each CVT is calculated, the median absolute deviation is used to estimate the noise standard deviation, and the initial estimate of the noise variance of each CVT is calculated.

[0023] By using the median absolute deviation (MAD) to estimate the initial noise variance, the robustness of the algorithm to measurement outliers is significantly improved. Compared with traditional estimation methods based on sample variance, MAD uses the median of the data as a benchmark, is insensitive to extreme outliers, and can effectively resist the influence of outliers caused by equipment momentary failures, strong interference, or abnormal data acquisition. This makes the evaluation of the initial estimate of the noise variance of each CVT more robust and reliable, and avoids the distortion of variance estimation by outlier data.

[0024] As a further improvement of the present invention, step S2 includes the following steps:

[0025] S2.1. Fix the actual voltage estimate, estimate the CVT error parameters, and solve for the ratio difference estimate and angle difference estimate by minimizing the objective function. The minimized objective function is:

[0026] ;

[0027] S2.2. Fix the CVT error parameters, estimate the true voltage estimate, and update the true voltage estimate by solving a linear optimization function. The linear optimization function is:

[0028] ;

[0029] in, This is an estimate of the difference. This is an estimate of the angle difference. The difference is the ratio. The difference in angle; The secondary voltage data of the i-th current transformer at time t; is the initial estimate of the actual voltage at time t; j is the imaginary unit; N is the number of voltage amplitudes of the in-phase CVT; T represents the total number of time points for data acquisition;

[0030] By decomposing the complex joint estimation problem into two relatively simple subproblems, S2.1 and S2.2, and iterating them alternately, the difficulty of direct solution is significantly reduced, ensuring the feasibility of the algorithm. In step S2.2, estimating the true voltage estimate is transformed into a linear weighted least squares problem with an analytical solution, which is computationally efficient and yields a deterministic result.

[0031] As a further improvement of the present invention: in step S2.1, the solutions for the ratio difference and angle difference are:

[0032] ;

[0033] in, As a weighting factor, It is a complex voltage value that includes both amplitude and phase. The difference is the ratio. ω represents the angle difference, j is the imaginary unit; T represents the total number of time points for data collection;

[0034] By cleverly transforming the complex nonlinear optimization problem into a weighted complex averaging problem, tedious numerical search iterations are avoided, resulting in a direct and efficient computation process. Secondly, the weighting factors... The design makes the solution process noise-resistant, automatically reducing the influence of high-noise measurement data in the estimation and improving the robustness of the results. The solution simultaneously derives the combined influence of the ratio difference and angle difference in complex form. This ensures the consistency of the coupling between amplitude error and phase error in the calculation, and has a low computational burden, making it suitable for real-time processing in online systems.

[0035] As a further improvement of the present invention: step S2.1 specifically includes:

[0036] By fixing the actual voltage estimate, estimating the CVT error parameters, constructing the likelihood function, and assuming measurement noise... The mean is 0 and the variance is . The Gaussian distribution, i.e. Then the likelihood function is:

[0037] ;

[0038] Then the log-likelihood function is:

[0039] ;

[0040] The optimization is performed with the goal of minimizing the CVT error-related parameters, resulting in the minimization objective function:

[0041] ;

[0042] Define complex voltage values ;

[0043] The solutions for the estimated ratio difference and the estimated angle difference are:

[0044] ;

[0045] ;

[0046] in, As a weighting factor, It is a complex voltage value that includes both amplitude and phase; This is an estimate of the difference. This is an estimate of the angle difference. The difference is the ratio. The difference in angle; The secondary voltage data of the i-th current transformer at time t; t represents the initial estimate of the actual voltage at time t; j is the imaginary unit; N is the number of voltage amplitudes of the in-phase CVT; T represents the total number of time points for data acquisition.

[0047] Within the maximum likelihood estimation (MLE) framework, we explicitly assume that the measurement noise follows a Gaussian distribution and construct a likelihood function, providing a solid statistical foundation for the parameter estimation process and ensuring that the obtained solution possesses statistical optimality (e.g., asymptotically unbiased and efficient). Secondly, through mathematical transformations, the complex nonlinear minimization problem is converted into a weighted complex average operation, thus obtaining an efficient analytical solution. The computation process is direct and stable, avoiding convergence problems that may arise from numerical iteration. Finally, weighting factors... The design is scientific, and it can adaptively adjust its contribution based on the reliability (noise level) of the data itself, further improving the accuracy and robustness of the estimation results.

[0048] As a further improvement of the present invention, step S3 includes the following steps:

[0049] S3.1 Initialize the maximum number of iterations and the convergence threshold ;

[0050] S3.2, Update the noise variance estimate:

[0051] ;

[0052] in, The secondary voltage data of the i-th current transformer at time t; The difference is the ratio. The difference in angle; t represents the initial estimate of the actual voltage at time t; j is the imaginary unit; T represents the total number of time points for data collection.

[0053] S3.3 Check convergence and calculate the iterative change of CVT error parameters. ,like If the number of iterations reaches the maximum number of iterations, then output the calculated ratio difference. sum of angle difference Otherwise, return to step S2.2 and continue iterating;

[0054] By dynamically updating and explicitly defining the convergence mechanism, the algorithm's adaptability and reliability are significantly improved. First, by explicitly setting the maximum number of iterations and the convergence threshold, a clear termination condition is provided, effectively ensuring the controllability and timeliness of the computation process and preventing it from falling into infinite loops or premature convergence. Second, step S3.2 recalculates the noise variance based on the latest parameter estimates, enabling the algorithm to dynamically reflect changes in the actual noise levels of each CVT, ensuring the accuracy of weighted optimization in subsequent iterations. Simultaneously, step S3.3 calculates the iterative change in the error parameters and sets dual termination conditions (…). (or reaching the maximum number of iterations), effectively preventing infinite loops while ensuring the accuracy of the results, making the algorithm both convergent deterministic and timely, enabling the entire process to automatically and robustly approach the optimal solution and output reliable ratio and angle difference results.

[0055] As a further improvement of the present invention: in step S3.1, the maximum number of iterations ranges from 200 to 400, and the convergence threshold ranges from 10. -6 ~10 -4 ;

[0056] By setting the maximum number of iterations to 200 to 400, sufficient optimization steps are provided for convergence under complex conditions, effectively avoiding insufficient solutions due to insufficient iterations. Simultaneously, a clear upper limit can forcibly terminate potential oscillations or non-convergence, ensuring the algorithm's timeliness and controllability. Secondly, the convergence threshold is set at 10. -6 ~10 -4 This approach strikes a balance between meeting the high accuracy requirements of power measurement and avoiding ineffective iterations caused by overly stringent thresholds. This combination allows the algorithm to achieve the optimal balance between computational efficiency and result accuracy, adapting to different field conditions and performance requirements, and ensuring the method's robustness and wide applicability.

[0057] As a further improvement of the present invention: in step S3.2, the iterative change amount for:

[0058] ;

[0059] in, This represents the voltage ratio difference estimate calculated for the i-th CVT in the latest iteration;

[0060] This represents the voltage ratio difference estimate calculated for the i-th CVT in the previous iteration;

[0061] This represents the voltage angle difference estimate calculated for the i-th CVT in the latest iteration;

[0062] This represents the estimated voltage angle difference value calculated for the i-th CVT in the previous iteration.

[0063] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned ALS-MLE-based CVT error calculation method.

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] 1. This invention simultaneously acquires amplitude and phase information and uses the log-likelihood function under the MLE framework for modeling, enabling synchronous and accurate calculation of the ratio and angle differences of CVTs, overcoming the error coupling problem caused by the separate processing often found in traditional methods. Iterative optimization using ALS enables the algorithm to converge efficiently and stably, making it suitable for online computation. Dynamic error calculation and correction based on multi-time-point data allows the method to adapt in real-time to dynamic error drift caused by CVT temperature and load changes, significantly improving the long-term accuracy and reliability of power system voltage measurement.

[0066] 2. This invention significantly improves the accuracy of error calculation and voltage measurement. Traditional CVT error calculation methods often handle amplitude or phase errors separately, easily neglecting the correlation between the two and struggling to address error coupling issues under complex operating conditions. This invention combines the probabilistic statistical advantages of Maximum Likelihood Estimation (MLE) with the iterative optimization capabilities of Alternating Least Squares (ALS), simultaneously solving for amplitude and phase angle error parameters based on the log-likelihood function. This allows for the simultaneous correction of both types of errors, fundamentally solving the shortcomings of traditional methods that suffer from "single correction and limited accuracy." In practical applications, it effectively reduces measurement deviations caused by error superposition, making voltage measurement data closer to the true value and providing core data support for high-precision monitoring of power systems.

[0067] 3. This invention can dynamically adapt to error changes under complex operating conditions. During power system operation, the error of a CVT dynamically changes with non-steady-state factors such as temperature fluctuations, humidity changes, and load switching. Traditional static calibration methods struggle to track these error changes in real time, easily leading to "error drift after calibration." This invention, by collecting secondary voltage data at multiple time points and combining iterative optimization characteristics of ALS, can update error parameters online in real time, dynamically matching the error characteristics of the CVT under different operating states. This breaks through the limitations of traditional methods that are "offline calibration and statically applicable," ensuring the accuracy of error calculation even in scenarios with changing operating conditions.

[0068] 4. This invention avoids system deviations caused by calibration errors. Traditional CVT error correction relies on offline calibration data. If there are accuracy deviations in the calibration process (such as differences between the calibration environment and the actual operating environment, or errors in the calibration equipment), it will directly lead to systematic deviations in subsequent voltage measurements, affecting power system control decisions. This invention, through a hybrid algorithm of MLE and ALS, does not rely on fixed offline calibration parameters. Instead, it dynamically solves for errors based on real-time acquired data, thus avoiding the impact of calibration errors on system measurements at the source and further improving the reliability of power system voltage monitoring.

[0069] 5. This invention provides strong support for the stable operation of power systems. Voltage measurement accuracy is a crucial foundation for power system dispatching, relay protection, and equipment condition assessment. This invention, through high-precision CVT error calculation and correction, ensures the accuracy and real-time performance of voltage measurement data: on the one hand, it provides accurate voltage data to the dispatch center, helping to optimize grid operation and avoid dispatching errors caused by voltage data deviations; on the other hand, it provides reliable measurement data for relay protection devices, ensuring accurate operation of protection devices during faults and reducing grid accident losses. Simultaneously, accurate error data can also provide a reference for condition-based maintenance of CVT equipment, extending equipment lifespan and indirectly ensuring the safe and stable operation of the power system. Attached Figure Description

[0070] Figure 1 This is a flowchart of a CVT error calculation method based on ALS-MLE according to the present invention. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0072] Example 1

[0073] like Figure 1 As shown, this invention provides a CVT error calculation method based on ALS-MLE, which aims to solve the problem that the non-steady-state characteristics of capacitive voltage transformers (CVTs) in power systems, caused by temperature, humidity, and load changes, lead to ratio difference errors and angle difference errors affecting voltage measurement accuracy.

[0074] This embodiment presents a CVT error calculation method based on ALS-MLE, applied to at least three in-phase CVTs on the same bus. The method calculates CVT error parameters, including ratio difference and angle difference, through the following steps:

[0075] S1. Data Acquisition and Model Building: Acquire secondary voltage data of the CVT at multiple time points, including amplitude and phase information; Based on the secondary voltage data, estimate the initial value of the true voltage at each time point and the initial value of the noise variance of each CVT.

[0076] S2. Joint Parameter Iterative Optimization: Starting from the initial estimated value, an objective function based on maximum likelihood estimation is constructed using the log-likelihood function, and an alternating optimization framework is used to iteratively solve the ratio difference, angle difference, and the true voltage estimate at each time point of the CVT; the alternating optimization framework includes: a step of updating the ratio difference and angle difference in at least one round based on the current noise variance estimate, and a step of updating the true voltage estimate in at least one round;

[0077] S3. Iterative Convergence and Output: Calculate the change in CVT error parameters after each iteration, determine whether to terminate the iteration based on the change, and output the final ratio difference and angle difference.

[0078] S4. Error Correction: Using the final ratio difference and angle difference, the amplitude and phase errors of the subsequent voltage measurement results of the corresponding CVT are compensated.

[0079] A hybrid algorithm combining ALS and MLE is used for online monitoring and calculation of CVT errors. This method first collects secondary voltage data of the CVT at multiple time points and analyzes the amplitude and phase information. Based on the log-likelihood function, maximum likelihood estimation (MLE) is used, along with iterative optimization using alternating least squares (ALS) to solve for the CVT error parameters. Finally, based on the solution results, both the amplitude and phase errors of the CVT are corrected to adapt to dynamic error changes during operation. Compared with traditional methods, this invention can simultaneously consider and correct the amplitude and phase errors of the CVT, adapting to dynamic error changes in voltage transformers during operation, significantly improving the accuracy of voltage measurement, avoiding system deviations caused by calibration errors, and using the above process to calculate the angle difference. This invention effectively improves the accuracy of CVT error calculation, providing a strong guarantee for the stable operation of the power system.

[0080] Furthermore, step S1 includes the following steps:

[0081] S1.1 Acquire secondary voltage data of the CVT at multiple time points, including amplitude and phase information, and calculate the initial estimate of the true voltage at each time point using truncated averaging. The voltage measured at time t... indivual( ≥3) Voltage data of in-phase CVT, let the i-th ( CVT at time t ( The secondary voltage data collected is ,

[0082] ;

[0083] in,

[0084] This represents the ratio difference of the i-th CVT. This represents the angle difference value of the i-th CVT;

[0085] This represents the standard value of the secondary voltage at time t. Based on the in-phase consistency of the primary voltage, the standard values ​​of different CVTs at the same time are the same.

[0086] This represents measurement noise, which is generally considered to conform to a Gaussian distribution.

[0087] Assume that the voltage amplitudes of multiple (N≥3) in-phase CVTs measured at time t are arranged in ascending order as follows: Set the truncation ratio Then the actual number of one-sided truncated tails, k, is:

[0088] ;

[0089] The initial true voltage amplitude is:

[0090] ;

[0091] Similarly, the initial true voltage phase can be calculated as:

[0092] ;

[0093] The initial estimate of the actual voltage at time t is .

[0094] S1.2. Estimating the initial value of noise variance based on the median absolute deviation (MAD) of the residuals: Based on the initial estimate of the true voltage obtained, calculate the initial residual of each CVT voltage. j0 represents the initial phase angle:

[0095] ;

[0096] Use the robust statistic MAD to estimate the noise standard deviation:

[0097] ;

[0098] in This indicates that the median of all data is taken.

[0099] The initial estimate of the noise variance .

[0100] Furthermore, step S2 includes the following steps:

[0101] S2.1. Fix the estimated true voltage value and estimate the CVT error parameter. For ease of calculation, convert it into a log-likelihood function, assuming measurement noise. The mean is 0 and the variance is . The Gaussian distribution, i.e. Then the likelihood function is:

[0102] ;

[0103] Then the log-likelihood function is:

[0104] ;

[0105] The problem is then optimized by minimizing the CVT error-related parameters, and the solution is transformed into:

[0106] ;

[0107] For this nonlinear optimization problem, we first define the complex voltage value. .

[0108] Furthermore, the above minimum value problem can be transformed into: finding and , making closest The weighted average;

[0109] The solution to the above problem is:

[0110] ;

[0111] Among them, weighting factors , It is a complex voltage value that includes both amplitude and phase. The difference is the ratio. The difference in angle;

[0112] S2.2. Fix the CVT error parameters and estimate the true voltage estimate. Similar to step S2.1, optimize the solution by minimizing the true voltage-related parameter part of the log-likelihood function. That is, transform the problem into:

[0113] ;

[0114] The solution to this linear optimization problem is:

[0115] ;

[0116] in, This is an estimate of the difference. This is an estimate of the angle difference. The difference is the ratio. The difference in angle; The secondary voltage data of the i-th current transformer at time t; t represents the initial estimate of the actual voltage at time t; j is the imaginary unit; N is the number of voltage amplitudes of in-phase CVTs; T represents the total number of time points for data acquisition.

[0117] Furthermore, step S3 includes the following steps:

[0118] S1.3 Initialize other parameters:

[0119] Set the maximum number of iterations. (Generally, 200~400 can be used);

[0120] Set convergence threshold (Generally acceptable) ~ );

[0121] S3.2, Update the noise variance estimate as follows:

[0122] ;

[0123] S3.3 Check convergence and calculate the iterative change of CVT error parameters. The specific formula is as follows:

[0124] ;

[0125] This represents the voltage ratio difference estimate calculated for the i-th CVT in the latest iteration;

[0126] This represents the voltage ratio difference estimate calculated for the i-th CVT in the previous iteration;

[0127] This represents the voltage angle difference estimate calculated for the i-th CVT in the latest iteration;

[0128] This represents the estimated voltage angle difference value calculated for the i-th CVT in the previous iteration;

[0129] like If the number of iterations reaches the maximum number of iterations, then output the calculated ratio difference. sum of angle difference Otherwise, return to step S2.2 and continue iterating.

[0130] Example 2

[0131] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements a CVT error calculation method based on ALS-MLE. This ALS-MLE-based CVT error calculation method is applied to at least three in-phase CVTs on the same bus, and calculates CVT error parameters including ratio difference and angle difference through the following steps: S1, Data Acquisition and Model Building: Acquire secondary voltage data of the CVT at multiple time points, including amplitude and phase information; Based on the secondary voltage data, estimate the initial estimated value of the true voltage at each time point and the initial estimated value of the noise variance of each CVT; S2, Joint Parameter Iterative Optimization: Using the initial estimated value... Starting from the log-likelihood function, an objective function based on maximum likelihood estimation is constructed, and an alternating optimization framework is used to iteratively solve for the ratio difference, angle difference, and the true voltage estimate at each time point of the CVT. The alternating optimization framework includes: updating the ratio difference and angle difference in at least one round based on the current noise variance estimate, and updating the true voltage estimate in at least one round. S3, Iterative convergence and output: Calculate the change in the CVT error parameters after each iteration, determine whether to terminate the iteration based on the change, and output the final ratio difference and angle difference. S4, Error correction: Use the final ratio difference and angle difference to compensate for the amplitude and phase errors of the subsequent voltage measurement results of the corresponding CVT.

[0132] This invention provides a computer-readable storage medium that, by solidifying a hybrid algorithm based on ALS-MLE, standardizes and makes portable the online calculation and dynamic correction of high-precision CVT errors, facilitating integration and deployment in various power monitoring systems and greatly improving the method's engineering applicability and ease of promotion. Secondly, through program execution, data acquisition, parameter iterative solution, and synchronous error correction can be automatically and continuously achieved without relying on manual offline calibration, effectively reducing operation and maintenance costs. Finally, this medium ensures the stable reproduction of the algorithm, providing a reliable and automated tool for power systems, continuously guaranteeing voltage measurement accuracy, and enhancing the safety and economy of power grid operation.

[0133] The functions described herein can be implemented in hardware, software executed by a processor, firmware, or any combination thereof. If implemented in software executed by a processor, the functions can be stored as one or more instructions or codes on or transmitted via a computer-readable medium. Other examples and embodiments are within the scope and spirit of this invention and the appended claims. For example, due to the nature of software, the functions described above can be implemented using software executed by a processor, hardware, firmware, hardwired, or any combination thereof. Furthermore, the functional units can be integrated into a single processing unit, or each unit can exist physically separately, or two or more units can be integrated into a single unit.

[0134] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For instance, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling, direct coupling, or communication connection may be through some interfaces; the indirect coupling or communication connection between units or modules may be electrical or other forms.

[0135] The units described as separate components may or may not be physically separate. Similarly, the components of the control device may or may not be physical units; they may be located in one place or distributed across multiple units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0136] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, read-only memory, random access memory, portable hard drives, magnetic disks, or optical disks.

[0137] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A CVT error calculation method based on ALS-MLE, characterized in that, For at least three CVTs operating on the same busbar in phase, the CVT error parameters, including ratio difference and angle difference, are calculated using the following steps: S1. Data Acquisition and Model Building: Acquire secondary voltage data of the CVT at multiple time points, including amplitude and phase information; Based on the secondary voltage data, estimate the initial value of the true voltage at each time point and the initial value of the noise variance of each CVT. S2. Joint parameter iterative optimization: Starting from the initial estimated value, the objective function based on the maximum likelihood estimation is constructed using the log-likelihood function, and the ratio difference, angle difference, and the true voltage estimate of the CVT at each time point are iteratively solved using the alternating optimization framework. The alternating optimization framework includes: a step of updating the ratio difference and angle difference values ​​in at least one round based on the current noise variance estimate, and a step of updating the true voltage estimate in at least one round; S3. Iterative Convergence and Output: Calculate the change in CVT error parameters after each iteration, determine whether to terminate the iteration based on the change, and output the final ratio difference and angle difference. S4. Error Correction: Using the final ratio difference and angle difference, the amplitude and phase errors of the subsequent voltage measurement results of the corresponding CVT are compensated. Step S1 includes the following steps: S1.1 Collect secondary voltage data of CVT at multiple time points, including amplitude and phase information, and use the truncated averaging method to calculate the initial estimate of the true voltage at each time point; S1.2 Calculate the initial residual based on the initial estimate of the actual voltage, and estimate the initial estimate of the noise variance of each CVT based on the median absolute deviation of the initial residual; Step S2 includes the following steps: S2.

1. Fix the actual voltage estimate, estimate the CVT error parameters, and solve for the ratio difference estimate and angle difference estimate by minimizing the objective function. The minimized objective function is: ； S2.

2. Fix the CVT error parameters, estimate the true voltage estimate, and update the true voltage estimate by solving a linear optimization function. The linear optimization function is: ； in, This is an estimate of the difference. This is an estimate of the angle difference. The difference is the ratio. The difference in angle; The secondary voltage data of the i-th current transformer at time t; t represents the initial estimate of the actual voltage at time t; j is the imaginary unit; N is the number of voltage amplitudes of in-phase CVTs; T represents the total number of time points for data acquisition.

2. The CVT error calculation method based on ALS-MLE according to claim 1, characterized in that, In step S1.1, the specific steps of the truncated average method are as follows: Assumption t Time measurement indivual The voltage amplitudes of the in-phase CVTs are arranged in ascending order as follows: Set the truncation ratio The initial estimate of the actual voltage at time t is obtained. ,in The voltage amplitude at time t is the actual value. Let t be the true phase of the voltage.

3. The CVT error calculation method based on ALS-MLE according to claim 2, characterized in that, Step S1.2 specifically includes: Based on the initial estimate of the actual voltage at time t, the initial residual of each CVT is calculated. The median absolute deviation is used to estimate the noise standard deviation, and the initial estimate of the noise variance of each CVT is calculated.

4. The CVT error calculation method based on ALS-MLE according to claim 3, characterized in that, In step S2.1, the solutions for the ratio difference and angle difference are: ； in, As a weighting factor, It is a complex voltage value that includes both amplitude and phase. The difference is the ratio. is the angular difference value, j is the imaginary unit; T represents the total number of time points for data collection.

5. The CVT error calculation method based on ALS-MLE according to claim 4, characterized in that, Step S3 includes the following steps: S3.1 Initialize the maximum number of iterations and the convergence threshold ; S3.2, Update the noise variance estimate: ； in, The secondary voltage data of the i-th current transformer at time t; The difference is the ratio. The difference in angle; t represents the initial estimate of the actual voltage at time t; j is the imaginary unit; T represents the total number of time points for data collection. S3.3 Check convergence and calculate the iterative change of CVT error parameters. ,like If the number of iterations reaches the maximum number of iterations, then output the calculated ratio difference. sum of angle difference Otherwise, return to step S2.2 and continue iterating.

6. The CVT error calculation method based on ALS-MLE according to claim 5, characterized in that, In step S3.1, the maximum number of iterations ranges from 200 to 400, and the convergence threshold ranges from 10. -6 ~10 -4 .

7. The CVT error calculation method based on ALS-MLE according to claim 6, characterized in that, In step S3.2, the iterative change amount for: ； in, This represents the voltage ratio difference estimate calculated for the i-th CVT in the latest iteration; This represents the voltage ratio difference estimate calculated for the i-th CVT in the previous iteration; This represents the voltage angle difference estimate calculated for the i-th CVT in the latest iteration; This represents the estimated voltage angle difference value calculated for the i-th CVT in the previous iteration.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements a CVT error calculation method based on ALS-MLE as described in any one of claims 1-7.

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