Voltage transformer error analysis method based on prior data weighting

Abstract

This invention discloses a voltage transformer error analysis method based on prior data weighting, including data acquisition, ratio error analysis, and phase error analysis. The ratio error analysis includes solving for the signal amplitude ratio between each channel, calculating global constraints, and estimating the ratio error. The phase error analysis includes solving for the signal phase difference between each channel, calculating global phase constraints, and estimating the phase error. This invention enables quantitative online analysis of voltage transformer errors under uninterrupted power supply conditions, providing a reliable basis for assessing the accuracy of power trading metering and for operation and maintenance decisions.

Description

Technical Field

[0001] This invention relates to a voltage transformer error analysis method, specifically a voltage transformer error analysis method based on prior data weighting, belonging to the field of power system measurement and energy metering technology. Background Technology

[0002] Voltage transformers operating in power systems, especially capacitive voltage transformers, will have errors that shift over time and due to environmental factors. This shift will affect the accuracy of metering in large-scale electricity transactions and the fairness and impartiality of electricity transactions.

[0003] Currently, error assessment of voltage transformers mainly relies on error tests conducted during power outage maintenance windows. However, with increasing demands for power supply reliability, power outages on high-voltage transmission lines are difficult, and many devices operate beyond their calibration periods for extended periods. Even when power outages are possible, the outage windows are short, making it difficult to obtain error data for a large number of operating transformers, especially older ones with long operating histories. This severely impacts the efficiency of error anomaly analysis. Furthermore, due to safety considerations, the voltage boosting conditions used in voltage transformer error tests during power outages differ from actual operating conditions (e.g., the voltage cannot be boosted to the rated voltage according to regulations, otherwise an accident would occur due to insufficient safety distance), failing to reflect the true error situation under actual operating conditions. Therefore, there is an urgent need for error analysis methods for voltage transformers under uninterrupted power conditions to assist in conducting transformer error analysis.

[0004] To address the aforementioned issues, researchers have proposed several error assessment schemes for voltage transformers under uninterrupted power conditions: 1) A method and system for assessing the error status of a capacitive voltage transformer, disclosed in CN109444791B, uses a synchronous signal to trigger the acquisition of measurement data from a three-phase capacitive voltage transformer, establishes statistical characteristic thresholds for the normal state using principal component analysis (PCA), and combines adaptive principal component analysis and variable contribution rate method to achieve online real-time assessment and anomaly diagnosis of the error status. This method can continuously monitor transformer error changes under uninterrupted power conditions, promptly detect and locate anomalies, but it mainly relies on the deviation of statistical characteristic thresholds to indirectly judge the error status, failing to directly provide the specific ratio error and phase error values ​​for each transformer. Furthermore, the principal component analysis model has high requirements for the purity and representativeness of the training data, and disturbances in the field environment may lead to misjudgments; 2) A method, device, and electronic equipment for online monitoring of capacitive voltage transformers, disclosed in CN119758217A. The method constructs an online monitoring model for capacitive voltage transformers, uses the first voltage measurement data of a historical time period for prediction, compares it with the actual measurement data of subsequent time periods, calculates the measurement error, and achieves online evaluation. This method can effectively separate the bus voltage fluctuation from the error generated by the CVT itself, and improve the detection accuracy of changes in CVT operating accuracy. However, its essence is deviation detection based on time series prediction. The accuracy of the prediction model is highly dependent on the quality and periodicity of historical data. When the bus voltage fluctuation pattern changes or the transformer error changes abruptly, the prediction error may increase, affecting the reliability of the evaluation results. 3) A capacitive voltage transformer error prediction method and device disclosed in announcement number CN114692505B constructs a prediction model based on RBF neural network, uses historical error data and real-time environmental parameters to accurately predict the error of the capacitive voltage transformer at the current moment, can identify the deterioration trend of the measurement error in advance, and achieve early warning when the error exceeds the limit. This method relies on a large amount of labeled historical error data as training samples. However, it is extremely difficult to obtain accurate error values ​​in actual operation, resulting in insufficient training samples or inaccurate labels, which limits the generalization ability and engineering applicability of the prediction model.

[0005] In summary, while existing technologies have achieved uninterrupted monitoring or error prediction of voltage transformers to varying degrees, they generally suffer from the following shortcomings: (1) Most methods can only give a qualitative judgment on whether the error exceeds the limit, and it is difficult to accurately estimate the specific ratio error and phase error values ​​of each transformer.

[0006] (2) It relies on complex statistical models or neural network models, has high requirements for the quality of training data, and has limited adaptability to the field.

[0007] (3) The existing prior data of the current transformer (such as handover test and periodic verification data) were not fully utilized to improve the accuracy of online evaluation. Summary of the Invention

[0008] The purpose of this invention is to provide a voltage transformer error analysis method based on prior data weighting to solve at least one of the above-mentioned technical problems. This method can directly utilize the measurement data of multiple transformers of the same origin, combine prior data constraints, and accurately estimate the error of each transformer without complex training.

[0009] This invention achieves the above objective through the following technical solution: a voltage transformer error analysis method based on prior data weighting, which includes the following steps: S1, Data Acquisition The secondary signals of multiple voltage transformers measuring the primary voltage at the same measuring point are connected to the synchronous sampling module to obtain the original waveform data of the synchronous sampling signal, calculate the amplitude and phase of each signal according to the period, and store them in the database. S2, Ratio Error Analysis S21. Solve the signal amplitude ratio between each channel: Calculate the ratio between each pair of measured amplitudes of the same source voltage transformers, use the Layda criterion to remove gross values, and then calculate the average or median as characteristic values ​​to obtain the relative proportional relationship of the measured values ​​of each voltage transformer interval. S22. Calculate global constraints: If there are voltage transformers with prior data, calculate global constraints based on the prior data; otherwise, use the weighted median algorithm to calculate global constraints. S23. Ratio error estimation: The natural logarithm of the amplitude ratio relationship between each interval is taken to transform it into a linear relationship. An overdetermined equation system is constructed in combination with the global constraints of each interval. The logarithm of the gain coefficient of each voltage transformer is obtained by solving the overdetermined equation system by the least squares method, and then the ratio error of each voltage transformer is calculated. S3, Phase Error Analysis S31. Solve for the phase difference between each channel: Calculate the phase difference between each pair of voltage transformers of the same source, use the Layda criterion to remove coarse values ​​and calculate the characteristic value to obtain the relative phase difference relationship between each voltage transformer. S32. Calculate global phase constraints: Obtain a subset of mutual inductors with prior phase error data, and calculate the mean of their combined phase errors as global constraints. S33. Phase error estimation: Combine the phase difference relationship between the two voltage transformers in the interval with the global phase constraint to construct an overdetermined equation system. Solve the overdetermined equation system using the least squares method to obtain the phase error of each transformer.

[0010] As a further aspect of the present invention: data acquisition adopts a temporary access method, and the secondary signals of different voltage transformers measuring the same measuring point are connected to the synchronous sampling module inside the monitoring and analysis device through an air switch. If the voltage transformers in the monitored interval are far apart, satellite synchronization is used to use multiple devices to synchronously sample the signals at different locations.

[0011] As a further aspect of the present invention: solving the signal amplitude ratio between each channel specifically includes: Taking phase A as an example, the amplitude sampling sequences of the measured values ​​at intervals 1 and 2 are as follows: , The relative proportion is calculated using the following formula:

[0012] in, This represents the relative ratio of the voltage sampling amplitudes at interval 1 to interval 2. G For theoretical ratios; The ratio of sampled values ​​is calculated using the Laida criterion to remove outliers, and the following formula is used:

[0013] in, For standard deviation, in each In the middle, the absolute value of the record exceeds The numerical indices form the elimination set. In all Removed from the list; After removing outlier values, the eigenvalues ​​are calculated using the following formula:

[0014] Generally, the mean is chosen; if the standard deviation is large, the median is used instead.

[0015] As a further aspect of the present invention: calculating global constraints based on prior data specifically includes: Prior gain calculation and collection of monitored transformer dataset. In this context, the subset has prior data. Based on subsets The ratio of the calibration data of each current transformer in the middle and secondary pressure drop data The overall ratio error was calculated. Then calculate the gain coefficient of the prior data. ; Measurement error identification, based on the gain coefficient calculated from prior data, is shown in the following formula: …

[0016] The gain coefficients calculated based on the sampled sequence are shown in the following formula:

[0017] True value It is unknowable, but based on the interrelationships, each can be calculated. Values ​​that make the proportions the same; If the prior data is accurate, the gain coefficient of the prior data... With the gain coefficient based on the sampling sequence ratio The values ​​are close, as shown in the following formula:

[0018] If the prior data of a certain current transformer is inaccurate, or if the error of the current transformer deviates significantly, then Outliers exist, and the method for identifying outliers is shown in the following formula:

[0019] The deviation coefficient was calculated based on the absolute median. A threshold can be set. If the deviation coefficient exceeds 30%, the prior data method cannot be used. Instead, the weighted median algorithm is used to calculate the constraint value. After global constraint calculation and filtering, the true values ​​of the gain coefficients for each unit are obtained. The following formula should be satisfied:

[0020] in, The absolute value of the gain coefficient based on prior data. To calculate the relative proportion of the gain coefficients based on the sampled sequence, the proportioning coefficient is obtained by minimizing the sum of squares. As shown in the following formula:

[0021] Calculate the proportionality coefficient Next, calculate the values ​​of all current transformers. The value is shown in the following formula: … …

[0022] The global constraints can then be calculated using the following formula: = .

[0023] As a further aspect of the present invention: the calculation of global constraints using a weighted median algorithm specifically includes: Weight calculation involves sampling the amplitude sequence at each interval. According to the elimination sequence number set After removing questionable values, the mean or median is calculated to obtain the characteristic values ​​of the amplitude sampling sequence of each interval transformer. As shown in the following formula:

[0024] The median of the characteristic values ​​of each interval transformer is calculated as shown in the following formula:

[0025] Calculate the eigenvalues ​​and median for each interval. relative distance between Add relative error To avoid coinciding with the median, the inverse of the relative distance is used as the initial weight. and normalized to As shown in the following formula:

[0026] Global constraint calculations utilize a weighted geometric mean to calculate the reference standard value. As shown in the following formula.

[0027]

[0028] Global constraints can be calculated using the following formula: =

[0029] in, It is the weighted sum of the natural logarithms of the measured values.

[0030] As a further aspect of the present invention, the ratio error estimation specifically includes: Based on the calculated amplitude ratio of each interval Taking the natural logarithm, we get and The linear relationship between them, let ,Will The proportional relationship is transformed into a linear relationship, as shown in the following formula:

[0031] Based on the global constraints of the calculation, all can be obtained. The constraint relationship is shown in the following equation:

[0032] Combining the above relationships and conditions, taking four intervals as an example, the pairwise proportional relationships between each interval, plus the global constraints of each interval, yield the following overdetermined system of equations:

[0033] in, The constraint relation matrix, This is the logarithmic form of the gain coefficients for each interval. For a sequence of constraints; Solving the overdetermined system of equations As shown in the following formula:

[0034] Obtain the logarithm of the gain coefficient for each interval. Through calculation The exponent is used to obtain the gain coefficient of each interval. The ratio error data is then calculated using the following formula:

[0035] in, The estimated ratio error data for each current transformer.

[0036] As a further aspect of the present invention, solving for the phase difference between signals in each channel specifically includes: The phase error of each interval transformer is , No. i Interval and the first j The phase difference between them is The Laida standard was used to remove outliers, and the mean or median was calculated. eigenvalues As shown in the following formula: .

[0037] As a further aspect of the present invention: calculating the global phase constraint specifically includes: Data set of monitored transformers In this subset, those with prior phase error data are considered a subset. The a priori data with phase error is the same as the subset with ratio error; subset Phase difference of calibration data for each current transformer and secondary pressure drop data The overall ratio error was calculated. The calculated comprehensive ratio error The global constraints are calculated as shown in the following formula: .

[0038] As a further aspect of the present invention, phase error estimation specifically includes: Taking four intervals as an example, the pairwise differences between each interval, plus the global constraints of each interval, yield the following overdetermined system of equations:

[0039] in, The constraint relation matrix, This is the logarithmic form of the gain coefficients for each interval. Given a sequence of constraints, solving the overdetermined equations allows direct calculation of the phase error vector of each current transformer. , .

[0040] The beneficial effects of this invention are: 1) The error level of the data acquisition equipment is controllable: The temporary access method is used to synchronously sample multiple voltage transformers of the same source. The error of the monitoring equipment can be calibrated before each use, avoiding the error drift problem caused by the long-term operation of electronic components under the fixed installation method.

[0041] 2) Based on the same source relationship of each current transformer at the same measuring point: Since the temporary access method has low requirements for signal access, the same source relationship of different current transformers measuring the same measuring point can be utilized (i.e., multiple devices measuring the same physical quantity). Multiple current transformers with the same source in the substation can be connected as much as possible, which can accurately reflect the relative relationship between the ratio error and phase error of each current transformer. 3) Layda's rule to eliminate gross values: By eliminating gross values ​​through the Layda criterion, abnormal data introduced by external interference and transmission errors are effectively filtered out, ensuring the reliability of subsequent calculations. By utilizing the physical relationship of measuring the same voltage using the same source transformers, and by solving the relative proportion and relative phase difference, the relative error relationship between each transformer can be accurately estimated without knowing the true value of the primary voltage. 4) Calculating global constraints based on prior data: This invention combines existing calibration data and secondary voltage drop data of some current transformers as prior constraints. Reliable samples are screened through consistency checks, and the global scale is determined by least squares fitting. At the same time, a weighted median algorithm is provided as an alternative when prior data is insufficient, so that this method can work stably under different data conditions. Finally, by constructing an overdetermined system of equations and solving the least squares solution, the ratio error and phase error estimates of each current transformer are obtained. This realizes the quantitative online analysis of voltage transformer errors under uninterrupted power supply conditions, providing a reliable basis for the accuracy assessment of power trading metering and operation and maintenance decisions. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the overall process of the present invention; Figure 2 This is a schematic diagram of the fixed installation and wiring of multiple voltage transformers according to the present invention; Figure 3 This is a schematic diagram of the temporary connection wiring for multiple voltage transformers according to the present invention; Figure 4 This invention describes the principle of the spatial monitoring and analysis device at different locations. Figure 5 This is a schematic diagram of the main process for ratio error analysis in this invention; Figure 6 This is a schematic diagram of the global constraint calculation process based on prior data in this invention; Figure 7 This is a schematic diagram illustrating the global constraint calculation process of the weighted median method of this invention; Figure 8 This is a schematic diagram of the main process of phase error analysis in this invention. Detailed Implementation

[0043] 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, and 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.

[0044] Example 1, as Figure 1 As shown, this embodiment provides a voltage transformer error analysis method based on prior data weighting. This voltage transformer error analysis method includes the following steps: First, data acquisition: The secondary signals of multiple voltage transformers measuring the primary voltage at the same measuring point are connected to the synchronous sampling module to obtain the original waveform data of the synchronous sampling signal, calculate the amplitude and phase of each signal periodically, and store them in the database.

[0045] Second, ratio error analysis.

[0046] Ratio error analysis specifically includes: 1) Solve for the signal amplitude ratio between each channel, calculate the ratio between each pair of measured amplitudes of the same source voltage transformers, use the Layda criterion to remove gross values, and then calculate the mean or median as characteristic values ​​to obtain the relative proportional relationship of the measured values ​​of each voltage transformer interval. 2) Calculate global constraints. If there are voltage transformers with prior data, calculate global constraints based on the prior data; otherwise, use the weighted median algorithm to calculate global constraints. 3) Ratio error estimation: The amplitude ratio relationship between each interval is transformed into a linear relationship by taking the natural logarithm. An overdetermined equation system is constructed by combining the global constraints of each interval. The logarithm of the gain coefficient of each voltage transformer is obtained by solving the overdetermined equation system by the least squares method, and then the ratio error of each voltage transformer is calculated.

[0047] Third, phase error analysis.

[0048] 1) Solve for the phase difference between each channel, calculate the phase difference between each pair of voltage transformers of the same source, use the Layda criterion to remove coarse values ​​and calculate the characteristic value to obtain the relative phase difference relationship between each voltage transformer; 2) Calculate the global phase constraint, obtain a subset of voltage transformers with prior phase error data, and calculate the mean of their comprehensive phase error as the global constraint; 3) Phase error estimation: Combine the phase difference relationship between the two voltage transformers in the interval with the global phase constraint to construct an overdetermined equation system. Solve the overdetermined equation system by the least squares method to obtain the phase error of each voltage transformer.

[0049] Example 2: This example takes a voltage transformer as the research object and provides a voltage transformer error analysis method based on Example 1, specifically including: 1. Research Subjects A voltage transformer is a proportional standard. The secondary value is obtained by multiplying the primary value by the attenuation factor and adding the phase deflection, as shown in the following formula:

[0050] in: It is a single quantity being measured, for example The left and right sides are the same for each voltage transformer; It is the actual attenuation factor of the voltage transformer, for example The voltage transformer has a theoretical transformation ratio of 5000, but due to errors, the actual transformation ratio is... Distributed around 5000, for example, 4998.7, while yes The reciprocal of; This is due to phase deviation, caused by the inherent phase difference in the voltage transformer itself, resulting in a change in the secondary quantity of the output. There is a slight phase deviation between the primary and secondary quantities, which is usually no more than ±10′.

[0051] In this embodiment, multiple voltage transformers are used to measure the same primary quantity. Because each voltage transformer ( Different errors result in different quadratic quantities. They are all different; their amplitudes and phases are not the same.

[0052] For ease of calculation, the attenuation factor is normalized, that is, the linear quantity is divided by the theoretical ratio, for example, by... Divided by theoretical ratio One dose Become Then the attenuation factor This then becomes a value near 1, and is intuitively related to the error. For example, the ratio error of a voltage transformer is +0.13%, which is the actual secondary amplitude. ,but It is 1.0013.

[0053] certainly, It is unknowable because only the quadratic value of the measured value can be known, that is... And the measured signal Unknowable.

[0054] Therefore, for a normalized first-order quantity whose amplitude varies slightly... The amplitude sampling model for multiple voltage transformers is shown in the following formula:

[0055] in, The normalized decay factor, To measure random errors, the magnitude is usually very small and follows a normal distribution centered at 0.

[0056] 2. Data Collection

[0057] Based on the measurement of the same voltage by multiple voltage transformers, the relative error of each device is analyzed by solving the relative relationship according to the measurement data.

[0058] 2.1 Brief Description of Working Scenario and Monitoring Hardware Equipment

[0059] like Figure 2 As shown, the monitoring object is a 220kV voltage transformer in a substation. The substation has two 220kV busbars operating in parallel via a bus tie switch. Since the impedance of the substation busbars (aluminum conduit busbars or GIS busbars) is approximately 0.0005Ω / m, the primary voltage difference at different points on the busbars is calculated to be no more than 10V under operating conditions. This difference can be ignored for voltage levels of 110kV and above. Therefore, the voltage transformers connected to the two main transformers (T1, T2) and the four lines (L1 to L4) can be approximated as having the same primary voltage.

[0060] The principle and structure of the monitoring equipment are shown in the attached figure. Figure 3As shown, the secondary windings (A, B, C, N, where A, B, and C represent three phases and N represents the neutral point) of the voltage transformers in each operating bay (bays 1, 2, ..., n) are connected to the monitoring and analysis device via an air switch in the junction box. Driven by the synchronous satellite signal, the analysis device synchronously samples the secondary signals of the three-phase voltage transformers in each bay. The secondary signals (A, B, C, N) of different voltage transformers measuring the same measuring point are connected to the acquisition and measurement device, for example, as shown in the attached diagram. Figure 2 The secondary signals from PT1 to PT6 are connected to the internal synchronous sampling module of the device through an air switch.

[0061] If the monitored voltage transformers are located far apart (e.g., not in the same compartment), and synchronous sampling cannot be achieved using a single monitoring device, then satellite synchronization is used. Multiple devices are employed to synchronously sample signals from different locations, as shown in the attached diagram. Figure 4 As shown.

[0062] 2.2 Fixed installation and temporary access working methods

[0063] Monitoring devices can be installed in a fixed manner or connected temporarily. Currently, most products in the industry are installed in a fixed manner. The advantage of this method is that it allows for continuous monitoring, but it has several disadvantages: first, it requires space in the substation's control cabinets, increasing safety risks; second, the sampling elements of the monitoring equipment are electronic, and their errors can shift with factors such as operating environment and time, making the sampling error of fixed-installation equipment gradually uncontrollable; third, some secondary circuits do not meet the conditions for fixed connection (e.g., lack of redundant terminal blocks). A few companies offer temporary connection methods, which supplement the fixed installation method. Besides the inability to achieve continuous monitoring, this method has advantages such as lower test wiring requirements, the ability to connect all current transformers at the same measurement point, easy sampling error calibration before use, no impact on the long-term operation of the substation's secondary system, and relatively lower safety risks. Therefore, this embodiment prioritizes the temporary connection method.

[0064] 2.3 Original Data Format

[0065] The monitoring and analysis device acquires synchronously sampled raw waveform data through measurement (or by acquiring data through shared energy meter data or other means, with the measurement error preferably not exceeding 0.1%), and calculates the amplitude and phase of the signal in each period (interval period can be 1s, 2s, etc.), storing it in a database. Typically, several hours of data are saved according to actual conditions; for example, with an interval period of 1s, see Table 1. It should be noted that intervals with prior data (such as handover test data or periodic test data) are placed on the left side of the table. For example, if three intervals have detection data, these three intervals are placed as interval 1, interval 2, and interval 3, and the remaining intervals without detection data are placed later.

[0066] Table 1 shows examples of data acquisition and processing.

[0067] 3. Ratio Error Analysis Process

[0068] 3.1 Solving for the signal amplitude ratio between each channel

[0069] like Figure 5 As shown, taking phase A as an example, the voltage transformers at intervals 1, 2, and 3 all measure the voltage of phase A. Since the measured voltage cannot be determined... It can only be done by calculating the relative proportions between the channels. To determine, among which i As one of the intervals for comparison, at the molecular position, j For another interval, in the denominator position, P For the sake of clarity and simplicity, the formula calculation assumes phase A, and the sampled value sequence is simplified to: The relative proportions are simplified to .

[0070] For example, the gain coefficients of interval 1 and interval 2 and It cannot be determined definitively, but the relative proportion can be calculated by the ratio of the amplitudes of the measurements at interval 1 and interval 2. For example, if interval 1 and interval 2 measure the same voltage, and the sampling sequences are respectively... , The relative proportion is calculated as follows:

[0071] in, This represents the relative ratio of the voltage sampling amplitudes at interval 1 to interval 2. G This is a theoretical variation ratio.

[0072] The ratio of sampled values ​​is marked by removing outliers using the Laida criterion, as shown in the following formula:

[0073] in, For standard deviation, in each In the middle, the absolute value of the record exceeds The numerical indices form the elimination set. In all They are removed from the list. For example, In the data, the absolute values ​​of serial numbers 4 and 19 exceed... Threshold, In the data, the absolute values ​​of the serial numbers 9, 56, and 197 exceed [a certain threshold]. The threshold, then in all In the middle, the serial number to be removed is The value.

[0074] After removing outlier values, the mean or median is calculated. Generally, the mean method is preferred; if the standard deviation is large, the median method is used, as shown in the following formula:

[0075] 3.2 Calculate global constraints

[0076] Based on the relative proportions of the measurements at each interval, only the relative proportions between the channels can be calculated; a global constraint still needs to be applied.

[0077] When the sample size is large enough (the number of current transformers simultaneously measuring the same voltage) n (Greater than 50), the product of all gain coefficients is 1, as shown in the following formula:

[0078] However, in reality, it's impossible to obtain a sufficiently large sample size, and the above constraints may not necessarily hold. For example, there may be cases where the error deviates significantly from the standard value in the positive direction, resulting in a product of actual gain coefficients. It will be greater than 1, and vice versa.

[0079] In this embodiment, the following method is used to approximate the target as accurately as possible. The value is calculated in two ways: with prior data and without prior data. Specifically, if more than 60% of the current transformers at each measuring point have data from the previous current transformer calibration and secondary voltage drop test (data obtained according to regulations, not test data obtained through extrapolation), then the constraint value is calculated using the prior data. Otherwise, the constraint value is calculated using the weighted median algorithm, as described below: (1) Calculation of constraint values ​​based on prior data A. Prior gain calculation like Figure 6 As shown, the dataset of monitored transformers is collected. In this context, the subset has prior data. For example, among intervals 1 to 5, intervals 1 to 3 have test data.

[0080] Based on subsets The ratio of the calibration data of each current transformer in the middle (Take the error value of the lower limit load) and secondary voltage drop data (If no pressure drop data is available, then) ,in (where 100 meters is the loop length, and each unit is 100 meters), the comprehensive ratio error is calculated. Note that here, since the error limit of the phase difference is small, under acceptable conditions, a simplified scalar superposition algorithm is used instead of the vector superposition algorithm.

[0081] Based on the comprehensive ratio error of each current transformer with prior data Calculate the gain coefficient of prior data .

[0082] B. Measurement Error Identification

[0083] The gain coefficients calculated based on prior data are shown in the following formula: …

[0084] The gain coefficients calculated based on the sampled sequence are shown in the following formula:

[0085] True value It is unknowable, but based on the interrelationships, each can be calculated. Values ​​that make the proportions the same.

[0086] If the prior data is accurate, the gain coefficient of the prior data... With the gain coefficient based on the sampling sequence ratio The values ​​are close, as shown in the following formula:

[0087] If the prior data of a certain current transformer is inaccurate, or if the error of the current transformer deviates significantly, then Outliers exist, and the method for identifying outliers is shown in the following formula:

[0088] The deviation coefficient was calculated based on the absolute median. Thresholds can be set, for example If the deviation coefficient exceeds 30%, the measurement value of the current transformer is considered unreliable and should be removed. If the deviation coefficient exceeds the threshold, the prior data method cannot be used, and the weighted median algorithm is used instead to calculate the constraint value.

[0089] C. Global Constraint Calculation

[0090] After screening, the gain coefficients based on prior data The absolute value is more reliable, while the gain coefficient based on the sampling sequence is more reliable. The relative proportions are relatively reliable; therefore, the true values ​​of the gain coefficients for each unit are... The following formula should be satisfied:

[0091] Calculate the proportionality coefficient by minimizing the sum of squares. As shown in the following formula:

[0092] Calculate the proportionality coefficient Next, calculate the values ​​of all current transformers. The value is shown in the following formula: … …

[0093] The calculation of global constraints is shown in the following formula: =

[0094] (2) Calculation of constraint values ​​based on weighted median

[0095] A. Weight Calculation

[0096] like Figure 7 As shown, the amplitude sampling sequence of each interval is... According to the elimination sequence number set After removing questionable values, the mean or median is calculated to obtain the characteristic values ​​of the amplitude sampling sequence of each interval transformer. As shown in the following formula:

[0097] The median of the characteristic values ​​of each interval transformer is calculated as shown in the following formula:

[0098] Calculate the eigenvalues ​​and median for each interval. relative distance between Add relative error To avoid coinciding with the median, the inverse of the relative distance is used as the initial weight. and normalized to As shown in the following formula:

[0099] B. Global Constraint Calculation

[0100] The reference standard value is calculated using the weighted geometric mean. As shown in the following formula: This represents the weighted sum of the natural logarithms of the measured values.

[0101] The global constraints can be represented by the following formula: =

[0102] 3.3 Ratio Error Estimation

[0103] The ratio of amplitudes between each interval calculated in section 3.1 Taking the natural logarithm, we get and The linear relationship between them, let ,Will The proportional relationship is transformed into a linear relationship, as shown in the following formula:

[0104] Based on the global constraints calculated in 3.2, all can be obtained. The constraint relationship is shown in the following equation:

[0105] Combining the above relationships and conditions, taking four intervals as an example, the pairwise proportional relationships between each interval, plus the global constraints of each interval, yield the following overdetermined system of equations, where... The constraint relation matrix, This is the logarithmic form of the gain coefficients for each interval. The sequence of constraints is shown in the following equation:

[0106] Solving the overdetermined system of equations The logarithm of the gain coefficient for each interval is obtained. As shown in the following formula:

[0107] calculate The gain coefficient for each interval can be obtained by calculating the exponent. And calculate the estimated ratio error data for each current transformer. As shown in the following formula:

[0108] 4. Phase error analysis process

[0109] 4.1 Solving for the signal phase difference between each channel

[0110] like Figure 8 As shown, similar to the amplitude calculation method, the phase error of each interval transformer is... , No. i Interval and the first j The phase difference between them is The Laida standard is applied to remove outliers, and methods for calculating the mean or median are used to calculate... eigenvalues As shown in the following formula:

[0111] 4.2 Calculate global constraints

[0112] Similar to phase error, if the sample size of the measured voltage transformers is large enough, according to the data distribution, the sum of the phase errors of each voltage transformer is 0, as shown in the following formula:

[0113] Similarly, because a sufficiently large sample size is unavailable, the above constraints may not hold. We will still rely on prior data to calculate the constraints.

[0114] Similarly, the monitored voltage transformer dataset In this subset, those with prior phase error data are considered a subset. Typically, the prior data with phase error is the same as the subset with ratio error.

[0115] subset Phase difference of the calibration data of each voltage transformer (Usually, the error data of the lower limit load is taken) and secondary voltage drop data. (If there is no pressure drop data, then set) The comprehensive ratio error was calculated. The calculated comprehensive ratio error The global constraints are calculated as shown in the following formula:

[0116] 4.3 Phase Error Estimation

[0117] Similarly, taking four intervals as an example, the pairwise differences between each interval, plus the global constraints of each interval, yield the following overdetermined system of equations, where The constraint relation matrix, This is the logarithmic form of the gain coefficients for each interval. The sequence of constraints is shown in the following equation:

[0118] Solving the overdetermined equations allows for the direct calculation of the phase error vector of each instrument transformer. , .

[0119] Working principle and process: First, amplitude and phase data of the secondary windings of each voltage transformer are obtained through synchronous sampling (since the true value of the primary voltage cannot be directly known). The ratio of amplitudes between each pair of transformers of the same source is calculated. This ratio is approximately equal to the ratio of the actual gain coefficients of the two transformers, thus eliminating the influence of the unknown primary voltage. Second, for the phase, the phase difference between each pair of transformers of the same source is directly calculated. After obtaining the relative proportional relationship and relative phase difference between all channels, a global constraint needs to be applied to convert the relative quantities into absolute error estimates. Priority is given to using some existing prior data of voltage transformers, including calibration ratio error and secondary voltage drop data, to calculate their comprehensive ratio error and phase error. The consistency is checked with the relative gain coefficient obtained from the sampling data, and transformers with unreliable prior data are eliminated. Finally, least squares fitting is used to determine the phase error. A proportionality coefficient is used to anchor all relative gain coefficients to an absolute scale, thus obtaining a global product constraint for all current transformers. If the prior data is insufficient or of poor quality, a weighted median algorithm is used instead. The weighted geometric mean is calculated as a virtual reference standard, using the reciprocal of the distance between the amplitude characteristic value of each channel and the median as the weight, thereby constructing a global constraint. Then, with both the relative proportionality relationship and the global constraint, the logarithm of the gain coefficient is used as the unknown quantity, and the multiplicative relationship is transformed into a system of linear equations. Together with the linear relationship of the phase difference, this forms an overdetermined system of equations. The least squares method is used to solve for the optimal estimate of the gain coefficient and phase deviation of each current transformer, and finally, the ratio error and phase error of each current transformer are calculated. Finally, throughout the process, the Laida criterion is used to remove coarse measurement values ​​caused by external interference, ensuring that the original data used in the calculation is clean and reliable.

[0120] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for error analysis of voltage transformers based on prior data weighting, characterized in that, The voltage transformer error analysis method includes the following steps: S1, Data Acquisition The secondary signals of multiple voltage transformers measuring the primary voltage at the same measuring point are connected to the synchronous sampling module to obtain the original waveform data of the synchronous sampling signal, calculate the amplitude and phase of each signal according to the period, and store them in the database. S2, Ratio Error Analysis S21. Solve the signal amplitude ratio between each channel: Calculate the ratio between each pair of measured amplitudes of the same source voltage transformers, use the Layda criterion to remove gross values, and then calculate the average or median as characteristic values ​​to obtain the relative proportional relationship of the measured values ​​of each voltage transformer interval. S22. Calculate global constraints: If there are voltage transformers with prior data, calculate global constraints based on the prior data; otherwise, use the weighted median algorithm to calculate global constraints. S23. Ratio error estimation: The natural logarithm of the amplitude ratio relationship between each interval is taken to transform it into a linear relationship. An overdetermined equation system is constructed in combination with the global constraints of each interval. The logarithm of the gain coefficient of each voltage transformer is obtained by solving the overdetermined equation system by the least squares method, and then the ratio error of each voltage transformer is calculated. S3, Phase Error Analysis S31. Solve for the phase difference between each channel: Calculate the phase difference between each pair of voltage transformers of the same source, use the Layda criterion to remove coarse values ​​and calculate the characteristic value to obtain the relative phase difference relationship between each voltage transformer. S32. Calculate global phase constraints: Obtain a subset of mutual inductors with prior phase error data, and calculate the mean of their combined phase errors as global constraints. S33. Phase error estimation: Combine the phase difference relationship between two voltage transformers in the interval with the global phase constraint to construct an overdetermined equation system. Solve the overdetermined equation system using the least squares method to obtain the phase error of each voltage transformer.

2. The voltage transformer error analysis method according to claim 1, characterized in that: In S1, data acquisition adopts a temporary access method, which connects the secondary signals of different voltage transformers measuring the same measuring point to the synchronous sampling module inside the monitoring and analysis device through an air switch. If the voltage transformers in the monitored interval are far apart, satellite synchronization is used to synchronously sample the signals at different locations using multiple devices.

3. The voltage transformer error analysis method according to claim 1, characterized in that: In step S21, solving for the signal amplitude ratio between each channel specifically includes: Taking phase A as an example, the amplitude sampling sequences of the measured values ​​at intervals 1 and 2 are as follows: , The relative proportion is calculated using the following formula: in, This represents the relative ratio of the voltage sampling amplitudes at interval 1 to interval 2. G For theoretical ratios; The ratio of sampled values ​​is calculated using the Laida criterion to remove outliers, and the following formula is used: in, For standard deviation, in each In the middle, the absolute value of the record exceeds The numerical indices form the elimination set. In all Outlier values ​​were removed from the list. After removing outlier values, the eigenvalues ​​are calculated using the following formula: Choose to calculate the mean; if the standard deviation is large, then use the median.

4. The voltage transformer error analysis method according to claim 1, characterized in that: In step S22, calculating the global constraints based on prior data specifically includes: Prior gain calculation and collection of data sets of monitored voltage transformers. In this context, the subset has prior data. Based on subsets The ratio of the calibration data of each voltage transformer in the middle and secondary pressure drop data The overall ratio error was calculated. Then calculate the gain coefficient of the prior data. ; Measurement error identification, based on the gain coefficient calculated from prior data, is shown in the following formula: … The gain coefficients calculated based on the sampled sequence are shown in the following formula: True value It is unknowable, but based on the interrelationships, each can be calculated. Values ​​that make the proportions the same; If the prior data is accurate, the gain coefficient of the prior data... With the gain coefficient based on the sampling sequence ratio The values ​​are close, as shown in the following formula: If the prior data of the voltage transformer is inaccurate or the voltage transformer error deviates, then Outliers exist, and the method for identifying outliers is shown in the following formula: The deviation coefficient was calculated based on the absolute median. A threshold is set. If the deviation coefficient exceeds 30%, the prior data method cannot be used. Instead, the weighted median algorithm is used to calculate the constraint value. Global constraint calculations, and the true values ​​of the gain coefficients of each unit after filtering. The following formula should be satisfied: in, The absolute value of the gain coefficient based on prior data. To calculate the relative proportion of the gain coefficients based on the sampled sequence, the proportioning coefficient is obtained by minimizing the sum of squares. As shown in the following formula: Calculate the proportionality coefficient Next, calculate the voltage transformers for all voltage transformers. The value is shown in the following formula: … … The global constraints can then be calculated using the following formula: = 。 5. The voltage transformer error analysis method according to claim 1, characterized in that: In step S22, the calculation of global constraints using the weighted median algorithm specifically includes: Weight calculation involves sampling the amplitude sequence at each interval. According to the elimination sequence number set After removing questionable values, the mean or median is calculated to obtain the characteristic values ​​of the amplitude sampling sequence of each voltage transformer interval. As shown in the following formula: The median of the characteristic values ​​of each voltage transformer in each bay is calculated as shown in the following formula: Calculate the eigenvalues ​​and median for each interval. relative distance between Add relative error To avoid coinciding with the median, the reciprocal of the relative distance is used as the initial weight. and normalized to As shown in the following formula: Global constraint calculations utilize a weighted geometric mean to calculate the reference standard value. As shown in the following formula: Global constraints are calculated using the following formula: = in, It is the weighted sum of the natural logarithms of the measured values.

6. The voltage transformer error analysis method according to claim 1, characterized in that: In step S23, the ratio error estimation specifically includes: Based on the calculated amplitude ratio of each interval Taking the natural logarithm, we get and The linear relationship between them, let ,Will The proportional relationship is transformed into a linear relationship, as shown in the following formula: Based on the calculated global constraints, all are obtained. The constraint relationship is shown in the following equation: The pairwise proportional relationships between each interval and the global constraints of each interval yield the following overdetermined system of equations: in, The constraint relation matrix, This is the logarithmic form of the gain coefficients for each interval. For a sequence of constraints; Solving the overdetermined system of equations As shown in the following formula: Obtain the logarithm of the gain coefficient for each interval. Through calculation The exponent is used to obtain the gain coefficient of each interval. The ratio error data is then calculated using the following formula: in, The estimated ratio error data for each current transformer.

7. The voltage transformer error analysis method according to claim 1, characterized in that: In step S31, solving for the phase difference between the signals in each channel specifically includes: The phase error of each voltage transformer in the interval is , No. i Interval and the first j The phase difference between them is The Laida standard was used to remove outliers, and the mean or median was calculated. eigenvalues As shown in the following formula: 。 8. The voltage transformer error analysis method according to claim 1, characterized in that: In step S32, calculating the global phase constraint specifically includes: Data set of monitored voltage transformers In this subset, those with prior phase error data are considered a subset. The a priori data with phase error is the same as the subset with ratio error; subset Phase difference of the calibration data of each voltage transformer and secondary pressure drop data The overall ratio error was calculated. The calculated comprehensive ratio error The global constraints are calculated as shown in the following formula: 。 9. The voltage transformer error analysis method according to claim 1, characterized in that: In S33, the phase error estimation specifically includes: The pairwise phase differences between each interval and the global constraints of each interval yield the following overdetermined system of equations: in, The constraint relation matrix, This is the logarithmic form of the gain coefficients for each interval. Given a sequence of constraints, the phase error vector of each voltage transformer is obtained by solving the overdetermined equations. , .

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