Estimation method for error difference between online operation and offline verification of voltage transformer

Abstract

The invention relates to a voltage transformer on-line operation and off-line verification error difference estimation method, which comprises the following steps of: drawing an equivalent circuit diagram with coupling stray capacitance according to a capacitor series voltage division structure of a voltage transformer; based on the equivalent circuit diagram, determining a relation function between online operation and offline verification error differences of the voltage transformer and stray capacitance and main capacitance values of the voltage transformer; constructing an exponential decay mapping relation function of the stray capacitance and the characteristic variables; constructing a simulation model, and solving parameters in an exponential decay mapping relation function based on a physical consistency index; constructing an error difference model, adding a physical consistency constraint item into the target function to construct a mixed loss function, and training the error difference model based on the mixed loss function; the input of the error difference model is a characteristic variable and a main capacitance value, and the output is error difference; according to the method, on-site rapid and accurate prediction and quantification of the uncertainty of the CVT error difference are realized, and richer decision information is provided for engineering application.

Description

Technical Field

[0001] This invention relates to the field of power system transformer monitoring, and in particular to a method for estimating the difference in error between online operation and offline verification of voltage transformers. Background Technology

[0002] With the continuous expansion of power system transmission capacity, the rapid increase in long-distance power transmission capability, and the gradual improvement of grid voltage levels, more stringent requirements are being placed on the accuracy and stability of various metering devices in the power system. With the advancement of robust smart grids and the construction of digital grids, communication and data acquisition in the power system are crucial components, and various power transformers are particularly important primary equipment.

[0003] Capacitive voltage transformers (CVTs) are among the most widely used power transformers. Due to their advantages such as high impulse insulation strength, avoidance of resonance caused by core saturation, simple manufacturing, small size, light weight, and significant economic benefits, CVTs are widely used in substations at voltage levels of 110kV and above, serving as a crucial component of power system metering. However, due to their more complex structure, CVTs are susceptible to interference from the surrounding environment during operation. In actual substations, numerous devices exist, and their energized states are complex. CVTs are severely affected by electromagnetic fields during online operation, and their errors are significantly influenced by these fields. In actual operation, CVTs may exhibit error characteristics different from their calibration results due to environmental interference. Many CVTs, although passing calibration, still exhibit significant errors. In substations, the accuracy of power metering and the reliability of protection device operation are highly dependent on the error characteristics of CVTs under actual operating conditions. However, offline calibration methods for CVTs, with their limited testing conditions, cannot fully simulate and reproduce the real operating conditions of transformers in the complex and ever-changing real-world power grid environment. Existing research largely focuses on analyzing the impact of single factors on the difference in errors between online and offline CVT operation, while the actual error difference is the result of the coupling effect of multiple factors. Furthermore, although electromagnetic field simulation can accurately analyze the influence of each factor, its modeling is complex and computationally time-consuming, making it difficult to apply in field settings or scenarios requiring rapid assessment. Therefore, developing a fast and accurate prediction tool to replace the complex and cumbersome electromagnetic field simulation is an urgent problem to be solved. Summary of the Invention

[0004] This invention addresses the technical problems existing in the prior art by providing a method for estimating the error difference between online operation and offline verification of voltage transformers. Through equivalent circuit diagram analysis, the physical expression of the error difference and the influence law of each parameter are obtained. A dataset is acquired using multi-parameter combined three-dimensional finite element electrostatic field simulation, and the relevant characteristics of the dataset are analyzed based on feature scatter plots. A nonlinear mapping relationship between stray capacitance and feature parameters is constructed. Physical consistency constraints are integrated into the XGBoost model loss function to construct a hybrid loss function, enabling rapid and accurate prediction of error differences. The prediction results obtained using this method have physical interpretability and higher reliability.

[0005] According to a first aspect of the present invention, a method for estimating the difference in error between online operation and offline verification of a voltage transformer is provided, comprising: Step 1: Draw the equivalent circuit diagram with coupled stray capacitance based on the capacitor series voltage divider structure of the voltage transformer. Determine the difference in error between online operation and offline verification of the voltage transformer based on the equivalent circuit diagram. The relationship function between the stray capacitance and the main capacitance C of the voltage transformer; the stray capacitance includes: the high-voltage stray capacitance during online operation. High-voltage stray capacitance introduced by changes in the angle during offline verification Stray capacitance to ground and interphase stray capacitance ; Step 2: Construct the exponential decay mapping function between the stray capacitance and the characteristic variables, including: cement column height H, phase-to-phase distance D, and the included angle θ of the offline verification leads; construct a simulation model to solve the parameters in the exponential decay mapping function based on the physical consistency index, which is determined based on the calculated error difference and the simulation error difference. Step 3: Construct an error difference model. Add a physical consistency constraint term to the objective function to obtain a hybrid loss function. Train the error difference model based on this hybrid loss function. The input to the error difference model is the feature variable and the principal capacitance value C, and the output is the error difference. ; Step 4: Based on the trained error difference model, estimate the error difference between online operation and offline verification of the voltage transformer under test.

[0006] Based on the above technical solution, the present invention can also be improved as follows.

[0007] Optionally, the process of determining the relation function in step 1 includes: Step 101: Based on the equivalent circuit diagram, determine the functional expression relating the output voltage of the voltage transformer during online operation to the stray capacitance and the main capacitance value C. The relationship between the output voltage of the voltage transformer during offline calibration and the stray capacitance and main capacitance value C is expressed by the functional expression. ; Step 102, determine the relation function as follows: The error difference was obtained. The relationship function between the stray capacitance and the main capacitance C of the voltage transformer.

[0008] Optionally, the exponential decay mapping function is: ; In the formula, , (i=1,2,3) are the parameters to be optimized.

[0009] Optionally, the process of solving for the parameters to be optimized in the exponential decay mapping function includes: Step 201: A finite element method (FEM) simulation model of the voltage transformer is built. Steady-state simulations of the three-dimensional electric field model of the voltage transformer are performed under different combinations of characteristic variable values ​​and operating conditions to obtain the error differences of the voltage transformer and construct a dataset of error differences between online operation and offline verification of the voltage transformer. : In the formula, m is the sample size. This represents the i-th sample. The error difference for the i-th sample is... ; Step 202, construct the Physical Consistency Index (PCI): ; In the formula, The error difference calculated to predict stray capacitance values. The true value of the error difference obtained from finite element simulation. These are the confidence weight coefficients derived from prior physical laws; Step 203, in the dataset The optimal parameters are obtained by optimizing the PCI value to the maximum.

[0010] Optionally, step 201 includes: Step 20101: Build a finite element simulation model of a 500kV voltage transformer; Step 20102: Select multiple discrete values ​​of the characteristic variables within a set range and combine them; wherein, the value range of the cement column height H is 0~4m, the value range of the phase distance D is 2~6m, the value range of the included angle θ of the offline verification lead is 30~90°, and the value range of the main capacitance C is 5000~10000pF; different operating conditions are set, including online operating conditions and offline verification conditions; Step 20103: In the simulation, the primary voltage is constant. The ratio error of the voltage transformer in the simulation is calculated using the intermediate output voltage. :

[0011] in, This is the intermediate output voltage value when there are no other objects around the single-phase voltage transformer; it is used to characterize the true value of the output voltage. This is the intermediate output voltage value of the simulated voltage transformer; Step 20104: Calculate the difference in error between online operation and offline verification of the voltage transformer: ; in, To account for the difference in error between online operation and offline verification of voltage transformers, The ratio error is for online simulation. The ratio error is used for offline verification simulation; Step 20105: Construct a dataset of errors between online operation and offline verification of voltage transformers. .

[0012] Optionally, step 203 includes: using a differential evolution algorithm to perform global optimization in a preset parameter space to avoid getting trapped in local optima; selecting multiple sets of random initial values ​​and using the L-BFGS-B algorithm to perform local fine search; and comprehensively evaluating the physical consistency index (PCI) of each candidate parameter combination to determine the optimal parameters.

[0013] Optionally, the hybrid loss function is:

[0014] In the formula, These are the weighting coefficients. Calculate the value for the error difference expression of the physical model; This represents the true value of the error difference obtained from finite element simulation.

[0015] Optionally, the error difference model is an XGBoost model, and the process of training the XGBoost model in step 3 further includes: The gradient is obtained by differentiating the hybrid loss function. With Hessian matrix The analytical expression:

[0016] The analytical expression is integrated into the split node gain calculation of the XGBoost model.

[0017] Optionally, the training process of the error difference model in step 3 further includes: using random parameter search combined with 5-fold cross-validation to optimize the hyperparameters of the model; the hyperparameters include: learning rate, maximum tree depth, row sampling rate, column sampling rate, L1 regularization, and L2 regularization; selecting the optimal parameters to complete the training of the model and obtain the optimal training result.

[0018] Optionally, step 4 includes: Keeping all hyperparameters of the error difference model unchanged, the objective function is set to predict the 5th percentile and 95th percentile respectively, and two independent error difference models are trained respectively; the data of the voltage transformer under test is input into the error difference model of the 5th percentile to obtain the lower bound of the prediction interval of the error difference, and the data of the voltage transformer under test is input into the error difference model of the 95th percentile to obtain the upper bound of the prediction interval of the error difference.

[0019] This invention provides a method for estimating the error difference between online operation and offline verification of voltage transformers. It establishes a CVT simulation platform to conduct simulation studies under different parameter combinations and operating conditions to obtain a dataset. Based on the error difference expression obtained from the equivalent circuit diagram, a nonlinear mapping and a hybrid loss function are constructed. Physical knowledge is integrated into the XGBoost model. Finally, parameter optimization completes the training of the prediction model for the error difference between online operation and offline verification of CVTs. This scheme guides the training of the machine learning model through a physical model, accelerating convergence speed and computational efficiency, achieving rapid and accurate prediction of error differences, and the model has physical interpretability and higher reliability. Attached Figure Description

[0020] Figure 1 A flowchart illustrating the method for estimating the difference between online operation and offline verification errors of a capacitive voltage transformer provided by the present invention; Figure 2 The equivalent circuit diagram of B-phase CVT online operation with coupling stray capacitance provided in the embodiment of the present invention; Figure 3 This is a schematic diagram of a data feature scatter matrix provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the error difference prediction results provided in an embodiment of the present invention; Figure 5This is a schematic diagram comparing the convergence speeds of different models provided in this embodiment of the invention; Figure 6 This is a schematic diagram of the error difference uncertainty prediction results provided in an embodiment of the present invention. Detailed Implementation

[0021] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0022] While existing simulations of the error differences between online operation and offline verification of capacitive voltage transformers can predict these differences, they still have limitations. How to achieve rapid and accurate on-site prediction of these error differences is a problem that urgently needs to be solved. Figure 1 A flowchart of a method for estimating the difference between online operation and offline verification errors of a voltage transformer provided by this invention is shown below. Figure 1 As shown, the error difference estimation method includes: Step 1: Draw the equivalent circuit diagram with coupled stray capacitance based on the capacitor series voltage divider structure of the voltage transformer. Determine the difference in error between online operation and offline verification of the voltage transformer based on the equivalent circuit diagram. The relationship function between the stray capacitance and the main capacitance C of the voltage transformer; stray capacitance includes: high-voltage stray capacitance during online operation. High-voltage stray capacitance introduced by changes in the angle during offline verification Stray capacitance to ground and interphase stray capacitance .

[0023] The purpose of step 1 is to obtain the physical knowledge of the error difference between online operation and offline verification of CVT, and to obtain the quantitative results of the influence law of each influencing factor on the error difference.

[0024] Step 2: Construct an exponential decay mapping function between stray capacitance and characteristic variables, including: cement column height H, phase-to-phase distance D, and the included angle θ of the offline verification leads; construct a simulation model to solve the parameters in the exponential decay mapping function based on the physical consistency index, which is determined based on the calculated error difference and the simulation error difference.

[0025] Step 3: Construct an error difference model. Add a physical consistency constraint term to the objective function to obtain a hybrid loss function. Train the error difference model based on this hybrid loss function. The inputs to the error difference model are the feature variables and the principal capacitance value C, and the output is the error difference. .

[0026] The four key feature variables input to the error difference model are the actual observable feature parameters in the substation: the height of the cement column H in meters, the phase-to-phase distance D in meters, the included angle θ of the offline verification leads in degrees, and the main capacitance value C in pF.

[0027] Step 4: Estimate the difference between online operation and offline verification errors of the voltage transformer under test based on the trained error difference model.

[0028] This invention provides a method for estimating the difference between online operation and offline verification errors of voltage transformers (CVTs), enabling rapid and accurate prediction and quantification of the uncertainty of CVT error differences on-site, and providing richer decision-making information for engineering applications.

[0029] Example 1 Embodiment 1 provided by this invention is an embodiment of a method for estimating the difference in error between online operation and offline verification of voltage transformers provided by this invention, combined with... Figure 1 It can be seen that the embodiments of this error difference estimation method include: Step 1: Draw the equivalent circuit diagram with coupled stray capacitance based on the capacitor series voltage divider structure of the voltage transformer. Determine the difference in error between online operation and offline verification of the voltage transformer based on the equivalent circuit diagram. The relationship function between the stray capacitance and the main capacitance C of the voltage transformer; stray capacitance includes: high-voltage stray capacitance during online operation. High-voltage stray capacitance introduced by changes in the angle during offline verification Stray capacitance to ground and interphase stray capacitance .

[0030] In practical implementation, an equivalent circuit diagram with coupled stray capacitors can be drawn based on the CVT capacitor series voltage divider structure. Figure 2 This is an equivalent circuit diagram of a B-phase CVT with coupled stray capacitors for online operation, provided as an embodiment of the present invention. Combined with... Figure 2 It can be seen that, in one possible embodiment, the process of determining the relational function in step 1 includes: Step 101: Based on the equivalent circuit diagram, determine the functional expression relating the output voltage of the voltage transformer during online operation to the stray capacitance and the main capacitance C. The functional expression relating the output voltage to the stray capacitance and the main capacitance C during offline calibration of a voltage transformer. .

[0031] Depend on Figure 2 The equivalent circuit diagram in the diagram can be used to derive the expression for the output voltage of the B-phase CVT:

[0032] Similarly, the expression for the output voltage of phase B during offline calibration can be derived as follows:

[0033] In the formula, , These are the high-voltage stray capacitors used during online operation and offline testing, respectively. , as well as , These are the stray capacitance to ground and the phase-to-phase stray capacitance during online operation and offline testing, respectively.

[0034] Step 102: Derive the expression for the error difference and perform simplified calculations.

[0035] Specifically, when a CVT is operating in a substation, its protection actions and energy metering depend on online operating errors. Therefore, the error difference between online operation and offline verification of the CVT is calculated based on the online operating error. : .

[0036] Directly substituting the parameters into the expression in step 101 is not feasible due to the large number of parameters and the complexity of the expression, which hinders the analysis of the influence of each parameter on the error difference. Therefore, the relevant parameters are simplified. Since the included angle of the high-voltage lead is fixed during online operation, it can be assumed that... The angle of the leads remains constant during offline testing, while it changes during offline testing. Considering that the CVT installation location remains unchanged during online operation and offline testing, it can be set as follows: The interphase stray capacitance mainly depends on the relative positions of the capacitor dividers. To simplify the calculation, we approximate it as... After simplification, we can obtain The expression is:

[0037] Step 103 reveals each stray capacitance pair The direction and sensitivity of the amplitude.

[0038] Specifically, regarding step 102 The expressions respectively calculate about , , Partial derivatives:

[0039] In the formula, .

[0040] Step 2: Construct an exponential decay mapping function between stray capacitance and characteristic variables, including: cement column height H, phase-to-phase distance D, and the included angle θ of the offline verification leads; construct a simulation model to solve the parameters in the exponential decay mapping function based on the physical consistency index, which is determined based on the calculated error difference and the simulation error difference.

[0041] In step 2, an exponential function is used to establish the mapping relationship between stray capacitance and characteristic parameters, and the exponential decay characteristic reflects the physical constraint of geometric layout on stray capacitance.

[0042] In one possible embodiment, the exponential decay mapping function is: .

[0043] In the formula, , (i=1,2,3) are the parameters to be optimized.

[0044] In one possible embodiment, the process of solving for the parameters to be optimized in the exponential decay mapping function includes: Step 201: A finite element method (FEM) simulation model of the voltage transformer is built. Steady-state simulations of the three-dimensional electric field model of the voltage transformer are performed under different combinations of characteristic variable values ​​and operating conditions to obtain the error differences of the voltage transformer and construct a dataset of error differences between online operation and offline verification of the voltage transformer. : In the formula, m is the sample size. This represents the i-th sample. For the error difference of the i-th sample, It is a four-dimensional feature vector. .

[0045] In one possible embodiment, step 201 includes: Step 20101: Build a finite element simulation model of a 500kV voltage transformer and study the influence of key structural parameters on the error characteristics of the CVT.

[0046] Step 20102: Select multiple discrete values ​​of characteristic variables within a set range and combine them; wherein, the value range of cement column height H is 0~4m, the value range of phase distance D is 2~6m, the value range of offline verification lead angle θ is 30~90°, and the value range of main capacitance C is 5000~10000pF; set different operating conditions including: online operating condition and offline verification condition.

[0047] In the specific implementation, the simulation sets four core variable parameters: cement column height H: refers to the height of the CVT body above the ground, which directly affects the electromagnetic coupling strength to the ground; three-phase spacing D: refers to the horizontal distance between the center points of two adjacent CVT phases, which directly affects the electromagnetic coupling strength between phases; offline calibration lead angle θ: the angle between the high-voltage lead and the CVT during simulated offline calibration (the angle is 90° during online operation); main capacitor value C: a core parameter of the CVT voltage divider, whose value directly affects the change of stray capacitance on the voltage division ratio. Based on engineering practice and parameter sensitivity analysis, multiple discrete values ​​of each parameter were selected and combined within a reasonable range.

[0048] Online operation condition: Apply rated three-phase power frequency voltage, with the high-voltage lead fixed at a 90° angle; Offline verification condition: Apply standard power frequency test voltage to a single-phase CVT, with the high-voltage lead angle set to θ, simulating the offline verification environment.

[0049] Step 20103: In the simulation, the primary voltage is constant. The ratio error of the voltage transformer in the simulation is calculated using the intermediate output voltage. :

[0050] in, This is the intermediate output voltage value when there are no other objects around the single-phase voltage transformer; it is used to characterize the true value of the output voltage. This is the intermediate output voltage value of the simulated voltage transformer.

[0051] Step 20104: Calculate the difference in error between online operation and offline verification of the voltage transformer: .

[0052] in, To account for the difference in error between online operation and offline verification of voltage transformers, For the ratio error of online simulation, Offline verification simulation ratio error.

[0053] Step 20105: Construct a dataset of errors between online operation and offline verification of voltage transformers. .

[0054] In practice, after obtaining the dataset, a data sample set is constructed based on a large number of simulation results, and feature analysis is performed on the dataset.

[0055] Plot the features using a scatter plot and calculate the Pearson correlation coefficient r for each feature:

[0056] In the formula, , For different feature values, , Its mean. Based on the feature analysis results of the dataset, select a regression model that meets the capability requirements.

[0057] Step 202, construct the Physical Consistency Index (PCI): .

[0058] In the formula, The error difference calculated to predict stray capacitance values. The true value of the error difference obtained from finite element simulation. These are the confidence weight coefficients derived from prior physical laws.

[0059] In practice The output value can be calculated based on the relationship function obtained in step 1 and the exponential decay mapping relationship function obtained in step 2. In one embodiment, the physical model output value is obtained through the nonlinear mapping relationship and the relationship between error difference and capacitance. for:

[0060] The confidence weighting coefficients are determined by the physical rationality of the stray capacitance mapping values ​​under this set of parameters. They are selected based on the physical structure and engineering experience. The range is 0~15pF. The range is 0~5pF. The range is 0~10pF. If all capacitance values ​​are within an empirically reasonable range, then... ,otherwise Approaching 0 ensures that the optimization results possess both high accuracy and strong physical interpretability.

[0061] Step 203, in the dataset The optimal parameters are obtained by optimizing the PCI value.

[0062] In one possible embodiment, to obtain the optimal parameters, a hybrid optimization strategy is adopted. Step 203 includes: using a differential evolution algorithm to perform global optimization in a preset parameter space to avoid getting trapped in local optima; selecting multiple sets of random initial values ​​and using the L-BFGS-B algorithm to perform local fine search; and comprehensively evaluating the Physical Consistency Index (PCI) of each candidate parameter combination to determine the optimal parameters.

[0063] Specifically, step 203 includes: Step 20301, Global Search Phase: The Differential Evolutionary Algorithm (DEA) is used to perform global optimization within a preset parameter space to avoid getting trapped in local optima. The DEA consists of four steps: 1) Initialization: Randomly generate NP individuals within the parameter boundaries to form the initial population: , D is the parameter dimension.

[0064] 2) Mutation: For each target vector Generate a mutation vector :

[0065] In the formula, , , Distinct integer indices randomly selected from [1, NP], and not equal to i; F is a mutation factor that controls the difference vector. The magnification factor.

[0066] 3) Crossover: Combining the target variable with the variable of variation to generate experimental variables. Binary cross is commonly used:

[0067] In the formula: For the mutation vector The j-th component; target vector The j-th component; CR is the crossover probability, which controls the proportion of components from the mutation vector; For randomly selected dimension indexes, ensure At least one component comes from the mutation vector.

[0068] 4) Selection: Greedy selection is performed based on the objective function value to determine the experimental vector. Or the target vector Entering the next generation of the population:

[0069] The objective function is the mean squared error (MSE).

[0070] In the formula, n is the number of samples; This represents the error difference value of the i-th sample; This represents the model prediction value for the i-th sample. The error difference expression is used for calculation. The parameter combination with the smallest MSE is selected as the candidate parameter combination.

[0071] Step 20302, Local Optimization Stage: Select multiple sets of random initial values ​​and perform a fine-grained local search using the L-BFGS-B algorithm. The algorithm iteration format is as follows:

[0072] In the formula, This represents the parameter vector for the k-th iteration; Describe the objective function exist The gradient vector at that point; This represents the inverse of the Hessian matrix at the k-th iteration. Approximate matrix; This is the step size determined through line search.

[0073] BFGS Update: Directly update the Hessian inverse approximation using the following formula. :

[0074] In the formula, ; Update the vector for the parameters; Update the gradient vector.

[0075] Step 20303, Candidate Screening Mechanism: Comprehensively evaluate the Physical Consistency Index (PCI) of each candidate parameter combination, which is defined as the error difference calculated in predicting the stray capacitance value. The true value of the error difference between ) and the finite element simulation ( The inverse of the absolute error between the two values, multiplied by a confidence weight coefficient derived from prior physical laws. .

[0076]

[0077] The parameter combination with the highest PCI value is selected as the optimal parameter set. The confidence weight coefficients are determined by the physical reasonableness of the stray capacitance mapping values ​​under this parameter set. If all capacitance values ​​are within an empirically reasonable range, then… ,otherwise Approaching 0 ensures that the optimization results possess both high accuracy and strong physical interpretability.

[0078] Step 3: Construct an error difference model. Add a physical consistency constraint term to the objective function to obtain a hybrid loss function. Train the error difference model based on this hybrid loss function. The inputs to the error difference model are the feature variables and the principal capacitance value C, and the output is the error difference. .

[0079] Since the relational function in step 1 depends on the drawn equivalent circuit diagram and some simplifications have been made, the calculation may not be accurate enough. Therefore, a machine learning algorithm is used to perform regression analysis on the data to obtain specific error difference values. A hybrid loss function is also introduced, which incorporates the physical penalty terms obtained in steps 1 and 2. The hybrid loss function with physical knowledge can guide parameter optimization during the XGBoost parameter optimization process, eliminate some parameters that do not conform to physical laws, and accelerate its calculation speed.

[0080] In one possible implementation, the hybrid loss function is:

[0081] In the formula, This is the weighting coefficient, and a value range of 0.7 to 1.0 is recommended. Calculate the value for the error difference expression of the physical model; This represents the true value of the error difference obtained from finite element simulation.

[0082] This hybrid loss function balances the data fit term and the physical penalty term through weighting coefficients: the data fit term minimizes the predicted value. With real labels Deviation; physics penalty term output by physics model Set a penalty for the baseline when the predicted value A penalty is applied when the prediction deviates from the protection point to ensure that the prediction results conform to the principle of electromagnetic coupling.

[0083] In one possible embodiment, the error difference model is an XGBoost model, and the process of training the XGBoost model in step 3 further includes: Taking the derivative of the mixed loss function, we obtain the gradient. With Hessian matrix The analytical expression:

[0084] By integrating analytical expressions into the split node gain calculation of the XGBoost model, training efficiency is improved while driving the model to learn data patterns and physical prior knowledge simultaneously.

[0085] In one possible embodiment, the training process of the error difference model in step 3 further includes: using random parameter search combined with 5-fold cross-validation to optimize the hyperparameters of the model; the hyperparameters include: learning rate, maximum tree depth, row sampling rate, column sampling rate, L1 regularization, and L2 regularization; selecting the optimal parameters to complete the training of the model and obtain the optimal training result.

[0086] Step 4: Estimate the difference between online operation and offline verification errors of the voltage transformer under test based on the trained error difference model.

[0087] In one possible embodiment, step 4 includes: Keeping all hyperparameters of the error difference model unchanged, the objective function is set to predict the 5th quantile (α=0.05) and the 95th quantile (β=0.95), respectively, and two independent error difference models are trained. The data of the voltage transformer under test is input into the 5th quantile error difference model to obtain the lower bound of the prediction interval of the error difference, and the data of the voltage transformer under test is input into the 95th quantile error difference model to obtain the upper bound of the prediction interval of the error difference.

[0088] Example 2 Embodiment 2 provided by the present invention is a specific application embodiment of the method for estimating the difference between online operation and offline verification error of voltage transformers provided by the present invention.

[0089] against A CVT model was built using COMSOL to construct a three-dimensional finite element simulation model. More than 3,000 simulation tests were conducted for different parameter combinations, resulting in a data sample set. :

[0090] in, The four parameters represent the height of the cement column, the interphase distance, the included angle of the offline verification leads, and the main capacitance value, respectively. This refers to the difference in error between online and offline CVT operation.

[0091] Plot the feature scatter plot matrix of the data sample set to obtain... Figure 3 The results shown in the figure illustrate the distribution of each feature parameter along the diagonal, with the upper triangular matrix representing the relationships between feature parameters and between features and the target variable. The Pearson correlation coefficient r of the features is calculated, yielding... This indicates that the features exhibit significant statistical independence; the target variable and each input feature show an identifiable nonlinear trend. Based on the scatter plot, this nonlinearity is relatively moderate and does not exhibit highly complex or oscillating characteristics.

[0092] Given the characteristics of the dataset mentioned above, this study selects regression models that must possess the following capabilities: (1) Capturing nonlinear relationships: It can accurately model the nonlinear mapping between features and target variables.

[0093] (2) High robustness: It is not sensitive to noise and potential outliers in the data, ensuring the stability of prediction.

[0094] (3) Avoid overfitting risk: It has good generalization ability under limited samples.

[0095] Based on the above analysis, the XGBoost model can effectively meet the comprehensive requirements of this study in terms of feature independence, moderate nonlinear modeling, robustness, generalization and interpretability. Therefore, the XGBoost model is selected as the regression prediction algorithm.

[0096] The dataset is input into a nonlinear mapping relationship between stray capacitance and features, and a hybrid optimization strategy is used for parameter optimization to obtain the nonlinear mapping relationship as follows:

[0097] The physical model output can be calculated using the nonlinear mapping relationship and the expression for the difference in errors between online and offline CVT operation. : ,in Take a typical value of 30pF.

[0098] Introducing physical model predictions into the objective function Construct a hybrid loss function:

[0099] The dataset was input into the XGBoost model, and hyperparameter optimization was performed using random parameter search combined with 5-fold cross-validation to obtain the optimal parameter combination: Table 1 Optimal Hyperparameter Configuration for XGBoost Regression Model

[0100] The final model was trained using the above optimal parameter configuration. It was then evaluated on an independent test set, and the model's prediction results on the test data are as follows: Figure 4 As shown, the residual values ​​between the predicted results and the actual values ​​are basically controlled within ±0.003%, which means that the deviation between the model-predicted online / offline CVT error difference and the actual difference obtained from the simulation is generally less than 0.003%. For CVT error assessment with high precision requirements, this level of prediction deviation can be ignored, fully verifying the effectiveness of the XGBoost model in this application.

[0101] To verify the effectiveness of the physical constraint mechanism, two models were compared under the same hardware environment: 1) Physical constraint model: using a hybrid loss function; 2) Pure data-driven model: using the standard squared error loss function. Figure 5The convergence processes of the two models are demonstrated. The physical constraint model converged after 273 iterations, while the pure data model converged after 262 iterations. However, the random search time of the physical constraint model was 5.29 seconds, which was 73.6% shorter than the 20.07 seconds of the pure data model. This advantage stems from the guiding effect of the physical regularization term on the parameter space: by constraining the predicted values ​​to be within a physically reasonable range, it effectively eliminates unreasonable parameter combinations and accelerates the model's computation speed.

[0102] Table 2 Model Prediction Performance

[0103] Table 2 summarizes the model's performance metrics on the test set: the model has high prediction accuracy and its prediction results have clear physical interpretability, meeting the engineering requirements for CVT error analysis.

[0104] To further quantify the uncertainty of the predictions, while keeping all optimal hyperparameters constant, the objective functions were set to predict the 5th quantile (α=0.05) and 95th quantile (β=0.95), respectively, and two independent XGBoost quantile regression models were trained. For a new input sample, the lower bound of the prediction interval for the α=0.05 model and the upper bound of the prediction interval for the β=0.95 model together constitute the 90% prediction interval for that sample. The 90% prediction interval of the model on the test data is shown below. Figure 6 As shown in the figure, this diagram visually illustrates the range of uncertainty in the predicted values, providing richer decision-making information for engineering applications.

[0105] This invention provides a method for estimating the difference between online and offline verification errors of voltage transformers (CVTs). It aims to address the engineering problem of significant differences between online and offline verification errors in CVTs, where traditional electromagnetic field simulation analysis is inefficient. The method proposes and verifies a highly efficient estimation method based on machine learning. Specifically, through parameterized three-dimensional electrostatic field simulation, the system generates over 3000 sets of sample data on the difference between online and offline CVT errors (Δε) under four key parameters and their combinations: installation height (H), phase-to-phase distance (D), offline verification lead angle (θ), and main capacitance value (C). An XGBoost regression model is constructed with H, D, θ, and C as inputs and Δε as output. The core innovation lies in integrating the analytical expression of CVT error difference and the exponential mapping relationship between stray capacitance and measurable geometric parameters into the model training framework, and designing a hybrid loss function that includes a physical consistency constraint term. This model not only achieves high-precision prediction of Δε and significantly improves the training convergence speed, but also possesses good physical interpretability. This method effectively overcomes the limitations of traditional three-dimensional electromagnetic field simulation modeling, which is complex and computationally time-consuming. It provides power system field operation and maintenance personnel and designers with an efficient, convenient, and reliable practical tool that can be directly used to quickly evaluate the difference in error between online and offline CVT operation.

[0106] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0107] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0108] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0109] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0110] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0111] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0112] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for estimating the difference in error between online operation and offline verification of a voltage transformer, characterized in that, The error difference estimation method includes: Step 1: Draw the equivalent circuit diagram with coupled stray capacitance based on the capacitor series voltage divider structure of the voltage transformer. Determine the difference in error between online operation and offline verification of the voltage transformer based on the equivalent circuit diagram. The relationship function between the stray capacitance and the main capacitance C of the voltage transformer; the stray capacitance includes: the high-voltage stray capacitance during online operation. High-voltage stray capacitance introduced by changes in the angle during offline verification Stray capacitance to ground and interphase stray capacitance ; Step 2: Construct the exponential decay mapping function between the stray capacitance and the characteristic variables, including: cement column height H, phase-to-phase distance D, and the included angle θ of the offline verification leads; construct a simulation model to solve the parameters in the exponential decay mapping function based on the physical consistency index, which is determined based on the calculated error difference and the simulation error difference. Step 3: Construct an error difference model. Add a physical consistency constraint term to the objective function to obtain a hybrid loss function. Train the error difference model based on this hybrid loss function. The input to the error difference model is the feature variable and the principal capacitance value C, and the output is the error difference. ; Step 4: Based on the trained error difference model, estimate the error difference between online operation and offline verification of the voltage transformer under test.

2. The error difference estimation method according to claim 1, characterized in that, The process of determining the relation function in step 1 includes: Step 101: Based on the equivalent circuit diagram, determine the functional expression relating the output voltage of the voltage transformer during online operation to the stray capacitance and the main capacitance value C. The relationship between the output voltage of the voltage transformer during offline calibration and the stray capacitance and main capacitance value C is expressed by the functional expression. ; Step 102, determine the relation function as follows: The error difference was obtained. The relationship function between the stray capacitance and the main capacitance C of the voltage transformer.

3. The error difference estimation method according to claim 1, characterized in that, The exponential decay mapping function is: ； In the formula, , (i=1,2,3) are the parameters to be optimized.

4. The error difference estimation method according to claim 3, characterized in that, The process of solving for the parameters to be optimized in the exponential decay mapping function includes: Step 201: A finite element method (FEM) simulation model of the voltage transformer is built. Steady-state simulations of the three-dimensional electric field model of the voltage transformer are performed under different combinations of characteristic variable values ​​and operating conditions to obtain the error differences of the voltage transformer and construct a dataset of error differences between online operation and offline verification of the voltage transformer. : In the formula, m is the sample size. This represents the i-th sample. The error difference for the i-th sample is... ; Step 202, construct the Physical Consistency Index (PCI): ； In the formula, The error difference calculated to predict stray capacitance values. The true value of the error difference obtained from finite element simulation. These are the confidence weight coefficients derived from prior physical laws; Step 203, in the dataset The optimal parameters are obtained by optimizing the PCI value to the maximum.

5. The error difference estimation method according to claim 4, characterized in that, Step 201 includes: Step 20101: Build a finite element simulation model of a 500kV voltage transformer; Step 20102: Select multiple discrete values ​​of the characteristic variables within a set range and combine them; wherein, the value range of the cement column height H is 0~4m, the value range of the phase distance D is 2~6m, the value range of the included angle θ of the offline verification lead is 30~90°, and the value range of the main capacitance C is 5000~10000pF; different operating conditions are set, including online operating conditions and offline verification conditions; Step 20103: In the simulation, the primary voltage is constant. The ratio error of the voltage transformer in the simulation is calculated using the intermediate output voltage. : in, This is the intermediate output voltage value when there are no other objects around the single-phase voltage transformer; it is used to characterize the true value of the output voltage. This is the intermediate output voltage value of the simulated voltage transformer; Step 20104: Calculate the difference in error between online operation and offline verification of the voltage transformer: ； in, To account for the difference in error between online operation and offline verification of voltage transformers, The ratio error is for online simulation. Offline verification simulation of the ratio error; Step 20105: Construct a dataset of errors between online operation and offline verification of voltage transformers. .

6. The error difference estimation method according to claim 4, characterized in that, Step 203 includes: using a differential evolution algorithm to perform global optimization in a preset parameter space to avoid getting trapped in local optima; selecting multiple sets of random initial values ​​and using the L-BFGS-B algorithm to perform local fine search; and comprehensively evaluating the Physical Consistency Index (PCI) of each candidate parameter combination to determine the optimal parameters.

7. The error difference estimation method according to claim 1, characterized in that, The hybrid loss function is: In the formula, These are the weighting coefficients. Calculate the value for the error difference expression of the physical model; This represents the true value of the error difference obtained from finite element simulation.

8. The error difference estimation method according to claim 1, characterized in that, The error difference model is an XGBoost model, and the process of training the XGBoost model in step 3 further includes: The gradient is obtained by differentiating the hybrid loss function. With Hessian matrix The analytical expression: The analytical expression is integrated into the split node gain calculation of the XGBoost model.

9. The error difference estimation method according to claim 1, characterized in that, The training process of the error difference model in step 3 further includes: using random parameter search combined with 5-fold cross-validation to optimize the hyperparameters of the model; the hyperparameters include: learning rate, maximum tree depth, row sampling rate, column sampling rate, L1 regularization and L2 regularization; selecting the optimal parameters to complete the training of the model and obtain the optimal training result.

10. The error difference estimation method according to claim 1, characterized in that, Step 4 includes: Keeping all hyperparameters of the error difference model unchanged, the objective function is set to predict the 5th percentile and 95th percentile respectively, and two independent error difference models are trained respectively; the data of the voltage transformer under test is input into the error difference model of the 5th percentile to obtain the lower bound of the prediction interval of the error difference, and the data of the voltage transformer under test is input into the error difference model of the 95th percentile to obtain the upper bound of the prediction interval of the error difference.

Images