A voltage transformer on-line operation and off-line error difference estimation method

Abstract

The present application relates to a kind of voltage transformer online operation and offline error difference estimation method for difference, comprising: according to the equivalent circuit diagram of voltage transformer capacitive series voltage divider structure with coupling stray capacitance, determine the relationship function of voltage transformer online operation and offline error difference for difference with the stray capacitance and main capacitance value of voltage transformer based on equivalent circuit diagram;Stray capacitance and the exponential decay mapping relationship function of characteristic variable are constructed;Simulation model is constructed based on physical consistency index to solve the parameter in exponential decay mapping relationship function;Error difference model is constructed, and physical consistency constraint term is added in objective function to construct hybrid loss function, and error difference model is trained based on hybrid loss function;The input of error difference model is characteristic variable and main capacitance value, and output is error difference;Realize the fast and accurate prediction of CVT error difference in field, and quantify its uncertainty, provide more abundant decision information for engineering application.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power system mutual inductor monitoring, in particular to a voltage mutual inductor online operation and offline calibration error difference estimation method. BACKGROUND

[0002] With the continuous expansion of power system transmission capacity, the long-distance transmission capacity increases rapidly, and the voltage level of the power grid is gradually improved, which puts forward more strict requirements on the accuracy and stability of various metering devices in the power system. With the promotion of strong smart grid and the construction of digital power grid, communication and data acquisition of the power system is a key link, and various power mutual inductors are particularly important primary equipment.

[0003] Capacitive voltage transformer (CVT) is one of the most widely used power mutual inductors. Because of its high impact insulation strength, avoiding resonance caused by core saturation, simple manufacturing, small size, light weight, and significant economic advantages, CVT is widely used in 110kV and above voltage level substations, and is an important component of power system metering. However, CVT has more complex structure, and is easily disturbed by the surrounding environment during operation. There are many devices around in the actual substation, and the devices are in complex energized state. CVT is seriously affected by electromagnetic field during online operation, and CVT error is obviously affected by electromagnetic field change. In actual operation, CVT may show different error characteristics from the test results, which is caused by the surrounding environmental disturbance. Many CVTs pass the test, but still show large error. In the substation, the accuracy of electric energy metering and the reliability of protection device action are highly dependent on the error characteristics of CVT in actual running state. However, the offline calibration method of CVT has single test condition, which cannot fully simulate and reproduce the real working state of mutual inductor in complex and changeable actual power grid running environment. The existing researches focus on the analysis of the influence of single factor on the error difference between CVT online operation and offline calibration, while the actual error difference is the result of multi-factor coupling. Although electromagnetic field simulation can accurately analyze the influence of each factor, its modeling is complex and time-consuming, which is difficult to apply in the field or in the scene that needs to be evaluated quickly. Therefore, how to develop a fast and accurate prediction tool to replace the complex and tedious electromagnetic field simulation is a problem to be solved. SUMMARY

[0004] The present application aims at the technical problems existing in the prior art, and provides a voltage transformer online operation and offline calibration error difference estimation method, obtains a physical expression of error difference and an influence law of each parameter through equivalent circuit diagram analysis, obtains a data set by using a three-dimensional finite element static electric field simulation of a multi-parameter combination, analyzes related characteristics of the data set according to a characteristic scatter diagram, constructs a nonlinear mapping relationship between stray capacitance and characteristic parameters, integrates a physical consistency constraint term into an XGBoost model loss function, constructs a hybrid loss function, realizes fast and accurate prediction of the error difference, and the prediction result obtained by the method has physical interpretability and higher reliability.

[0005] According to a first aspect of the present application, a voltage transformer online operation and offline calibration error difference estimation method is provided, comprising:

[0006] Step 1: an equivalent circuit diagram with coupled stray capacitance is drawn according to a capacitance series voltage division structure of a voltage transformer, and a voltage transformer online operation and offline calibration error difference is determined based on the equivalent circuit diagram and a relationship function of stray capacitance and main capacitance value C of the voltage transformer; the stray capacitance includes: high-voltage stray capacitance in online operation , high-voltage stray capacitance introduced by offline calibration angle change , ground stray capacitance , and phase-to-phase stray capacitance .

[0007] Step 2: an exponential decay mapping relationship function of the stray capacitance and characteristic variables is constructed, the characteristic variables include: cement column height H, phase-to-phase distance D, and offline calibration lead angle θ; a simulation model is constructed to solve parameters in the exponential decay mapping relationship function based on a physical consistency index, and the physical consistency index is determined based on calculated error difference and simulated error difference;

[0008] Step 3: an error difference model is constructed, a physical consistency constraint term is added to a target function to construct a hybrid loss function, and the error difference model is trained based on the hybrid loss function; input of the error difference model is the characteristic variables and the main capacitance value C, and output of the error difference model is the error difference .

[0009] Step 4: a voltage transformer to be measured is subjected to online operation and offline calibration error difference estimation based on the trained error difference model.

[0010] On the basis of the above technical solution, the present application can also be improved as follows.

[0011] Optionally, the process of determining the relationship function in step 1 includes:

[0012] Step 101, based on the equivalent circuit diagram, determining the expression of the relationship function of the output voltage of the voltage transformer during online operation and the stray capacitance and the main capacitance value C , the expression of the relationship function of the output voltage of the voltage transformer during offline calibration and the stray capacitance and the main capacitance value C ;

[0013] Step 102, determining the relationship function as , obtaining the error difference and the relationship function of the stray capacitance and the main capacitance value C of the voltage transformer.

[0014] Optionally, the exponential decay mapping relationship function is:

[0015] ;

[0016] In the formula, , (i=1, 2, 3) are to be optimized parameters.

[0017] Optionally, the process of solving the to-be-optimized parameters in the exponential decay mapping relationship function comprises:

[0018] Step 201, adopting finite element simulation to build a voltage transformer electric field model, simulating the three-dimensional electric field model of the voltage transformer under different characteristic variable value combinations and operating conditions, obtaining the error difference of the voltage transformer, and constructing a voltage transformer online operation and offline calibration error difference dataset : ; In the formula, m is the sample number, represents the i-th sample, is the error difference of the i-th sample, ;

[0019] Step 202, constructing a physical consistency index PCI:

[0020] ;

[0021] In the formula, is the error difference calculated for the predicted stray capacitance value, is the error difference true value obtained by finite element simulation, is a confidence weight coefficient derived from prior physical laws;

[0022] Step 203, optimizing in the dataset with the maximum PCI value as the target to obtain the optimal parameters.

[0023] Optionally, the step 201 comprises:

[0024] Step 20101, build a 500kV voltage transformer finite element simulation model;

[0025] Step 20102, select a plurality of discrete values of the characteristic variable within a set range for combination; wherein the value range of the cement column height H is 0-4m, the value range of the inter-phase distance D is 2-6m, the value range of the offline calibration lead angle θ is 30-90°, and the value range of the main capacitance value C is 5000-10000pF; different operating conditions are set, including online operating conditions and offline calibration conditions;

[0026] Step 20103, in the simulation, the primary voltage is constant, and the ratio error of the simulation voltage transformer is calculated by using the intermediate output voltage :

[0027]

[0028] wherein, is the intermediate output voltage value when there is no other object around the single-phase voltage transformer, and is used to represent the output voltage true value, is the intermediate output voltage value of the simulation voltage transformer;

[0029] Step 20104, calculate the error difference between the online operation and the offline calibration of the voltage transformer:

[0030] ;

[0031] wherein, is the error difference between the online operation and the offline calibration of the voltage transformer, is the ratio error of the online operation simulation, is the ratio error of the offline calibration simulation;

[0032] Step 20105, construct a voltage transformer online operation and offline calibration error difference data set .

[0033] Optionally, the step 203 includes: adopting a differential evolution algorithm to perform global optimization in a preset parameter space, avoiding falling into a local optimal solution; selecting a plurality of groups of random initial values, and performing local fine search by using an L-BFGS-B algorithm; and determining an optimal parameter by comprehensively evaluating a physical consistency index PCI of each candidate parameter combination.

[0034] Optionally, the mixed loss function is:

[0035]

[0036] In the formula, is a weight coefficient, 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.

[0037] Optionally, the error difference model is an XGBoost model, and the process of training the XGBoost model in step 3 further includes:

[0038] The gradient is obtained by differentiating the hybrid loss function. With Hessian matrix The analytical expression:

[0039]

[0040] The analytical expression is integrated into the split node gain calculation of the XGBoost model.

[0041] 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.

[0042] Optionally, step 4 includes:

[0043] 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.

[0044] 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

[0045] Figure 1A flowchart of an online operation and offline error difference estimation method of a capacitive voltage transformer is provided in the present application.

[0046] Figure 2 An equivalent circuit diagram of a B-phase CVT online operation with coupled stray capacitance is provided for the embodiment of the present application.

[0047] Figure 3 A data feature scatter plot matrix diagram is provided for the embodiment of the present application.

[0048] Figure 4 An error difference prediction result diagram is provided for the embodiment of the present application.

[0049] Figure 5 A comparison diagram of convergence speeds of different models is provided for the embodiment of the present application.

[0050] Figure 6 An error difference uncertainty prediction result diagram is provided for the embodiment of the present application. DETAILED DESCRIPTION

[0051] The principles and characteristics of the present application are described below in combination with the accompanying drawings, and the examples are only used to explain the present application and not to limit the scope of the present application.

[0052] Although the simulation calculation of the error difference between the online operation and offline calibration of the capacitive voltage transformer can achieve the prediction of the error difference, there are still defects. How to achieve the fast and accurate prediction of the error difference on site is a problem to be solved. Figure 1 A flowchart of a voltage transformer online operation and offline error difference estimation method is provided in the present application, as shown in Figure 1 The error difference estimation method comprises:

[0053] Step 1, according to the capacitive series voltage division structure of the voltage transformer, an equivalent circuit diagram with coupled stray capacitance is drawn, and the relationship function between the voltage transformer online operation and offline error difference and the stray capacitance and the main capacitance value C of the voltage transformer is determined based on the equivalent circuit diagram. The stray capacitance includes: high-voltage stray capacitance in online operation high-voltage stray capacitance introduced by offline calibration angle change ground stray capacitance and phase-to-phase stray capacitance .

[0054] The purpose of step 1 is to obtain the physical knowledge of the CVT online operation and offline error difference, and to obtain the quantitative results of the influence law of each influencing factor on the error difference.

[0055] Step 2, the exponential decay mapping relationship function of stray capacitance and characteristic variables is constructed, and the characteristic variables include: cement column height H, interphase distance D and offline calibration wire angle θ; the simulation model is constructed based on a physical consistency index to solve the parameters in the exponential decay mapping relationship function, and the physical consistency index is determined based on the calculated error difference and the simulated error difference.

[0056] Step 3, an error difference model is constructed, a physical consistency constraint term is added to a target function to construct a hybrid loss function, and the error difference model is trained based on the hybrid loss function; the input of the error difference model is characteristic variables and main capacitance value C, and the output is error difference .

[0057] The four key characteristic variables input into the error difference model are the actual observable characteristic parameters in the transformer substation, the cement column height H is in units of m, the interphase distance D is in units of m, the offline calibration wire angle θ is in units of °, and the main capacitance value C is in units of pF.

[0058] Step 4, the trained error difference model is used to estimate the online operation and offline calibration error difference of the to-be-measured voltage transformer.

[0059] The error difference estimation method for the online operation and offline calibration of the voltage transformer provided by the application realizes the fast and accurate prediction of the CVT error difference on site and quantifies the uncertainty, thereby providing more abundant decision information for engineering application.

[0060] Embodiment 1

[0061] Embodiment 1 provided by the application is an embodiment of the error difference estimation method for the online operation and offline calibration of the voltage transformer provided by the application, which is combined with Figure 1 It can be known that the error difference estimation method embodiment includes:

[0062] Step 1, an equivalent circuit diagram with coupled stray capacitance is drawn according to the capacitance series voltage division structure of the voltage transformer, and a relationship function of the voltage transformer online operation and offline calibration error difference and the stray capacitance and main capacitance value C of the voltage transformer is determined based on the equivalent circuit diagram; the stray capacitance includes: high-voltage stray capacitance , high-voltage stray capacitance introduced by offline calibration angle change , ground stray capacitance and interphase stray capacitance .

[0063] In the specific implementation, the equivalent circuit diagram with coupled stray capacitance can be drawn according to the CVT capacitance series voltage division structure, Figure 2 and an equivalent circuit diagram with coupled stray capacitance for B-phase CVT online operation is provided for the embodiment of the application.Figure 2 It can be seen that, in one possible embodiment, the process of determining the relational function in step 1 includes:

[0064] 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. .

[0065] 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:

[0066]

[0067] Similarly, the expression for the output voltage of phase B during offline calibration can be derived as follows:

[0068]

[0069] 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.

[0070] Step 102: Derive the expression for the error difference and perform simplified calculations.

[0071] 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. :

[0072] .

[0073] 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 stray capacitance between phases 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:

[0074]

[0075] Step 103, the effect of each stray capacitance on the direction and sensitivity of the amplitude.

[0076] Specifically, the partial derivatives of the expression in step 102 with respect to the stray capacitance, the amplitude, and the phase are calculated respectively.

[0077]

[0078] In the formula, the direction and sensitivity of the amplitude are determined.

[0079] Step 2, constructing an exponential decay mapping relationship function between the stray capacitance and the characteristic variables, including the cement column height H, the interphase distance D, and the offline calibration wire angle θ; constructing a simulation model based on a physical consistency index to solve the parameters in the exponential decay mapping relationship function, and the physical consistency index is determined based on the calculated error difference and the simulated error difference.

[0080] In step 2, an exponential function is used to establish the mapping relationship between the stray capacitance and the characteristic variables, and the physical constraints of the geometric layout on the stray capacitance are reflected through the exponential decay characteristics.

[0081] In one possible implementation manner, the exponential decay mapping relationship function is as follows:

[0082] .

[0083] In the formula, the direction and sensitivity of the amplitude are determined. (i=1, 2, 3) are the parameters to be optimized.

[0084] In one possible implementation manner, the process of solving the parameters to be optimized in the exponential decay mapping relationship function includes:

[0085] Step 201, using finite element simulation to build a voltage transformer electric field model, and simulating the three-dimensional electric field model of the voltage transformer under different combinations of characteristic variable values and operating conditions to obtain the error difference of the voltage transformer, and constructing an error difference dataset of the voltage transformer under online operation and offline calibration : ; in the formula, m is the number of samples, and represents the i th sample, is the error difference of the i th sample, is a four-dimensional feature vector, and m is the number of samples. ​​​​​​​​​​​

[0086] In a possible implementation manner, step 201 comprises:

[0087] Step 20101, a 500 kV voltage transformer finite element simulation model is built, and the influence of key structural parameters on the error characteristics of the CVT is studied.

[0088] Step 20102, a plurality of discrete values of the characteristic variables are selected within a set range for combination; wherein the value range of the cement column height H is 0-4 m, the value range of the inter-phase distance D is 2-6 m, the value range of the off-line detection lead angle θ is 30-90°, and the value range of the main capacitance value C is 5000-10000 pF; different operating conditions are set, including an on-line operating condition and an off-line detection condition.

[0089] In a specific implementation, four core variable parameters are simulated: the cement column height H, which refers to the height of the CVT body from the ground and directly affects the electromagnetic coupling strength to the ground; the three-phase distance D, which refers to the horizontal distance between the center points of two adjacent CVT phases and directly affects the electromagnetic coupling strength between phases; the off-line detection lead angle θ, which simulates the angle between the high-voltage lead and the CVT during off-line detection (the on-line running angle is 90°); and the main capacitance value C, which is a core parameter of the CVT divider and directly affects the change of the stray capacitance on the division ratio. According to engineering practice and parameter sensitivity analysis, a plurality of discrete values of each parameter are selected within a reasonable range for combination.

[0090] The on-line operating condition: the rated three-phase power frequency voltage is applied, and the high-voltage lead is fixed at an angle of 90°; the off-line detection condition: the standard power frequency test voltage is applied to the single-phase CVT, and the high-voltage lead angle is set to θ to simulate the off-line detection environment.

[0091] Step 20103, in the simulation, the primary voltage is constant, and the ratio error of the voltage transformer in the simulation is calculated by using the intermediate output voltage

[0092]

[0093] wherein, is the intermediate output voltage value when there is no other object around the single-phase voltage transformer, and is used to represent the output voltage true value, is the intermediate output voltage value of the simulated voltage transformer.

[0094] Step 20104, the error difference between the on-line operation and the off-line detection of the voltage transformer is calculated:

[0095] .

[0096] wherein, is the error difference between the on-line operation and the off-line detection of the voltage transformer, ​The ratio error of the online running simulation, The ratio error of the offline calibration simulation.

[0097] Step 20105, constructing a voltage transformer online running and offline calibration error difference dataset .

[0098] In a specific implementation, after obtaining the dataset, a data sample set is constructed according to a large number of simulation results, and the dataset is analyzed for features.

[0099] The data is plotted in a feature scatter plot, and the Pearson correlation coefficient r of the feature is calculated:

[0100]

[0101] In the formula, , is the value of different features, , is the mean value. According to the feature analysis result of the dataset, a regression model that meets the capacity requirement is selected.

[0102] Step 202, constructing a physical consistency index PCI:

[0103] .

[0104] In the formula, is the error difference calculated for predicting the stray capacitance value, is the error difference true value obtained by finite element simulation, is the confidence weight coefficient derived from the prior physical law.

[0105] In a specific implementation, can be calculated according to the relationship function obtained in step 1 and the exponential decay mapping relationship function obtained in step 2. In one embodiment, by the nonlinear mapping relationship and the relationship between the error difference and the capacitance, the physical model output value is:

[0106]

[0107] The confidence weight coefficient is determined by the physical reasonableness of the stray capacitance mapping value under the set of parameters. According to the physical structure and engineering experience, the range is 0~15pF, the range is 0~5pF, the range is 0~10pF, if all the capacitance values are within the experienced reasonable range, , otherwise tends to 0, so as to ensure that the optimization result has high precision and strong physical interpretability.

[0108] Step 203, optimization is performed in the data set with the PCI value as the target to obtain the optimal parameters.

[0109] In a possible embodiment, to obtain the optimal parameters, a hybrid optimization strategy is adopted, and step 203 includes: performing global optimization in the preset parameter space by using a differential evolution algorithm to avoid falling into a local optimal solution; selecting multiple groups of random initial values, and performing local fine search by using an L-BFGS-B algorithm; and comprehensively evaluating a physical consistency index PCI of each candidate parameter combination to determine the optimal parameters.

[0110] Specifically, step 203 includes:

[0111] Step 20301, global search stage: global optimization is performed in the preset parameter space by using a differential evolution algorithm to avoid falling into a local optimal solution. The differential evolution algorithm includes four steps.

[0112] 1) Initialization: NP individuals are randomly generated in the parameter boundary to form an initial population: , , and D is the parameter dimension.

[0113] 2) Mutation: a mutation vector is generated for each target vector :

[0114]

[0115] In the formula, , , are mutually different integers randomly selected from [1, NP] and not equal to i; F is a mutation factor, controlling the amplification multiple of the differential vector .

[0116] 3) Crossover: the target variable and the mutation variable are combined to generate a test variable , and a binomial crossover is commonly used:

[0117]

[0118] In the formula, is the jth component of the mutation vector ; is the jth component of the target vector ; CR is a crossover probability, controlling the proportion of components from the mutation vector; is a randomly selected dimension index, ensuring that at least one component comes from the mutation vector.

[0119] 4) Selection: Greedy selection based on objective function value to determine the trial vector or target vector Enter the next generation population:

[0120]

[0121] For the objective function, i.e., the mean square error MSE:

[0122]

[0123] where n is the number of samples; represents the error difference value of the i-th sample; represents the model prediction value of the i-th sample, which is calculated by the error difference expression. The parameter combination with the minimum MSE is selected as the candidate parameter combination.

[0124] Step 20302, local optimization phase: Select multiple groups of random initial values and use the L-BFGS-B algorithm for local fine search. The algorithm iteration format is:

[0125]

[0126] where represents the parameter vector of the k-th iteration; represents the objective function at the gradient vector at ; represents the approximation matrix of the inverse of the Hessian matrix at the k-th iteration; is the step length determined by line search. BFGS update: Update the Hessian inverse approximation directly using the following formula :

[0127]

[0128]

[0129] where ; is the parameter update vector; is the gradient update vector.

[0130] Step 20303, candidate screening mechanism: Comprehensive evaluation of the physical consistency index (PCI) of each candidate parameter combination, which is defined as the error difference calculated by the predicted stray capacitance value ( ) and the true value of the error difference obtained by finite element simulation ( ​​the reciprocal of the absolute error between the predicted value and the true value, multiplied by a confidence weight coefficient derived from prior physical laws .

[0131]

[0132] The parameter combination with the largest PCI value is selected as the optimal parameter, where the confidence weight coefficient is determined by the physical reasonableness of the stray capacitance mapping value under the parameter combination. If all capacitance values are within the empirically reasonable range, then , otherwise tends to 0, thereby ensuring that the optimization result has both high precision and strong physical interpretability.

[0133] Step 3, constructing an error difference model, adding a physical consistency constraint term to the objective function to construct a hybrid loss function, and training the error difference model based on the hybrid loss function; the input of the error difference model is the feature variable and the main capacitance value C, and the output is the error difference .

[0134] Since the relationship function in step 1 depends on the equivalent circuit diagram drawn and some simplification and calculation may not be accurate enough, a machine learning algorithm is used to perform regression analysis on the data to obtain specific error difference values, and a hybrid loss function is introduced. The hybrid loss function introduces the physical penalty term obtained in steps 1 and 2, and the hybrid loss function with physical knowledge can guide the parameter optimization in the XGBoost parameter optimization process, exclude some parameters that do not conform to the physical laws, and speed up the calculation speed.

[0135] In one possible embodiment, the hybrid loss function is:

[0136]

[0137] wherein is the weight coefficient, and the recommended value range is 0.7-1.0, is the calculated value of the physical model error difference expression; is the error difference true value obtained by finite element simulation.

[0138] The hybrid loss function balances the data fitting term and the physical penalty term through the weight coefficient: the data fitting term minimizes the deviation between the predicted value and the true label ; the physical penalty term sets a penalty based on the physical model output as the benchmark, and applies a penalty when the predicted value deviates from the protection point, ensuring that the prediction result conforms to the electromagnetic coupling principle.

[0139] In a possible embodiment, the error difference model is an XGBoost model, and the process of training the XGBoost model in step 3 further includes:

[0140] The derivative of the hybrid loss function is obtained to obtain the gradient and the analytical expression of the Hessian matrix :

[0141]

[0142] The analytical expression is integrated into the split node gain calculation of the XGBoost model, which improves the training efficiency and drives the model to learn the data rules and physical priori knowledge at the same time.

[0143] In a 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; and the optimal parameters are selected to complete the training of the model to obtain the optimal training result.

[0144] Step 4, based on the trained error difference model, the online operation and offline error difference estimation of the voltage transformer to be tested are performed.

[0145] In a possible embodiment, step 4 includes:

[0146] All hyperparameters of the error difference model are kept unchanged, the target function is set to the predicted 5% quantile (α=0.05) and 95% quantile (β=0.95) respectively, and two independent error difference models are trained; the data of the voltage transformer to be tested are input into the 5% quantile error difference model to obtain the lower limit of the prediction interval of the error difference, and the data of the voltage transformer to be tested are input into the 95% quantile error difference model to obtain the upper limit of the prediction interval of the error difference.

[0147] Embodiment 2

[0148] The embodiment 2 provided by the application is a specific application embodiment of the voltage transformer online operation and offline error difference estimation method provided by the application.

[0149] For type CVT, a three-dimensional finite element simulation model is built by using COMSOL, more than 3000 groups of simulation tests are performed for different parameter combinations, and a data sample set is obtained:

[0150]

[0151] Among them, The four parameters represent the height of the cement column, the distance between the columns, the angle between the off-line calibration lead, and the main capacitance value, respectively. The error difference between CVT online operation and off-line calibration.

[0152] Draw the feature scatter plot matrix of the data sample set, and get Figure 3 The results are shown in the figure. The diagonal line represents the distribution of each feature parameter, and the upper triangular matrix represents the relationship between the feature parameters and the target variable. Calculate the Pearson correlation coefficient r of the features, and get , indicating that the features exhibit significant statistical independence; the target variable and each input feature exhibit a discernible nonlinear trend. Based on the scatter plot observation, the degree of nonlinearity is relatively moderate and does not exhibit a highly complex or oscillatory characteristic.

[0153] Given the characteristics of the above data set, the regression model selected in this study must have the following capabilities:

[0154] (1) Capture non-linear relationships: accurately model the non-linear mapping between features and target variables.

[0155] (2) High robustness: insensitive to noise and potential outliers in the data, ensuring prediction stability.

[0156] (3) Avoid overfitting risk: good generalization ability under limited samples.

[0157] Based on the above analysis, the XGBoost model can effectively meet the comprehensive requirements of this study in terms of feature independence, moderate non-linear modeling, robustness, generalization, and interpretability. Therefore, the XGBoost model is selected as the regression prediction algorithm.

[0158] The data set is input into the stray capacitance and the non-linear mapping relationship of the features, and a hybrid optimization strategy is used for parameter optimization, resulting in a non-linear mapping relationship:

[0159]

[0160] Through the non-linear mapping relationship and the expression of the error difference between CVT online operation and off-line calibration, the physical model output : , where takes a typical value of 30 pF.

[0161] Introduce the physical model prediction value into the objective function to construct a hybrid loss function:

[0162]

[0163] The dataset is input into the XGBoost model, and a random parameter search combined with 5-fold cross-validation is used for hyperparameter optimization, and the optimal parameter combination is:

[0164] Table 1 Optimal hyperparameter configuration of XGBoost regression model

[0165]

[0166] The final model is trained using the above optimal parameter configuration. The prediction results of the model on the test data are shown in Figure 4 The residual value between the predicted value and the actual value is basically controlled within ±0.003%, which means that the deviation between the predicted CVT online / offline error difference and the actual difference obtained by simulation is generally less than 0.003%. For high-precision CVT error evaluation, this level of prediction deviation can be basically ignored, which fully verifies the effectiveness of the XGBoost model in this application.

[0167] To verify the effectiveness of the physical constraint mechanism, two models are compared under the same hardware environment: 1) physical constraint model: using a hybrid loss function; 2) pure data-driven model: using a standard squared error loss function. Figure 5 The convergence process of the two models is shown in the figure. The physical constraint model converges after 273 iterations, and the pure data model converges after 262 iterations; but the physical constraint model takes 5.29 seconds for random search, which is 73.6% shorter than the 20.07 seconds of the pure data model. This advantage is due to the guiding effect of the physical regularization term on the parameter space: by constraining the predicted value within a physically reasonable range, it effectively excludes unreasonable parameter combinations and speeds up the model calculation.

[0168] Table 2 Model prediction performance

[0169]

[0170] Table 2 summarizes the performance indicators of the model on the test set: the model has high prediction accuracy, and its prediction results have clear physical interpretability, meeting the engineering requirements of CVT error analysis.

[0171] To further quantify the uncertainty of the prediction, keep all the optimal hyperparameters unchanged, and set the objective function to predict the 5% quantile (α=0.05) and the 95% quantile (β=0.95) respectively, and train two independent XGBoost quantile regression models. For a new input sample, the lower bound of the prediction interval is predicted by the α=0.05 model, and the upper bound of the prediction interval is predicted by the β=0.95 model, and the two together form the 90% prediction interval of the sample. The 90% prediction interval of the model on the test data is shown in Figure 6As shown in the figure, the uncertainty range of the predicted value is intuitively displayed, providing more abundant decision-making information for engineering applications.

[0172] The embodiment of the application provides an online operation and offline error difference estimation method of a voltage transformer, aiming at the engineering problems that the online operation error and the offline error of the CVT are significantly different and the traditional electromagnetic field simulation analysis efficiency is low, a high-efficiency estimation method based on machine learning is proposed and verified. Specifically, more than 3000 groups of sample data of the CVT online / offline error difference (Δε) under the conditions of four key parameters including installation height (H), interphase distance (D), offline test lead angle (θ) and main capacitance value (C) and combinations thereof are generated by parameterized three-dimensional electrostatic field simulation. An XGBoost regression model with H, D, θ and C as inputs and Δε as output is constructed. The core innovation point is that the analytical expression of the CVT error difference and the exponential mapping relationship between the stray capacitance and the measurable geometric parameters are integrated into the model training framework, and a hybrid loss function including physical consistency constraint terms is designed. The model not only realizes high-precision prediction of Δε, significantly improves the training convergence speed, but also has good physical interpretability. The method effectively overcomes the limitations of traditional three-dimensional electromagnetic field simulation modeling complexity and time-consuming calculation, and provides an efficient, convenient and reliable practical tool for power system field operation and design personnel, which can be directly used for rapid evaluation of the online operation and offline error difference of the CVT.

[0173] It should be noted that in the above embodiments, the description of each embodiment has its own emphasis, and the parts not described in detail in a certain embodiment can be referred to the related description of other embodiments.

[0174] Those skilled in the art should understand that the embodiments of the application can be provided as a method, a system, or a computer program product. Therefore, the application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the application can take the form of a computer program product implemented 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.

[0175] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 means for functionally implementing the steps in one or more flow or blocks

[0176] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 means for functionally implementing the steps in one or more flow or blocks

[0177] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 means for functionally implementing the steps in one or more flow or blocks

[0178] While the preferred embodiments of the application have been described, additional variations and modifications can be employed by those skilled in the art. Therefore, the appended claims are intended to cover all such variations and modifications as falling within the scope of the application.

[0179] Obviously, numerous modifications and variations of the present application are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims and their equivalents, the application can be practiced otherwise than as specifically described.

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, and The parameters to be optimized are i=1,2,3.

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. 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. .

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. The error difference calculated to predict stray capacitance values; The true value of the error difference obtained from finite element simulation. Minimize the predicted value for the data fitting term.

8. The error difference estimation method according to claim 7, 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.

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