GIS isolation switch breakdown voltage characteristic interval fitting and modeling method

Abstract

The invention relates to a characteristic interval fitting and modeling method for breakdown voltage between GIS (Gas Insulated Switchgear) disconnecting switches, which is characterized in that on the basis of an actually measured scatter diagram of breakdown voltage, optimal distribution fitting is carried out on the scatter diagram, the distribution interval is predicted, and upper and lower boundary curves are calculated, so that subsequent modeling is facilitated. On the basis of an original simulation model, randomness of breakdown voltage is introduced to be combined with a reignition arc module to form a new model, and the new model is combined with an arc quenching module, a switch control module and an arc resistance module to form a new GIS disconnecting switch dynamic reignition arc simulation model. According to the invention, simulation of switch gap arc reignition randomness and extinguishing phenomenon is realized, and then the peak value distribution condition and the maximum peak value of the VFTO are analyzed. According to the method, the simulation precision is improved, the influence of the switching operation on the VFTO can be evaluated more accurately, and the reliability analysis of an electrical system is enhanced.

Description

Technical Field

[0001] The present invention relates to the technical field of breakdown voltage characteristic analysis between disconnectors, and particularly relates to a method for fitting and modeling the breakdown voltage characteristic interval between GIS disconnectors. Background Art

[0002] During the process of a gas-insulated switchgear (GIS) disconnector closing and opening an unloaded short bus, an arc will be generated, which will cause very fast transient overvoltage (VFTO), posing an insulation threat to the GIS and its connected equipment, polluting the electromagnetic environment of secondary equipment, and seriously affecting the safe and stable operation of the power system. The breakdown voltage characteristics (BDV) between disconnectors affect the generation of arcs and are closely related to the accurate simulation of VFTO. Therefore, in-depth research on the breakdown voltage characteristics between disconnectors, especially on its dispersion, is of great significance for the subsequent simulation research of VFTO.

[0003] The article (Han Bin, Lin Jiming, Chen Weijiang, etc. Influence of Disconnector Operating Speed on Very Fast Transient Overvoltage [J]. Proceedings of the CSEE, 2011, 31(31): 12-16.) assumes that the disconnector contacts move at a uniform speed, assumes that the discharge voltage has a polarity effect and is proportional to the gap distance, and proposes a simulation method for the positive and negative polarity discharge voltage curves. This method represents the breakdown voltage with a linear curve, which simplifies the model. However, the assumption that the breakdown voltage is proportional to the switch gap distance and the contacts move uniformly cannot simulate the complex situation of the disconnector in the actual GIS, and ignores the limitations of the linear model, the dispersion of the breakdown voltage distribution of different disconnectors, and the randomness of breakdown occurrence.

[0004] The article (Wu Xiuxiu, Li Yuanfang, Yang Xin, etc. Research on the Dynamic Breakdown Characteristics of GIS Disconnector Operations under SF6 / N2 Dielectric Conditions and Calculation of Its Switching Overvoltages [J]. Power System Technology, 2024, 48(4): 1742-1751.) establishes a multi-physical field coupling model and obtains a fitting curve of the breakdown voltage. However, the coupling model cannot well simulate the complex electromagnetic environment in the actual GIS and cannot consider the randomness of breakdown.

[0005] In summary, the existing breakdown characteristic curves of disconnectors cannot well meet the requirements of accuracy and simulation practicality, and there is not much research on the interval of the breakdown characteristic distribution, resulting in most of the results of the VFTO simulation model having only a fixed value at the same phase angle, and it is impossible to understand the fluctuations generated under breakdown randomness and objective conditions. Summary of the Invention

[0006] For the technical problem that the breakdown curve of GIS disconnectors is relatively simple and the restriking arc model cannot reflect the randomness of multiple breakdowns, the present invention provides a method for fitting the breakdown voltage distribution interval according to the breakdown voltage scatter plot. By dividing time slices, the optimal interval is fitted, solving the problem of the dispersion of the breakdown voltage; and according to the fitted interval, a method for modeling the restriking arc of GIS disconnectors is provided, no longer based on the assumption that the moving speed of the disconnector, the breakdown voltage and the switch gap distance are proportional, solving the problem of the randomness of breakdowns, making the model more in line with the actual situation and improving the accuracy of the model.

[0007] The technical solution adopted by the present invention is as follows:

[0008] A method for fitting the breakdown voltage distribution interval according to the breakdown voltage scatter plot, based on the measured scatter plot of the breakdown voltage, performs an optimal distribution fitting on the scatter plot, predicts its distribution interval, and calculates its upper and lower bound curves.

[0009] It includes the following steps:

[0010] S1: Plot the breakdown voltage distribution scatter plot:

[0011] Based on the GIS layout, different types of disconnectors and different operating speeds, obtain the variation relationship of the breakdown voltage of the contact gap with time;

[0012] S2: Based on the scatter plot of the entire time period, select the function model with the smallest error:

[0013] While maintaining a low residual, the hyperbolic model's gradually slowing growth characteristic highly coincides with the non-linear variation law of the electric field distribution during the contact separation process, so it is selected as the optimal model.

[0014] S3: Divide the data of the entire time period into multiple time slices to capture the dynamic change characteristics of the breakdown voltage distribution.

[0015] S3.1. Sort the breakdown events in time series, with the target spark number n s as the constraint condition, adaptively adjust the time slice width △T to ensure that the number of sparks n k ∈[n s -δ, n s +δ], where δ is the tolerance threshold, and the implementation steps include:

[0016] a1. Initialize the starting point T start ;

[0017] a2. Slide the time window until the cumulative number of sparks ≥ n s ;

[0018] a3. Record the end point Tend , calculate ΔT = T end - T start ;

[0019] a4. Iterate until full - time coverage is achieved.

[0020] S3.2. The candidate distributions include: Gaussian distribution, log - normal distribution, Gamma distribution, Laplace distribution.

[0021] Evaluate the goodness of fit through the log - likelihood value and tests, and select the optimal distribution;

[0022] Log - likelihood value: Measures the ability of the model to explain the probability density of the data. The larger the value, the better the fit;

[0023] K - S test p - value: Quantifies the difference between the empirical distribution and the hypothesized distribution. The larger the p - value, the better the fit.

[0024] Comprehensively consider its goodness of fit and select the optimal distribution model for each time slice.

[0025] S4: Quantify the probability distribution characteristics of the breakdown voltage within each time slice. According to the optimal distribution model selected in S3, calculate the probability density function PDF and cumulative distribution function CDF of each time slice;

[0026] Probability density function PDF: Characterizes the probability distribution form of the breakdown voltage;

[0027] Cumulative distribution function CDF: Used to determine the confidence interval;

[0028] S5: Generate the upper and lower bound curves of the full - time distribution.

[0029] In S3 above, according to the scatter distribution type within different time slices ΔT, the candidate distributions include:

[0030] Gaussian distribution:

[0031] Log - normal distribution:

[0032] Gamma distribution:

[0033] Laplace distribution: In the above formula, represents the probability density function of the random variable ; Indicates the magnitude of the breakdown voltage of positive and negative polarities. U represents the actual value of the breakdown voltage. μ represents the mean in the Gaussian distribution and Laplace distribution; σ represents the standard deviation in the Gaussian distribution. θ represents the scale parameter of the Gamma distribution. b represents the scale parameter of the Laplace distribution. Γ(k) represents the Gamma function. k represents the shape parameter of the Gamma distribution.

[0034] In S5, fit the scatter distribution range of the entire time period. Taking the reference curve as the maximum probability point at each time, that is, at the peak of the probability density function PDF, find the offset based on the reference function within a 95% confidence interval. Specifically as follows:

[0035] The positions X1 and X2 corresponding to the cumulative probabilities of 0.025 and 0.975 in the 95% confidence interval can be calculated by the formula:

[0036] F(X1) = 0.025;

[0037] F(X2) = 0.075;

[0038] F(X) is the cumulative distribution function CDF of the time slice corresponding distribution;

[0039] Calculate the offset l1, l2 equivalent to the peak voltage X Peak :

[0040] l1 = X1 - X Peak ;

[0041] l2 = X2 - X Peak ;

[0042] Obtain the upper and lower bound curves G u (X), G d (X) of each time slice based on the reference curve:

[0043] G u (X) = G(X) + l1;

[0044] G d (X) = G(X) + l2;

[0045] In the formula, G(X) is the reference function.

[0046] GIS disconnector dynamic restriking arc simulation model modeling method, including the following steps:

[0047] Step 1: According to the actual line parameters, set the equivalent parameters of the model, and the initial parameters of the restriking arc control module, arc extinction control module, arc resistance control module, and switch module;

[0048] Step 2: Set the simulation step size, and the simulation time interval T satisfies

[0049] Step 3: The reignition arc control module obtains the voltage signal difference △U across the disconnector contacts and outputs a reignition arc occurrence signal. △U = U 电源侧 -U 负载测 , sets the breakdown voltage between the disconnector contacts and When △U > 0, judge Output a reignition arc signal to the arc resistance control module; when △U < 0, judge Output a reignition arc signal to the arc resistance control module;

[0050] Step 4: The arc extinction control module obtains the current signal I at the switch connection line t and the current signal I at an interval of one time duration (t-T) , and outputs an arc extinction occurrence signal; K is the current extinction threshold. When I t ×I (t-T) < 0 and |I t -I (t-T) | < K, output an arc extinction signal to the arc resistance control module; if the above conditions are not met, the simulation step size progresses and this step is repeated;

[0051] Step 5: The switch module determines the breakdown duration according to the breakdown voltage scatter plot obtained from the experiment according to the original parameter settings, judges whether the switch operation is completed. If not, repeat Step 3 and Step 4; if the operation is completed, make corresponding adjustments to the state of the switch and the resistance value of the controlled resistor.

[0052] In the said Step 3, the expression of the breakdown voltage between the disconnector contacts is:

[0053]

[0054] In the formula, is the upper and lower bound function curves of the positive breakdown voltage over the entire time period; is the upper and lower bound function curves of the negative breakdown voltage over the entire time period; RAN(1) is a random number in [0, 1].

[0055] In the said Step 3, the output value R B (t) of the arc resistance control module when receiving the reignition arc signal is expressed as:

[0056]

[0057] In the formula, R0 is the arc extinction resistance after the end of the last reignition arc. When first breaking down, take R0 = 1×10 12 ; Z is the sum of the wave impedance of the line at both ends of the switch and the wave impedance of the disconnector rod at both ends; t αis the breakdown delay time, and R is the equivalent resistance in the steady arcing state. In step 4, the output value R B (t) is expressed as:

[0058]

[0059] In the formula, g is the arc conductance; u s is the instantaneous value of the voltage gradient; i s is the instantaneous value of the arc current; P s (g) is the arc heat dissipation power related to the arc conductance; τ s (g) is the insulation recovery time constant related to the arc conductance.

[0060] For the method for fitting and modeling the breakdown voltage characteristic interval between GIS disconnectors of the present invention, the technical effects are as follows:

[0061] 1) In addition to the linear model and the quadratic function model, the present invention further considers the ExpDec1 model and the Hyperbl model to preliminarily fit the breakdown voltage distribution. This not only prevents overfitting but also reduces the residual volatility, and more comprehensively and accurately fits the breakdown voltage distribution.

[0062] 2) In addition to the gauss distribution and the weibull distribution, the present invention further considers the Lognormal distribution, the Gamma distribution, and the Laplace distribution, and can more accurately predict the breakdown voltage distribution.

[0063] 3) In order to optimally predict the distribution range of the breakdown voltage, the present invention divides the scatter plot into several parts for distribution fitting, calculates the offset according to the optimal distribution of each segment based on the reference function, and fits out the distribution interval for the entire time period. Through segmented fitting and offset calculation, the present invention can accurately capture the breakdown voltage distribution characteristics in different time periods, improve the prediction accuracy; reduce the computational complexity, enhance the flexibility and robustness of the model, and adapt to the data characteristics of complex dynamic changes.

[0064] 4) The present invention gives a restriking arc model considering breakdown randomness, introduces a random number RAN(1), can completely simulate the randomness of breakdown occurrence, solves the problem that the simulation does not consider the actual breakdown randomness, and makes the simulation results closer to the actual situation.

[0065] 5) The present invention also has the following advantages:

[0066] ①. The simulation macroscopic waveform is roughly consistent with the measured waveform; ②. The simulation full-phase-angle VFTO peak fluctuation distribution is roughly consistent with the measured full-phase-angle VFTO peak distribution; ③. The error between the simulation full-phase-angle VFTO peak and the measured full-phase-angle VFTO peak is small.

[0067] 6) The present invention is used in the simulation main circuit of the opening and closing transient process of GIS disconnectors to simulate the randomness of arc re-ignition and the extinction phenomenon in the switch gap, and then analyze the peak value distribution and the maximum peak value of VFTO. This method improves the simulation accuracy, can more accurately evaluate the impact of switch operation on VFTO, and enhances the reliability analysis of the electrical system.

[0068] 7) The present invention effectively simulates the breakdown randomness in GIS, overcomes the limitations of the existing methods that cannot simultaneously consider the breakdown randomness and simulation modeling, and provides more accurate technical support for VFTO analysis and model optimization. Brief Description of the Drawings

[0069] The present invention will be further described below in conjunction with the drawings and embodiments;

[0070] Figure 1 It is a schematic diagram of the arc re-ignition control module of the arc re-ignition simulation model of GIS disconnector of the present invention.

[0071] Figure 2 It is a schematic diagram of the arc extinction control module of the arc re-ignition simulation model of GIS disconnector of the present invention.

[0072] Figure 3 It is a complete simulation flowchart.

[0073] Figure 4 It is a comparison chart of the distribution probability between the measured data and the arc re-ignition simulation model of GIS disconnector.

[0074] Figure 5 It is a scatter plot of the breakdown voltage distribution and a curve fitting diagram.

[0075] Figure 6 It is the prediction of the breakdown voltage distribution range during the whole period and the upper and lower bound curves.

[0076] Figure 7 It is a relationship diagram of the PDF and BDV distribution probability characteristics.

[0077] Figure 8 It is the CDF of the Gamma distribution with a 95% confidence interval.

[0078] Figure 9 It is a fitting curve diagram of the log-likelihood value.

[0079] Figure 10 It is a fitting curve diagram of the K-S test evaluation value. Detailed Embodiment

[0080] A method for fitting the breakdown voltage distribution interval according to the breakdown voltage scatter plot, the method comprising: plotting the breakdown voltage distribution scatter plot, selecting a reference fitting function, determining the distribution type within each time slice ΔT, fitting the interval of each time slice ΔT, predicting the distribution interval of the breakdown voltage, and re-ignition arc simulation modeling. Based on the measured scatter plot of the breakdown voltage, perform an optimal distribution fitting on the scatter plot, predict its distribution interval, and calculate its upper and lower bound curves.

[0081] It includes the following steps:

[0082] S1: Plot the breakdown voltage distribution scatter plot:

[0083] Obtain the distribution characteristics of the breakdown voltage through measured data. It varies based on the GIS layout method, the type of disconnector, and the operating speed, and according to the measured results, obtain the relationship between the breakdown voltage of the contact gap and time; specifically as follows:

[0084] Based on the measured data set of the 1100 kV GIS equipment of Xi'an High Voltage Apparatus Research Institute Co., Ltd., select the positive breakdown voltage data under the condition of the opening speed of 0.39 m / s, and the negative polarity method is similar. As Figure 5 shown is the breakdown voltage distribution scatter plot and curve fitting.

[0085] S2: Select the reference fitting function:

[0086] Determine the overall change law of the breakdown voltage during the whole period, and provide a reference for subsequent segmented fitting. Based on the scatter plot of the whole period, select the function model with the smallest error;

[0087] The reference fitting functions include: linear function model, quadratic function model, exponential decay relationship model (ExpDec1 model), hyperbolic relationship model (Hyperbl model). Considering the normalized form and COD of the sum of squared residuals of different distribution fittings comprehensively, select the model with smaller error, and at the same time consider the overfitting situation and select the best model. Specifically as follows:

[0088] Select the linear fitting model, quadratic polynomial fitting model, exponential decay relationship model (ExpDec1 model), sine model, and hyperbolic relationship model (Hyperbl model), and compare and analyze the five fitting models. Table 1 is the comparison diagram of the fitting models. Although the sine model has the best statistical indicators, its periodic characteristics are contrary to the monotonically increasing characteristics of BDV, and there is a significant overfitting risk; although the ExpDec1 model has a smaller residual, the exponential decay trend is contradictory to the growth law of the measured data. The hyperbolic model (Hyperbl) has a highly consistent growth rate slowdown characteristic with the non-linear change law of the electric field distribution during the contact separation process while maintaining a low residual, so it is selected as the optimal model. Specifically as follows:

[0089] Taking the data mentioned in A1 as an example, considering that the higher the degree of the polynomial, the greater the possibility of overfitting and the application of the fitting model will be affected, a linear fitting model, a quadratic polynomial fitting model, a model with an exponential decay relationship (ExpDec1 model), a sine model, and a model with a hyperbolic relationship (Hyperbl model) are selected for comparative analysis of the five fitting models.

[0090] Using the reduced chi-square and the coefficient of determination R 2 as evaluation indicators, R 2 →1 indicates a strong model interpretability, but overfitting needs to be vigilant; the smaller the reduced chi-square, the lower the residual volatility. As shown in Table 1.

[0091] Table 1 Comparison of fitting models

[0092]

[0093] Although the sine model has the best statistical indicators, its periodic characteristics are contrary to the monotonic growth characteristics of BDV, and there is a significant risk of overfitting; although the ExpDec1 model has smaller residuals, the exponential decay trend is inconsistent with the growth law of the measured data. While maintaining a relatively low residual, the hyperbolic model (Hyperbl) is highly consistent with the non-linear change law of the electric field distribution during the contact separation process, so it is selected as the optimal model.

[0094] S3: Adaptive time slice division and determination of the distribution type; specifically as follows:

[0095] Divide the full-time data into multiple time slices to capture the dynamic change characteristics of the breakdown voltage distribution.

[0096] S3.1. Sort the breakdown events in time series, with the target number of sparks n s as the constraint condition, adaptively adjust the time slice width △T to ensure that the number of sparks n k ∈[n s -δ, n s +δ], where δ is the tolerance threshold. The implementation steps include:

[0097] a1. Initialize the start point T start ;

[0098] a2. Slide the time window until the cumulative number of sparks ≥ n s ;

[0099] a3. Record the end point T end , calculate △T = T end -T start ;

[0100] a4. Iterate until full-time coverage.

[0101] This method balances statistical stability (n s ≥ 20) and time resolution (△T ≤ 1ms), avoiding the risks of overfitting or underfitting in fixed segmentation.

[0102] S3.2. The breakdown voltage characteristic BDV distribution within each time slice needs to optimize the best fitting model through statistical tests. The candidate distributions include: Gaussian distribution, lognormal distribution, Gamma distribution, Laplace distribution.

[0103] Evaluate the goodness of fit through the log-likelihood value and the Kolmogorov-Smirnov (K-S) test, and select the optimal distribution:

[0104] Log-likelihood value: Measures the ability of the model to explain the probability density of the data. The larger the value, the better the fit;

[0105] K-S test p-value: Quantifies the difference between the empirical distribution and the hypothesized distribution. The larger the p-value, the better the fit.

[0106] Taking the data mentioned in A1 as an example, the comparison of the log-likelihood value and the K-S test evaluation value of the data in each time slice is shown in the figure, as Figure 9 、 Figure 10 shown. Considering the goodness of fit comprehensively, select the optimal distribution model for each time slice.

[0107] S4: Fit the probability distribution within each time slice; specifically as follows:

[0108] Quantify the probability distribution characteristics of the breakdown voltage within each time slice. According to the optimal distribution model selected in S3, calculate for each time slice:

[0109] Probability density function (PDF): Characterizes the probability distribution form of the breakdown voltage, as Figure 7 shown.

[0110] Cumulative distribution function (CDF): Used to determine the confidence interval, as Figure 8 shown.

[0111] S5: Generate the upper and lower bound curves of the full-time distribution; specifically as follows:

[0112] Integrate the fitting results of each time slice to predict the global distribution interval of the breakdown voltage. Based on the fitting results, calculate the offset within each time period, so as to obtain the interval where the random occurrence probability of BDV is greater than 0.95. For the convenience of simulation calculation, fit the upper and lower bound curves, as Figure 6 shown.

[0113] In S3, according to the scatter distribution types within different time slices, the candidate distributions include:

[0114] Gaussian distribution:

[0115] Log-normal distribution:

[0116] Gamma distribution:

[0117] Laplace distribution: In the above formula, represents the probability density function (PDF) of the random variable describing the probability distribution of the variable at different values. represents the magnitude of the breakdown voltage of positive and negative polarities. U represents the actual value of the breakdown voltage. μ represents the mean (location parameter) in the Gaussian distribution and Laplace distribution; in the log-normal distribution, it represents the mean of lnU. σ represents the standard deviation in the Gaussian distribution; in the log-normal distribution, it represents the standard deviation of lnU.

[0118] θ represents the scale parameter of the Gamma distribution, controlling the degree of dispersion of the distribution. b represents the scale parameter of the Laplace distribution. Γ(k) represents the Gamma function (extended factorial function), which is used as the normalization constant for the Gamma distribution. k represents the shape parameter of the Gamma distribution, controlling the distribution shape (such as skewness).

[0119] In S4, find the probability density function (PDF) and cumulative distribution function (CDF) corresponding to the scatter points within each time slice △T, specifically as shown in Figure 7 and Figure 8 , corresponding to the PDF and CDF of the 3rd time slice respectively. The PDF characterizes its probability distribution, and the CDF characterizes the distribution interval satisfying the 95% confidence interval. For the 3rd time slice, the Gamma distribution is selected as the optimal model due to the highest log-likelihood value and significant K-S p value. Its PDF and CDF accurately depict the BDV distribution characteristics.

[0120] In S5, fit the scatter distribution range of the entire time period. Using the reference curve as the maximum probability point for each time, that is, at the peak of the probability density function (PDF), take the 95% confidence interval to find its offset based on the reference function. Specifically as follows:

[0121] Taking the 3rd time slice as an example, the Gamma distribution is selected as the optimal model due to the highest log-likelihood value and significant K-S p value. Its probability density function PDF is as shown in Figure 7 accurately depicting the probability characteristics of the BDV distribution.

[0122] The positions X1 and X2 corresponding to the cumulative probabilities of 0.025 and 0.975 for the 95% confidence interval can be calculated by the formula:

[0123] F(X1) = 0.025;

[0124] F(X2) = 0.075;

[0125] F(X) is the cumulative distribution function (CDF) of the distribution corresponding to the time slice ΔT;

[0126] Calculate the offsets l1 and l2 corresponding to the peak voltage X Peak :

[0127] l1 = X1 - X Peak ;

[0128] l2 = X2 - X Peak ;

[0129] Obtain the upper and lower bound curves G u (X), G d (X) of each time slice ΔT based on the reference curve:

[0130] G u (X) = G(X) + l1;

[0131] G d (X) = G(X) + l2;

[0132] In the formula, G(X) is the reference function.

[0133] The modeling method of the GIS disconnector dynamic restriking arc simulation model includes the following steps:

[0134] Step 1: Set the equivalent parameters of the model, and the initial parameters of the restriking arc control module, arc extinction control module, arc resistance control module, and switch module according to the actual line parameters; specifically as shown in Table 2;

[0135] Table 2 Input and output of each module parameter of the model

[0136]

[0137] Step 2: Set the simulation step size, and the simulation time interval T satisfies Here, take 10 -8 or smaller;

[0138] Step 3: The restriking arc control module obtains the voltage signal difference ΔU across the disconnector contacts and outputs a restriking arc occurrence signal. ΔU = U 电源侧 -U 负载测 , set the breakdown voltage between the disconnector contacts and When ΔU > 0, judge Output the re-ignition arc signal to the arc resistance control module; when △U < 0, judge Output the re-ignition arc signal to the arc resistance control module;

[0139] Step 4: The arc extinction control module obtains the current signal I at the switch connection line t and the current signal I separated by a time interval (t-T) , and output the arc extinction occurrence signal; K is the current extinction threshold, which is a constant, and here it is taken as 0.1. When I t ×I (t-T) < 0 and |I t -I (t-T) | < K, output the arc extinction signal to the arc resistance control module; if the above conditions are not met, the simulation step size is incremented and this step is repeated;

[0140] Step 5: The switch module determines the breakdown duration according to the breakdown voltage scatter diagram obtained from the experiment according to the original parameter settings, and judges whether the switch operation is completed. If not, repeat Step 3 and Step 4; if the operation is completed, the state of the switch and the resistance value of the controlled resistor are adjusted accordingly.

[0141] In the said Step 3, the expression of the breakdown voltage between the disconnector contacts is:

[0142]

[0143] In the formula, is the upper and lower bound function curves of the positive breakdown voltage over the entire time period; is the upper and lower bound function curves of the negative breakdown voltage over the entire time period; RAN(1) is a random number in [0,1].

[0144] In the said Step 3, the output value R B (t) of the arc resistance control module when receiving the arcing signal is expressed as:

[0145]

[0146] In the formula, R0 is the arc extinction resistance after the end of the last re-ignition arc, and R0 = 1×10 12 is taken at the first breakdown; Z is the sum of the wave impedance of the line at both ends of the switch and the wave impedance of both ends of the disconnector rod; t α is the breakdown delay, and R is the equivalent resistance in the stable arcing state.

[0147] In the said Step 4, the output value R B (t) of the arc resistance control module when receiving the arc extinction signal is expressed as:

[0148]

[0149] In the formula, g is the arc conductance; us is the instantaneous value of the voltage gradient; i s is the instantaneous value of the arc current; P s (g) is the arc heat dissipation power related to the arc conductance; τ s (g) is the insulation recovery time constant related to the arc conductance.

[0150] The above parts are all composed of components in the simulation software ATP-EMTP.

[0151] In order to verify the correctness of the model provided by the present invention, according to the VFTO test results of the 1100 kV GIS of Xi'an XD Electric Co., Ltd. in the Wuhan UHV AC Test Base, the measured data of the VFTO peak distribution during opening is compared with the simulation data of the original linear model and the model of the present invention as Figure 4 shown. The square root sum of the peak VFTO occurrence probability errors in each interval of the calculation model and the measured data is shown in Table 3.

[0152] Table 3 Square root sum of the peak VFTO occurrence probability errors in each interval

[0153]

[0154] In order to compare with the existing models, the breakdown expression of the linear model is used as a control and simulations are carried out to obtain the maximum peak value of VFTO under the full phase angle, and the results are shown in Table 4.

[0155] Table 4 Maximum peak value of VFTO

[0156]

[0157] As Figure 4 shown, compared with the existing models, the distribution probability of the model of the present invention is closer to the measured values; as shown in Table 3, in terms of simulating the distribution probability of VFTO, the model of the present invention is more accurate than the existing models, with smaller errors, and can better predict the magnitude and occurrence probability of VFTO in GIS. As shown in Table 4, in terms of predicting the peak value of VFTO, the model of the present invention is more accurate than the existing models, with smaller errors, closer to the actual situation, and can better predict the maximum VFTO generated by the disconnector, providing a basis for protecting the line.

[0158] A method for fitting and modeling the breakdown voltage characteristic interval between GIS disconnectors according to the present invention is based on the measured scatter plot of the breakdown voltage, performs optimal distribution fitting on it, predicts its distribution interval, and calculates its upper and lower bound curves for subsequent modeling. On the basis of the original simulation model, the randomness of the breakdown voltage is introduced and combined with the restriking arc module to form a new model, which together with the arc extinction module, switch control module, and arc resistance module forms a new dynamic restriking arc simulation model for GIS disconnectors.

[0159] The breakdown voltage characteristic interval fitting and modeling method for GIS disconnectors provided by the present invention realizes the simulation of the arc reignition and extinction phenomena in the switch gap. The VFTO simulation peak distribution is roughly consistent with the measured peak distribution, and the error between the maximum simulated VFTO and the maximum measured VFTO is very small, which can prove the correctness of the modeling method provided by the present invention.

Claims

1. A method for fitting the breakdown voltage distribution interval according to the breakdown voltage scatter plot, characterized in that: Based on the measured scatter plot of the breakdown voltage, perform an optimal distribution fitting on the scatter plot, predict its distribution interval, and calculate its upper and lower bound curves.

2. The method for fitting the breakdown voltage distribution interval according to the breakdown voltage scatter diagram as described in claim 1, wherein: It includes the following steps: S1: Plot the scatter plot of the breakdown voltage distribution: Based on different GIS layouts, disconnector types, and operating speeds, obtain the variation relationship of the breakdown voltage of the contact gap with time; S2: Based on the scatter plot of the entire time period, select the hyperbola model with the smallest error as the optimal model; S3: Divide the data of the entire time period into multiple time slices to capture the dynamic variation characteristics of the breakdown voltage distribution; S4: Quantify the probability distribution characteristics of the breakdown voltage within each time slice. According to the optimal distribution model selected in S3, calculate the probability density function PDF and cumulative distribution function CDF of each time slice; Probability density function PDF: Characterize the probability distribution form of the breakdown voltage; Cumulative distribution function CDF: Used to determine the confidence interval; S5: Generate the upper and lower bound curves of the entire time period distribution.

3. The method for fitting the breakdown voltage distribution range according to the breakdown voltage scatter diagram as described in claim 2, wherein: S3 includes the following steps: S3.

1. Sort the breakdown events in time series. With the target number of sparks n s as the constraint condition, adaptively adjust the time slice width △T to ensure that the number of sparks n k ∈[n s -δ, n s +δ], where δ is the tolerance threshold; S3.

2. Evaluate the goodness of fit through the log-likelihood value and test, and select the optimal distribution; Log-likelihood value: Measure the ability of the model to explain the data probability density. The larger the value, the better the fit; K-S test p-value: Quantify the difference between the empirical distribution and the hypothesized distribution. The larger the p-value, the better the fit; Considering its goodness of fit comprehensively, select the optimal distribution model for each time slice.

4. The method for fitting the breakdown voltage distribution interval according to the breakdown voltage scatter plot as claimed in claim 3, wherein: The implementation steps of S3.1 include: a1. Initialize the starting point T of the time slice start ; a2. Slide the time window until the cumulative number of sparks ≥ n s ; a3. Record the end point T end , calculate ΔT = T end - T start ; a4. Iterate until the entire time period is covered.

5. The method for fitting the breakdown voltage distribution range according to the breakdown voltage scatter plot as described in claim 3, wherein: In S3, according to the scatter distribution type within different time slices △T, the candidate distributions include: In the above formula, represents the probability density function of the random variable ; represents the magnitude of the breakdown voltage of positive and negative polarities; U represents the actual value of the breakdown voltage; μ represents the mean in the Gaussian distribution and the Laplace distribution; σ represents the standard deviation in the Gaussian distribution; θ represents the scale parameter of the Gamma distribution; b represents the scale parameter of the Laplace distribution; Γ(k) represents the Gamma function; k represents the shape parameter of the Gamma distribution.

6. The method for fitting the breakdown voltage distribution interval according to the breakdown voltage scatter diagram as described in claim 2, wherein: In S5, fit the scatter distribution range of the entire time period. Taking the reference curve as the maximum probability point of each time, that is, at the peak of the probability density function PDF, take the 95% confidence interval to find its offset based on the reference function; Specifically as follows: The positions X1 and X2 corresponding to the 95% confidence interval with cumulative probabilities of 0.025 and 0.975 are calculated by the formula: F(X1) = 0.025; F(X2) = 0.075; F(X) is the cumulative distribution function CDF of the corresponding distribution of the time slice; Calculate the offsets l1 and l2 corresponding to the peak voltage X Peak : l1 = X1 - X Peak ; l2 = X2 - X Peak ; Obtain the upper and lower bound curves G of each time slice based on the reference curve u (X), G d (X): G u (X) = G(X) + l1; G d (X) = G(X) + l2; In the formula, G(X) is the reference function.

7. Modeling method for dynamic restriking arc simulation model of GIS disconnector, characterized in that It includes the following steps: Step 1: According to the actual line parameters, set the equivalent parameters of the model, and the initial parameters of the restrike control module, arc extinction control module, arc resistance control module, and switch module; Step 2: Set the simulation step size. The simulation duration interval T satisfies ; Step 3: The reignition arc control module obtains the voltage signal difference △U across the disconnector contacts and outputs a reignition arc occurrence signal; △U = U 电源侧 -U 负载测 , sets the breakdown voltage between the disconnector contacts and When △U > 0, judge Output a reignition arc signal to the arc resistance control module; when △U < 0, judge Output a reignition arc signal to the arc resistance control module; Step 4: The arc extinction control module obtains the current signal I at the switch connection line t and the current signal I separated by a time interval (t-T) , and outputs an arc extinction occurrence signal; K is the current extinction threshold. When I t ×I (t-T) < 0 and |I t -I (t-T) | < K, an arc extinction signal is output to the arc resistance control module; if the above conditions are not met, the simulation step size is incremented and this step is repeated; Step 5: The switch module is set according to the original parameters. Determine the breakdown duration from the scatter plot of the breakdown voltage obtained by the experiment, and judge whether the switch operation is completed. If not, repeat Step 3 and Step 4; If the operation is completed, make corresponding adjustments to the state of the switch and the resistance value of the controlled resistor.

8. The modeling method of the GIS disconnector dynamic restriking arc simulation model according to claim 7, characterized in that: In the said Step 3, the expression of the breakdown voltage between the disconnector contacts is: In the formula, is the upper and lower bound function curves of the positive breakdown voltage over the entire time period; is the upper and lower bound function curves of the negative breakdown voltage over the entire time period; RAN(1) is a random number in the range of [0, 1].

9. The modeling method of the dynamic restriking arc simulation model of the GIS disconnector according to claim 7, characterized in that: In the step 3, the output value R B (t) of the arc resistance control module upon receiving the arc ignition signal is expressed as: wherein, R0 is the arc extinction resistance after the end of the last restriking arc, and R0 = 1×10 is taken at the first breakdown 12 ; Z is the sum of the line wave impedance at both ends of the switch and the wave impedance at both ends of the disconnecting switch rod; t α is the breakdown delay, and R is the equivalent resistance in the steady arcing state.

10. The modeling method of the GIS disconnector dynamic restriking arc simulation model according to claim 7, characterized in that: In step 4, the output value R of the arc resistance control module upon receiving the arc extinction signal B (t) is expressed as: where g is the arc conductance; u s is the instantaneous value of the voltage gradient; i s is the instantaneous value of the arc current; P s (g) is the arc heat dissipation power related to the arc conductance; τ s (g) is the insulation recovery time constant related to the arc conductance.

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