Power transmission line lightning resistance evaluation method based on unscented transformation method

Abstract

The invention relates to the technical field of power system evaluation, and discloses a power transmission line lightning resistance evaluation method based on an unscented transformation method, and the method comprises the following steps: building an electromagnetic transient model of a lightning stroke power transmission system, and obtaining the core parameters of a power transmission line; generating a Sigma point set based on an unscented transformation method, and enabling the allocated Sigma point set to meet mean and covariance characteristics of original probability distribution of the core parameters; an exponential regression model is adopted to carry out curve fitting on the insulator Voltage-Time critical curve, and an intersection point of the fitted curve and the insulator Voltage-Time critical curve is calculated; and calculating the lightning trip-out rate of the power transmission line in combination with the ground lightning density and the transverse attraction width of the lightning conductor to complete the lightning resistance evaluation of the power transmission line. According to the method, the unscented transformation method and the transient program are combined, the limitation of a traditional Monte Carlo method is broken through, the number of evaluated samples in the process is greatly reduced, the calculation time is remarkably shortened, and the calculation efficiency is improved.

Description

Technical Field

[0001] This invention relates to the field of power system assessment technology, and more specifically, to a method for assessing the lightning withstand performance of transmission lines based on the unscented transformation method. Background Technology

[0002] Transmission lines, as the arteries of the power system, are most susceptible to unplanned outages caused by lightning strikes. Lightning is an unpredictable phenomenon, and the lightning withstand capability of transmission lines is a crucial indicator for assessing the reliability of the transmission system. To accurately estimate the expected number of transmission line outages, the randomness of lightning phenomena must be considered. Currently, the mainstream methods for this task are based on Monte Carlo methods (MCM), which estimate the distribution of lightning overvoltages and the lightning protection performance of transmission lines by considering various statistical data related to lightning current characteristics, thereby predicting the expected number of outages. However, MCM often requires several minutes or even hours to complete a single estimation, necessitating significant computation time.

[0003] The Unscented Transform Method (UTM), a novel probability distribution propagation algorithm, approximates the probability distribution without delinearizing the function by selecting a Sigma point set, exhibiting higher accuracy and stability in nonlinear systems. However, a complete technical solution has not yet been developed for assessing lightning overvoltage in transmission lines, particularly lacking Sigma point weight optimization and log-normal distribution fitting methods tailored to the characteristics of lightning overvoltage distribution. This prevents existing technologies from being directly applied to lightning protection assessment scenarios for transmission lines. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for evaluating the lightning withstand performance of transmission lines based on the unscented transformation method. By employing a set of points related to the input statistical data to achieve an approximate nonlinear mapping, the lightning overvoltage on the insulator string is estimated, significantly reducing the number of samples evaluated during the process and substantially improving computational efficiency.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for evaluating the lightning withstand performance of transmission lines based on the unscented transformation method includes the following steps:

[0007] S1. Establish an electromagnetic transient model (ATP) of the lightning-struck transmission system. The electromagnetic transient model includes conductors, towers, grounding devices, and insulator strings. At the same time, obtain the core parameters of the transmission line, including the probability density functions of lightning current amplitude, wavefront time, and voltage phase angle.

[0008] S2. Generate a Sigma point set based on the Unscented Transform (UTM) method, and assign weights to the Sigma point set so that the assigned Sigma point set satisfies the mean and covariance characteristics of the original probability distribution of the core parameters; input the Sigma points one by one into the ATP model to obtain the maximum overvoltage at both ends of the insulator string corresponding to each Sigma point. and the time of occurrence of maximum overvoltage The exponential regression model was used to analyze the above. and Perform curve fitting and calculate the intersection point between the fitted curve and the insulator's voltage-time critical curve. ,in This refers to the critical breakdown voltage of the insulator.

[0009] S3, obtained based on S2 The sample is analyzed, and its mean and standard deviation are calculated. A log-normal distribution model is constructed to estimate the probability density function of the maximum overvoltage. The probability density function is then used to calculate the values ​​greater than a certain threshold. The probability of lightning strikes is calculated by combining the ground flash density and the lateral attraction width of the lightning protection wire. Complete the lightning resistance performance assessment of the transmission lines.

[0010] As a preferred embodiment of the present invention, in S1, when the lightning strike height of the tower is less than 60 meters, the tower in the electromagnetic transient model is modeled using a lossless transmission line model, and the propagation speed of the tower is approximately 80% of the speed of light.

[0011] As a preferred embodiment of the present invention, the wave impedance of the tower described in S1 pass Calculation, where For conductor height, The radius of the conductor;

[0012] Through Calculate the mutual impedance of conductors with the same height. ,in For the first The center of the root conductor and the first The distance between the centers of the root conductors;

[0013] Re-passing

[0014] Calculate the equivalent wave impedance of a multi-conductor tower system. In the formula The number of parallel conductors, when the tower's inclined planes and crossarms are ignored. =4.

[0015] As a preferred embodiment of the present invention, the grounding device in S1 is modeled as a resistor in the ATP model, wherein the resistance value is the impulse grounding impedance of the grounding system, and the impulse grounding impedance is the ratio of the grounding potential rise to the peak value of the applied current.

[0016] As a preferred embodiment of the present invention, the waveform of the lightning current in S1 is represented by the sum of seven Heidler functions, as shown in the following formula: In the formula, for The lightning current at any given moment; For the first The lightning current amplitude of each Heidler function; , The first Wavefront time and wavetail time of a Heidler function; For the first The waveform exponent of a Heidler function;

[0017] and , , , The parameter selection satisfies:

[0018]

[0019]

[0020]

[0021]

[0022] In the formula, , ), ; This is the first peak value of the current. This is the second peak value of the current. The time interval between 10% and 90% of the first peak; , and The value of satisfies the preset range.

[0023] As a preferred embodiment of the present invention, the random input variable vector in S2 Its mean Covariance ;

[0024] The maximum overvoltage model for insulator strings is as follows: The statistical parameters of the maximum lightning overvoltage are obtained by formula... ,Mode Estimate;

[0025] The average value of the maximum overvoltage. The standard deviation of the maximum overvoltage. As weight, For =Sigma= points, This represents the total number of Sigma points.

[0026] The Sigma point S is obtained through the formula , , calculate;

[0027] Weight Through ,Mode calculate;

[0028] in, The number of random variables, with a value of 2; Used to reduce prediction errors and provide degrees of freedom Set to == 0.15;

[0029] The total number of Sigma points Through calculate.

[0030] As a preferred embodiment of the present invention, the exponential regression model in S2 is: In the formula, and For a given coefficient;

[0031] The voltage-time critical curve of the insulator is as follows: As shown; in the above formula, For time, This is the length of the insulator string;

[0032] The intersection This is the intersection of the curves defined by the Voltage-Time Critical Curve Formula and the Exponential Regression Model Formula for insulators.

[0033] As a preferred embodiment of the present invention, the maximum overvoltage in S3 is greater than... The probability is the ratio of the number of insulator breakdowns to the total number of simulations. .

[0034] As a preferred embodiment of the present invention, the lateral attraction width of the lightning protection wire in S3 is obtained by means of... calculate, The lateral attraction width of the lightning protection wire, The spacing of the lightning protection wires is set to 0 here due to the tower structure; The average equivalent attraction radius;

[0035] The average equivalent attraction radius is expressed by the formula calculate, The average height of the conductor most susceptible to lightning strikes;

[0036] The average height of the lightning protection wire is determined by the formula. ; The height of the lightning protection wire at the tower, The height of the lightning protection wire at the midpoint of the span. The lightning protection wire is sag.

[0037] As a preferred embodiment of the present invention, the lightning tripping rate in S3 By the following formula:

[0038] In the formula, For ground flash density, The lateral attraction width of the lightning protection wire, For the maximum overvoltage greater than The probability of.

[0039] The beneficial technical effects of this invention are:

[0040] The method combining Unscented Transformation (UTM) and Transient Procedure (ATP) overcomes the limitations of the traditional Monte Carlo method (MCM), significantly reduces the number of samples evaluated during the process, greatly reduces computation time, and improves computational efficiency.

[0041] By replacing a large number of random samples with a small number of Sigma points, misjudgments of lightning strike risk due to technical biases can be avoided. This helps to provide a more reliable quantitative basis for lightning protection of transmission lines and significantly shortens the calculation cycle. It also helps to improve the timeliness of lightning resistance performance assessment of transmission lines and provides technical support for emergency decision-making.

[0042] It can avoid excessive investment in materials such as insulators and lightning protection wires, reduce maintenance costs during the operation and maintenance phase, help control the economic investment of transmission lines throughout their entire life cycle from design to operation, and shorten the design cycle.

[0043] Accurate assessment and risk prediction can reduce the tripping rate of transmission lines due to lightning strikes, reduce unplanned outages, and help ensure the overall power supply stability of the power grid. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating the present invention. Detailed Implementation

[0045] In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, the specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0046] Combination Figure 1 The present invention provides the following embodiments:

[0047] A method for evaluating the lightning withstand performance of transmission lines based on the unscented transformation method includes the following steps:

[0048] S1. Establish an electromagnetic transient model (ATP) of the lightning-struck transmission system. The electromagnetic transient model includes conductors, towers, grounding devices, and insulator strings. At the same time, obtain the core parameters of the transmission line, including the probability density functions of lightning current amplitude, wavefront time, and voltage phase angle.

[0049] S2. Generate a Sigma point set based on the Unscented Transform (UTM) method, and assign weights to the Sigma point set so that the assigned Sigma point set satisfies the mean and covariance characteristics of the original probability distribution of the core parameters; input the Sigma points one by one into the ATP model to obtain the maximum overvoltage at both ends of the insulator string corresponding to each Sigma point. and the time of occurrence of maximum overvoltage The exponential regression model was used to analyze the above. and Perform curve fitting and calculate the intersection point between the fitted curve and the insulator's voltage-time critical curve. ,in This refers to the critical breakdown voltage of the insulator.

[0050] S3, obtained based on S2 The sample is analyzed, and its mean and standard deviation are calculated. A log-normal distribution model is constructed to estimate the probability density function of the maximum overvoltage. The probability density function is then used to calculate the values ​​greater than a certain threshold. The probability of lightning strikes is calculated by combining the ground flash density and the lateral attraction width of the lightning protection wire. Complete the lightning resistance performance assessment of the transmission lines.

[0051] Furthermore, in S1, when the lightning strike height of the tower is less than 60 meters, the tower in the electromagnetic transient model is modeled using a lossless transmission line model, and the propagation speed of the tower is approximately 80% of the speed of light, with a value of approximately... m / s. When the tower height is less than 60 meters, the attenuation effect of its structure on electromagnetic propagation is negligible. The tower structure includes crossarms, horizontal components, etc. The lossless transmission line model can accurately match the electromagnetic propagation law of the tower in this scenario. The propagation speed of 80% of the speed of light is a measured fitting value based on the tower material properties and structural dimensions, which conforms to the actual electromagnetic transient propagation characteristics. This avoids electromagnetic propagation errors caused by improper model selection, ensures the modeling accuracy of the tower part, and provides a reliable model foundation for subsequent insulator string overvoltage calculations.

[0052] Furthermore, the wave impedance of the tower described in S1 Through the following formula Calculation, where For conductor height, The radius of the conductor;

[0053] Through Calculate the mutual impedance of conductors with the same height. ,in For the first The center of the root conductor and the first The distance between the centers of the root conductors;

[0054] Re-passing Calculate the equivalent wave impedance of a multi-conductor tower system. In the formula The number of parallel conductors, when the tower's inclined planes and crossarms are ignored. =4.

[0055] The self-wave impedance formula is based on the principle of electromagnetic radiation from conductors, reflecting the impedance characteristics of a single conductor. The mutual wave impedance formula considers the electromagnetic coupling effect between conductors, quantifying the mutual influence between adjacent conductors. The equivalent wave impedance simplifies the multi-conductor system into a single transmission line model through weighted averaging, balancing computational complexity and accuracy. It accurately quantifies the electromagnetic impedance characteristics of the tower, avoiding overvoltage simulation errors caused by impedance calculation deviations. The equivalent treatment of multi-conductor systems ensures model realism while simplifying the subsequent ATP model calculation process, improving evaluation efficiency.

[0056] As a preferred embodiment of the present invention, the grounding device in S1 is modeled as a resistor in the ATP model, wherein the resistance value is the impulse grounding impedance of the grounding system, and the impulse grounding impedance is the ratio of the grounding potential rise to the peak value of the applied current.

[0057] The core of a grounding system's current-discharging capacity during a lightning strike depends on its impulse grounding impedance, a parameter that directly reflects the relationship between the rise in grounding potential and the peak value of the lightning current. Modeling in terms of resistance aligns with the simulation logic of the ATP model for linear components, enabling rapid response to transient changes in lightning current. It accurately simulates the grounding system's discharge effect on lightning current, realistically reflecting the grounding device's suppression effect on insulator string overvoltage. Resistance-based modeling simplifies the construction and calculation of the ATP model, improving the efficiency of electromagnetic transient simulation.

[0058] As a preferred embodiment of the present invention, the waveform of the lightning current in S1 is represented by the sum of seven Heidler functions, as shown in the following formula: In the formula, for Lightning current at any given time, measured in kA; For the first The lightning current amplitude of each Heidler function, in kA; , The first The wavefront and wavetail times of each Heidler function, in units of... ; For the first The waveform exponent of a Heidler function;

[0059] and , , , The parameter selection satisfies:

[0060]

[0061]

[0062]

[0063]

[0064] In the formula, , ), ; This is the first peak value of the current. This is the second peak value of the current. The time interval between 10% and 90% of the first peak; , and The value of the value satisfies the preset range. This embodiment provides the following range for reference:

[0065]

[0066] .

[0067] The combination of seven Heidler functions can cover the multi-peak, wide-time-domain characteristics of negative lightning discharge, with each function corresponding to the lightning current variation pattern at different stages. The parameter formulas are obtained by fitting measured lightning data, which can accurately match the current waveform characteristics of lightning strikes of different intensities. It realistically reproduces the dynamic change process of lightning current during actual lightning strikes, providing an excitation source that conforms to real-world scenarios for the ATP model. The parameterized settings can be adapted to lightning strike environments of different regions and intensities, improving the versatility and accuracy of the evaluation method.

[0068] As a preferred embodiment of the present invention, the random input variable vector in S2 Its mean Covariance ;

[0069] The maximum overvoltage model for insulator strings is as follows: The mean and standard deviation of the maximum lightning overvoltage are respectively obtained by formula... ,Mode Estimate;

[0070] The average value of the maximum overvoltage. The standard deviation of the maximum overvoltage. As weight, For =Sigma= points, This represents the total number of Sigma points.

[0071] The Sigma point S is obtained through the formula , , calculate;

[0072] Weight Through ,Mode calculate;

[0073] in, The number of random variables, with a value of 2; Used to reduce prediction errors and provide degrees of freedom Set to == 0.15;

[0074] The total number of Sigma points Through calculate.

[0075] The random input variable vector focuses on two key influencing factors: peak lightning current and voltage phase angle. Their mean and covariance are defined according to statistical laws. The Sigma point generation and weight allocation formulas are based on the principle of unscented transformation, ensuring that a small number of Sigma points can accurately approximate the mean and covariance of the original probability distribution. The mean and standard deviation estimation formulas quantify the statistical characteristics of overvoltage through weighted summation. Replacing a massive number of random samples with a small number of Sigma points significantly reduces the number of simulations in the ATP model, improving evaluation efficiency. The optimized design of weights and Sigma points ensures the accuracy of probability distribution propagation, avoiding statistical errors caused by insufficient sample size, thus balancing efficiency and accuracy.

[0076] Furthermore, the exponential regression model described in S2 is... In the formula, and For a given coefficient;

[0077] The voltage-time critical curve of the insulator is as follows: As shown; in the above formula, For time (μs). The length of the insulator string is (m).

[0078] The intersection point (VUT, tUT) is the intersection point of the curves defined by the Voltage-Time critical curve formula for insulators and the exponential regression model formula.

[0079] The exponential regression model can effectively fit the nonlinear relationship between the maximum overvoltage and the occurrence time, which is consistent with the decay characteristics of lightning overvoltage; the voltage-time critical curve of the insulator is based on the insulator breakdown mechanism and quantifies the critical breakdown voltage at different time scales; the intersection calculation accurately locates the breakdown critical state of the insulator by solving simultaneous equations.

[0080] Furthermore, the probability that the maximum overvoltage is greater than VUT, as stated in S3, is the ratio of the number of insulator breakdowns to the total number of simulations. It simplifies the calculation process of overvoltage over-limit probability, eliminating the need for complex integration calculations; it is based on actual simulation results, ensuring the authenticity and reliability of the probability values ​​and providing accurate input for trip rate calculation.

[0081] Furthermore, the lateral attraction width of the lightning protection wire described in S3 is obtained through a formula. calculate, The lateral attraction width of the lightning protection wire, The spacing of the lightning protection wires is set to 0 here due to the tower structure; The average equivalent attraction radius;

[0082] The average equivalent attraction radius is expressed by the formula calculate, The average height of the conductor most susceptible to lightning strikes is the lightning protection wire. The formula for the lateral attraction width of the lightning protection wire is based on the attraction principle of the lightning leader. The power function relationship between the average equivalent attraction radius and the conductor height conforms to the physical laws of lightning strikes. The calculation of the average height of the lightning protection wire takes into account the sag effect and can truly reflect the actual spatial position of the lightning protection wire.

[0083] The average height of the lightning protection wire is determined by the formula. ; The height of the lightning protection wire at the tower, The height of the lightning protection wire at the midpoint of the span. The lightning protection wire is sag.

[0084] As a preferred embodiment of the present invention, the lightning tripping rate in S3 By the following formula: In the formula, For ground flash density, The lateral attraction width of the lightning protection wire, For the maximum overvoltage greater than The probability of.

[0085] This method enables a quantitative assessment of the lightning resistance performance of transmission lines. The tripping rate directly reflects the risk of the line being struck by lightning and shut down. The formula comprehensively covers key influencing factors related to lightning strikes, and the assessment results have strong engineering applicability, providing a direct decision-making basis for line lightning protection design and operation and maintenance optimization.

[0086] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for evaluating the lightning withstand performance of transmission lines based on the unscented transformation method, characterized in that, Includes the following steps: S1. Establish an electromagnetic transient model (ATP) of the lightning-struck transmission system. The electromagnetic transient model includes conductors, towers, grounding devices, and insulator strings. At the same time, obtain the core parameters of the transmission line, including the probability density functions of lightning current amplitude, wavefront time, and voltage phase angle. S2. Generate a Sigma point set based on the Unscented Transformation (UTM) method, and assign weights to the Sigma point set so that the assigned Sigma point set satisfies the mean and covariance characteristics of the original probability distribution of the core parameters. The Sigma points are input one by one into the ATP model to obtain the maximum overvoltage across the insulator string corresponding to each Sigma point. and the time of occurrence of maximum overvoltage ; The exponential regression model was used to analyze the above. and Perform curve fitting and calculate the intersection point between the fitted curve and the insulator's voltage-time critical curve. ,in This refers to the critical breakdown voltage of the insulator. S3, obtained based on S2 The sample is analyzed, and its mean and standard deviation are calculated. A log-normal distribution model is constructed to estimate the probability density function of the maximum overvoltage. The probability density function is then used to calculate the values ​​greater than a certain threshold. The probability of lightning strikes is calculated by combining the ground flash density and the lateral attraction width of the lightning protection wire. Complete the lightning resistance performance assessment of the transmission lines.

2. The method for evaluating the lightning withstand performance of transmission lines based on the unscented transformation method according to claim 1, characterized in that, In S1, when the lightning strike height of the tower is less than 60 meters, the tower in the electromagnetic transient model is modeled using a lossless transmission line model, and the propagation speed of the tower is approximately 80% of the speed of light.

3. The method for evaluating the lightning withstand performance of transmission lines based on the unscented transformation method according to claim 2, characterized in that, The wave impedance of the tower described in S1 pass Calculation, where For conductor height, The radius of the conductor; Through Calculate the mutual impedance of conductors of the same height ,in For the first The center of the root conductor and the first The distance between the centers of the root conductors; Re-passing Calculate the equivalent wave impedance of a multi-conductor tower system. In the formula The number of parallel conductors, when the tower's diagonal lines and crossarms are ignored. =4.

4. The method for evaluating the lightning withstand performance of transmission lines based on the unscented transformation method according to claim 1, characterized in that, The grounding device described in S1 is modeled as a resistor in the ATP model. The resistance value is the impulse grounding impedance of the grounding system, which is the ratio of the grounding potential rise to the peak value of the applied current.

5. The method for evaluating the lightning withstand performance of transmission lines based on the unscented transformation method according to claim 1, characterized in that, The waveform of the lightning current described in S1 is represented by the sum of seven Heidler functions, as shown in the following formula: In the formula, for The lightning current at any given moment; For the first The lightning current amplitude of each Heidler function; , The first Wavefront time and wavetail time of each Heidler function; For the first The waveform exponent of a Heidler function; and , , , The parameter selection satisfies: In the formula, , ), ; This is the first peak value of the current. This is the second peak value of the current. The time interval between 10% and 90% of the first peak; , and The value of satisfies the preset range.

6. The method for evaluating the lightning withstand performance of transmission lines based on the unscented transformation method according to claim 1, characterized in that, S2 random input variable vector Its mean Covariance ; The maximum overvoltage model for insulator strings is as follows: The statistical parameters for maximum lightning overvoltage include the mean and standard deviation. Mean passed Calculation, standard deviation Estimate; The average value of the maximum overvoltage. The standard deviation of the maximum overvoltage. As weight, For Sigma points, This represents the total number of Sigma points. The Sigma point Through , , calculate; Weight Through ,Mode calculate; in, The number of random variables, with a value of 2; Used to reduce prediction errors and provide degrees of freedom Set to == 0.15; The total number of Sigma points Through calculate.

7. The method for evaluating the lightning withstand performance of transmission lines based on the unscented transformation method according to claim 1, characterized in that, The exponential regression model described in S2 is In the formula, and For a given coefficient; The voltage-time critical curve of the insulator is as follows: As shown; in the above formula, For time, This is the length of the insulator string; The intersection This is the intersection of the curves defined by the Voltage-Time Critical Curve Formula and the Exponential Regression Model Formula for insulators.

8. The method for evaluating the lightning withstand performance of transmission lines based on the unscented transformation method according to claim 3, characterized in that, The maximum overvoltage mentioned in S3 is greater than The probability is the ratio of the number of insulator breakdowns to the total number of simulations. .

9. The method for evaluating the lightning withstand performance of transmission lines based on the unscented transformation method according to claim 1, characterized in that, The lateral attraction width of the lightning protection wire described in S3 is obtained through a method... calculate, The lateral attraction width of the lightning protection wire, The spacing of the lightning protection wires is set to 0 here due to the tower structure; The average equivalent attraction radius; The average equivalent attraction radius is expressed by the formula calculate, The average height of the conductor most susceptible to lightning strikes; The average height of the lightning protection wire is determined by the formula. ; The height of the lightning protection wire at the tower, The height of the lightning protection wire at the midpoint of the span. The lightning protection wire is sag.

10. The method for evaluating the lightning withstand performance of transmission lines based on the unscented transformation method according to claim 9, characterized in that, The lightning tripping rate mentioned in S3 By the following formula: In the formula, For ground flash density, The lateral attraction width of the lightning protection wire, For the maximum overvoltage greater than The probability of.

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