A direct calibration method for traveling wave arrival time difference of transmission line faults based on waveform image translation matching

Abstract

This invention relates to a direct calibration method for the arrival time difference of traveling waves in transmission line faults based on waveform image translation matching, belonging to the field of power system protection technology. The invention reads the fault waveform and the proposed ranging algorithm, extracts the waveform centerline; calculates the average slope of each point based on the waveform centerline coordinates, selects a unique start-end point pair, and calibrates the region of interest (ROI) required for ranging; calculates the coarse pixel distance between ROIs and determines the translation interval, and performs translation in unit pixel steps based on this interval; calculates the area difference within the ROI during the translation process, determines the optimal matching displacement from the point of minimum area difference, converts it into a time difference, and substitutes it into the ranging algorithm to achieve ranging.

Description

Technical Field

[0001] This invention relates to a method for directly calibrating the arrival time difference of traveling waves in transmission line faults based on waveform image translation matching, belonging to the field of power system protection technology. Background Technology

[0002] The power grid connects electricity production and consumption, serving as a crucial network platform, a central link in energy transition, and a core hub for carbon emission reduction in the power system. my country's vast territory and the inverse distribution of energy production bases and load consumption centers necessitate the formation of long-distance, high-capacity power transmission as the backbone of the power grid. With the increasing prevalence of high-voltage and high-efficiency power systems, the system's tolerance and resilience to faults have significantly weakened. Faults in high-voltage, long-distance, high-capacity transmission lines pose serious risks, making line inspection difficult and resulting in substantial losses due to outages. Accurate and timely location of line faults is of paramount importance for rapid fault repair and hazard identification, ensuring the safe and stable operation of the system, reducing transmission delays, guaranteeing reliable power delivery, and promoting societal energy transition and carbon emission reduction.

[0003] Traditional time-difference traveling wave ranging algorithms generally rely on a fixed rule to accurately calibrate the arrival times of each wavefront required for ranging, and then perform subtraction to achieve the distance measurement. Considering that the measured waveform is significantly affected by the field fault environment, calibrating each wavefront individually is difficult, and it is hard to find the same reference point for two wavefronts based on the same rule. This means the subtraction result itself contains a large error, causing the final ranging result to deviate from the true value. Therefore, researching a method that can adaptively find the wavefront reference point and accurately measure the equidistant intervals of wavefronts is of great value for improving the accuracy of traveling wave ranging and enhancing the engineering application of traveling waves. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a direct calibration method for the arrival time difference of traveling waves in transmission line faults based on waveform image translation matching, so as to realize the calibration of the wavefront interval of the fault waveform, thereby effectively calculating the time difference between the wavefronts required for ranging and realizing ranging.

[0005] The technical solution of this invention is: a method for directly calibrating the arrival time difference of traveling waves in transmission line faults based on waveform image translation matching, the specific steps of which are as follows:

[0006] Step 1: Read the fault waveform and the ranging algorithm to be used, and extract the center line of the waveform based on the fault waveform image.

[0007] Step 2: Calculate the average slope of each point based on the centerline coordinates of the waveform, select a unique start and end point pair and mark the region of interest required for ranging. Determine whether the wave head required for the ranging algorithm is met based on the number of regions of interest. If it is met, proceed to Step 3. If it is not met, read the new waveform and proceed to Step 1.

[0008] Step 3: Calculate the coarse pixel distance between regions of interest and determine the translation interval. Based on this interval, translate the wavefront to be matched in unit pixel steps and match it with another wavefront required for time difference calculation.

[0009] Step 4: Calculate the area difference within the region of interest during the translation process, generate the translation distance-area difference curve, determine the optimal matching displacement from the minimum point of this curve, and directly convert it into time difference through a linear correspondence, which is then substituted into the ranging algorithm to finally achieve ranging.

[0010] Step 1 specifically refers to:

[0011] Step 1.1: Read the fault waveform and the ranging algorithm to be used. The method described in this invention is not sensitive to current traveling waves and voltage traveling waves. Therefore, both the fault current waveform and the fault voltage waveform can be used as fault waveforms for time difference calibration.

[0012] Step 1.2: Based on the read fault waveform, extract the waveform center line using the grayscale centroid algorithm. The formula for the grayscale centroid algorithm is:

[0013]

[0014] In the formula, k is the horizontal pixel width of the waveform image; h(x k ,y i ) represents the grayscale value corresponding to the k-th column coordinate of the waveform image; M represents the pixel width of the corresponding column of the waveform curve. According to formula (1), the waveform curve can be obtained from low to high x-coordinate (x) k ,y k The centerline formed by connecting the point sets is used as an approximation.

[0015] Step 2 specifically includes:

[0016] Step 2.1: Based on the waveform centerline coordinates extracted in Step 1, and under the premise that the initial direction of change is taken as the positive direction, from x... s =1 to start traversing, calculate the left and right average slope k of the i-th pixel of the waveform center line. l (i), k r (i). The left and right sides of the i-th pixel are n a (n a ≠1 and n a Formula for calculating the average slope of an even number of pixels:

[0017]

[0018] Where, n a The number of pixels in the left and right neighboring regions of each point can be taken as 0.5% to 1% of the total horizontal pixels of the window.

[0019] Step 2.2: Based on the average slope obtained in Step 2.1, calculate the change in the average slope Δk, thereby determining the sets A and B of the rising edge start and end points. If Δk(i) of the i-th point is greater than a certain threshold, then point (x i ,y i ) belongs to the starting set A. If the Δk(i) of the i-th point is less than a certain threshold, then the point (x) belongs to the starting set A. i ,y i If the endpoint set belongs to B, then the definition of the change in average slope can be formed:

[0020] Δk(i)=k r (i)-k l (i)(3)

[0021] Considering that the varying complexity of actual waveforms may cause certain calibration errors, the tuning formula is provided to ensure the applicability of the method of this invention:

[0022]

[0023] In this invention, k TH A tangent value of 60° to 75° can be used.

[0024] Step 2.3: Based on the start and end point sets A and B selected in Step 2.2, further extract the most significant feature points using the positional and distance constraints of adjacent start and end point coordinates, and use these as the unique start and end point pairs a(x a ,y a b(x) b ,y b Define η as the percentage of the horizontal distance between the start and end points relative to the total horizontal pixels of the waveform. x The percentage of the distance between the start and end points to the total vertical pixels of the waveform is η. D The difference between the average slope to the right of the starting point and the average slope to the left of the ending point is Δk. ab Its formula is:

[0025]

[0026] In the formula, X TOTAL This represents the total horizontal pixels of the waveform. Y TOTAL k represents the total vertical pixels of the waveform. r (a) represents the average slope to the right of the starting point. k l (b) is the average slope to the left of the endpoint.

[0027] Knowledge of abrupt changes and wavefront spacing in traveling waves can be translated into geometric constraints on the waveform image region. These geometric constraints can be expressed as: the starting and ending points are adjacent in horizontal coordinates; the distance between the starting and ending points exceeds a certain threshold; and the average right slope of the starting point is close to the average left slope of the ending point. The formulas are as follows:

[0028]

[0029] In the formula, ε x ε is the threshold value for the horizontal axis. k D is the average slope threshold; TH ε is the distance threshold. Combined with extensive experimental data, tests show that ε... x A dosage of 2% to 15% is acceptable. ε k A value of 0.1 to 0.7 is acceptable. (D) TH A range of 15% to 30% can be taken. Starting with a(x) a ,y a ), endpoint b(x) b ,y b Using the coordinates as a reference, the start and end points of the waveform ROI rectangular region can be determined as (x, y). a -ε,y a +ε), (x b +ε,y b -ε).

[0030] Step 2.4: Determine whether to stop searching for ROIs based on the ranging algorithm. If yes, retain the current ROI information and increment the number of identified ROIs by 1. Otherwise, it means that ROI identification still needs to be continued in the current image, so traverse the areas to be analyzed after the identified ROIs and proceed to Step 2.2.

[0031] Step 2.5: Determine if the number of identified regions of interest (ROIs) meets the wavefront count required for time difference calculation. If it does, proceed to Step 3. Otherwise, if two waveforms have already been read, determine that ROI calibration has failed and exit ranging. If the required number of waveforms is not met, continue reading and visualizing fault data, and proceed to Step 1.

[0032] Step 3 specifically refers to:

[0033] Step 3.1: Define the distance between the centers of the two regions of interest in the waveform as the coarse pixel distance x. rough Coarse pixel distance definition:

[0034] x rough =x ROIB -x ROIA (7)

[0035] In the formula, x ROIi(i = A, B) are the x-coordinates of the center points of the fixed region of interest and the region of interest to be translated, respectively.

[0036] Step 3.2: Define the translation interval of the region of interest as [p a ,p b The definition is determined based on the coarse pixel distance in Step 3.1:

[0037] [p a ,p b ] = [x rough -w,x rough +w] (8)

[0038] In the formula, w is the interval offset, w = max{w1,w2} / 2, and w1 and w2 are the horizontal pixel widths of the two regions of interest, respectively.

[0039] Step 3.3: Continuously translate the region of interest to be translated within the translation interval towards the fixed region of interest by unit pixel distance, and match it.

[0040] Step 4 specifically refers to:

[0041] Step 4.1: Calculate the number of pixels between two rising edges in the region of interest during each translation process, defined as the area difference S. Δ This generates the translation distance-area difference curve. The area S is defined as follows:

[0042]

[0043] In the formula, f(x,y) is the traveling wave waveform function, and y a +ε is the lower bound of the ordinate, x b +ε、x a -ε represents the upper and lower limits determined by the ROI.

[0044] The area enclosed by the two translated ROI waveforms can be obtained by the difference between the areas enclosed by the two ROI waveforms and the lower bound of the fixed ROI's ordinate. The area enclosed by the two wavefront ROIs can be obtained by the difference between the areas formed by the two waveforms and the lower bound of the ROI. The area difference S Δ Definition:

[0045]

[0046] In the formula, S Δ S represents the difference in ROI area. A S′ B f represents the area enclosed by the group of two points within a fixed ROI and the lower bound of the ROI, respectively. A (x A ,y Af is a fixed-point group traveling wave waveform function. B (x B +Δx,y B +Δy) is the traveling wave waveform function after the point group to be translated is translated. b +ε、x a -ε represents the upper and lower limits determined by the fixed ROI.

[0047] Considering the discrete implementation in computers, the ROI area difference is obtained by intersecting and merging the sets of pixels enclosed by curves:

[0048] S Δ =S A -S B =(S A ∪S B )-(S A ∩S B (11)

[0049] Step 4.2: Define the distance the region of interest to be translated is Δx as the correction pixel distance when the area difference between the two rising edges during the fine-tuning translation process is minimized. refine Based on the x-coordinate b of the minimum point of the translation distance-area difference curve from Step 4.1. min The corrected pixel distance definition can be obtained as follows:

[0050] Δx refine =b min ×step-w (12)

[0051] In the formula, b min is the x-coordinate of the point corresponding to the minimum value of the area difference curve. step is the translation step size.

[0052] Step 4.3: Define the sum of the coarse pixel distance and the corrected pixel distance as the optimal matching displacement x between the two wavefronts. pixel This reflects the optimal pixel spacing between the two wavefronts. The optimal matching displacement is defined as follows:

[0053] x pixel =x rough +Δx refine (13)

[0054] By utilizing the linear correspondence between pixel intervals and time axis intervals, the optimal matching displacement can be directly converted into a time difference Δt. The time difference conversion formula is as follows:

[0055] Δt AB =|t A0 -t B0 -x pixel ·N data / (f s ·N pixel(14)

[0056] In the formula: t i0 (i = A, B) are the absolute time scales of the starting time windows for the fixed waveform and the waveform to be shifted left, respectively. N pixel N represents the effective pixel width of the waveform horizontally. data To truncate the data width. s The sampling rate needs to be converted to MHz.

[0057] Step 4.4: Substitute the time difference obtained in Step 4.3 into the ranging algorithm to achieve ranging.

[0058] The beneficial effects of this invention are: it can reliably determine the group of abrupt change points of traveling waves from the perspective of macroscopic image insight by utilizing the characteristics of the average slope change of the waveform curve, transforming theoretical knowledge into geometric constraints of the waveform region, realizing the detection of the region of interest, adaptively obtaining the optimal matching displacement and directly converting it into the time difference required for ranging, avoiding the difficulty of calibrating the precise arrival time of each wavefront one by one in traditional ranging methods, and can be widely applied to various time difference traveling wave ranging principles such as single-end, double-end, and multi-end. It has the advantages of being intuitive, highly interpretable, and robust, and can effectively avoid errors caused by inconsistent selection of wavefront reference points and mismeasurements caused by miscalibration of reference points under noisy conditions. It has great value for improving the engineering application effect of traveling waves. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of a 220kV transmission line model;

[0060] Figure 2 It is a traveling wave waveform diagram of the fault current;

[0061] Figure 3 This is a diagram showing the specific implementation steps of Step 1;

[0062] Figure 4 This is the result of extracting the center line using the grayscale centroid method;

[0063] Figure 5 This is a diagram showing the specific implementation steps of Step 2;

[0064] Figure 6 This is a diagram showing the calibration results of the region of interest for the first wave head of the waveform;

[0065] Figure 7 This is a diagram showing the calibration results of the region of interest (ROI) of the reflected wave from the first fault point in the waveform.

[0066] Figure 8 This is a diagram showing the specific implementation steps of Step 3;

[0067] Figure 9 This is a diagram showing the specific implementation steps of Step 4;

[0068] Figure 10 This is a schematic diagram of the area difference during the translation process;

[0069] Figure 11 It is a curve of translation distance versus area difference. Detailed Implementation

[0070] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0071] Example 1: Building a system based on PSCAD / EMTDC Figure 1 The 220kV transmission line model shown has 4 outgoing lines on the m-side bus (excluding the fault line itself) and 3 outgoing lines on the n-side bus (excluding the fault line itself). The faulty line is 100km long and an A / B phase-to-phase fault occurs 75km from the m-end observation point. The transition resistance is 50Ω, the fault angle is 80°, and the sampling rate is 1MHz. 35dB Gaussian white noise is added to the fault current simulation data obtained at the line end. The fault current waveform is as follows. Figure 2 As shown. The specific implementation steps are as follows:

[0072] Step 1: Read the fault waveform and the ranging algorithm to be used. Extract the center line of the waveform from the fault waveform image. The specific implementation steps are as follows: Figure 3 As shown.

[0073] Step 1.1: Read the fault current waveform at the m end of the transmission line and use the traditional single-end ranging algorithm.

[0074] Step 1.2: Based on the read fault waveform, extract the waveform centerline using the grayscale centroid algorithm, such as... Figure 4 The effect shown.

[0075] Step 2: Calculate the average slope of each point based on the coordinates of the waveform centerline, select a unique start-end point pair, and calibrate the region of interest required for distance measurement. The specific implementation steps are as follows: Figure 5 As shown, the advantage of this step is that it graphically presents the fault traveling wave data, reliably determines the group of abrupt change points of the traveling wave from a macroscopic perspective by utilizing the average slope change of the waveform curve, and transforms theoretical knowledge into geometric constraints of the waveform region, thereby achieving reliable detection of ROI.

[0076] Step 2.1: Based on the waveform centerline coordinates extracted in Step 1, the direction of increasing x-coordinate is defined as the positive direction. Starting from xs=1, traverse the waveform centerline, taking 10 pixels for each pixel, and calculate the left and right average slopes kl and kr of each pixel.

[0077] Step 2.2: Based on the average slope obtained in Step 2.1, calculate the change in the average slope Δk, thereby determining the starting and ending sets A and B of the rising edge. Select the threshold for the change in the average slope kTH = tan(75°). When kTH > tan(75°), the point is considered to belong to the starting set A, and when kTH < -tan(75°), the point is considered to belong to the ending set B.

[0078] Step 2.3: Based on the start and end point sets A and B selected in Step 2.2, εx is set to 8%, εk to 0.7, and DTH to 15%. Using positional and distance constraints on adjacent start and end point coordinates, the most significant feature points are further extracted, resulting in the unique start and end point pair a1(331,730) and b1(355,135) for the initial traveling wave. ε is set to 30px, yielding the start point coordinates (301,760) and end point coordinates (385,105) of the initial traveling wave's region of interest. The region of interest calibration results for the first wave head are as follows: Figure 6 As shown in Table 1.

[0079]

[0080] Table 1: Screening Results of the Region of Interest Start and End Points for the First Wave Head in Single-Ended Ranging

[0081] Step 2.4: Based on the traditional single-end ranging algorithm, stop searching for ROIs, retain the current ROI information, and increment the number of identified ROIs by 1, num=1.

[0082] Step 2.5: According to the traditional single-end ranging algorithm, two wavefronts are required. The current waveform image has only identified one region of interest (ROI), which is deemed insufficient to meet the algorithm's requirements. Since the number of images read is insufficient for two images, the same fault data is read and visualized, proceeding to Step 1.2. The ROI is identified until the region to be analyzed after the first wavefront ROI is identified again before stopping the search. The current ROI information is retained, and the number of identified ROIs is incremented by 1, i.e., iterating from xs = 385 onwards. Using the same constraints, the unique start and end point pair a2(569, 609) and b2(589, 336) of the first fault point reflected wave are obtained, corresponding to the start coordinates (539, 639) and end coordinates (619, 306) of the ROI. The ROI calibration result of the first fault point reflected wave is as follows. Figure 7 As shown in Table 2, the number of wavefronts num = 2 at this time, which is considered to meet the algorithm conditions, and proceed to Step 3.

[0083]

[0084] Table 2: Screening Results of Region of Interest Start and End Points for First Fault Point Reflected Waves in Single-Ended Ranging

[0085] Step 3: Calculate the coarse pixel distance between regions of interest and determine the translation interval. Based on this interval, perform translation with a unit pixel step. The specific implementation steps are as follows: Figure 8 As shown.

[0086] Step 3.1: Define the distance between the horizontal coordinates of the centers of the two regions of interest in the waveform as the coarse pixel distance xrough.

[0087] xrough=xROIB-xROIA=579-343=236

[0088] Step 3.2: Define the local fine translation interval of the region of interest as [pa, pb].

[0089] [pa,pb]=[xrough-w,xrough+w]=[236-84 / 2,236+84 / 2]=[194,278]

[0090] Step 3.3: Continuously translate the region of interest to be translated within the translation interval towards the fixed region of interest by unit pixel distance, and match it.

[0091] Step 4. Calculate the area difference within the region of interest during the translation process. Determine the optimal matching displacement from the point of minimum area difference and convert it into a time difference. Substitute this into the ranging algorithm to finally achieve distance measurement. The specific implementation steps are as follows: Figure 9 As shown.

[0092] Step 4.1: Calculate the number of pixels between two rising edges within the region of interest during each translation process, defining it as the area difference SΔ, thereby generating a translation distance-area difference curve. The effect is as follows: Figure 10 , Figure 11 As shown, this step uses the area difference enclosed by the ROI during the translation process as a measure of the matching degree between the two point groups. Its advantage is that it utilizes the geometric invariance of the wavefront and the continuity of the change in the propagation path of the traveling wave during the cyclic translation process to continuously distribute the area difference during the wavefront matching process.

[0093] Step 4.2: Define the distance the region of interest to be translated is at which the area difference between the two rising edges is minimized during the translation matching process as the corrected pixel distance Δxrefine. The corrected pixel distance can be calculated based on the x-coordinate bmin of the minimum point of the translation distance-area difference curve in Step 4.1.

[0094] Δxrefine=bmin×step-w=41×1-84 / 2=-1

[0095] Step 4.3: Define the sum of coarse pixel distance and corrected pixel distance as the optimal matching displacement xpixel between the two wavefronts, which reflects the optimal pixel interval between the two wavefronts;

[0096] xpixel=xrough+Δxrefine=236-1=235

[0097] By utilizing the linear correspondence between pixel interval and time axis interval, the optimal matching displacement can be directly converted into time difference Δt;

[0098] ΔtAB=|tA0-tB0-xpixel×Ndata / (fs×Npixel)|=|0-235×2000 / (1×931)|=504.834μs

[0099] Step 4.4: Substitute the time difference obtained in Step 4.3 into the ranging algorithm to achieve ranging.

[0100] x=0.298×504.834 / 2=75.22km

[0101] Based on the minimum ROI area criterion, this invention can adaptively obtain the optimal matching displacement through coarse and fine two-stage translation and directly convert it into the time difference required for ranging, thus avoiding the difficulty of traditional ranging methods that require calibrating the precise arrival time of each wavefront one by one.

[0102] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for direct calibration of the arrival time difference of traveling waves in transmission line faults based on waveform image translation matching, characterized in that: Step 1: Read the fault waveform and the ranging algorithm to be used, and extract the waveform centerline; Step 2: Calculate the average slope of each point based on the coordinates of the waveform centerline, select a unique start and end point pair, and calibrate the region of interest required for distance measurement; Step 3: Calculate the coarse pixel distance between regions of interest and determine the translation interval. Based on this interval, perform translation with a unit pixel step. Step 4: Calculate the area difference within the region of interest during the translation process, determine the optimal matching displacement from the point of minimum area difference and convert it into time difference, then substitute it into the ranging algorithm to finally achieve ranging; Step 2 specifically includes: Step 2.1: Replace the fault waveform curve with the waveform center line extracted in Step 1. Under the premise that the initial change direction is the positive direction, start traversing from xs=1 and calculate the left and right average slopes of the i-th pixel of the waveform center line. Step 2.2: Based on the average slope obtained in Step 2.1, calculate the change in the average slope to determine the set of the start and end points of the rising edge; Step 2.3: Based on the set of start and end points selected in Step 2.2, the most significant feature points are further extracted using the position and distance constraints of adjacent start and end point coordinates. These points are used as unique start and end point pairs, and the start and end points of the diagonal of the waveform's rectangle of interest are determined according to these start and end point pairs. Step 2.4: Determine whether to stop searching for ROI based on the ranging algorithm. If yes, retain the current ROI information and increment the number of identified ROIs by 1; otherwise, traverse the area to be analyzed after the identified ROIs and proceed to Step 2.

2. Step 2.5: Determine whether the number of identified regions of interest (ROIs) meets the wavefront count required for time difference calculation. If it does, proceed to Step 3; otherwise, if two waveforms have been read, determine that ROI calibration has failed and exit ranging. If the number of reads is not met, continue reading fault data and image processing, then proceed to Step 1.

2. The method for direct calibration of the arrival time difference of traveling waves in transmission line faults based on waveform image translation matching according to claim 1, characterized in that... Step 1 specifically refers to: Step 1.1: Read the fault waveform and the ranging algorithm to be used. The waveform includes the fault current waveform and the fault voltage waveform. The ranging algorithm includes the traditional single-end ranging algorithm, the traditional double-end ranging algorithm, the double-end asynchronous ranging algorithm, and the loop wavefront ranging algorithm. Step 1.2: Based on the read fault waveform, extract the center line of the waveform using the grayscale centroid algorithm.

3. The method for direct calibration of the arrival time difference of traveling waves in transmission line faults based on waveform image translation matching according to claim 1, characterized in that... Step 3 specifically refers to: Step 3.1: Calculate the coarse pixel distance xrough between the centers of the two regions of interest in the waveform image; Step 3.2: Calculate the translation interval of the region of interest as [pa, pb] based on the coarse pixel distance in Step 3.1; Step 3.3: Continuously translate the region of interest to be translated within the translation interval towards the fixed region of interest by unit pixel distance, and match it.

4. The method for direct calibration of the arrival time difference of traveling waves in transmission line faults based on waveform image translation matching according to claim 1, characterized in that... Step 4 specifically refers to: Step 4.1: Calculate the number of colored pixels between two rising edges in the region of interest during each translation process, denoted as the area difference SΔ, and generate the translation distance-area difference curve accordingly; Step 4.2: Record the distance the region of interest to be translated is when the area difference between the two rising edges is the minimum during the fine translation process. This distance is the corrected pixel distance Δxrefine. The corrected pixel distance is calculated based on the x-coordinate bmin of the minimum point of the translation distance-area difference curve in Step 4.

1. Step 4.3: Record the sum of coarse pixel distance and corrected pixel distance as the optimal matching displacement xpixel between the two wavefronts, and use the linear correspondence between pixel distance and time interval to directly convert the optimal matching displacement into time difference Δt; Step 4.4: Substitute the time difference obtained in Step 4.3 into the ranging algorithm to achieve ranging.

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