CN105868872A - Power distribution network lightning disaster failure prediction method - Google Patents

Abstract

The invention provides a power distribution network lightning disaster failure prediction method. The method comprises the steps that a lightning partition is determined based on multiple times of forecasts of lightning ranges; the direct stroke ground lightning probability and the lightning induction overvoltage occurrence probability of circuits where poles and towers are located are determined; the lightning stroke tripping probability is determined according to the lightning shielding failure tripping probability and the beat back tripping probability of the circuits where the poles and towers are located; the lightning induction overvoltage tripping probability of the circuits where the poles and towers are located is determined according to the induced overvoltage maximum value of wires, the lightning induction overvoltage failure rate of the circuits where the poles and towers are located is obtained by establishing a fuzzy mathematical model, and therefore the lightning induction overvoltage tripping probability of the circuits where the poles and towers are located is obtained, wherein the lightning current intensity is taken into consideration; by establishing a power distribution circuit temperature model, the instantaneous failure probability of a feeder section in an area to be detected is determined according to the service duration of power distribution circuits; a power distribution circuit lightning disaster power distribution circuit failure probability model with aging failure and correction taken into consideration is established; the failure probability of the feeder section in the area to be detected is predicated.

Description

Power distribution network lightning disaster fault prediction method

Technical Field

The invention relates to the technical field of power distribution, in particular to a power distribution network lightning disaster fault prediction method.

Background

In recent years, with the rapid development of power grids, lightning damage faults frequently occur, a power distribution network is used as the most direct and key part between a power system and users, and lightning disasters become the main hazards for safe and reliable operation of the power distribution network in China.

At present, lightning fault prediction means are as follows: some power grid fault rate regression models are established based on limited serious thunderstorm events, relevant meteorological data and power grid fault data by utilizing mathematical statistics and analysis, but the thunderstorm events are few, the time interval is long, the real-time performance is poor, and the prediction is limited; some consider only the thunder and lightning change trend and do not consider the influence of thunder and lightning current intensity on the probability of lightning induced overvoltage faults of the distribution lines; some lightning fault probability predictions only consider single lightning disasters, but in practice, lightning often occurs simultaneously along with rainfall, raindrops in a discharge gap can enhance the air gap field intensity and distort, and the lightning flashover probability is directly influenced; some consider only the condition that the thunder and lightning leads to the trouble of distribution lines, do not consider the influence of the ageing effect of line itself.

Therefore, the method and the device can forecast the lightning subareas of the power distribution network, take the lightning current intensity and rainfall intensity into consideration, and influence of the line aging in various aspects, so as to forecast the probability of lightning faults, and have great significance for enhancing the power distribution network to resist lightning disasters.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a power distribution network lightning disaster fault prediction method.

The technical scheme of the invention is as follows:

a power distribution network lightning disaster fault prediction method comprises the following steps:

step 1: determining lightning partitions of the area to be detected based on multi-time lightning range forecast, and determining the position and lightning falling probability of each lightning partition at the next time;

step 1.1: counting the lightning occurrence time and place of the area to be detected according to the lightning positioning system, and carrying out area division according to the longitude and latitude of the area to be detected to obtain each lightning-falling dense area;

step 1.2: carrying out binarization processing on the thunderbolt dense area, shaping the thunderbolt dense area subjected to binarization processing by adopting an eight-neighborhood boundary tracking algorithm to obtain each thunder partition, and determining the thunderbolt probability of the t-time thunder partition;

step 1.3: determining a development track of t +1 time of each thunder sub-area, namely the thunder sub-area of t +1 time, by optimal matching of the adjacent thunder sub-areas of t-2 time, t-1 time and t time, and determining the thunder falling probability of the t +1 time thunder sub-area according to the thunder falling probability of the t-2 time, t-1 time and t time thunder sub-areas;

the formula for determining the lightning falling probability of the secondary lightning subarea at the time t +1 according to the lightning falling probability of the secondary lightning subareas at the time t-2, the time t-1 and the time t is as follows:

$q_{t+1}=\frac{\underset{t-2}{\overset{t}{\Σ}}{q}_t}{3};$

wherein t is more than or equal to 2, q_t+1Probability of lightning loss of the sub-lightning sub-zone at t +1, q_tThe probability of lightning falling of the secondary lightning subarea at t.

Step 2: establishing a power grid distribution line lightning fault comprehensive partition model, wherein the power grid distribution line lightning fault comprehensive partition model comprises the following steps:

$P_{line}^{t+1}=1-\underset{i=1}{\overset{h}{\Π}}\[1-P_{iTa}^{t+1}{P}_{ir}-P_{iTb}^{t+1}{P}_{ig}\];$

wherein,the probability of lightning trip-out of the feeder section of the area to be detected at t +1 time is h is the number of towers of the feeder section of the area to be detected,the probability of direct lightning strike at time t +1 of the line on which the ith base tower is positioned, P_irIs the lightning trip probability of the line on which the ith base tower is positioned,probability of occurrence of lightning induced overvoltage of t +1 time of line in which ith base tower is located, P_igThe probability of lightning induced overvoltage tripping at the time of t +1 of the line where the ith base tower is located;

and step 3: partitioning each tower of the distribution line as a unit, and determining an effective area of each tower, which is struck by lightning, and an effective area of lightning induced overvoltage, so as to obtain the probability of direct lightning strike and lightning strike of the line t +1 where each tower is located and the probability of lightning induced overvoltage occurrence of the line t +1 where each tower is located;

step 3.1: determining the critical distance of lightning stroke conductors of towers in the area to be measuredFrom y_miniAnd critical distance y of each tower induced voltage flashover_maxi；

Step 3.2: determining an effective area of each tower subjected to lightning stroke and an effective area of lightning induced overvoltage according to the tower electrical geometric model;

the lightning strike effective area of the tower is a distance y from the tower in the direction perpendicular to the distribution line by taking the tower as a center_miniAnd distribution line direction 1/2 range;

the effective area of the lightning induced overvoltage is a distance y from the pole tower in the direction perpendicular to the distribution line by taking the pole tower as the center_maxiAnd distribution line direction 1/2 range.

Step 3.3: and determining the direct lightning strike and lightning fall probability of the time t +1 of the line where each tower is located and the lightning induced overvoltage occurrence probability of the time t +1 of the line where each tower is located according to the lightning strike occurrence effective area and the lightning induced overvoltage effective area of each tower.

Probability of direct lightning strike for time t +1 on line where ith base tower is locatedThe calculation formula of (2) is as follows:

$P_{iTa}^{t+1}=\frac{{a^{\′}}_{t+1}}{a_{t+1}}{q}_{t+1};$

wherein, a'_t+1The overlapping area of the effective area of the ith base tower lightning stroke at t +1 and the secondary lightning subarea at t +1 of the tower, a_t+1The ith radical when it is t +1The area of the lightning subarea where the tower is located;

probability of occurrence of t + 1-time lightning induced overvoltage of line on which ith base tower is locatedThe calculation formula of (2) is as follows:

$P_{iTb}^{t+1}=\frac{{b^{\′}}_{t+1}}{a_{t+1}}{q}_{t+1};$

wherein, b'_t+1The effective area of the lightning induced overvoltage of the ith tower base at the time of t +1 is the overlapping area of the secondary lightning subarea at the time of t +1 where the tower is located.

And 4, step 4: the lightning shielding failure trip probability of the line where the tower is located is obtained according to the tower electrical geometric model, the counterattack trip probability of the line where the tower is located is determined by utilizing a Monte Carlo method, and the lightning shielding failure trip probability of the line where each tower is located is determined according to the lightning shielding failure trip probability of the line where the tower is located and the counterattack trip probability of the line where the tower is located;

step 4.1: according to the tower electrical geometric model, obtaining the lightning shielding failure rate of the line where the tower is located;

lightning shielding rate P of line on which ith base tower is positioned_iαThe calculation formula is as follows:

wherein,for angle of incidence of lightning, /)_ibThe horizontal distance l corresponding to the shielding failure exposure arc of the line on which the ith base tower is positioned_iaThe horizontal distance corresponds to the lightning conductor protection arc of the line where the ith base rod tower is located;

step 4.2: obtaining the lightning shielding trip-out probability of the line where the tower is located according to the lightning shielding failure rate of the line where the tower is located;

probability P of lightning shielding failure tripping of line on which ith base tower is positioned_isThe calculation formula is as follows:

P_is＝ηP_iα；

wherein eta is an arc establishing rate;

step 4.3: simulating and counting the lightning counterattack tripping probability of the line on which each tower is positioned by using a Monte Carlo method;

step 4.4: and taking the sum of the lightning shielding failure trip probability of the line where the tower is located and the tower counterattack trip probability of the line where the tower is located as the lightning trip probability of the line where the tower is located, and obtaining the lightning trip probability of the line where each tower is located.

And 5: determining the probability of lightning induced overvoltage tripping of the line where the tower is located according to the maximum value of the induced overvoltage on the lead, and obtaining the lightning induced overvoltage failure rate of the line where the tower is located by constructing a fuzzy mathematical model so as to obtain the probability of lightning induced overvoltage tripping of the line where each tower is located, wherein the probability of lightning induced overvoltage tripping of the line where each tower is located is considered;

step 5.1: determining the probability of lightning induced overvoltage tripping of the line where the tower is located according to the maximum value of the induced overvoltage on the lead;

probability P (I) of lightning induced overvoltage tripping of line where tower is located_min) The calculation formula is as follows:

$P\left(I_{\min }\right)={10}^{-\frac{I_{\min }}{88}}={10}^{-\frac{U_{50\%}S}{25h_d}};$

wherein,is the insulator impulse discharge voltage with a discharge probability of 50%, I_mAmplitude of lightning current, h, for lightning striking the earth_dThe height of the overhead line to the ground is defined, and S is the horizontal distance from a lightning stroke point to the overhead line;

step 5.2: establishing a fuzzy mathematical model, taking a lightning excitation parameter and a line span parameter as the input of the fuzzy mathematical model, taking a lightning induced overvoltage fault rate as the output of the fuzzy mathematical model, combining the lightning excitation parameter and the line span parameter, establishing a fuzzy control rule, and defuzzifying by adopting a maximum membership method to obtain the lightning induced overvoltage fault rate;

step 5.3: and calculating the lightning induced overvoltage tripping probability of the line where each tower is positioned, considering the lightning current intensity, according to the lightning induced overvoltage tripping probability of the line where the tower is positioned and the lightning induced overvoltage fault rate.

Step 6: inputting the direct lightning strike lightning-down probability of the time t +1 of the line where each tower is located, the lightning induced overvoltage occurrence probability of the time t +1 of the line where each tower is located, the lightning trip-out probability of the line where each tower is located and the lightning induced overvoltage trip-out probability of the line where each tower is located, which considers the lightning current intensity, into the power grid distribution line lightning fault comprehensive partition model to obtain the lightning trip-out probability of the time t +1 of the feeder line section of the area to be measured;

and 7: determining the probability of instantaneous fault occurrence of the feeder line section of the area to be detected at the next moment according to the service time of the distribution line by establishing a distribution line temperature model;

and 8: establishing a distribution line fault probability model under consideration of aging failure and correction of distribution line lightning disasters;

the distribution line fault probability model considering aging failure and correcting the distribution line under the lightning disaster is as follows:

$P^{t+1}=P_{lf}^{t+1}+P_{line}^{t+1}-P_{lf}^{t+1}{P}_{line}^{t+1};$

wherein, P^t+1The probability of the fault of the feeder section of the area to be measured at t +1,the probability of instantaneous fault occurring at the next moment of the feeder line segment of the area to be detected;

and step 9: inputting the lightning trip probability of the feeder section of the area to be detected at the time of t +1 and the instantaneous fault probability of the feeder section of the area to be detected at the next time into a model for predicting the fault probability of the feeder section of the area to be detected at the time of t +1 by considering aging failure and correcting the fault probability of the distribution line under the lightning disaster of the distribution line.

The invention has the beneficial effects that:

the invention provides a method for predicting lightning disaster faults of a power distribution network, which aims at the strong regionality of lightning activities in China, firstly carries out lightning area division on administrative areas, and then carries out detailed longitude and latitude division on corresponding areas, thereby reducing the workload of data mining and simultaneously ensuring that lightning monitoring data are clearer and more accurate; the influence of the lightning current intensity on the lightning induced overvoltage fault probability of the power distribution network is considered, a fuzzy mathematical model is constructed to analyze the lightning fault probability, and the reliability and the accuracy of the operation of the fault probability of the distribution network line are improved; the lightning fault probability prediction only considers a single lightning disaster generally, and the influence of rainfall on the arc establishment rate of the insulator is taken into consideration, so that the accuracy of the lightning trip probability prediction is further improved; aging failure of the line is also an important factor influencing the probability of the lightning disaster fault, and the influence is comprehensively considered in the prediction and calculation method of the probability of the lightning disaster fault; the lightning trip-out phenomenon caused by direct lightning strike or induced lightning in the power distribution network is comprehensively modeled, so that the accuracy of lightning zone prediction and line lightning trip-out probability is improved.

Drawings

FIG. 1 is a flow chart of a method for predicting a lightning disaster fault of a power distribution network according to an embodiment of the present invention;

FIG. 2 is a flow chart of determining the location and lightning strike probability of each lightning sub-zone at the next time in accordance with an embodiment of the present invention;

FIG. 3 is a diagram illustrating the result of identifying a circular lightning strike zone in accordance with an embodiment of the present invention;

FIG. 4 is a schematic diagram of secondary lightning partitions when determining each lightning partition t +1 in accordance with an embodiment of the present invention;

fig. 5 is a flowchart for calculating the probability of direct lightning strike and lightning strike for each tower time t +1 and the probability of occurrence of lightning induced overvoltage for each tower time t +1 in the embodiment of the invention;

FIG. 6 is a sectional view of a line insulation flashover caused by lightning in accordance with an embodiment of the present invention;

FIG. 7 is a schematic view of the active area of a mast tower for lightning strikes and the active area of a lightning induced overvoltage in accordance with an embodiment of the present invention;

FIG. 8 is a flowchart for determining lightning trip-out probabilities of towers according to tower lightning shielding failure trip-out probabilities and tower counterattack trip-out probabilities in the embodiment of the present invention;

FIG. 9 is an electrical geometry model of a tower according to an embodiment of the present invention;

fig. 10 is a flowchart for determining the probability of lightning induced overvoltage tripping of each tower considering lightning current intensity according to the embodiment of the present invention;

FIG. 11 is a distribution diagram of membership functions of lightning excitation parameters according to an embodiment of the present invention;

FIG. 12 is a graph of membership function distribution for line step distance parameters in accordance with an embodiment of the present invention;

FIG. 13 is a graph of membership function distribution for lightning induced overvoltage failure rate in accordance with an embodiment of the present invention;

FIG. 14 is a diagram of a distribution line temperature model according to an embodiment of the present invention;

fig. 15 is a lightning forecast evaluation index curve according to the embodiment of the present invention.

Detailed Description

The following detailed description of embodiments of the invention refers to the accompanying drawings.

A method for predicting a lightning disaster fault of a power distribution network is shown in figure 1 and comprises the following steps:

step 1: and determining the lightning subareas of the area to be detected based on the multi-time lightning range forecast, and determining the positions and the lightning falling probability of the lightning subareas at the next time, as shown in fig. 2.

Step 1.1: and counting the lightning occurrence time and place of the area to be detected according to the lightning positioning system, and carrying out area division according to the longitude and latitude of the area to be detected to obtain each lightning-falling dense area.

In the present embodiment, because of the uncertainty of lightning itself, the lightning range is first predicted when a lightning stroke fault is studied. At present, the thunder and lightning monitoring network in China is usually partitioned by longitude and latitude, but in reality, the thunder and lightning activities in China have strong regionality, thunder and lightning occur frequently in the southeast coastal areas, and the number of thunder and lightning in the northwest areas is relatively small. Therefore, area division can be adopted according to lightning data observed by a meteorological department for many years, and detailed longitude and latitude division is carried out on the corresponding area, so that unnecessary workload is reduced.

Step 1.2: and (3) carrying out binarization (0-1) processing on the thunderbolt dense area, shaping the thunderbolt dense area subjected to binarization processing by adopting an eight-neighborhood boundary tracking algorithm to obtain each thunder and lightning partition, and determining the thunderbolt probability of the t-time thunder and lightning partition.

In this embodiment, the thunderbolt dense area is binarized, the binarized thunderbolt dense area is shaped by an eight-neighborhood boundary tracking algorithm to obtain each thunderbolt subarea, and finally, a circular thunderbolt subarea recognition result map is obtained, as shown in fig. 3. From FIG. 3, the longitude and latitude coordinates of the central point L of each lightning sub-area at time t are (x, y), the radius is r, and the lightning falling probability q of the lightning sub-area at time t is obtained_tThe formula (2) is shown in formula (1):

$q_t=\frac{n^{\′}}{N^{\′}}---\left(1\right)$

and N 'is the total number of landmines in the sub-area of the next landmine at t, and N' is the total number of landmines in the administrative area to be detected at t.

Step 1.3: and determining the development track of the t +1 hour of each thunder partition, namely the thunder partition of the t +1 hour, by optimal matching of the adjacent t-2, t-1 and t hour thunder partitions, and determining the thunder falling probability of the t +1 hour thunder partition according to the thunder falling probability of the t-2, t-1 and t hour thunder partitions.

In this embodiment, in order to obtain the optimal trajectory, by optimally matching the t-2, t-1, and t-time lightning partitions adjacent to each other, it is assumed that a shorter movement trajectory between 2 lightning partitions has a higher possibility, and a movement trajectory between 2 lightning partitions having similar areas has a higher possibility, and a development trajectory of each lightning partition at t +1 time, that is, the lightning partition at t +1 time is determined as shown in fig. 4.

The formula for determining the lightning falling probability of the secondary lightning subarea at the time of t +1 according to the lightning falling probability of the secondary lightning subareas at the times of t-2, t-1 and t is shown as the formula (2):

$q_{t+1}=\frac{\underset{t-2}{\overset{t}{\Σ}}{q}_t}{3}---\left(2\right)$

wherein t is more than or equal to 2, q_t+1Probability of lightning loss of the sub-lightning sub-zone at t +1, q_tThe probability of lightning falling of the secondary lightning subarea at t.

Step 2: and establishing a power grid distribution line lightning fault comprehensive partition model.

In this embodiment, it is considered that the towers on the same distribution line are in a series relationship, and if any tower on the line fails, the feeder section of the area to be tested will fail, and the failure probability of the line is equal to that of the tower. And h pole towers are arranged on the feeder line section of the area to be detected.

The comprehensive partition model of the lightning faults of the power distribution line of the power grid is shown as the formula (3):

$P_{line}^{t+1}=1-\underset{i=1}{\overset{h}{\Π}}\[1-P_{iTa}^{t+1}{P}_{ir}-P_{iTb}^{t+1}{P}_{ig}\]---\left(3\right)$

wherein,the probability of lightning trip-out of the feeder section of the area to be detected at t +1 time is h is the number of towers of the feeder section of the area to be detected,the probability of direct lightning strike at time t +1 of the line on which the ith base tower is positioned, P_irIs the lightning trip probability of the line on which the ith base tower is positioned,probability of occurrence of lightning induced overvoltage of t +1 time of line in which ith base tower is located, P_igAnd the probability of lightning induced overvoltage tripping at the time of the ith base tower line t + 1.

And step 3: each pole tower of the distribution line is used as a unit to be partitioned, and an effective area where each pole tower is struck by lightning and an effective area where each pole tower is induced by lightning overvoltage are determined, so that the probability of direct lightning strike and lightning strike of the line where each pole tower is located at time t +1 and the probability of occurrence of lightning induced overvoltage of the line where each pole tower is located at time t +1 are obtained, as shown in fig. 5.

Step 3.1: determining the critical distance y of lightning stroke conductors of towers in the area to be measured_miniAnd critical distance y of each tower induced voltage flashover_maxi。

In this embodiment, the flashover zone of the line insulation caused by lightning is shown in fig. 6.

Critical distance y of lightning stroke conductor of ith base tower_miniThe formula (4) is shown as follows:

$y_{\min i}=\sqrt{{r_s}^2-{(r_g-h_d)}^2}---\left(4\right)$

wherein,in order to achieve the distance between the lightning and the ground,for lightning strike distance of lightning conductor, I_mAmplitude of lightning current, h, for lightning striking the earth_dIs the height of the overhead line to the ground.

Critical distance y of induced voltage flashover of ith base tower_maxiIs represented by equation (5):

$1.5CFO=39.657\frac{I_m{h}_d}{y_{\max i}}---\left(5\right)$

wherein, CFO is the line induced overvoltage exceeding 1.5 times of critical flashover voltage.

Step 3.2: and determining the lightning strike effective area and the lightning induced overvoltage effective area of each tower according to the tower electrical geometric model.

In the present embodiment, the effective area of the tower where lightning strikes occur and the effective area of the lightning induced overvoltage are shown in fig. 7. The effective lightning stroke area of the tower is y distance from the tower in the direction perpendicular to the distribution line by taking the tower as the center_miniAnd distribution line direction 1/2 range. The effective area of the lightning induced overvoltage is a distance y from the pole tower in the direction perpendicular to the distribution line by taking the pole tower as the center_maxiAnd distribution line direction 1/2 range.

Step 3.3: and determining the direct lightning strike and lightning fall probability of the time t +1 of the line where each tower is located and the lightning induced overvoltage occurrence probability of the time t +1 of the line where each tower is located according to the lightning strike occurrence effective area and the lightning induced overvoltage effective area of each tower.

In the present embodiment, the formula for calculating the direct lightning strike probability of the ith mast tower at t +1 time is shown in formula (6):

$P_{iTa}^{t+1}=\frac{{a^{\′}}_{t+1}}{a_{t+1}}{q}_{t+1}---\left(6\right)$

wherein, a'_t+1The overlapping area of the effective area of the ith base tower lightning stroke at t +1 and the secondary lightning subarea at t +1 of the tower, a_t+1The area of the lightning subarea where the ith base tower is located is t + 1.

The formula for calculating the probability of occurrence of the lightning induced overvoltage of the ith base tower at t +1 time is shown as formula (7):

$P_{iTb}^{t+1}=\frac{{b^{\′}}_{t+1}}{a_{t+1}}{q}_{t+1}---\left(7\right)$

wherein, b'_t+1The effective area of the lightning induced overvoltage of the ith tower base at the time of t +1 is the overlapping area of the secondary lightning subarea at the time of t +1 where the tower is located.

And 4, step 4: the lightning shielding failure trip probability of the line where the tower is located is obtained according to the tower electrical geometric model, the counterattack trip probability of the line where the tower is located is determined by utilizing a Monte Carlo method, and the lightning shielding failure trip probability of the line where each tower is located is determined according to the lightning shielding failure trip probability of the line where the tower is located and the counterattack trip probability of the line where the tower is located, as shown in FIG. 8.

Step 4.1: and obtaining the lightning shielding failure rate of the line on which the tower is positioned according to the tower electrical geometric model.

In the present embodiment, the electrical geometry model of the tower is shown in fig. 9, and as can be seen from fig. 9, r_cIn order to realize the distance hit by the wire,r_sfor lightning strike distance of lightning conductor, r_gThe distance of impact on the ground is set,the influence of the landform and the lightning incidence direction on the shielding failure rate of the distribution line is considered for the lightning incidence angle, namely the included angle between the lightning guide and the ground vertical direction_sHeight of the lightning conductor, h_cIs the height of the wire, theta₁Exposure of critical wire strike distance r on arc for strike_cAngle with the horizontal plane, theta₂Exposure of critical wire strike distance r under arc for strike_c ^*And the included angle between the lightning protection angle theta and the horizontal plane is the lightning protection angle theta.

Lightning shielding rate P of line on which ith base tower is located_iαThe calculation formula is shown in formula (8):

wherein,for angle of incidence of lightning, /)_ib＝B′C＝r_c(cosθ₁-cosθ₂) The horizontal distance l corresponding to the shielding failure exposure arc of the line on which the ith base tower is positioned_ia＝OC＝r_ccos θ₁+2(h_s-h_c) And tan theta is the horizontal distance corresponding to the lightning conductor protection arc of the line where the ith base tower is located.

Step 4.2: and obtaining the probability of lightning shielding failure tripping of the line of the tower according to the lightning shielding failure rate of the line of the tower.

In this embodiment, the probability P of lightning shielding failure trip of the line on which the ith base tower is located_isThe calculation formula is shown in formula (9):

P_is＝ηP_iα(9)

wherein eta is the arc rate.

Step 4.3: and simulating and counting the lightning counterattack tripping probability of the line on which each tower is positioned by using a Monte Carlo method.

Step 4.3.1: setting the simulation times to be N, and defining y_kShows the results of the k-th simulation, if a counterattack causes a flashover, then y_k1, otherwise y_k＝0。

Step 4.3.2: randomly generating a [0, 1]]Uniformly distributed random number r₁If r is₁＞P_iαThen step 4.3.3 is performed, otherwise step 4.3.4 is performed.

Step 4.3.3: randomly generating a [0, 1]]Uniformly distributed random number r₂If r is₂If g is less than g, g is the striking rate, counterstriking y occurs_kStep 4.3.5 is performed, otherwise, y_kStep 4.3.5 is performed, which is 0.

Step 4.3.4: judging whether the current simulation times reach the simulation times N, if so, executing the step 4.3.5, otherwise, returning to the step 4.3.2,

step 4.3.5, the counterattack trip rate is counted to obtain a progressive statistical estimation value ξ of the counterattack trip rate and obtain the counterattack trip probability P_ic。

In the present embodiment, the asymptotic statistical estimation value ξ of the counterattack trip rate is represented by equation (10):

$\mathrm{\ξ}=\frac{\underset{k=1}{\overset{N}{\Σ}}{y}_k}{N}---\left(10\right)$

probability of counterattack tripping P_icAs shown in formula (11):

P_ic＝ηξ (11)

wherein η is the arc-establishing rateAccording to the experiment and the operation experience, the arc rate η is 4.5E^0.7514 (%) where E is the gradient of the average operating voltage (effective value) of the insulator string, kV/m, raindrops can enhance the air gap field strength and distort, so that E is increased, and the arc-establishing rate is increased.

The occurrence of lightning disasters is generally accompanied by rainfall, and the probability of lightning stroke faults can be directly increased by the rainfall. Firstly, the dielectric constant of rainwater is far greater than that of air, and raindrops in a discharge gap can enhance the field intensity of the air gap and distort the air gap, so that the development and generation of initial electron collapse and streamer are facilitated; and the accumulation of water droplets effectively reduces the insulation distance of the air gap, thus resulting in a reduction in gap flashover voltage.

In addition, in the case of rainfall with low intensity, humidity mainly affects, and as water molecules increase, the probability of electrons being adsorbed by water molecules also increases, and the number of free electrons in the space gap decreases, thereby suppressing the progress of discharge, so that the increase in humidity causes the power frequency flashover voltage of the air gap to increase.

However, lightning is a cloud discharge phenomenon, and lightning disasters are often accompanied by strong rains, so that the influence of humidity is far smaller than the influence of rainwater on the field intensity distortion of air gaps.

Step 4.4: and taking the sum of the lightning shielding failure trip probability of the line where the tower is located and the tower counterattack trip probability of the line where the tower is located as the lightning trip probability of the line where the tower is located, and obtaining the lightning trip probability of the line where each tower is located.

In the present embodiment, the lightning trip probability P of the line on which the ith base tower is located_irIs represented by formula (12):

P_ir＝P_ic+P_is(12)

and 5: the lightning induced overvoltage tripping probability of the line where the tower is located is determined according to the maximum value of the induced overvoltage on the lead, and the lightning induced overvoltage fault rate of the line where the tower is located is obtained by constructing a fuzzy mathematical model, so that the lightning induced overvoltage tripping probability of the line where each tower is located is obtained by considering the lightning current intensity, as shown in fig. 10.

Step 5.1: and determining the probability of lightning induced overvoltage tripping of the line where the tower is located according to the maximum value of the induced overvoltage on the wire.

In the present embodiment, the probability of lightning induced overvoltage trip P (I)_min) The calculation formula is shown in formula (13):

$P\left(I_{min}\right)={10}^{-\frac{I_{\min }}{88}}={10}^{-\frac{U_{50\%}S}{25h}}---\left(13\right)$

wherein,the voltage of the impact discharge of the insulator when the discharge probability is 50 percent, the induced overvoltage on the lead, I_mAmplitude of lightning current, h, for lightning striking the earth_dAnd S is the horizontal distance from a lightning stroke point to the overhead line.

In the present embodiment, the distribution line passing through the city is generally shielded by nearby tall buildings or trees, and therefore, many lightning trip accidents of the distribution line are caused by induced overvoltage generated when a nearby object is struck by lightning. The main component of the lightning induced overvoltage is generated in the lightning strike-back process, namely, when a descending leader develops, a ground protuberance generates an upward development of an upward leader, the two leaders generate strong discharge, and positive and negative charges in the respective leaders are neutralized. Lightning inductorThe overvoltage comprises two components of electrostatic induction and electromagnetic induction, and the electrostatic component plays a main role because a main discharge channel is vertical to a lead, the mutual inductance is small, and the electromagnetic induction is weak. Therefore, according to the related theoretical analysis and experimental measurement results, when the distance between the lightning stroke point and the line causes the lightning induced overvoltage to be generated on the wire, the insulator impulse discharge voltage U is obtained when the discharge probability is 50 percent_50％Equal to the maximum value U of the induced overvoltage on the conductor_maxAs shown in equation (14):

$U_{max}=25\×\frac{I_m{h}_d}{S}---\left(14\right)$

step 5.2: the method comprises the steps of constructing a fuzzy mathematical model, using a lightning excitation parameter and a line span parameter as input of the fuzzy mathematical model, using a lightning induced overvoltage fault rate as output of the fuzzy mathematical model, combining the lightning excitation parameter and the line span parameter, setting a fuzzy control rule, and defuzzifying by adopting a maximum membership method to obtain the lightning induced overvoltage fault rate.

In this embodiment, the probability of an induced overvoltage fault on the distribution line is related to the lightning current amplitude, in addition to the line height and the distance between the line and the lightning strike point. Factors influencing the lightning current amplitude relate to multiple factors, and a usable model is lacked between the lightning current amplitude and the line fault rate. The lightning excitation parameter E is obtained by constructing a fuzzy mathematical model_l＝a_va_ta_sa_cAnd line span parameter L_pAs input to the fuzzy mathematical model.

Wherein, a_vThe lightning current wave velocity coefficient, namely the lightning current wave parameter, can be measured by a lightning current wave monitoring device arranged on a high mountain or a high tower.At lightning current echo speed 1.3 × 10⁸The m/s is a reference (the coefficient is 1), the larger the echo propagation rate is, the faster the voltage at the position closest to a lightning stroke point reaches a peak value, the larger the lightning current amplitude is, the higher the echo speed is, the lightning current echo speed coefficient is increased (1-1.2), and the lower the echo speed is, the lower the lightning current echo speed coefficient is (0.8-1).

a_tThe wave front time coefficient of the lightning current can be measured by a lightning current waveform monitoring device. The wave front time of the lightning current is taken as a reference (the coefficient is 1), the wave front time is reduced by a longer wave front time coefficient (0.6-1), and when the wave front time is less than 0.5 mu s, the amplitude of the lightning current is larger, and the coefficients are all 1. The shorter the wave front time, the faster the voltage reaches a peak value nearest to the lightning strike point, and the larger the lightning current amplitude.

a_cTo the ground conductivity coefficient, a_sShielding coefficients for the surrounding environment. The method comprises the steps that a plain area and the ground are taken as ideal conductors and an environment without shields is taken as a reference (the coefficient is 1), the ground conductivity coefficient is increased (1-1.3) for a terrain with small ground conductivity and obvious induction effect on the development of a lightning down leader, and the ground conductivity coefficient is reduced (0.8-1) for a terrain with large ground conductivity and obvious obstruction effect on the lightning down leader; the coefficient (1-2) is increased for the open environment without shielding and beneficial to the formation of the lightning induced overvoltage, and the coefficient (0.5-1) is decreased for the environment with trees, buildings and the like which are not beneficial to the formation of the lightning induced overvoltage.

6 fuzzy subsets are adopted for lightning excitation parameters to cover parameter ranges: little lightning excitation (E)_vs) Little lightning excitation (E)_s) Lightning excitation, etc. (E)_m) Large lightning excitation (E)_bl) Very much lightning excitation (E)_vl) Very large lightning excitation (E)_el) The distribution of the membership function is shown in FIG. 11.

The range of line range coefficients is covered with 4 fuzzy subsets for the line range parameters: small line parameter (L)_s) Line parameters, medium (L)_m) Large line parameter (L)_l) The line parameters are very large (L)_vl) Which isThe distribution of the membership function is shown in fig. 12.

Covering the value range [0, 1] of the lightning induced overvoltage fault rate by 7 fuzzy subsets: very small (ES), Very Small (VS), small (S), medium (M), large (L), Very Large (VL), very large (EL). The distribution of the membership function is shown in fig. 13.

According to the analysis about the influence of different factors on the probability of the lightning induced overvoltage fault, the lightning excitation parameters and the line span parameters are combined, 24 fuzzy control rules are set, and 24 fuzzy control rules can be set, as shown in table 1:

TABLE 1 fuzzy control rules

And defuzzifying by adopting a maximum membership method to obtain the lightning induced overvoltage fault rate mu, wherein the division of the fuzzy membership function needs to be continuously checked and perfected in the later practical application.

Step 5.3: and calculating the lightning induced overvoltage tripping probability of the line where each tower is positioned, considering the lightning current intensity, according to the lightning induced overvoltage tripping probability of the line where the tower is positioned and the lightning induced overvoltage fault rate.

In this embodiment, the lightning induced overvoltage fault probability P of the line on which the tower is located is considered after the lightning current intensity is considered_igAs shown in equation (15):

P_ig＝μP(I_min) (15)

step 6: and inputting the direct lightning trip-out probability of the time t +1 of the line where each tower is located, the lightning induced overvoltage occurrence probability of the time t +1 of the line where each tower is located, the lightning trip-out probability of the line where each tower is located and the lightning induced overvoltage trip-out probability of the line where each tower is located, which considers the lightning current intensity, into the power grid distribution line lightning fault comprehensive partition model to obtain the lightning trip-out probability of the time t +1 of the feeder line section of the area to be detected.

And 7: and determining the instantaneous fault probability of the feeder line section of the area to be detected at the next moment according to the service time of the distribution line by establishing a distribution line temperature model.

In the embodiment, the distribution line has different aging failure conditions along with the service time, and high-temperature annealing is a main cause of life loss. Therefore, the service time of the wire is directly influenced by the temperature of the wire. Since the influence of the heat generated by the coincidence current of the line itself and the external environment temperature change on the line itself is most significant, a distribution line temperature model as shown in fig. 14 is established.

In fig. 14: n is the wire mass, C_PThe specific heat capacity of the lead is J/kg DEG C; i is the conductor current, A, theta_lThe line operating temperature, deg.C; theta₀The initial temperature of the wire, DEG C; theta_aAmbient temperature, deg.C; q is the sum of heat in the distribution line service process; q_rW/m is the heat transferred by radiation; and t is the service time of the line.

Therefore, through a large amount of experiments and data analysis, the expected life L of the distribution line can be known₁The relationship between the heat exchange and the line operating temperature in the line service process is shown as the formula (16):

L₁＝Qe^-λθ(16)

where λ is a constant related to the conductor mass and material properties.

The distribution line aging process accords with Weibull distribution and is only related to the shape parameter β through the accelerated life test of the lead or the estimation of failure data record, η_lAs a scale parameter (characteristic lifetime parameter), there is η_l＝L₁Then, the cumulative probability distribution function F of the distribution line is obtained_la(1|θ_l) As shown in equation (17):

$F_{la}\left(1\right|{\mathrm{\θ}}_l)=1-e^{-{\[t/L_1(Q,{\mathrm{\θ}}_l)\]}^{\mathrm{\β}}}---\left(17\right)$

according to the definition of the conditional probability, the distribution line is at theta_lProbability of instantaneous fault occurring at t +1 moment after t time of service at temperatureAs shown in equation (18):

$P_{lf}^{t+1}=\frac{F_{la}(t+1|{\mathrm{\θ}}_l)-F_{la}\left(t\right|{\mathrm{\θ}}_l)}{(1-F_{la}(t|{\mathrm{\θ}}_l\left)\right)}---\left(18\right)$

and 8: and establishing a distribution line fault probability model considering aging failure and correcting the distribution line under the lightning disaster.

In the present embodiment, the distribution line fault probability model considering aging failure and correcting a distribution line lightning disaster is represented by formula (19):

$P^{t+1}=P_{lf}^{t+1}+P_{line}^{t+1}-P_{lf}^{t+1}{P}_{line}^{t+1}---\left(19\right)$

wherein, P^t+1The probability of the fault of the feeder section of the area to be measured at t +1,and the instantaneous fault probability of the feeder line segment of the area to be detected at the next moment.

In the embodiment, the lightning monitoring information is acquired in time-sharing manner, so that the failure probability of the distribution line occurring at the time when the failure probability is t +1 due to aging failure and lightning disaster correction is considered.

And step 9: inputting the lightning trip probability of the feeder section of the area to be detected at the time of t +1 and the instantaneous fault probability of the feeder section of the area to be detected at the next time into a model for predicting the fault probability of the feeder section of the area to be detected at the time of t +1 by considering aging failure and correcting the fault probability of the distribution line under the lightning disaster of the distribution line.

In this embodiment, in order to evaluate the accuracy of the lightning partition prediction, the lightning partition is adoptedProduct detection rate index R_PODFalse alarm rate index R of area of thunder area_FARAnd the number of landings detection rate index R_LDPAs shown in formulas (20) to (22):

$R_{POD}=\frac{E\∩A^{*}}{A}\×100\%---\left(20\right)$

$R_{FAR}=\frac{E\∩\stackrel{\‾}{A}}{E}\×100\%---\left(21\right)$

$R_{LDP}=\frac{(E\∩A^{*})min\{P^{t+1},P\}}{Ap}\×100\%---\left(22\right)$

wherein E is the predicted area of the region to be measured, A^*In order to be the actual lightning area,actual area of non-lightning area E ∩ A^*In order to forecast the area of the accurate lightning area,for error prediction of area, P, of lightning region^t+1To predict the probability of lightning loss, P is the actual probability of lightning loss, (E ∩ A)^*)min{P^t+1P is the number of successfully predicted landmines, and AP is the number of actual landmines in the lightning area.

In the embodiment, the method of the invention is adopted to forecast the lightning occurrence range every 1min, and corresponding indexes are calculated, and the curve of each index changing along with time is shown in figure 15. As can be seen from the curve change, the detection rate R of the area of the thunder area is determined in the whole forecasting process_PODOver 70 percent, and false alarm rate R of area of the thunder area_FARLess than 30%, and a detection rate of falling lightning number R_LDPBasically, the accuracy of the method is higher than 75 percent.

Claims (7)

1. A power distribution network lightning disaster fault prediction method is characterized by comprising the following steps:

step 1: determining lightning partitions of the area to be detected based on multi-time lightning range forecast, and determining the position and lightning falling probability of each lightning partition at the next time;

step 2: establishing a power grid distribution line lightning fault comprehensive partition model, wherein the power grid distribution line lightning fault comprehensive partition model comprises the following steps:

$P_{line}^{t+1}=1-\underset{i=1}{\overset{h}{\Π}}\[1-P_{iTa}^{t+1}{P}_{ir}-P_{iTb}^{t+1}{P}_{ig}\];$

wherein,the probability of lightning trip-out of the feeder section of the area to be detected at t +1 time is h is the number of towers of the feeder section of the area to be detected,the probability of direct lightning strike at time t +1 of the line on which the ith base tower is positioned, P_irIs the lightning trip probability of the line on which the ith base tower is positioned,probability of occurrence of lightning induced overvoltage of t +1 time of line in which ith base tower is located, P_igThe probability of lightning induced overvoltage tripping at the time of t +1 of the line where the ith base tower is located;

and step 3: partitioning each tower of the distribution line as a unit, and determining an effective area of each tower, which is struck by lightning, and an effective area of lightning induced overvoltage, so as to obtain the probability of direct lightning strike and lightning strike of the line t +1 where each tower is located and the probability of lightning induced overvoltage occurrence of the line t +1 where each tower is located;

and 4, step 4: the lightning shielding failure trip probability of the line where the tower is located is obtained according to the tower electrical geometric model, the counterattack trip probability of the line where the tower is located is determined by utilizing a Monte Carlo method, and the lightning shielding failure trip probability of the line where each tower is located is determined according to the lightning shielding failure trip probability of the line where the tower is located and the counterattack trip probability of the line where the tower is located;

and 5: determining the probability of lightning induced overvoltage tripping of the line where the tower is located according to the maximum value of the induced overvoltage on the lead, and obtaining the lightning induced overvoltage failure rate of the line where the tower is located by constructing a fuzzy mathematical model so as to obtain the probability of lightning induced overvoltage tripping of the line where each tower is located, wherein the probability of lightning induced overvoltage tripping of the line where each tower is located is considered;

step 6: inputting the direct lightning strike lightning-down probability of the time t +1 of the line where each tower is located, the lightning induced overvoltage occurrence probability of the time t +1 of the line where each tower is located, the lightning trip-out probability of the line where each tower is located and the lightning induced overvoltage trip-out probability of the line where each tower is located, which considers the lightning current intensity, into the power grid distribution line lightning fault comprehensive partition model to obtain the lightning trip-out probability of the time t +1 of the feeder line section of the area to be measured;

and 7: determining the probability of instantaneous fault occurrence of the feeder line section of the area to be detected at the next moment according to the service time of the distribution line by establishing a distribution line temperature model;

and 8: establishing a distribution line fault probability model under consideration of aging failure and correction of distribution line lightning disasters;

the distribution line fault probability model considering aging failure and correcting the distribution line under the lightning disaster is as follows:

$P^{t+1}=P_{lf}^{t+1}+P_{line}^{t+1}-P_{lf}^{t+1}{P}_{line}^{t+1};$

wherein, P^t+1The probability of the fault of the feeder section of the area to be measured at t +1,the probability of instantaneous fault occurring at the next moment of the feeder line segment of the area to be detected;

and step 9: inputting the lightning trip probability of the feeder section of the area to be detected at the time of t +1 and the instantaneous fault probability of the feeder section of the area to be detected at the next time into a model for predicting the fault probability of the feeder section of the area to be detected at the time of t +1 by considering aging failure and correcting the fault probability of the distribution line under the lightning disaster of the distribution line.

2. The method for predicting the lightning disaster fault of the power distribution network according to the claim 1, wherein the step 1 comprises the following steps:

step 1.1: counting the lightning occurrence time and place of the area to be detected according to the lightning positioning system, and carrying out area division according to the longitude and latitude of the area to be detected to obtain each lightning-falling dense area;

step 1.2: carrying out binarization processing on the thunderbolt dense area, shaping the thunderbolt dense area subjected to binarization processing by adopting an eight-neighborhood boundary tracking algorithm to obtain each thunder partition, and determining the thunderbolt probability of the t-time thunder partition;

step 1.3: determining a development track of t +1 time of each thunder sub-area, namely the thunder sub-area of t +1 time, by optimal matching of the adjacent thunder sub-areas of t-2 time, t-1 time and t time, and determining the thunder falling probability of the t +1 time thunder sub-area according to the thunder falling probability of the t-2 time, t-1 time and t time thunder sub-areas;

the formula for determining the lightning falling probability of the secondary lightning subarea at the time t +1 according to the lightning falling probability of the secondary lightning subareas at the time t-2, the time t-1 and the time t is as follows:

$q_{t+1}=\frac{\underset{t-2}{\overset{t}{\Σ}}{q}_t}{3};$

wherein t is more than or equal to 2, q_t+1Probability of lightning loss of the sub-lightning sub-zone at t +1, q_tThe probability of lightning falling of the secondary lightning subarea at t.

3. The method for predicting the lightning disaster fault of the power distribution network according to the claim 1, wherein the step 3 comprises the following steps:

step 3.1: determining the critical distance y of lightning stroke conductors of towers in the area to be measured_{min i}And critical distance y of each tower induced voltage flashover_{max i}；

Step 3.2: determining an effective area of each tower subjected to lightning stroke and an effective area of lightning induced overvoltage according to the tower electrical geometric model;

step 3.3: and determining the direct lightning strike and lightning fall probability of the time t +1 of the line where each tower is located and the lightning induced overvoltage occurrence probability of the time t +1 of the line where each tower is located according to the lightning strike occurrence effective area and the lightning induced overvoltage effective area of each tower.

4. The method for predicting the lightning disaster fault of the power distribution network according to the claim 1, wherein the step 4 comprises the following steps:

step 4.1: according to the tower electrical geometric model, obtaining the lightning shielding failure rate of the line where the tower is located;

lightning shielding rate P of line on which ith base tower is positioned_iαThe calculation formula is as follows:

wherein,for angle of incidence of lightning, /)_ibOn-line with the ith basic towerHorizontal distance, l, corresponding to the shielding arc of the road_iaThe horizontal distance corresponds to the lightning conductor protection arc of the line where the ith base rod tower is located;

step 4.2: obtaining the lightning shielding trip-out probability of the line where the tower is located according to the lightning shielding failure rate of the line where the tower is located;

probability P of lightning shielding failure tripping of line on which ith base tower is positioned_isThe calculation formula is as follows:

P_is＝ηP_iα；

wherein eta is an arc establishing rate;

step 4.3: simulating and counting the lightning counterattack tripping probability of the line on which each tower is positioned by using a Monte Carlo method;

step 4.4: and taking the sum of the lightning shielding failure trip probability of the line where the tower is located and the tower counterattack trip probability of the line where the tower is located as the lightning trip probability of the line where the tower is located, and obtaining the lightning trip probability of the line where each tower is located.

5. The method for predicting the lightning disaster fault of the power distribution network according to the claim 1, wherein the step 5 comprises the following steps:

step 5.1: determining the probability of lightning induced overvoltage tripping of the line where the tower is located according to the maximum value of the induced overvoltage on the lead;

probability P (I) of lightning induced overvoltage tripping of line where tower is located_min) The calculation formula is as follows:

$P\left(I_{\min }\right)={10}^{-\frac{I_{\min }}{88}}={10}^{-\frac{U_{5\%}S}{25h_d}};$

wherein,is the insulator impulse discharge voltage with a discharge probability of 50%, I_mAmplitude of lightning current, h, for lightning striking the earth_dThe height of the overhead line to the ground is defined, and S is the horizontal distance from a lightning stroke point to the overhead line;

step 5.2: establishing a fuzzy mathematical model, taking a lightning excitation parameter and a line span parameter as the input of the fuzzy mathematical model, taking a lightning induced overvoltage fault rate as the output of the fuzzy mathematical model, combining the lightning excitation parameter and the line span parameter, establishing a fuzzy control rule, and defuzzifying by adopting a maximum membership method to obtain the lightning induced overvoltage fault rate;

step 5.3: and calculating the lightning induced overvoltage tripping probability of the line where each tower is positioned, considering the lightning current intensity, according to the lightning induced overvoltage tripping probability of the line where the tower is positioned and the lightning induced overvoltage fault rate.

6. The method for predicting the lightning disaster fault of the power distribution network according to claim 3, wherein the effective lightning stroke area of the tower is a distance y away from the tower in a direction perpendicular to the power distribution line by taking the tower as a center_{min i}And distribution line direction 1/2 range;

the effective area of the lightning induced overvoltage is a distance y from the pole tower in the direction perpendicular to the distribution line by taking the pole tower as the center_{max i}And distribution line direction 1/2 range.

7. The method for predicting lightning disaster faults of power distribution network according to claim 3, wherein the probability of direct lightning strike at time t +1 of the line where the ith base tower is locatedThe calculation formula of (2) is as follows:

$P_{iTa}^{t+1}=\frac{{a^{\′}}_{t+1}}{a_{t+1}}{q}_{t+1};$

wherein, a'_t+1The overlapping area of the effective area of the ith base tower lightning stroke at t +1 and the secondary lightning subarea at t +1 of the tower, a_t+1The area of the lightning subarea where the ith base tower is located when the t +1 is obtained;

probability of occurrence of t + 1-time lightning induced overvoltage of line on which ith base tower is locatedThe calculation formula of (2) is as follows:

$P_{iTb}^{t+1}=\frac{{b^{\′}}_{t+1}}{a_{t+1}}{q}_{t+1};$

wherein, b'_t+1The effective area of the lightning induced overvoltage of the ith tower base at the time of t +1 is the overlapping area of the secondary lightning subarea at the time of t +1 where the tower is located.