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

A kind of power distribution network Lightning Disaster failure prediction method

Technical field

The present invention relates to distribution technique field, be specifically related to a kind of power distribution network Lightning Disaster failure prediction method.

Background technology

In recent years, along with the fast development of electrical network, thunderbolt frequently occurs, power distribution network as between power system and user Direct and crucial part, Lightning Disaster has become as the main harm of China's power distribution network safe and reliable operation.

At present, lightning fault predicting means has: have based on limited serious thunderstorm event and relevant weather data and electric network fault Data, utilize Mathematical Statistics Analysis, set up electric network fault rate regression model, but thunderstorm event is less, and time interval is longer, real Time property is poor, has the biggest limitation to prediction；The only consideration thunder and lightning variation tendency having does not considers that intensity of lightning current is to distribution line thunder The impact of electric induction overvoltage probability of malfunction；Some lightning fault probabilistic forecastings only consider single Lightning Disaster, but in reality, thunder Electricity is frequently accompanied by rainfall and occurs simultaneously, and the raindrop in discharging gap can make the air gap enhanced intensity and be distorted, direct shadow Ring the size of lightning flash over probability；Have only considers the situation that thunder and lightning causes distribution line to break down, and does not considers that circuit itself is old Change the impact of effect.

Therefore realize the forecast to power distribution network thunder and lightning subregion, consider that intensity of lightning current, rainfall intensity and circuit itself are aging many Aspect affects, and then prediction lightning fault probability, and to strengthening, power distribution network opposing Lightning Disaster is significant.

Summary of the invention

For the deficiencies in the prior art, the present invention proposes a kind of power distribution network Lightning Disaster failure prediction method.

The technical scheme is that

A kind of power distribution network Lightning Disaster failure prediction method, comprises the following steps:

Step 1: determine the thunder and lightning subregion in region to be measured based on time many thunder and lightning scope forecasts, and determine that each thunder and lightning in lower a period of time time divides The position in district and thunderbolt probability；

Step 1.1: according to lightning location system statistics region to be measured thunder and lightning time of origin and place, carry out region according to its longitude and latitude Divide, obtain each thunderbolt close quarters；

Step 1.2: thunderbolt close quarters is carried out binary conversion treatment, uses eight neighborhood to the thunderbolt close quarters after binary conversion treatment Edge following algorithm carries out shaping, obtains each thunder and lightning subregion, the thunderbolt probability of time thunder and lightning subregion when determining t；

Step 1.3: during by the Optimum Matching of thunder and lightning subregion secondary when adjacent t-2, t-1, t is determined each thunder and lightning subregion t+1 Secondary development track, i.e. secondary during t+1 thunder and lightning subregion, determine according to the thunderbolt probability of the thunder and lightning subregion of when t-2, t-1, t time The thunderbolt probability of time thunder and lightning subregion during t+1；

The thunderbolt probability of time thunder and lightning subregion when the described thunderbolt probability according to the thunder and lightning subregion of when t-2, t-1, t time determines t+1 Formula is as follows:

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

Wherein, t >=2, q_t+1For the thunderbolt probability of during t+1 thunder and lightning subregion, q_tThunderbolt probability for during t thunder and lightning subregion.

Step 2: set up electrical network distribution line lightning fault comprehensive sub-areas model, described electrical network distribution line lightning fault total score Section model is:

$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,For the thunder and lightning tripping operation probability that region to be measured feeder line section is secondary when t+1, h is the shaft tower of region to be measured feeder line section Number,Direct attack thunderbolt probability secondary when being the i-th base shaft tower place circuit t+1, P_irIt it is the thunderbolt jumping of the i-th base shaft tower place circuit Lock probability,Thunder and lightning induction voltage probability of happening secondary when being the i-th base shaft tower place circuit t+1, P_igIt it is the i-th base shaft tower institute The thunder and lightning induction voltage tripping operation probability secondary when circuit t+1；

Step 3: carry out subregion in units of each shaft tower of distribution line, determines that each shaft tower occurs effective coverage and the thunder and lightning sense of thunderbolt Answer the effective coverage of overvoltage, thus direct attack thunderbolt probability when obtaining each shaft tower place circuit t+1 time and each shaft tower place circuit Thunder and lightning induction voltage probability of happening secondary during t+1；

Step 3.1: determine critical distance y of the thunderbolt wire of each shaft tower in region to be measured_miniCritical with each shaft tower induced voltage flashover Distance y_maxi；

Step 3.2: determine that each shaft tower occurs the effective coverage of thunderbolt and having of thunder and lightning induction voltage according to shaft tower electric geometry method Effect region；

Described shaft tower occurs the effective coverage of thunderbolt to be vertical distribution line direction distance shaft tower y centered by shaft tower_miniAnd distribution wire In the range of the span of direction, road 1/2；

The effective coverage of described thunder and lightning induction voltage is vertical distribution line direction distance shaft tower y centered by shaft tower_maxiAnd distribution In the range of line direction 1/2 span.

Step 3.3: occur the effective coverage of thunderbolt and the effective coverage of thunder and lightning induction voltage to determine each shaft tower place according to each shaft tower Thunder and lightning induction voltage probability of happening secondary when direct attack thunderbolt probability secondary during circuit t+1 and each shaft tower place circuit t+1.

Direct attack thunderbolt probability secondary during described i-th base shaft tower place circuit t+1Computing formula be:

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

Wherein, a '_t+1Effective coverage and secondary thunder and lightning subregion during the t+1 at this shaft tower place for during t+1 the i-th base shaft tower generation thunderbolt Overlapping area, a_t+1Area for during t+1 the i-th base shaft tower place thunder and lightning subregion；

Thunder and lightning induction voltage probability of happening secondary during described i-th base shaft tower place circuit t+1Computing formula be:

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

Wherein, b '_t+1Effective coverage and secondary thunder during the t+1 at this shaft tower place for during t+1 the i-th base shaft tower thunder and lightning induction voltage The overlapping area of electricity subregion.

Step 4: obtain the thunderbolt tripping operation probability of shaft tower place circuit according to shaft tower electric geometry method, utilize Monte Carlo Method determines shaft tower place circuit counterattack tripping operation probability, and thunderbolt tripping operation probability and shaft tower institute according to shaft tower place circuit are online The counterattack tripping operation probability on road determines the lightning stroke trip probability of each shaft tower place circuit；

Step 4.1: according to shaft tower electric geometry method, obtain the thunderbolt rate of shaft tower place circuit；

Thunderbolt rate P of described i-th base shaft tower place circuit_iαComputing formula is as follows:

Wherein,For thunder and lightning angle of incidence, l_ibIt it is the shielding exposure arc pair of the i-th base shaft tower place circuit The horizontal range answered, l_iaIt it is the horizontal range that the earth-wire protection arc of the i-th base shaft tower place circuit is corresponding；

Step 4.2: obtain the thunderbolt tripping operation probability of shaft tower place circuit according to the thunderbolt rate of shaft tower place circuit；

The thunderbolt tripping operation probability P of described i-th base shaft tower place circuit_isComputing formula is as follows:

P_is=η P_iα；

Wherein, η is probability of sustained arc；

Step 4.3: utilize monte carlo method simulation to count the back flashover tripping operation probability of each shaft tower place circuit；

Step 4.4: the shaft tower counterattack tripping operation probability sum of the thunderbolt of shaft tower place circuit is tripped probability and shaft tower place circuit As the lightning stroke trip probability of this shaft tower place circuit, obtain the lightning stroke trip probability of each shaft tower place circuit.

Step 5: determine the thunder and lightning induction voltage tripping operation probability of shaft tower place circuit according to induced overvoltage maximum on wire, Obtain the thunder and lightning induction voltage fault rate of shaft tower place circuit by building fuzzy mathematical model, thus obtain considering that lightning current is strong The thunder and lightning induction voltage tripping operation probability of each shaft tower place circuit of degree；

Step 5.1: determine the thunder and lightning induction voltage tripping operation probability of shaft tower place circuit according to induced overvoltage maximum on wire；

The thunder and lightning induction voltage tripping operation probability P (I of described shaft tower place circuit_min) computing formula is as follows:

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

Wherein,It is insulator impulse sparkover voltage when 50% for discharge probability, I_mLightning current for thunderbolt the earth Amplitude, h_dFor overhead transmission line to ground level, S is the lightning strike spot horizontal range to overhead transmission line；

Step 5.2: by building fuzzy mathematical model, using thunder and lightning excitation parameters and line span parameter as fuzzy mathematical model Input, using thunder and lightning induction voltage fault rate as the output of fuzzy mathematical model, by thunder and lightning excitation parameters and line span parameter It is combined, sets up fuzzy control rule, use maximum membership degree method de-fuzzy, obtain thunder and lightning induction voltage fault rate；

Step 5.3: thunder and lightning induction voltage tripping operation probability and thunder and lightning induction voltage fault rate according to shaft tower place circuit calculate and examine Consider the thunder and lightning induction voltage tripping operation probability of each shaft tower place circuit of intensity of lightning current.

Step 6: by thunder and lightning sense when attacking thunderbolt probability, each shaft tower place circuit t+1 directly time during each shaft tower place circuit t+1 time Answer overvoltage probability of happening, the lightning stroke trip probability of each shaft tower place circuit and consider each shaft tower place circuit thunder of intensity of lightning current Electric induction overvoltage tripping probability input electrical network distribution line lightning fault comprehensive sub-areas model, obtains region to be measured feeder line section and exists Thunder and lightning tripping operation probability secondary during t+1；

Step 7: by setting up distribution line temperature model, determines subsequent time region to be measured according to distribution line active time Feeder line section generation transient fault probability；

Step 8: set up and consider ageing failure and revise distribution line under distribution line Lightning Disaster to break down probabilistic model；

Described consideration ageing failure and to revise the probabilistic model that breaks down of distribution line under distribution line Lightning Disaster as follows:

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

Wherein, P^t+1For the region to be measured feeder line section probability that breaks down when t+1 time,For a period of time under the feeder line section of region to be measured Carve and transient fault probability occurs；

Step 9: thunder and lightning tripping operation probability secondary when t+1 for region to be measured feeder line section and region to be measured feeder line section subsequent time are occurred wink Time probability of malfunction input consider ageing failure and revise distribution line under distribution line Lightning Disaster and break down probabilistic model prediction The probability that during t+1, secondary region to be measured feeder line section breaks down.

Beneficial effects of the present invention:

The present invention proposes a kind of power distribution network Lightning Disaster failure prediction method, the present invention is directed to China's lightening activity and has the strongest ground Territory property, first carries out the division in thunder and lightning region, then respective regions carries out careful longitude and latitude division, decrease administrative region The workload of data mining, also makes lightning monitoring data apparent, accurately simultaneously；Consider intensity of lightning current size distribution The impact of net thunder and lightning induction voltage probability of malfunction takes into account, and builds fuzzy mathematical model and be analyzed lightning fault probability, Improve distribution line probability of malfunction reliability of operation and accuracy；Lightning fault probabilistic forecasting normally only considers single thunder and lightning calamity Evil, takes into account rain fall the impact of insulator probability of sustained arc here, improves the precision of thunder and lightning tripping operation probabilistic forecasting further； The ageing failure of circuit own is also to affect the key factor that Lightning Disaster probability of malfunction is very important, and this impact is considered thunder In the prediction of electricity disaster probability of malfunction and computational methods；By the thunder calamity tripping operation that in power distribution network, either direct lightning strike or induced lightening cause Phenomenon carries out comprehensive modeling, improves minefield prediction and the accuracy rate of transmission line caused by lightning strike probability.

Accompanying drawing explanation

Fig. 1 is the flow chart of power distribution network Lightning Disaster failure prediction method in the specific embodiment of the invention；

Fig. 2 is position and the flow chart of thunderbolt probability determining each thunder and lightning subregion in lower a period of time time in the specific embodiment of the invention；

Fig. 3 is thunderbolt subregion recognition result figure circular in the specific embodiment of the invention；

Time thunder and lightning subregion schematic diagram when Fig. 4 is to determine each thunder and lightning subregion t+1 in the specific embodiment of the invention；

When Fig. 5 is to calculate each shaft tower t+1 in the specific embodiment of the invention time when attacking thunderbolt probability and each shaft tower t+1 directly time The flow chart of thunder and lightning induction voltage probability of happening；

Fig. 6 is to be caused line insulation flashover block plan by thunder and lightning in the specific embodiment of the invention；

Fig. 7 is that in the specific embodiment of the invention, shaft tower occurs the effective coverage of thunderbolt and effective district signal of thunder and lightning induction voltage Figure；

Fig. 8 is to determine each bar according to shaft tower thunderbolt tripping operation probability and shaft tower counterattack tripping operation probability in the specific embodiment of the invention The flow chart of the lightning stroke trip probability of tower；

Fig. 9 is the electric geometry method of shaft tower in the specific embodiment of the invention；

Figure 10 is each shaft tower thunder and lightning induction voltage tripping operation probability determining in the specific embodiment of the invention and considering intensity of lightning current Flow chart；

Figure 11 is the membership function scattergram of thunder and lightning excitation parameters in the specific embodiment of the invention；

Figure 12 is the membership function scattergram of line span parameter in the specific embodiment of the invention；

Figure 13 is the membership function scattergram of thunder and lightning induction voltage fault rate in the specific embodiment of the invention；

Figure 14 is distribution line temperature model figure in the specific embodiment of the invention；

Figure 15 is lightning forecasting evaluation index curve in the specific embodiment of the invention.

Detailed description of the invention

Below in conjunction with the accompanying drawings the specific embodiment of the invention is described in detail.

A kind of power distribution network Lightning Disaster failure prediction method, as it is shown in figure 1, comprise the following steps:

Step 1: determine the thunder and lightning subregion in region to be measured based on time many thunder and lightning scope forecasts, and determine that each thunder and lightning in lower a period of time time divides The position in district and thunderbolt probability, as shown in Figure 2.

Step 1.1: according to lightning location system statistics region to be measured thunder and lightning time of origin and place, carry out district according to its longitude and latitude Territory divides, and obtains each thunderbolt close quarters.

In present embodiment, due to the uncertainty of thunder and lightning self, so it is pre-first to carry out thunder and lightning scope when studying lightning fault Report.China's lightning monitoring network is frequently with longitude and latitude subregion at present, but actually China's lightening activity has the strongest region, Southeastern coastal areas thunder and lightning is multiple, and the Northwest is relatively fewer.So can take according to the lightning data that meteorological department observes for many years Region divides, then respective regions carries out careful longitude and latitude division, reduces unnecessary workload.

Step 1.2: thunderbolt close quarters is carried out binaryzation (0-1) and processes, the thunderbolt close quarters after binary conversion treatment is adopted Carry out shaping with eight neighborhood edge following algorithm, obtain each thunder and lightning subregion, the thunderbolt probability of time thunder and lightning subregion when determining t.

In present embodiment, thunderbolt close quarters is carried out binary conversion treatment, the thunderbolt close quarters after binary conversion treatment is used Eight neighborhood edge following algorithm carries out shaping, obtains each thunder and lightning subregion, finally gives the thunderbolt subregion recognition result figure of circle, as Shown in Fig. 3.When be can get t by Fig. 3 the latitude and longitude coordinates of time each thunder and lightning regional center (RC) point L for (x, y), radius be r, during t time The thunderbolt probability q of thunder and lightning subregion_tComputing formula such as formula (1) shown in:

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

Wherein, n ' is the thunderbolt sum in during t thunderbolt subregion, the thunderbolt sum that N ' is during t administrative region to be measured.

Step 1.3: during by the Optimum Matching of thunder and lightning subregion secondary when adjacent t-2, t-1, t is determined each thunder and lightning subregion t+1 Secondary development track, i.e. secondary during t+1 thunder and lightning subregion, determine according to the thunderbolt probability of the thunder and lightning subregion of when t-2, t-1, t time The thunderbolt probability of time thunder and lightning subregion during t+1.

In present embodiment, in order to obtain optimal trajectory, by the optimum to thunder and lightning subregion secondary when adjacent t-2, t-1, t Join, it is assumed that between 2 thunder and lightning subregions, shorter motion track has bigger probability, 2 thunder and lightning by stages that area is similar Motion track has bigger probability, determines development track secondary during each thunder and lightning subregion t+1, and i.e. secondary during t+1 thunder and lightning divides District is as shown in Figure 4.

The formula of the thunderbolt probability of time thunder and lightning subregion when thunderbolt probability according to the thunder and lightning subregion of when t-2, t-1, t time determines t+1 As shown in formula (2):

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

Wherein, t >=2, q_t+1For the thunderbolt probability of during t+1 thunder and lightning subregion, q_tThunderbolt probability for during t thunder and lightning subregion.

Step 2: set up electrical network distribution line lightning fault comprehensive sub-areas model.

In present embodiment, it is believed that be series relationship between the shaft tower on same distribution line, then the arbitrary shaft tower on circuit occurs Fault region the most to be measured feeder line section arises that fault, then the probability of malfunction of circuit is equal to the probability of malfunction of this shaft tower.If district to be measured Territory feeder line section has h shaft tower.

Shown in electrical network distribution line lightning fault comprehensive sub-areas model such as 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,For the thunder and lightning tripping operation probability that region to be measured feeder line section is secondary when t+1, h is the shaft tower of region to be measured feeder line section Number,Direct attack thunderbolt probability secondary when being the i-th base shaft tower place circuit t+1, P_irIt it is the thunderbolt jumping of the i-th base shaft tower place circuit Lock probability,Thunder and lightning induction voltage probability of happening secondary when being the i-th base shaft tower place circuit t+1, P_igIt it is the i-th base shaft tower institute The thunder and lightning induction voltage tripping operation probability secondary when circuit t+1.

Step 3: carry out subregion in units of each shaft tower of distribution line, determines that each shaft tower occurs effective coverage and the thunder and lightning sense of thunderbolt Answer the effective coverage of overvoltage, thus direct attack thunderbolt probability when obtaining each shaft tower place circuit t+1 time and each shaft tower place circuit Thunder and lightning induction voltage probability of happening secondary during t+1, as shown in Figure 5.

Step 3.1: determine critical distance y of the thunderbolt wire of each shaft tower in region to be measured_miniCritical with each shaft tower induced voltage flashover Distance y_maxi。

In present embodiment, thunder and lightning cause line insulation flashover subregion as shown in Figure 6.

Critical distance y of the thunderbolt wire of the i-th base shaft tower_miniComputing formula such as formula (4) shown in:

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

Wherein,For thunder and lightning the earth hit away from,Hit away from, I for lightning conducter_mFor The amplitude of lightning current of thunderbolt the earth, h_dFor overhead transmission line to ground level.

Critical distance y of the induced voltage flashover of the i-th base shaft tower_maxiComputing formula such as formula (5) shown in:

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

Wherein, CFO is that line influence overvoltage has exceeded 1.5 times of critical flashover voltages.

Step 3.2: determine that each shaft tower occurs effective coverage and the thunder and lightning induction voltage of thunderbolt according to shaft tower electric geometry method Effective coverage.

In present embodiment, there is the effective coverage of effective coverage and the thunder and lightning induction voltage being struck by lightning as shown in Figure 7 in shaft tower.Bar Tower occurs the effective coverage of thunderbolt to be vertical distribution line direction distance shaft tower y centered by shaft tower_miniWith distribution line direction 1/2 In the range of span.The effective coverage of thunder and lightning induction voltage is vertical distribution line direction distance shaft tower y centered by shaft tower_maxi In the range of the span of distribution line direction 1/2.

Step 3.3: occur the effective coverage of thunderbolt and the effective coverage of thunder and lightning induction voltage to determine each shaft tower place according to each shaft tower Thunder and lightning induction voltage probability of happening secondary when direct attack thunderbolt probability secondary during circuit t+1 and each shaft tower place circuit t+1.

In present embodiment, shown in the computing formula such as formula (6) attacking thunderbolt probability directly secondary during the i-th base shaft tower place circuit t+1:

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

Wherein, a '_t+1Effective coverage and secondary thunder and lightning subregion during the t+1 at this shaft tower place for during t+1 the i-th base shaft tower generation thunderbolt Overlapping area, a_t+1Area for during t+1 the i-th base shaft tower place thunder and lightning subregion.

Shown in the computing formula such as formula (7) of thunder and lightning induction voltage probability of happening secondary during the i-th base shaft tower place circuit t+1:

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

Wherein, b '_t+1Effective coverage and secondary thunder during the t+1 at this shaft tower place for during t+1 the i-th base shaft tower thunder and lightning induction voltage The overlapping area of electricity subregion.

Step 4: obtain the thunderbolt tripping operation probability of shaft tower place circuit according to shaft tower electric geometry method, utilize Monte Carlo Method determines shaft tower place circuit counterattack tripping operation probability, and thunderbolt tripping operation probability and shaft tower institute according to shaft tower place circuit are online The counterattack tripping operation probability on road determines the lightning stroke trip probability of each shaft tower place circuit, as shown in Figure 8.

Step 4.1: according to shaft tower electric geometry method, obtain the thunderbolt rate of shaft tower place circuit.

In present embodiment, the electric geometry method of shaft tower as it is shown in figure 9, as shown in Figure 9, r_cHit away from, r for wire_sFor keeping away Thunder line hits away from, r_gFor ground hit away from,For the angle in thunder and lightning angle of incidence, i.e. lightning leader direction perpendicular to the ground, examine Landform and the impact on distribution line risk of shielding failure of the thunder and lightning incident direction, h are considered_sFor the height of lightning conducter, h_cFor the height of wire, θ₁Expose critical wire on arc for shielding to hit away from r_cWith the angle of horizontal plane, θ₂Expose arc lower critical wire for shielding to hit away from r_c ^*With water The angle of plane, θ is earth-wire protection angle.

Thunderbolt rate P of the i-th base shaft tower place circuit_iαShown in computing formula such as formula (8):

Wherein,For thunder and lightning angle of incidence, l_ib=B ' C=r_c(cosθ₁-cosθ₂) it is the i-th base The shielding of shaft tower place circuit exposes the horizontal range that arc is corresponding, l_ia=OC=r_ccos θ₁+2(h_s-h_c) tan θ is the i-th base shaft tower The horizontal range that the earth-wire protection arc of place circuit is corresponding.

Step 4.2: obtain the thunderbolt tripping operation probability of shaft tower place circuit according to the thunderbolt rate of shaft tower place circuit.

In present embodiment, the thunderbolt tripping operation probability P of the i-th base shaft tower place circuit_isShown in computing formula such as formula (9):

P_is=η P_iα (9)

Wherein, η is probability of sustained arc.

Step 4.3: utilize monte carlo method simulation to count the back flashover tripping operation probability of each shaft tower place circuit.

Step 4.3.1: set number realization as N, defines y_kRepresent the result of kth time simulation, if counterattack causes flashover, then y_k=1, otherwise y_k=0.

Step 4.3.2: randomly generate [0,1] equally distributed random number r₁If, r₁＞ P_iα, then perform step 4.3.3, no Then perform step 4.3.4.

Step 4.3.3: randomly generate [0,1] equally distributed random number r₂If, r₂＜ g, g for hitting bar rate, then occur anti- Hit y_k=1, perform step 4.3.5, otherwise, y_k=0, perform step 4.3.5.

Step 4.3.4: judge whether present day analog number of times reaches number realization N, if so, performs step 4.3.5, otherwise, returns Return step 4.3.2,

Step 4.3.5: statistics counterattack trip-out rate, obtains strikeing back the progressive statistic estimated value ξ of trip-out rate, obtains counterattack tripping operation general Rate P_ic。

In present embodiment, shown in the progressive statistic estimated value ξ such as formula (10) of counterattack trip-out rate:

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

Counterattack tripping operation probability P_icAs shown in formula (11):

P_ic=η ξ (11)

Wherein, η is probability of sustained arc.According to test and operating experience, probability of sustained arc η=4.5E^0.75-14 (%), wherein E is insulator chain Average running voltage (virtual value) gradient, kV/m, raindrop can make the air gap enhanced intensity and be distorted, and make E increase, Thus improve probability of sustained arc.

Lightning Disaster is general all along with rainfall while occurring, and rainfall can directly increase lightning fault probability.First rainwater is situated between Electric constant is much larger than the dielectric constant of air, and the raindrop in discharging gap can make the air gap enhanced intensity and be distorted, and this has It is beneficial to initiating electron and collapses the development with multiple abscess and generation；And the gathering of water droplet effectively reduces the insulation distance of the air gap, institute To cause gap flashover voltage to reduce.

It addition, for the little rainfall of intensity, humidity accounts for main impact, along with hydrone increases, general by Water Molecular Adsorption of electronics Rate also increases, and the free electron number in spatial joint clearance reduces, thus suppresses the development of electric discharge, so the increase of humidity can make air The Power Flashover Voltage in gap rises.

But, thunder and lightning is a kind of high in the clouds electric discharge phenomena, and Lightning Disaster often with heavy showers, sees the shadow by humidity so integrating Ring the impact making the air gap field intensity distortion much smaller than rainwater.

Step 4.4: the shaft tower counterattack tripping operation probability sum of the thunderbolt of shaft tower place circuit is tripped probability and shaft tower place circuit As the lightning stroke trip probability of this shaft tower place circuit, obtain the lightning stroke trip probability of each shaft tower place circuit.

In present embodiment, the lightning stroke trip probability P of the i-th base shaft tower place circuit_irFormula such as formula (12) shown in:

P_ir=P_ic+P_is (12)

Step 5: determine the thunder and lightning induction voltage tripping operation probability of shaft tower place circuit according to induced overvoltage maximum on wire, Obtain the thunder and lightning induction voltage fault rate of shaft tower place circuit by building fuzzy mathematical model, thus obtain considering that lightning current is strong The thunder and lightning induction voltage tripping operation probability of each shaft tower place circuit of degree, as shown in Figure 10.

Step 5.1: determine the thunder and lightning induction voltage tripping operation probability of shaft tower place circuit according to induced overvoltage maximum on wire.

In present embodiment, thunder and lightning induction voltage tripping operation probability P (I_min) shown in computing formula such as formula (13):

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

Wherein,It is insulator impulse sparkover voltage when 50% for discharge probability, the induced overvoltage on wire, I_mFor the amplitude of lightning current of thunderbolt the earth, h_dFor overhead transmission line to ground level, S is the lightning strike spot horizontal range to overhead transmission line.

In present embodiment, the distribution line through city is typically subject to covering of neighbouring high constructure or tree, so distribution wire The induced overvoltage produced when mostly road thunder and lightning trip accident is object neighbouring due to thunderbolt causes.Thunder and lightning induction voltage main Composition produces during Fields of Lightning Return Stroke, and i.e. while descending leader development, earth bulge produce raw head-on guide upwards send out Exhibition, there is strong electric discharge in the two, its each the positive and negative charge in guide be neutralized.Thunder and lightning induction voltage includes electrostatic induction With two components of electromagnetic induction, owing to main discharge passage is vertical with wire, mutual inductance is little, and electromagnetic induction is weak, so electrostatic component rises Main Function.So according to relevant theory analysis and experimental measurements, when the distance of lightning strike spot Yu circuit makes to produce on wire During thunder and lightning induction voltage, discharge probability is insulator impulse sparkover voltage U when 50%_50%Equal to the induced overvoltage on wire It is worth greatly U_maxAs shown in formula (14):

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

Step 5.2: by building fuzzy mathematical model, using thunder and lightning excitation parameters and line span parameter as fuzzy mathematical model Input, using thunder and lightning induction voltage fault rate as the output of fuzzy mathematical model, by thunder and lightning excitation parameters and line span parameter It is combined, sets up fuzzy control rule, use maximum membership degree method de-fuzzy, obtain thunder and lightning induction voltage fault rate.

In present embodiment, on distribution line induced overvoltage probability of malfunction except with line levels, circuit and lightning strike spot spacing Outside the Pass having, also relevant with amplitude of lightning current.And the factor affecting amplitude of lightning current further relates to many factors, and amplitude of lightning current And lack available model between line failure rate.By building fuzzy mathematical model, by thunder and lightning excitation parameters E_l= a_va_ta_sa_cWith line span parameter L_pInput as fuzzy mathematical model.

Wherein, a_vFor lightning current echo wave speed coefficient, i.e. lightning current wave shape parameter, can be by being arranged on the thunder and lightning of high mountain or high tower Stream waveform monitoring device records.With lightning current echo wave speed 1.3 × 10⁸On the basis of m/s (coefficient is 1), echo propagation rate is the biggest, Reaching peak value the soonest from lightning strike spot voltage the most nearby, and amplitude of lightning current is the biggest, what echo wave speed was bigger heightens lightning current echo speed Degree coefficient (1～1.2), reduction lightning current echo wave speed coefficient (0.8～1) that echo wave speed is less.

a_tFor time coefficient before lightning current wave, can be recorded by lightning current waveform monitoring device.With lightning current wave front time 0.5 μ s On the basis of (coefficient is 1), the reduction wave front time coefficient (0.6～1) that wave front time is longer, when wave front time less than 0.5 μ s time, Amplitude of lightning current is relatively big, and coefficient is 1.Wave front time is the shortest, reaches peak value, and thunder and lightning the soonest from lightning strike spot voltage the most nearby Stream amplitude is the biggest.

a_cFor earth conductivity coefficient, a_sFor surrounding enviroment screening factor.With plains region, the earth is as perfact conductor with unshielded On the basis of the environment of thing (coefficient is 1), little to earth conductivity, the development of thunder and lightning descending leader is had obvious inducing action Landform heightens earth conductivity coefficient (1～1.3), big to earth conductivity, thunder and lightning descending leader is had obvious inhibition Landform reduces earth conductivity coefficient (0.8～1)；To open, unshielded thing, be conducive to the ring that thunder and lightning induction voltage formed Coefficient (1～2) is heightened in border, is unfavorable for that the environment that thunder and lightning induction voltage is formed turns down coefficient (0.5～1) to having tree and building etc..

Thunder and lightning excitation parameters use 6 fuzzy subsets cover parameter area: thunder and lightning encourages the least (E_vs), thunder and lightning encourage little (E_s)、 Thunder and lightning encourages medium (E_m), the big (E of thunder and lightning excitation_bl), the very big (E of thunder and lightning excitation_vl), the very big (E of thunder and lightning excitation_el), its The distribution of membership function is as shown in figure 11.

Line span parameter is contained the scope of line span coefficient: the little (L of line parameter circuit value with 4 fuzzy subsets_s), circuit ginseng Medium (the L of number_m), the big (L of line parameter circuit value_l), the very big (L of line parameter circuit value_vl), the distribution of its membership function is as shown in figure 12.

Thunder and lightning induction voltage fault rate is covered its codomain [0,1] with 7 fuzzy subsets: the least (ES), the least (VS), little (S), in (M), big (L), very big (VL), very big (EL).Dividing of its membership function Cloth is as shown in figure 13.

According to analysis thunder and lightning induction voltage probability of malfunction affected about different factors, by thunder and lightning excitation parameters and line span Parameter is combined, and sets up 24 fuzzy control rules, can set up 24 fuzzy control rules, as shown in table 1:

Table 1 fuzzy control rule

Using maximum membership degree method de-fuzzy, obtain thunder and lightning induction voltage fault rate μ, the division of fuzzy membership function needs Practical application afterwards constantly to be checked and perfect.

Step 5.3: thunder and lightning induction voltage tripping operation probability and thunder and lightning induction voltage fault rate according to shaft tower place circuit calculate and examine Consider the thunder and lightning induction voltage tripping operation probability of each shaft tower place circuit of intensity of lightning current.

In present embodiment, it is considered to the thunder and lightning induction voltage probability of malfunction P of shaft tower place circuit after intensity of lightning current_igSuch as formula (15) Shown in:

P_ig=μ P (I_min) (15)

Step 6: by thunder and lightning sense when attacking thunderbolt probability, each shaft tower place circuit t+1 directly time during each shaft tower place circuit t+1 time Answer overvoltage probability of happening, the lightning stroke trip probability of each shaft tower place circuit and consider each shaft tower place circuit thunder of intensity of lightning current Electric induction overvoltage tripping probability input electrical network distribution line lightning fault comprehensive sub-areas model, obtains region to be measured feeder line section and exists Thunder and lightning tripping operation probability secondary during t+1.

Step 7: by setting up distribution line temperature model, determines subsequent time region to be measured according to distribution line active time Feeder line section generation transient fault probability.

In present embodiment, distribution line is along with the length of active time, and its ageing failure situation is the most different, and high annealing is it The main cause of life loss.Visible, conductor temperature directly affects wire active time.And the electric current that meets of circuit itself produces Heat and ambient temperature change the most notable on the impact of circuit itself, so the distribution line temperature that foundation is as shown in figure 14 Degree model.

In Figure 14: n is wire quality, C_PHold for wire specific heat, J/kg DEG C；I is current in wire, A, θ_lTransport for circuit Trip temperature, DEG C；θ₀For wire initial temperature, DEG C；θ_aFor ambient temperature, DEG C；Q is heat during distribution line is on active service Summation；Q_rFor the heat of radiation transmission, W/m；T is circuit active time.

Therefore through substantial amounts of experiment and data analysis, it is known that life expectancy L of distribution line₁Heat during being on active service with circuit Shown in exchange and circuit running temperature relation such as formula (16):

L₁=Qe^-λθ (16)

Wherein, λ is the constant relevant to conductor quality and material properties.

Estimate to obtain through wire accelerating lifetime testing or fail data record: distribution line ageing process meets Weibull distribution, only Relevant with form parameter β；η_lFor scale parameter (characteristics life parameter), make η here_l=L₁, then distribution line accumulation is obtained Probability-distribution function F_la(1|θ_l) as shown in formula (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 conditional probability, distribution line is at θ_lAt a temperature of be on active service after the t time, there is transient fault in the t+1 moment ProbabilityAs shown in formula (18):

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

Step 8: set up and consider ageing failure and revise distribution line under distribution line Lightning Disaster to break down probabilistic model.

In present embodiment, it is considered under ageing failure and correction distribution line Lightning Disaster, distribution line breaks down probabilistic model such as Shown in 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+1For the region to be measured feeder line section probability that breaks down when t+1 time,For a period of time under the feeder line section of region to be measured Carve and transient fault probability occurs.

In present embodiment, owing to lightning monitoring information is that timesharing time obtains, it is contemplated that ageing failure and correction distribution line thunder Probability of malfunction is occurred time to break down when being t+1 probability under electricity disaster.

Step 9: thunder and lightning tripping operation probability secondary when t+1 for region to be measured feeder line section and region to be measured feeder line section subsequent time are occurred wink Time probability of malfunction input consider ageing failure and revise distribution line under distribution line Lightning Disaster and break down probabilistic model prediction The probability that during t+1, secondary region to be measured feeder line section breaks down.

In present embodiment, in order to assess thunder and lightning subregion accuracy of the forecast, use minefield area recall rate index R_POD, minefield Area false alarm rate index R_FARWith thunderbolt number recall rate index R_LDP, as shown in formula (20)-(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 region area to be measured of forecast, A^*For actual thunder and lightning region area,For actual non-thunder and lightning region area； E∩A^*For forecasting accurate thunder and lightning region area,For forecast thunder and lightning region area, P by mistake^t+1For forecast thunderbolt probability, P is Actual thunderbolt probability, (E ∩ A^*)min{P^t+1, P} is for forecasting successful thunderbolt number, and AP is the thunderbolt number in actual thunder and lightning region.

In present embodiment, use the every 1min of the inventive method to forecast a thunder and lightning occurrence scope, and calculate its corresponding index, The time dependent curve of each index is as shown in figure 15.From curvilinear motion it can be seen that in whole forecasting process, face, minefield Long-pending recall rate R_PODReach more than 70%, minefield area false alarm rate R_FARLess than 30%, thunderbolt number recall rate R_LDPThe biggest In 75%, thus demonstrate the minefield forecasting procedure that the inventive method proposed and there is higher accuracy rate.

Claims (7)

1. a power distribution network Lightning Disaster failure prediction method, it is characterised in that comprise the following steps:

Step 1: determine the thunder and lightning subregion in region to be measured based on time many thunder and lightning scope forecasts, and determine that each thunder and lightning in lower a period of time time divides The position in district and thunderbolt probability；

Step 2: set up electrical network distribution line lightning fault comprehensive sub-areas model, described electrical network distribution line lightning fault total score Section model is:

$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,For the thunder and lightning tripping operation probability that region to be measured feeder line section is secondary when t+1, h is the shaft tower of region to be measured feeder line section Number,Direct attack thunderbolt probability secondary when being the i-th base shaft tower place circuit t+1, P_irIt it is the thunderbolt jumping of the i-th base shaft tower place circuit Lock probability,Thunder and lightning induction voltage probability of happening secondary when being the i-th base shaft tower place circuit t+1, P_igIt it is the i-th base shaft tower institute The thunder and lightning induction voltage tripping operation probability secondary when circuit t+1；

Step 3: carry out subregion in units of each shaft tower of distribution line, determines that each shaft tower occurs effective coverage and the thunder and lightning sense of thunderbolt Answer the effective coverage of overvoltage, thus direct attack thunderbolt probability when obtaining each shaft tower place circuit t+1 time and each shaft tower place circuit Thunder and lightning induction voltage probability of happening secondary during t+1；

Step 4: obtain the thunderbolt tripping operation probability of shaft tower place circuit according to shaft tower electric geometry method, utilize Monte Carlo Method determines shaft tower place circuit counterattack tripping operation probability, and thunderbolt tripping operation probability and shaft tower institute according to shaft tower place circuit are online The counterattack tripping operation probability on road determines the lightning stroke trip probability of each shaft tower place circuit；

Step 5: determine the thunder and lightning induction voltage tripping operation probability of shaft tower place circuit according to induced overvoltage maximum on wire, Obtain the thunder and lightning induction voltage fault rate of shaft tower place circuit by building fuzzy mathematical model, thus obtain considering that lightning current is strong The thunder and lightning induction voltage tripping operation probability of each shaft tower place circuit of degree；

Step 6: by thunder and lightning sense when attacking thunderbolt probability, each shaft tower place circuit t+1 directly time during each shaft tower place circuit t+1 time Answer overvoltage probability of happening, the lightning stroke trip probability of each shaft tower place circuit and consider each shaft tower place circuit thunder of intensity of lightning current Electric induction overvoltage tripping probability input electrical network distribution line lightning fault comprehensive sub-areas model, obtains region to be measured feeder line section and exists Thunder and lightning tripping operation probability secondary during t+1；

Step 7: by setting up distribution line temperature model, determines subsequent time region to be measured according to distribution line active time Feeder line section generation transient fault probability；

Step 8: set up and consider ageing failure and revise distribution line under distribution line Lightning Disaster to break down probabilistic model；

Described consideration ageing failure and to revise the probabilistic model that breaks down of distribution line under distribution line Lightning Disaster as follows:

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

Wherein, P^t+1For the region to be measured feeder line section probability that breaks down when t+1 time,For a period of time under the feeder line section of region to be measured Carve and transient fault probability occurs；

Step 9: thunder and lightning tripping operation probability secondary when t+1 for region to be measured feeder line section and region to be measured feeder line section subsequent time are occurred wink Time probability of malfunction input consider ageing failure and revise distribution line under distribution line Lightning Disaster and break down probabilistic model prediction The probability that during t+1, secondary region to be measured feeder line section breaks down.

Power distribution network Lightning Disaster failure prediction method the most according to claim 1, it is characterised in that described step 1 is wrapped Include following steps:

Step 1.1: according to lightning location system statistics region to be measured thunder and lightning time of origin and place, carry out region according to its longitude and latitude Divide, obtain each thunderbolt close quarters；

Step 1.2: thunderbolt close quarters is carried out binary conversion treatment, uses eight neighborhood to the thunderbolt close quarters after binary conversion treatment Edge following algorithm carries out shaping, obtains each thunder and lightning subregion, the thunderbolt probability of time thunder and lightning subregion when determining t；

Step 1.3: during by the Optimum Matching of thunder and lightning subregion secondary when adjacent t-2, t-1, t is determined each thunder and lightning subregion t+1 Secondary development track, i.e. secondary during t+1 thunder and lightning subregion, determine according to the thunderbolt probability of the thunder and lightning subregion of when t-2, t-1, t time The thunderbolt probability of time thunder and lightning subregion during t+1；

The thunderbolt probability of time thunder and lightning subregion when the described thunderbolt probability according to the thunder and lightning subregion of when t-2, t-1, t time determines t+1 Formula is as follows:

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

Wherein, t >=2, q_t+1For the thunderbolt probability of during t+1 thunder and lightning subregion, q_tThunderbolt probability for during t thunder and lightning subregion.

Power distribution network Lightning Disaster failure prediction method the most according to claim 1, it is characterised in that described step 3 is wrapped Include following steps:

Step 3.1: determine critical distance y of the thunderbolt wire of each shaft tower in region to be measured_{min i}Critical with each shaft tower induced voltage flashover Distance y_{max i}；

Step 3.2: determine that each shaft tower occurs the effective coverage of thunderbolt and having of thunder and lightning induction voltage according to shaft tower electric geometry method Effect region；

Step 3.3: occur the effective coverage of thunderbolt and the effective coverage of thunder and lightning induction voltage to determine each shaft tower place according to each shaft tower Thunder and lightning induction voltage probability of happening secondary when direct attack thunderbolt probability secondary during circuit t+1 and each shaft tower place circuit t+1.

Power distribution network Lightning Disaster failure prediction method the most according to claim 1, it is characterised in that described step 4 is wrapped Include following steps:

Step 4.1: according to shaft tower electric geometry method, obtain the thunderbolt rate of shaft tower place circuit；

Thunderbolt rate P of described i-th base shaft tower place circuit_iαComputing formula is as follows:

Wherein,For thunder and lightning angle of incidence, l_ibIt it is the shielding exposure arc pair of the i-th base shaft tower place circuit The horizontal range answered, l_iaIt it is the horizontal range that the earth-wire protection arc of the i-th base shaft tower place circuit is corresponding；

Step 4.2: obtain the thunderbolt tripping operation probability of shaft tower place circuit according to the thunderbolt rate of shaft tower place circuit；

The thunderbolt tripping operation probability P of described i-th base shaft tower place circuit_isComputing formula is as follows:

P_is=η P_iα；

Wherein, η is probability of sustained arc；

Step 4.3: utilize monte carlo method simulation to count the back flashover tripping operation probability of each shaft tower place circuit；

Step 4.4: the shaft tower counterattack tripping operation probability sum of the thunderbolt of shaft tower place circuit is tripped probability and shaft tower place circuit As the lightning stroke trip probability of this shaft tower place circuit, obtain the lightning stroke trip probability of each shaft tower place circuit.

Power distribution network Lightning Disaster failure prediction method the most according to claim 1, it is characterised in that described step 5 is wrapped Include following steps:

Step 5.1: determine the thunder and lightning induction voltage tripping operation probability of shaft tower place circuit according to induced overvoltage maximum on wire；

The thunder and lightning induction voltage tripping operation probability P (I of described shaft tower place circuit_min) computing formula is as follows:

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

Wherein,It is insulator impulse sparkover voltage when 50% for discharge probability, I_mLightning current for thunderbolt the earth Amplitude, h_dFor overhead transmission line to ground level, S is the lightning strike spot horizontal range to overhead transmission line；

Step 5.2: by building fuzzy mathematical model, using thunder and lightning excitation parameters and line span parameter as fuzzy mathematical model Input, using thunder and lightning induction voltage fault rate as the output of fuzzy mathematical model, by thunder and lightning excitation parameters and line span parameter It is combined, sets up fuzzy control rule, use maximum membership degree method de-fuzzy, obtain thunder and lightning induction voltage fault rate；

Step 5.3: thunder and lightning induction voltage tripping operation probability and thunder and lightning induction voltage fault rate according to shaft tower place circuit calculate and examine Consider the thunder and lightning induction voltage tripping operation probability of each shaft tower place circuit of intensity of lightning current.

Power distribution network Lightning Disaster failure prediction method the most according to claim 3, it is characterised in that described shaft tower generation thunder The effective coverage hit is the distance shaft tower y of vertical distribution line direction centered by shaft tower_{min i}Model with distribution line direction 1/2 span In enclosing；

The effective coverage of described thunder and lightning induction voltage is vertical distribution line direction distance shaft tower y centered by shaft tower_{max i}And distribution In the range of line direction 1/2 span.

Power distribution network Lightning Disaster failure prediction method the most according to claim 3, it is characterised in that described i-th base shaft tower Direct attack thunderbolt probability secondary during the circuit t+1 of placeComputing formula be:

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

Wherein, a '_t+1Effective coverage and secondary thunder and lightning subregion during the t+1 at this shaft tower place for during t+1 the i-th base shaft tower generation thunderbolt Overlapping area, a_t+1Area for during t+1 the i-th base shaft tower place thunder and lightning subregion；

Thunder and lightning induction voltage probability of happening secondary during described i-th base shaft tower place circuit t+1Computing formula be:

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

Wherein, b '_t+1Effective coverage and secondary thunder during the t+1 at this shaft tower place for during t+1 the i-th base shaft tower thunder and lightning induction voltage The overlapping area of electricity subregion.