CN102927949A - Transmission line icing predication method based on multi-element physical quantity mathematical model - Google Patents

Abstract

A kind of powerline ice-covering prediction technique based on multi-element physical quantity mathematical model includes the following steps: that (1) obtains the temperature and humidity and wind-force meteorologic parameter at current time; (2) judge whether current each meteorological data meets icing condition, temperature -8~0 DEG C respectively, humidity 90%RH or more, 2~7m/s of wind speed go to (3) if meeting condition, otherwise enter the sampling period next time, that is, return to (1); (3) it is compared by the data value that tension sensor obtains with initial value, if

Illustrate that conducting wire has icing, go to step (4), otherwise returns to (1); (4) current environment atmospheric pressure value is obtained by ground based terminal, calculates ice covering thickness b; (5) by ice covering thickness, the parameters such as temperature and humidity calculate the comprehensive than carrying of any time ti conducting wire; (6) the axial stress σ x at span endpoint is obtained than carrying by comprehensive, enables σ x=σ max, calculated break off remnant time t, early warning is issued by terminal. The present invention realizes that effectively monitoring, accuracy are good.

Description

Powerline ice-covering Forecasting Methodology based on polynary physical quantity mathematical model

Technical field

The present invention relates to a kind ofly affects modeling by polynary physical quantity (wind-force, temperature, humidity, raindrop, air pressure etc.) to ice coating of power line, thereby sends the realization of the powerline ice-covering Forecasting Methodology of early warning.

Background technology

South China met with snow disaster in 2008, the general icing of transmission line of electricity, cause the transmission line of electricity fracture in the serious situation, where icing is serious because circuit can't be judged by Utilities Electric Co., and will when rupture, so can't in time implement the preventive measure such as deicing, thereby can not effectively avoid the broken string of circuit, the phenomenon such as tower of falling, this is the ubiquitous problem of present powerline systems.

Powerline ice-covering is one of most important disaster of electric system, go deep into the research in this field, at first to understand fully the reason of defeated powerline ice-covering and form mechanism, to provide applicable line ice coating forecast model for the typical meteorological condition simultaneously, accurately judge ice covering thickness and the concrete icing position of circuit, for the anti-ice damage design of transmission line of electricity provides important parameter.

Based on the mathematical model of polynary physical quantity on the icing impact, by the analysis to the line of electric force stressing influence, consider the common climatic factor of nature, comprise air themperature, humidity, wind direction and wind velocity, Liquid water content, drop diameter etc., affect simultaneously the factor of icing in conjunction with wire itself, such as conductor structure and material surface performance etc., can realize the effective prediction to the powerline ice-covering situation, so that the ice covering thickness of prediction is more near truth.

Summary of the invention

Can't in time monitor in order to solve current power line icing situation, so that can't effectively avoid broken string, fall the situation such as tower, the present invention has designed based on polynary physical quantity thereby electric power line ice-covering thickness has been carried out the mathematical model that mathematical modeling is effectively predicted the powerline ice-covering situation, provides a kind of and realizes that effective monitoring, accuracy well, are effectively avoided breaking and the powerline ice-covering Forecasting Methodology based on polynary physical quantity mathematical model of the phenomenon of falling the tower.

The technical solution adopted for the present invention to solve the technical problems is:

A kind of powerline ice-covering Forecasting Methodology based on polynary physical quantity mathematical model, described Forecasting Methodology comprises the steps:

(1) adopt Temperature Humidity Sensor, wind sensor to obtain humiture and the wind-force meteorologic parameter of current time;

(2) judge respectively whether current each weather data satisfies the icing condition, that is: temperature-8～0 ℃, more than the humidity 90%RH, wind speed 2～7m/s then forwards (3) to if satisfy condition, otherwise enters the next time sampling period, namely turns back to (1);

(3) data value and the initial value that obtain by tension pick-up compare, if

Illustrate that wire has icing, forward step (4) to, otherwise turn back to (1);

(4) obtain the current environment atmospheric pressure value by ground based terminal, calculate ice covering thickness b, computing formula is as follows:

$b={\∫}_0^{t_i}f(t,T,V,p)\mathrm{dt}---\left(13\right)$

The ice covering thickness Δ r of unit is expressed as:

$\mathrm{\Δr}=\frac{t\sqrt{{\left(\mathrm{VW}\right)}^2+{\left(P{\mathrm{\ρ}}_0\right)}^2}}{{\mathrm{\ρ}}_i\mathrm{\π}}---\left(7\right)$

Wherein, V is wind speed (m/s), and W is airborne Liquid water content (g/m ³), t is rain time (s); P is rainfall intensity (mm/h), ρ ₀The density (g/cm of water ³), t is rain time (s);

W=aP ^b, a wherein, b is constant, with rainfall intensity P and humidity conversion, P satisfies following relation:

$P=\frac{1}{\mathrm{\ρg}}{\∫}_0^{p_{z_0}}\mathrm{qdp}---\left(8\right)$

Wherein, q is specific humidity, and p is air pressure (MPa), and ρ is aqueous water density (g/cm ³), g is acceleration of gravity (m/s ²),

Be surface pressure (MPa);

Specific humidity q calculates according to vapour pressure e (hPa), and the pass of it and vapour pressure is:

$q=\frac{\mathrm{\ϵe}}{p-(1-\mathrm{\ϵ})e}---\left(9\right)$

In the formula,

μ _v, μ _dBe respectively the average molar mass of steam and dry air;

The humidity value that adopts humidity sensor to obtain is a relative humidity, and its expression formula is:

$f=\frac{e}{E}\×100\%---\left(10\right)$

Wherein, E is the saturation vapour pressure (hPa) under the same temperature;

In conjunction with formula (7)-(10), the ice covering thickness Δ r of the unit of obtaining is about the expression formula of time t, temperature T, wind speed V and air pressure p:

Δr＝f(t，T，V，p) (11)；

Formula (11) is converted into differential form, and the both sides integration can obtain formula (13);

(5) calculate any time t by ice covering thickness and humiture _iThe comprehensive ratio of wire carries g ₅, computing formula is:

$g_5=\sqrt{{g_3}^2+{g_4}^2}---\left(20\right)$

Wherein, g ₄For the level ratio carries g ₃For vertical than year;

$g_3=g_1+g_2=\frac{\mathrm{gq}}{A}+\frac{\mathrm{g\&rho;\&pi;b}({2\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA00002111904800011.png,HDA00002111904800022.png"\; state="\{\{state\}\}">r</figure-callout>}}_0+b)\&times;{10}^{-3}}{A}---\left(17\right)$

Wherein, g ₁For the wire ratio carries g ₂For the icing ratio carries, g is acceleration of gravity, and q is linear mass (kg/m), and ρ is the density (g/cm of icing ³), r ₀Be the radius (mm) of wire, A is the long-pending (mm of conductive wire cross-section ²);

$g_4=0.6128K_z\mathrm{\&alpha;C}({2\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA00002111904800011.png,HDA00002111904800022.png"\; state="\{\{state\}\}">r</figure-callout>}}_0+2b)\frac{V^2}{A}$

$=1.2256K_z\mathrm{\&alpha;C}({\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA00002111904800011.png,HDA00002111904800022.png"\; state="\{\{state\}\}">r</figure-callout>}}_0+b)\frac{V^2}{A}---\left(19\right)$

Wherein, K _zBe height variation coefficient of wind pressure, α is uneven factor of wind speed, and C is wind carrier model coefficient;

(6) pass through comprehensively than carrying a g ₅Obtain the axial stress σ at line of electric force span end points place _x, make σ _x=σ _Max, calculate fracture t excess time, and send early warning signal.

Technical conceive of the present invention is: adopt Temperature Humidity Sensor, wind sensor to obtain the meteorologic parameters such as the humiture of current time and wind-force, then go out the icing situation of current time circuit by calculated with mathematical model, further dope the icing situation of any time, draw the ratio that the line of electric force of any time bears and carry (comprising level than carrying, carrying and ice anharmonic ratio from anharmonic ratio and carry), and then calculate the axial stress of arbitrary point on this moment circuit; The line of electric force maximum value of meeting with stresses that provides according to power department simultaneously compares, when the prediction value of meeting with stresses and the line of electric force maximum value of meeting with stresses near the time, represent that line of electric force soon ruptures; Calculate from fracture excess time, send early warning, remind relevant department to carry out deicing and combat a natural disaster work.

Because the present invention adopts wireless sensor node network and background monitoring center to match, and in conjunction with the form of early warning mechanism, can solve well the monitoring problem of transmission line of electricity, remove complicated processes and the maintenance times of hand inspection from, both Cost reductions, having improved again simultaneously the reliability of monitoring, is a kind of real-time system that ultra-high-tension power transmission line is monitored and reported to the police that is conducive to.

In the present invention simultaneously, each sensor node (comprising tension pick-up, Temperature Humidity Sensor and wind sensor) merges, carry out unified power supply management, and node adopts Miniature wind-driven generator to power, fundamentally solve high-tension electricity and change the problems such as battery difficulty.

Beneficial effect of the present invention is: realize that effectively monitoring, accuracy well, are effectively avoided broken string and fallen tower.

Description of drawings

Fig. 1 is wire stressing conditions synoptic diagram of the present invention.

Fig. 2 is unit length inside conductor icing situation synoptic diagram of the present invention.

The schematic vector diagram that ratio carried when Fig. 3 was wire icing of the present invention.

Its any point predicted stresses value and the maximum value of meeting with stresses trend graph when Fig. 4 is wire icing of the present invention.

Fig. 5 is wire icing prediction algorithm process flow diagram of the present invention.

Embodiment

The invention will be further described below in conjunction with accompanying drawing.

With reference to Fig. 1～Fig. 5, a kind of powerline ice-covering Forecasting Methodology based on polynary physical quantity mathematical model comprises the steps:

(1) adopts Temperature Humidity Sensor, wind sensor to obtain the meteorologic parameters such as the humiture of current time and wind-force, these parameters are analyzed;

(2) judge that respectively whether current each weather data satisfies the icing condition, is mainly: temperature-8～0 ℃, more than the humidity 90%RH, wind speed 2～7m/s then forwards (3) to if satisfy condition, otherwise enters the next time sampling period, namely gets back to (1);

(3) data value and the initial value that obtain by tension pick-up compare, if

Illustrate that wire has icing, forward step (4) to, otherwise turn back to (1);

(4) obtain the current environment atmospheric pressure value by ground based terminal, calculate ice covering thickness b;

(5) by ice covering thickness, the calculation of parameter any time t such as humiture _iThe comprehensive ratio of wire carries g;

(6) carry the axial stress σ that obtains span end points place by comprehensive ratio _x, make σ _x=σ _Max, calculate fracture t excess time, send early warning by terminal, notice relevant department carries out deicing and combats a natural disaster work.

Because the meteorologic factors such as humiture, wind-force are less on the impact of wire, the sampling period that we set the icing monitoring is 10 minutes.In a sampling period, it is not very greatly that ice covering thickness changes, and we do not need to upgrade wire fracture excess time at every turn.After each image data, just calculate ice covering thickness, if with front once poor be not very large, then no longer down calculate, but the predicted time before keeping, until ice covering thickness exists significant change just to recomputate.

With reference to Fig. 1: described line of electric force stressing conditions, can calculate by the Tensity size that acts on the trolley wire and electric wire material, sectional area and the factors such as load of bearing and obtain.In order to characterize and compare the stressing conditions of electric wire, usually carry out the Mechanics Calculation of electric wire with the value on the unit cross section.Can call stress (σ) to the tension force that acts on the unit cross section, unit is N/mm ²Or MPa; The load that bears on electric wire unit length, the unit cross section is called than carrying (g), the N/mm of unit ²M or MPa/m represent.In the icing situation, the vertical ratio of electric wire carries (g _v) comprise that wire carries (g from anharmonic ratio _V1) and an icing ratio year (g _V2):

$g_v=g_{v1}+g_{v2}=\frac{{\mathrm{qg}}_n}{A}+\frac{0.9\mathrm{\&pi;}{g}_{n}b(b+D)\&times;{10}^{-3}}{A}---\left(1\right)$

Wherein, q is electric wire linear mass (kg/m); g _nBe acceleration of gravity (N/kg); A is electric wire sectional area (mm ²); B is ice covering thickness (mm); D is electric wire external diameter (mm).The electric wire level is than carrying (g _h) be:

$g_h=\frac{(D+2b)W_o\mathrm{\&alpha;}{\mathrm{\&mu;}}_{\mathrm{sc}}{\mathrm{\&mu;}}_z{\mathrm{\&mu;}}_{\mathrm{\&theta;}}\&times;{10}^{-3}}{A}---\left(2\right)$

Wherein, W _oBe benchmark blast standard value; α is the blast nonuniformity coefficient; μ _ScBe the electric wire Shape Coefficient; μ _zBe height variation coefficient of wind pressure; μ _θVariation factor for the blast box haul.When having ice that wind is arranged, the comprehensive ratio of electric wire carries g and is:

The axial stress σ of electric wire any point C _x(N/mm ²) and this to the relational expression between the minimum point discrepancy in elevation be:

σ _x＝σ ₀+g(y-y ₀) (3)

Wherein, σ ₀Be the horizontal stress of electric wire lowest part, y and y ₀Be respectively the ordinate value (m) at electric wire C point and O point place.By following formula as can be known, on the point that the electric wire relative height is higher in same shelves, its axial stress is larger.Therefore, we must be contained in it higher place of line of electric force relative position in the installation tension sensor.

With reference to Fig. 2: in theory, in the unit area, the water yield that drops on the horizontal direction on the line of electric force is: w _h=VWt, wherein V is wind speed (m/s), W is airborne Liquid water content (g/m ³), t is rain time (s); The water yield that drops on the vertical direction on the line of electric force is: w _v=P ρ ₀T, wherein P is rainfall intensity (mm/h), ρ ₀The density (g/cm of water ³), t is rain time (s).Then the total precipitation in the line of electric force unit area is:

$w=\mathrm{\&gamma;\&beta;}\sqrt{{w_v}^2+{w_h}^2}=\mathrm{\&gamma;\&beta;t}\sqrt{{\left(\mathrm{VW}\right)}^2+{\left({\mathrm{P\&rho;}}_0\right)}^2}---\left(4\right)$

Wherein γ is collision coefficient (0＜γ≤1), and β is the freezing fraction (0＜β≤1) that rainfall becomes icing.Consider in the actual environment, the reason such as the temperature that forms icing is lower, and rain speed is less, we get γ=1 and β=1.

As shown in Figure 2, the cross section of line of electric force is circle, and we suppose that ice evenly overlays on the line of electric force surface.If the radius of i line of electric force (containing ice) is r constantly _i, can be got by mass conservation theorem:

${2r}_i\&CenterDot;\mathrm{\&gamma;\&beta;t}\sqrt{{\left(\mathrm{VW}\right)}^2+{\left(P{\mathrm{\&rho;}}_0\right)}^2}={\mathrm{\&rho;}}_i({{\mathrm{\&pi;r}}_{i+1}}^2-\mathrm{\&pi;}{r_i}^2)---\left(5\right)$

ρ wherein _iThe density of this place's icing.The following formula abbreviation is got

${2r}_{i}t\sqrt{{\left(\mathrm{VW}\right)}^2+{\left(P{\mathrm{\&rho;}}_0\right)}^2}={\mathrm{\&rho;}}_i\mathrm{\&pi;}(r_{i+1}+r_i)(r_{i+1}-r_i)$

$\&ap;{2r}_i{\mathrm{\&rho;}}_i\&CenterDot;\mathrm{\&Delta;r}---\left(6\right)$

Further the displacement abbreviation can get ice covering thickness

$\mathrm{\&Delta;r}=\frac{t\sqrt{{\left(\mathrm{VW}\right)}^2+{\left(P{\mathrm{\&rho;}}_0\right)}^2}}{{\mathrm{\&rho;}}_i\mathrm{\&pi;}}---\left(7\right)$

Get the relation of Liquid water content and rainfall intensity, W=aP by BEST (1949) model ^b, a wherein, b is constant.We are below with rainfall intensity P and humidity conversion.

P satisfies following relation in the certain hour:

$P=\frac{1}{\mathrm{\&rho;g}}{\&Integral;}_0^{{\mathrm{<figure-callout\; id="0"\; label="p\; z"\; filenames="HDA00002111904800011.png,HDA00002111904800022.png"\; state="\{\{state\}\}">p</figure-callout>}}_{z_{}}}\mathrm{qdp}---\left(8\right)$

Wherein, q is specific humidity, and p is air pressure (MPa), and ρ is aqueous water density (g/cm ³), g is acceleration of gravity (m/s ²),

Be surface pressure (MPa).

In actual applications, specific humidity is calculated according to vapour pressure e (hPa) usually, and the pass of it and vapour pressure is:

$q=\frac{\mathrm{\&epsiv;e}}{p-(1-\mathrm{\&epsiv;})e}---\left(9\right)$

In the formula,

μ _v, μ _dBe respectively the average molar mass of steam and dry air.Get as calculated ε=0.622.

The humidity value that adopts humidity sensor to obtain among the present invention is a relative humidity, and its expression formula is:

$f=\frac{e}{E}\&times;100\%---\left(10\right)$

Wherein E is the saturation vapour pressure (hPa) under the same temperature, can obtain by tabling look-up.

In conjunction with formula (7)-(10), finally obtain ice covering thickness Δ r about the expression formula of time t, temperature T, wind speed V and air pressure p:

Δr＝f(t，T，V，p) (11)

Be converted into differential form

dr＝f(t，T，V，p)dt (12)

The both sides integration can obtain t _iIce covering thickness constantly

$b={\&Integral;}_0^{t_i}f(t,T,V,p)\mathrm{dt}---\left(13\right)$

With reference to Fig. 3: the ratio of wire carries computation process.

1. wire carries g from anharmonic ratio ₁(N/ (mmm ²))

Carrying from anharmonic ratio is that the ratio that the overhead line conductor own wt causes carries, and is calculated as follows:

$g_1=\frac{\mathrm{gq}}{A}---\left(14\right)$

Wherein g is acceleration of gravity, and q is linear mass (kg/m), and A is the long-pending (mm of conductive wire cross-section ²).

2. the ice anharmonic ratio of wire is carried g ₂(N/ (mmm ²))

Wire that icing quality on the wire causes is called the ice anharmonic ratio and carries (N/ (mmm than carrying ²)), use symbol g ₂The long ice coating wire analysis of 1m is got in expression, and at this moment the volume V of icing cylinder is

V＝π(r ₀+b) ²-πr ₀ ²＝πb(2r ₀+b)×10 ^-6 (15)

Then icing anharmonic ratio carries and is

$g_2=\frac{\mathrm{g\&rho;V}}{A\&times;1}=\frac{\mathrm{g\&rho;\&pi;b}({2\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA00002111904800011.png,HDA00002111904800022.png"\; state="\{\{state\}\}">r</figure-callout>}}_0+b)\&times;{10}^{-3}}{A}---\left(16\right)$

The vertical of wire always than carrying is when to sum up, having wind that ice is arranged

$g_3=g_1+g_2=\frac{\mathrm{gq}}{A}+\frac{\mathrm{g\&rho;\&pi;b}({2\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA00002111904800011.png,HDA00002111904800022.png"\; state="\{\{state\}\}">r</figure-callout>}}_0+b)\&times;{10}^{-3}}{A}---\left(17\right)$

3. the level of wire is than carrying g ₄(N/ (mmm ²))

The level of wire is the wire that causes of the suffered Action of Wind pressure of guide line than carrying than carrying because general wind action direction in surface level, therefore wind pressure ratio is carried be called wire level than carrying.The formation of blast is the pressure that Air Flow kinetic energy produces in the wire adverse wind face.

15 ℃ of temperature, when pressure was 0.101325MPa, the density of dry air was 1.2255kg/m ³, 1m then ³The kinetic energy of air (also being velocity head) is

$q=\frac{1}{2}m{V}^2=0.6128V^2---\left(18\right)$

Wherein V is wind speed (m/s), and q is velocity head, and m is 1m ³The quality of air.

Velocity head namely aerodynamic energy acts on " theoretical blast " on the unit area windward side.During icing, the facing the wind diameter of wire is 2r ₀+ 2b, by formula (18) wind pressure ratio is carried and is

$g_4=0.6128K_z\mathrm{\&alpha;C}({2\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA00002111904800011.png,HDA00002111904800022.png"\; state="\{\{state\}\}">r</figure-callout>}}_0+2b)\frac{V^2}{A}\&times;{10}^{-3}$

$=1.2256K_z\mathrm{\&alpha;C}({\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA00002111904800011.png,HDA00002111904800022.png"\; state="\{\{state\}\}">r</figure-callout>}}_0+6)\frac{V^2}{A}\&times;{10}^{-3}---\left(19\right)$

K wherein _zBe height variation coefficient of wind pressure, α is uneven factor of wind speed, and C is that wind carrier model coefficient is (during icing, C=1.2).

4. the comprehensive ratio of wire carries g ₅(N/ (mmm ²))

The comprehensive ratio of wire carries, be guide line level than carry and vertical than year vector with.Its expression formula is

$g_5=\sqrt{{g_3}^2+{g_4}^2}---\left(20\right)$

With reference to Fig. 4: As time goes on, ice covering thickness increases gradually, and the comprehensive ratio of wire carries gradually and increases, and the axial tension stress of its any point also increases thereupon, and is whole in rising trend.The maximal value that meets with stresses of wire remains unchanged, and is worth to be σ _MaxWhen the axial stress curve of wire rises gradually, and σ _MaxWhen intersecting, illustrate that this moment, wire reached the maximal value that wire can bear because the wire deadweight adds the axial stress of icing impact, wire will rupture.And t _iBegin to wire fracture excess time from icing monitoring exactly, and t ₀It is the moment that system sends early warning.

Claims (1)

1. powerline ice-covering Forecasting Methodology based on polynary physical quantity mathematical model, it is characterized in that: described Forecasting Methodology comprises the steps:

(1) adopt Temperature Humidity Sensor, wind sensor to obtain humiture and the wind-force meteorologic parameter of current time;

(2) judge respectively whether current each weather data satisfies the icing condition, that is: temperature-8～0 ℃, more than the humidity 90%RH, wind speed 2～7m/s then forwards (3) to if satisfy condition, otherwise enters the next time sampling period, namely turns back to (1);

(3) data value and the initial value that obtain by tension pick-up compare, if

Illustrate that wire has icing, forward step (4) to, otherwise turn back to (1);

(4) obtain the current environment atmospheric pressure value by ground based terminal, calculate ice covering thickness b, computing formula is as follows:

$b={\&Integral;}_0^{t_i}f(t,T,V,p)\mathrm{dt}---\left(13\right)$

The ice covering thickness Δ r of unit is expressed as:

$\mathrm{\&Delta;r}=\frac{t\sqrt{{\left(\mathrm{VW}\right)}^2+{\left(P{\mathrm{\&rho;}}_0\right)}^2}}{{\mathrm{\&rho;}}_i\mathrm{\&pi;}}---\left(7\right)$

Wherein, V is wind speed (m/s), and W is airborne Liquid water content (g/m ³), t is rain time (s); P is rainfall intensity (mm/h), ρ ₀The density (g/cm of water ³), t is rain time (s);

W=aP ^b, a wherein, b is constant, with rainfall intensity P and humidity conversion, P satisfies following relation:

$P=\frac{1}{\mathrm{\&rho;g}}{\&Integral;}_0^{p_{z_0}}\mathrm{qdp}---\left(8\right)$

Wherein, q is specific humidity, and p is air pressure (MPa), and ρ is aqueous water density (g/cm ³), g is acceleration of gravity (m/s ²),

Be surface pressure (MPa);

Specific humidity q calculates according to vapour pressure e (hPa), and the pass of it and vapour pressure is:

$q=\frac{\mathrm{\&epsiv;e}}{p-(1-\mathrm{\&epsiv;})e}---\left(9\right)$

In the formula, μ _v, μ _dBe respectively the average molar mass of steam and dry air;

The humidity value that adopts humidity sensor to obtain is a relative humidity, and its expression formula is:

$f=\frac{e}{E}\&times;100\%---\left(10\right)$

Wherein, E is the saturation vapour pressure (hPa) under the same temperature;

In conjunction with formula (7)-(10), the ice covering thickness Δ r of the unit of obtaining is about the expression formula of time t, temperature T, wind speed V and air pressure p:

Δr＝f(t，T，V，p) (11)；

Formula (11) is converted into differential form, and the both sides integration can obtain formula (13);

(5) calculate any time t by ice covering thickness and humiture _iThe comprehensive ratio of wire carries g ₅, computing formula is:

$g_5=\sqrt{{g_3}^2+{g_4}^2}---\left(20\right)$

Wherein, g ₄For the level ratio carries g ₃For vertical than year;

$g_3=g_1+g_2=\frac{\mathrm{gq}}{A}+\frac{\mathrm{g\&rho;\&pi;b}({2r}_0+b)\&times;{10}^{-3}}{A}---\left(17\right)$

Wherein, g ₁For the wire ratio carries g ₂For the icing ratio carries, g is acceleration of gravity, and q is linear mass (kg/m), and ρ is the density (g/cm of icing ³), r ₀Be the radius (mm) of wire, A is the long-pending (mm of conductive wire cross-section ²);

$g_4=0.6128K_z\mathrm{\&alpha;C}({2r}_0+2b)\frac{V^2}{A}\&times;{10}^{-3}$

$=1.2256K_z\mathrm{\&alpha;C}(r_0+b)\frac{V^2}{A}\&times;{10}^{-3}---\left(19\right)$

Wherein, K _zBe height variation coefficient of wind pressure, α is uneven factor of wind speed, and C is wind carrier model coefficient;

(6) pass through comprehensively than carrying a g ₅Obtain the axial stress σ at line of electric force span end points place _x, make σ _x=σ _Max, calculate fracture t excess time, and send early warning signal.

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