CN107977492A - Based on the non-linear windage yaw reliability degree calculation method of Monte Carlo insulator chain - Google Patents

Abstract

The invention discloses one kind to be based on the non-linear windage yaw reliability degree calculation method of Monte Carlo insulator chain, follows the steps below：Transmission line of electricity research object is set, the windage yaw angle value of insulator chain is calculated using the straight rod method of rigidity；According to overhead transmission line specification, shaft tower and insulator chain connection structure are established, and selectes the stochastic variable that the connection structure is related to, distribution function corresponding with stochastic variable is determined according to stochastic variable；Establish geometrical relationship corresponding with bindiny mechanism；Establish the insulator chain windage yaw invalidation functions function with stochastic variable；Insulator chain windage yaw reliability is calculated using Meng Takaluo methods.Beneficial effect：Good reliability, calculating process is simple, can meet the requirement of the prior art.

Description

Calculation Method of Nonlinear Windage Reliability Based on Monte Carlo Insulator String

technical field

The invention relates to the field of power transmission lines, in particular to a method for calculating the nonlinear windage reliability of an insulator string based on a Monte Carlo method.

Background technique

Under the action of wind load, the insulator strings of overhead transmission lines and the transmission wires suspended will produce wind deflection swings of different periods. During the swing process, if the distance between the electrified part and the tower is less than the allowable electrical clearance, a discharge will occur between the transmission line and the tower, that is, a wind deflection flashover accident will occur. The wind-biased flashover of insulator strings will seriously threaten the normal operation of the power grid system, and cause huge economic losses and social impacts.

In the calculation of the wind angle of overhead high-voltage transmission lines in China, the insulator string is usually simplified as a rigid rod or chord polygon, and the wind angle of the insulator string is calculated by the static method under the design average wind speed. These two methods are also used in engineering practice, and the causes of windage accidents are analyzed accordingly. In this regard, some experts and scholars have questioned that the calculation of wind deflection angle in my country's design regulations does not consider the dynamic effect of wind load. Therefore, people began to use the finite element method to simulate and study the dynamic wind deflection response of insulator strings under the action of random fluctuating wind. Since then, many scholars at home and abroad have been using finite element software to establish a multi-body model of insulator string-conductor coupling, and through the harmonic superposition method to simulate the random fluctuating wind field considering the spatial correlation of fluctuating wind and the variation of wind speed along the height, finally The wind deflection response under the change of parameters such as different gear span, height difference and design wind speed is analyzed. However, the establishment of the finite element model is complicated. For the case where the height difference between adjacent towers and calculation towers is small, the process of establishing a model using finite elements is cumbersome, and for transmission lines, the structures of each adjacent tower are different. Using finite element to build a model is a waste of time, and the work efficiency of the staff is low. Therefore, it is necessary to propose a simple method to calculate the nonlinear wind deflection reliability of the insulator string when the height difference between the adjacent tower and the calculation tower is small.

Contents of the invention

In view of the above problems, the present invention provides a method for calculating the nonlinear windage reliability of insulator strings based on the Monte Carlo method. The method considers the dynamic effect of wind load, and uses the rigid straight rod method to calculate the windage angle value, and then determines Wind deflection reliability of insulator strings.

In order to achieve the above object, the concrete technical scheme that the present invention adopts is as follows:

A nonlinear windage reliability calculation method based on Monte Carlo insulator strings, the key lies in the following steps:

S1: Set the research object of the transmission line, according to the wind load, gravity load on the insulator string, the gravity load on the wire, and the wind load on the wire, use the rigid straight rod method to calculate the wind deflection angle value of the insulator string;

S2: According to the specification of overhead transmission lines, establish the connection structure between the tower and the insulator series, and select the random variables involved in the connection structure, and determine the distribution function corresponding to the random variables according to the random variables;

S3: Build the connection structure and random variables according to step S2, and establish the geometric relationship corresponding to the connection mechanism;

S4: According to the geometric relationship in step S3 and the windage angle value in step S1, establish a windage failure function function of insulator strings with random variables;

S5: According to the random variable, the distribution function of the random variable, and the failure function function of the wind deflection of the insulator string, the reliability of the wind deflection of the insulator string is calculated using the Monte Carlo method.

Through the above design, when the height difference between adjacent towers and calculation towers is small, the rigid straight rod method is used to calculate the windage angle value, taking into account the wind load, gravity load, conductor gravity load, and conductor stress of the insulator string. The reliability of wind deflection of the insulator string is calculated by combining the influence factors such as the wind load and the Monte Carlo method. The reliability is good, the calculation process is simple, and it can meet the requirements of the existing technology.

Further, the content of step S1 is:

According to the wind load and gravity load on the insulator string, the gravity load on the wire, and the wind load on the wire, the formula for calculating the wind deflection angle of the insulator string is:

In formula (1):

G _h is the wind load on the insulator string: G _h ＝W ₀ μ _z A ₁ ;

G _v is the gravity load of the insulator string: G _v = p ₂ l;

W _v is the gravity load of the wire:

W _h is the wind load on the wire: W _h = αW ₀ μ _z μ _sc β _c dL _p sin ² θ;

Among them, α is the wind pressure uneven coefficient; W ₀ is the basic wind pressure standard value; μ _z is the wind pressure altitude variation coefficient; μ _sc is the wire shape coefficient; β _c is the wind load adjustment coefficient; d is the outer diameter of the wire; L _p is the conductor span represented by the load node; p ₁ , p ₂ are the gravity loads per unit length of the conductor and insulator string; l ₁ , l ₂ are the left and right spans on both sides of the tower; h ₁ , h ₂ , Respectively, the left and right height difference between the hanging points of the wires on both sides of the pole tower and the middle hanging point; T is the tension of the wire; A1 is the area of the insulator string subjected to wind pressure; l is the length of the insulator string.

Using the above scheme, the wind deflection angle is calculated by using the rigid straight rod method, taking into account the dynamic effect of wind load. In the calculation, the wind pressure non-uniformity coefficient α is equal to 1.0. The values of all other parameters are taken in full accordance with the provisions of GB50545-2010 "Code for Design of 110kV-750kV Overhead Transmission Lines".

To further describe, the random variable variables include: wind speed, wire weight, insulator string length, span, insulator string weight, air gap circle radius, wire tension, height difference between adjacent towers and calculation towers, wire outer diameter, Insulator string outer diameter.

Among them, the distribution function and parameters of random variables are shown in Table 1. Due to the large difference in the statistical distribution of wind speed, this paper downloaded the annual maximum wind speed data in the past 50 years in the area where the transmission line is located from the China Meteorological Data Sharing website, and calculated according to GB50009-2012 "Building Structure Load Code" and GB50545-2010 " Statistical parameters of wind speed are calculated according to the provisions of "Code for Design of 110kV-750kV Overhead Transmission Lines". Since the height difference of the calculated transmission line is very small, the influence of the wire tension on the wind angle is small, so the tension and the height difference are assumed to be constant.

Table 1 Statistical parameters for designing random variables

design random variable average coefficient of variation distribution type Wind speed v(m/s ² ) 23.635 0.205 Extremum Type I Conductor weight p ₁ (N/m) 10.805 0.07 Normality Insulator string length l(m) 6.832 0.05 Normality Gap L _P (m) 550 0.05 Normality Self-weight of insulator string p ₂ (N/m) 1776.2 0.07 Normality Air gap circle radius r(m) 3.7 - Value Wire tension T(N) 55393 - Value Height difference (m) 3.353 - Value Wire outer diameter (mm) 32.4 0.05 Normality Insulator String Outer Diameter (mm) 360 0.05 Normality

To further describe, the specific content of step S5 using the Monte Carlo method to calculate the wind deviation reliability of the insulator string is as follows:

S51: Number the selected random variables, 1, 2, 3...I; and determine the distribution function of each random variable

S52: Generate N uniformly distributed random numbers r _i ^j in the interval (0-1) in MATLAB by multiplication and congruence method;

S53: Bring the random number r _i ^j into the distribution function to obtain a random sampling value

S54: the random sampling value that step S53 obtains Substitute into the insulator string wind deflection failure function Z, and count, when Z<0, the number n of insulator string wind deflection failures;

S55: According to the formula Obtain the failure probability p _f of the insulator string due to wind deflection;

S56: Calculate the windage reliability index of the insulator string by the formula β=-Φ ^-1 (p _f ), where: Φ ^-1 (·) represents the inverse function of the standard normal distribution, p _f represents the failure probability, and β represents the reliability index.

Beneficial effects of the present invention: it is suitable for the case where the height difference between adjacent towers and calculation towers is small, and the rigid straight rod method is used to calculate the windage angle value, taking into account the wind load, gravity load, and wire load on the insulator string. Influencing factors such as gravity load and wind load on conductors, combined with the Monte Carlo method, calculates the wind deflection reliability of insulator strings. The reliability is good, the calculation process is simple, and it can meet the requirements of the existing technology.

Description of drawings

Fig. 1 is method flowchart of the present invention;

Fig. 2 is a schematic diagram of a pole tower and a suspension insulator string of the present invention;

Figure 3 is a schematic diagram of the simulation of the research object;

Fig. 4 is a schematic diagram of the wind speed time course at No. 1 hanging point in Fig. 3;

Figure 5 is a schematic diagram of the comparison between the simulated point turbulence intensity and the B-type landform turbulence intensity;

Fig. 6 is a schematic diagram of comparison between the power spectrum at the feature point and the target power spectrum;

Fig. 7 is the relational graph of wind speed mean value and wind deviation reliability index;

Fig. 8 is a graph showing the relationship between the mean value of the conductor's own weight and the index of windage reliability;

Fig. 9 is a graph showing the relationship between the mean value of the outer diameter of the conductor and the windage reliability index;

Detailed ways

The specific implementation manner and working principle of the present invention will be further described in detail below in conjunction with the accompanying drawings.

It can be seen from Fig. 1 that a nonlinear windage reliability calculation method based on Monte Carlo insulator strings is characterized by following the steps below:

S1: Set the research object of the transmission line, according to the wind load, gravity load on the insulator string, the gravity load on the wire, and the wind load on the wire, use the rigid straight rod method to calculate the wind deflection angle value of the insulator string;

Among them, the formula for calculating the windage angle value of the insulator string is:

In the above formula:

G _h is the wind load on the insulator string: G _h ＝W ₀ μ _z A ₁ ;

G _v is the gravity load of the insulator string: G _v = p ₂ l;

W _v is the gravity load of the wire:

W _h is the wind load on the wire: W _h = αW ₀ μ _z μ _sc β _c dL _p sin ² θ;

Among them, α is the wind pressure uneven coefficient; W ₀ is the basic wind pressure standard value; μ _z is the wind pressure altitude variation coefficient; μ _sc is the wire shape coefficient; β _c is the wind load adjustment coefficient; d is the outer diameter of the wire; L _p is the conductor span represented by the load node; p ₁ , p ₂ are the gravity loads per unit length of the conductor and insulator string; l ₁ , l ₂ are the left and right spans on both sides of the tower; h ₁ , h ₂ , Respectively, the left and right height difference between the hanging points of the wires on both sides of the pole tower and the middle hanging point; T is the tension of the wire; A ₁ is the area of the insulator string under the wind pressure; l is the length of the insulator string.

S2: According to the specification of overhead transmission lines, establish the connection structure between the tower and the insulator series, and select the random variables involved in the connection structure, and determine the distribution function corresponding to the random variables according to the random variables;

The random variable variables include: wind speed, wire weight, insulator string length, span, insulator string weight, air gap circle radius, wire tension, height difference between adjacent towers and calculation towers, wire outer diameter, insulator string outer diameter .

S3: Build the connection structure and random variables according to step S2, and establish the geometric relationship corresponding to the connection mechanism; in this embodiment, the tower form is taken as an example for illustration, see Figure 2 for details.

S4: According to the geometric relationship in step S3 and the windage angle value in step S1, establish a windage failure function function of insulator strings with random variables;

B represents the length of the cross-arm; l represents the length of the insulator string; r represents the radius of the air gap circle; α represents the angle of inclination between the cross-arm and the tower body, and the tower α in this paper is 115°; Represents the windage angle.

Among them, the statistical parameter values of random variables in the wind deflection failure function function of insulator strings are shown in Table 1. Since the height difference of the transmission line calculated in this scheme is very small, the influence of the wire tension on the wind angle is small, so the tension and the height difference are assumed to be constant values.

S5: According to the random variable, the distribution function of the random variable, and the failure function function of the wind deflection of the insulator string, the reliability of the wind deflection of the insulator string is calculated using the Monte Carlo method.

S51: Number the selected random variables, 1, 2, 3...I; and determine the distribution function of each random variable

S52: Generate N uniformly distributed random numbers r _i ^j in the interval (0-1) in MATLAB by multiplication and congruence method;

S53: Bring the random number r _i ^j into the distribution function to obtain a random sampling value

S54: the random sampling value that step S53 obtains Substitute into the insulator string wind deflection failure function Z, and count, when Z<0, the number n of insulator string wind deflection failures;

S55: According to the formula Obtain the failure probability p _f of the insulator string due to wind deflection;

S56: Calculate the windage reliability index of the insulator string by the formula β=-Φ ^-1 (p _f ), where: Φ ^-1 (·) represents the inverse function of the standard normal distribution, p _f represents the failure probability, and β represents the reliability index.

Through the above scheme, in order to explain the rationality of using the rigid straight rod method to calculate the wind angle. The following is a comparative analysis by introducing the finite element model:

In this example, the research object is: take a 500kV 3-span line as the research object, there are 2 strain towers and 2 straight towers, each span is 550m long, the total length is 1650m, and there is no corner in the entire span. See Figure 3 for details. The physical parameters of the research object ACSR are shown in Table 2. The physical parameters of the insulator strings on the strain tower and straight tower are shown in Table 3.

Table 2 Physical parameters of ACSR

Calculated cross-sectional area/mm ² Elastic coefficient/MPa Linear density/(kg·km ^-1 ) Initial tension/kN 621 630 00 191 7 55.4

Table 3 Physical parameters of insulator strings

Location Length/m Elastic coefficient/MPa Mass/kg Tension tower 8.330 72000 1614 straight line tower 6.832 72000 1238

Simulation of pulsating wind:

Using the Davenport spectrum S _u (f):

In the formula: x=1200ω/U ₁₀ , ω is the circular frequency, n is the frequency, k is a constant related to the landform, assuming that the calculated transmission line is located in the B-type landform, take k=0.005. U10 is the wind speed at a height of 10m.

Due to the large scale of the transmission line along the direction of the conductor, this paper considers the spatial correlation of the fluctuating wind speed between different positions of the wire, and uses the cross power spectral density function of the fluctuating wind speed to represent the correlation of the fluctuating wind speed between two points i and j in space degree, the specific form is as follows:

In the formula is the phase angle, and Coh(ω) is the spatial correlation function recommended by Davenport.

The fluctuating wind field is simulated by the harmonic superposition method: the total length of the simulation time history is 1024s, the time step is 0.25s, the frequency interception range is 0.00rad/s-6.28rad/s, and the number of sampling frequency points is 4096. A wind speed simulation point is selected every 10m along the line direction on the wire, and a total of 166 random wind speed points are generated. When the average wind speed at a height of 10m is 30m/s, among the research objects generated by simulation, the time-history curve of wind speed at No. 1 suspension point, the specific time-history curve of wind speed is shown in Figure 4.

In order to test the accuracy of the wind speed simulation, the turbulence intensity and power spectral density of the characteristic points of the simulated wind field are compared with the target wind speed spectrum as shown in Fig. 5 and Fig. 6. From Figures 5 and 6, it can be seen that the simulated values of wind field turbulence intensity and wind speed are in good agreement with the theoretical values.

After simulating the wind speed, the wind load time history is calculated using the following formula, which is applied to the numerical model.

In the formula: ρ is the air density, the standard value is 1.225 5kg/m ³ ; D is the equivalent windward diameter of the wire; L is the node length; C _D is the drag coefficient; Uz _{and Vz} are the average wind speed and Pulsating wind speed. The damping ratio of the wire is taken as 0.4%, and the influence of the pneumatic damping on the wire.

Based on the above research objects, the results of rigid straight rod method and finite element method are compared.

In Table 4: the time-history statistical value of the wind angle at different standard wind speeds for the No. 1 suspension point and the value of the wind angle calculated according to the rigid straight rod method. in: Represents the value of the windage angle calculated by the rigid straight rod method; Represents the mean value of the time-history curve of wind angle calculated by ANSYS; Represents the maximum value of the time history curve of wind angle calculated by ANSYS; δ represents the relative error between the value of wind angle calculated by the rigid straight rod method and the maximum value of time history curve of wind angle calculated by ANSYS.

In Table 4, under different standard wind speeds, the aerodynamic damping effect, the "pull" effect of the strain towers at both ends of the multi-stage line model on the out-of-plane swing of the transmission line, and the distance between each stage line are considered in the calculation of the finite element model. Under the premise of mutual coupling effect, the result of the wind angle calculated by the rigid straight rod method is also within the acceptable error range of the project. Then the result of the wind angle calculated by the rigid straight rod method is safe and reasonable.

Analysis of Influencing Factors of Wind Deviation Reliability of Insulator Strings:

According to GB 50068-2001 "Unified Standards for Reliability Design of Building Structures", the reliability index of the limit state of normal service should be 0~1.5 according to the reversibility degree. In this paper, the target reliability index of insulator string wind deflection is selected as 1.5 for verification.

In order to check whether the wind deflection reliability index of the tower designed according to the current code meets the requirements under different statistical parameters of the design random variable. First assume that the cross-arm length B of the tower is an unknown parameter of the structure, in the case of known other parameters in Table 4. Follow the steps below to calculate:

1) Determine the standard value of each parameter according to the design random variables in Table 5. The design value of the wind speed is based on the provisions of GB50545-2010 "Code for Design of 110kV-750kV Overhead Transmission Lines": 500kV transmission lines take the design wind speed value with a return period of 50 years. The standard values of other design random variables are selected according to the provisions of GB50009-2012 "Code for Building Structure Loads".

2) Using the normal service limit state combination, the standard value of each design random variable is substituted into the formula , to calculate the cross-arm length B.

3) After the cross-arm length B is determined, use the MC method to calculate its corresponding reliability index.

4) Change the statistical parameter value of a design random variable, and then repeat steps 1) to 3) to obtain the relationship curve between the mean value of wind speed and the reliability index of wind deviation, see Figure 7 for details; See Figure 8 for details; see Figure 9 for the relationship curve between the average value of the outer diameter of the wire and the windage reliability index.

It can be seen from Figure 7 that with the increase of the average wind speed, the wind deflection reliability index of the tower designed according to the current code will continue to decrease. This means that in areas with high average wind speed, when the tower is designed according to the current normative method, the wind deviation reliability index of the insulator series may be lower than the target reliability index. However, in areas where the average wind speed is small, the wind deflection reliability index of the insulator string obtained by designing the tower according to the current specification method fully meets the requirements of the target reliability index.

It can be seen from Figure 7 that with the decrease of the average weight of the wire, the wind deflection reliability index of the tower designed according to the current code will continue to decrease.

From Figure 8, it can be seen that with the increase of the average value of the outer diameter of the conductor, the wind deflection reliability index of the insulator string of the tower designed according to the current code will continue to decrease. This means that for conductors with large outer diameter or small self-weight, when the tower is designed according to the current specifications, the wind deflection reliability index of the insulator string may be lower than the target reliability index.

(1) When the height difference is small and the wind pressure non-uniformity coefficient is 1.0, the result error of the rigid straight rod method in the code to calculate the wind angle is within an acceptable range, and it can be considered that the rigid straight rod in the code law is reasonable.

(2) In areas with high average wind speed, due to the nonlinearity of the insulator string wind deflection failure function function, the reliability index of the insulator string wind deflection reliability index of the tower designed according to the current code method may be lower than the target reliability index. Therefore, it is suggested that in areas with large average wind speed, a higher design wind speed value with a return period greater than 50 years should be taken to improve the wind deviation reliability index.

(3) In areas where the average wind speed is small, the wind deflection reliability index of insulator strings for towers designed according to the current code method can fully meet the requirements of the target reliability index. It is recommended that a minimum design wind speed value should not be selected in the wind deflection calculation , but directly select the local wind speed value.

(4) The use of conductors with larger self-weight and smaller outer diameter in the design stage will improve the reliability index of wind deflection of its insulator strings.

It should be noted that the above description is not intended to limit the present invention, and the present invention is not limited to the above-mentioned examples. Those skilled in the art may make changes, modifications, additions or replacements within the scope of the present invention. It should also belong to the protection scope of the present invention.

Claims (4)

1. one kind is based on the non-linear windage yaw reliability degree calculation method of Monte Carlo insulator chain, it is characterised in that according to following steps Carry out：

S1：Setting transmission line of electricity research object, the gravity laod of wind load, gravity laod, conducting wire according to suffered by insulator chain, Wind load suffered by conducting wire, the windage yaw angle value of insulator chain is calculated using the straight rod method of rigidity；

S2：According to overhead transmission line specification, shaft tower and insulator chain connection structure are established, and selectes what the connection structure was related to Stochastic variable, distribution function corresponding with stochastic variable is determined according to stochastic variable；

S3：Connection structure and stochastic variable are built according to step S2, establish geometrical relationship corresponding with bindiny mechanism；

S4：According to the geometrical relationship of step S3 and the windage yaw angle value of step S1, the insulator chain windage yaw with stochastic variable is established Invalidation functions function；

S5：According to stochastic variable, the distribution function of stochastic variable and insulator chain windage yaw invalidation functions function, illiteracy Taka is used Lip river method calculates insulator chain windage yaw reliability.

2. the non-linear windage yaw reliability degree calculation method of the insulator chain according to claim 1 based on Monte Carlo, it is special Sign is that the content of step S1 is：

Wind load suffered by the gravity laod of wind load, gravity laod, conducting wire according to suffered by insulator chain, conducting wire, calculates exhausted The windage yaw angle value formula of edge substring is：

In formula (1)：

G_hIt is wind load suffered by insulator chain：G_h=W₀μ_zA₁；

G_vIt is the gravity laod of insulator chain：G_v=p₂l；

W_vIt is the gravity laod of conducting wire：

W_hIt is the wind load suffered by conducting wire：W_h=α W₀μ_zμ_scβ_cdL_psin²θ；

Wherein, α is wind evil attacking lung；W₀For fundamental wind pressure standard value；μ_zFor height variation coefficient of wind pressure；μ_scFor wire body Type coefficient；β_cFor Wind Load Adjustment Coefficients；D is the outside diameter of conducting wire；L_pIt is the conducting wire span representated by load node；p₁、p₂Respectively For the gravity laod on conducting wire and insulator chain unit length；l₁、l₂The respectively left and right span of shaft tower both sides；h₁、h₂, respectively For the left and right height difference of the relatively middle hanging point of shaft tower both sides conducting wire hanging point；T is wire tension；A₁The face of wind pressure is born for insulator chain Product；L is insulator chain length.

3. the non-linear windage yaw reliability degree calculation method of the insulator chain according to claim 1 based on Monte Carlo, it is special Sign is that the stochastic variable variable includes：Wind speed, conducting wire dead weight, the dead weight of insulator chain length, span, insulator chain, air Height difference, wire diameter, insulator chain outside diameter between gap radius of circle, wire tension, adjacent shaft tower and calculating shaft tower.

4. the non-linear windage yaw reliability degree calculation method of the insulator chain according to claim 1 based on Monte Carlo, it is special Sign is that the particular content of step S5 is：

S51：Selected stochastic variable is numbered, 1,2,3 ... I；And determine the distribution function of each stochastic variable

S52：N number of equally distributed random number in section (0~1) is generated in MATLAB using multiplicative congruential method

S53：By random numberBring into distribution function, obtain random sampling value

S54：The random sampling value that step S53 is obtainedSubstitute into insulator chain windage yaw invalidation functions function Z, and count, work as Z During ＜ 0, the number n of insulator chain windage yaw failure；

S55：According to formulaObtain insulator chain windage yaw failure probability p_f；

S56：Pass through formula β=- Φ^-1(p_f) insulator chain windage yaw RELIABILITY INDEX is calculated, wherein：Φ^-1() is representing standard just The inverse function of state distribution, p_fFailure probability is represented, β represents RELIABILITY INDEX.