Method for calculating deicing normal service reliability of ice-coated power transmission line

Abstract

The invention relates to a method for calculating deicing normal service reliability of an iced power transmission line, and belongs to the technical field of safe deicing of the iced power transmission line. According to the invention, through determining the power transmission line icing thickness truncation probability distribution, calculating the deicing completion degree coefficient of the icing power transmission line, determining the normal service performance function of the power transmission line, calculating the stress of the power transmission line and calculating the reliability and the failure probability, the reliability of the icing power transmission line during deicing is comprehensively and concisely established; probability-based evaluation indexes are provided for normal service of the ice-coated power transmission line, and the safety and reliability of the power transmission line under severe weather conditions are improved. According to the method, the operation reliability of the power transmission line after deicing can be accurately calculated, the safety and reliability of the power transmission line under the severe weather condition are improved, scientific and real-time data support can be provided for power system management, and optimization management and risk prevention of an intelligent power grid are facilitated.

Description

Technical Field

[0001] The invention relates to a method for calculating the normal service reliability of deicing of ice-covered transmission lines, and belongs to the technical field of safe deicing of ice-covered transmission lines. Background Art

[0002] In cold temperate climates or high altitude areas, power transmission lines are often covered with ice and snow. Icing can have a variety of negative effects on transmission lines, including increasing line loads, causing line sway and vibration, and even causing line breakage and power system failures. Therefore, in order to ensure the stability and security of power supply, effective de-icing measures are particularly important for transmission networks.

[0003] At present, there are a variety of transmission line deicing technologies widely used, such as hot line ice melting, mechanical ice breaking, chemical coatings, and deicing with the help of robotic technology. These technologies have their own advantages and disadvantages, but there is a common problem that the deicing effect cannot be accurately evaluated in real time. After deicing is completed, the service capacity of the line often needs to be determined by manual inspection or empirical assumptions, which brings certain uncertainties and risks. As the power system develops towards intelligence and automation, higher requirements are placed on the operation and maintenance of transmission lines. The service reliability of iced transmission lines has become one of the key factors to ensure the safe operation of power systems. Although the existing technology can solve the problem of transmission line icing to a certain extent, there is a lack of a high-accuracy and real-time deicing effect of iced transmission lines and a reliability evaluation method during normal service. How to quantify the normal service reliability of transmission lines after deicing has become an urgent problem to be solved. Summary of the invention

[0004] In order to solve the problems existing in the above-mentioned prior art, the present invention provides a method for calculating the normal service reliability of de-icing of ice-covered transmission lines. The present invention can accurately calculate the operating reliability of the transmission lines after de-icing, thereby improving the safety and reliability of the transmission lines under severe weather conditions. Moreover, the present invention can provide scientific and real-time data support for power system management, which is helpful for the optimized management and risk prevention of smart grids.

[0005] To achieve the above object, the present invention provides a technical solution: a method for calculating the normal service reliability of deicing of ice-covered transmission lines, characterized by comprising the following steps:

[0006] S1. Determine the truncated probability distribution of the ice thickness of the transmission line: When the transmission line is naturally iced and there is no human intervention in the icing process of the transmission line, the probability density function of the ice thickness D of the transmission line is assumed to be f D (d) The cumulative distribution function of ice thickness on transmission lines is F D(d) The lower limit of the ice thickness of the transmission line is greater than 0 mm. When human intervention occurs in the ice coating of the transmission line, a threshold deicing mechanism is introduced, and the ice thickness has an upper limit d ice ; 0mm and d ice As the truncated random variable D of ice thickness t The left truncation point and the right truncation point of the ice thickness are obtained based on the original probability distribution of the ice thickness D. The truncation probability density function and the cumulative distribution function of the ice thickness of the transmission line are obtained. Dt (d) and F Dt (d) The cumulative degrees are:

[0007]

[0008] S2. Calculate the deicing completion coefficient of ice-covered transmission lines: According to the damage caused to the transmission lines by multiple deicing operations and the attenuation of the carrying capacity of the transmission lines during service, establish the deicing completion coefficient κ;

[0009] S3. Determine the function function of normal service of the transmission line: the maximum tension at the lowest point of the transmission line sag does not exceed 60% of the breaking force of the transmission line, the tension at the suspension point of the transmission line is greater than the tension at the lowest point of the transmission line sag, and the maximum tension at the suspension point is increased by 10% compared with the tension at the lowest point of the sag, that is, the maximum tension at the suspension point of the transmission line does not exceed 66% of the breaking force of the transmission line; then, according to the maximum tension at the lowest point of the transmission line sag and the maximum tension at the suspension point of the transmission line, the function function of normal service of the transmission line is obtained as follows:

[0010] Z=RS=z(D,V,H,A)=κK e HA-σ′ x A (2)

[0011] Where R is the tensile strength of the conductor, S is the load effect, κ is the deicing completion coefficient, K e is the tension limit coefficient for safe operation of the transmission line, H is the material yield strength of the conductor, A is the cross-sectional area of ​​the conductor, σ′ x is the axial stress of the transmission line, σ′ x A represents the tension T on the conductor, V is the wind speed, and D is the random variable of ice thickness on the transmission line;

[0012] S4. Calculate the stress of the transmission line: The overhead transmission line is a twisted wire composed of multiple strands of fine metal wires. Under the action of wind load, the transmission line will deflect due to wind. At this time, the catenary shape equation y(x) of the overhead line suspended between the two towers is as follows:

[0013]

[0014] in:

[0015]

[0016] In the formula, γ h and γ v are the horizontal and vertical specific loads respectively, γ′ is the uniform specific load acting along the length of the overhead line in the windward plane, h′ is the height difference of the windward plane, β′ is the height difference angle of the windward plane, and σ0′ is the axial stress at the lowest point of the windward plane;

[0017] in:

[0018]

[0019] h′=h cos η (6d)

[0020]

[0021] Where q is the mass per unit length of the transmission line, A is the cross-sectional area of ​​the transmission line, g is the acceleration of gravity, D is the ice thickness, and c is the outer diameter of the transmission line; β c is the wind load adjustment factor for transmission lines, α f is the wind speed non-uniformity coefficient, μ sc is the shape factor of the overhead line, θ is the angle between the wind direction and the line direction, σ0 is the service stress of the transmission line, β is the height difference angle, η is the wind deviation angle, h is the height difference, and l is the span;

[0022] The axial stress at any point in the windage plane is:

[0023]

[0024] Substituting equations (5) and (6) into equation (7), we get σ′ x Function expression about variables D and V:

[0025] σ′ x =g x (D,V) (8)

[0026] Substituting formula (8) into formula (2), we get the function function of normal service of transmission line:

[0027] Z=RS=z(D,V,H,A)=κK e HA-g x (D,V)A (9)

[0028] Where R is the tensile strength of the conductor, S is the load effect, κ is the deicing completion coefficient, K e is the tension limit coefficient for safe operation of the transmission line, H is the material yield strength of the conductor, A is the cross-sectional area of ​​the conductor, g x (·) is the function of the axial stress of the transmission line with respect to D and V;

[0029] S5. Calculate the reliability and failure probability. The specific steps are as follows:

[0030] (1) Normalization of non-normal random variables: The two non-normal random variables, ice thickness D and wind speed V, are normalized. At the same time, the probability distribution and probability density function of ice thickness D are transformed into the truncated random variable D. t The distribution function and probability density function of are:

[0031]

[0032] Where D′ and V′ are the ice thickness D, t and the equivalent normalized variable of wind speed V, is the design point coordinate;

[0033] in,

[0034]

[0035] (2) Calculate sensitivity: The mean and standard deviation of the original function are approximately calculated by Taylor series expansion. The sensitivity α X The weight is calculated using the following formula:

[0036]

[0037] In the formula, the approximate performance function Z X At the design point x * The functional function Z of formula (9) is expanded according to Taylor series and taken to the first order term; is a random variable X i The standard deviation of

[0038] (3) Calculate the approximate performance function Z X The mean and standard deviation of: After normalization, the approximate function Z is calculated based on the characteristics of the normal distribution. X The mean and standard deviation The calculation formula is as follows:

[0039]

[0040] In the formula, μ X is the mean vector of random variables, σ X is the standard deviation vector of random variables, α X is the sensitivity vector;

[0041] (4) Calculate the reliability index: Z X It is a linear combination of independent normally distributed random variables, which also obeys the normal distribution. The reliability index β ice Calculated by the following formula:

[0042]

[0043] Then iterative calculation is performed, and the design point iteration adopts the following formula:

[0044]

[0045] In the formula, is a random variable X i The mean of

[0046] According to the requirement of the random variable of the first-order second moment method that it has a complete distribution, for the truncated distribution variable D of ice thickness, t , the coordinates of the design points during the iteration process When it falls outside the allowable range, the nearest pullback method is used to correct the ice thickness component d in the design point iteration formula (15). t , correct it to the allowed range, the correction formula is as follows:

[0047]

[0048] (5) Calculate the failure probability: Based on the reliability index β ice , calculate the failure probability P f , the calculation formula is as follows:

[0049] P f =Φ(-β ice ) (17)

[0050] Where Φ(·) is the standard normal distribution function.

[0051] Moreover, the expression of the deicing completion coefficient κ in step S2 consists of two parts, the first part is the reduction of bearing capacity caused by material damage during the deicing process, which is defined as the deicing damage coefficient κ1, and the second part is the reduction of bearing capacity caused by material damage during the service process, which is defined as the deicing damage coefficient κ2;

[0052] The expressions of κ1 and κ2 are as follows:

[0053]

[0054] Where, 0<κ1≤1; n is the nth deicing in the service cycle, m is the maximum number of experiments obtained through thermal tests or mechanical knocking tests for the transmission line to meet the continued service capacity; κ a is a constant, determined by m;

[0055]

[0056] Where, 0<κ2≤1; i is the service year, j is the required service years; κ b is a constant, determined by j;

[0057] According to κ1 and κ2, κ=κ1κ2.

[0058] Moreover, in steps S3 and S4, the transmission line safe operation tension limit coefficient K e Take 60% at the lowest point of the transmission line sag and 66% at the suspension point of the transmission line.

[0059] Furthermore, in step S4, x=0 and x=1 are substituted into Japanese σ′ x =g x (D, V) The axial stress of the conductor at the suspension point is:

[0060]

[0061] Where β is the height difference angle, l is the span, h is the height difference, and η is the wind deviation angle.

[0062] Moreover, in step S4, the point where the highest point of the transmission line is connected to the tower is the transmission line suspension point; l is the span, when the lowest point of the transmission line sag is within the span, that is, 0≤x≤l, according to the formula Take the derivative of x, and then find the minimum value to get the coordinate point of the lowest point of the sag of the transmission line in the section; when the lowest point of the sag of the transmission line is outside the section, that is, x<0 or x>l, take the lowest point in height as the lowest point of the sag of the transmission line.

[0063] According to the above technical solution, the method provided by the present invention for calculating the reliability of normal service of deicing of ice-covered transmission lines is to comprehensively and concisely establish the reliability of deicing of ice-covered transmission lines by determining the truncated probability distribution of ice thickness of transmission lines, calculating the deicing completion coefficient of ice-covered transmission lines, determining the normal service function of transmission lines, calculating the stress of transmission lines, and calculating the reliability and failure probability, so as to provide a probability-based evaluation index for the normal service of ice-covered transmission lines, thereby improving the safety and reliability of transmission lines under severe weather conditions. Compared with the prior art, the present invention has the following advantages:

[0064] (1) Because the technical solution adopted by the present invention accurately reflects the actual icing conditions of the transmission line by determining the truncated probability distribution of the ice thickness of the transmission line, the present invention can more accurately guide the deicing operation and ensure the safe operation of the transmission line under severe weather conditions.

[0065] (2) Because the technical solution adopted by the present invention provides a means to quantitatively measure the de-icing effect by calculating the de-icing completion coefficient of ice-covered transmission lines, the present invention can improve the deficiencies in the existing technology in line status assessment and provide more accurate data support for power system management and maintenance.

[0066] (3) Because the technical solution adopted by the present invention reduces line failures caused by icing by calculating the stress of the transmission line and its reliability and failure probability, the present invention can ensure the safe and reliable operation of the transmission line without excessive maintenance, avoid unnecessary maintenance expenses, and reduce the losses that may be caused by line accidents, thereby having good economic efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 Flow chart of the method for calculating the normal service reliability of de-icing of ice-covered transmission lines;

[0068] Figure 2 Wind deflection diagram of transmission line under wind load. DETAILED DESCRIPTION

[0069] The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited to the following embodiments.

[0070] In the technical solution provided by the present invention, a method for calculating the normal service reliability of deicing of ice-covered transmission lines is provided, and its flow chart is as follows: Figure 1 As shown, the specific steps are as follows:

[0071] S1. Determine the truncated probability distribution of the ice thickness of the transmission line: When the transmission line is naturally iced and there is no human intervention in the icing process of the transmission line, the probability density function of the ice thickness D of the transmission line is assumed to be f D (d) The cumulative distribution function of ice thickness on transmission lines is F D (d) The lower limit of the ice thickness of the transmission line is greater than 0 mm. When human intervention occurs in the ice coating of the transmission line, a threshold deicing mechanism is introduced, and the ice thickness has an upper limit d ice ; 0mm and d ice As the truncated random variable D of ice thickness t The left truncation point and the right truncation point of the ice thickness are obtained based on the original probability distribution of the ice thickness D. The truncation probability density function and the cumulative distribution function of the ice thickness of the transmission line are obtained. Dt (d) and F Dt (d) The cumulative degrees are:

[0072]

[0073] S2. Calculate the deicing completion coefficient of ice-covered transmission lines: According to the damage caused to the transmission lines by multiple deicing operations and the attenuation of the carrying capacity of the transmission lines during service, establish the deicing completion coefficient κ;

[0074] The expression of deicing completion coefficient κ consists of two parts. The first part is the reduction of bearing capacity caused by material damage during deicing, which is defined as deicing damage coefficient κ1. The second part is the reduction of bearing capacity caused by material damage during service, which is defined as deicing damage coefficient κ2.

[0075] The expressions of κ1 and κ2 are as follows:

[0076]

[0077] Where, 0<κ1≤1; n is the nth deicing in the service cycle, m is the maximum number of experiments obtained through thermal tests or mechanical knocking tests for the transmission line to meet the continued service capacity; κ a is a constant, determined by m;

[0078]

[0079] Where, 0<κ2≤1; i is the service year, j is the required service years; κ b is a constant, determined by j;

[0080] According to κ1 and κ2, κ=κ1κ2.

[0081] S3. Determine the function function of normal service of the transmission line: the maximum tension at the lowest point of the transmission line sag does not exceed 60% of the breaking force of the transmission line, the tension at the suspension point of the transmission line is greater than the tension at the lowest point of the transmission line sag, and the maximum tension at the suspension point is increased by 10% compared with the tension at the lowest point of the sag, that is, the maximum tension at the suspension point of the transmission line does not exceed 66% of the breaking force of the transmission line; then, according to the maximum tension at the lowest point of the transmission line sag and the maximum tension at the suspension point of the transmission line, the function function of normal service of the transmission line is obtained as follows:

[0082] Z=RS=z(D,V,H,A)=κK e HA-σ′ x A (2)

[0083] Where R is the tensile strength of the conductor, S is the load effect, κ is the deicing completion coefficient, K e is the tension limit coefficient for safe operation of the transmission line, H is the material yield strength of the conductor, A is the cross-sectional area of ​​the conductor, σ′ x is the axial stress of the transmission line, σ′ x A represents the tension T on the conductor, V is the wind speed, and D is the random variable of ice thickness on the transmission line;

[0084] In this embodiment, the transmission line safe operation tension limit coefficient K e Take 60% at the lowest point of the transmission line sag and 66% at the suspension point of the transmission line.

[0085] S4. Calculate the stress of transmission lines: Overhead transmission lines are twisted wires made of multiple strands of fine metal wires. Under the action of wind load, the transmission lines will deflect. Figure 2 As shown, the catenary shape equation y(x) of the overhead line hanging between the two towers is as follows:

[0086]

[0087] in:

[0088]

[0089] In the formula, γ h and γ v are the horizontal and vertical specific loads respectively, γ′ is the uniform specific load acting along the length of the overhead line in the windward plane, h′ is the height difference of the windward plane, β′ is the height difference angle of the windward plane, and σ0′ is the axial stress at the lowest point of the windward plane;

[0090] in:

[0091]

[0092] h′=h cos η (6d)

[0093]

[0094] Where q is the mass per unit length of the transmission line, A is the cross-sectional area of ​​the transmission line, g is the acceleration of gravity, D is the ice thickness, and c is the outer diameter of the transmission line; β c is the wind load adjustment factor for transmission lines, α f is the wind speed non-uniformity coefficient, μ sc is the shape factor of the overhead line, θ is the angle between the wind direction and the line direction, σ0 is the service stress of the transmission line, β is the height difference angle, η is the wind deviation angle, h is the height difference, and l is the span;

[0095] In this embodiment, the transmission line safe operation tension limit coefficient K e At the lowest point of the transmission line sag, it is 60%, and at the suspension point of the transmission line, it is 66%. σ0 is the service stress of the transmission line, which is determined by the transmission line model.

[0096] The axial stress at any point in the windage plane is:

[0097]

[0098] Substituting equations (5) and (6) into equation (7), we get σ′ x Function expression about variables D and V:

[0099] σ′ x =g x (D,V) (8)

[0100] Substitute x=0 and x=l into Japanese σ′ x =g x (D, V) The axial stress of the conductor at the suspension point is:

[0101]

[0102] Substituting formula (8) into formula (2), we get the function function of normal service of transmission line:

[0103] Z=RS=z(D,V,H,A)=κK e HA-g x (D,V)A (9)

[0104] Where R is the tensile strength of the conductor, S is the load effect, κ is the deicing completion coefficient, K e is the tension limit coefficient for safe operation of the transmission line, H is the material yield strength of the conductor, A is the cross-sectional area of ​​the conductor, g x (·) is the function of the axial stress of the transmission line with respect to D and V;

[0105] In this embodiment, the point where the highest point of the transmission line is connected to the tower is the transmission line suspension point; l is the span. When the lowest point of the transmission line sag is within the span, that is, 0≤x≤l, according to the formula Take the derivative of x, and then find the minimum value to get the coordinate point of the lowest point of the sag of the transmission line in the section; when the lowest point of the sag of the transmission line is outside the section, that is, x<0 or x>l, take the lowest point in height as the lowest point of the sag of the transmission line.

[0106] S5. Calculate the reliability and failure probability. The specific steps are as follows:

[0107] (1) Normalization of non-normal random variables: The two non-normal random variables, ice thickness D and wind speed V, are normalized. At the same time, the probability distribution and probability density function of ice thickness D are transformed into the truncated random variable D. t The distribution function and probability density function of are:

[0108]

[0109] Where D′ and V′ are the ice thickness D, t and the equivalent normalized variable of wind speed V, is the design point coordinate;

[0110] in,

[0111]

[0112] (2) Calculate sensitivity: The mean and standard deviation of the original function are approximately calculated by Taylor series expansion. The sensitivity α X The weight is calculated using the following formula:

[0113]

[0114] In the formula, the approximate performance function Z X At the design point x * The functional function Z of formula (9) is expanded according to Taylor series and taken to the first order term; is a random variable X i The standard deviation of

[0115] (3) Calculate the approximate performance function Z X The mean and standard deviation of: After normalization, the approximate function Z is calculated based on the characteristics of the normal distribution. X The mean and standard deviation The calculation formula is as follows:

[0116]

[0117] In the formula, μ X is the mean vector of random variables, σ X is the standard deviation vector of random variables, α X is the sensitivity vector;

[0118] (4) Calculate the reliability index: Z X It is a linear combination of independent normally distributed random variables, which also obeys the normal distribution. The reliability index β ice Calculated by the following formula:

[0119]

[0120] Then iterative calculation is performed, and the design point iteration adopts the following formula:

[0121]

[0122] In the formula, is a random variable X i The mean of

[0123] According to the requirement of the random variable of the first-order second moment method that it has a complete distribution, for the truncated distribution variable D of ice thickness, t , the coordinates of the design points during the iteration process When it falls outside the allowable range, the nearest pullback method is used to correct the ice thickness component d in the design point iteration formula (15). t , correct it to the allowed range, the correction formula is as follows:

[0124]

[0125] (5) Calculate the failure probability: Based on the reliability index β ice , calculate the failure probability P f , the calculation formula is as follows:

[0126] P f =Φ(-β ice ) (17)

[0127] Where Φ(·) is the standard normal distribution function.

[0128] Take a transmission line in a mountainous area as an example. The conductor model is JL / G1A-400 / 50, and the conductor parameters are as follows: the mass per unit length q is 1511kg / km, the outer diameter c of the conductor is 27.63mm, and the cross-sectional area A is 451.55mm2; the line design ice thickness is 25mm. The transmission line span is 300m; the height difference angle is 15.2 degrees; the relevant random variables are shown in Table 1.

[0129] Table 1 Statistical parameters of random variables

[0130] random variable Statistical distribution Mean Coefficient of variation Ice thickness D Extreme Type I 20.00 0.18 Wind speed V Extreme Type I 5.00 0.50 Cross-sectional area A Normal 451.55 0.05 Tensile strength H Normal 273.28 0.10

[0131] The nth deicing in the service cycle, m is set to 5; κ a = 1.2. At this time, the de-icing completion coefficient κ1 = 0.98.

[0132] Service year i = 5 years, j is set to 30 years; κ b =1.1. At this time, the de-icing completion coefficient κ1 = 0.93.

[0133] According to the deicing completion coefficient, we get κ = κ a× κ b＝ 0.98 × 0.93=0.9114.

[0134] Then, the above method for calculating the normal service reliability of de-icing of iced transmission lines based on the de-icing completion degree is used to calculate the failure probability of de-icing of transmission lines. The failure probability of de-icing under various working conditions is shown in Table 2.

[0135] Table 2 Deicing failure probability of transmission line under different working conditions

[0136]

[0137] From the data listed in the table above, it can be seen that the deicing failure probability obtained by the calculation method described in this patent has the following characteristics. Compared with condition 1, the failure probability of conditions 2, 3 and 4 considering the deicing condition is significantly lower than the failure probability without considering the deicing condition. Obviously, for transmission lines with deicing operations, not considering the change in failure probability caused by deicing will lead to an excessively high failure probability of transmission lines, which is not conducive to evaluating the effect of deicing technology as a disaster prevention and mitigation measure for ice-covered transmission lines.

[0138] Compared with Condition 2, Condition 3 also considers deicing and considers the random variable of ice thickness as a truncated probability distribution. However, the failure probability of Condition 3 considering the deicing completion coefficient is also significantly greater than the failure probability of Condition 2 considering only deicing.

[0139] Compared with Condition 3, Condition 4 considers the deicing completion coefficient and adopts the normal service function function. Condition 4 considers the deicing completion coefficient but does not adopt the normal service function function. The failure probability of Condition 4 is significantly lower than that of Condition 3. Considering the actual situation, if the transmission line cannot continue to serve normally, it has actually lost its function as a transmission line and also needs to be repaired or replaced. From this aspect, the transmission line at this time has been damaged. Condition 4 establishes a function function based on the yield limit of commonly used transmission lines, and its failure probability is very small. Although the probability of being judged as easy to fail after exiting the normal service state is very small, it is easy to overestimate the bearing capacity of the transmission line, allowing the transmission line that cannot be in normal service to continue to serve, which may cause related accidents.

[0140] It can be seen that the present invention can provide more accurate and practical calculation results for the reliability assessment of normal service of transmission line deicing, give scientific guidance for disaster prevention and mitigation of transmission lines, and has great engineering application value.

Claims

1. A method for calculating the normal service reliability of deicing of ice-covered transmission lines, characterized in that The following steps are involved: S1. Determine the truncated probability distribution of the ice thickness of the transmission line: When the transmission line is naturally iced and there is no human intervention in the icing process of the transmission line, the probability density function of the ice thickness D of the transmission line is assumed to be f D (d) The cumulative distribution function of ice thickness on transmission lines is F D (d) The lower limit of the ice thickness of the transmission line is greater than 0 mm. When human intervention occurs in the ice coating of the transmission line, a threshold deicing mechanism is introduced, and the ice thickness has an upper limit d ice ; 0mm and d ice As the truncated random variable D of ice thickness t The left truncation point and the right truncation point of the ice thickness are obtained based on the original probability distribution of the ice thickness D. The truncation probability density function and the cumulative distribution function of the ice thickness of the transmission line are obtained. Dt (d) and F Dt (d) are: S2. Calculate the deicing completion coefficient of ice-covered transmission lines: According to the damage caused to the transmission lines by multiple deicing operations and the attenuation of the carrying capacity of the transmission lines during service, establish the deicing completion coefficient κ; S3. Determine the function function of normal service of the transmission line: the maximum tension at the lowest point of the transmission line sag does not exceed 60% of the breaking force of the transmission line, the tension at the suspension point of the transmission line is greater than the tension at the lowest point of the transmission line sag, and the maximum tension at the suspension point is increased by 10% compared with the tension at the lowest point of the sag, that is, the maximum tension at the suspension point of the transmission line does not exceed 66% of the breaking force of the transmission line; then, according to the maximum tension at the lowest point of the transmission line sag and the maximum tension at the suspension point of the transmission line, the function function of normal service of the transmission line is obtained as follows: Z=RS=z(D,V,H,A)=κK e HA-σ′ x A (2) Where R is the tensile strength of the conductor, S is the load effect, κ is the deicing completion coefficient, K e is the tension limit coefficient for safe operation of the transmission line, H is the material yield strength of the conductor, A is the cross-sectional area of ​​the conductor, σ′ x is the axial stress of the transmission line, σ′ x A represents the tension T on the conductor, V is the wind speed, and D is the random variable of ice thickness on the transmission line; S4. Calculate the stress of the transmission line: The overhead transmission line is a twisted wire composed of multiple strands of fine metal wires. Under the action of wind load, the transmission line will deflect due to wind. At this time, the catenary shape equation y(x) of the overhead line suspended between the two towers is as follows: in: In the formula, γ h and γ v are the horizontal and vertical specific loads respectively, γ′ is the uniform specific load acting along the length of the overhead line in the windward plane, h′ is the height difference of the windward plane, β′ is the height difference angle of the windward plane, and σ0′ is the axial stress at the lowest point of the windward plane; in: h′=h cos η (6d) Where q is the mass per unit length of the transmission line, A is the cross-sectional area of ​​the transmission line, g is the acceleration of gravity, D is the ice thickness, and c is the outer diameter of the transmission line; β c is the wind load adjustment factor for transmission lines, α f is the wind speed non-uniformity coefficient, μ sc is the shape factor of the overhead line, θ is the angle between the wind direction and the line direction, σ0 is the service stress of the transmission line, β is the height difference angle, η is the wind deviation angle, h is the height difference, and l is the span; The axial stress at any point in the windage plane is: Substituting equations (5) and (6) into equation (7), we get σ′ x Function expression about variables D and V: σ′ x =g x (D,V) (8) Substituting formula (8) into formula (2), we get the function function of normal service of transmission line: Z=RS=z(D,V,H,A)=kK e HA-g x (d,V)A (9) Where R is the tensile strength of the conductor, S is the load effect, κ is the deicing completion coefficient, K e is the tension limit coefficient for safe operation of the transmission line, H is the material yield strength of the conductor, A is the cross-sectional area of ​​the conductor, g x (·) is the function of the axial stress of the transmission line with respect to D and V; S5. Calculate the reliability and failure probability. The specific steps are as follows: (1) Normalization of non-normal random variables: The two non-normal random variables, ice thickness D and wind speed V, are normalized. At the same time, the probability distribution and probability density function of ice thickness D are transformed into the truncated random variable D. t The distribution function and probability density function of are: Where D′ and V′ are the ice thickness D, t and the equivalent normalized variable of wind speed V, is the design point coordinate; in, (2) Calculate sensitivity: The mean and standard deviation of the original function are approximately calculated by Taylor series expansion. The sensitivity α X The weight is calculated using the following formula: In the formula, the approximate performance function Z X At the design point x * The functional function Z of formula (9) is expanded according to Taylor series and taken to the first order term; is a random variable X i The standard deviation of (3) Calculate the approximate performance function Z X The mean and standard deviation of: After normalization, the approximate function Z is calculated based on the characteristics of the normal distribution. X The mean and standard deviation The calculation formula is as follows: In the formula, μ X is the mean vector of random variables, σ X is the standard deviation vector of random variables, α X is the sensitivity vector; (4) Calculate the reliability index: Z X It is a linear combination of independent normally distributed random variables, which also obeys the normal distribution. The reliability index β ice Calculated by the following formula: Then iterative calculation is performed, and the design point iteration adopts the following formula: In the formula, is a random variable X i The mean of According to the requirement of the random variable of the first-order second moment method that it has a complete distribution, for the truncated distribution variable D of ice thickness, t , the coordinates of the design points during the iteration process When it falls outside the allowable range, the nearest pullback method is used to correct the ice thickness component d in the design point iteration formula (15). t , correct it to the allowed range, the correction formula is as follows: (5) Calculate the failure probability: Based on the reliability index β ice , calculate the failure probability P f , the calculation formula is as follows: P f =Φ(-β ice ) (17) Where Φ(·) is the standard normal distribution function.

2. The method for calculating the normal service reliability of deicing of ice-covered transmission lines according to claim 1 is characterized in that: The expression of the deicing completion coefficient κ in step S2 consists of two parts. The first part is the reduction in bearing capacity caused by material damage during the deicing process, which is defined as the deicing damage coefficient κ1. The second part is the reduction in bearing capacity caused by material damage during the service process, which is defined as the deicing damage coefficient κ2. The expressions of κ1 and κ2 are as follows: Where, 0<κ1≤1; n is the nth deicing in the service cycle, m is the maximum number of experiments obtained through thermal tests or mechanical knocking tests for the transmission line to meet the continued service capacity; κ a is a constant, determined by m; Where, 0<κ2≤1; i is the service year, j is the required service years; κ b is a constant, determined by j; According to κ1 and κ2, k=κ1k2.

3. The method for calculating the normal service reliability of deicing of ice-covered transmission lines according to claim 1 is characterized in that: In step S3 and step S4, the transmission line safe operation tension limit coefficient K e Take 60% at the lowest point of the transmission line sag and 66% at the suspension point of the transmission line.

4. The method for calculating the normal service reliability of deicing of ice-covered transmission lines according to claim 1 is characterized in that: In step S4, x=0 and x=1 are substituted into Japanese σ′ x =g x (D, V) The axial stress of the conductor at the suspension point is: Where β is the height difference angle, l is the span, h is the height difference, and η is the wind deviation angle.

5. The method for calculating the normal service reliability of deicing of ice-covered transmission lines according to claim 1 is characterized in that: In step S4, the point where the highest point of the transmission line is connected to the tower is the transmission line suspension point; l is the span. When the lowest point of the transmission line sag is within the span, that is, 0≤x≤l, according to the formula Take the derivative of x, and then find the minimum value to get the coordinate point of the lowest point of the sag of the transmission line in the section; when the lowest point of the sag of the transmission line is outside the section, that is, x<0 or x>l, take the lowest point in height as the lowest point of the sag of the transmission line.

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