Method for calculating deicing composite failure probability of power transmission line based on conditional probability

Abstract

The invention relates to a method for calculating deicing composite failure probability of an iced power transmission line based on conditional probability, and belongs to the technical field of safe deicing of the iced power transmission line. The composite failure probability of the ice-coated power transmission line is finally determined by calculating the deicing safety probability of the ice-coated power transmission line, determining the truncation probability distribution of the ice-coated thickness of the power transmission line, determining the yield limit performance function of the power transmission line, calculating the stress of the power transmission line and calculating the reliability and the failure probability. A reliability evaluation system during deicing of the iced power transmission line is comprehensively and simply established, a probability-based evaluation index is provided for normal service of the iced power transmission line, and the icing disaster resistance of the power transmission line is improved. According to the method, multiple factors such as the deicing technology types, the icing thickness deviation degree during deicing and the ice body falling duration are comprehensively considered, the deicing reliability of the ice-coated power transmission line can be analyzed more comprehensively and accurately, the icing disaster resisting capacity of the power transmission line is improved, and power transmission accidents caused by icing are reduced.

Description

Technical Field

[0001] The invention relates to a method for calculating the composite failure probability of deicing of a transmission line based on conditional probability, and belongs to the technical field of safe deicing of ice-covered transmission lines. Background Art

[0002] In the power system, the stable operation of transmission lines is crucial to ensure power supply. However, in cold regions or seasons, transmission lines are often affected by icing, which not only increases the weight of the line, but may also cause serious accidents such as line breakage and tower collapse. Therefore, timely and effective deicing of transmission lines is one of the key measures to ensure the reliability of the transmission system.

[0003] At present, traditional deicing methods include physical deicing (such as beating with insulating rods), thermal deicing (such as heating by electric current) and chemical deicing. These methods have their own advantages and disadvantages, but they all face certain limitations, such as high operational risks, low efficiency, and large environmental impact. In addition, when evaluating the deicing effect and the reliability of transmission lines, existing technologies often lack comprehensive consideration of various variables and uncertainties in the deicing process, such as the diversity of deicing technologies, changes in ice thickness, and the time it takes for ice to fall off. 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 probability of composite failure of de-icing of transmission lines based on conditional probability. The present invention can comprehensively and concisely establish the reliability of de-icing of ice-covered transmission lines, and the present invention can provide a probability-based evaluation index for the normal service of ice-covered transmission lines, thereby improving the ability of transmission lines to resist icing disasters.

[0005] To achieve the above object, the present invention provides a technical solution: a method for calculating the probability of composite failure of deicing of transmission lines based on conditional probability, which specifically includes the following steps:

[0006] S1. Calculate the safety probability of deicing of ice-covered transmission lines: The influence of thermal deicing and mechanical deicing on the reliability of ice-covered transmission lines is characterized by the deicing technical coefficient γ, which is called event M. The probability of event M is calculated as follows:

[0007]

[0008] Where, 0<γ≤1; I is the thermal ice-melting current, t is the ice-melting time; F is the external force during mechanical deicing, and p is the number of times or duration of the external force F acting;

[0009] The ice thickness deviation coefficient ξ is used to characterize the ice thickness deviation of the transmission line during deicing, and is called event N. The probability of event N is calculated as follows:

[0010]

[0011] Where, 0<ξ≤1; d0 is the set de-icing thickness threshold, d ice is the actual ice thickness measured during deicing, σ is a measurement index parameter, which represents the magnitude of the measurement error;

[0012] According to the influence of the randomness of ice shedding time, shedding amount and shedding position on the de-icing reliability of ice-covered transmission lines, the ice shedding duration coefficient α is introduced; the ice shedding duration coefficient α is used to characterize the influence of ice shedding on the de-icing reliability of ice-covered transmission lines, and is called event Q; the probability of event Q is calculated as follows:

[0013]

[0014] Where, 0<α≤1, α=1 means the entire transmission line is iced off at the same time; τ is the minimum recorded value of the shedding duration; α0 is a constant determined by τ; t is the ice-shedding duration;

[0015] Assume that the de-icing safety probability of ice-covered transmission lines is event C, and the part of the de-icing normal service reliability of ice-covered transmission lines that can be calculated is event B, then event C and event B together constitute the conditional probability; event C belongs to the occurrence condition, and event B belongs to the occurrence event when event C occurs; according to the above conditions, assuming that events M, N, and Q are completely independent, the de-icing safety probability P(C) of ice-covered transmission lines is calculated as follows:

[0016] P(C)=ω=P(MNQ)=P(M)P(N)P(Q)=αξγ (4)

[0017] Where, 0<ω≤1; α is the ice shedding time coefficient, ξ is the ice thickness deviation coefficient, and γ is the deicing technology coefficient;

[0018] S2. 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:

[0019]

[0020] S3. Determine the yield limit function of the transmission line: When the de-icing mechanism is introduced into the ice-covered transmission line, the distribution of ice changes, and the upper limit of the maximum ice thickness decreases. The yield strength of the material used in the transmission line is taken as the limit state, and its function is:

[0021] Z=RS=HA-σ′ x A (6)

[0022] Where: R is the tensile strength of the conductor, S is the load effect; 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 wire;

[0023] 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:

[0024]

[0025] in:

[0026]

[0027] In the formula, γ h and γ v are the horizontal and vertical specific loads, γ ′ is the uniformly distributed load acting along the length of the overhead line in the wind deflection plane, h ′ is the height difference of the wind deflection plane, β ′ is the height difference angle of the windward plane, σ0′ is the axial stress at the lowest point of the windward plane;

[0028] in:

[0029]

[0030] h′=h cos η (10d)

[0031]

[0032] 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 scis 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;

[0033] The axial stress at any point in the windage plane is:

[0034]

[0035] Substituting equations (9) and (10) into equation (11), we get σ′ x Function expression about variables D and V:

[0036] σ′ x =g x (D,V) (12)

[0037] Substituting formula (8) into formula (2), we get the function function of normal service of transmission line:

[0038] Z=RS=z(D,V,H,A)=HA-g x (D,V)A (13)

[0039] 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;

[0040] S5. Calculate the reliability and failure probability. The specific steps are as follows:

[0041] (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:

[0042]

[0043] Where D′ and V′ are the ice thickness D, t and the equivalent normalized variable of wind speed V, is the design point coordinate;

[0044] in,

[0045]

[0046] (2) Calculate sensitivity: The mean and standard deviation of the original function are approximately calculated by Taylor series expansion. The sensitivity α XThe weight is calculated using the following formula:

[0047]

[0048] In the formula, the approximate performance function Z X At the design point x * The functional function Z of formula (13) is expanded according to Taylor series and taken to the first order term; is a random variable X i The standard deviation of

[0049] (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:

[0050]

[0051] 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;

[0052] (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 β0 is calculated by the following formula:

[0053]

[0054] Then iterative calculation is performed, and the design point iteration adopts the following formula:

[0055]

[0056] In the formula, is a random variable X i The mean of

[0057] 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 ice thickness component d in the design point iteration formula (19) is corrected by the nearest pullback method. t , correct it to the allowed range, the correction formula is as follows:

[0058]

[0059] (5) Calculate the failure probability: Calculate the failure probability P based on the reliability index β0 f0 , we can get the deicing normal service reliability part of the ice-covered transmission line, that is, the probability of event B. The specific calculation formula is as follows:

[0060] P(B)=P f0 =Φ(-β0) (21)

[0061] Where Φ(·) is the standard normal distribution function.

[0062] S6. Calculate the composite failure probability: Assume that events B and C are independent, and calculate the final composite failure probability P of the ice-covered transmission line based on the failure probability P(B) and the deicing safety probability P(C). f , the specific calculation formula is as follows:

[0063] P f =P(B|C)=P(C)P(B) (22)

[0064] Substituting equation (4) and equation (21) into equation (22), we can obtain the composite failure probability of ice-covered transmission lines:

[0065] P f =ωΦ(-β0)=αξγΦ(-β0) (23)

[0066] Where Φ(·) is the standard normal distribution function.

[0067] The further improvement of the above method is:

[0068] In step S1, thermal deicing is to remove ice by passing electric current through the electric wires to generate heat and melt the ice on the wires, while mechanical deicing is to remove ice by knocking on the transmission lines manually or by drones or by using deicing robots.

[0069] Different technologies in step S1 have different effects on internal forces when de-icing transmission lines. Thermal ice melting introduces additional heat to increase the temperature of the transmission lines, thereby affecting the stress on the lines; mechanical de-icing introduces external forces, thereby affecting the stress on the lines; among the introduced external forces, knocking has an impact on the ice-covered transmission lines, and the de-icing robot increases the vertical load on the ice-covered transmission lines.

[0070] In step S1 , the functions g(I, t) and q(F, p) are exponential functions, and the specific parameters of the exponential functions g(I, t) and q(F, p) are determined according to the deicing record parameters of previous years.

[0071] According to the above technical scheme, the method provided by the present invention for calculating the composite failure probability of deicing of transmission lines based on conditional probability calculates the safety probability of deicing of ice-covered transmission lines, determines the truncated probability distribution of ice thickness of transmission lines, determines the yield limit function of transmission lines, calculates the stress of transmission lines, and calculates the reliability and failure probability, and finally determines the composite failure probability of ice-covered transmission lines, comprehensively and concisely establishes a reliability evaluation system for deicing ice-covered transmission lines, provides a probability-based evaluation index for the normal service of ice-covered transmission lines, and improves the ability of transmission lines to resist ice disasters. Compared with the prior art, the present invention has the following advantages:

[0072] (1) Because the technical solution adopted by the present invention sets the de-icing safety factor and comprehensively considers multiple factors such as the type of de-icing technology, the deviation of ice thickness during de-icing, and the duration of ice shedding, the present invention can more comprehensively and accurately analyze the reliability of de-icing of ice-covered transmission lines.

[0073] (2) Because the technical solution adopted by the present invention establishes the probability distribution of ice thickness of transmission lines under deicing conditions based on truncated distribution, the present invention can better describe the uncertainty of ice thickness under actual conditions, thereby improving the scientificity and practicality of the analysis.

[0074] (3) Because the technical solution adopted by the present invention establishes a functional function based on the yield limit state of the transmission line, the present invention can intuitively evaluate the reliability of the transmission line during the deicing process, providing an important reference basis for the design and maintenance of the transmission line.

[0075] (4) Because the technical solution adopted by the present invention provides a probability-based evaluation index for the normal service of the transmission line, the present invention can improve the ability of the transmission line to resist icing disasters, reduce power transmission accidents caused by icing, ensure the stable operation of the power system, reduce maintenance costs and avoid economic losses caused by accidents. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 Flowchart of the method for calculating the probability of composite failure of transmission line deicing based on conditional probability. DETAILED DESCRIPTION

[0077] 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.

[0078] In the technical solution provided by the present invention, a method for calculating the composite failure probability of deicing of transmission lines based on conditional probability is provided, and its flow chart is as follows: Figure 1 As shown, the specific steps include:

[0079] S1. Calculate the safety probability of deicing of ice-covered transmission lines: The influence of thermal deicing and mechanical deicing on the reliability of ice-covered transmission lines is characterized by the deicing technical coefficient γ, which is called event M. The probability of event M is calculated as follows:

[0080]

[0081] Where, 0<γ≤1; I is the thermal ice-melting current, t is the ice-melting time; F is the external force during mechanical deicing, and p is the number of times or duration of the external force F acting;

[0082] The ice thickness deviation coefficient ξ is used to characterize the ice thickness deviation of the transmission line during deicing, and is called event N. The probability of event N is calculated as follows:

[0083]

[0084] Where, 0<ξ≤1; d0 is the set de-icing thickness threshold, d ice is the actual ice thickness measured during deicing, σ is a measurement index parameter, which represents the magnitude of the measurement error and is determined according to the accuracy of the measurement technology;

[0085] According to the influence of the randomness of ice shedding time, shedding amount and shedding position on the de-icing reliability of ice-covered transmission lines, the ice shedding duration coefficient α is introduced; the ice shedding duration coefficient α is used to characterize the influence of ice shedding on the de-icing reliability of ice-covered transmission lines, and is called event Q; the probability of event Q is calculated as follows:

[0086]

[0087] Where, 0<α≤1, α=1 means the entire transmission line is iced off at the same time; τ is the minimum recorded value of the shedding duration; α0 is a constant determined by τ; t is the ice-shedding duration;

[0088] Assume that the de-icing safety probability of ice-covered transmission lines is event C, and the part of the de-icing normal service reliability of ice-covered transmission lines that can be calculated is event B, then event C and event B together constitute the conditional probability; event C belongs to the occurrence condition, and event B belongs to the occurrence event when event C occurs; according to the above conditions, assuming that events M, N, and Q are completely independent, the de-icing safety probability P(C) of ice-covered transmission lines is calculated as follows:

[0089] P(C)=ω=P(MNQ)=P(M)P(N)P(Q)=αξγ (4)

[0090] Where, 0<ω≤1; α is the ice shedding time coefficient, ξ is the ice thickness deviation coefficient, and γ is the deicing technology coefficient;

[0091] In this embodiment, thermal deicing is to remove ice by passing electric current through the wires to generate heat and melt the ice on the wires, and mechanical deicing is to remove ice by knocking on the transmission lines manually or by drones or by deicing robots. Different technologies have different effects on internal forces when deicing transmission lines. Thermal deicing introduces additional heat to increase the temperature of the transmission lines, thereby affecting the stress on the lines; mechanical deicing introduces external forces, thereby affecting the stress on the lines. Among the introduced external forces, knocking has an impact on the ice-covered transmission lines, and the deicing robots increase the vertical load on the ice-covered transmission lines.

[0092] Functions g(I, t) and q(F, p) are exponential functions, and their specific parameters are determined based on the deicing record parameters of previous years.

[0093] S2. 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:

[0094]

[0095] S3. Determine the yield limit function of the transmission line: When the de-icing mechanism is introduced into the ice-covered transmission line, the distribution of ice changes, and the upper limit of the maximum ice thickness decreases. The yield strength of the material used in the transmission line is taken as the limit state, and its function is:

[0096] Z=RS=HA-σ′ x A (6)

[0097] Where: R is the tensile strength of the conductor, S is the load effect; 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 wire;

[0098] 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:

[0099]

[0100] in:

[0101]

[0102] In the formula, γ h and γ v are the horizontal and vertical specific loads, γ ′ is the uniformly distributed load acting along the length of the overhead line in the wind deflection plane, h ′ is the height difference of the wind deflection plane, β ′ is the height difference angle of the windward plane, σ0′ is the axial stress at the lowest point of the windward plane;

[0103] in:

[0104]

[0105] h′=h cos η (10d)

[0106]

[0107] 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;

[0108] The axial stress at any point in the windage plane is:

[0109]

[0110] Substituting equations (9) and (10) into equation (11), we get σ′ x Function expression about variables D and V:

[0111] σ′ x =g x (D,V) (12)

[0112] 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:

[0113]

[0114] Substituting formula (8) into formula (2), we get the function function of normal service of transmission line:

[0115] Z=RS=z(D,V,H,A)=HA-g x (D,V)A (13)

[0116] Where R is the tensile strength of the conductor, S is the load effect, H is the material yield strength of the conductor, A is the cross-sectional area of ​​the conductor, and g is x (·) is the function of the axial stress of the transmission line with respect to D and V;

[0117] 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.

[0118] S5. Calculate the reliability and failure probability. The specific steps are as follows:

[0119] (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:

[0120]

[0121] Where D′ and V′ are the ice thickness D, t and the equivalent normalized variable of wind speed V, is the design point coordinate;

[0122] in,

[0123]

[0124] (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:

[0125]

[0126] In the formula, the approximate performance function ZX At the design point x * The functional function Z of formula (13) is expanded according to Taylor series and taken to the first order term; is a random variable X i The standard deviation of

[0127] (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:

[0128]

[0129] 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;

[0130] (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 β0 is calculated by the following formula:

[0131]

[0132] Then iterative calculation is performed, and the design point iteration adopts the following formula:

[0133]

[0134] In the formula, is a random variable X i The mean of

[0135] 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 ice thickness component d in the design point iteration formula (19) is corrected by the nearest pullback method. t , correct it to the allowed range, the correction formula is as follows:

[0136]

[0137] (5) Calculate the failure probability: Calculate the failure probability P based on the reliability index β0 f0 , we can get the deicing normal service reliability part of the ice-covered transmission line, that is, the probability of event B. The specific calculation formula is as follows:

[0138] P(B)=P f0 =Φ(-β0) (21)

[0139] Where Φ(·) is the standard normal distribution function.

[0140] S6. Calculate the composite failure probability: Assume that events B and C are independent, and calculate the final composite failure probability P of the ice-covered transmission line based on the failure probability P(B) and the deicing safety probability P(C). f , the specific calculation formula is as follows:

[0141] P f =P(B|C)=P(C)P(B) (22)

[0142] Substituting equation (4) and equation (21) into equation (22), we can obtain the composite failure probability of ice-covered transmission lines:

[0143] P f =ωΦ(-β0)=αξγΦ(-β0) (23)

[0144] Where Φ(·) is the standard normal distribution function.

[0145] Taking 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 of the conductor is 27.63mm, 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 variable parameters are shown in Table 1.

[0146] Table 1 Random variable parameters

[0147]

[0148]

[0149] The DC ice melting technology in thermal deicing technology is adopted, and the function g(I,t) is taken as an exponential function:

[0150]

[0151] In the formula, the parameters are A = 2.54, B = 1.86, I = 1300A, t = 42.36°C, i = 1200A, τ = 40.52°C. At this time, the deicing technical coefficient γ = 0.56.

[0152] Assume that the de-icing thickness threshold d0 = 20 mm, and the actual ice thickness d measured during de-icing ice =22mm, measurement index parameter σ = 2.4. At this time, the ice thickness deviation coefficient ξ = 0.91.

[0153] Assume that the minimum value of the shedding time record value τ = 45min; α0 = 3.2; the deicing time t = 55min. At this time, the ice thickness deviation coefficient α = 0.94.

[0154] According to the above data, the de-icing safety probability ω = 0.56*0.91*0.94 = 0.48.

[0155] According to the de-icing safety probability, the failure probability of de-icing of transmission lines under different working conditions is calculated. The calculation results are shown in Table 2.

[0156] Table 2 Failure probability of deicing of transmission lines under different working conditions

[0157]

[0158] It can be seen from the data listed in the above table that the specific results of the deicing failure probability obtained by the calculation method of the present invention are as follows: compared with working condition 1, working condition 2 does not consider the ice thickness as a truncated distribution, so the failure probability of working condition 2 is the failure probability of working condition 1 multiplied by the deicing safety probability; compared with working conditions 1 and 2, the failure probability of working condition 3 is greater than the failure probability of working condition 2 but less than the failure probability of working condition 1. In general, whether considering the ice thickness as a truncated distribution or considering the deicing safety probability will reduce the failure probability; working condition 4 is significantly lower than working conditions 1 and 2, indicating that deicing is an effective disaster prevention and mitigation measure for transmission lines. By considering the truncated distribution and the deicing safety probability, the failure probability of deicing ice-covered transmission lines can be obtained more accurately, providing relevant references for the setting of deicing thresholds.

[0159] It can be seen that the present invention can provide more accurate evaluation results for the de-icing reliability and de-icing failure probability assessment of ice-covered transmission lines, and provide data support for de-icing disaster prevention and mitigation measures for ice-covered transmission lines, which has important practical significance for improving the safety and reliability of transmission lines and ensuring power supply.

Claims

1. A method for calculating the probability of composite failure of deicing of transmission lines based on conditional probability, characterized in that The following steps are involved: S1. Calculate the safety probability of deicing of ice-covered transmission lines: The influence of thermal deicing and mechanical deicing on the reliability of ice-covered transmission lines is characterized by the deicing technical coefficient γ, which is called event M. The probability of event M is calculated as follows: Where, 0<γ≤1; I is the thermal ice-melting current, t is the ice-melting time; F is the external force during mechanical deicing, and p is the number of times or duration of the external force F acting; The ice thickness deviation coefficient ξ is used to characterize the ice thickness deviation of the transmission line during deicing, and is called event N. The probability of event N is calculated as follows: Where, 0<ξ≤1; d0 is the set de-icing thickness threshold, d ice is the actual ice thickness measured during deicing, σ is a measurement index parameter, which represents the magnitude of the measurement error; According to the influence of the randomness of ice shedding time, shedding amount and shedding position on the de-icing reliability of ice-covered transmission lines, the ice shedding duration coefficient α is introduced; the ice shedding duration coefficient α is used to characterize the influence of ice shedding on the de-icing reliability of ice-covered transmission lines, and is called event Q; the probability of event Q is calculated as follows: Where, 0<α≤1, α=1 means the entire transmission line is iced off at the same time; τ is the minimum recorded value of the shedding duration; α0 is a constant determined by τ; t is the ice-shedding duration; Assume that the de-icing safety probability of ice-covered transmission lines is event C, and the part of the de-icing normal service reliability of ice-covered transmission lines that can be calculated is event B, then event C and event B together constitute the conditional probability; event C belongs to the occurrence condition, and event B belongs to the occurrence event when event C occurs; according to the above conditions, assuming that events M, N, and Q are completely independent, the de-icing safety probability P(C) of ice-covered transmission lines is calculated as follows: P(C)=ω=P(MNQ)=P(M)P(N)P(Q)=αξγ (4) Where, 0<ω≤1; α is the ice shedding time coefficient, ξ is the ice thickness deviation coefficient, and γ is the deicing technology coefficient; S2. 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: S3. Determine the yield limit function of the transmission line: When the de-icing mechanism is introduced into the ice-covered transmission line, the distribution of ice changes, and the upper limit of the maximum ice thickness decreases. The yield strength of the material used in the transmission line is taken as the limit state, and its function is: Z=RS=HA-σ′ x A (6) Where: R is the tensile strength of the conductor, S is the load effect; 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 wire; 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, γ ′ is the uniformly distributed load acting along the length of the overhead line in the wind deflection plane, h ′ is the height difference of the wind deflection plane, β ′ is the height difference angle of the windward plane, σ0′ is the axial stress at the lowest point of the windward plane; in: h′=hcosη (10d) 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 (9) and (10) into equation (11), we get σ′ x Function expression about variables D and V: σ′ x =g x (D,V) (12) Substituting formula (8) into formula (2), we get the function function of normal service of transmission line: Z=RS=z(D,V,H,A)=HA-g x (D,V)A (13) 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 (13) 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 β0 is 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 ice thickness component d in the design point iteration formula (19) is corrected by the nearest pullback method. t , correct it to the allowed range, the correction formula is as follows: (5) Calculate the failure probability: Calculate the failure probability P based on the reliability index β0 f0 , we can get the deicing normal service reliability part of the ice-covered transmission line, that is, the probability of event B. The specific calculation formula is as follows: P(B)=P f0 =Φ(−β0) (21) Where Φ(·) is the standard normal distribution function. S6. Calculate the composite failure probability: Assume that events B and C are independent, and calculate the final composite failure probability P of the ice-covered transmission line based on the failure probability P(B) and the deicing safety probability P(C). f , the specific calculation formula is as follows: P f =P(B|C)=P(C)P(B) (22) Substituting equation (4) and equation (21) into equation (22), we can obtain the composite failure probability of ice-covered transmission lines: P f =ωΦ(-β0)=αξγΦ(-β0) (23) Where Φ(·) is the standard normal distribution function.

2. The method for calculating the probability of composite failure of deicing of transmission lines based on conditional probability according to claim 1 is characterized by: In step S1, thermal deicing is to remove ice by passing electric current through the electric wires to generate heat and melt the ice on the wires, while mechanical deicing is to remove ice by knocking on the transmission lines manually or by drones or by using deicing robots.

3. The method for calculating the probability of composite failure of deicing of transmission lines based on conditional probability according to claim 1, characterized in that: Different technologies in step S1 have different effects on internal forces when de-icing transmission lines. Thermal ice melting introduces additional heat to increase the temperature of the transmission lines, thereby affecting the stress on the lines; mechanical de-icing introduces external forces, thereby affecting the stress on the lines; among the introduced external forces, knocking has an impact on the ice-covered transmission lines, and the de-icing robot increases the vertical load on the ice-covered transmission lines.

4. The method for calculating the probability of composite failure of deicing of transmission lines based on conditional probability according to claim 1, characterized in that: In step S1 , the functions g(I, t) and q(F, p) are exponential functions, and the specific parameters of the exponential functions g(I, t) and q(F, p) are determined according to the deicing record parameters of previous years.

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