Method for calculating breakage probability of ice-coated distribution line based on mechanical property analysis

Abstract

The invention discloses a mechanical property analysis-based icing distribution line breakage probability calculation method, relates to the technical field of distribution lines, and solves the problem that in the prior art, due to the fact that the model, erection mode and the like of a distribution line are obviously different from those of a power transmission line, defects still exist in the aspect of icing and breakage risk assessment of the distribution line. According to the method, the stress state of the distribution line under the action of icing and wind load is analyzed by establishing a tension model, the horizontal tension and the vertical tension are calculated respectively, and a resultant tension formula is deduced. Thirdly, on the basis of the reliability theory, a broken line probability model is constructed, and influences of random variables such as the icing thickness, the wind speed and the line resistance are considered; and finally, the line breakage probability under the conditions of different icing thicknesses and height differences is evaluated, and an effective risk early warning basis is provided for an electric power department.

Description

Technical Field

[0001] The present invention relates to the technical field of power distribution lines, and in particular to a method for calculating the disconnection probability of an ice-covered power distribution line based on mechanical property analysis. Background Art

[0002] Power systems are subject to various natural disasters, particularly grid icing, which severely impacts the safe and stable operation of power systems and causes significant socioeconomic losses. As ice thickness increases, the stress on distribution lines, towers, insulators, and other equipment increases. Combined with strong winds, this can cause severe accidents such as power line disconnections. Therefore, assessing the risk of distribution line disconnections caused by icing and providing early warning of disconnections under icing conditions is crucial for minimizing grid losses.

[0003] Early warning systems for power lines, also known as transmission line monitoring systems, analyze data collected by terminals to provide warning information to relevant departments. In the 1970s, the United States pioneered research on online transmission line monitoring. Subsequently, many other countries conducted research on communication and sensor technologies related to transmission line monitoring. In the 1980s, Japan also conducted research on monitoring power equipment. Starting in the 1990s, monitoring systems for transmission line icing, galloping, and insulator contamination emerged internationally. In the 1990s, transmission line condition monitoring technology was widely used in Europe. Research on transmission line monitoring systems in China began relatively late, but has developed rapidly. While research on transmission line monitoring systems began in my country in the 1990s, by 2008, significant progress had been made in the research, development, and promotion of overhead line monitoring products. By the early 2000s, monitoring systems for transmission line icing, windage, and galloping had been developed in China, providing data support for related warnings. Current research mainly focuses on the prediction of ice thickness and the risk assessment of ice coverage on transmission lines. However, due to the significant differences between the types and installation methods of distribution lines and transmission lines, there are still deficiencies in the risk assessment of ice-disconnection on distribution lines.

[0004] In view of this, a method for calculating the disconnection probability of ice-covered distribution lines based on mechanical property analysis is needed. Summary of the Invention

[0005] In view of the fact that the existing technology is still insufficient in assessing the risk of line disconnection caused by icing on distribution lines due to the significant differences in distribution line models and installation methods compared to transmission lines, the present invention provides a method for calculating the probability of line disconnection caused by icing on distribution lines based on mechanical property analysis, which can more accurately assess the impact of icing on distribution line disconnection. The specific technical solution is as follows:

[0006] A method for calculating the disconnection probability of an ice-covered distribution line based on mechanical property analysis includes the following steps:

[0007] Under the condition of height difference, the horizontal tension and vertical tension are calculated respectively, and then the composite tension is calculated from the horizontal tension and vertical tension;

[0008] The total ultimate force of the line is calculated based on the line cross-sectional area and tensile strength, and then the safety factor is calculated by combining the total ultimate force and the resultant tension;

[0009] Set the coefficient of variation and take the product of the coefficient of variation and the safety factor as the standard deviation of the safety factor;

[0010] The reliability index is calculated by combining the safety factor and the standard deviation of the safety factor, and the probability of disconnection is obtained using the standard normal distribution cumulative distribution function.

[0011] Preferably, the horizontal tension is not directly affected by the height difference, but is determined by the horizontal component of the resultant load, and the calculation formula is as follows:

[0012]

[0013] Where q total represents the total load per unit length, f avg represents the average sag and L is the span.

[0014] Preferably, when considering the height difference, the average sag is calculated as follows:

[0015]

[0016] At this time, the horizontal tension calculation formula is as follows:

[0017]

[0018] Preferably, the vertical tension includes the vertical components of ice load and wind load, and is calculated as follows:

[0019] T V =q total L+ΔT h

[0020] Where q total Indicates the total load per unit length, L is the span, ΔT h It is the additional tension caused by the height difference.

[0021] Preferably, the calculation formula of the synthetic tension is as follows:

[0022]

[0023] Where, T H is the horizontal tension, TV For vertical tension.

[0024] Preferably, the safety factor is calculated as follows:

[0025] η=R / T total

[0026] Where η is the safety factor, R is the total limit force, T total For synthetic tension.

[0027] Preferably, the calculation formula of the total limit force is as follows:

[0028]

[0029] Where σ i is the tensile strength of the i-th material part, A i is the cross-sectional area of ​​the i-th material.

[0030] Preferably, the calculation formula of the reliability index is as follows:

[0031]

[0032] Where η is the safety factor, σ η is the standard deviation of the safety factor.

[0033] A computer-readable storage medium includes a stored program, wherein when the program is run, the device where the computer-readable storage medium is located is controlled to execute the above-mentioned method for calculating the probability of disconnection of ice-covered distribution lines based on mechanical property analysis.

[0034] A processor is used to run a program, wherein when the program is run, the method for calculating the probability of disconnection of an ice-covered distribution line based on mechanical property analysis as described above is executed.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] This paper analyzes the stress state of distribution lines under icing and wind loads by establishing a tension model, calculating horizontal and vertical tensions separately and deriving a formula for the combined tension. Next, based on reliability theory, a line-disconnection probability model is constructed, accounting for the influence of random variables such as ice thickness, wind speed, and line resistance. Finally, the line-disconnection probability is evaluated for different ice thicknesses and elevation differences, providing effective risk warnings for the power sector. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly describes the drawings required for the specific embodiments or the description of the prior art. Similar elements or parts are generally identified by similar reference numerals throughout the drawings. Elements or parts in the drawings are not necessarily drawn to scale.

[0038] Figure 1 is a flow chart of the method of the present invention;

[0039] Figure 2 A three-dimensional relationship diagram of wind speed, ice cover and elevation difference. DETAILED DESCRIPTION

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0041] It will be understood that when used in this specification and the appended claims, the terms “comprises” and “comprising” indicate the presence of described features, integers, steps, operations, elements and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof.

[0042] It should also be understood that the terms used in the present specification are only for the purpose of describing particular embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0043] It should be further understood that the term "and / or" used in the present description and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.

[0044] In one embodiment of the present invention, a method for calculating the disconnection probability of ice-covered distribution lines based on mechanical property analysis is provided. Figure 1 As shown, the following steps are included:

[0045] Under the condition of height difference, the horizontal tension and vertical tension are calculated respectively, and then the composite tension is calculated from the horizontal tension and vertical tension;

[0046] The total ultimate force of the line is calculated based on the line cross-sectional area and tensile strength, and then the safety factor is calculated by combining the total ultimate force and the resultant tension;

[0047] Set the coefficient of variation and take the product of the coefficient of variation and the safety factor as the standard deviation of the safety factor;

[0048] The reliability index is calculated by combining the safety factor and the standard deviation of the safety factor, and the probability of disconnection is obtained using the standard normal distribution cumulative distribution function.

[0049] The calculation formula and model designed for each step are further explained below.

[0050] Assume the span is L, the height difference between the two supports is h (the upper support is higher than the lower support), under the height difference condition, the total tension of the conductor under ice and wind load can be divided into two parts: horizontal tension T H and vertical tension T V .

[0051] The horizontal tension of the conductor is not directly affected by the height difference and is determined by the horizontal component of the resultant load:

[0052]

[0053] Where q total represents the total load per unit length (combined load of ice and wind), L is the span, f avg It represents the average sag. When considering the height difference, its calculation formula is:

[0054]

[0055] Substituting this formula into formula (1) yields the horizontal tension calculation formula:

[0056]

[0057] Based on this formula, when the span L and the combined ice and wind load per unit length q are known, the horizontal tension of the conductor can be calculated.

[0058] The vertical tension is caused by the resultant of the distributed loads, including the ice load (in the vertical direction) and the vertical component of the wind load (if the wind is not completely horizontal).

[0059] The calculation formula is:

[0060] T V =q total L+ΔT h

[0061] Where ΔT h is the additional tension caused by the height difference, and the calculation formula is:

[0062]

[0063] Synthetic tension T totalIt is the synthesis of horizontal tension and vertical tension, and the calculation formula is:

[0064]

[0065] The limit state equation of the structure is defined as:

[0066] Z=RT total

[0067] Where R is the ultimate resistance of the conductor, which obeys the mean μ R and standard deviation σ R Normal distribution of T total is the synthetic tension (a random variable controlled by ice thickness t and wind speed v); when Z < 0, the system fails and the probability of line breakage is expressed as P f =P(R <T total ).

[0068] Random variables include:

[0069] (1) Load q total : Determined by the joint distribution of ice thickness t and wind speed v. total =q ice +q wind , ice load and wind load can be described by normal distribution or lognormal distribution.

[0070] (2) Resistance R: the ultimate force of the conductor.

[0071] (3) Height difference h: The height difference may have a fixed value or be considered as a random variable.

[0072] As for load parameters, wind speed and ice thickness can be monitored at any time and can be approximated as constant and not as random variables.

[0073] As for the resistance parameter, due to factors such as wire aging, it can be regarded as a random variable and is generally considered to obey the normal distribution N(μ R ,σ R 2 ); If the coefficient of variation C V When taking 1%, μ R and σ R Calculate according to the following formula:

[0074]

[0075] As for the height difference, once the conductor is installed, the height difference is a constant and is not a random variable.

[0076] The disconnection probability is calculated as follows:

[0077]

[0078] Where: μ η =μ R / μ T is the mean safety factor; is the standard deviation of the safety factor; Φ(·) is the cumulative distribution function of the standard normal distribution.

[0079] The broken line probability formula can be solved using the improved primary reliability method (FORM) f =P(R <T total ), the steps are as follows:

[0080] Step 1: Create a standardized space:

[0081]

[0082] Step 2: Construct the limit state surface:

[0083]

[0084] Step 3: Solve the reliability index β:

[0085]

[0086] Step 4: Calculate the failure probability:

[0087] P f =Φ(β).

[0088] The specific implementation process of this embodiment is further described below with reference to specific examples.

[0089] The distribution lines in an ice-prone area of ​​a province in southern China were selected as the analysis object. The model of a distribution conductor is LGJ-35 / 6, ​​and the tensile strength of the aluminum part is σ 铝 =120MPa, tensile strength of steel part σ 钢 =1250Mpa, total cross-sectional area A 总 =A 铝 +A 钢 =35+6=41mm 2 , conductor diameter d = 10.4 mm, span L = 495 m, sag 10 m, air density ρ 空气 =1.225kg / m 3 , ice density ρ 冰 =900kg / m 3 , drag coefficient C d =1.2, acceleration due to gravity: g = 9.8 m / s 2 .

[0090] According to the above known parameters, the total limit force of the conductor can be calculated as R = σ 铝 ·A铝 +σ 钢 ·A 钢 =11.7kN. The following two scenarios are used to calculate the probability of wire breakage.

[0091] 3.1 Scenario 1: Ice thickness t = 10 mm, wind speed 0, height difference h = 5 m.

[0092] (1) Calculation of icing and wind loads

[0093] The combined load of icing and wind is divided into vertical load (icing) and horizontal load (wind load).

[0094] 1) Ice load

[0095] The ice load per unit length is:

[0096] q 冰 =πdtρ 冰 g=π·0.0104*0.01*900*9.8=2.89N / m

[0097] Total ice load:

[0098] F 冰 =q 冰 L = 2.89 * 495 = 1431.55N

[0099] 2) Wind load Since the wind speed is zero, the total wind load F 风 =0N.

[0100] The total load per unit length is:

[0101] q 总 =q 冰 +q 风 =2.89+0=2.89N / m

[0102] Total load:

[0103] F 总 =F 冰 +F 风 =1431.55N

[0104] (2) Tension calculation

[0105] The effect of height difference h = 5m on tension is calculated by adding additional tension ΔT h To calculate.

[0106] 1) Horizontal tension

[0107] The horizontal tension formula is:

[0108] T H =q 总 L2 / 8f 平均 =2.89·495 2 / 8·10=8800N

[0109] 2) Vertical tension

[0110] The vertical tension is calculated as follows:

[0111] T V =q 总 L+hT H / L=2.89·495+5·8800 / 495=1500N

[0112] 3) Synthetic tension

[0113] T 总 =sqrt(T H 2 +T V 2 )=8800N

[0114] (3) Calculation of disconnection probability

[0115] 1) Safety factor

[0116] The safety factor is:

[0117] η=R / T 总 =11700 / 8800=1.33

[0118] 2) Standard deviation

[0119] Assuming the coefficient of variation C V =0.1, the standard deviation of the safety factor is:

[0120] σ η =η·C V =1.33·0.1=0.133

[0121] 3) Disconnection probability

[0122] The probability of disconnection is calculated from the standard normal distribution:

[0123]

[0124] P f =Φ(β)=Φ(-2.54)≈0

[0125] Disconnection probability P f ≈0, indicating that under the conditions of ice thickness of 10 mm, wind speed of 0 m / s, and height difference of 5 m, the tension is lower than the ultimate force of the conductor and the probability of conductor breakage is close to 0.

[0126] 3.2 Scenario 2: Ice thickness: t = 30 mm, wind speed 5 m / s, height difference h = 0 m.

[0127] (1) Load calculation

[0128] 1) Ice load

[0129] The load per unit length of ice is:

[0130] q 冰 =πdtρ 冰 g

[0131] q 冰 =π·0.0104·0.03·900·9.8≈8.67N / m

[0132] The total ice load is:

[0133] F 冰 =q 冰 L = 8.67·495 ≈ 4289.3 N

[0134] 2) Wind load

[0135] The load per unit length of wind load is:

[0136] q 风 =ρ 空气 C d v 2 A / 2

[0137] The windward area of ​​the conductor is A = d·1 = 0.0104m, and we can get:

[0138] q 风 =1.225·1.2·5 2 0.0104 / 2≈0.191N / m

[0139] The total load of wind load is:

[0140] F 风 =q 风 L = 0.191 495 ≈ 94.5 N

[0141] From this we can get the resultant load and total load:

[0142] q 总 =q 冰 +q 风 =8.67+0.191≈8.861N / m

[0143] F 总 =F 冰 +F 风 =4289.3+94.5≈4383.8N

[0144] (2) Tension calculation

[0145] 1) Horizontal tension

[0146] Horizontal tension:

[0147] T H =q 总 L 2 / 8f

[0148] Assuming the average sag is f = 10m (empirical value), substitute:

[0149] T H =8.861·495 2 / 8·10≈27,186N

[0150] 2) Vertical tension

[0151] The vertical tension is:

[0152] T V =q 总 L = 8.861 495 ≈ 4383.8 N

[0153] 3) Synthetic tension

[0154] T 总 =sqrt(T H 2 +T V 2 )=sqrt(27186 2 +4383.8 2 )≈27,542N

[0155] (3) Calculation of disconnection probability

[0156] 1) Safety factor

[0157] η=R / T 总 =11,700 / 27,542≈0.425

[0158] 2) Safety factor distribution

[0159] Consider the coefficient of variation C of resistance and load V =0.1 (empirical value), the standard deviation of the safety factor is:

[0160] σ η =η·C V =0.425·0.1=0.0425

[0161] 3) Disconnection probability

[0162] The probability of disconnection is calculated using the standard normal cumulative distribution function Φ:

[0163]

[0164] P f =Φ(β)=Φ(13.53)≈1

[0165] Comparing with scenario 1, it can be seen that when the ice thickness is 30 mm and the wind speed is 5 m / s, although there is no height difference, the total tension far exceeds the ultimate tensile strength R = 11.7 kN, and the probability of wire breakage is close to 1.

[0166] Similarly, the probability of line breakage can be calculated when the wind speed is constant at 5m / s, the ice thickness changes from 10mm to 30mm, and the height difference changes from 0m to 10m. Figure 2 The three-dimensional relationship diagram shown in the figure shows that when the ice thickness is constant, the greater the height difference, the greater the probability of line breakage; when the height difference is constant, the greater the ice thickness, the greater the probability of line breakage.

[0167] In summary, the method for calculating the probability of line disconnection of ice-covered distribution lines proposed in the present invention can more accurately evaluate the impact of ice on line disconnection of distribution lines. Through numerical simulation, the present invention analyzes the impact of different ice thicknesses, wind speeds, and line height differences on the probability of line disconnection. The results show that ice thickness and wind speed are the main influencing factors, and as the degree of ice increases, the probability of line disconnection increases significantly. The research results provide a scientific basis for risk assessment and early warning of power systems under extreme weather conditions, and help to improve the safety and stability of distribution lines. In addition, the method proposed in the present invention can provide a reference for disaster prevention and risk management of other similar power facilities.

[0168] Those skilled in the art will appreciate that the units of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition of each example has been generally described in terms of function in the above description. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0169] In the embodiments provided by the present invention, it should be understood that the division of units is merely a logical function division, and there may be other division methods in actual implementation, for example, multiple units can be combined into one unit, one unit can be split into multiple units, or some features can be ignored, etc.

[0170] In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing unit, each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0171] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, read-only memory (ROM, Read-0nly Memory), random access memory (RAM, Random Access Memory), mobile hard disk, magnetic disk or optical disk, etc., various media that can store program code.

[0172] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or make equivalent replacements for some or all of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and description of the present invention.

Claims

1. A method for calculating the probability of disconnection of ice-covered distribution lines based on mechanical property analysis, characterized in that: The following steps are involved: Under the condition of height difference, the horizontal tension and vertical tension are calculated respectively, and then the composite tension is calculated from the horizontal tension and vertical tension; The total ultimate force of the line is calculated based on the line cross-sectional area and tensile strength, and then the safety factor is calculated by combining the total ultimate force and the resultant tension; Set the coefficient of variation and take the product of the coefficient of variation and the safety factor as the standard deviation of the safety factor; The reliability index is calculated by combining the safety factor and the standard deviation of the safety factor, and the probability of disconnection is obtained using the standard normal distribution cumulative distribution function.

2. The method for calculating the probability of disconnection of an ice-covered distribution line based on mechanical property analysis according to claim 1 is characterized in that: The horizontal tension is not directly affected by the height difference, but is determined by the horizontal component of the resultant load. The calculation formula is as follows: Where q total represents the total load per unit length, f avg represents the average sag and L is the span.

3. The method for calculating the probability of disconnection of ice-covered distribution lines based on mechanical property analysis according to claim 2, characterized in that: When considering the height difference, the average sag is calculated as follows: At this time, the horizontal tension calculation formula is as follows:

4. The method for calculating the probability of disconnection of an ice-covered distribution line based on mechanical property analysis according to claim 1, characterized in that: The vertical tension includes the vertical components of ice load and wind load and is calculated as follows: T V =q total L+ΔT h Where q total Indicates the total load per unit length, L is the span, ΔT h It is the additional tension caused by the height difference.

5. The method for calculating the probability of disconnection of ice-covered distribution lines based on mechanical property analysis according to claim 1, characterized in that: The calculation formula of the synthetic tension is as follows: Where, T H is the horizontal tension, T V For vertical tension.

6. The method for calculating the probability of disconnection of ice-covered distribution lines based on mechanical property analysis according to claim 1, characterized in that: The safety factor is calculated as follows: n=R / T total Where η is the safety factor, R is the total limit force, T total For synthetic tension.

7. The method for calculating the probability of disconnection of ice-covered distribution lines based on mechanical property analysis according to claim 6, characterized in that: The calculation formula of the total ultimate force is as follows: Where σ i is the tensile strength of the i-th material part, A i is the cross-sectional area of ​​the i-th material.

8. The method for calculating the probability of disconnection of ice-covered distribution lines based on mechanical property analysis according to claim 1, characterized in that: The calculation formula of reliability index is as follows: Where η is the safety factor, σ η is the standard deviation of the safety factor.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium includes a stored program, wherein when the program is run, the device where the computer-readable storage medium is located is controlled to execute the method for calculating the probability of disconnection of ice-covered distribution lines based on mechanical property analysis according to any one of claims 1 to 8.

10. A processor, characterized in that: The processor is used to run a program, wherein the program, when running, executes the method for calculating the probability of disconnection of an ice-covered distribution line based on mechanical property analysis according to any one of claims 1 to 8.

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