Reliability Analysis and Safety Improvement Measures Research of Transmission Line Tower-Line Structure under Ice-Wind Conditions

The tower-line structure system of transmission line is a whole composed of tower structure, insulator, fittings and grounding wire and other components or subsystems. Its reliable operation is of great significance to the safe and stable operation of power system. In this paper, the reliability analysis method of transmission line tower-line structure system under the combination of ice and wind is modeled. Firstly, the reliability index of pole-tower structure, insulator, fittings and grounding wire is calculated by checking point method of first-order second-moment method. Then, the reliability calculation method of series structure system is used to calculate pole-tower structure, insulator, fittings and grounding wire. Finally, taking a straight tower and tension tower as examples, the system reliability indices of pole-tower structure, insulator, fittings and ground wire under ice-wind combination are calculated and analyzed, which can provide reference and guidance for disaster prevention of transmission lines.


Introduction
Transmission lines are affected by climate, topography and other conditions, and freezing disasters often occur [1][2]. In the case of icing, the overstress will lead to failure of the more fragile element if the stress of each element exceeds the design value. In the case of strong winds, line galloping will lead to broken guide wires, damaged poles and towers, and dropped metal tools, etc., seriously affecting the stable operation of the transmission lines [3][4]. Therefore, it is necessary to analyze the reliability of transmission line tower structure system in combination of ice and wind to reduce transmission line failures. The reliability of each part directly affects the reliability of the whole tower structure system [5]. At present, there are many researchers studying on the reliability of tower components at home and abroad, but there are few researches on the reliability of tower line structure system. Reliability analysis for failure modes of single structural members mainly includes first-order second-moment method, Monte-Carlo simulation method, random finite element method [6][7][8], etc. This paper applied a second order moment method of the checking point method, the combination of ice wind tower, under the condition of insulator, hardware, conducting ground components reliability was analyzed, and according to the results put forward the suggestions for the improvement of reliability of transmission line, this method gived a fixed set of analytical steps, applicable to the random variable for calculating structural reliability index, arbitrary conditions the convergence speed and high precision.

Calculation Methods for Component Reliability and Statistical Characteristics of Basic Variables
This chapter first introduced the calculation method of each component reliability index in transmission line tower structure system, and then gived the statistical characteristics of load and resistance, which were the basic variables that affect the reliability of transmission line components.

Calculation Method of Component Reliability
The check point method in the first-order second-moment method often used for reliability analysis of tower structures was used to calculate the reliability index of components. When the structural function Z of the research object obeyed normal distribution, the calculation formula of the reliability index of components was: where, μZ is the average value of function Z and δZ was the standard deviation. On the contrary, if the structural function does not obey the normal distribution, it is necessary to convert its variables into random variables subject to the normal distribution through equivalent normalization.
After equivalent normalization, the reliable index can be expressed as: where, sensitivity coefficient of function composed of random variables can be expressed as: Coordinate of check calculation point: The mean value, standard deviation, reliability index and sensitivity coefficient of equivalent normal random variable were all functions of the value of checking points. The reliability index were to be calculated by equivalent iterative calculation method. If, *(1) *(0) xx  − ,  was the specified allowable error, it will be terminated.

Statistical Characteristics of Permanent Loads
In the analysis of structural reliability, normal distribution was often used to describe the probability distribution of random variables such as material properties and permanent loads. In the transmission line, the permanent load was mainly the deadweight of tower structure, insulator and guide wire, which was denoted by G. Introduce the coefficient of variation,  ,

Statistical Characteristics of Wind Loads
The current design specification and manual [9], in determining the basic wind speed, the meteorological stations should be in accordance with local 10 min interval average annual maximum wind speed of statistical samples, and USES the extremum Ⅰ type distribution as a statistical model of probability distribution.
When the wind speed was 33 m/s (design base year), the probability distribution function of wind load was: In the type: In the type: , k W was the standard value of wind load specified in the code.

Statistical Characteristics of Icing Loads
Icing on transmission lines was widespread in China, and ice damage accidents have been occurred in transmission lines in many regions of China [10]. The formation of ice coating on the surface of transmission wires was mainly promoted by: lower temperature (-10-0 ℃), higher air humidity (relative humidity above 90%), and lower wind speed (generally 0-10 m/s) [11]. The ice loads were assumed to be the extremum I type distribution, and its annual maximum probability distribution function can be represented as: where, I1  was the location parameter of the maximum weight distribution of icing. I1 u --The relationship between them and the mean value and standard deviation of weight of icing cover was as follows:

Statistical Characteristics of Mechanics Resistance
In the analysis of structural reliability, the probability characteristics of random variables such as structural mechanics resistance ware often described by lognormal distribution. When random variables obeyed the lognormal, the probability distribution function was: The statistical characteristics of load and resistance in transmission line design were shown in table 1. The number of insulators in each string is 10, 15 and 20 respectively.

Tower Structure Subsystem
Transmission line towers were composed of multiple pole members. Under the joint action of pole member gravity, insulator gravity, guide wire gravity, wind load and icing load, tower forces are balanced to form a statically indeterminate structure. However, if one of the rods failed, the stress of the entire tower were to be distributed again. If multiple towers failed and these towers formed a failure path, the failure of the entire tower system were caused. As there may be multiple failure paths leading to the failure of one tower system, and these failure paths were or logic for the failure of the whole tower system, it was necessary to calculate the reliability of the tower system under multiple failure paths by using the method of series structure system.
Suppose that the series system has n function function, and the function of the i link is: In the type, i R , Gi S , I i S and W i S --The resistance of the first member, the axial force generated by the dead weight of the member, the axial force generated by the icing load, and the axial force generated by the wind load. Normalize the equivalent of random variables and carry out iterative calculation to obtain the reliability index and obtain the reliability index i  and sensitivity coefficient of the first The correlation coefficient between the I member and the j member can be calculated as follows: In the type, GG i j  --The correlation coefficient between the axial forces generated by the dead weight on the member was related to the positions of the two members, taking 0.5. The calculation of system reliability was a high-dimensional integral problem . In practice, simplified approximate calculation method was generally adopted: where, ()  was the probability distribution function of random variables subject to standard normal distribution, and ()   was its probability density function. The equivalent reliability index was: where, 1 () −  was the inverse function of the probability distribution function, and the variable was the standard normal random variable.

Insulator Subsystem
The failure of insulators on a transmission tower was constructed into a series system. The calculation method of system reliability was the same as that of tower structure system. V insulator was selected  The system reliability index and sensitivity coefficient of variable of v-insulator subsystem were calculated by using the method in section 3.1 of this paper.

Hardware Subsystem and Lead Wire Subsystem
The function of the hardware was: where, R was the resistance of suspension clip (random variable); 5 W --wind load (random variable) when the wire is icing; 3 W --vertical load (random variable) when the wire was icing. The function of the Conductor and Ground wire were: where, R --resistance of the conductor (random variable); G T --tension (random variable) generated by permanent load on the guide wire; Qi T --the i tension generated by the first variable load on the conductor (random variable).
The system reliability index and sensitivity coefficient of variables of the hardware subsystem and the lead wire subsystem were calculated by the method in section 3.1 of this paper.

An example is Given to Calculate
In this paper, the 220 kV voltage grade steel pipe column SGZK4-48 straight line tower and SGJ-42 tensile tower were taken as research objects, and the parameters were shown in table 2. The reliability index of each element of the two tower types under the condition of basic wind speed of 33 m/s and ice cover thickness of 10 mm were calculated. According to the method in chapter 3 of this paper, the component reliability index and sensitivity coefficient of each variable of tower structure, insulator, metal implement and guide wire under icewind combination were calculated as shown in tables 3-6 respectively. According to the method in chapter 4 of this paper, the system reliability index and sensitivity coefficient of equivalent function of the four subsystems were calculated as shown in table 7.   [7] stipulates that the target reliability index of brittle failure of structural components is 4.2 and that of ductile failure is 3.2. Starting from the weak components with low component reliability index in table 3, these components were strengthened appropriately to improve the component reliability that can easily evolve into failure points. By tables 4 and 5 shown that straight line tower insulator of the wire and the wire tension tower of hardware component reliability was relatively low, in the disaster prevention for this two parts corresponding to strengthen, as in "V" by adding child spacing on insulator string rod decrease offset under wind load, to alleviate the imbalance between the insulator string stress, the hardware with large mechanical strength, etc. In addition, among the reliability index of the tower-conductor and GW system, the GW system was on the low side in a straight line tower, which shown that under the combination of ice wind, conductor and ground wire break line drop probability was bigger, from table 6 can be seen, lowest component reliability index was ground wires, therefore, it was necessary to take corresponding measures the transmission line ground wire in the area of ice disaster and wind disaster occurred frequently, especially line tower, reasonable reduce the span transmission lines, wind and ice disaster environment more reasonable to increase the number of transmission tower, wire tension, to reduce the transmission line can effectively reduce the harm caused by the line galloping. It indicated from table 7 that, under rated icing load and rated wind load, the system reliability index of each subsystem of transmission