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main study the Uncertainties factors affecting line outage

rate as follows:

1) Temperature: The temperature changes will cause

expansion and contraction of the line, and thus cause the

lines sag and stress changes, and will affect the electrical

parameters of the line. Higher temperatures, due to ther-

mal expansion factors, the lines sag increase and the

length elongate, which impact the safe distance of the

wire-to-ground and cross across, and make the line resis-

tance increases, and thus increasing the power loss in the

line transfer power; When the temperature decreases, due

to the cold shrink effect, the line length becomes shorter,

the stress is increased, affecting the mechanical strength

of the wire.

2) Wind: effects of wind on the overhead line are

mainly in three aspects: Firstly, it will increase the load

of wires and towers when the wind blows on the towers,

conductors and its accessories; Secondly, with the action

of the wind, the wire will deviate from the vertical plane,

which will change the ground distance of the live wire,

cross arm, towers, etc; Thirdly, the wire will vibrate and

dancing in the wind, and the vibration will cause the wire

fatigue, in severe condition it will cause broken stocks or

short line, dancing makes chaos between the upper and

lower rows of wire .

3) Lightning: line tripping caused by lightning can

reach 70% of the total number of line tripping. And it can

trigger a chain of reactions after being struck by lightning,

such as wires blown, insulator broken, switch trip, etc.

Being struck by lightning, over-voltage of overhead lines

will result in flashover accident of insulation breakdown.

4) Line Icing: Line Icing cause wire and towers form-

ing a vertical load, line load increasing, may cause the

disconnection and connection fittings destruction even

down rod accident; Otherwise, ice-shedding difference or

uneven may cause overhead lines jump, easily leading to

flashover between parallels or between the wire and the

lightning conductor, then burn wires or lightning conductor.

2.2. The Method of Fuzzy Theory to Deal with

Uncertain Factors

The fuzzy uncertain factors are different from random

factors, there is no exact probability distribution, and

classical probability statistical methods can not be used

to describe it. The fuzzy set theory introduced by Zadeh

Professor is a powerful tool to deal with and descript the

fuzzy uncertain factors. The fuzzy set allows for the de-

scription of concepts in which the boundary is not sharp.

Besides, a fuzzy set concerns whether an element be-

longs to the set and to what degree it belongs. It does not

consider the situations where elements do not belong to.

As a result, the range of fuzzy set is in [0,1]. A fuzzy set

is mathematically defined by Zadeh as:

,()

A

xxxX

(1)

where is the membership function of in A, and X is the

universe of objects with elements x. In the case of the

classical “crisp” set A, membership of x in A can be

viewed as a characteristic function that can obtain two

discrete values:

1;

() 0;

A

ifx A

xifx A

(2)

For the fuzzy set A, the value of the membership func-

tion can be anywhere between 0 and 1, making it differ-

ent from a crisp set. Membership function of a fuzzy set

expresses to what degree the value of x is compatible

with the concept of A.

There is a wide variety of forms for fuzzy numbers,

and triangular fuzzy numbers and trapezoidal fuzzy

numbers are the most widely used in practical applica-

tions. Trapezoidal fuzzy number is function based on left

expand function L(x) and right expand function R(x). As

shown in Figure 1, it is a L-R fuzzy numbers described

by the real parameters in (a, b, c, d), and the representa-

tion of its membership function as:

(),

1.0,

() (),

0,

L

Lx axb

bxc

xRx cxd

others

(3)

where L(x) = (x-a) / (b-a) for [a, b] single increasing

function; R(x) = (d-x)/(d-c) of [c,d] within a single reduc-

tion function; the trapezoidal fuzzy numbers center value

is (b + c) / 2; a, d, respectively, is the left and right

borders of the fuzzy numbers.

Trapezoidal fuzzy numbers to characterize fuzzy fea-

tures of the value have better usability. In power systems,

the generator, load, and component failure status pa-

rameters can be described by the trapezoidal fuzzy num-

ber. For example, predict the maximum load of a system

within a year, the fuzzy predictive method may conclude

that: “the highest load will not be greater than 900 MW

or less than 750 MW, more possibly from 800 MW to

850 MW”, then it is more appropriate to indicates it adopt-

ing the trapezoidal fuzzy number, as Figure 1 shows.

Figure 1. Trapezoidal fuzzy function.

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