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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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