The mechanical effects of short-circuit currents in - Montefiore

centers are normally balanced by bar sections, in
order to minimize the current flows and risks. Under
such conditions, the electrodynamic stresses are very
often noticeably reduced compared to the more
penalizing layouts. The stresses and operating
practices very often narrow down the number of
possible scenarios to only a few cases. It then
becomes feasible to achieve a good order of
magnitude for the electrodymanic stresses likely to
occur in such operating situations.
5.2.3.2.3. Flexible Busbars
The dynamic response of the cables often minimizes
the quadratic variation of the Laplace force depending
on the intensity of the current. Adaptations of
simplified methods were developed specifically for
bundle cable connections [Ref 90]. This aspect is
currently being examined.
5.2.3.3 CALCULATING THE DISTRIBUTION OF
MECHANICAL LOADS
On the basis of the elementary distributions of
primary variables, we can, for example, associate a
bending force FI ( , ϕ, V,
θ ) with an amplitude
probability density f ( I) . g( ϕ) . hV ( , θ ) . This is
the case for the cumulative distribution function
(C.D.F.) below, corresponding to the case I=constant
during a three-phase fault in a transfer situation (two
busbars).
%
Cumulative Distribution Function of loads
100
90
80
70
60
50
40
30
20
10
0
0% 20% 40% 60%
ratio Load / Fo
80% 100% 120%
Figure 5.16 Fo(L) overall view of C.D.F.
88
%
2,0
1,8
1,6
1,4
1,2
1,0
0,8
0,6
0,4
0,2
0,0
Cumulative Distribution Function of loads
90% 100% 110% 120% 130% 140%
ratio loads / Fo
Figure 5.17 Fo(L) extremity of C.D.F
Fo : design loads
The irregularities of these function are the result of
discretization. This type of function can nevertheless
be approached using an analytical method.
Case with one random variable
If we consider only the variable ϕ, the distribution
function of stress according to (5.12) takes the
following form for a uniform distribution:
(5.20) ( )
FC
m
m I C
21 ( + ) 2
arccos( 2 . −1− )
= . α.
m
π
where the values are defined in the interval [Cmin(I), Cmax(I)] with Cmax(I)=αI² and Cmin(I)= αI²/(1+m).
Outside this interval, the following extension is
adopted: FC ( ) = 1, if C< Cmin(I) and FC ( ) = 0 , if
C> Cmax(I). %
100
90
80
70
60
50
40
30
20
10
0
Figure 5.18
Cumulative Distribution Function of loads
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
Loads / Fo
1
Uniform Distribution
Beta Distribution
For a non-uniform phase distribution, for example a
Beta distribution, condensed over the interval [0,π/2]
established on the basis of the data in Figure 5.9, we
can plot the second curve of Figure 5.18 on which the
maximum load values are less probable. With a