The mechanical effects of short-circuit currents in - Montefiore

C.D.F. ϕ given by Φϕ ( ϕ ) , we would obtain the
following load distribution:
m
FC ( )
m I C
⎛
21 ( + ) 2 ⎞
⎜ arccos( . −1− )
2
⎟
= Φ ⎜
m
ϕ ϕ o +
. α.
⎟
⎜
2
⎟
⎝
⎠
Case with several random variables
If g(V) is the wind distribution, the C.D.F. of loads is
given by:
( )
= ∞
∫0 Ψ CI , gV ( ). FCVI ( , , ). dV
with
21 ( + m)
2 2
arccos( 2 .( C−βV ) −1− )
FCV ( , , I)
= m. α.
I
m
π
ignoring own weight and assuming that the wind is
perpendicular to the tubes.
Similarly, if we know the distribution of the current
h(I), we can write:
ax
Κ( C) = ∫ ∫ g V h I F C V I dV dI
∞ Im
( ). ( ). ( , , ). .
0
Imin
Combination of various faults
The load distribution function can be calculated by
weighting the distributions of the various types of
fault as indicated below:
F( S) = F1( S) . pr( phasetoearth)
+
2( )
with F( S)
+ 3(
)
on a phase to earth fault, F ( S)
fault, F ( S)
F S . pr( phasetophase) F S . pr( threephase)
1 corresponding to the fault distribution
2 a phase to phase
3 a three-phase fault, and with
pr( phasetoearth) + pr( phasetophase) + pr( threephase)
=1
. In this case, the (λ,η) parameters of 5.2.3.8 must be
adjusted accordingly.
5.2.3.4 CHARACTERIZATION OF MECHANICAL
STRENGTH
The mechanical strength of the various components
(post insulator breaking load, yield strength of
metallic structures: tube, tower, substructure, etc.) is
also a random variable dependent upon the
manufacturing characteristics of the various
components.
The curve below gives an example of variation in
breaking load for a ceramic post insulator:
89
3,0%
2,5%
2,0%
1,5%
1,0%
0,5%
0,0%
Cumulative Distribution function of
Strength
0,7 0,8 0,9 1 1,1 1,2
Strength / Specified minimum failing load
Figure 5.19 Strength distribution function
This figure is based on manufacturer's data
established using a Gaussian strength distribution
G L
1 L−a ⎛ ⎞ ∞
2
− ( )
2 σ ⎜ ⎟ = e dL
⎝ FR
⎠ ∫ . . The mean value is in
0
G
this case between 1.4 and 1,5 FR and the standard
G
deviation σ is around 16% of FR . These data can be
obtained from major equipment manufacturers.
5.2.3.5 CALCULATING THE RISK OF FAILURE
The variation of the risk integral as a function of Γ or
G
rather of its reverse Fo/ FR is plotted below in semilogarithmic
coordinates:
Risk
1,E-02
1,E-04
1,E-05
1,E-06
1,E-07
Risk
0,7 0,8 0,9 1,0 1,1 1,2
1,E-03
Figure 5.20 Risk integral
Fo / Specified minimum failing load
We note that a 10% variation in this ratio causes the
risk integral to vary by a factor of 3 to 10, depending
G
on the operating point Fo/ FR . With the 0.7 safety
factor recommended by CIGRE, for combined shortcircuit
and wind loads represented in 5.2.3.3 (Figure
5.16 and Figure 5.17), the risk integral is here around
10 -6 for one post insulator.