The mechanical effects of short-circuit currents in - Montefiore

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our cases). It means that the energy input, which is
severely increased by the asymmetry of the current
(the first peak of the short-circuit current can be
more than 2.5 times rms value and the energy is
proportional to the square of the current) is totally
converted into increase of the tension to create
pinch.
Subspan length effect. Manuzio neglected subspan
length effect, which was consistent with no pinch,
but does not reflect the actual situation as we
observed in our tests, even for very large subspan
length. In fact , if we imagine that subconductor are
moving with fixed end, the subconductor length (in
a first rough estimate) will have to increase by
about the subconductor spacing (if we imagine that
initially parallel subconductors came into contact
along all subspan length, except very close to the
spacer. It means that, following Hooke’s law, the
pinch could be estimate by: σ = εE
or
Fpi
as
as
= E or Fpi
EA
A ls
ls
= where as is the
bundle diameter, ls the subspan length and EA the
product of the elasticity modulus times the
subconductor cross section. As EA is very large,
such rough estimation will produce incredibly high
pinch Fpi . Such approach clearly point out that
subconductor tension cannot remain constant
during contact, as Manuzio suggested.
The new simplified method developed must include
such parameters. Many ways have been tried. Looking
for the simplest one and trying to be as close as possible
to known IEC methods, we finally decided to use actual
IEC 60865-1 (based on the work developed inside
CIGRE and published [Ref 55]) for evaluation of pinch
tension in substation structures. We adapted the method
to be used also for overhead lines, simply by
implementing a constant tower stiffness of 100N/mm
for both supports of one span and we focused our goal
on the use of the output of IEC60865-1 (the pinch) see
also [Ref 1], to evaluate spacer compression using the
following method:
66
Compressive force on spacer
Y(x
)
lnc
θ
Figure 3.66 Subconductor shape of a twin bundle during a pinch
(spacer on the left side)
In Figure 3.66, one subconductor is reproduced near
spacer location, at the instant of maximum pinch and
maximum spacer compression. The x axis represents the
bundle center and the subconductor (straight line) is
joining the center of the bundle keeping a certain
distance, depending on subconductor diameter. Lnc is
called the non contact length which is unknown and
must be evaluated. Between the spacer location and
contact point, the subconductor shape is like a parabola.
The compressive spacer force is the projection of the
pinch on the spacer at spacer location (the pinch
direction is given by the tangent which has a deviation θ
from horizontal). The pinch is the traction in the
subconductor, more or less constant along the
subconductor. In this simple approach, the bending is
completely neglected so that subconductor shape near
the spacer can be reproduced as shown in the figure.
Half of the spacer compression is given by :
c = pi.
sin( ) x=
0 F F θ
Another way to express it is to use equilibrium equation
with electromagnetic load on the non-contact length
(here expressed for twin bundle) :
l
nc
2 cos( θ ( x))
Fc
= 0,
2.
I . ∫ dx
2y(
x)
0
where the short-circuit current I is given in kA and is
the so called time average short-circuit current taking
into account the asymmetry as defined in CIGRE
brochure [Ref 1, equation 4.27, page 49]
where
2
as
− d ⎛ x ⎞ ⎛ x ⎞ as
y ( x)
= . ( as
d).
+
2 ⎜
l ⎟ − −
⎜
nc
l ⎟
⎝ ⎠ ⎝ nc ⎠ 2
and
cos( θ
) =
1
⎛ ∂y
⎞
1+
⎜ ⎟
⎝ ∂x
⎠
2
x