The mechanical effects of short-circuit currents in - Montefiore

Typical examples are the conductors shown in Figure
2.11a. At one end a flexible connection to another
equipment can be fastened, or in the span there could be
an additional mass, e.g. the contact of a disconnector.
For the cantilever ends and the drawn kind of supports,
the factor γ lies between the specified limits; the value
to be taken depends on the lengths of the cantilever end
and the freedom of movement of that end. In the case of
the additional mass in the span, the frequency can be
calculated with the factor cm stated above. Alternatively,
in all cases the relevant natural frequency can be
estimated according to the equation (2.38) from the
maximum displacement max y due to dead load:
(2.46)
f
c
=
=
1
2π
1
2π
cF
≈
m
F
mg
n
1
2π
gn
=
max y
1 F
m max y
1
2π
gn
max y
where cF is the spring coefficient, m the overall mass, F
the dead load due to m and gn = 9,81 m/s 2 the
acceleration of gravity. From this the numerical
equation follows which is given in Figure 2.11.
More complicated connections, e.g. swan-neck bends
between different levels in Figure 2.11b, can be
investigated with sufficient accuracy. Lets assume that
the sides have equal lengths and are full stiff against
torsion; in this case the static line perpendicular to the
conductor plane for ϕ = 180°, i.e. straight beam both
ends fixed, fits also for 90° ≤ ϕ < 180°, the frequency is
correct. The other extreme is no stiffness against
torsion, the sides will sag like cantilever beams for ϕ =
90°; the frequency will be reduced to 63 % compared
with the ideal stiff conductor. Both limits are used in
substations: Tubes in HV-substations are stiff whereas
rectangular profiles in MV- LV-substations are not stiff.
For frequency-estimation, tubes can be ‘straightened’
and good results can be obtained after reduction of 5 %
to 15 % depending on the length of the sides .
24
a)
b)
clamp, cabel
flexible joint
mass of disconnector-contact
A
B
ϕ
max y
1,57 < γ < 2,46
2,46 < γ < 3,56
alternatively:
fc 5
≈
Hz max y
cm
sectional view AB:
displacements
Figure 2.11 Estimation of relevant frequency
a) Cantilever beam and beam with
additional masses
b) swan-neck bend
2.2.5. Section moduli of main and sub-conductors
The stresses σm and σs according to equations (2.5) and
(2.6) depend on the section moduli Zm of the main
conductor and Zs of the sub-conductor. For Zm it is to
distinguish whether the main conductor is a single
conductor, or consists of two or more sub-conductors
with rectangular profile or of two sub-conductors with
U-profile. If the main conductor is made up of subconductors,
there can be either no connecting piece or
the connecting pieces act as spacers or as stiffening
elements. In addition, the direction of the
electromagnetic force is important.
For calculation of section moduli the distribution of
bending stresses has to be taken into account. Axial
forces do not occur, the conductors are assumed to
move free in the clamps.
2.2.5.1 Section modulus of a single conductor
Figure 2.12a shows a single conductor, for example
with rectangular cross section Am. The vector m Mr is the
outer moment caused by the force Fm on the main
conductor. It lies in the centre Sm and makes
compressive stress above the neutral fibre O-O and
tensile stress below. The maximum stress σm in the
outer fibres at ±dm/2 follows from equation (2.25)