The mechanical effects of short-circuit currents in - Montefiore

V σ
3
2,5
2
1,5
1
mechanical resonance of the conductor with
2f
f
17
L1
L2
L3
RX / = 0,07
Λ = 0
Λ = 0,2
0,5
0
0,02
HV-arrangements
0,05 0,1 0,2 0,5
( f )
1
( 2 f )
2
usual MV- and
LV-arrangements
5 10
fc f /
calculated
standardized curve
Figure 2.2 Calculated factors Vσ in the outer conductors L1 and L3 in the case of a three-phase short circuit as function of the related relevant
natural frequency fc/f of the conductor and the logarithmic damping Λ, both ends fixed [Ref 8, Ref 9, Ref 19]. Also the standardised
curve is given
In Figure 2.2, R/X is 0,07, resp. κ = 1,81. When κ
decreases, the maxima of the electromagnetic forces in
equations (2.15), (2.16), (2.18) decrease proportional to
κ 2 , the decaying and the frequent term decrease too,
whereas the constant and the double frequent term are
independent. That means Vσ increases. The curves in
Figure 2.2 move to higher values while the standardised
curve follows the minima. In the case of R/X ≤ 0,15
resp. κ ≥ 1,64 the results are not very different.
Sub-conductors are treated as beams with both ends
fixed. They act as main conductors but with other
frequencies. To calculate the stress in the subconductors,
the factor Vσs is set to unity (= 1) without
consideration of the relevant natural frequency fcs. With
consideration of the relevant natural frequency fcs the
same figures can be used as for Vσ, but fc is to be
replaced by fcs.
Single-phase systems are to be handled in the same way.
2.2.3.3 Forces on the sub-structures
The forces on the sub-structures of the conductors are
also calculated from the static short-circuit load Fm [Ref
1, Ref 4, Ref 8, Ref 9, Ref 19, Ref 20]:
(2.30)
F = V V αF
d
F
VF considers the dynamic response and α the
distribution on the sub-structures.
Fd acts at the clamp on the top of the insulator. If the
supports assumed to be rigid, the moment along the
insulator is linear. Supports in LV- and MV-substations
r
m
fulfil this. Supports in HV-arrangements have a lower
stiffness and influence the oscillation of the system.
Along sub-structures of 110-kV-, 220-kV- and 380-kVsubstations,
the maximum dynamic moments are
calculated by means of Transfer-Matrix-Method [Ref
20, Ref 24]. Figure 2.3 shows the results for the
arrangement with two spans, described in [Ref 1,
Volume 2, Case 1]. The measured values are also drawn
and show a good agreement. The dynamic moment is
nearly linear. In addition, the moment is given which
follows from a static load with the maximum value of
the electromagnetic force; it is linear. In both cases, the
maxima of the moments and with this the maximum
stresses occur in the bottom of the insulators and steel
support structures. This justifies to take Fd as an
equivalent static force at the clamp which gives the
same moments as the dynamic force.
The stress at the bottom of the insulator by Fd must not
be higher than the minimum failing load of the insulator
which is given as a force FI at the top of the insulator.
Therefore the moments have to fulfil the following
equation
F h +
h ≤ F h
( ) (2.31) d I c I I