The mechanical effects of short-circuit currents in - Montefiore

Tension during the short-circuit
The mechanical tension given by this relation leads to
the study of the following function :
y = 3.cos δ + 3. r2.sinδ− 2χ
i
since δδδδ ′
2 is always positive, the following relation is
true : cos δ + .sin δ ≥ χ
r2 i
The consequence is : y ≥ χχχχ i .
The maximum of the tension is reached when
δδδδ = δδδδ 12 , . Effectively the derived value is equal to 0
for this value :
dy
=− 3.sin δ + 3. r2
.cos δ = 0
dδ
tg δ = r δ = δ
2 1, 2
This maximum has a value :
2
y = 3. 1+ r − 2χ
M 2 i
This maximum is reached for
t Min ( )
T ⎛ res2
⎞
1 = ⎜ k.
π −ϕ
⎟
k ⎝ 2π
⎠
if ϕ < 0 then k = 0 else ϕ > 0 k = 1
The variation of the tension between the starting
position y=1 and this maximum is equal to :
2
∆y = y − y = 3 1+ r −1− 2
. .χ If
M M o 2
i
≥ then ϕ 2 =∆yM else
Tk2 t1
Tk2 with
< t1 ϕ 2 = ∆ y
∆y = 3.cos δ + r .sinδ
− 2χ −1
( )
k2 2 k2 i
The tension at anchoring points during this second
short-circuit is given by the equation (*34). For the
equation (*33), the influence of the heating due to the
first short-circuit can also be analyzed.
Influence of the first-fault heating
In IEC 60865, the heating is not taken into account
during the movement. The heating is used to estimate
the distance between the two conductors ( CD ).
But in case of a reclosure, it is necessary to
understand the influence of the first-fault heating :
-in the state change equation for the tensile force
during the second short-circuit.
-on the second short-circuit drop force.
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The applied force during a short-circuit F t to
anchoring points is given by the relation (*34).
The equation for state changes allows calculation of
tensions at anchoring points by the use of the formula
of the IEC 60865, described in (*33).
The heating modifies this change state equation as
following :
3 3 2 * 2
*
+ 2 + + + 1+ 2 + 2
( )
( ) ( )
ϕ ψ ϕ ζ ζ ψ ϕ ζ ζ ψ
*
− ζ 2 + ϕ ϕ + ζ = 0
* α. ∆θ. Es .
=
with ζ
F st
The drop force can change with the heating . The IEC
60865 does not take into account this influence. It is
also neglected here because this heating influence is
very low.
Value of angle at the end of the second shortcircuit.
⎛ Tk2
⎞
δ k2 = δ1, 2 + ( δ i −δ1,
2)
cos⎜
2π
⎟ +
⎝ Tres2
⎠
Tres2δ′ i ⎛ Tk2
⎞
sin⎜2π
⎟
2π
⎝ T ⎠
res2
2
2 8π
δ ′ k2= [ r δ k + δ k − χ
2 2.sin 2 cos 2 i]
T
Free movement after the short-circuit
The equation (4.4 volume 1 of [Ref 1]) is the rule for
the movement. Its first range linked with the above
conditions leads to :
[ r2 k2 i ]
2 2
δ′ = 2ω cos δ + .sinδ
− χ
The maximum angle δ m2
after the second shortcircuit
is given by :
cos
= r
( δ m2
) = χ i − r2.
sinδ
k 2
( sinδ
− sinδ
) + cos(
δ )
2
i
k 2
Work of LAPLACE forces
Work of LAPLACE forces after the first short -
circuit is given by :
T = Mg 0.
8b
r.
sin δ
L1
= Mg 0.
8b
c
c ( k )
( 1−
cos(
δ ) )
m
Work of LAPLACE forces after the second short -
circuit is expressed by :
m