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20

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Full resolution (JPEG) - On this page / på denna sida - 1958, H. 2 - Effect of Non-slandard Surge Voltages on Insulation, by Sune Rusck

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retical value 1 from equation (10) may at a first
glance be considered too great. In this connection it
must, however, be borne in mind that owing to the
cubic relation a difference of let us say 20 per cent
may be caused by an error of only 6 per cent in
the voltage U(t) or the function (20 +10s). As a
consequence the equations (9) and (10) can hardly
be used to precalculate the time lag of a spark gap
if a good accuracy is wanted, but the relation

X

J U3(t)dt= constant is of course very well suited

o

to compare the disruptive effect of a non-standard
surge voltage with a standard voltage if the time
lag of the latter is known. It is interesting to see
that the same relation is found by Andrew R Jones1
in an other way. It must, however, be noted that in
the latter investigation the integration of the voltage
is carried out from the beginning of the surge and
not as in the present paper from that moment when
U(t) exceeds U0(s). At surges with steep fronts this
difference is of no importance.

Velocity of the leader stroke

It may now be of interest to use the deduced
equations to compute the propagation of the leader. In
figure 4 the time and the instantaneous velocity of
the leader have been computed as functions of the
distance the leader has covered. The distance of the
gap is assumed to be 50 cm and the voltage constant
and equal to 400 kV. It can be noted that it takes
about 85 % of the total time to bridge the first
50 % of the gap. The initial velocity of the leader
is in this case 7.9 cm/us. During the propagation
across the gap the velocity increases and attains
immense values when the sparkover is nearly
completed. As all the measurements of the time lags have
been carried out with voltages less than 1.6 times the
breakdown voltage the shape of the velocity curve
in the last part of the discharge is obtained as the
result of an extrapolation. The general shape of the
t and v curves is however in accordance with actual
measurements of the velocity of the leader reported
elsewhere1’2’3.

Table i. Results of a series of tests with steep surges

Fig. A. The time t and velocity v as functions of s-x.

Breakdown voltage

On the assumption that the leader stroke merely
acts as an extension of the electrodes of the gap the
condition for the leader stroke to be stopped and the
breakdown avoided is

U0(x)>U(t) (11)

Combining equations (8) and (11) the following
equation is obtained.

x

(tTT\)3< 1–FTFT-n f 173 (0 dt (12)

\Uo(s)l To U0 (s) j

o

If the breakdown voltage of a gap subjected to an
irregular surge is to be calculated two quantities
must be known viz. the breakdown voltage of the
gap U0(s), when a long surge is applied, and the
quantity r0t/03(s). Referring to equation (9) the last
one can be determined with an arbitrarily varying

X

voltage as the value of the integral J U3(t)dt.

Distance of the gap s = 50 cm
Th = 5 jis Th — 10 [is Th = 20 [is

Voltage f( V dt Voltage [( UW Volta§e J| U(t) y

kV 1 \20 + 10s/ kV ! \20 + 10s/ kV I \20 + 10s

440 0.98 430 1.18 382 1.11

474 0.89 462 1.13 420 1.22

506 0.86 529 1.21 484 1.31

561 0.87 571 1.22 516 1.17

616 1.12 561 1.25

595 1.29

Distance of the gap s = 25 cm

244 1.22 224 1.05 213 1.13
290 1.28 240 1.01 227 1.12
324 1.30 271 1.09 254 1.12
363 1.26 304 1.16 275 1.15
396 1.15 330 1.23 302 1.26
356 1.19 323 1.23

ELTEKNIK 1958 1 20

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