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32IUJI32IWEQHJHJHJJOP,E9UWEEIOWUWEUHJQWHJWQHHWQJDHJ

WJKXJASLJXLASSJA SHORT-CIRCUIT DESIGN FORCES IN POWER

LINES AND SUBSTATIONS

1

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1. INTRODUCTION

Short-circuit currents in power lines and substations induce electromagnetic forces acting on

the conductors. The forces generated by short-circuit forces are very important for high-

voltage bundle conductor lines, medium-voltage distribution lines, and substations, where

spacer compression forces and interphase spacings are significantly affected by them.

Power Lines and Substations

Short-circuit mechanical design loads have been a subject of significant importance for

transmission line and substation design for many years, and numerous papers, technical

brochures and standards have been published (Manuio 1!"#$ %oshino 1!#&$ %avard et al.

1!'"$ )*+ 1!!"$ )*+ &&$ ) 1!! and 1!!"$ /ilien and 0apailiou &&&. 2nder

short-circuit forces, there are some similarities and some differences between the behavior of

fle3ible bus and power lines.

4or both the power lines and substations, the electromagnetic forces are similar in their origin

and shapes because they come from short-circuit current () 1!''. 5evertheless, as listed

below, there are some major differences between short-circuit effects on substation bus

systems and power lines6

0ower lines are subjected to short-circuit current intensity, which is only a fraction of thelevel met in substation bus systems. The short-circuit level is dependent on short-circuit

location, because longer lengths of lines mean larger impedance and lower short-circuit

level. The level also depends on power station location and networ7 configuration.

0ower line circuit configuration may not be a horiontal or vertical arrangement, thusinducing other spatial components of the forces than in bus systems, and the movement

may be 8uite different.

0ower lines have much longer spans and thus much larger sags than fle3ible bus and rigidbus. This induces a very low basic swing fre8uency of the power line span (a fraction of

one %. Therefore the oscillating components of the force at the networ7 fre8uency (and

its double have negligible action on power lines.

0ower line phase spacings are much larger than those in substations, and this has adramatic reduction effect on forces between phases.

9undle conductors in power lines have much larger subspans than in substations, and

bundle diameter is often larger, too. Sometimes very large bundle diameter and a largenumber of subconductors are used compared to bundled substation fle3ible bus. This has

significant effects on the phenomenon because long subspans reduce the effect of bundle

collapse upon the tension in the subconductors during short circuit conditions. 4ig. 1

demonstrates the distortion of the subconductors of a 8uad bundle around a fle3ible spacer

during a short-circuit, 7nown as the pinch effect, which causes the tension increase.

:ue to differences in structure height and stiffness, power line towers have significantlylower fundamental natural fre8uencies than substation structures. ;ne result is that the

substation structures are more li7ely to respond dynamically to the sudden increase in

tension that results from the pinch effect.

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0ower line design load includes severe wind action and in some cases heavy ice loadsacting on much larger spans than in substations. Therefore design loads due to short

circuits may be of the same order as design wind and ice loads in substations, but much

less in transmission lines.

Bundle Conductor Lines

4or bundle conductor lines, during a fault, the subconductors of the bundle move closer to

each other due to strong attraction forces because of the very short distance between

subconductors (4igure1.

:etailed discussions of this phenomenon were given by Manuio and %oshino (Manuio

1!"#$ %oshino 1!#&.

4rom their initial rest position, the subconductors move towards each other, remaining more

or less parallel in most of the subspan, e3cept close to the spacer (4igures 1 and . pinch,?

while it is associated primarily with the change in angle, can be further increased by the rise

in tension in the subconductors due to bundle collapse. This jump results from the fact that

subconductor length in the collapsed condition is greater than in the normal condition.

The pinch is ma3imum when the wave propagation stops towards the spacer, position e in

4igure . The triangle of collapse then performs oscillations through positions d-c-d-e-d-c-e-

d-c and so on as long as electromagnetic force is still on, but with decreasing amplitude. )f the

short circuit is long enough, the pinch oscillations result in a >permanent? oscillating force,

sensibly lower than pea7 value, typically @&A.

:uring the fault, the spacer is strongly compressed. The compression is related to ma3imum

pinch force in the conductor and the angle between the spacer and the subconductor.

4igure 1 3ample of 8uad bundle before and during short-circuit test at @& 7

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2pward movement of the whole span follows the rapid contraction of the bundle and reduces

the conductor tension, but does not reduce the ma3imum forces on the spacers occurring

during initial impact.

4igure

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large enough to cause cable contact and even permanent wrap-up at the middle of the span.

4or double-circuit towers, the circuit subjected to the short circuit could force its phases to

come in contact with another circuit, thus causing outages on both circuits. There may also be

sag increases, up to several times the initial sag in distribution lines, due to heating effects

under short circuit, which may significantly affect the amplitude of movements.

ven though the inward swing could be short of interphase contact, if the phase spacing isless than the critical flashover distance, and the inward swing occurs at the time that voltage is

restored by automatic reclosure, there will be a second fault.

Cery large movements may be seen on distribution lines. 4igure shows the motion produced

during full-scale testing on an actual line. This is from an actual three-phase short-circuit test

on a 1@-7C distribution line near /iDge, 9elgium (/ilien and Cercheval 1!'#. The photo

shows an instantaneous position of the conductors ta7en during the test. The fault current

level was 7

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4ig 33 6 rigid busbar response to ta given electromagnetic force similar to a two-phase fault

with asymmetrical component in the short-circuit current. The transient response is given for

different busbar first eigenfre8uency between 1.# % and 1@& %. (e3tract from )*+

brochure 5E 1&@, 1!!".

4ig 33 6 a tested rigid bus (all details in )*+ brochure 1&@, 1!!", Measurement points are

located as S, ), (constrains. Short-circuit of 1" 7< during 1@ ms with automatic

reclosure after ==@ ms and a second fault of &@ ms with same amplitude as the first one.

"

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2. FAULT CURRENTS AND INTERPHASE FORCES

< short-circuit current wave shape consists of an ? is rather low, typically & to '& ms, compared tosubstations where it is typically #& to && ms.

1

-

.

( (sin( sin(

( (sin( sin(

( (sin( sin(

t

rms

t

rms

t

rms

i t I t e

i t I t e

i t I t e

= +

= +

= + + +

(

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0is the vacuum magnetic permeability H =1&-#%Bm.

ais the interphase distance (m.

The force, being due to current flow, very much depends on phase shift between currents. )t

generally includes6

0seudo-continuous : component, with a time-constant decay,

ontinuous dc component, sometimes, and

Two oscillating

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4igure = Two different geometric arrangements for a three-phase circuit and the

electromagnetic force reference directions on each phase corresponding to 8uation . The

numbers 1, , and are phase numbers.

)t must be noted that the level of the pea7 force, about && 5Bm in 4igure @, is far greater than

the conductor weight and is proportional to the s8uare of the current. 9ut the continuous

component is much lower, about & 5Bm in this case, as shown later. 2nder actual short-

circuit levels and clearances, it is closer to the conductor weight, but acts, in most cases, in the

other direction. See upper right panel in 4igure @.

4igure @ 3ample of calculated three-phase short-circuit current wave shape and

corresponding loads on a horiontal or vertical circuit arrangement.

1&

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4igure ! Typical tension oscillogram in one subconductor during and after the fault, for the

"&-m span length configuration (1@ 75 initial. )rms @ 7< (pea7 !& 7

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4igure 1& Typical tension oscillogram in one subconductor during and after the fault for the

3 &-m span length configuration (1@ 75 initial. )rms @ 7< (pea7 !& 7

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3. INTERPHASE EFFECTS UNDER SHORT CIRCUITS

Maximum Tensile Loads during Moement of the Phases

4igure 11 shows a typical response of a bundle conductor two-phase fault in a horiontal

arrangement ()*+ 1!!". 9oth cable tension versus time (4igure11 left and phase

movement in a vertical plane at mid-span (4igure 11 right are shown. ;n the cable tension

curve, three ma3ima (and their corresponding time on the abscissa have been indicated,

which is discussed below. ;n the phase movement curve at mid-span, the curve has been

mar7ed by dots every &.1 s to get an idea of the cable speed, and in particular to show that the

short circuit ends before there is significant movement of the phase.

Typical ma3imum loads (4igures 11 and 1 that could influence design appear when total

energy (including a large input during short circuit has to be mainly transformed to

deformation energy.

0ea7 design load could occur under the following three conditions6

1. Ma3imum swing-out 4t(at time ttin 4igure 11leftand s8uare 1 in 4igure 11 right6 verylittle 7inetic energy (cable speed close to ero and potential energy with reference to

gravity, so that a large part is converted in deformation energyIthat is, increase of

tension. )n power lines, tt occurs always after the end of the short circuit (the cable

position at the end of the short circuit (&.1 s is indicated in 4igure 11 right.

. Ma3imum 4fat the e3treme of downward motion (at time tfin 4igure 11 leftand s8uare

in 4igure 11 right6 generally more critical because of a loss of potential energy of gravity

due to the cable position at that moment. tfalways occurs after the end of the short circuit.

. The pinch effect 4pi (at a very short time after short-circuit inception at tpi. The pinch

effect only occurs with bundle conductors, when subconductors come close to each other6tpialways occurs during short circuit.

4igure 11 /eft 4igure6 Tensile force (left time evolution of a typical twin-bundle

span during two-phase short circuit between horiontal phases. Three ma3ima6 4piat

time Tpi(so-called pinch effect, due to bundle collapse, 4tat time Tt(the ma3imum

of the force due to ma3imum swing of the span represented by circle point 1 on the

right figure, and 4f at time Tf (the ma3imum of the force due to cable drop

represented by circle in the right figure. Typically, Tpi-=& ms, TtL1. s and TfH = s

1

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+ight figure6 Movement of one phase (right in a vertical plane at mid-span (F and

are the two orthogonal a3es ta7en in the vertical plane at mid-span, perpendicular to

the cable. is vertical, -1& m is the initial point showing sag, and F is horiontal and

transverse to the cable. Such movement has been calculated for a two-phase fault of

" 7< (duration &.1 s end of short circuit being noted on the figure on a F @#&

mm9eaubourg? tower (the circuit configuration is shown by points T, +, and S in 4igure 1 forloading conditions (/ilien and :al Maso 1!!&6

1. three-phase fault of #. 7