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1. INTRODUCTION

Short-circuit currents in power lines and substations induce electromagnetic forces acting onthe conductors. The forces generated by short-circuit forces are very important for high-voltage bundle conductor lines, medium-voltage distribution lines, and substations, wherespacer 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 fortransmission 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 &&&. 2ndershort-circuit forces, there are some similarities and some differences between the behavior offle3ible bus and power lines.

4or both the power lines and substations, the electromagnetic forces are similar in their originand shapes because they come from short-circuit current () 1!''. 5evertheless, as listed

below, there are some major differences between short-circuit effects on substation bussystems 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-circuitlocation, because longer lengths of lines mean larger impedance and lower short-circuitlevel. 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 rigid

bus. This induces a very low basic swing fre8uency of the power line span (a fraction ofone %. Therefore the oscillating components of the force at the networ7 fre8uency (andits 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 hassignificant effects on the phenomenon because long subspans reduce the effect of bundlecollapse upon the tension in the subconductors during short circuit conditions. 4ig. 1demonstrates the distortion of the subconductors of a 8uad bundle around a fle3ible spacerduring 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 thesubstation structures are more li7ely to respond dynamically to the sudden increase intension 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 shortcircuits may be of the same order as design wind and ice loads in substations, but muchless in transmission lines.

Bundle Conductor Lines

4or bundle conductor lines, during a fault, the subconductors of the bundle move closer toeach other due to strong attraction forces because of the very short distance betweensubconductors (4igure1.

:etailed discussions of this phenomenon were given by Manuio and %oshino (Manuio1!"#$ %oshino 1!#&.

4rom their initial rest position, the subconductors move towards each other, remaining moreor less parallel in most of the subspan, e3cept close to the spacer (4igures 1 and . <fter firstimpact, which for power lines is typically around =& to 1&& ms after fault inception, there is a

rapid propagation of the wave in the noncontact one near the spacers, se8uence c-d-e of4igure . The inward slope of the subconductors at the spacer results in a component ofsubconductor tension that tends to compress the spacer. This compressive force, or >pinch,?while it is associated primarily with the change in angle, can be further increased by the risein tension in the subconductors due to bundle collapse. This jump results from the fact thatsubconductor 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 in4igure . 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 theshort 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<, showingdistortion of the subconductors. ;ne fle3ible spacer at mid-span (courtesy 0fistererBSefag.

The subconductor movements occur at very high acceleration. 4or e3ample, a =& 7< fault ona twin bundle of "& mm conductor, with a separation of =& cm, may have acceleration up to

several tens of g, depending on the instantaneous current value. Spacers are subjected tocompression forces$ and these instantaneous compression loads can be very high.

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2pward movement of the whole span follows the rapid contraction of the bundle and reducesthe conductor tension, but does not reduce the ma3imum forces on the spacers occurringduring initial impact.

4igure <ttraction of subconductors of a bundle at a spacer during a short-circuit(Manuio 1!"#.

Interphase Effects and Distribution Lines

The video available on my web site ([email protected] contains someshort-circuit tests on rigid bus, fle3ible bus and high-voltage overhead lines and distributionlines.4ault currents produce an impulse tending to ma7e the separate phases of a circuit swing awayfrom each other, independently of whether the phases are bundled. The impulse that causesthis lasts only as long as the fault, so it is brief relative to the fundamental period of the span.

The momentum from the impulse carries the phases outward for a certain distance before theirtension arrests and reverses the motion. They then swing inward. This inward swing may be

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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 tocome in contact with another circuit, thus causing outages on both circuits. There may also besag increases, up to several times the initial sag in distribution lines, due to heating effectsunder 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 isrestored by automatic reclosure, there will be a second fault.

Cery large movements may be seen on distribution lines. 4igure shows the motion producedduring full-scale testing on an actual line. This is from an actual three-phase short-circuit teston a 1@-7C distribution line near /iDge, 9elgium (/ilien and Cercheval 1!'#. The photoshows an instantaneous position of the conductors ta7en during the test. The fault currentlevel was 7<. The reduction in phase spacing may be particularly dramatic on medium-voltage lines, even if the short-circuit level is much lower.

4igure )nstantaneous position of the conductors ta7en during three-phase short-circuit teston 1@-7C distribution line near /iDge (/ilien and Cercheval 1!'#.

Substation with rigid busbars

The behavior of a rigid bus under short-circuit load is very depending of its first naturaleigenmode and eigenfre8uency. )ndeed electromagnetic forces includes pseudo-continuouscomponent combined with a @& % and a 1&& % component.

Some e3ample are shown on the ne3t figure.

The transient response is thus very depending on the voltage as low voltage (say #& 7Cwould have a short bar length and a reduced sie tubular bar, when high voltage (typically =&&7C would have long bar length and large tubes.

Moreover the busbar is installed on supporting insulators which have their owneigenfre8uencies, close to @& % for 1@& 7C level. So that dynamics of such structures is farfrom obvious and case dependent.

@

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4ig 33 6 rigid busbar response to ta given electromagnetic force similar to a two-phase faultwith asymmetrical component in the short-circuit current. The transient response is given fordifferent 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 arelocated as S, ), (constrains. Short-circuit of 1" 7< during 1@ ms with automaticreclosure after ==@ ms and a second fault of &@ ms with same amplitude as the first one.

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4ig 33 test results. The first eigenfre8uency of the whole structure is about . %. There is8uasi no effect of the @& % nor of the 1&& % component of the force. <s damping wasnegligeable, as time to reclosure was particularly dramatic compared to structure oscillation,the second fault induced about twice as much constrains compared to the first fault.

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2. FAULT CURRENTS AND INTERPHASE FORCES

< short-circuit current wave shape consists of an < component and a decaying :component due to the offset of the current at the instant of the fault. The < componentgenerally is of constant amplitude for the duration of the fault, and although the systemthrough which the fault passes is multimesh, it can usually be assigned a single >global? time

constant for the decay of the : component. )n high-voltage lines, and even more in low-voltage lines, because the ratio FB+, reactance to resistance, is much less at low-voltage level,the global time constant of the system >τ? 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

τ

τ

τ

ω φ φ

π π ω φ φ

π π ω φ φ

−

−

−

= + −

= + − − −

= + + − +

(<mperes 1

Ghere

)rms is the root-mean-s8uare value of the short-circuit current (<.

ω H πf is the networ7 pulsation (radBs e8ual to 1= radBs in urope and ## radBs in the2nited States.

τ is the networ7 time constant (H /B+ at the location of the fault (s.

φ is an angle depending on the time of fault occurrence in the voltage oscillation (rad.<symmetry is very dependent on φ. )n the case of a two-phase fault, it is possible to have noasymmetry if φ H & rad.

<ccording to the basic physics of electromagnetism for a three- or a two-phase arrangement,there is always a repulsion force between phases from each other. 4or a single-phase fault,only one current is involved. )n the case of bundle conductors, it is generally considered thatthe short-circuit current is e8ually divided among all subconductors. The force acting betweensubconductors of the same phase is an attractive force, as discussed in Section .

)n the general case of parallel conductors, the force, F n(t) in 5Bm, applied on each of the phases can be e3pressed by6

& 1 .1 -

1

& - .1 -

-

& 1 . - .

.

( . ( ( . ( (

( . ( ( . ( (

( . ( ( . ( (

i t i t i t i t F t x

a a


a a


a a

µ

π

µ

π

µ

π

= − − ÷ = − ÷ = + ÷

(5Bm

Ghere

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µ 0 is the vacuum magnetic permeability H =π1&-# %Bm.

a is the interphase distance (m.

The force, being due to current flow, very much depends on phase shift between currents. )tgenerally includes6

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

• ontinuous dc component, sometimes, and

• Two oscillating < components, one at networ7 fre8uency, with a time-constant decay,and one at the double of the networ7 fre8uency, which is not damped.

)n the case of a two-phase fault, the force is proportional to the s8uare of the current. Thus italways has the same directionIthat is, a repulsion between the two faulted phases.

)n the case of a three-phase fault, it is much more comple3. )n flat-phase configuration,illustrated by the top view of 4igure =, the middle phase has a ero mean value, and at leastone of the outer phases has forces similar to those generated by a two-phase fault (4igure @left .

The same location in a networ7 gives two different values of current for three- or two-phasefaults with a ratio &.'"" between them. 4or e3ample, a =.' 7< three-phase fault would give a&.1 7< two-phase fault at the same location. Therefore, a three-phase fault has to beconsidered for estimation of design forces.

4igures = (top and @ give e3amples of currents and forces on horiontal, or purely vertical,

arrangements. )n the case of an e8uilateral triangular arrangement, 4igure = (bottom, theforces are similar on all three phases, similar to the force on phase 1 for the horiontalarrangement.

4igure @ shows the currents and forces applied to each phase during a three-phase fault withan asymmetry chosen to create the ma3imum peak force on one outer phase as calculatedusing 8uation . This is for a horiontal or vertical arrangement of the circuit. The faultcurrent is =.' 7< rms with pea7 currents of !&.=, #!., and "1. 7<. The time constant is #&ms, and the short-circuit duration is &.=@ seconds. The current fre8uency is @& %. The loadsshown are per unit length for a H " m clearance between phases. The repulsion pea7 load on

phase 1 is ' 5Bm. (φ H 1.! rad. The signs convention is positive in the directions shown in

the upper diagram in 4igure =.

9ut the time dependence of the forces is very different on the outer phases compared tomiddle phase. ;n the outer phases, the force is unidirectional and has a significant continuouscomponent. ;n phase , the continuous component is ero (e3cept during the asymmetrical

part of the wave.

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4igure = Two different geometric arrangements for a three-phase circuit and theelectromagnetic force reference directions on each phase corresponding to 8uation . Thenumbers 1, , and are phase numbers.

)t must be noted that the level of the pea7 force, about && 5Bm in 4igure @, is far greater thanthe conductor weight and is proportional to the s8uare of the current. 9ut the continuouscomponent 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 theother direction. See upper right panel in 4igure @.

4igure @ 3ample of calculated three-phase short-circuit current wave shape andcorresponding loads on a horiontal or vertical circuit arrangement.

1&

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Thus the interphase effects, for the case of horiontal or purely vertical arrangement only,may be summaried as6

1. The design force on the horiontal or vertical three-phase arrangement is the force due to athree-phase fault considering the outer phase with appropriate asymmetry. Ta7ing intoaccount the fact that only the continuous dc component has to be considered, the force on

an outer phase can be appro3imated by 8uation . This is the horiontal repulsion forcefor the horiontal arrangement, or the vertical repulsion force for the vertical arrangement6

- - B

.

&.(&.#@ 1."1" t F I e

a

τ −= + (5Bm

Ghere

a is the interphase distance (m.

I 3 the rms three-phase fault at that location (7<.

τ is the networ7 time constant at that location (s.

t is time (s.

. The forces considered above cannot be directly applied to structure design loads, becausethe structural response to these loads has to be ta7en into account.

The continuous dc component acting after the short transient during the asymmetrical period of the current is obtained by using t H infinity in 8uation . 4or e3ample, in4igure @, the continuous dc component after transient is given by6

-&. =.' &.#@ &."

F x= = 5Bm

11

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3. BEHAVIOR OF BUNDLE CONDUCTORS UNDER SHORT CIRCUITS

:etailed behavior of bundle conductors under short circuit is most easily illustrated throughshort-circuit tests in actual bundles. Some results from a program of tests at the Cei7isubstation in %ungary are used here for that purpose (/ilien and 0apailiou &&&.

The systematic single-phase fault tests on twin conductors were performed in the 1!!&s on a power line with a double deadended span, with a length of "& m, with the followingcharacteristics (4igure "6

Span length "& mSub conductor type <S+ ;5:;+ (=@@ mmJ, φ H #.# mm, 1.@ 7gBm, 2TS 1@ 75Spacing &.=@# murrent @ 7< (!& 7< pea7, Time constant ms:uration &.1# to &. sSagging tensions 1@, @, or @ 75 (per subconductor<ll cases are single-phase faults$ the return path is through the groundSupporting structure6

Stiffness6 about '.@ 1&" 5Bm4irst eigen fre8uency6 about 1= %

4igure " Test arrangement applying short circuits to a "&-m span length with onespacer at mid-span. (/ilien and 0apailiou &&&.

measurement

"& m

1

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4igure # Two test span arrangements for spacer compression tests (/ilien and0apailiou &&&.

4igure # shows installation of rigid spacers and measurement points (bold lines for the "&-msubspan (4igure # top and &-m subspan (4igure # bottom. 4or the &-m sub-span, twospacers were installed close to each other so as to receive half the contribution. Theinstallation of measurement is such that actual load for spacers in power lines would be twicethe measured value.

The following oscillograms were recorded (4igure '. ;n the left hand side, the "&-m spanlength results are presented, and on the right-hand side, the &-m span length results are

presented. )t should be noted that the actual >pinch? occurs during the first appro3imately &.seconds, while the fault current is on, and that the other >spi7es? in the records arise fromsubse8uent motion of the bundle.

Sagging tension 15 kN - 35/90 kA

-2000

-1000

0

1000

2000

3000

4000

0 0,2 0,4 0,6 0,8 1

time (s)

c o m p r e s s i v e l o a d ( N )

subspan length 60 m


-3000

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0

1000

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3000

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5000

6000

0 0,2 0,4 0,6 0,8 1 1,2 1,4

time (s)

o m p r e s s v e

o a

s

N )

subspan length 30 m

measurement

& m & m

1

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-4000

-2000

0

2000

4000

6000

8000

0 0,2 0,4 0,6 0,8 1 1,2 1,4

time (s)

C o m p r e s s i v e l o

a d s ( N )

subspan length 60 m


-4000

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0

2000

4000

6000

8000

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

time (s)

C o m p r e s s i v e

l o a d ( N )

subspan length 30 m


-3000

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0

1000

2000

3000

4000

5000

6000

7000

0 0,2 0,4 0,6 0,8 1 1,2 1,4

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C o m p r e s s i v e l o a d s ( N )

subspan length 60 m


-3000

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0

1000

2000

3000

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7000

0 0,2 0,4 0,6 0,8 1 1,2 1,4

time (s)

C o m p r e s s i v e l o a d s ( N )

subspan length 30 m

4igure ' Typical tests results on spacer compression on "&-m and &-m subspan length, at @7< on twin-bundle line 3 ondor, with different sagging tensions. %alf of the compression isgiven. The drawings are covering short-circuit and significant after short-circuit time to bettersee the wave propagation effects after the end of the short circuit. (ourtesy 0fistererBSefag.

<fter the short circuit, the subconductors separate from each other during a long transient,with wave propagation along each subspan (as can be seen in the video that accompanies this

boo7 and in 4igure '. :uring that transient, significant tensile forces (the opposite ofcompression are applied on the spacers, the level of which reach about @&A of the ma3imumcompression load. )n spite of their smaller magnitude, the effect of these tension forces on thespacer must be considered separately, because some spacer attachments are not as strong intension as they are in compression. < particular e3ample is the attachment using an open or>saddle? clamp, with helical rods to capture the subconductor. These loads are repeated withevery passage of the wave up and down the span. 5ote the shorter repetition time in the &-mspan. These loads decay very slowly, so that many repeated such loads have to be ta7en intoaccount.

The graphs in 4igure ' show the effect of gradually increasing initial tension before the faultfrom 1@ 75 (1.@A :S to @ 75 ('A :S. The effect on propagation speed can be seen

in the after short-circuit pea7s, but the influence on ma3imum pinch is limited in actual range,as predicted by Manuio (the pinch being proportional to the s8uare root of the tension, and it

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is particularly valid for long subspans, as used in power lines and as validated by ManuioKstest arrangements (Manuio 1!"#.

)n case of spring-type dampers, which could be compressed by the pinch, there could be alarge increase of these tensile loads acting on spacer attachment as the rela3ation of energystored in spring compression during short-circuit is released after the end of the short circuit.

:epending on the configurations of the spacer and spacer dampers, the short-circuit forcescould cause large bending moment in the conductor and the elements of the spacer.

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<, &.1' s courtesy0fistererBSefag.

)n these tests, limited to one-phase fault, there is no interphase effect but, due to the incrementin tension caused by the pinch, the whole phase jumps up after short-circuit inception andfalls down afterwards. This behavior induces some tension changes in the conductors, as can

be seen in 4igures ! and 1&. )t is notable that the pinch effect (the first pea7 during the fault inthe first &.1' s in the conductor has a smaller tension rise than that which occurs, at &.!seconds, as the phase falls. )n both cases, the latter is limited to 1.' times the initial staticsagging tension.

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4. 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 horiontalarrangement ()*+ 1!!". 9oth cable tension versus time (4igure11 left and phasemovement in a vertical plane at mid-span (4igure 11 right are shown. ;n the cable tensioncurve, 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 beenmar7ed by dots every &.1 s to get an idea of the cable speed, and in particular to show that theshort circuit ends before there is significant movement of the phase.

Typical ma3imum loads (4igures 11 and 1 that could influence design appear when totalenergy (including a large input during short circuit has to be mainly transformed todeformation energy.

0ea7 design load could occur under the following three conditions6

1. Ma3imum swing-out 4t (at time tt in 4igure 11left and s8uare 1 in 4igure 11 right 6 verylittle 7inetic energy (cable speed close to ero and potential energy with reference togravity, so that a large part is converted in deformation energyIthat is, increase oftension. )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 4f at the e3treme of downward motion (at time tf in 4igure 11 left and s8uare in 4igure 11 right 6 generally more critical because of a loss of potential energy of gravitydue to the cable position at that moment. tf always occurs after the end of the short circuit.

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

effect only occurs with bundle conductors, when subconductors come close to each other6t pi always occurs during short circuit.

4igure 11 /eft 4igure6 Tensile force (left time evolution of a typical twin-bundlespan during two-phase short circuit between horiontal phases. Three ma3ima6 4 pi attime T pi (so-called pinch effect, due to bundle collapse, 4t at time Tt (the ma3imumof the force due to ma3imum swing of the span represented by circle point 1 on theright figure, and 4f at time Tf (the ma3imum of the force due to cable droprepresented by circle in the right figure. Typically, T pi -=& ms, Tt N1. s and Tf H = s

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+ight figure6 Movement of one phase (right in a vertical plane at mid-span (F and Oare the two orthogonal a3es ta7en in the vertical plane at mid-span, perpendicular tothe cable. O is vertical, -1& m is the initial point showing sag, and F is horiontal andtransverse 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 @#&mm <ST+ on a =&&-m span length (sag 1& m (/ilien and :al Maso 1!!&.

)t is interesting to compare the level of these loads with typical overhead line design loadsrelated to wind or ice problem (lectra 1!!1. 4igure 11 shows results of such a casecalculated by simulation on a typical =&&-7C overhead line configuration. 4igure 1 showscable tension versus time in different dynamic loading conditions, as e3plained in the legend.)t can be seen that cable tensions due to short-circuit currents are significantly smaller thanother causes such as ice shedding.

4igure 1 Simulated longitudinal loads applied on attachment point on a cross arm on a

>9eaubourg? tower (the circuit configuration is shown by points T, +, and S in 4igure 1 forloading conditions (/ilien and :al Maso 1!!&61. three-phase fault of #. 7<. two-phase fault of " 7<. initial wind of "& 7mBh followed by a gust at 1&& 7mBh for @ seconds on a 8uarter of the

span=. shedding of ice sleeve of " 7gBm

!eduction in Phase Spacing

<fter the initial outward swing, the phases move towards each other. 4or the case illustratedin 4igure 11, this inward movement e3ceeds = m per phase. That means a phase-spacingreduction of more than ' m. ;ther cases are shown in 4igures 1 and 1= (only the rectangularenvelope of the movement is given for different configurations and short-circuit level.

The timing of this inward swing may be such that the phase spacing is less than the criticalflashover distance at the time that voltage is restored by automatic reclosure. That wouldinduce a second fault with the dramatic conse8uence of a loc7-out circuit brea7er operation,with all its conse8uences (power outage.

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4igure 1 alculated envelopes of phase-conductor movements for three types of loadingconditions on a >9eaubourg? tower (the figure is drawn in a vertical plane located at mid-span6 +, S, and T are their phase locations in still conditions (/ilien and :al Maso 1!!&61. two-phase short-circuit " 7< either +T, +S, or TS. three-phase short-circuit #. 7<. initial wind speed of "& 7mBh followed by a wind gust at 1&& 7mBh during @ s on a 8uarter

of the span.

4igure 1= alculated envelope of phase-conductor movements for two-phase faults ofdifferent rms amplitude (/ilien and :al Maso 1!!&.

Distribution Lines

<s mentioned earlier, very large movements may be seen on distribution lines (4igure .4igure 1@ shows a case of two circuits on the tower, where the faulted circuit forces some ofits phases to get in contact with the second (healthy circuit, inducing a fault in the othercircuit so that both circuits trip out.

%ow to estimate the re8uired interphase spacing is discussed further in Section @ (8uation '

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4igure 1@ Three-phase short-circuit on 1@-7C line (left circuit, with autoreclosure. a H faultinception, b H &.1 s, end of the first fault, c H&.= s, time of reclosing, and d H 1.= s end of thesecond fault and definitive removal of the voltage on the line. Short-circuit of #&& < on a1"@-m span length, conductor !. mm <<< (/ilien and Cercheval 1!'#.

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5. ESTIATION OF DESIGN LOADS

The most critical effects on power lines are6

1. 4or bundle conductors6 spacer compression (8uation =.

. 4or power lines in general, but particularly for distribution lines6 reduction in phase

spacing (8uation ' for high-voltage line.

. To a much lesser e3tent, and generally having negligible effect compared to other 7ind ofloading6 tension increase generating longitudinal and transverse loads (8uation # forlongitudinal load due to interphase effect.

The loads under no. above due to short circuits should be considered by line designers byincluding them in the loading schedule for structures. Since there are three ways to have one

phase fault, three to have a two-phase fault, and one to have a three-phase fault, there may beseven different loading conditions. They must, of course, be ta7en separately, since theseevents cannot occur simultaneously.

<dvanced calculation methods (/ilien 1!', l <dnani 1!'#, Gendt et al 1!!", :eclerc81!!', Stein et al &&& may be used for any situation.

Bundle Conductors in Transmission Lines

Manuio developed a simple method for spacer compression effect in bundle conductors(Manuio 1!"#.

1&log ( B

c st s F kI F s φ = (5 =

Ghere6

4st is initial sagging tension for each subconductor (5.

k is a correction factor depending on the number of subconductors.

7 twin H 1.@#.

7 trippleH 1.==.

7 8uad H 1.#.

) is the rms short-circuit valueBphase (7<.

s is the bundle diameter, related to subconductor separation >as? by the formula (n H number

of subconductors6sin(1'& B

sa

sn

=°

(m @

φs is the subconductor diameter (m.

Example:

1

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onsider a case of a short circuit of @ 7< (rmsBphase acting on a twin <S+ ondor (#.#mm diameter conductor with &.=@# m conductor separation, tensioned at @75Bsubconductor. 8uation = gives a spacer compression force of6

1&1.@# @ @&&& log (&.=@# B &.&## !@'"

c F x x = =

%owever, in the analysis by Manuio (Manuio 1!"#, short-circuit current asymmetry wasneglected.

That has been ta7en into account in ) "&'"@ for evaluating the ma3imum tension in theconductor during fault. 9ut ) "&'"@ gives no recommendation for spacer compression.

;ther methods to estimate spacer compression forces have been proposed (%oshino 1!#&$0on et al. 1!!$ /ilien and 0apailiou &&&. Some tests performed in anada (0on et al. 1!!on spacer dampers for power-line-estimated spacer-compression design load up to & 75 fortypical configurations and anticipated short-circuit levels.

ManuioKs method can be safely applied to faults with ma3imum asymmetry through a correctionfactor of @A (multiply all k factors by 1.@. )n fact, ManuioKs method is very simple to applycompared to other methods. )t may not be accurate enough for use with respect to substationfle3ible bus.

<lternatively, if we define 4 pi (as shown in 4igure 11 as the ma3imum tensile load in onesubconductor during the bundle pinch, another best fit would be to use Manuio method (withoutcorrection factor, but using 4 pi pinch value instead of initial static pull. 4 pi can be evaluated by )"&"'@ method.

4 pi increases linearly (and not with the s8uare with short-circuit current. That is because a stronger

short-circuit current will increase contact length, thus reducing acting parts of the conductors.

ote: In the use of IE! method "0#"$ to e%aluate F pi & there is a need to introduce the so'

called supporting structure stiffness* In this application& that stiffness is not simpl+ the

static stiffness of supporting structure& but must take into account insulator chain mo%ement

during the first tens of milliseconds of the fault to arri%e at an e,ui%alent stiffness (which in

fact would permit e%aluation of span end mo%ement& from short'circuit inception up to the

maximum pinch %alue& after about -0 to .0 ms /n heuristic e%aluation indicates that a good

estimate for such e,ui%alent stiffness ma+ be to consider in most of the practical cases a %alue

of 0$ 1m

Despacering as a Means to Limit Pinch Effect

:espacering (removal of spacers is an antigalloping measure (see Section =.@ for some power lines. )t has been used up to the =@-7C level for twin bundles of limited diameter. )nsuch cases, the bundle is turned in vertical or slightly obli8ue position, and conductorseparation is increased compared to a spacered bundle. Moreover, it has been recommendedto use larger subconductor spacing at the middle of the span (compared to end of the spanI for e3ample, &." m at ends and &.' m at mid-span.

Such configurations may suffer from the >7issing? phenomenon under high electrical load, because electromagnetic forces also act under load current. <t such current levels,nevertheless, the electrostatic repulsion (due to voltage cannot be neglected. )t can be shown

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that, at surge impedance loading (S)/, e8uilibrium e3ists between attraction and repulsionforces. 0ower flows are often several times (up to four times the S)/, so that attraction forcesare generally stronger than repulsion. ;ne of the major problems of such configurations islin7ed to possible stic7ing of the subconductors following a perturbation. <s electromagneticforces depend on distances, there e3ists a distance under which the subconductors alwayscome together and stic7 together, and it is very difficult to separate them without opening the

circuit. Stic7ing induces large permanent noise and increase in corona. To avoid such problems, line designers have developed several proposals li7e the >hoop? spacer (see Section=.@.

2nder short circuit, these configurations result in clashing between subconductors and, as>subspan? length (H span length in this case is very large, there is little increment in tension.9ut, in the case of hoop spacers or similar, the conductor clashing destroys these light spacers

beyond a certain level of short-circuit current.

Interphase Effects" Estimation of Tension Increase and !eduction in Phase Spacing

The following discussion pertains to the case of horiontalBvertical configuration and neglectstemperature heating effects (/ilien and :al Maso 1!!&. ;nly one span is considered.

a H interphase distance (m.

m H mass per unit of length of one phase (7gBm.

)rms H root mean s8uare of the three phase short-circuit currentBphase (7<.

τ H time constant of the short-circuit asymmetric component decay (s.

tcc H duration of the fault (H time of first fault N time of second fault if auto-reclosing (s.

2 H span length (m.

Tst H phase conductor static tension before the fault condition (5.

E/12 H conductor e3tensional stiffness (product of Poung modulus times cross sectiondivided by span length (5Bm.

H tower stiffness (5Bm (order of amplitude 1&@ 5Bm.

f H initial sag (m.

4 H ma3imum displacement (m.

1. The energy imparted to the conductor is given by6

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--

&

&. ( 1 . . =

rms cc I t 2

E m a m

τ += (Qoules "

. The ma3imum tension in the conductor during movements6

- &

ma3

st

E 5 5

2

E/

= ++

#

. The ma3imum displacement of one phase (ero to pea76

-

- -&

E 4 f f

mg2

÷

= + − ÷ ÷ ÷

'

That ma3imum may be observed in the case when the conductors are moving away fromeach other. 9ut phase spacings can be critical when the phases move bac7 towards eachother, in which case there is generally lower displacement (say, '&A of the separationmovement. )n this case, the clearances may be reduced (the most dramatic case being atwo-phase fault by 3 &.' 3 + or 1." +.

=

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The combined values of Tma3 and + result in a transverse load on the suspension tower inthe case of a horiontal arrangement, for e3ample.

There is very limited e3perimental validation of these formulas, because full-scale tests on power lines have not been conducted.

)t must be noted that advanced methods (finite elements can be used to evaluate theseeffects (details are given in )*+ brochure 1=-&&.

)t is estimated that these formulas give results with &A precision on the conservativeside.

Example:

4or e3ample, consider the following6

Short-circuit current at " 7< during 1&& ms (with time constant "& ms on a twin <ST+@#& mm (m H 3 1.@@ H .1 7gBm with interphase distance a H '.@ m, span length of =&&

m and initial sagging tension of 3 1&&& H "&&& 56

nergy imparted to the conductor using 8uation "6

- -- -

&

&. ( &. " (&.1&& &.&"&1 1 =&&. .1 . 1&'&

. = '.@ .1 =rms cc

I t x 2 x E m

a m x

τ + += = =

Qoule

s

Gith conductor Poung modulus H @." 3 1&1&

5Bm

and tower stiffness of RH @ 3 1&@

5Bm,the ma3imum conductor tension is calculated as6

-

ma3

1& " @

1&'&"&&& ##1#

=&&

@."1& @#&1& @1&

x5

x x −

= + = + ÷

5ewtons

<ssuming an initial sag of !.' m, the ma3imum displacement of one phase is 6

- -

- - -& 1&'&!.' !.' -#.''- -

.1 !.'1 =&&

E 4 f f

mg2 x x

÷ ÷= + − = + − = ÷ ÷ ÷ ÷ ÷ ÷

means + H @. m

Thus the reduction in phase spacing is 3 &.' 3 @. H '. m.

)t means that the remaining clearance is '.@ - '. H &. m.

4or the same case at =@ 7<, the results are6

& H '1 Qoules

Tma3 H ""#& 5

@

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+emaining clearance H =. m

)t can be noted that that energy varies as the fourth power of the short-circuit current.

This is due to the fact that short-circuit forces vary with the s8uare of the current, so the speedof the conductor at the end of the short-circuit also varies with the s8uare of the current, andenergy in the system varies with the s8uare of that speed.

The Case of #umpers

<t deadend structures, jumpers are used to connect the adjacent spans. These jumpers alsoreact during short circuit6

)nterphase forces may cause jumper swing with possible drastic reduction of clearance withtower legs or cross arms. Such effects may easily be limited by installation of appropriatehold-down weights.

)n case of bundle configuration, subspan length in the jumper cannot be large. Thus, the pinch

effect may cause the jumpers to bound upward toward the tower cross arms. 2se of shortsubspans in jumpers may be recommended to avoid clashing. Their use in substations may beof interest in that connection.

+eference ()*+ 1!!" e3plains how to choose short subspans to avoid conductor clashing.

Interphase Spacers as a Mean to Limit Clearances Problem Lin$ed with Short Circuit

)nterphase spacers have been proposed to solve the phase-clearance problem during shortcircuits (:eclerc8 1!!'. 3perience has shown that appropriate installation of such devicesmay effectively maintain appropriate clearances since conductor movement is restricted atsome location in the span.

< major challenge is defining the design load on these interphase spacers. Tests can be performed, and some are available on the video accompanying this boo7. <dvancedcalculation methods may also help to define these loads. )nterphase spacers may be subjectedto bending stresses induced by conductor movements.

"

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!. REFERENCES

Manuio . 1!"#. /n in%estigation of forces on bundle conductor spacers under

fault conditions ) Trans. ;n 0ower <pparatus and Systems, V"#. $!, 5E, 1!"#, pp1""-1'@.

Seriawa, 1!"#. P. 6eha%iour of dead'end suspension double'conductor bus during

short'circuit . The Qournal of the )nstitute of lectrical ngineers of Qapan, V"# $%, 5E11, 5ov 1!"#, pp 1&&-111

%. %oshino, 1!#&. Estimate of forces exerted against spacers when fault+ condition

occurs. ) Trans on 0ower <pparatus and Systems, V"#. $&, 5E#, pp 1=#@-1='=

/ilien, Q./ 1!'., !ontraintes et cons7,uences 7lectrom7cani,ues li7es au passage

du courant dans les structures en cables. 0h: 1!'. ollections des publications dela 4acult des Sciences <ppli8ues de lK2niversit de /iDge, 5E'#

Tsana7as, :.$ 0apadias, 9.#3 Influence of short'circuit duration on d+namic

stresses in substations. ) Trans. 0ower <pp. Syst. 1& (1!', pp =!-@&1

l <dnani, M. 1!'#. Efforts 7lectrod+nami,ues dans les liaisons 8 haute tension

constitu7es de faisceaux de conducteurs. 0h: 1!'#. ollections des publications dela 4acult des Sciences <ppli8ues de lK2niversit de /iDge, 5E11.

/ilien, Q./., l <dnani M., 1!'". Faisceaux de conducteurs et efforts

7lectrod+nami,ues 9ers une approche num7ri,ue fiable 0roceedings of )MontechK'" onference on < 0ower Systems. 0p #!-'=

Q./. /ilien, 0. Cercheval. 1!'#. roblems linked to changes in the arrangement of

double circuit line conductors. )nternational onference on lectricity :istribution.)+: 1!'#, session (cable and overhead lines. 0roceedings , report d.&= ("

pages.

) "&!&! 1!''. Short'circuit current calculation in three'phase a c s+stems.*eneva6 ), 1!''

2oading and strength of o%erhead transmission lines /T+< nE1#. 1!!1(published by G* &" of S .

M.9ulot, /.:emoulin 1!! . !ontribution of 4eliabilit+ anal+ses to the stud+ of the

effects of short'circuit& 0roceedings of the @th )nternational symposium on short-circuit currents in power system.

M.*audry, P.Maugain 1!! Influence of the wind on the mechanical design of

transmission structures against short'circuits, 0roceedings of the @th )nternationalsymposium on short-circuit currents in power system

. 0on, <. *oel, S. Rrishnasamy, %. *rad. 1!!. !ompressi%e loads on spacer'

dampers due to short'circuit currents. < report. Transmission Section, linehardware subsection, March &, 1!!, Montral, ubec.

#

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) "&'"@-1 1!!. Short'circuit currents ' !alculation of effects art :

;efinitions and calculation method& *eneva6 ), 1!!

5 "&'"@-1 1!!. Short'circuit currents ' !alculation of effects art :

;efinitions and calculation method . 9russels6 5/, 1!!

) "&'"@- 1!!=. Short'circuit currents ' !alculation of effects art <: Examples

of calculation. *enDve6 ), 1!!=.

*. de Gendt, T. Tiet, <6M. Miri, +. <hlers, 5. Stein 1!!" ;+namic and Static

!ase Stress /nal+sis of a =9 Substation with Stranded !onductors (5est'4esults'

!alculation). 0roceedings of the >th Int S+mposium on short'circuit currents in

ower S+stems& 1!!".

)*+-1&@ 1!!". 5he mechanical effects of short'circuit currents in open'air

substations (4igid and flexible bus'bars) 0aris6 )*+U, technical brochure 5E1&@. volumes (1'& pages.

:eclerc8, *.1!!'. 5ests with droppers and interphase spacers. 0roceedings of the'th )nternational Symposium on Short-ircuit urrents in 0ower Systems, 9russels(9elgium, '-1& ;ctober 1!!', 0roceedings pp. 1=-1='

Stein, 5.$ Meyer, G.$ Miri, <.M. &&& 5ests and !alculation of Short'!ircuit

Forces and ;isplacements in =igh 9oltage Substations with Strained !onductors

and ;roppers. T0 1& (&&& 5o. , pp 11V1'

Q./. /ilien, . %ansenne, R.;. 0apailiou. Q. Rempf <000 Spacer !ompression for a

tripple conductor arrangement . ) Trans. ;n 0ower :elivery, V"#. 15, 5E1, pp"-=1, Qanuary &&&.

Q./. /ilien, R.;. 0apailiou <000 !alculation of Spacer !ompression for 6undle

2ines under Short'!ircuit . ) Trans. ;n 0ower :elivery, V"# 15, 5E, pp'!-'=@.

)*+-1= &&. 5he mechanical effects of short'circuit currents in open'air

substations (4igid and flexible bus'bars) (art II) )*+U, technical brochure 5E1=. volumes (&& pages.

Q./. /ilien and 4. :al Maso, 1!!& !ontribution to 2ine ;esign b+ /ccurate

redetermination of Se%ere but ?ccasional Stresses )*+ 0lenary session, 1!!&,

0aris, +eport -1&.:.*. %avard, .Q.0on, %.<.wing,*.:.:umol and <.. Gong, .#"& robabilistic

Short @ !ircuit uprating of Station 6us S+stem'Aechanical /spects& ) 0S

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