IEEE Transactions on Power Apparatus and Systems, Vol. PAS-100, No. 4, April 1981EXPERIMENTAL INVESTIGATIONS OF CORONA-INDUCED VIBRATION
ON HIGH VOLTAGE CONDUCIORS 1WIT11H DIFFERENT TYPES OF SUPPORTS
Luan C. Phan, Senior Mrtber, IEEELhiversitd du Qu6bec a ChicoutimiChicoutimi, QuEbec, Canada.G7H 2B1
Takayoshi AdachiYamaguchi UniversityTbkiwadai, Ube, Japan
Marc-Andre AllaireUniversit6 du Qu6bec a ChicoutimiChicoutimi, Qudbec, Canada.G7H 2B1
ABSTRACT
Although corona-induced vibration has been ob-served on power-line conductors under wet weather con-ditions, very few experirmntal studies have been pub-lished on the subject.
In order to investigate the range of electricalfields in which different types of vibration may occur,three experimental set-ups are made with a conductorinstalled in the center of a cylindrical mesh cage.
In the first set-up, a smooth conductor is simplysupported at the two ends by insulators (beam type ofvibration). In the second arrangement, the smooth con-ductor is suspended by two pairs of springs, one ateach end (mass-spring system). In the third set-up, amechanical tension is applied to the two ends of anACSR stranded conductor. Six nozzles are used to spraythe conductor with a controlled precipitation intensi-ty-
In the mass-spring type of vibration, the conduc-tor vibrates in a small range of electrical fieldstrengths between 5.5 ky/cm and 13 kV/cm at the con-ductor surface. With the beam type of vibration it isfound that the precipitation intensity has no effectupon the amplitude of the vibration and the coronacurrent. However the time constant of the vibrationbuild-up decreases with increasing precipitation in-tensity. The amplitude of the vibration increases withincreasing applied fields strengths (without turningoff the H.V. source) above 11 ky/cm. On the other hand,with decreasing applied fields the amplitude of vibra-tion is zero at field strengths above 22 ky/cm; it in-creases with decreasing fields up to a maxirmn at ana.c. field of about 20 kV/cm or a d.c. field of 18kV/cm.
Mechanical energy, damping energy and input elec-trical energy fed to the conductor are also calculatedor measured as a function of the applied electricfield.
The width of the ranges of electric field inwhich steel-reinforced aluminium conductor (ACSR) vi-brates increases with the natural frequency of thesystem. At constant natural frequency the amplitude ofthe vibration of an ACSR conductor is small under acapplied voltage and highest under negative dc voltage.From the damping energy and the amplitude of the vi-
bration measured, the corona-induced force per unitlenght of the ACSR conductor used is estimated.
Amnng the three experimental arrangements used,it is observed that, within the range of the electricfield strengths on actual transmission lines, the vi-bration of the conductor is very strong when it issimply supported.
INTRODUCTIONAn unavoidable consequence of the transmission of
electrical energy at high voltage or extra high voltageis the corona. Together with corona loss, radio andtelevision interference and audible noise, vibration ofthe conductors are generally induced under wet condi-tions. The observed phenomena of corona-induced vibra-
tion has been the subject of several publications [1,2,3,4,5,61 and same technical reports. According tothese observations, the critical voltage gradient tocause this phenomenon is between 15 and 23 ky/cm.It has also been observed [21 that the critical fielddecreases with increase in conductor diameter and a re-duction of the line voltage stopped the vibration. Theamplitude of the vibration is less than 10 cm with amaxinum observed at about 120 cm. The frequency variesfran about 0.7 to 5 Hz. A laboratory study under HVDC[71 showed that vibration occured even at a low gradi-ent voltage of 11 ky/cm. An analytical study of thephenomenon is attempted recently by Shah and Mbrgan [81.However, more experimental studies are needed before acomplete analytical study is undertaken.
In order to investigate the range of electricfield strength in which different types of vibrationmay occur, three experimental set-ups with differenttypes of supports are built at the University of Quebecat Chicoutimi.
EXPERIMENTAL ARRANMENTS
Set-up 1: Beam type of vibration
In this set-up, a smnooth hollow aluminium conduc-tor is simply supported at two ends by the insulators(Fig. 1). The test conductor is placed at the axis of acylindrical mesh-cage. The cage has an ID of l m and thethree parts are isolated from each other: the centralpart has a 2 m length while the two end sections have alength of 0.3 m and a lateral curvature equal to the
Dimension in m
80 SM 682-5 A paper recommended and approved by, theIEEE Transmission & Distribution Committee of theIEEE Power Engineering Society for presentation atthe IEEE PES Summer Meeting, Minneapolis, Minnesota,July 13-18, 1980. Manuscript submitted January 24,1980; made available for printing June 6, 1980.
Fig. 1 Experimental arrangement with a conductor sim-
radius of the central cage. Tap water is sprayed fransix nozzles Wagner No 5 at an angle of 300 with thevertical plane containing the conductor. Angle of theconical spray of these nozzles is 60°. Current pulsesare measured with a large band Hewlett Packard VTVM4100. The amplitude of the vibration is measured withstrain gauges connected to a Vishay Instrument strainindicator model P350A.
Set-up 2: Mass-spring type of vibration
The conductor is suspended in this by two pairsof springs of equal stiffness. Although this experi-mental arrangeme.nt simulate satisfactorily only thecentral part of a real transmission line span, it hasthe advantage in its simplicity and its vibration atlow frequency. Therefore this set-up is used to inves-tigate the mechanism of the corona-induced vibration[7,91.
Set-up 3: Vibration of an ACSR stranded conductor
This arrangement is similar to the first set-upbut an ACSR stranded conductor is used instead of asmooth conductor. Also, in order to keep the strandedconductor straight, a mechanical tension is applied tothe two ends of the conductor. Dimension and weight ofnine conductors used are given in Table I (free lengthOf Vibration for conductors E,F,G and ACSR).
TABLE I
Dimensions and weights of conductors used
ejected now with a momentum, a mechanical reactiveforce upwards will be felt by the conductor, which ispushed up this time by the sum of the mechanical reac-tive force and the electrostatic forces. As the aboveprocess continues, the mechanical reactive force in-creases and the amplitude of the vibration increasesuntil the up and down motion of the conductor is syn-chronized with the ejection of the drops.
From the above mechanism, it can be seen that thefrequency of vibration is thus approximately the naturalfrequency of the system and the intensity of the vi-bration depends upon the above mentioned mechanicalreactive force of the conductor, in other words, uponthe way the conductor is suspended, i.e. on the exper-imental arrangement.
1.- Set-up 1 (beam type of vibration).
Fig. 2 shows the effect of the precipitation rateon the amplitude of the vibration, corona current orleakage current mre exactly, and the vibration buildup time, the electric field being kept constant (16.5kV/cm). It may be seen that the build up time con-stant To decreases with increasing precipitation rate,due to the decrease of the time interval needed to re-cover the lost water of the suspended drop between theejection of droplets. On the other hand, in a steadystate of vibration, the amplitude of vibration and co-rona current are nostly constant while 1± precipitationrates are varied between 2 and 6 cm/h. Therefore, aconstant precipitation rate of 2.6 cmh is used in allthe following experiments.
A
__GS (ACSRnodified*)
Dia.(an)
1.825
Length(an)
300
Weight(kg)
1.24
B 2.3 300 1.735
C 2.65 300 1.54
D 3.25 300 1.313
E 1.6 357 0.69
F 3.2 357 1.56
3.8 357 3.25
2.15 284 1.97ACSR
(Carillon) 3.05 358 5.92* reinforced by a copper tube of 1.47 an in diameter.
RESULTS AND DISCUSSION
The mechanism of the vibration has been discussedin a previous paper L9] by the authors. It may be sum-marized as follows: under wet conditions and in thepresence of an electric field, suspended drops areformed at the lower surface of the conductor. Thesesuspended drops are strained under the electrostaticpressure until the ejection of a drop (or droplets).Then electrostatic forces, namely the coulomrbian re-
pulsive force between the ejected drops and the sus-
pended drops and the reactive force due to ionic windpush the conductor up. The resulting force is weak atfirst. Meanwhile the suspended drops recover the lossof water and strained again under the electrostaticpressure. On the other hand the conductor, by itschange in direction at the lowest position contributesto the ejecting force.Since the drops (or droplets) are
s To20
16
cmIA2
4
OL
Conductor F-90kV (-16.5 kV/cm)
.J A
20 30 40 50
Precipitation rote (mm/h)
I
60
gA90
8070
Fig. 2 Effect of the precipitation rate on differentparameters.
Current patterns at different states of vibrationof the conductor are shown in Fig. 3: During the build-up of the vibration, current pattern contains a d.c.ccponent while in a steady state the d.c. componentis nearly zero and the frequency of current pulses isequal to the natural frequency of the system (6.8 Hz).Detailed examination of the shape of the current pulsesshows that during the first second of the build-up ofthe vibration crackling corona [101 is observed, thensmall corona pulses (hissing corona) [101 are super-imposed on a d.c. canponent. The amplitude of thesecurrent pulses increases with increasing amplitude ofthe vibration.
In this experimental arrangement the conductor isin the first node of vibration with maximmn amplitudein the center. The other modes of vibration are notobserved. Fig. 4 shows the peak-to-peak amplitude ofvibration at the center of the conductor F as a func-tion of electrical field strength at the surface of theconductor.
l1
H.V.on
ITo
11.0cm.LOOM.
H .V.off
zus
(a) Typical recording of vibration of conductor FV=-9OkV (-16.5kV/cm)
H.V. on
1977
tern (Fig. 6) for decreasing applied voltages above110 kV (20 ky/cm). In fact, as seen previously, for thevibration to be established there must be a synchroni-zation between the current pulses (or the ejection ofdrops) and the motion of the conductor. Since each cur-rent pulse corresponds to the ejection of a drop (or astream of droplets) from the suspended drop [91, it maybe argued that wherever an important d.c. component ex-ists in the current pattern there is no synchronizationbetween the ejection of drops and the motion of theconductor, i.e. no vibration induced by corona. Resultssimilar to those reported in Figs 4, 5, 6 are also ob-tained with conductor G.
H.V. off
I=O-
l.2mA 20s A
(b) Build-up of current
I=0TW
0.2mA is
4..
Ctc
0
0S.,
(c) Current pattern in region A(f= 6.8 Hz)
Fig. 3 Current pattern at difCerent states of vibration
Conductor F (3.2 cm)0: d.c.+x : d.c.- Field decreasing
(no vibrationobserved) ! Field
8 12 16 20 24Electric field strength (kV/cm)
Fig. 5 Amplitude of current versus increasing and de-creasing applied field strength
Increasing applied voltage (kV) Decreasing applied voltage kV)0 60 90 120 160 160 130 100 90 60 0
o: d.c. +fi x *d:c:-
6O.C.
O 2 H. increasing
zo I / j | HVdecreasing_ y 1 o.cdc.
E l-.d.c.-
2 1 6 20 24 28-Electric field strength (kV/cm)
Fig. 4 Amplitude of the vibration versus field strengthat the surface of the conductor.
It is seen that the amplitude of the vibration in-creases with increasing applied fields above 11 ky/cm,but with decreasing fields, the vibration starts onlyat de field strengths below 20 ky/cm and the two curvescoincide at about 18 ky/cm. -Concurrently a strong hys-teresis loop is observed (Fig. 5): the current-fieldcurves taken with increasing potential and then withdecreasing potential coincide only at field strengthsbelow 18 ky/cm.
The absence of the vibration of the conductor atdecreasing applied fields has been observed with a realtransmission line [2-1 and may be explained by the pres-ence of an important d.c. cxxponent in the current pat-
Fig. 6 Current patterns with increasing and decreasingapplied voltages.
2.- Mass-spring type of vibration.
Fig. 7 shows the peak-to-peak amplitude of vibra-tion as a function of the applied field. It is seenthat the shape of the curves corresponding to thesmooth conductor is very different from that obtainedwith the first set-up. Also the smooth conductor sus-pended by springs vibrates at field strengths lowerthan that observed in the first experimental arran-genent, in which the smooth conductor is simply sup-ported.
Fig. 7 shows also that while the maximum ampli-tude of vibration of the mass-spring system varies withthe stiffness of the springs, i.e. with the naturalfrequency of the system, the range in which the smoothconductor vibrates is unchanged. However the electricfield strength at maximum amplitude of vibration ap-pears to increase (except the curve corresponding tofn=1.63 Hz) with the natural frequency, which is in-.versely proportional to the square root of the mass ofthe conductor. This fact may explain the decrease of
T- T
50 70 110 140 150 110 80 50
H.VU off
I=0
Conductor F (3.2 cm) 0dc-
r 1~~~~~~min
Vibration No vibration Vibrationobserved
1978
the critical field with increase in conductor size asobserved by Edward [2].
On the other hand, it is seen (Fig. 7) that an al-uminium stranded conductor reinforced by a copper tube(conductor S) vibrates at field strengths higher thanthat of a smooth aluminiun conductor. Visual and pho-tographic observations show that the base of the sus-pended drops covers always nore than a strand of theconductor. Compared to the suspended drops of the samesize, i.e. the same base, under a snooth conductor itis evident that the surface tension is larger with thedrop suspended under the stranded conductor. In otherwords, the suspended drops under a stranded conductorneeds a stronger electrostatic force to eject a drop(or a stream of droplets) and as a result the electricfield needed to excite the corona induced vibration isstronger with stranded conductor than with the smoothcoductor.
FA400sec A
02V
1--- ON
50pAI
0 kV -30kV -70WV -40W(a) Amplitude of current pulses at different rates
of vibration (build-up and damping)
E
%.2
0
._
m0
0
la
Smooth conductor D (2.35 cm)dce
oa 1.63Hzv a 1.83 Hza* 2.05 Hz
2.73HzAn 4.07 Hz
Modifiedstronded conductor
8 12 16 20 24Electric field strength (kV/cm)
Fig. 7 Vibrational amnplitude of snooth and modifiedACSR conductors in the mass-spring system ver-sus applied field strength.
The synchronization between the up and down notionof the conductor B, at 1.83 Hz natural frequency, andthe current pulses is shown in Fig. 8. In a steadystate of vibration, i.e. in region B and F (Fig. 8a)each current pulse corresponds to the ejection of adrop. Also it can be seen (Figs 8c and 8g) that theejection of drops occurs at the lower peak position ofthe conductor and scmetimes at the upperpeak position.When the vibration is in built-up or damped (regions A,
C and E, Fig. 8a) the current pulses are randcmly dis-tributed (Figs 8b, Sd and 8f). On the other hand, at-70 kV, the amplitude. of the vibration is small (Fig.8a) and the current pattern contains a d.c. cmponent.
In addition, Fig. 8e show that the ejection of the dropmay occur at any position of the conductor and the fre-quency of current pulses is higher than that of the vi-bration.
sec r 7
(b) Current pulses in region A
sec I -O-
0.2V
2HA 4'6.
(c) Vibration amplitude and currentpulses in region B
hsoc v . ... -sE --0
50sA!it- '~t!t I'I,f;Il>ftil- ttt 9gkJ
(d) Current pulses in region C
Isac 0
5O/AALI t ;
(e) Current pulses in region D
ISfc
(f) Current pulses in region E
3.- Vibration of ACSR conductor
A photograph of the experTmental arrangement isshown in Fig. 9. Fig. 10 shows the peak-to-peak ampli-tude of the vibration of the ACSR conductor used (42/7,Al/St stranding) as a function of the applied fieldstrength at the surface of the conductor. It can beseen that at constant natural frequency, i.e. constantmechanical tension applied at the two ends of the con-ductor, the amplitude of.the vibration is highest withnegative dc field and lowest with ac fields. These re-sults may be explained by the fact that usually, at thesame applied voltage, corona activities in air arestronger under negative field than that under positivefields because of the lower negative corona-onset volt-age. [The relative low amplitude of the vibration of astranded conductor under ac applied voltage, carmpared
0.2 V!
[\i \I7 1 r
10^41''A1
(g) Vibration amplitude and currentpulses in region F
Fig. 8 Current patterns at different states of vibra-tion of the mass-spring system.
vibrationamotude
lof
a c D E
A
-q
to the dc one, is observed not only with the presentset-up but also with the mass-spring system. It may beattributed to the low repulsive force between the e-jected drop and the suspended drop due to the varia-tion of the instanteneous (60 Hz) value of the ap-plied field. In addition, for ac applied fields above21 kVrms/cm, the conductor also undergoes a lateraloscillation. In fact for about 30 suspended drops perunit length of the conductor, it is observed that thereare only 20 drops located exactly at the bottom line ofthe conductor. This phenemena is not observed withsmooth conductors. In order to record only the verticalvibration two wooden supports are placed horizontallybetween the insulators supporting the conductor and thewall, as seen in Fig. 9. For a natural frequency fl Z
3.7 Hz the frequency of lateral oscillation neasured isft = 2.3 f1.
Fig. 9 Experimental arrangent for ACSR conductor.
f a 6.3Hz / ACSR conductor (3.05cm)I A )'\ x *dc-
E,0.4 _ x zacc
1979of natural frequency. Indeed in a laboratory set-up,due to the short length of the conductor,the mechanicaltension applied should be small (eq. (1)) in order toreproduce the typical natural frequencies existing onpower lines. It may be seen from Fig. 11 that the widthof the range of the electric field strengths in whichthe conductor vibrates increases significantly as afunction of the natural frequency of the system. Inaddition the field strength at maximum amplitude of vi-bration increases with the natural frequency and theratio of the frequency to the above mentioned field isnearly constant.
8 12 16 20 24Electric field strength (kV/cm)
Fig. 11 Vibration of ACSR conductor at differentnatural frequencies.
4.- Calculation of energies as a function of appliedfiel-ds.Three kinds of energy mentioned below are calcu-
lated:
Wd : damping energy i.e. energy lost by friction dur-ing one cycle of vibration (J).
W : emechanical energy in the system for a steadystate of vibration (J).
Wf : electric energy fed by the power source to theconductor during one cycle of vibration (J).
Consider first the mass-spring system set-up 2,which is simpler to analyse than the first system.
In a steady state of vibration, the equation ofmotion of the conductor is:
iy + y + ky = F(t) (2)
u -
8 12 16 20 24
Electric field strength (kV/cm)Fig. 10 Amplitude of the vibration of ACSR conductor
versus field strength.
For a constant length, L, of the conductor, thenatural frequency of the system varies with the squareroot of the mechanical tension T applied to the ends ofthe conductor [11] as
wn = 2nTrfi2 (1)where n is the vibration node and m is the mass of theconductor. In the present experiments the mechanicaltention T is varied in order to obtain different values
Where m and y are the mass and the amplitude ofthe oonductor respectively, y is the damping factor andk is the spring constant. F (t) is the sum of the elec-trostatic forces, namely the ooulcmbian repulsive forcebetween the ejected drops and the conductor, the repul-sive force between the space charge and the conductor,the reactive force due to the corona wind, the gravita-tional force of the suspended drops, the mechanicalreactive force felt by the conductor at the ejection ofdrops, etc. Thus it is difficult to determine the exactform of the excitation force F(t). However, it is seenin Fig. 8 that in a steady state of vibration, the con-ductor vibrates in a nearly sinusoidal fonm at the nat-ural frequency of the system and the energy lost byfriction per cycle, called damping energy Wd is givenby [9]
Wd = Tri wnyo2 (3)
The naperian logarithm of the ratio of the succes-sive amplitude of the conductor during the damping is
1980
defined as the logarithmic decrerent
6=log = log (YQ= e yi+l e y)i
The damping factor y can now be determined fromthe logarithmic decrement 6
n n YOy ~~log'T6
=
n e Yior
2m Yo 2m yOy iTF loge - = T- log -
n ey I e(5)
where T. = iT1 n
Figure 12 shows Ti as a function of Yo/yi obtainedduring the free-vibration (H.V. cut-off).
600 F400 F
_200 _1-
00E~100I-
\ ACSR conductorfa5.6 Hz
Set-up m
60 F
40 Fddx2.35cm
'Conductor 8 f a 1.84Hzi Set-up H
.0 0.8 0.6 0.4 0.2Amplitude ratio yi/yo
Fig. 12 Damping tin versus amplitude ratio yi/yo.
With the new value of y in equation (5), equation(3) becomes
Wd2 i (wnyo) loge yi (6)
The nechanical energy, i.e. kinetic and potentialenergy in the mass-spring system (indicator 2 indicatesset-up 2) is:
W 1 v2
and the average value is [91
W, = M2 (Wnty ) 2
(7)
(8)
Finally the electric energy fed to the conductorduring a period Tn may be approximated by:
W = VITf n
(9)
where V is the applied voltage, I is the measuredcurrent. With a smooth hollow aluminium conductor, thenatural frequency w and the damped frequency wd are
nearly equal within B.A percent. Therefore, hereafterno difference will be made between w and w In order
to evaluate the damping energy and the nec.anical en-
ergy in set-up 1, where the conductor is simply sup-
ported and the amplitude y varies sinusoidally, in asteady state, with the length of the conductor, it issuggested to divide the conductor in sections of lengthdx.
If a is the cross section of the conductor, p isthe density of the conductor, the mechanical energy ofan elementary conductor of length dx may be considered
as similar to that obtained with set-up 2 (cf. eq. (7).
1 .2= 2 padxy x)
and the rechanical energy of the total conductorof length L is
1 LWin = 2 pa 22(x)dx
0(10)
Since the amplitude of the conductor is maximum atthe center of its length (x = L) and the variation ver-sus time should be similar to that obtained in system2, y may be given by
TrXy=yOsn -L coswx t (11)
As the mechanical energy is the sum of the po-tential energy and the kinetic energy, when y = 0, y ismaximal, the potential energy is zero and the nechani-cal energy is equal to the kinetic energy
. sx
Ymax = wnyosTherefore
w in equation (10) beccnesml- 1 (wnyo) Lsin2 dx
= 2ypano) 212
L
W=M4 (Wny ) 2ml(wy)2
(12)
(13)
Compared with the expression of the mechanicalenergy of the mass-spring system (cf. eq.(8)), this re-sult shows that the equivalent mass mi of the conductorin set-up 1 is half of the real mass of the conductor.
Consequently the damping energy in the set-up 1may be obtained from equation (6) with me= m :e2f
WJdl 2i (Wnyo) loge YO (14)
Fig. 13 shows the three kinds of energy in set-up1. The coFresponding energies in the mass-spring sys-tem have b$en presented in a previous publication. Itcan be seen that Wd is very small compared to W . ButWd is the energy needed to maintain the motion gf theconductor during one cycle of vibration, which is equalto the energy consumed by friction. Therefore the totalenergy loss is very important.
n Conductor F(3.2ccm) (%)dc+
'? W 0.30
O Wd
8 Wd/Wf 0.2
1cal enryi e-p1(odco 0pysp
Ep4 p0.1
0-2~ 16 20 24 28
Electric field strength (kV/cm)
Fig. 13 Damnping energy, nechanical energy and electri-cal energy in set-up 1 (conductor simply sup-ported) under positive applied voltage.
Figs 14a, 14b, 14c show different energies in-volved in the vibration of the ACSR conductor used un-der positive, negative and ac applied fields respec-tively. These energies are calculated by the samemethod as used in the beam type of vibration. Hereagain the electric energy Wf increases with the appliedfield in the sane manner as that of the corona current,i.e. independently of the two other kinds of energy.While Wf is consumed mostly by corona activities andother losses [ 9] the average energy, per cycle, trans-mitted to the conductor in a steady state at the reso-nance is nearly equal to Wd.
.-
-o
30
0-
3
3:
8 12 16 20Electric field strength (kV/cm)
a) positive applied voltageI ... ACSR conductor
--
0V
3ibE
3~,.
1981
5.- Order of magnitude of the corona-induced force foran ACSR conductor.
Although the natural frequencies used (c.f. Fig.11) in the third set-up are in the same range as thatobserved on a transmission line E31 the similarity be-tween them is not unquestionable. Therefore it issuggested that only an order of magnitude of the am-plitude of the acting force will be evaluated in thepresent work. This order of magnitude will be com-pared with that obtained by Shah and Morgan E8] wherethe acting force is an impulsive force. To estimate theorder of magnitude of the amplitude F of the excita-tion force F(t), here after called "corona inducedforce", F(t) is approximated by a sinusoidal function.With this assumption Fo may be obtained as the ratio ofthe damping energy per cycle to the product of Tr andhalf the value of the peak-to-peak amplitude of the vi-bration [12]
F _ (15)
In set-up 1 and 2 ,due to the elasticity of smoothaluminium conductor and that of the springs, the me-chanical reactive force felt by the conductor at theejection of drops is large. As a result the peak-to-peak amplitude of vibration (Figs 4 and 7) in theseset-ups is much larger than that measured with an ACSRconductor in set-up 3. With values of W and y frconFigs 13 and 4 respectively, for an app¶ied fi8ld of16 ky/cm, the amplitude F of the corona-induced forcein the beam type of vibra?ion obtained from equation(15) is 9xl0 2N.
Fig.15 shows that the order of magnitude of coronainducqd force per unit length of ACSR conductor is cbout4xl0 N/m under ac applied voltage The maxisum valueof the vibrational force is 10 N/i under a negativefield of about 15 kV/cm. Thus the corresponding forcefor 4 conductors in a subspan of 100 m in length is a-bout 40N (4kgf). In addition, it is observed that whenthe amplitude of vibration of the ACSR conductor is im-portant (Table II, V = 60-70 kVrms), among 27 suspendeddrops per meter (Fig.16), there are 3 drops located farfrom the bottom line of the conductor. Table II- showsalso that, at the above nentioned applied voltages,eachsuspended drop ejects about 2 drops per second in anaverage. IWith a natural frequency of 5.6Hz, this resultmeans that the number of ejection per meter per cyclefrom each suspended drop is about 0.36. On the otherhand the maximum force exerted per drop on the con-ductor at an applied field of 17 kV/cm, obtained from atheoretical study by Shah & Mbrgan [8] is 2.9xl03N.Thecorresponding maxirn force per mreter exerted by 24drops located near the bottom line, with 0.36 ejection
8 12 16 20 24Electric field strength (kV/cm)
c) ac applied voltageFig. 14 Damping energy, mechanical energy and electrical
energy in the vibration of an ACSR conductor.(fn = 6.3 Hz)
Electric field strength(k/cm)
Fig. 15 Corona-induced force per unit length of ACSRconductor versus applied field strength(fn = 6.3 Hz)
1982
per cycle, is 2.5x10-2N/m. Although it is unlikely thatall the above 24 suspended drops keep a spherical shapeas supposed by Shah & Morgan the value of 2.5x10-2N/nMis still of the same order of magnitude as obtained inthese experiments.
TABLE II
Distribution and ejection of drops on an ACSR conduc-tor (fn = 5.6 Hz) under ac applied voltage
V(kV) E(kV/cn) Ns Nk Nes Nec
0 0 27 0 0.28 0.05
50 9.3 28 2.2 1.03 0.19
60 11.1 27 3.2 2.06 I 0.37
70 13 27 2.8 1.82 0.36
80 14.9 27 2.7
90 16.7 27 2.2
95 17.6 27 1.5
Ns: number of suspended drops per metertor.
of the conduc-
NI: number of drops per meter located at the lateralsurface (far from the bottom line) of the conduc-tor.
Nes: number of ejection per second per suspended drop.
N number of ejection per cycle (of vibration) perec: suspended drop.
The number of ejection per suspended drop shown inTable II is obtained from visual observation. 'Am ob-servers have counted the ejections from one suspendeddrop during 100 seconds, the operation is repeated 3tines and the obtained results are the average value of6 series of counts.
The number of suspended and "lateral" drops permeter shown in Table II is also the average number ofdrops observed on 2 m length of the conductor. This isthe reason why Ng appears in fractional numbers.
It is seen mn Table II that the number of ejectionper suspended drop is maximum at a field strength be-tween 11 and 13 kVv,s/cm. Although the amplitude of vi-bration presented in Fig. 10 corresponds to a naturalfrequency of 6.3 Hz, it is shown that the amplitude ofvibration is maximum at a field strength of about12 kVns/cm. Thus it can be argued that the amplitudeof the vibration is maximum when the number of ejectionfrom a suspended drop is maximum. Indeed the number ofejection per cycle from a suspended drop is less than 1with an ACSR oonductor in the range of natural frequen-cies used. The number of ejection at ac field strengthsabove 13 kV/cm cannot be counted visually. It appearsthat the suspended drops eject continuously small drop-lets. Concurrently the amplitude of the vibration ofthe conductor decreases. These observations are in a-greement with the results shown in Fig. 8e and alsowith the description of the shape of the ejected dropsfrom a sTooth hollow aluminiun HVDC conductor in a mass-spring configuration [9].
CONCLUSIONS
1. In the mass-spring system, which is a first ordersystem, smooth aluminium conductors vibrate in asmall range of the electric field strengths at thesurface of the conductor between 5 and 13 kV/cm.This range of electric field is independant of thenatural frequency of the system.
2. An ACSR modified conductor vibrates, in the mass-spring systen,at higher field strengths due to thehigher surface tension at the base of the sus-pended drops.
3. Smooth aluminium conductors simply supported vi-brate with very large amplitude, which increaseswith increasing applied field strengths above11 kV/cm. The amplitude of the vibration is zerofor decreasing fields above ± 18 ky/cm or 20kVrms/cm.
4. Damping energy, i.e. the energy needed to overcomethe friction, is very small conpared to the elec-trical energy fed to the conductor. The total lossof energy in the system is very important.
5. The width of the range of the electric fields inwhich ACSR conductor vibrates increases with thenatural frequency of the system, which varies withthe length of the conductor and the applied me-chanical tension.
6. Order of magnitude of the corona-induced force2perunit length presents a maximum of about 4x10- N/mfor the ACSR conductor used under ac excitation.The oorresponding vaJ,e under a negative field of15 kV/cm is about 10 YN/m.
A 0',WEGEE
This work is supported by National Research Councilof Canada and the Departnent of Education of Quebec.The authors wish to thank Dr P. Mc:Comber and Dr J.L.
Fig. 16: Distribution of drops on ACSR conductor at Laforte for useful discussions, Mr C.d'Amours for tech-E - 13 kVrrs/cm. nical help and Mr L. Lemieux for drawing the diagrams.
1983
[1] A.T. Edwards and J.M. Boyd, "Bundle-Conductor-Spa-cer Design Requirements and Development of SpacerVibration Damper" IEEE Trans. vol PAS-84, pp. 924-932, Oct. 1965
[2] A. Edward, "Conductor Galloping" Electra, vol. 12,pp. 31-48, March 1970.
[3] M.D. Powbottam and R.R. Aldham-Hughes, "SubspanOscillation A Review of Existing Knowledge",CIGRE,report no 22-02, 1970.
[4] V. Winants and M. Riez, "Conductor Galloping onOverhead Lines" CIGRE, report no 22-06, 1970.
[5] E.W. Dillard, Discussion on "Transmission LineVibration due to Sleet" by J.P. Den Hartog, AIEETrans. pp. 1082-1083, Dec. 1932.
[6] H.B. White, Discussion on "Progress Report on theInvestigation of Galloping of Transmission LineConductors" by A.T. Edwards and A. Madeyski,Trans. AIEE, vol. 75, p. 685, 1956.
[7] G.M. Lemanxzyk, P.M. Morris and R.L. Wardlaw, "Co-rona Induced Vibration of High Voltage conductors"Proc. of 5th Can. Conf. App. Mech., pp. 237-238,Fredericton, May 1975
PHAN CONG LUAN (SM'77) was bornin Hue, Viet-Nam, on November22, 1941. He received the Di-planas in Mathematics- Physics-Chemistry (MPC) and in GeneralPhysics fran the Faculty ofSciences, University of Saigonin 1960 and 1961. He caiTi toCanada in 1961 and received theB.Sc. and M.Sc. degrees in e-lectrical engineering and inphysics respectively in 1964
and 1966 from Iaval University. In 1970 he receivedthe Ph.D. degree in electrical engineering fram the sameUniversity.
He joined the University of Quebec at Chicoutimiin September 1969 as an Assistant Professor. During hissabbatical year in 1972-1973 he had been a guest re-searcher at the Centre de Recherche Atmospherique HenriDessen, Lannemzan, France.
He founded the research group in 1974 on Icingand High Voltage at the University of Quebec and waspromted Full Professor in 1978. Dr Phan is now theDirector of the Centre de Recherche du Moyen-Nord CRMlNof the University of Quebec. His field of research in-cludes corona, icing on H.V. conductors and insulators,electrostatic and collection efficiency of atmnsphericparticles.
Dr Phan is the author or co-author of more than20 scientific publications. Besides IEEE, Dr Phan is anenber of the Order of Engineers of Quebec, the Elec-trostatic Society of America and the International Gla-ciological Society.
[81 K.S. Shah and J.D. Morgan, "Analytical Study ofHigh Voltage Transmission Line Oscillations Indu-ced by Electrostatic Forces", IEEE PES WinterPower Meeting, paper no A-78 168-7, New-York, Feb.1978
[9] C.L. Phan and T. Adachi "A Laboratory Study ofCorona-Induced Vibration of HVDC Snooth AluminiumConductors in a Mass-Spring Configuration" to bepublished in Jour. of Electrostatic, Elsevier,i980
[10] M. Akazaki, "Corona Phenamena fran Water Drops cnSmoth Conductors under High Direct Voltage" IeTTrans. PAS, vol. 84, pp. 1-8, Jan. 1965
[11] R.D. Blevins "Flow-Induced Vibration" Van NostrandReinhold, 236 pages, 1977
[12] A.H. Church-"Mechanical Vibrations" John& Sons, 1963, p. 148
Wiley
TAyAYoSHI ADACHI was born inOita, Japan, on August 7, 1933.He received the B.S.E.E. degreefram Kyushu-kogyo University,Fukuoka, Japan, in 1955, andPh.D. degree frcm the TbkyoUniversity, in 1976.Fran 1961 to 1965, he was alecturer in Kokuritsu-Ube Jun-ior College, Yamaguchi, Japan.Since 1965, he has joined Ya-maguchi University, as an as-
sistant professor. Fran Decenber 1977 to November 1978,he was a guest researcher at the University of Quebec atChicoutimi, Canada. His research interests are in theionic wind due to the corona discharge, the corona in-duced wire-vibration and an electrostatic precipitator.
Dr Adachi is a member of the Institute of ElectricEngineers, Japan, and a nember of the Institute of Elec-trostatics, Japan.
MARC A. ALLAIRE was born inQuebec City, Canada, on Novem-ber 10, 1950. He received hisB. Sc. and M.Sc. degrees inPhysics in 1971 and 1973 re-spectively, fran the Laval U-niversity, Quebec. Canada. In1973-74, he was with the Insti-tut National des Sciences Ap-pliqu6es (INSA), Lyon, France.Framn 1974 to 1976, he worked asa research assistant in theDepartment of Applied Sciences
at the University of Quebec at Chicoutimi.Since 1977 he is professor at the Departnent of
Electrotechnic at the College of Chicoutimi. Mr Allairecontinues to collaborate with the research group onIcing and High Voltage at the University of Quebec.
1984
Discussion
K. S. Shah (Union Electric Co., St. Louis, Missouri): The authorsshould be commended for their efforts to experimentally investigate thephenomena of corona induced vibration. This is still a very rarelydiscussed subject and any experimental or analytical results or reportson actual occurrences would greatly help to achieve a better under-standing of the phenomena.
In this paper, the authors also have attempted to evaluate amagnitude of the acting force. In the analytical study with Dr. Morgan,referenced in the paper, it was-determined that the forces acting on thewater drops are directly related to the size of the water drop on thetransmission line. Does authors experimental investigation support thisresult? It has also been observed [i] that the water drops move along thebottom of the conductor and the conductor vibration probably startsand intensifies mostly from spray-plume action at the low portion of thesag where water drops on the conductor bottom have the highestamount of incidence and smaller separations. Did the authors try to in-clude, in their experiments, the effect of a transmission line sag on thespatial distribution of the drops?The other parameters influencing the water drop corona and the
distribution and ejection of the drops are aging of the conductor, im-purities on the conductor, different levels of support at two ends of aline, different conductor configurations, and possible interaction tovibration from bundled conductors. Although the authors have mostlyused smooth conductors for their experiments, do they have any com-ments on this? Eventually, the effect of wind should be included also.
REFERENCE
[1] H. H. Newell, Tseng-Wu Liao, and F. W. Warburton, "Coronaand RI Caused by Particles on or Near EHV Conductors: II - FoulWeather", IEEE Transactions on Power Apparatus and Systems,Vol. PAS-87, No. 4, pp. 911-927, April 1968.
Manuscript received August 11, 1980.
L. C. Phan, T. Adachi, and M. A. Allaire: The authors would like tothank Dr. Shah for his interest in their work.
Regarding Dr. Shah's first question, it is difficult, in a laboratory set-up, to control the size of the suspended drop which depends upon theapplied electric field and the dimension of the conductor. In a previousreport referred in the paper (to be published in Jour. of Electrostatics) itwas shown that at the start of the vibration the ejected drop is spherical,but it becomes elongated when the amplitude of the vibration is max-imum. On the other hand the shape of the suspended drop is related tothat of the ejected drop. In a study on corona discharge from the dropssuspended under a smooth conductor (1) the author has also shown thatthe optimum volume of the suspended drop decreases almost linearlywith an increasing diameter of the conductor.
Concerning Dr. Shah's second question, due to the short length ofthe conductor used it is difficult to produce a sag without a modifica-tion of the electric field along the conductor.Among "other parameters" mentioned by Dr. Shah in the last ques-
tion only the effect of the wind has been investigated. A simple systemusing three fans was used to produce a wind perpendicular to the con-ductor in the horizontal plane and preliminary results show that a windvelocity of 12 miles/h does not stop the vibration excited by the waterdrop corona. Also the amplitude of the vibration is more importantwhen the two sources of excitation (wind and water drop corona) arepresent.
In addition our most recent results show that for low precipitation in-tensities, the amplitude of vibration of the ACSR conductor used in-creases linearly with the increasing precipitation intensity between 0 and20 mm/h.
REFERENCE
[11 C. L. Phan, P. Pirotte, R. Brunelle, and N. G. Trinh, "A study ofCorona Discharges at the Water Drop Over the FreezingTemperature Range". IEEE Trans. on Power Apparatus andSystems, vol. PAS-93, No. 2, April 1974, pp. 727-734.
