Corona discharge and electrical charge on water drops dripping from D.C. transmission conductors — an experimental study in laboratory

Journal of Electrostatics, 6 ( 1 9 7 9 ) 2 3 5 - - 2 5 7

235

© Elsevier Scientific Publishing C o m p a n y , A m s t e r d a m - - P r i n t e d in T h e N e t h e r l a n d s

C O R O N A DISCHARGE AND ELECTRICAL CHARGE ON WATER DROPS DRIPPING F R O M D.C. TRANSMISSION CONDUCTORS AN EXPERIMEN. TAL STUDY IN L A B O R A T O R Y - -

MASANORI HARA, SHINJI ISHIBE and MASANORI AKAZAKI

Faculty of Engineering, Kyushu University, 6-10-1, Hakozaki, Higashi-ku, Fukuoka-shi (Japan) ( R e c e i v e d S e p t e m b e r 10, 1 9 7 8 ; a c c e p t e d in revised f o r m N o v e m b e r 24, 1 9 7 8 )

Summary In r a i n y w e a t h e r , charge carriers f r o m a d.c. t r a n s m i s s i o n c o n d u c t o r t o g r o u n d c o n s i s t of m o l e c u l a r ions p r o d u c e d b y c o r o n a discharge a n d w a t e r d r o p s w h i c h drip f r o m t h e cond u c t o r or are c h a r g e d o n t h e i r way t o ground. In this paper, t h e b e h a v i o r o f c h a r g e d w a t e r d r o p s d r i p p i n g f r o m t h e c o n d u c t o r a n d t h e c o r o n a discharge o n t h e m were investigated t o o b t a i n basic d a t a o n i o n flow e l e c t r i f i c a t i o n p h e n o m e n a in foul w e a t h e r . F o u r d i s t i n c t m o d e s o f specific charge o f w a t e r d r o p s were f o u n d a n d t h e effects of flow r a t e of w a t e r s u p p l i e d t o t h e c o n d u c t o r , c o n d u c t o r size a n d s m o o t h n e s s o f t h e c o n d u c t o r surface o n t h e m were measured. Moreover, a r e l a t i o n b e t w e e n c o r o n a discharge, t h e specific charge o n w a t e r d r o p s a n d t h e d r i p p i n g f a s h i o n o f w a t e r d r o p s has b e e n described. U n d e r an o p e r a t i n g field s t r e n g t h o n a d.c. t r a n s m i s s i o n c o n d u c t o r , t h e specific charge o n w a t e r d r o p s f r o m a positive c o n d u c t o r m a y r e a c h 6 × 10 -4 C/kg a n d plays a n i m p o r t a n t role in b u i l d i n g u p a high voltage o n a n o b j e c t w i t h a high leakage resistance o f t h e o r d e r o f 101' o h m s or more.

1. Introduction Increase in transmission line voltages has necessitated the study of the electrical environment in the proximity of high voltage transmission lines [1--5]. In particular, d.c. electric field effects produced by ion flow electrification from the d.c. lines are a new problem to be analyzed and which do not appear in the case of a.c. [2]. During periods of fair weather, the ion flow electrification phenomena may be explained b y the behavior of molecular,ions which move along the comp o u n d ~nes of the electric lines of force (E) and streamlines of wind ( ~ / K i ) where W is the wind velocity and Ki the mobility of the ions [6, 7]. In rainy weather, on the other hand, electrical charges on water drops dripping from a d.c. c o n d u c t o r should be considered. The trajectory of the charged drop may depend not only on the c o m p o u n d lines ( ~ + ~/Ki) b u t also on the charge-tomass ratio of the drop and its radius and weight. When the field strength on the c o n d u c t o r is lower than the corona threshold, the electrification is conduc-

236 ted only by charged water drops. Moreover, the electrification voltage of an object with a very large leakage resistance placed under d.c. lines may be determined by the action of charged water drops rather than by molecular ions, and its value may become much larger than by the ions, so much as to repulse the charged water drops too. Then the voltage build-up reaches a saturated condition. In the power industry, although many studies [8--14] on corona discharge from water drops hanging on a conductor have been carried out to obtain information relating to power loss, the radio interference level and the acoustic noise level created by corona, only little information [14] has been reported concerning charged drops from a d.c. conductor. On the other hand, scientists in other fields have done excellent studies on the stability of charged drop and of uncharged drop in the presence of an external field [15--23], and on corona discharge from water drops [24--27]. The purpose of this work is to obtain basic data, the specific charge and radius of water drops, from d.c. transmission line conductors. Other objectives are to show experimentally the relationship between modes of corona discharge and the dripping manner of water drops from the conductor, and their threshold conditions. 2. Experimental Set.up Experiments were performed with a coaxial cylinder shown in Fig.1. The outer conductor consists of a mesh cylinder and two copper guard cylinders which are grounded. The mesh cylinder with a diameter of 70 cm and 150-cm long was grounded through a resistance for corona current measurement. Brass cylinders with radius, rc, of 0.25, 0.5, 0.75, 1, 1.15, 1.6 and 2.25 cm were used as an inner conductor, and was energized by d.c. voltage up to 150 kV, positive or negative. Tap water drops having a conductivity of 267 gS/cm at 20 ° C were allowed to fall through the outer mesh cylinder to strike the inner energized conductor. The rate of water fall onto the conductor could be controlled by adjusting the stopcock supported above the mesh cylinder. In order to measure electrical charge on the water drop, the separation of charged drops from molecular ion by corona discharge was done by a charge separator which consists of six tapered brass tubes with knife edges to avoid the reflection of drops fallen on them. The specific charge, M, of water drops dripping from the conductor was obtained from the ratio of charge to mass of the water collected in a Faraday cup. The size of the drops was measured by three methods: under low applied voltage, the drop diameter was 3.1--3.4 ram, determined from the measurement of the weight of 100 mother drops. The existence of satellites was neglected. As the applied voltage was increased so that the diameter was 0.1--3.2 mm, photographs were taken by a still camera with a Nikkor 200-mm lens and a micro flash-lamp. As the diameter at higher voltages becomes smaller than 0.45 mm, the drops were collected in silicon oil having a viscosity of 5000 cs on a slide glass and were magnified 20 times by

237

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the universal projector NIKON-6CT2 enabling the size of drops to be measured. 3. Experimental results and discussions

3.1 Modes o f corona discharge and specific charge Typical measured characteristics of the specific charge, M, to the field strength, Ec, on the surface of the smooth inner conductor are shown in Figs.2 (a) and (b) where data are dispersed in the hatched region. It can be seen that the characteristics may be considered to consist of four modes as illustrated schematically in Fig.3. Mode I occurs at a low field strength where the specific charge gradually increases with the field strength. Increasing the field strength beyond a certain value, point A in Fig.3, the specific charge suddenly decreases to some values which depend on the size of the inner conductor, and it recovers to the level of A between points B and B'. This region is termed Mode II. As the field strength is further increased, a polarity effect appears. In fact, the value of the specific charge of water drops from a positive conductor indicates a sharp m a x i m u m at point C in Fig.3. Its value depends on the inner conductor size and the flow rate of water supplied to the inner conductor. However, with a negative inner conductor, those characteristics do not appear or are n o t remarkable. The region from the recovered point B' to the point C is defined as Mode III where the value of the specific charge increases with the field strength. The remaining region corresponding to still higher field strengths is Mode IV. Among the conductors used in this experiment, the transition between Modes III and IV for a

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negative polarity occurred on the tested conductor of 0.25-cm radius only as shown in Fig.2(b). Akazaki and Lin [9, 11] have previously defined two corona modes; "Crackling and Hissing Corona". Here corona discharge was classified into four modes, i.e. No-Corona (NC), Crackling Corona (CC), Hissing Corona (HC) and Wire Corona (WC). The CC occurs at the m o m e n t of the removal of water drops C

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Fig. 3. Modes of corona discharge and specific charge, low f l o w rate o f supplied water, . . . . high f l o w rate of water supplied. (a) positive inner c o n d u c t o r , (b) negative inner conductor. NC: No-Corona, CC: Crackling Corona, HC: Hissing Corona, WC: Wire Corona.

241 from the c o n d u c t o r or during a deformation of the pendant drop and produces the crackling sound therefore this mode does not appear on the drop of water supported in the lower of two plates as used by Barreto [27]. When the supply of water was stopped in this experiment the CC did not appear. Continuously maintained corona accompanied by the continuous hissing sound appears on a water drop with a conical tip. This is termed Hissing Corona. The WC is corona discharge from the inner c o n d u c t o r and always accompanies the HC, and it t o o gives a hissing noise. These modes do not always correspond to the modes of the specific charge as shown in Figs.2 and 3. The starting field strength of the CC is a little higher than at the boundary of Modes I and II. The Mode II and the point C appear in the regions of the CC and the HC, respectively. 3. 2 Observation and size measurement o f water drops Instantaneous shadow photographs of water drops in different modes are shown in Fig.4. Pictures were taken with single flash of a b o u t 1.8 ps duration. Under no applied voltage a water drop hanging from the conductor is distorted by the unbalance of forces due to surface tension, gravity and pressure in which the latter t w o forces increase with the flow of water supplied to the drop till it disintegrates. The stability of the drops is discussed analytically by Paddy and Pitt [28--30] and Michael and Williams [31]. In the present experiment, since water always flows down along the surface of the conductor, the critical conditions for the stability of a pendant drop become unsatisfied as soon as they are reached. The head part of the pendant drop gradually becomes spherical and it becomes almost a complete sphere at the m o m e n t of removal from the neck as shown in Fig.4(a-4). Then the neck breaks away from the conductor (see Fig.4(a)). In Mode I, a dripping fashion of water drops is the familiar form with no applied voltage. A pendant drop at first begins to move down and is distorted into a spheroidal head with a neck. The head and neck turn into a mother and some satellites when the drop breaks away from the c o n d u c t o r (see Figs.4(b) and (c)). The number of the satellite increases with the field strength on the conductor. The spheroidal head just before it leaves the neck becomes gradually longer with increasing the field strength. At the upper limit of Mode I (at the point A), the ratio of the major and minor axes of the drop which has an approximately spheroidal shape is a b o u t 1.9 as shown in Figs.4(d--4) and (e--4). A conical tip as in Fig.4 (e--4} was observed sometimes. As the field strength on the c o n d u c t o r increases to the value at point B in Mode II, the profile of an elongated pendant drop becomes slender and has a conical tip. The first electrical disconnection of the pendant drop from the c o n d u c t o r occurs at the c o n d u c t o r side of the neck (see Figs.4 (f) and (g)). This fact may be important in explaining the remarkable reduction of the specific charge in the Mode II region. That is, in the case of Figs.4(f) and (g), the specific charge of water drops is determined at the stage of Figs.4(f--5} and (g--5) which show the m o m e n t the pendant drop leaves the conductor. Contrary to this, in Mode I, the specific charge of the mother drop is deter-

Fig.4. Dripping fashion of water drops from s m o o t h c o n d u c t o r with 1.6-cm radius: (a) no applied voltage, (b) Ec= 4 kV/cm (Mode I), (c) Ec = --4 k V / c m (Mode I), (d) Ec = 5.2 kV/ cm (near the point A), (e) E c = --5.2 kV/cm (near the point A), (f) Ec = 6.3 kV/cm (near the point B, Mode II), (g) E c = --6.3 kV/cm (near the point B, Mode II), ( h ) E c = 8 kv/cm (Mode III), (i) E c = --8 kV/cm (Mode III), (j) Ec = 10.1 k V / c m (at the starting point of the HC, Mode III), (k) Ec = --10.1 kV/cm (at the starting point of the HC, Mode III), (1) E c ffi 14.2 k V / c m (at point C), (m) Ec = --14.2 k V / c m (Mode III), (n) Ec = 16 kV/cm (Mode IV), (o) E c = - - 1 6 kV/cm (Mode III).

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0

246

mined at the stage of Figs.4(b--5) and (c--5). However, part of the neck is charged up after the mother drop leaves the neck, before disintegrating into several satellites. As the field strength increases further, a pendant drop becomes more slender and cylindrical and has a conical cap at an earlier stage. Therefore the distinction of a mother drop and the corresponding satellites becomes difficult, as shown in Figs.4(h) and (i). Initial disruption from the pendant drop occurs at its tip, the same as in Mode I. This may be one of the reasons that the specific charge recovers to a higher level in Mode III. When the field strength is increased beyond a certain value, a sudden transition from a drop with a round tip to a conical shape occurs before it elongates, as shown in Figs.4(j) and (k). If the supply of water was stopped at a suitable volume of drop hanging from the conductor, the conical shape as shown in Figs.4(j--2) and (k--2) was maintained for a long time. As the water supplied flows down along the conductor surface, the drop elongates with a conical tip and eventually breaks into droplets. The base part of the drop has a conical shape with an angle less than the Taylor's angle of 49.3 °, just before the transition occurs, and the conical tip after the transition has a sharper angle (see Figs.4(j) and (k)). Corona discharge (HC) occurs continuously on the conical tip till it breaks. Further increase in the field strength results in a marked polarity effect. At a positive conductor, fine mist is emitted from the conical tip at the point C as shown in Fig.4(1) and at higher field strength the conical drop vibrates up i

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Fig.5. Distribution of drop radius from smooth conductor. Measuring methods; • weight; o still camera and projector; X slide glass covered with silicon oil and projector. (a) positive inner conductor, (b) negative inner conductor.

and d o w n v i o l e n t l y and emits several d r o p l e t s d u r i n g o n e cycle o f the vibrat i o n (see Fig.4(n)). With a negative c o n d u c t o r , a fine mist is n o t p r o d u c e d as s h o w n in Figs.4(m) and (o). T h e radius o f a m o t h e r d r o p and its satellites was m e a s u r e d as shown in Fig. 5. A c u m u l a t i v e d i s t r i b u t i o n o f t h e radius was a p p r o x i m a t e d b y the logar i t h m i c o - n o r m a l d i s t r i b u t i o n and a c u m u l a t i v e value o f t h e 50% and a range b e t w e e n 5% t o 95% have b e e n illustrated b y a circle or a cross and a vertical line. T h e i r characteristics are as follows: In the Mode I region, t h e m o t h e r d r o p radius is a l m o s t c o n s t a n t and is a b o u t t h r e e t i m e s or m o r e o f t h e c o r r e s p o n d i n g satellites. T h e r e is n o p o l a r i t y effect. In the M o d e II region, the m o t h e r d r o p radius a b r u p t l y decreases and t h e r e is no p o l a r i t y effect. In the Modes III and IV regions, with a c o n s t a n t field strength t h e d r o p radius f o r a positive c o n d u c t o r is smaller t h a n f o r a negative c o n d u c t o r and has a sharp m i n i m u m at the field strength c o r r e s p o n d i n g t o t h e p o i n t C.

3. 3. Effects o f conductor radius on the specific charge and on the starting field strength o f the specific charge mode and the corona discharge mode With a c o n s t a n t field strength o n the c o n d u c t o r and f o r a c o n s t a n t w a t e r s u p p l y f l o w rate, the specific charge in t h e Mode I region increases linearly with t h e c o n d u c t o r radius, and its slope increases with increasing field strength as s h o w n in Fig.6. T h e values at t h e p o i n t s A and B increase with a decrease in

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Fig.6. Specific c h a r g e as a f u n c t i o n o f c o n d u c t o r r a d i u s . - - - v a l u e at t h e p o i n t s A, B a n d C, --Mode I, - . . . . M o d e I I , - - - - M o d e I I I , - - - - - M o d e IV. • E c = 1 k V / c m , o E c = 4 k V / c m , • E c = 6 k V / c m , a Ec = 8 k V / c m , • Ec = 10 k V / c m , © Ec = 20 k v / c m . ( a ) p o s i t i v e i n n e r c o n d u c t o r , (b) negative inner c o n d u c t o r .

the conductor radius and they coincide for a smaller c o n d u c t o r as seen in Figs.2(a) and (b) and 6. The maximum value of the specific charge (at the point C) for the positive conductor almost linearly increases with the conductor radius. Figure 7 shows a field strength at the points A, B and C and at the starting of the CC, the HC and the WC. The starting field strength of the WC agrees well with the calculated value from the well-known equation [32]: Ewc = 30.5(1 + 0.305/x/rc). However, other threshold field strengths have an expression of the form:

(1)

249

Ei

K(1 + H/rc)

=

(2)

where K and H are constants listed in Table 1. It can be seen from Fig.7 that the point C at which the maximum ion flow is produced by water drops appears in practical transmission lines because the operating field strength on the transmission conductor is chosen to be about 16--20 kV/cm to suppress corona loss and radio interference by corona discharge.

3.4 Effects of the water supply flow rate on specific charge Changing the flow rate of the water supply in the region 0.001--0.1 g/s, the specific charge in Modes I, II and III reduces slightly at a high flow rate for both polarities of the inner conductor as shown in Fig.8. A pronounced de-

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Fig.7. Field strength at the points A, B and C and at the start of the CC, HC and WC. + CC (positive and negative), × HC (positive and negative), WC (positive and negative), o at the point A (positive), • at the point A (negative), = at the point B (positive), • at the point B (negative), © at the point C (positive). TABLE 1

Constants in eqn. (2) Field Strength

K

H

Eqn. No.

E A (at the point A) E B (at the point B) E c (at the point C) ECC (at starting of

3.2 4.5 11.3 3.31

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10-I

--~ [g/sec]

Fig.& Effect of the flow rate of supplied water on specific charge. (a) positive innner conductor, (b) negative inner conductor. crease in specific charge with the flow rate appears at a high field strength in Mode III and in Mode IV because the equilibrium between the flow rates of dropping from, and supply to, the c o n d u c t o r breaks dow n and t he fine mist as shown in Fig.4(1) replaces drops of larger size observed in a region of a low field strength o f Mode III. In fact, the sharp m a x i m u m in the characteristics of the specific charge saturates in the region 0.001--0.006 g/s. Under rainy conditions, for example, at a rainfall of 10 m m / h and with a c o n d u c t o r o f 1.6-cm radius, the water supply flow rate on 10-cm length of the c o n d u c t o r is a b o u t 0.0089 g/s. Therefore, it is considered t hat the flow rate

251

in operating transmission lines may be on the order of 10 -3 g/s per water drop hanging on the conductor in heavy rain. Thus, all experiments were performed using a flow rate of about 0.004 g/s.

3. 5 Effects of the smoothness of a conductor Experiments described in previous sections were performed with smooth conductors. It is felt that the various characteristics shown above are affected by the smoothness of the conductor surface. Quite likely the strands of the aluminum cable steel reinforced ( ACSR ) is an influence. In order to study this effect, additional experiments were performed with a ACSR conductor having a cross-section of 810 mm 2 (7 steel and 45 aluminum strands) which is used in practical EHV and UHV transmission lines and has the m a x i m u m radius of 1.92 cm. The general trend of experimental results was the same as in the case of the smooth conductor as shown in Figs.2(c) and (d) where the abscissa indicates the m a x i m u m field strength on the ACSR conductor. Although the field strength on the surface of the ACSR conductor used is increased 1.38 times of that for a smooth cylinder with its envelope c o n t o u r as a result of strands in the present set-up, experimental results with the ACSR conductor fit well with those by the smooth cylinder as shown in Figs.6 and 7 if the field enhancement factor by strands is neglected. According to Akazaki and Lin [ 11], the radio interference and corona loss on stranded wire under rainy conditions were determined by taking the equivalent field strength calculated as for a smooth cylinder having as diameter the m a x i m u m diameter of the stranded wire, because water tends to smooth out the electric field on the wire filling the space between the strands. This explanation appears to be correct for the present case too. One other reason should be added. The threshold of the WC will be determined by the field strength in the vicinity of the conductor, i.e. in the space within the distance of electron avalanche. Hence the maximum field strength on the strands should be used to estimate the threshold voltage of the WC. On the other hand, the behavior of water drops and the threshold of the CC and the HC may depend mainly on the field in the space within the length of the pendant drops from the conductor surface and the effect of the strands on the field is negligible. Then the characteristics of the CC, the HC and the specific charge is determined by the equivalent field strength rather than by the m a x i m u m value. 3. 6 Discussion 3. 6.1 Instability of drops, corona mode and specific charge In the present work, five forces, viz. surface tension, pressure in the water drop, gravity, electrical force and reactive force by ionic wind (i.e. corona wind), should be considered to discuss the stability of the drop. Since the external electric field distribution near the drop is non-uniform, a quantitative analysis on the instability criterion is difficult, but a qualitative explanation may be as follows.

252

With no or a low applied voltage a pendant drop on the conductor exhibits an instability in equilibrium among surface tension, pressure and gravity and it breaks away. When an electrical force acting on a drop becomes comparable with the gravitational force, electrical instability (Taylor's instability, Rayleigh's instability or a mixture of those} will grow. Neglecting the non-uniformity of the external electric field, this field strength can be found from the intersection of the measured specific charge in Fig.2 and a line of MEext = g where g is the gravitational acceleration, and is about 4 kV/cm for a 1.6-cm-radius conductor and about 7.5 kV/cm for 0.25-cm radius. Since a drop departing from the conductor elongates in a l o w field region, the effective field strength acting on the drop becomes smaller than the value at the intersection mentioned above. Considering this fact, the above statements relating to the critical field strength and its increase with decrease in the conductor radius agree reasonably with the condition at point A in Fig. 2. However, the problem is to know which instability develops in this critical field or what is the corresponding specific charge. AcRayleigh [C/kg] 5 Vonnegut & Neubauer(one-half of the Rayleigh's l i m i t ) Ryce ( o n e - s i x t h o f the Rayleigh's l i m i t )

~

E

o

10-5 D_

inner conductor pos. 0

-

~

neg. • : mother

II

0 D : satellite F = 0.004 g/sec

®l

i\ o

o

o 5

lC~ t

5

radius of water drop,

I 5

1 rd

Fig.9. Specific charge as a f u n c t i o n o f drop radius.

[mm]

253 '10-s / r ..... n3.5 II

2.5 ~

-,, o

b

~

Ray]eigh

"-4-

-

a

~2

uer

F : 0.004 g/seo

-~ 2

i

I

2.5 3 radius of water drop, I'd

"1

3.5 [mm]

Fig.10. Specificchargeat the point A taken with variousinnerconductors o positiveinner conductor, • negativeinnerconductor. cording to Figs.4(d--4) and (e--4), the distortion ratio of the head part of the pendant drop just before it leaves the neck is a b o u t 1.9 and does n o t break after its removal. Moreover, the pole tip of the head part sometimes becomes conical in shape as arrowed in Fig.4(e--4). This suggests that the primary electrical instability at the tip of the pendant drop grows as the Taylor instability. On the other hand, as can be seen in Fig.9, the specific charge at the point A for a 1.6cm-radius c o n d u c t o r as obtained from Figs.2 and 5 is very near the l~ayleigh limit which is the maximum value the water drop can attain if the existence of satellites is neglected. However, charge on the satellites cannot be neglected because the specific charge suddenly decreases if the neck, which becomes satellites, first leave the conductor as shown in Fig.4(f} and (g}. Hence the complete coincidence of the specific charge at point A and the Rayleigh limit in Fig.9 is an accidental result. In fact, as the c o n d u c t o r radius becomes smaller, the size of the mother drop at point A decreases and the corresponding specific charge increases. However, the relationship between them does not lie on the Rayleigh limit as shown in Fig.10. Since the field strength on the spheroidal drop at the threshold of the Taylor instability is slightly lower than that on the spherical drop under the Rayleigh condition if the radius of curvature on the pole of the spheroidal drop is the same as the radius of the sphere, the specific charge on water drops at the Taylor criterion may be comparable with the Rayleigh limit. Again, the pendant drop at first is pulled down b y the gravitational and electrical forces and elongates into a low external-field region. Then the induced charge density on the drop is high enough to develop the Taylor instability at point A. Hence a starting field strength of the CC identifies the geometrical stability criterion b y an electrical force. This result appears to agree reasonably with

254 the conclusion by English [24] and Dawson [26] according to whom the cause of discharge at about atmospheric pressure is surface instability on drops. The transition between corona modes CC and HC corresponds to the formation of a conical water drop which is produced by another instability explained by Taylor [20]. Studies on specific charge have been done by Rayleigh [ 15], Zeleny [ 16], Vonnegut et al. [17], Hendricks [18], Ryce [19], Doyle et al. [33], Ogata [22] and others in no, or weak, corona. In the present work, in Modes III and IV, satellites which return to the inner conductor were often observed. It may be that the satellite produced from the inner conductor side of the mother drop is charged to a polarity opposite to that of the conductor by the electrostatic induction prior to its dissipation. Another reason is the neutralization of charge on water drops by violent Hissing Corona. Therefore the theories of the abovementioned authors do not apply directly to explain the present results in Modes III and IV. Figures 9 and 10 illustrate that the present results have the same tendency with respect to the drop radius as suggested by above authors, i.e. M ~ 1 / x / r d , where r d is the drop radius. 3. 6.2. C u r r e n t a n d e l e c t r i f i c a t i o n by charge o n w a t e r d r o p

Denoting the a m o u n t of rainfall by h m m / h , the radius of the transmission conductor and rain drop by rc and rr mm, respectively, the collection efficiency of the conductor for a rain drop by f and the specific charge on water drops dripping from the conductor by M, then the current carried by water drops from the conductor can be written as follows, id = 556 h M f ( r c + rr)

(pA/km).

(3)

Taking f = 1, rc = 20 mm, rr = 0.5 mm, h = 10 m m / h and M = 5 × 10 -4 C/kg, the current becomes 55.6 p A / k m which is a few percent of the corona current in practical transmission lines. Since the trajectory of charged drops near the ground level is determined mainly by the gravitational force as mentioned in the Introduction, the drop falls within a narrow limited region under the conductor of d.c. lines. Hence the m a x i m u m current density under d.c. lines due to water drops may be 10-8--10-9 A/m: (assuming the dispersion width of the drops to be 1--10 m). As stated in a previous paper [6], the electrification voltage of a spherical object in a uniform field by molecular ions can be written as follows, V1 = Eext (D + 3r0 ~), 1 ~=1+

-

[(

2ur0 p R I K i for ~ > - 1 and D 3r0 (4ur0p R I K i +1)

(4) 1

2

D

1+

2~ro p R i K i

3~r02 p R I K i

1/2

],

255

for ~ < - - 1 where Rl is the leakage resistance of the object, ro is the radius of the object, D the height of the center of the object, p the charge density of molecular ions and where Ki is the mobility of ions. On the other hand, the electrification voltage by charged drops is as follows:

V2 = Rlid,

(5)

where id is the current carried by charged drops through the object. The value of i d is independent of the leakage current if the electrified electric field on the top of the object is lower than a few hundred kV/m which corresponds to an electrified voltage of several hundred kV. At higher electrification voltages the charged drop is repulsed from the object and the voltage will saturate. As an example, taking p = (1--500) X 10 -9 CIm 3, id = 10-7--10 -~1 A and Ki = 2 X 10 -4 m2/Vs as typical values under practical transmission lines, the electrification voltage on an object was calculated and is shown in F i g . l l shere the saturation in V2 was neglected because the present objective is to compare with the value of V1 and 172 lower than the saturated value of V2. It can be seen from this figure that the contribution of the charge due to drop becomes important for the electrification of the object under the practical transmission lines when the leakage resistance of the object becomes of the order of 10 u ohms or more. 10 lo ;.=10 -7 A

:==.

10 °

v,//7 /;'

5xl Cg

10 6

,~l,#l f #,l#'l l#'"'-

lo-! ~xIQ~

>

-

1~ 11

io~ 5xlU 10 ~

# /#" /// l/ #, #,

o

71

"

oz

gy,;>',,'," , ,

,;;,,,',",, " 10 -z

r

='Okv/"" E" 1

/ / /

10 -4 V" 10 7

/

/

-..

I

I

I

I

10 !

10 u

10II

1015

leakage resistance,

RI

I 1017

[~ ]

Fig. 11. E l e c t r i f i c a t i o n voltage o n a spherical c o n d u c t i n g o b j e c t by m o l e c u l a r ion or c h a r g e d w a t e r drops, m o l e c u l a r i o n , - -- - charged drops.

256

4. Conclusion (1) The characteristics of the specific charge on water drops from a d.c. transmission smooth conductor may be classified into four modes in which the specific charge has different field-dependence for each mode. (2) Four corona modes on a smooth conductor under rainy conditions are recognizable; No-Corona, Crackling Corona, Hissing Corona and Wire Corona, and do not always correspond to the modes of the specific charge. (3) The dripping fashion of water drops from the smooth conductor changes with increase in the field strength and is related closely to the modes of the specific charge. (4) Items (1) through (3) apply equally well to stranded conductors (ACSR). (5) Although the starting field strength of wire corona from a stranded conductor is determined by the maximum field strength on the strands, the performance of the Crackling Corona and Hissing Corona and the characteristics of the specific charge of water drops depends on the equivalent field strength calculated as for a smooth conductor having the maximum diameter of the stranded conductor. (6) When the leakage resistance of an object with dimensions of a few tens of centimeters becomes 10 ~ ohms or more under practical transmission lines, the contribution of charged drops from the line conductor to voltage build-up on the object is more severe than the corona current. Moreover, the effects of the conductor size and the flow rate of the water supply on the specific charge and the relation between the dropping fashion and the specific charge were investigated.

Acknowledgements The authors wish to thank Dr S. Ogata for the useful suggestion to take photographs of the drops.

References 1 V.P. Korobkova, Yu.A. Morozov, M.D. Stolarov and Yu.A. Yakub, Influence of the electric field in 500 and 750 kV switchyards on maintenance staff and means for its protection, CIGRE, Paper number 23--06, (1972). 2 Biological Studies Task Team of BPA: Electrical and biological effects of transmission lines: A review, Bonneville Power Administration, Portland, Oregon USA, (1977). 3 G.D. Friedlander, UHV: onward and upward, IEEE Spectrum, February, 57 (1977). 4 G.E. Atoian, Are there biological and physiological effects due to extra high voltage installations?, IEEE Trans. Power Appar. Syst., PAS--97 (1978) 8. 5 J.E. Bridges, Environmental considerations concerning the biological effects of power frequency (50 or 60 Hz) field effects, IEEE Trans. Power Appar. Syst., PAS--97 (1978) 19. 6 M. Hara, N. Hayata and M. Akazaki, Basic studies on ion flow electrification phenomena, J. Electrostatics, 4 (1978) 349.

257 7 M. Hara, I-L Chishaki and M. Akazaki, Calculation of electrification current and energy

resulting from ion flow under d.c. transmission lines, J. Electrostatics, 6 (1979) 29. 8 L Boulet and B.J. Jakubczyk, Ac corona in foul weather: I--Above freezing point, IEEE Trans. Power Appar. Syst., PAS--83 (1964) 508. 9 M. Akazaki, Corona discharge from water drops on smooth conductors under high direct voltage, IEEE Trans. Power Appar. Syst., PAS--84 (1965) 1. 10 Y. Tsunoda and K. Arai, Corona discharge from water drops on a cylindrical conductor surface, JIEE Jpn., 84 (1964) 1430. 11 ~¢L Akazaki and S. Lin, Corona discharge from water drops dripping onto inner conductor of co-axial cylinder, JIEE Jpn., 88 (1968) 909. 12 I-I.I-L Newell, T.W. Liao and F.W. Warburton, Corona and RI caused by particles on or near EHV conductors: II--Foul weather, IEEE Trans. Power Appar. Syst., PAS--87 (1968) 911. 13 F. Inna, G.L. Wilson and J.D. Bosack, Spectral characteristics of acoustic noise from metallic protrusions and water drops in high electric field, IEEE Paper number C 73 164--1, IEEE PES Winter Meeting, New York (1973). 14 J.E. Houburg and J.R. Melcher, Current-driven, corona-terminated water jets as sources of charged droplets and audible noise, IEEE Paper number C 73 165--8, IEEE PES Winter Meeting, New York (1973). 15 Lord Rayleigh, On the equilibrium of liquid conducting masses charged with electricity, Philos. Mag., 14 (1882) 184. 16 J. Zeleny, The instability of electrified liquid surfaces, Phys. Rev., 10 (1917) 1. 17 B. Vonnegut and R.L. Neubauer, Production of monodisperse liquid particles by electrical atomization, J. Colloid Sci., 7 (1962) 616. 18 C.D. Hendricks, Jr., Charged droplet experiment, J. Colloid Phys., 17 (1962) 249.. 19 S.A. Ryce, An equilibrium value for the charge to mass ratio of droplets produced by electrostatic dispersion, J. Colloid Sci., 19 (1964) 490. 20 G. Taylor, The disintegration of water drops in an electric field, Proc. R. Soc., London, A280 (1964) 383. 21 M.A. Abbas and J. Latham, The disintegration and electrification of charged water drops falling in an electric field, Q. J. R. Meteorol. Soc., 95 (1969) 63. 22 S. Ogata, K. Kawashima, O. Nakaya and H. Shinohara, Stability of charged drop issuing from a fine capillary, J. Chem. Eng. Jpn., 9 (1976) 440. 23 E. Brarzabadi and A.G. Bailey, The profiles of axially symmetric electrified pendant drops, J. Electrostatics, 5 (1978) 369. 24 W.N. English, Corona discharge from a water drop, Phys. Rev., 74 (1948) 179. 25 G.A. Dawson, Pressure dependence of water-drop corona onset and its atmospheric importance, J. Geophys. Res., 74 (1969) 6859. 26 G.A. Dawson, Electrical corona from water-drop surfaces, J. Geophys. Res., 75 (1970) 2153. 27 E. Barreto, Electrically produced submicroscopic aerosols, Aerosol Sci., 2 (1971) 219. 28 J.F. Paddy, The profiles of axially symmetric menisci, Philos. Trans., 269A (1971) 265. 29 J.F. Paddy and A.R. Pitt, The stability of axisymmetric menisci, Philos. Trans., 275A (1973) 489. 30 E. Pitt, Stability of pendant drops. Part 2. Axial Symmetry, J. Fluid Mech., 63 (1974) 487. 31 D.H. Michael and P.G. Williams, The equilibrium and stability of axisymmetric pendant drops, Proc. R. Soc. London, A351 (1976) 117. 32 The Institute of Electrical Engineers of Japan: High Voltage Engineering I (Book in Japanese), 151 (1946). 33 A. Doyle, R.D. Moffett and B. Vonnegut, Behaviour of evaporating electrically charged droplets, J. Colloid Sci., 19 (1964) 136.