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Partial Discharge Investigation and Electric Field

Analysis of Different Oscillation Modes of Water

Droplets on the Surface of Polymeric Insulator under

Tangential AC Electric Field Stress

M. H. Nazemi and V. Hinrichsen

High Voltage Laboratories

Technische Universität Darmstadt

Darmstadt, Germany

nazemi@hst.tu-darmstadt.de 

 Abstract  — For this contribution, different oscillation modes

of a 20 microliter water droplet on the hydrophobic surface of a

silicone rubber insulator under tangential AC electric field stress

were investigated, using a high speed camera. Since thedeformation of water droplet increases the local electric field

stress at the triple zones, an electric field analysis at the triple

zone is performed to find the worst case of water droplet

oscillation modes. Different kinds of water droplet deformation

at four dominant oscillation modes, namely mode No. 1 to mode

No. 4, which were found experimentally, are simulated and

compared. These results show that mode Nos. 1 and 3 provide

higher electric field values at the triple zone in comparison to

mode Nos. 2 and 4. In parallel, partial discharge inception

voltages of a 20 microliter water droplet located on the

hydrophobic surface of a silicone rubber insulator under

tangential AC electric field stress are measured in the frequency

range of 20 Hz to 100 Hz. With the aid of frame analysis of the

captured videos, the mode number of water droplet oscillation ateach frequency is obtained, and the measured partial discharge

inception voltages at each oscillation mode are compared with

electric field simulation results. Partial discharge investigations

confirmed that the water droplets oscillating at mode Nos. 1 and

3 have lower inception voltages compared to PD inception

voltages of water droplets that oscillate at mode Nos. 2 and 4.

These measurements also show that inception voltage makes a

step whenever the oscillation mode of water droplet changes.

 Keywords—water droplet; partial discharge; oscillation mode;

hydrophobic surface; electric field

I.  I NTRODUCTION

Application of polymeric insulators in high voltageengineering has been extended recently because of their lowweight, resistance to vandalism, high contamination resistanceand – most important – hydrophobic surfaces [1-3]. However,surface degradation of polymeric insulators due to aging aswell as their surface discharge mechanisms are amongst themost challenging questions for researchers nowadays. Agingof the polymeric insulator surface can gradually decreasehydrophobicity of the surface, which leads to corona and evensurface flashovers. Under wet conditions, water droplets areformed on the surface of polymeric insulators, which enhance

the electric field especially nearby the triple zones (thecommon line between air, water droplet and insulator surface)[2-5]. Periodical deformation of a water droplet in an AC

electric field makes it difficult to find an exact value of anelectric field enhancement factor. In [6] the authors reportedfour dominant oscillation modes of individual water dropletson hydrophobic insulator surfaces under high voltagetangential electric field stress. These oscillation modes, whichare named Mode 1 to Mode 4, were categorized in a widerange of droplet volume and frequency of the applied electricfield. Fig. 1 shows these four dominant oscillation modes. Inmode No.1 the water droplet elongates towards the electrodesand develops sharp edges on one side periodically. In mode

 No.2 the water droplet oscillates upwards and downwards twotimes per cycle of the applied electric field. The water dropletat mode No.3 moves in a way that two different peaks occur in

its left and right part during one half-cycle each of the appliedelectric field. In mode No.4 stronger oscillation occurs at thetop of the water droplet [6].

Fig. 1. Four dominant oscillation modes of a water droplet on silicone

rubber surface under tangential electric field stress [6]

For this contribution, different oscillation modes of a 20 µlwater droplet on the hydrophobic surface of a silicone rubberinsulator under tangential AC electric field stress in thefrequency range of 20 Hz to 100 Hz are investigated, using ahigh speed camera. Different kinds of water dropletdeformation at four dominant oscillation modes (mode No.1 tomode No.4), which were found in the experiments, aresimulated, and the electric field near the triple zone isanalyzed to find the worst case of water droplet’s oscillationmode. In parallel, partial discharge inception voltages of a20 µl water droplet located on a silicone rubber surface under

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tangential AC electric field stress in the frequency range of20 Hz to 100 Hz are measured. The measured partial dischargeinception voltages at each oscillation mode are compared withelectric field simulation results.

II.  TEST SETUP 

Fig.2 shows the setup for an individual water droplet on an

insulating surface under tangential electric field stress [3, 6].This setup consists of two high-voltage electrodes, which areembedded in insulating material plates from opposite sides.Applying a high voltage of adjustable frequency to theelectrodes generates a virtually homogenous tangential electricfield on the surface. Individual water droplets are placed

 between the electrodes, using a high precision pipette. Tomake the water droplet more visible, methylene blue is used tocolorize the water droplet (which was proven to have noimpact on the electrical and mechanical properties of thedroplet).

Oscillation of the water droplet under applied electric fieldstress is captured by a SHIMADZU Hyper Vision (HPV2)high speed camera with 1000 frames per second. After eachmeasurement the surface is cleaned and a new water droplet is

 placed on the specimen’s surface. To measure the PDinception voltage of the water droplet on the surface, anaccurate PD measurement system based on IEC 60270requirements is provided (see Fig.3). The MPD 600 OmicronPD measurement system is used inside a shielded test cabinetwith background noise level of less than 1 pC.

Fig. 2. Configuration of test specimen (Dimensions in mm)

Fig. 3. Partial Discharge measurement circuit

III.  R ESULTS 

 A.   Electric Field Simulation

Since the water droplet oscillates under AC electric fieldstress periodically [2, 6], one cycle of this oscillation isanalyzed. With the help of the captured videos four differentframes of water droplet oscillation during one cycle of each

mode are selected (See Table. I). Dimensions of the waterdroplet are measured in each frame. The water droplet atinitial condition has 4 mm length, while after voltageapplication and due to elongation towards the electrodes itslength reaches 5 mm at mode 1 and 4.4 mm at modes 2, 3 and4. The E-field distribution is simulated in the following partsusing CST EM-Studio® software. The applied voltage in allthe cases is 1 kV (±500V). In order to achieve best accuracy of

the results, a thin ring of silicone rubber at the position ofwater droplets on the insulating surface is considered, whichallows the software refining the mesh quality at the triplezones. Fig.4 shows the simulation model. Because the value ofmaximum electric field at the triple line reaches to infinity inthe ideal case, the software has a singularity problem at thetriple lines. In other words, by increasing the mesh quality, thevalue of maximum E-field strength at the triple lines will beincreased. Special criteria of convergence have to be fulfilledto be sure that the simulation results are physically correct [3].For this contribution, the mesh quality step sizes are varied

 between three different values in all simulation cases. Atca. 80% of simulation cases, it is observed that these threemesh qualities have the same maximum field strength values

at the distance of about 0.1 mm away from the triple line ofthe water droplet. It shall be noted that considering the E-fieldvalue at 0.1 mm distance from the edge of the water droplet isalso physically correct because the discharge in triple zonesneed a certain minimum volume to develop an avalanche ofelectrons. Since the E-field enhancement factor at triple line isstrongly dependent on the software accuracy and thesingularity problem at triple line, considering the converge

 point instead of the triple line is the first option to eliminatethe singularity problem, but this converge point is alsodependent on the mesh quality. There are several differentcalculated or simulated E-field enhancement factors in theliterature, which may confuse the reader to find the exact E-

field enhancement factor. For this contribution four oscillationmodes of a single water droplet on the surface of an insulatorwere compared, considering same initial conditions and meshqualities in all simulation cases. It shall be noted that the E-field enhancement factors can vary based on different initialassumptions. The authors are working to develop a method tofind a future better definition of the E-field enhancementfactor based on the integral of an ionization coefficient over acertain volume near the triple zones. The simulation result ofthe test object without water droplet is shown in Fig.5. The E-field between electrodes and at the position of water droplet isalmost merely tangential (parallel to the surface). The E-fieldvalue at the center of the test object can be considered as aconstant value of  E 0  equals to 0.4 kV/cm. Fig.6 shows a

typical case of simulation with three mesh qualities. In thefollowing, the average E-field value at 0.1 mm distance fromthe triple line from three different mesh qualities is consideredas the maximum E-field value E m.

Fig. 4. Simulation model; overal view (left) and zoomed in view (right)

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0

0.1

0.2

0.3

0.4

-20 -10 0 10 20

   E  -   F   i   e    l    d    (    k   V    /   c   m    )

X mm

 

0

0.5

1

1.5

2

2.5

-10 -5 0 5 10

   E  -   F   i   e    l    d    (    k   V    /   c   m    )

X (mm)

0

0.5

1

1.5

2

2.5

2 2.5 3 3.5

  mesh 0.1

  mesh 0.3

  mesh 0.5

TABLE I. FOUR DIFFERENT SHAPES OF A 20 µL WATER DROPLET UNDER

ONE CYCLE OF TANGENTIAL AC E-FIELD STRESS

Initial condition

(non-deformed)

Frame 1 Frame 2 Frame 3 Frame 4

Mode 1

Mode 2

Mode 3

Mode 4

Fig. 5. Tangential E-field of the test object without water droplet

The maximum E-field at each kind of deformed waterdroplet is normalized by the constant E-field at initialcondition ( E 0). So the field enhancement factor k  is defined asfollows:

0 E 

 E k  m=   (1)

where  E m  is the maximum tangential E-field at 0.1 mmdistance from the triple line of a deformed water droplet and

 E 0 corresponds to constant E-field at the center of the testobject without water droplet.

The simulation of a non-deformed water droplet at initialcondition results in a maximum tangential E-field at 0.1 mmdistance from the triple line of 1.15 kV/cm. Thus, presence ofthe water droplet on the surface increases the tangentialcomponent of the E-field at the converge point by factor ofabout 2.9 (i.e. 1.15/0.4). Since the water droplet shape changesdifferently at different modes, four different kinds of waterdroplet oscillation at four modes based on Table. I aresimulated and compared with the maximum E-field of a waterdroplet at initial condition (non-deformed droplet).

Considering (1), the field enhancement k  factors for each caseare calculated. Table. II summarizes the results of k   factorsfor different degrees of deformation. As can be seen, the k  factor for mode 1 in all of the four cases is higher than for theother modes. The reason is firstly the length of the waterdroplet, which is bigger than that of the other modes, andsecondly the low contact angle of water droplet at mode 1 incomparison with the other modes. Considering the maximum k  factor, it seems that the deformation of water droplet atmode 1 increases the local E-field at converge point by factorof 3.51 which is 22% more than maximum E-field in presence

of non-deformed water droplet on the surface. Thisenhancement is 3.10, 3.22 and 3.16 respectively for modenumbers 2, 3 and 4. It shall be noted that these enhancementsare only due to different shapes of water droplet, when thelengths of water droplet are constant. Considering that thelength of water droplet can also change during itsdeformations, the enhancement E-field factors can be higher.An E-field enhancement factor of up to 8 is reported in [3]

under different initial conditions. Mode numbers 2, 3 and 4were found to have only few differences of their k   factors atdifferent frames. This can also be explained by their samelengths. It is also visible that the field enhancement is higherfor lower contact angles of the water droplets.

Fig. 6.  Typical case of simulation (mode 1 frame 4) with three values of

mesh quality

TABLE II. ENHANCEMENT FACTOR OF DIFFERENT FRAMES AT DIFFERENT

MODES 

E-field enhancement factor k  

Fr.1 Fr.2 Fr.3 Fr.4 Max.

Mode 1 3.45 3.36 3.25 3.51 3.51

Mode 2 3.10 3.07 3.04 3.02 3.10

Mode 3 3.22 3.19 3.16 3.13 3.22

Mode 4 3.16 3.02 3.04 3.07 3.16

Fig. 7 compares the maximum k  factors of four modes. As

can be seen, mode No.1 has a big margin from the other

modes. It is also observable that mode numbers 1 and 3 result

in higher E-field enhancement factor than mode numbers 2

and 4.

2.90

3.00

3.10

3.20

3.30

3.40

3.50

3.60

    k

    f   a   c   t   o   r Mode 1

Mode 2

Mode 3

Mode 4

 

Fig. 7. Enhancement factor k for different modes

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4.15

4.2

4.25

4.3

4.35

4.4

4.45

4.5

4.55

4.6

4.65

0 10 20 30 40 50 60 70 80 90 100

   P   D

   i   n   c   e   p   t   i   o   n   E  -    f   i   e   l   d

   k   V   r .   m .   s .    /

   c   m 

Frequency (Hz)

mode 1

mode 2

mode 3

mode 4

 

 B.   Partial Discharge Measurements

As described in the introduction, an accurate PDmeasurement system based on IEC 60270 requirements isapplied (see Fig. 3). Using the MPD 600 Omicron PDmeasurement system, the PD inception voltage of a20 micro liter water droplet located on the surface of siliconerubber surface under tangential AC E-field is measured.Before each measurement the surface of specimen is cleaned

to avoid any effect of dust on the experiment. A new waterdroplet is placed carefully between the electrodes, using

 pipette. The voltage is slowly increased in small steps of about300 V until the first signal of partial discharges (1 pC) isdetected. This procedure is repeated six times. The averagevalue, normalized to atmospheric standard conditions(humidity directly at the triple zone is basically unknown andwas assumed to be the same as in far distance to the droplet),is noted as PD inception voltage. From this voltage theinception field strength is determined by calculating of E-fieldstrength at the center of the test object without water dropletunder this measured PD inception voltage. A large number ofmeasurements in a wide range of frequencies between 20 Hz

to 100 Hz are performed. Results are depicted in Fig. 8. Withthe aid of captured videos, the oscillation modes of the 20 µlwater droplet are observed. It has oscillation mode number 1at 20, 30 and 40 Hz and mode number 2 at 50 Hz. Modenumber 3 is found to occur at 60 and 70 Hz, and at 80 Hz to100 Hz the water droplet has oscillation mode number 4. As afirst finding, the water droplet oscillates at higher modes withincreasing frequency. Secondly, mode numbers 1 and 3 resultin lower values of PD inception voltage than mode numbers 2and 4 (see Fig.8). These results are in full agreement with thesimulation results, which show that mode numbers 1 and 3result in higher E-field enhancement factors than modenumbers 2 and 4. The reason can be explained by comparisonof the contact angles of the water droplets at different modes.

A water droplet at mode numbers 1 and 3 has lower contactangles than at mode numbers 2 and 4. The other interestingresult is that the PD inception voltage makes a step when theoscillation mode of water droplet changes. These steps or

 jumping can be seen at frequencies 40, 50 and 60 Hz, at whichthe mode numbers change (Fig. 8). It is finally worthmentioning that inception field strengths may differ for 50 Hzand 60 Hz power frequency due to possibly differentoscillation modes at these frequencies. More investigationsabout these phenomena are reported in [6].

IV.  CONCLUSION AND OUTLOOK  

For this contribution, oscillation modes of a 20 micro liter

water droplet on the surface of silicone rubber insulator undertangential AC electric field were investigated. Four differentdeformations at four dominant oscillation modes, namelymode No.1 to mode No.4, were simulated and compared withPD inception voltages of a water droplet at these oscillationmodes. Simulation results show that the mode Nos.1 and 3

 provide higher electric field strength at the triple zone incomparison to mode Nos.2 and 4. Experimentally determined

 partial discharge inception voltages in the frequency range of20 Hz to 100 Hz confirm the simulation results. Waterdroplets oscillating at mode Nos.1 and 3 were found to have

lower PD inception voltage in comparison to mode Nos.2 and4. The measurements also show that PD inception voltagemakes a step whenever the oscillation mode of water dropletchanges. An improved method to determine the E-fieldenhancement factor shall be developed in the future work tofind a physically correct value of maximum electric fieldstrength at the triple zones. These investigations shall becontinued to develop a simulation model of water droplet

deformation and movement on the surface of polymericinsulators in order to precisely predict the partial dischargeinception field strength.

Fig. 8. PD inception E-field for 20 µl water droplet on the SR surface

under tangential AC electric field stress

ACKNOWLEDGMENT

These investigations are part of a cooperation with other

research groups in the frame of the Collaboration Research

Center Transregio 75 “Droplet Dynamics Under Extreme

Ambient Conditions” (http://www.sfbtrr75.de/). The authorswould like to thank the DFG (Deutsche

Forschungsgemeinschaft) for the financial support of this

 project.

R EFERENCES 

[1]  R. Hackam, “Outdoor HV Composite Polymer Insulators”, IEEE. Trans.DEI, Vol. 6, pp. 262-268, 1999.

[2]  S. Keim, D. Koenig and V. Hinrichsen, “Experimental Investigations onElectrohydrodynamic Phenomena at Single Droplets on InsulatingSurfaces”, IEEE. Conf. Electr. Insul. Dielectr. Phenom., pp.133-136,2003.

[3]  S. Feier-Iova, “The Behavior of Water Droplet on Insulating SurfacesStressed by Electric Field” PhD Thesis, TU-Darmstadt, 2009.

http://tuprints.ulb.tu-darmstadt.de/2008/

[4]  A. J. Phillips, D. J. Childs and H. M. Schneider, “Aging of Non-CeramicInsulators due to Corona from Water Drops”, IEEE Trans. PowerDelivery, Vol. 14, No. 3, pp. 1081-1089, 1999.

[5]  M.H. Nazemi, V. Hinrichsen, “Partial Discharge of Water Droplets onPolymeric Insulating Surfaces”, 12th  International Electrical InsulationConference, INSUCON 2013, Birmingham, UK, May 2013.

[6]  M.H. Nazemi, V. Hinrichsen, “Experimental Investigations on WaterDroplet Oscillation and Partial Discharge Inception Voltage onPolymeric Insulating Surfaces under the Influence of AC Electric FieldStress”, IEEE Trans. Dielectric Insul., Vol. 20, No.2, pp. 443-453, 2012.

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