IEEE Transactions on Dielectrics and Electrical Insulation Vol. 20, No. 2; April

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1 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 2, No. 2; April Experimental Investigations on Water Droplet Oscillation and Partial Discharge Inception Voltage on Polymeric Insulating Surfaces under the Influence of AC Electric Field Stress M. H. Nazemi and V. Hinrichsen Technische Universität Darmstadt Landgraf-Georg-Str Darmstadt, Germany ABSTRACT Water droplets on hydrophobic surfaces of polymeric insulators oscillate under applied high voltage electric field stress. Deformation of the droplets increases local electric field stress in the triple zones, causing lower partial discharge inception voltage and consequently affecting the ageing performance of the insulator. For this contribution dominant modes of single water droplet oscillation on hydrophobic surfaces were investigated in a wide range of droplet volume and frequency of applied electric field using a high speed camera. 3D frame analysis showed for all volumes an increasing trend of mode number with frequency in the range of 2 to Hz. Experimentally found resonance frequencies for water droplets on a hydrophobic surface approximately correlate with published frequencies of free water droplets. Conductivity showed no effect on the pattern of water droplet oscillation. Partial discharge inception voltages on two different hydrophobic surfaces (silicone rubber and epoxy resin) with conductive and non-conductive (distilled) water droplets were measured. These measurements showed that inception voltage makes a step whenever the oscillation mode of water droplet changes. Conductivity of the water droplets was found to have no effect on the inception voltage on silicone rubber surfaces having a high degree of hydrophobicity, whereas conductive droplets on epoxy resin with lower hydrophobicity lead to lower inception voltages. Index Terms - Water droplet, electric field, oscillation mode, polymeric insulator, hydrophobicity and partial discharge inception voltage. 1 INTRODUCTION BEHAVIOR of water droplets located on hydrophobic surfaces of insulators under high voltage electric field stress is interesting for designers and manufacturers of non-ceramic insulators (NCIs) for outdoor as well as for indoor application. Changing the shape of a water droplet due to E-Field stress affects the homogeneity of the E-Field present on the insulator surface and causes partial discharges (PD) in the triple zone (the common border line between air, water droplet and insulator surface) and, consequently, electro-chemical ageing of the insulator surface [1-5]. Deformation of water droplets under high electric field stress was investigated theoretically [5-] and experimentally [1, 5-6, -] earlier. Also several electrostatic simulations have been performed to find an enhancement factor of electric field due to stationary Manuscript received 2 June 2, in final form December 2. water droplets [3, 5,, 13-14], but as the water droplets are changing their shape dynamic simulation tools that take this effect into account are still needed. In [14-16] theoretical computations and experimental results of electric field and potential distribution along insulators were investigated. A useful IEEE task force [17] provides some guidelines about the electric field distribution on polymeric insulators. Some more investigations on degradation of polymeric insulators were also carried out in [2, 1-21]. Studies about oscillation and break up of water droplet under uniform electric field were published [3, 22-23]. The basic investigation of water droplet corona is reported in [24] and many contributions continue to investigate more corona and partial discharges due to water droplets [2-21, 25-34]. Deformations of free falling water droplets in high-voltage electric fields were also studied and results published in [34-36]. However, there is still a lack of systematic knowledge about typical oscillation modes especially on insulator surfaces and their relation to partial discharge inception voltages. 7-7/13/$ IEEE

2 444 M. H. Nazemi and V. Hinrichsen: Experimental Investigations on Water Droplet Oscillation and Partial Discharge Inception Voltage In the experimental work for this paper dominant oscillation modes of individual water droplets on insulator surfaces of different degrees of hydrophobicity under high voltage tangential electric field stress were identified using a high speed camera. These oscillation modes were categorized in a wide range of droplet volume and frequency of the applied electric field. Correlations between critical frequencies and mechanical resonance frequencies of free water droplets were made, and the effects of volume and conductivity of the water droplet were considered. An accurate PD measurement setup was used to determine the PD inception voltages in all of the cases. Correlation between PD inception voltages and dominant oscillation modes were investigated and are discussed here. These investigations are part of a larger interdisciplinary research project on electro-mechanical simulation of droplet oscillation under the influence of an electric field and computational prediction of PD inception voltage affected by the periodically changing droplet shape in the frame of the DFG (Deutsche Forschungsgemeinschaft) Collaboration Research Center Transregio 75 Droplet Dynamics Under Extreme Ambient Conditions. 2 TEST SETUP Behavior of water droplets under tangential and normal components of electric field was investigated in [14], where it was shown that the tangential E-Field component is more severe than the normal component. Therefore, only a merely tangential E-Field is being considered in this paper. To investigate the behavior of an individual water droplet on an insulating surface under tangential E-Field stress, a setup according to Figure 1 has been developed [1, 5, 13]. This setup consists of two high-voltage electrodes, which are embedded in insulating plates from opposite sides. A virtually homogenous tangential electric field is generated on the surface when voltage is applied to these two electrodes. Silicone rubber (SR) and epoxy resin (ER) are used as two insulating materials with different degrees of hydrophobicity (wettability classes, WC, acc. to [37]). This is illustrated in Figure 2 by two identical water droplets on the surfaces with no electric field, corresponding to WC 1 (contact angle > ) in case of SR and approx. WC 3 (contact angle 45 ) in case of ER. Insulating material Opposite side embedded electrodes Figure 1. Configuration of test specimen (Dimensions are in mm). a) SR, WC 1 b) ER, WC 3 Figure 2. Degree of surface hydrophobicity of silicone rubber (SR) and epoxy resin (ER) specimens without E-Field. 2.1 OSCILLATION MEASUREMENT SETUP The experimental setup for mechanical oscillation measurements is shown in Figure 3. To generate a high voltage of adjustable frequency, a signal generator, a power amplifier and a test transformer are used. The output of the test transformer is connected to the specimen via a resistor. Using a mirror system a 3D-view video of the water droplet can be captured with the aid of a high speed camera. The sample is placed in front of the camera such that the front view of the water droplet is taken directly by the camera and top and side views are visible in two mirrors, which are placed in appropriate angles to reflect the top and side view pictures of the water droplet towards the camera. Thus, in each frame a 3D-view is captured. High intensity illumination is provided by several white power LEDs in order to minimize heat generation, which would affect the droplet volume during measurement. The overall test setup is shown in Figures 4a and 4b. A simple FEM simulation confirmed that the mirrors have no effect on the tangential electric field distribution at the location of the droplet. Figure 5 compares the results of tangential and absolute component of electric field on the SR surface in the two cases with and without mirror system at a test voltage of 1 kv between electrodes. E tan and E abs represent the tangential and the normal components of electric field and X represent the distance from the center of test object in x- direction. As can be seen, the mirrors have effect only on the normal component of electric field, which, however, is not interesting for these investigations, whereas the tangential component remains unchanged. Power amplifier Signal generator Hz 1 MHz Resistor, 1MΩ HV electrode Test Transformer.3/ kv, kva Test object High speed camera Figure 3. Experimental setup for oscillation measurement. Earth electrode

3 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 2, No. 2; April PARTIAL DISCHARGE MEASUREMENT The MPD 6 Omicron partial discharge measurement system is used for PD inception voltage measurement. Background noise inside the shielded test cabinet is below 1 pc. The setup fulfills the requirements of IEC 627. Figure 6 shows the measurement circuit. a) mirror system b) high speed camera Power amplifier Resistor, 1MΩ Figure 4. Test setup with mirror system and high speed camera The SHIMADZU Hyper Vision (HPV2) high speed camera with frames per second is used to capture the videos. In order to make the water droplet more visible, methylene blue is used to colorize the water droplet. Preinvestigations showed that this has only negligible effect on conductivity and permittivity of water droplet. For each measurement one individual water droplet, having a volume of 2, 4, 6, or µl, is placed on the specimen s surface between the electrodes. After each measurement the water droplet is replaced by a new one because of its permanent deformation by previous voltage application. The surface is cleaned between the measurements to remove any dust and to provide the same initial value of surface hydrophobicity. Conductivity of the water is measured before each experiment. E tan (V/cm) E abs (V/cm) X (cm) a) tangential E-Field X (cm) b) absolute E-Field with mirror without mirror with mirror without mirror Figure 5. Electric field simulation of the setup with and without mirror system. Signal generator Hz 1 MHz Calibration Test Transformer.3/ kv, kva Sample Figure 6. Partial Discharge measurement circuit according to IEC EXPERIMENTAL RESULTS 3.1 OSCILLATION ANALYSIS A large set of videos with water droplet volume variation from 2 to µl in the frequency range of 2 to Hz on the two different surface materials (SR and ER) were captured. Comparison of the captured videos shows that dominant oscillation modes develop on the SR surface with its high degree of hydrophobicity. On the ER surface, due to its lower degree of hydrophobicity, almost all of the modes seem to be identical. Four different oscillation modes of the water droplet dominantly occur on the SR surface. These modes, which are named mode No.1 to mode No.4, are illustrated in Figure 7. In mode No.1 the water droplet periodically develops sharp edges on one side and elongates towards the electrodes two times per cycle of the applied electric field. In this case the water droplet has two different peaks on its shape, each one related to one half-cycle. Mode No.2 consists of two up and down shrinking positions. The water droplet stretches upwards and then shrinks back down. In mode No.3 the water droplet moves in a way that two different peaks occur in its left and right part during one half-cycle each of the applied electric field. Stronger oscillation at top of the water droplet can be seen in mode No.4, which has periodically three or more peaks on its shape during oscillation. Mode analysis in the range of 2 to Hz shows an increasing trend of mode number with frequency for all investigated volumes, having approximately the same slope (Figure ). Figure shows a linear trend line of applied voltage frequency as a function of water droplet volume for each mode. Comparing the results for different volumes in the range of investigated frequencies shows a decrease in frequency with increasing volume for each modes. In order to find the critical frequencies of water droplet oscillation under tangential electric field stress, 3D recorded frames were analyzed. C k PD U

4 446 M. H. Nazemi and V. Hinrichsen: Experimental Investigations on Water Droplet Oscillation and Partial Discharge Inception Voltage Without E Field Mode 1 Mode 2 Mode 3 Mode 4 Figure 7. Four dominant oscillation modes of a water droplet on SR surface under tangential E-Field stress. Mode Number water droplet in each frame according to Figure the value of an A d factor can be derived in each frame. This A d factor is the ratio of the length x of water droplet to its height z in the front view of each frame. Dividing an actual A d value by the reference value A d, which is calculated from the water droplet dimensions x and z before voltage application, results in the normalized A dn factor. Figure illustrates the meaning of the A d factors. Figure exemplarily shows the resulting A dn factors for a 2 µl water droplet in the investigated range of frequencies. The higher the resonance frequency of water droplet oscillation, the higher is the value of A dn factor. The 2 µl water droplet has an increase in A dn at 2 Hz which is due to the difference in mode numbers at different volumes and frequencies. The 2 µl water droplet oscillates at mode number 1 at 2 Hz. When resonance occurs at mode number 1, an increase in A dn is expected. Water droplet elongates towards the electrodes at mode number 1, which increases the length of the droplet and consequently leads to a bigger value of A dn in case of resonance. By increasing the volume of the water droplet, the mode number of oscillation increases, so for large volumes resonance occurs at high mode numbers, which leads to lower but still considerable difference between the A dn value at resonance frequency and at the other frequencies. For example, the difference between A dn values of µl water droplet at 6 Hz which oscillates at mode number 4 is also considerable in comparison with the other frequencies. The summarized results of resonance frequencies in the volume range of 2 to µl and frequencies between 2 and Hz are depicted in Figure 13. The highest A dn factors for each volume represent critical resonance frequencies µl 4 µl 6 µl µl µl Linear (2 µl) Linear (4 µl) Linear (6 µl) Linear ( µl) Linear ( µl) Figure. Mode number vs. frequency for 2, 4, 6, and µl water droplets. t = 5 ms ms 15 ms 2 ms 25 ms 3 ms 35 ms 4 ms 45 ms 5 ms Figure. 3D recorded frames of 2 µl water droplet oscillation during one cycle of applied 2 Hz sinusoidal E-Field (first row: front view, second row: side view and third row: top view) Mode 1 Mode 2 Mode 3 Mode 4 Linear (Mode 1) Linear (Mode 2) Linear (Mode 3) Linear (Mode 4) Figure. Linear trend line of applied voltage frequency vs. water droplet volume for each mode. Figure shows sample 3D recorded frames of water droplet oscillation during one cycle of the applied sinusoidal E-Field. By measuring the dimensions of the a) before voltage application b) during voltage application X X Ad Ad Z Z Ad Normalized Ad factor A d Figure. A d factor definition. Resonance frequencies of free water droplets were investigated and reported in the literature in several publications. According to the basic finding in [34], the

5 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 2, No. 2; April resonance frequency of a free water droplet can be calculated in the following form: A dn A dn (Average Value) nn ( 1)( n 2) n 3 a where; : Resonance angular frequency of a free water droplet n (rad/s); n 2 fn : Surface tension (N/m) n : Mode number a : Radius of water droplet (m) ρ : Density (kg/m 3 ) Figure. Resulting A dn factors for a sample 2 µl water droplet Figure 13. Summarized resonance frequencies of water droplet oscillation. By converting the radius of the (spherical) water droplet to its volume and considering that uncharged water droplets oscillate with twice the frequency of the applied electric field, whereas charged droplets oscillate with the original frequency only [22], a relation of resonance frequency versus volume of water droplet in different modes can be plotted. According to [22] the water droplet on the surface can be modeled using a mass-spring-damper mechanical (1) Hz 3Hz 4Hz 5Hz 6Hz 7Hz Hz Hz Hz model. The kinetic equation is expressed by: 2 d x dx M D K x F 2 dt dt (2) where; M, D and K are mass, damping constant and spring constant, respectively. x is the displacement of the water droplet and t represents the time. F is the main external force which can be expressed by Maxwell or Coulomb force respectively for uncharged and charged droplets [22]. Considering the Maxwell force in case of an uncharged drop results in: F E E sin t E (1 cos 2 t) (3) where E is the electric field and ω is the angular frequency of the applied voltage. Solving Equation (2), considering only the steady state condition, results in displacement with twice the frequency of E: x () t A B cos(2 t ) ss In case of a charged droplet and considering the Coulomb force, we have [22]: F q E q E sin t (5) which leads to the water droplet displacement with same frequency as that of the applied electric field: x () t C cos(2 t ) ss The captured movement of a water droplet in one cycle of its movement was plotted for all the volumes of 2 to µl and for all frequencies in the range of 2 to Hz. Comparing the frequency of water droplet movement in one cycle with applied voltage frequency showed that in some cases the water droplet vibrates with twice the frequency of the applied voltage, but, in some other cases the frequency of water droplet movement was the same as for the applied voltage frequency. The reason is assumedly that in some cases water droplet was charged with existing free charge carriers in the lab which lead to the movement with the same frequency of that of the applied voltage. (This will be investigated in detail in future work). Figure 14a and 14b show two typical one cycle movements of uncharged and charged water droplets, respectively. In this figure the normalized x-position of water droplet in one cycle of its movement is plotted. Figure 14a shows a movement of 2 µl water droplet at 2 Hz applied voltage oscillating at 4 Hz ( uncharged case) and Figure 14b shows a movement of 6 µl water droplet at 7 Hz applied voltage oscillating at 7 Hz ( charged case). Figures 15 and 16 show the results of resonance frequency of a free water droplet versus its volume for both uncharged and charged conditions. The experimentally found resonance frequencies for water droplets on insulator surfaces are also depicted in these two figures. As can be seen, the experimentally found resonant frequencies for water droplets on a wettability class (WC) 1 insulating surface, on which the water droplet has a contact angle of (4) (6)

6 44 M. H. Nazemi and V. Hinrichsen: Experimental Investigations on Water Droplet Oscillation and Partial Discharge Inception Voltage more than [37], are approximately correlated with frequencies of both charged and uncharged free water droplets. a) Uncharged 2 µl water droplet at 2 Hz: mechanical oscillation at twice the frequency of applied voltage. b) Charged 6 µl water droplet at 7 Hz: mechanical oscillation at the same frequency of applied voltage Figure 14. Ttypical one cycle movements of uncharged and charged water droplet. Normalized X Position Normalized X Position ms 4 Hz time (ms) ms 7 Hz time (ms) Expr.found Mode 1 Expr.found Mode 2 Expr.found Mode 3 Expr.found Mode 4 Mode 1 Free water droplet Mode 2 Free water droplet Mode 3 Free water droplet Mode 4 Free water droplet Figure 15. Correlation between experimentally found resonance frequencies and uncharged free water droplet resonance frequencies. Comparing the captured videos of conductive and nonconductive water droplets additionally shows that conductivity, varied in the range of 3 µs/cm to 17 ms/cm, has no effect on the pattern of water droplet oscillation under tangential E-Field stress Expr.found Mode 1 Expr.found Mode 2 Expr.found Mode 3 Expr.found Mode 4 Mode 1 Free water droplet Mode 2 Free water droplet Mode 3 Free water droplet Mode 4 Free water droplet Figure 16. Correlation between experimentally found resonance frequencies and charged free water droplet resonance frequencies. 3.2 PD INCEPTION VOLTAGE ANALYSIS The test circuit of partial discharge measurement is shown in Figure 6. After each measurement the surface of the specimen is cleaned, and a new water droplet is carefully placed on the surface symmetrically between electrodes. The voltage is slowly increased in small steps of about 3 V up to the first signal of partial discharges (1 pc) is detected. This procedure is repeated six times, and the average value is noted as PD inception voltage. A large number of measurements for water droplet volumes of 2, 4, 6, and µl in a wide range of frequencies between 2 to Hz was performed. First investigation was the effect of conductivity on PD inception voltage. To have an idea about the water conductivity, different water conductivities are listed in Table 1 [3]. The conductivity of different types of water at 25 C are also reported in [3], so pure, deionized and rain water have, respectively, conductivities of about.55, 1 and 5 μs/cm. Water droplet with conductivities below 3 µs/cm can be considered as a non-conductive water droplet. Drinking water has a conductivity of 5 μs/cm [3] and conductivity of industrial wastewater can reach up to ms/cm [3]. In our experiment, water droplet with conductivity of 3 µs/cm and 17 ms/cm are used respectively as non-conductive and conductive droplets. It turns out that conductivity of the water droplet has no effect on the inception voltage on SR surfaces having a high Table 1. Different type of water Conductivity [3]. Water type Conductivity (µs/cm) Deionized water.5-3 Pure rainwater <15 Freshwater rivers - Marginal river water -16 Brackish water 16-4 Saline water >4 Seawater 51 5 Industrial waters - degree of hydrophobicity (WC 1 with contact angle > ). But a conductive droplet on an ER surface, which has a lower degree of hydrophobicity (ca. WC 3 with contact angle of about 45 ), results in lower inception voltages. In other words, influence of conductivity of a water droplet on

7 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 2, No. 2; April PD inception voltage depends on the hydrophobicity of the surface. The more hydrophobic the surface, the lower will be the effect of water droplet conductivity on PD inception voltage. In the following, the angle given in parenthesis indicates the contact angle. Figure 17 compares the results of PD inception voltage of conductive (17 ms/cm) and non-conductive (3 µs/cm) water droplets on SR ( ) as well as on ER(45 ) for 2 and µl water droplets at three frequencies (2, 5 and Hz) of the applied electric field. The PD inception voltages of 2 µl non-conductive water droplets on SR ( ) are measured as., 13 and. kv r.m.s. respectively at 2, 5 and Hz. The PD inception voltage was the average value of six measurements with standard deviation of approximately 4 V at all three mentioned frequencies. A 2 µl nonconductive water droplet on ER(5 ) resulted the PD inception voltages of.,.2 and.1 kv r.m.s. with standard deviation of 2, 27 and 1 V from six measurements respectively at 2, 5 and Hz. As it can be seen, PD inception voltage on the ER (5 ) is lower than on the SR ( ) due to its lower class of hydrophobicity. Results of µl non-conductive water droplet on SR ( ) and ER (45 ) showed also the considerable difference between these two different materials (compare columns (1) and (3) of Figure 17b). In order to compare two materials, the PD inception voltages of a non-conductive water droplet at 2 and Hz on the surface of silicone rubber and epoxy resin are illustrated in Figure 1. As it can be seen, on the surface of both materials, the PD inception voltage decreases when volume of water droplet increases. The reason is that larger water drops bridge a greater distance between HV and earth electrodes which increases the electric field at triple points and consequently leads to the lower PD inception voltage. Comparing the PD inception voltage of a 2 µl non-conductive water droplet on SR ( ) and on ER (5 ) shows that at 2 Hz, there is a difference of about 2 kv r.m.s. (17%) in PD inception voltage. This difference reaches to.2 kv r.m.s. (2.4%) for µl droplet. The similar investigation at Hz shows a difference of 1.6 kv r.m.s. (.7%) in PD inception voltage for 2 µl water droplet which reduces to.6 kv r.m.s. (5.%) for µl droplet. The reason is that by increasing the water droplet volume, the contact angle of drop on SR surface decreases. In other words, larger drops result in lower degrees of hydrophobicity on SR surface, so the larger the water droplet, the smaller will be the difference between hydrophobicity class of SR and ER surfaces. Therefore the smaller droplets have a bigger difference of PD inception voltage on two different surfaces. Difference between PD inception voltages of conductive and non-conductive droplets on the SR ( ) were very small (.6% for 2 µl at Hz or 1% for µl at 2 Hz), but on the ER(45 ) with lower degree of hydrophobicity, the conductive droplet had a lower value of PD inception voltage. Difference in this case was observed as 5.3% for 2 µl at Hz or 4% for µl at 2 Hz (1) (2) (3) (4) (1) (2) (3) (4) (1) (2) (3) (4).7 2 Hz 5 Hz Hz a) 2 µl water droplet on SR ( ) and ER (45 ) (1) (2) (3) (4) (1) (2) (3) (4) (1) (2) (3) (4) 2 Hz 5 Hz Hz b) µl water droplet on SR ( ) and ER(45 ) Figure 17. Effect of water droplet conductivity on PD inception voltage for SR ( ) and ER (45 ) (1): Non-conductive water droplet on SR, (2): Conductive water droplet on SR, (3): Non-conductive water droplet on ER, (4): Conductive water droplet on ER % % Figure 1. PD inception voltages of a non-conductive water droplet on the surface of silicone rubber and epoxy resin, top: at 2 Hz, bottom: at Hz..1 SR ER. 2.4 % SR ER 5. %

8 45 M. H. Nazemi and V. Hinrichsen: Experimental Investigations on Water Droplet Oscillation and Partial Discharge Inception Voltage In order to compare the results of PD inception voltages with other results in the literature [4, 2], the test object was modeled with three-dimensional finite element CST-Studio software [4], and the measured PD inception voltages were converted to the PD inception electric field on the insulator surface without water droplet. This field is referred to as applied E-Field. Figure 1 shows the results of PD inception E-Field of a non-conductive water droplet on SR ( ) at 5 Hz as a function of water droplet volume. The observed results are similar to the results obtained by Phillips et al. [4] and Lopez et al. [2]. As it can be seen, the applied E-field required for PD inception decreases with increasing water droplet volumes. PD inception E Field, r.m.s. value (kv/mm) Figure 1. PD inception E-Field as a function of water droplet volumes for SR surface. Figure 2 presents the average value of measured PD inception voltages of non-conductive water droplet on SR ( ) as a function of water droplet volumes. Comparing the results of Figure 2 with A dn values depicted in Figure 13 shows that the resonance condition does not always lead to lower partial discharge inception voltages. For example, the 4 and µl water droplets have a lowest PD inception voltage respectively at 3 and 2 Hz which are different from the main obtained resonance frequencies of 5 and 6 Hz which can be seen as higher A dn in Figure SR() Lopez et al. [2] Philips et al. [4] 2 Hz 3 Hz 4 Hz 5 Hz 6 Hz 7 Hz Hz Hz Hz Figure 2. PD inception voltage as a function of water droplet volumes. Another result is obtained by comparison of PD inception voltages for different volumes at different frequencies. Figure 21 shows the summarized results of measured PD inception voltages for non-conductive water droplets on SR ( ) under tangential E-Field stress. Obviously for small droplets (2, 4 and 6 µl), by increasing the frequency, the PD inception voltage increases. This follows the trend of mode numbers depending on frequency. The reason is that at higher frequencies the upper part (the peak) of the small water droplet is moving more than the rest. Regarding that partial discharges would start in the triple zone of water droplet (see, e.g., [5]), and that the bottom part of water droplet stays unchanged at high frequencies, higher values of PD inception voltage are expected. The PD inception voltage of large volume droplets ( and µl), increases also with increase in frequency up to 5 Hz, because larger water droplets bridge a greater distance between the HV and ground electrodes thus automatically increasing the field at the triple point. At frequencies higher than 5 Hz there is a small difference in PD inception voltage of large water droplets. The reason could be due to similarity behavior of large water droplets at high frequencies which cause low difference in PD inception values. It can also be observed that small volume droplets (2, 4 and 6 µl) result in similar patterns and larger volumes ( and µl) also result in similar patterns, but different from those of lower volumes. These two different patterns are depicted in Figure 22 separately µl 4 µl 6 µl µl µl Figure 21. Summarized results of measured PD inception voltages for non-conductive water droplet on SR ( ) under tangential E-Field stress. The most interesting result is that PD inception voltage makes a step when the oscillation mode of water droplet changes. For example, a 2 µl water droplet has oscillation mode numbers 1, 2 and 3, respectively, at 4, 5 and 6 Hz. Distinct differences in PD inception voltages at these three frequencies were detected (Figure 23a). The reason can be explained due to different shapes of water droplet oscillations at different modes. As in Figure 7 can be seen, the contact angle of water droplet at mode numbers 1 and 3 are lower than water droplet contact angles at mode numbers 2 and 4. Comparison of PD inception voltages and mode numbers in several cases shows that mode numbers 1 and 3 result in lower values of PD inception voltage than mode numbers 2 and 4. Another example can be found for a 6 µl water droplet, which has mode numbers 3, 4 and 2, respectively, in the frequency range of 5 to 7 Hz, leading to steps in PD inception voltage values in this range of

9 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 2, No. 2; April frequencies. In this case again mode number 3 had lower value of PD inception voltage in comparison with mode numbers 2 and 4. Mode number 4 had a maximum value of PD inception voltage because the most part of oscillation at this mode appears at the top of the water droplet which affects little on triple points. More investigations showed that the other steps in inception voltages were correlated to differences in mode numbers. PD inception voltage, r.m.s (kv) µl 4 µl 6 µl a) small volumes (2, 4 and 6 µl) µl µl b) large volumes ( and µl) Figure 22. Frequency analysis of PD inception voltages for nonconductive water droplet on SR ( ) under tangential E-Field stress (two different patterns). 4 CONCLUSION In these investigations a large set of water droplet oscillations on hydrophobic surfaces of polymeric insulators under high-voltage tangential electric field stress and their related partial discharge inception voltages were measured and discussed. Four dominant oscillation modes of water droplets on hydrophobic insulator surfaces under tangential electric field stress in a wide range of volume and frequency were defined. With the aid of 3D video frame analysis, critical resonant frequencies were obtained and compared with resonance frequencies of free water droplets as reported in the literature. The experimentally found resonant frequencies for water droplet on insulating surfaces with hydrophobicity class of WC 1 were approximately correlated with resonance frequencies of both charged and uncharged free water droplets mode 1 mode 2 mode 3 a) 2 µl water droplet mode 3 mode 4 mode b) 6 µl water droplet Figure 23. Step in inception voltage when the oscillation mode of water droplet changes. Partial discharge inception voltage analysis shows that for all volumes the PD inception voltage increases with frequency, which is correlated with mode numbers increasing with frequency. According to mode definitions, modes No.1 and No.3 are found to result in lower values of PD inception voltage in comparison with modes No.2 and No.4, but the resonance condition does not lead to lower value of partial discharge inception values. Steps in the PD inception voltages are obtained when the oscillation modes of water droplet change. Conductivity of the water droplets on silicone rubber insulating surface with contact angle of about has effect neither on oscillation mode patterns nor on PD inception voltages. However, for surfaces of lower hydrophobicity, such as epoxy resin with contact angle of about 45, conductive droplets result in lower inception voltages. The reported investigations are introduced to form a basic for a deeper understanding of electrical discharge phenomenon on polymeric insulator surfaces and for development of tools for prediction of PD inception field strength. To make the results more realistic, more investigations of multi droplets on inclined surfaces of polymeric insulators as well as localization of discharges are planned to be performed, which will be closer to practical applications. In parallel a dynamic simulation of water droplet oscillation on polymeric insulation surfaces

10 452 M. H. Nazemi and V. Hinrichsen: Experimental Investigations on Water Droplet Oscillation and Partial Discharge Inception Voltage under the influence of an AC electric field considering both electrical and mechanical forces is in progress in another collaborating research group in this project. The goal is the identifications of worst case with regard to PD inception field strength by simulations rather than by complex experimental investigations. After validation of the simulation results with these experimental investigations, a general prediction of inception voltages for polymeric insulators in presence of water droplets should be achievable. ACKNOWLEDGEMENT The authors would like to thank the DFG (Deutsche Forschungsgemeinschaft) for the financial support of this project in the frame of the Collaboration Research Center Transregio 75 Droplet Dynamics Under Extreme Ambient Conditions. REFERENCES [1] S. Keim, D. Koenig and V. Hinrichsen, Experimental Investigations on Electrohydrodynamic Phenomena at Single Droplets on Insulating Surfaces, IEEE. Conf. Electr. Insul. Dielectr. Phenom, pp , 23. [2] R. Sundararajan, S. Sundhur and T. Asokan, Electrohydrodynamics of Water Droplets on Polymer Surfaces, IEEE. 34th IAS Annual Meeting, Indust. App. Conf, Vol. 3, pp , 1. [3] K. Adamiak and J.M. Floryan, Dynamics of Water Droplet Distortion and Breakup in a Uniform Electric Field, IEEE Trans. Indust. App, Vol. 47, No. 6, pp , 2. [4] A. J. Phillips, D. J. Childs and H. M. Schneider, Aging of Non- Ceramic Insulators due to Corona from Water Drops, IEEE Trans. Power Delivery, Vol. 14, No. 3, pp. 1-, 1. [5] S. Feier-Iova, The Behavior of Water Droplet on Insulating Surfaces Stressed by Electric Field, Ph.D. Thesis, TU-Darmstadt, 2. [6] A.M. Imano and A. Beroual, Deformation of Water Droplets on Solid Surface in Electric Field, J. Colloid and Interface Sci., Vol. 2, pp. 6-7, 26. [7] G. Supeene, Ch. R. Koch and S. Bhattacharjee, Deformation of a Droplet in an Electric Field: Nonlinear Transient Response, J. Colloid and Interface Sci., Vol. 31, pp , 2. [] J.C. Baygents, N.J. Rivette and H.A. Stone, Electrohydrodynamic deformation and interaction of drop pairs, J. Fluid Mech., Vol. 36, pp , 1. [] Y. Zhu, K. Haji, M. Otsubo, Ch. Honda and N. Hayashi, Electrohydrodynamic Behaviour of Water Droplet on an Electrically Stressed Hydrophobic Surface, J. Appl. Phys., Vol. 3, pp , 26. [] Y. Higashiyama and M. Kosano, Relation between Extension of a Filamentary Channel from a Water Droplet Placed on a Hydrophobic Sheet under AC Field and Flashover via the Droplet, IEEE. Indust. App. Conf, pp , 27. [] T. Yamada, T. Sugimoto, Y. Higashiyama, M. Takeishi and T. Aoki, Resonance Phenomena of a Single Water Droplet Located on a Hydrophobic Sheet under AC Electric Field, IEEE Trans. Indust. App., Vol. 3, No.1, pp. 5-65, 23. [] T. Schütte and S. Hörnfeldt, Dynamics of Electrically Stressed Water Drops on Insulating Surfaces, IEEE. Int l. Sympos. Electr. Insul., pp , 1. [13] S. Feier-Iova and V. Hinrichsen, Partial Discharge Inception Voltage of Water Drops on Insulating Surfaces Stressed by Electrical Field, IEEE. Electr. Insul. Conf (EIC), pp , 2. [14] B. Sarang, P. Basappa, V. Lakdawala and G. Shivaraj, Electric Field Computation of Water Droplets on a Model Insulator, IEEE Elec. Insul. Conf, pp , 2. [15] H. El-Kishky and R. S. Gorur, Electric Field Computation on an Insulating Surface with Discrete Water Droplets, IEEE Trans. Dielect. Electr. Insul, Vol. 3, No. 3, pp , 16. [16] Z. Guan, L. Wang, B. Yang, X. Liang and Z. Li, Electric Field Analysis of Water Drop Corona, IEEE. Trans. Power Delivery, Vol. 2, No. 2, pp. 64-6, 25. [17] A. J. Phillips, J. Kuffel, A. Baker, J. Burnham, A. Carreira, E. Cherney, W. Chisholm, M. Farzaneh, R. Gemignani, A. Gillespie, Th. Grisham, R. Hill, T. Saha, B. Vancia and J. Yu, Electric Fields on AC Composite Transmission Line Insulators, IEEE Taskforce on Electric Fields and Composite Insulators, IEEE Trans. Power Delivery, Vol. 23, No. 2, pp. 23-3, 2. [1] J.P. Reynders, I.R. Jandrell and S.M. Reynders, Surface Ageing Mechanisms and their Relationship to Service Performance of Siliconee Rubber Insulation, th Int l. Sympos. High Voltage Eng., Vol. 4, pp. 54-5, 1. [1] CIGRE Working Group D1.14, Evaluation of Dynamic Hydrophobicity Properties of Polymeric Materials for Non-Ceramic Outdoor Insulation; Retention and Transfer of Hydrophobicity, 2. [2] A. Krivda, D. Birtwhistle, S. Coyne and H. Liu, Discharge phenomena between water drops on polymer surfaces, Int l. Sympos. High Voltage Eng., Bangalore, India, Paper No. 4-6, 21. [21] A. Krivda and D. Birtwhistle, "Breakdown between water drops on wet polymer surfaces", IEEE Conf. Electr. Insul. Dielectr. Phenomena (CEIDP), pp , 21. [22] O. Fujii, K. Honsali, Y. Mizuno and K. Naito, Vibration of a Water Droplet on a Polymeric Insulating Material Subjected to AC Voltage Stress, IEEE Trans. Dielectr. Electr. Insul, Vol. 17, No. 2, pp , 2. [23] J.D. Sherwood, Break-up of fluid droplets in electric and magnetic fields, J. Fluid Mechanics, Vol.1, pp , 1. [24] W. N. English, Corona from a Water Drop, Phys. Rev., Vol. 74, No. 2, pp. 17-1, 14. [25] A.J. Philips, D.J. Childs and H.M. Schneider, Water drop corona effects on full-scale 5 kv non-ceramic insulators, IEEE Trans. Power Delivery, Vol.14, pp , 1. [26] T. Cheng, D.C. Jolly and D.J. King, Surface flashover of water repellent insulators under moist conditions, IEEE Trans. Electr. Insul., Vol., pp , 177. [27] C. Konski and H. Thacher, The Distortion of aerosol droplets by an electric field, J. Phys. Chem., Vol. 57, No., pp. 55-5, 153. [2] I.J.S. Lopes, Sh.H. Jayaram and E.A. Cherney, A Study of Partial Discharges from Water Droplets on a Siliconee Rubber Insulating Surface, IEEE. Trans. Dielectr. Electr. Insul, Vol. No. 2, pp , 21. [2] A.M. Imano, AC Discharge Current Characteristics and LI Flashover Field Intensity of Water Droplets on Insulated Solid Surface, J. Electr. Eng., Vol. 6, No. 1, pp. 24-2, 2. [3] X. Zhang and S.M. Rowland, Behavior of Low Current Discharges between Water Drops, IEEE. Conf. Electr. Insul. Dielectr. Phenomena, pp , 2 [31] H. Gao, Zh. Jia, Y. Mao, Zh. Guan and L. Wang Effect of Hydrophobicity on Electric Field Distribution and Discharges along Various Wetted Hydrophobic Surfaces, IEEE Trans. Dielectr. Electr. Insul., Vol. 15, No. 2, pp , 2. [32] H. Deng, Zh. He, J. Ma, Y. Xu, J. Liu and R. Guo, Initiation and Propagation of Discharge in Liquid Droplets: Effect of Droplet Sizes, IEEE Trans. Plasma Sci., Vol. 3, No., pp , 2. [33] Y. Zhu, M. Otsubo, C. Honda, Y. Hashimoto and A. Ohno, Mechanism for Change in Leakage Current Waveform on a Wet Silicone Rubber Surface; A Study using a Dynamic 3-D Model, IEEE Trans. Dielectr. Electr. Insul., Vol., No. 3, pp , 25. [34] S.B. Sample and B. Raghupathy, Quiescent Distortion and Resonant Oscillations of Liquid Drop in an Electric Field, Int l. J. Eng. Sci., Vol., pp. 7-, 17. [35] Y.M. Jung, H. Ch. Oh and I.S. Kang, Electrical Charging of a Conducting Water Droplet in a Dielectric Fluid on the Electrode Surface, J. Colloid and Interface Sci., Vol. 322, pp , 2. [36] M. Szakáll, S.K. Mitra, K. Diehl and S. Borrmann, Shapes and Oscillations of Falling Raindrops-A Review, J. Atmospheric Research, Vol. 7, pp , 2. [37] IEC/TS 6273, Guidance on the measurement of wettability of insulator surfaces, First edition, [3] S. Sutar, C. Switzer and J. Codling, Ribbons of Blue Handbook, published by SciTech Discovery Centre, 1.

11 IEEE Transactions on Dielectrics and Electrical Insulation Vol. 2, No. 2; April [3] Conductivity Theory and Practice booklet, Radiometer Analytical, SAS (Société par actions simplifiée), [4] EM-CST Studio, Mohammad Hossein Nazemi was born in Darab, Iran in 17. He received the B.Sc. and M.Sc degrees from the PWUT and Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran both in electrical engineering in 21 and 23, respectively. From 23 to 2 he worked at MOSHANIR power engineering consultants as a senior electrical engineer. In 2 he started a research project at the University of Tehran, and after two years he joined the Technische Universität Darmstadt as a scientific researcher. He joined TUD in 2 and is currently working on a project with the aim of a Dr.-Ing degree. Mr. Nazemi s research fields are high-voltage testing, partial discharge measurement and polymeric insulators. Volker Hinrichsen (M 4) was born in Westerland/Sylt, Germany in 154. He received both the "Dipl.-Ing." and "Dr.-Ing." degrees in electrical engineering from the Technical University of Berlin in 12 and 1, respectively. He joined Siemens Power Transmission and Distribution in 1 as a test engineer in the high-voltage laboratories and became R&D Director of the Siemens Surge Arrester Division in 12. In 21 he joined Technische Universität Darmstadt as a full professor in high-voltage engineering. Currently he is head of the highvoltage group and the accredited kv test field at the TU Darmstadt and is active in education, research and testing. Volker Hinrichsen is a member of CIGRE and VDE and chairman and member, respectively, of several national and international scientific and standardization committees on surge arresters, insulation systems, insulation coordination, vacuum breakers and testing within IEC, IEEE, CIGRE and VDE/DKE.