Development of a Simple Experimental Setup for the Study of the Formation of Dry Bands on Composite Insulators

Abstract

This paper introduces a new geometry for the study of dry band formation. Firstly, a thermoelectric simulation of a 69 kV uniformly polluted composite insulator was performed. The results obtained show that thermal stress is greater at the rod surface where current density is maximum. In order to experimentally reproduce the constriction of current density lines on the insulator rod surface, which is the cause of dry band formation, the development of a new simple geometric setup, which was then tested experimentally, was proposed. For this purpose, an ESDD value corresponding to a high level of pollution was used for each polluted sample, and the samples were placed in a climate chamber at constant 90% relative humidity and a constant ambient temperature of 20 °C. Low-voltage tests permitted the determination of the wetting duration, which corresponds to the maximum surface conductance of the polluted layer. The values obtained agree with the 10–40 min duration recommended in IEC 60507. Moreover, the tests performed at a higher voltage demonstrated the efficiency of the proposed setup to simulate the complex process of dry band formation in a reproducible way in terms of leakage current and temperature behavior. The proposed setup is a new and simple method that can be easily used by the electrical industry to develop new material for the next generation of overhead line composite insulators without requiring costly HV equipment.

1. Introduction

Electrical energy is generally transported over long distances using high-voltage (HV) overhead transmission lines supported by pylons. The mechanical connection and electrical insulation between the lines and the pylons are provided by insulators. In polluted environments, these lines are subjected to flashover phenomena, which can negatively affect the quality and reliability of the electrical energy supply. The field of research on the electrical flashover of polluted composite insulators is quite extensive because of the disastrous economic and humanitarian consequences resulting from the interruption of electrical supply [1,2,3,4,5,6,7]. Power outages caused by polluted insulator flashovers are often difficult to identify after an incident, and, moreover, some occur in remote and uninhabited places. It is therefore necessary to continue carrying out research to deepen our knowledge of flashover phenomena under atmospheric pollution conditions. According to the literature, insulator flashover takes place in four steps: the deposition of a solid layer of pollution on an insulator surface, the progressive wetting of the pollution layer, the development of dry zones and the initiation of partial arcs and, finally, the extension of partial arcs to flashover if conditions are favorable. The drying of certain parts of the pollution layer is therefore one of the phenomena that influence the circumvention of the insulator. This drying, which is the direct consequence of the appearance of dry bands, is due to local heating linked to leakage currents and partial discharges on wet layers [8]. Once dry band arcs have formed, they can propagate to flashover if the resistance per unit length of the discharge is less than the resistance per unit length of the liquid contaminant on the insulator surface [9].

Numerous studies on dry bands and partial arc discharge on the surface of insulators have been carried out around the world. Most of the experimental studies are based on the use of simple rectangular geometries, where dry bands are simulated by clean zones [10,11,12,13]. Thus, in some cases, dry bands are artificially formed by masks made of an acrylic glass strip, which is removed after wetting is completed [10,11,12,13]. Another method consists of making a hole in the center of the rectangular geometry model in order to fix the location of the dry strip and prevent its formation near the power supply electrodes [14]. Even though these methods allow the position and width of the dry bands to be controlled, they do not allow for the reproduction of the real process of dry band formation induced by a local rise in temperature. Thus, these methods only permit the electrical behavior of the sample under test to be studied, making us incapable of understanding the behavior of a real composite insulator exposed to pollution. In addition, even though there are numerical studies in the literature making it possible to understand the influence of the dimensions of dry bands, their number, and their location on potential and electric field distribution, they do not discuss the initiation process and the formation of dry bands. These are most often simulated by air at predefined locations. Archad A. et al. [15], in their numerical simulations of polluted insulators, modeled dry bands as clean portions, thus creating a break in the pollution layer. Numerical simulations [15,16] and infrared thermography images [17] also show that, for composite insulators, electrical and thermal stresses are relatively greater at the junctions between the rod and sheds [15,16]. Unfortunately, these results cannot be observed using rectangular geometries.

In this context, this paper presents a new and simple geometry permitting the reproduction of the electrothermal process of dry band formation, which can be found on real polluted composite insulators. The proposed geometry allows, in the first step, for the study of the behavior of the conductance of the polluted layer during the wetting phase, which meets the specifications of IEC 60507 [18]. Moreover, the proposed geometry permits, in a simple manner, the investigation of the electrothermal behavior of the polluted layer leading to the formation of dry bands.

2. Thermoelectric Simulations of 69 kV Composite Insulator

2.1. Model of the 69 kV Composite Insulator

In this section, we describe a quick thermoelectric numerical simulation that was carried out using a 69 kV Sediver composite insulator with a uniform pollution layer [19]. The aim of this simulation is to verify the location of the concentration of the leakage current, as well as the maximum temperature, as reported in the literature [15,16,17]. The general geometry and characteristics of the insulator used in this study are shown in Figure 1 and Table 1.

As the 69 kV Sediver composite insulator is supposed to be uniformly polluted, simulations can be performed using a 2D-axisymmetric finite element method (FEM) with the commercial software Comsol Multiphysics^® from COMSOL, Inc., Burlington, VT, USA, version 5.5. Due to the low leakage current value flowing on the surface of the polluted insulator, the magnetic energy can be negligible compared to the electric energy. In this situation, the modeling of the polluted insulator may be considered as an electro-quasi-static (EQS) problem. Thus, the electric field can be decoupled from the magnetic field, which means that the electric field E can be expressed only in terms of the electric potential gradient as follows [20]:

(1)$\overrightarrow{\mathrm{E}}=-\nabla \mathrm{V}$

where E and V represent the electric field (V/m) and the electric potential (V), respectively.

The temperature computation is considered as a heat transfer in solids problem; this can be described by the following heat conduction expressed in Equation (2), which can be applied in homogeneous and isotropic media for a steady state [20]:

(2)$\left(-\mathrm{k}\nabla \mathrm{T}\right)+\mathrm{Q}=0$

where T, k and Q represent the temperature (K), thermal conductivity (W/(m·K)) and the heat source (W/m³), respectively.

The multiphysics coupling between the two forms of physics is obtained using the resistive heat of each subdomain in the electric field module as a heat source in the heat transfer module. The heat source Q describes the heat generation within the domain and is determined by [20]

(3)$\mathrm{Q}={\mathsf{\sigma }\mathrm{E}}^2$

The different simulations were performed using the thermoelectric properties presented in Table 2. The pollution was modeled using a uniform layer with a constant thickness of 1 mm. A phase-to-ground voltage of 39.84 kV was applied to the composite insulator.

2.2. Thermoelectric Results Obtained for the 69 kV Composite Insulator

This section presents the E-field, current density and temperature distribution computed at the surface of the polluted layer along the leakage distance of the insulator, as shown in Figure 2, Figure 3 and Figure 4, respectively. From the results obtained, it can be observed that the maximum E-field values are obtained at the extremity of the insulator sheds. Conversely, the temperature and current density reach maximum values at the insulator rod surface. These results, which are in agreement with those of previous works [15,16], demonstrate that the thermal stress present on a polluted composite insulator is higher at the rod surface where the current density is maximum. As illustrated by the results in Figure 3, it can also be observed that the current density at the insulator rod surface is about 3.5 time greater than that at the shed extremity.

Thus, the presence of greater thermal stress combined with a higher current density increases the probability of the appearance of a dry band on the rod surface. Consequently, any development of a new geometry to study dry band formation must integrate this fact by using one part of a large section to represent the sheds and one part of a small section to represent the rod surface.

3. Development of the New Experimental Model for Dry Band Studies

3.1. Design of the New Geometry

Figure 5 presents the final version of the new geometry and its dimensions used to simulate the real process of dry band formation observed during the pollution tests of composite insulators. The choice of the size and geometry of the model was guided by several considerations. Firstly, it had to simulate the constriction of leakage current lines on the rod surface (between insulator sheds) accordingly with Figure 3. As such, the geometry had to contain a larger part, corresponding to the shed, and a smaller one, corresponding to the rod. Secondly, the chosen geometry had to be simple and symmetrical in order to allow for the calculation of the analytical relation between the conductivity and the resistance of the pollution layer. Moreover, the dimensions of the chosen geometry had to be small enough to facilitate both the pollution layer application and the wetting and test phases using a small climatic chamber. Finally, the dimensions depended on mechanical considerations considering the material used in the fabrication. For example, in the case of glass material, the thinner part of the sample should be large enough to support the cutting process.

For numerical simulations, it is necessary to know the electrical conductivity and thickness of the pollution layer. Experimentally, however, it is only possible to measure the electrical resistance of the entire pollution layer. In spite of this, the proposed simple geometry allows for the analytical determination of the electrical surface conductivity from the electrical resistance measured. Hence, the surface conductivity γ(S) of the pollution layer as a function of the total resistance R(Ω) can be approximated as follows:

(4)$\mathsf{\gamma }=\frac{2.232}{R}=2.232\frac{\mathrm{I}}{{\mathrm{V}}_{\mathrm{ap}}}$

where I (A) is the current, and V_ap (V) is the applied voltage measured during the humidification test.

From Equation (4), it can be concluded that the form factor of the proposed geometry is equal to 2.232.

3.2. Thermoelectric Simulation of the Proposed Geometry

To verify the validity of the proposed new geometry concept, a 3D thermoelectric simulation was performed with the proposed geometry using the commercial software Comsol Multiphysics. For the simulation and, at first, approximation, the polluted insulator values of 2 were used. The polluted layer thickness was assumed to be constant and fixed at 1 mm. The applied voltage was fixed at 2 kV, and the external temperature was fixed at 20 °C.

Figure 6 presents the profiles of the current line distribution (Figure 6a) and the surface temperature (Figure 6b) obtained after 70 s, which corresponds to the time required to obtain some hot spots at around 100 °C at specific points on the surface sample for the simulation parameters used. Figure 7 and Figure 8 present the corresponding current density and surface temperature obtained along the axial distance (horizontal axis of symmetry) and the narrow part (vertical axis of symmetry) of the model, respectively.

As a general observation, the results show that the current density is effectively greater at the narrow part of the model, as expected, which results in an increase in the temperature at the same place, as both are directly linked. More specifically, it can be observed in Figure 7a that the current density at the center of the model (middle of the narrow part) is around 3.3 times higher than that at the electrodes (larger part), which is of the same aspect ratio order as that obtained for the 69 kV composite insulator (Figure 3). Moreover, it can also be observed in Figure 7a that the current density is almost uniform along the narrow part of the geometry, except for the two extremities of the narrow part. At these two specific points, the current density increases drastically by a factor 4 (Figure 8a), resulting in the appearance of hot spots, as illustrated in Figure 6b and Figure 8b, where the highest temperature values are measured at the two sharp points. From these results, it can be concluded that dry band formation is initiated at the two identified sharp points of the geometry, where the temperature is the highest and extends along the narrow part of the geometry and where the average temperature is maximum. This assumption is validated in the next section on the experimental testing of the proposed geometry.

4. Experimental Test Protocol

In order to validate the capacity of the proposed geometry to simulate the process of dry band formation, several tests in a climatic chamber were performed. These experiments permitted the development of a test protocol, including the application of the polluted layer, the control of the humidification period and the final tests under different applied voltages.

4.1. Pollution of the Sample

In order to validate the proposed geometry, five samples were produced (Figure 9), and they were made of 5 mm-thick Plexiglas plates according to the geometry described in Figure 5. Aluminum tape was used as an electrode in the voltage test. The pollution solution was applied on the surface of the samples using a spraying system consisting of a low-pressure compressed-air gun and a compressor both from FUJISPRAY SEMI-PRO2 from Fujispray systems, Toronto, Canada. The gun was placed vertically between 15 and 20 cm from the surface of the samples. This method of application results in more uniform pollution layers on the surface of the tested samples. Once applied, the pollution layer was allowed to dry at room temperature for at least 24 h as recommended by IEC 60507 [18]. Figure 9b presents a view of the pollution layer obtained on the Plexiglas sample after drying using the low-pressure gun.

For the preliminary tests, the pollution solution was made from 500 mL of demineralized water, 33 g of salt and 40 g of kaolin; this corresponds to an average salt deposition density (ESDD) value of 1.34 mg/cm² ± 5.53%, which was obtained from a measurement performed on height samples following Standard IEC 60507 [18] and using the following equations:

(5)$\mathrm{ESDD}=\left(S_a\times V_s\right)/A$

where A is the sample surface area in cm², V_s is the solution volume in cm³, and S_a is the pollution solution salinity in mg/cm³, which is given by

(6)$S_a={\left(5.7\times {\sigma }_{20}\right)}^{1.03}$

where σ₂₀ is the pollution layer conductivity at 20 °C in mS/cm.

This ESDD value, which corresponds to a very severe level of pollution [2,21,22,23], also demonstrated the repeatability of the pollution application method. The measurements were performed using a scale RADWAG PS 1000.R1 with a readability of 0.001 g and a conductivity meter Yokogawa SC72 SC Meter with a resolution of 0.001 µS/cm–0.1 °C.

4.2. Experimental Setup and Procedure

The tested samples were deposited in a climate chamber, Envirotronics Grand Rapids. MI49508 (Figure 10), to control ambient humidity (with a steam generator) and temperature. The samples were first weighed, cleaned and dried before the pollution layers were applied. The polluted and weighed sample was then deposited into the climate chamber set at a humidity level of 95 ± 5% and an average temperature of 20 ± 3 °C. At the end of a series of tests, the salt deposition density (ESDD) on the surface of the samples was measured using Equation (5).

Concerning the tests performed under applied voltage, two different tests were carried out. The first test, called the low-voltage procedure, was developed to measure the evolution of the pollution layer conductivity during the humidification phase. The second test, called the dry band test procedure, was performed at a higher applied voltage in order to simulate the appearance of a dry band. These two procedures are described in more detail in the following sections.

4.2.1. Low-Voltage Test Procedure

In order to measure the evolution of the electrical conductivity of the pollution layer during the humidification phase, the procedure schematized in Figure 11 was used. In this procedure, an alternating voltage is delivered via a 0–240 V Variac supplied by a fixed 120 V sector. To prevent the pollution layer from heating up (which can affect its resistivity), an electronic switch is inserted in the circuit to energize the sample only for the time required to measure the electric current and voltage. A Tektronix P6015A probe with a bandwidth of 75 MHz is used to measure the voltage drop between the two electrodes of the sample under test. A 1 Ohm resistor shunt is used for the indirect measurement of the current through the sample. An NI USB-6216 acquisition card, driven by MATLAB software from The MathWorks, Natick, MA, USA, version R2018a, enables measurement data to be acquired and saved for future processing.

4.2.2. Dry Band Test Procedure

High-voltage tests were also carried out with the new geometry to observe the effectiveness of dry band formation in the stress zone. The Variac (Figure 11) was replaced with a high-voltage source, while the electronic switch was removed from the system. A thermal camera Optris PI400 from Optris infrared sensing, Portsmouth, USA, was added to measure and record the temperature distribution on the pollution layer surface over the dry band zone formation. At the end of each series of tests, the ESDD of the samples was evaluated according to the procedure described in IEC 60507.

5. Experimental Results and Discussion

5.1. Electrical Conductivity Profile during Low-Voltage Test

The humidification test enables the evolution of the electrical resistance of the pollution layer to be followed during the humidification stage by measuring the electric current at low voltage. This permits the verification of the repeatability of the application pollution method, as well as the determination of the duration of the humidification necessary to reach the maximum conductivity, which corresponds to the maximum leakage current value on the surface of the polluted sample during the dry band test procedure.

Figure 12 presents an example of the evolution of the resistance and the conductance of the pollution layer obtained for three samples with similar ESDD values during the humidification period. The surface conductivity is simply determined using Equation (4). The results in Figure 12 show that the humidification phase is repeatable for the same order of ESDD. Indeed, the results demonstrate that the evolution of the surface conductivity follows, for an average ESDD of 1.34 mg/cm² ± 5.53% for the three samples presented, the same pattern with a maximum average value of about 0.162 mS ± 4.90% obtained for an average time of 810 s ± 1.84%. When the pollution layer is dry, its electrical resistance is very high, and its electrical conductivity very low. When the sample is placed inside the climate chamber, the water absorption starts, as well as the dissolution of the salt in the water. The electrical conductivity of the layer increases to a maximum value, which corresponds to the saturation of the pollution layer with water. The results obtained with the proposed geometry are in good agreement with those from the clean fog test, which was performed on composite insulators, as reported in the literature [24]. Hence, the results obtained demonstrate that the proposed simple geometry, combined with the use of a climate chamber with an integrated humidification system, is sufficient to adequately simulate the humidification process of a polluted layer in a repeatable way in accordance with the international standard requirements [18].

5.2. Experimental Simulation of Dry Band Formation

Once the polluted sample reached its maximum surface conductivity, which was defined during the humidification test, HV was applied in order to generate the formation of the dry band. Preliminary tests were performed for an average ESDD of 1.34 mg/cm² and for three different applied voltages: 2 kV (Figure 13a), 4 kV (Figure 13b) and 6 kV (Figure 13c).

From the results of Figure 13, it can be observed that the dry bands obtained for the different applied voltages form appropriately in the middle of the geometry, as expected due to the results of the thermoelectric simulations. Despite the random character of dry band formation, it can be observed that the dry bands obtained for the ESDD values of the same order are quite similar in dimension and position for the same applied voltage. This confirms the repeatability of the proposed geometry and its ability to simulate the complex process of dry band formation. When the applied voltage is increased to 4 kV, for an equivalent average ESDD value, the width of the dry band increases significantly, as illustrated by the results in Figure 13b. The same is observed for an applied voltage of 6 kV (Figure 13c), with an increase in the width of the dry band. This observation is in good agreement with the literature [24,25,26,27]. In fact, when the voltage is higher, thermal energy is more important, as it leads to greater evaporation, so the dry area is larger for the same level of pollution present on the sample surface. This is confirmed by the examples in Figure 14, which presents the IR imaging of the dry band obtained for the maximum temperature for each applied voltage. In this figure, it can be observed that the zone of the maximum temperature extends with the increase in the applied voltage, resulting in an increase in the dry band width, as observed in Figure 13. This also confirms that more thermal energy is provided for the formation of the dry band as the applied voltage is increased.

As expected, this is also observed in Figure 15, which shows the evolution of the temperature for different applied voltages, as well as the maximum current value, which was measured at the center of the dry band formation zone. As it can be observed, the evolution of the temperature obtained in the center of the dry band formation zone depends on the applied voltage. In particular, it can be observed that the time to the appearance of a dry band decreases as the applied voltage is increased. As previously mentioned, higher applied voltages generate greater thermal energy and, consequently, accelerate the process of evaporation and the formation of dry bands. However, it is interesting to note that the maximum temperature reached does not seem to be significantly affected by the applied voltage, as its value, which is around 70 °C, is the same for each applied voltage.

Concerning the evolution of the current in Figure 15, it is interesting to observe that the current is somewhat constant during the dry band formation process until it suddenly drops. This drop occurs at the moment that the formation of the dry band is completed along the narrow part of the sample, as well as corresponding to the maximum temperature at the center of the dry band. When the formation of the dry band is completed, the equivalent resistive circuit is interrupted and almost becomes capacitive with a drastic reduction in the current intensity flowing in the pollution layer. This results in less thermal energy dissipating in the pollution layer, which explains the sudden decrease in temperature observed in Figure 15.

Finally, the current evolution in Figure 15 confirms the validity and repeatability of the pollution layer application method due to the fact that its maximum value is somewhat proportional to the applied voltage, which is expected for the same order of ESDD values.

As a final observation, Figure 16 presents, for an applied voltage of 2 kV, the thermal IR imaging of the dry band formation at three distinct times regarding the evolution presented in Figure 15 obtained for the same applied voltage. Hence, Figure 16a corresponds to the time t = 2 s after the application of 2 kV in Figure 15, Figure 16b corresponds to the time t = 66 s, and Figure 16c corresponds to the time t = 117 s. The temperature showing in the three subfigures in Figure 16 is the average temperature measured inside the rectangular highlighted zone in white, whereas T_max is the maximum temperature measured inside that same zone. As it can be observed in this figure, the maximum temperature is obtained at the sharp edge of the sample geometry, as confirmed by the simulation results in Figure 8b. In Figure 16a–c, it can be seen that the temperature increases with time from the sharp edges to the center of the geometry, as expected from the simulation results. In other words, this means that the formation of the dry band is initiated at the two sharp edge extremities and progresses to the middle of the geometry until a complete dry band is formed.

6. Conclusions

In this paper, a new simple geometry to experimentally simulate the complex process of dry band formation on the surface of polluted composite insulators was proposed and validated. The proposed geometry simply simulates the effect of current line constriction obtained on the rod of a polluted composite insulator where dry band formation is generally observed.

The first step of the development of the proposed geometry was to use numerical simulations to determine the E-field, temperature and current density distributions along a 69 kV uniformly polluted composite insulator. The results obtained were then compared to the results obtained from the thermo-electrical simulations of the proposed geometry covered with a uniform pollution layer. The results obtained clearly demonstrate that thermal stresses and current density are more significant on the narrow part of the proposed geometry, allowing for the numerical results obtained for the polluted composite insulator at the rod surface to be correctly reproduced.

The second step was to experimentally test a proposed geometry model made of Plexiglass using a climate chamber to reproduce fog conditions. The different tests conducted used a heavy level of pollution with an average ESDD of 1.34 mg/cm². Low-voltage tests were used to determine the wetting duration, which corresponds to the maximum surface conductance of the polluted layer. The values obtained agree with the 10–40 min duration recommended in IEC 60507. The preliminary simulations performed with a high voltage demonstrated that using the proposed geometry allows the complex process of dry band formation to be correctly reproduced in a controlled manner. Excellent repeatability was obtained in terms of ESDD values, as well as in terms of current, temperature and the dimensions of the dry bands, depending on the applied HV voltage.

Hence, the preliminary results demonstrate that the proposed geometry permits the easy study and characterization of the different parameters influencing the formation of dry bands on composite insulators. By combining the simplicity of the proposed geometry with a small climate chamber and a small HV source, it becomes easy to test different materials (RTV, glass, superhydrophobic materials, etc.) in order to evaluate their behavior under atmospheric pollution at a reduced time and price compared to full-scale insulator tests. The influence of the material and pollution severity on the proposed geometry will be addressed in a future paper. Moreover, the repeatability obtained with the proposed geometry can be very useful to develop and validate numerical models aiming to simulate the process of dry band formation or partial arc initiation and propagation on the surface of polluted insulators, as will be featured in future papers using the proposed geometry.

Author Contributions

Thermoelectric simulations were performed by K.G. and M.-A.A., who was also responsible for the experimental investigation and the original draft preparation, whereas validation, review and editing, visualization and supervision were under the responsibility of C.V., who was also responsible for funding acquisition. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

This study did not require ethical approval.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. Geometry of the Sediver composite insulator [18].

Figure 2. E-field distribution at the surface of the polluted 69 kV composite insulator.

Figure 3. Current density distribution.

Figure 4. Temperature distribution.

Figure 5. Geometry and dimensions (in mm) of the proposed experimental model.

Figure 6. Thermoelectric simulation of the proposed geometry for a surface conductivity of 1 mS/m and an external temperature of 20 °C with (a) current line distribution represented by the red arrows and (b) surface temperature distribution.

Figure 7. Results obtained along the axial distance of the model for a volume conductivity of 1 mS/m and an external temperature of 20 °C with (a) the current density distribution and (b) the surface temperature distribution.

Figure 8. Results obtained along the vertical distance of the narrow part of the model for a volume conductivity of 1 mS/m and an external temperature of 20 °C with (a) the current density distribution and (b) the surface temperature distribution.

Figure 9. View of Plexiglass geometry before and after the pollution layer was obtained after drying using a low-pressure gun with (a) clean sample and (b) polluted sample.

Figure 10. Climate chamber.

Figure 11. Low- and high-voltage test setup diagram.

Figure 12. Example of three surface conductance evolutions obtained during the humidification period for an average ESDD of 1.34 mg/cm2.

Figure 13. Examples of dry band formation obtained on the Plexiglass sample for an average ESDD of 1.34 mg/cm2 for applied voltages of (a) 2 kV, (b) 4 kV and (c) 6 kV.

Figure 14. Examples of temperature distribution obtained with the IR camera in the zone of dry band formation (marked with red arrow) for applied voltages of (a) 2 kV, (b) 4 kV and (c) 6 kV for an average ESDD of 1.34 mg/cm2.

Figure 15. Examples of evolution of the maximum current value and of the temperature measured at the center of the dry band as function of applied voltage, for average ESDD of 1.34 mg/cm2.

Figure 16. Examples of temperature distribution evolution obtained with the IR camera in the dry band formation zone for an applied voltage of 2 kV and for an average ESDD of 1.34 mg/cm2, where the maximum temperature Tmax obtained inside the rectangular highlight zone is equal to (a) 34.6 °C at t = 0 s, (b) 60.8 °C and (c) 70.3 °C.

Table 1

Sediver composite insulator characteristics [19].

Voltage level, kV	69
Length X, mm	866
ϕD1, mm	92
ϕD2, mm	72
Shed number	21
Leakage distance, mm	1410

Table 2

Thermoelectric properties of the materials.

Materials	$\mathbf{Relative} \mathbf{Permittivity} \left({\mathit{\epsilon }}_{\mathit{r}}\right)$	$\mathbf{Density} (\mathbf{kg}/{\mathit{m}}^3)$	Electrical Conductivity (S/m)	Thermal Conductivity (W/(m·K))
Rod	7.2	2500	$1\times {10}^{-14}$	0.04
Envelop	4.6	1200	$1\times {10}^{-14}$	0.2
Metal ends	1	7850	$4.032\times {10}^6$	44.5
Pollution layer	81	2.6	${10}^{-3}$	0.6
Air	1	1.225	$1\times {10}^{-15}$	0.024

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