Impact of atmospheric conditions on the flash-over voltage of the transmission line insulators using central composite design | Scientific Reports

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The insulators of overhead power lines play a crucial role in maintaining the reliability of transmission and distribution networks. Because they are exposed to harsh and dynamic environmental conditions, it is essential to investigate the impact of environmental parameters such as pollution, inclined angle with the cross arm, and temperature on the dielectric performance of the insulators of overhead lines. Conventionally, the effect of such parameters can be investigated through experimental measurements of the insulator flashover voltage. However, this approach is costly and time-consuming and calls for the isolation of the lines to conduct the test, causing interruption to the entire grid. As such, there is an essential need to develop a new methodology to quantify the flashover voltage of overhead insulators operating under various environmental conditions, which is the main aim of this paper. The Central Composite Design is employed to develop a mathematical correlation between the insulator flash over voltage as a dependent variable and three environmental parameters: pollution level, inclined angle, and temperature as independent variables. The robustness of the developed equation is validated through extensive experimental measurements of the insulator’s flash overvoltage under various conditions. Results reveal a good agreement between the actual and predicted flashover voltage using the developed correlation, as the absolute error for all investigated samples is less than 6%.

Transmission and distribution line insulators are crucial for safe and reliable electrical power networks, preventing leakage current, providing mechanical support, and ensuring safety1. Proper design, installation, and maintenance are essential for continuous power delivery. Regular inspection and maintenance prevent deterioration and ensure proper functioning2,3.

Temperature variations, pollution, and the inclined angle significantly impact transmission line insulator performance4,5,6,7. Extreme temperatures can cause fatigue and degradation, while pollution can cause surface contamination and conductive paths8,9,10,11. The inclined angle can also affect mechanical stress, potentially leading to failure. Regular inspections, cleaning, and use of pollution-resistant materials are crucial for maintaining insulator reliability12,13,14.

Dielectric insulator failure can occur due to various factors, including surface and long-rod flashovers, mechanical failure, corona discharge, surface tracking, erosion, loss of hydrophobicity, high-frequency vibrations, manufacturing defects, and aging15. Surface flashovers occur when surface contamination or inadequate insulation coordination causes conductive paths on the insulator surface, allowing current to flow across it16,17. Mechanical failure can result from high wind loads, ice accumulation, and cracks due to thermal, mechanical, or manufacturing defects18. Corona discharge occurs when partial discharges occur on the insulator’s surface, leading to energy loss and deterioration over time. Surface tracking occurs when a conductive path forms due to contamination or conducting materials, potentially leading to partial discharge and failure19. Understanding failure modes is crucial for designing robust insulation systems and identifying preventive maintenance schemes to ensure reliable operation and avoid catastrophic failures20,21,22,23.

Research on the impact of temperature, pollution, and insulator inclined angle on insulator performance has provided valuable insights2,3,13,14. However, limitations include limited field data, simplified models, complex interaction between factors, and limited long-term investigations. Restricted access to comprehensive field data and the complexity of environmental factors make it challenging to understand their combined effects. Long-term studies are essential for understanding aging mechanisms and cumulative environmental impact24. Environmental conditions, including pollution levels, can vary significantly across different regions and seasons, making research findings from one location unsuitable for other areas10. Insufficient standardization for insulator performance testing can hinder comparability25,26,27. Pollution’s dynamic nature makes predicting pollutant deposition rates on insulator surfaces challenging. Emerging contaminants like nanoparticles and industrial byproducts may not be considered in traditional research, necessitating ongoing research. Research may lag as new materials are developed, requiring adaptation to real-world environments. Climate change and adaptation are crucial for future insulator performance28. Future research should focus on comprehensive field studies, standardized testing protocols, and emerging data collection technologies.

The correlation between the three environmental parameters: temperature, pollution, inclined angle, and the insulator’s flashover voltage, can be addressed using one method of the Design of Experiment (DOE) approach29,30,31,32,33. Central composite Design (CCD) is a methodology of DOE that can identify a mathematical correlation of the above parameters. The CCD is a response surface methodology used in experimental design to model complex relationships between independent variables and observed responses29. CCD enables researchers and engineers to efficiently explore the effects of multiple variables on a response of interest, leading to improved processes, products, or systems, especially when the investigated relationship is complex and is of non-linear behavior. The method comprises a factorial or fractional factorial design with center points and additional axial points, often located at the hypercube face34. The three main key features of the CCD can be summarized below:

Factorial or Fractional Factorial Design: explores the main effects of different factors on the response variable.

Center points: runs conducted at the central values of experimental factors to provide insight into the response variability at the experimental domain’s center.

Axial points: runs performed along experimental design axes to estimate curvature in response surface and fit a second-order polynomial model.

The CCD offers several advantages, including efficient exploration of factor space, curvature estimation, statistical efficiency, flexibility, and robustness to noise. It helps to understand the main effects of factors and their interactions with fewer experimental runs compared to full factorial designs. CCD also enables the estimation of curvature in response surfaces, especially when factors and responses are not linear.

Insulators should undergo three flashover tests to ensure optimal performance: dry power frequency, wet power frequency, and impulse frequency flashover35,36. These tests verify the insulator’s characteristics under lightning and switching surge voltages, ensuring the insulator’s longevity and reliability. The power frequency voltage test is conducted in wet conditions and applies to insulator groups below 245 kV. Flashover or failure should not occur after 1 min of voltage application. To identify the flashover voltage, increase the applied 75% withstand voltage by two steps: increasing the voltage at a high rate to 75% of the flashover voltage VFO, and changing the rate to 2%×VFO/s until flashover. Record the flashover voltage 2–3 min later22,23,27,37. The voltage class requires fast-front and slow-front dry surge tests to simulate lightning surges. The slow front-end overvoltage test for extra high voltage (EHV) equipment above 245 kV on insulators is standardized. Standard 1.2/50-microsecond lightning impulses and 250/2500 microsecond switching impulses are applied with both positive and negative polarity. Minor surface marks or chipping are permissible37. The electrical connection structure diagram of the flashover experiment is shown in Fig. 1.

Electrical connection structure diagram of the flashover experiment.

Egyptian Electricity Holding Company has set specifications for Pin-type porcelain insulators 11 kV, as per EDMS 10-100-2. These insulators will be installed in medium voltage distribution networks of Egyptian Electricity Distribution Companies (EDCs) and will undergo testing based on IEC 60383-1 before service. The environmental conditions of the testing are: -5 and + 45 °C maximum and minimum daily ambient temperature, the altitude must be 1000 m above sea level, 45 days per year thunderstorm is assumed, the maximum rainfall is 250 mm annually, 35 m/s is the maximum wind speed and the solar energy radiation exceeds 110 W/m2. The specifications provide a comprehensive overview of the insulators’ performance and design. The technical specifications for the 11 kV Pin-type porcelain insulators include high-quality, uniform, smooth, brown, and defect-free porcelain with a fully glazed finish. The insulation should not be directly bonded to the pin metal but connected with a lead or copper sleeve using clean cement. The insulator should be integrally formed, with a radius of the upper slot of at least 12 mm, and be resistant to atmospheric conditions like salt, steam, ozone, acid, alkali, dust, and sandy storms. The electrical and mechanical characteristics of Pin–type insulators are listed in Table 1.

Insulators are mounted on cross-arms at various angles under pollution and temperature conditions. High voltage can be applied to the upper fitting while the lower fitting is grounded. The test process must be identified to meet standards, and each experiment run is specified to create a simulation equation. Investigated insulators are thoroughly cleaned according to IEC 60,507 clause 5.227. A thermal cycle tests an insulator by immersing it in cold and hot water to remove moisture, and then a voltage is applied until a flashover occurs. The test is repeated five times, and the flashover voltage is calculated as the average of the five measured values. If no cracks or holes appear, the test is considered successful. The temperature is varied by placing the insulator next to a heater of variable temperatures. The pollution level is varied by preparing three insulators with three layers of different salt thicknesses on their surfaces. The experiment involves spraying the insulator three times, operating steam in a designated chamber, placing the insulation in a room, applying a voltage of 1 kV depending on the leakage path, measuring the leakage current every 2 min, gradually increasing the voltage to 2 kV when the current reaches 50 µS, and holding the voltage constant for 15 min. A lightning pulse of 1.2 µs/50 µs is used to test the withstand voltage and determine the breakdown voltage. A Hall effect sensor measures the leakage current during breakdown, while high-end cameras are installed to capture the failure events. Wind causes stresses on the insulator and decreases the angle with the cross-arm due to force and longitudinal unbalanced loads, as shown in Fig. 238. When the insulator inclines, the vertical flashover distance is directly proportional to the intensity of the electric field (EF). A shorter distance enhances the electric fields’ ability to ionize the air, triggering the flashover13,14. Figure 3 shows the insulators at an angle of 90° on the cross arm with different pollution concentrations. Figure 4 shows the setup of the insulators with the same temperature and pollution concentration at different inclined angles with the cross arm. Figure 5 depicts the flashover with the increased applied voltage at a pollution level corresponding to 1.5 mm salt thickness, 60 °C inclined angle, and a temperature of 15 °C.

Forces on the insulators due to wind effect.

Three insulators with different pollution levels at 90° inclined angle, and a temperature of 15 °C.

Three Insulators at different inclined angles with at the same temperature and pollution level.

The flashover voltage measurement setup for an insulator with a 1.5 mm salt layer at inclined angle 60° and a temperature of 15 °C.

The results of the experiments that were carried out on the insulators at different conditions were addressed. Figure 6 shows that pollution concentration affects flashover voltage at different angles. It shows that flashover voltage decreases when pollution concentration increases, while an angle increase leads to a rise at constant insulator temperature. A significant reduction occurs when the angle decreases. At a 90-inclined angle, flashover voltage occurs through the shed to the grounding path via the cross arm. At 60°, the path is shorter, indicating that the inclined insulator angle influences the flashover path and breakdown voltage. Figure 7 shows the impact of pollution on flashover voltage in insulators at 15 to 35 °C with a fixed angle. The flashover voltage decreases with increased temperature as insulation becomes more conductive, potentially leading to electrical breakdown and flashover. This highlights the importance of insulator temperature in designing electrical systems to ensure safety and reliability. Regular inspection and maintenance of insulators are crucial for preventing pollution buildup and ensuring optimal performance. Figure 8 shows that an increase in pollution thickness decreases flashover voltage, while an increase in inclined insulation angle increases it. Figure 9 shows that an increase in insulator temperature reduces flashover voltage, while a decrease in the inclined insulator angle also decreases flashover voltage.

Variation of VFO with the change in Pollution and inclined angle.

Effect of pollution and temperature on the VFO.

Effect of Pollution and insulation’s inclined angle on the VFO.

Variation of VFO with the variation of inclined angle and insulator’s temperature.

One assessment approach relies on statistical representation. As a result, each measurement is repeated ten times to determine the mean and standard deviation. The CDF describes the likelihood of the insulator’s VFO. In other words, it expresses the oil reliability, the reliability function, and the survival function. Figure 10 shows the CDF at the variation of insulators’ pollution to explain the probability of occurrence of VFO or breakdown based on the variation of insulators’ pollution. At 85 kV, the probability of VFO occurrence with pollution’s thickness of 0.5 mm is 10%. On the other hand, at 1.5 mm pollution, the probability of VFO increases to 95%. Figures 11 and 12 illustrate the CDF at the variation of the inclined angle of the cross arm and the insulators’ temperature. In Fig. 11, the VFO probability occurrence is high at a low cross-arm inclined angle, where at 90 kV, the probability of VFO occurrence is 90% for a 30° inclined angle and 0% for 60 and 90°. In Fig. 12, at 90 kV, the occurrence probability of VFO is 2% at 15 °C. Still, it is 95% and 100% at 25 and 35 °C, respectively.

In addition, The Weibull distribution has been identified as the best acceptable probabilistic assessment approach for VFO. As a result, this study uses the CDF based on the Weibull distribution to conduct statistical assessments of dielectric breakdown strength. The Weibull model is provided by (1):

where, V refers to the variable breakdown voltage while α and β are the scale and shape parameters of the Weibull distribution, respectively.

The Weibull distribution was used to analyze insulators’ VFO with variations in pollution, inclined angle, and temperature. Shape and scale parameters regulated its form and size. The model parameters (α and β) were derived from 10 VFO data performed on the insulators. These parameters were approximated using laboratory measurements and validated using Weibull curves. The results provide valuable insights into insulators’ VFO.

The effect of insulators’ pollution, inclined angle, and temperature on the VFO using the probability plot for a Weibull distribution is shown in Figs. 13 and 14, and 15, respectively. The probability of VFO at 1.5 mm pollution thickness is higher than that at 0.5 mm. The VFO probability is 50% at 1.5 mm. Still, it is only 1% at 0.5 mm, as shown in Fig. 13. Figure 14 indicates that at 90 kV, the probability of VFO occurrence is 100% at 30° inclined angles, but it is 0% at 60 and 90°. An increase in insulators temperature will increase the probability of VFO occurrence.

Commulative Density Function for pollution variation (30°, 25 °C).

Cumulative Density Function for Inclined Angle Variation (0.5 mm, 30oC).

Commulative Density Function for temperature variation (0.5 mm, 30o).

Probability plot for Weibul distribution for pollution variations.

Probability plot for Weibul distribution for inclined angle variations.

Probability plot for Weibul distribution for Temperature variations.

Experiments reveal the relationship between independent variables and the dependent variable, which is measured through statistical analysis. However, some changes in the dependent variable may not be attributed to changes in the independent variables, causing the study to consume more time and increase the cost of experiments. Therefore, it is crucial to consider the individual effects of these variables on the output29,30,39. Moreover, the interaction between independent variables and each other should be investigated. Observations may suggest some variables affect the output, but statistical analysis reveals otherwise. This highlights the importance of the DOE, which processes data directly affecting the output and removes redundant data that do not affect the response31. DOE features the advantage of the reduced number of experiments required to identify a mathematical correlation between experiment variables. Full factorial, fractional factorial, response surface, and D-optimal designs are different. Response surface methodology (RSM) is a collection of mathematical and statistical tools for modeling and analyzing situations to enhance variable-influenced responses. One of these designs is the central composite design, which will be elaborated in the following section.

The CCD technique is an experimental design in the response surface approach that devlops a quadratic equation of the response and the independent variables29,30,31,39. Sequential experiments are preferred for this purpose, providing valuable information about the lack of fit tests39. The relation between independent factors and response is clarified using mathematical principles based on the experimental domain and mathematical modeling of the response. The response (flashover voltage) is explored using three independent variables: temperature (T), pollution (P), and insulator inclination angle with the tower’s cross-arm (A). The experimental domain contains maximum, minimum, and mean values, as shown in Table 2.

CCD is a composite of traditional factorial design (23) with additional selected points, as shown in Fig. 1639. There are three types: circumscribed, inscribed, and free-centered. This study employs the CCD type, with star points located in the centre of each face of the factorial space. Table 2 shows three levels for each experiment variable: lowest, mean, and maximum limit.

The three experimental factors for CCD.

The number of experimental runs (N) needed to construct the CCD is calculated based on k factors influencing the experimental response as given by (2).

The study uses a cube-centered cubic factor with three points (Co), 2k at the corner, and non-center points (2k), referring to the star or axial section of the CCD used to calculate the quadratic terms in the polynomial connecting the experimental variables and response. As stated in (2), the CCD requires seventeen experimental runs for three experimental parameters.

The CCD model’s quadratic equation can be constructed using seventeen experimental runs, focusing on the flashover voltage (in kV). Table 3 presents the coded and actual values of the factors used to measure the insulator’s flashover voltage.

The quadratic equation that relates the input parameters and the output can be built as in (3)

where Y represents the response, Xi refers to the input variables influencing the experiment response, XiXj are two-ways interactions with number calculated as k (k-1)/ 2, where k is the number of input variables, Xi2 is the second order of variables. βο, βI, βij and βii are the coefficients of the quadratic equation while ε is the error of the equation. The B parameters of (3) can be computed as in (4)

x is the experiment matrix, y refers to VFO.

The coded matrix x, containing the code values of each parameter, is constructed based on the domain of each parameter in Table 3. The matrix also includes the square of each parameter and the interaction between them. The transpose of the matrix is represented by xt, while the vector matrix y represents the response for each run. The coefficients of the quadratic Eq. (3) can be obtained using Eq. (4).

The quadratic equation has Nβ coefficients, which may be computed using (5) and the number of experimental components (k).

k equals 3, so Nβ has 10 coefficients from βo: β9. The coefficient values β can be computed based on Eq. (4) using MATLAB.

Table 4 lists the obtained values for the CCD model. Table 5 gives the statistical results of the suggested model. The R-squared and Adjust R-squared are found to be 0.996 and 0.991, respectively, which reveals the proposed model’s robustness. In addition, the P-value is very small, which removes the null hypothesis.

The quadratic equation that links the VFO and the three parameters; P, A, and T based on the results in Table 4 is given in (6)

Figure 17 depicts the values of Eq. (6) coefficients. Figure 18 illustrates the variation in the experiment output with the experimental parameters. Results show thatthe inclined angle of the insulator and insulator temperature significantly influence VFO. The variation of the VFO ranged from 83 to 120 kV when the inclined angle varies from minimum to maximum code (− 1, 1). On the other hand, the change of temperature from minimum to maximum (− 1, 1) changes VFO from 120 to 106 kV. The variation of VFO due to changes in pollution level is not significant as shown in Fig. 18.

Coefficient values of Eq. (6)

Variation of VFO with the input variable based on Eq. (6)

Equation (6) has been validated using experimental measurements for new 15 samples data and comparing the actual VFO with the calculated one using the proposed equation as shown in Table 6. Results indicate that the absolute error of the calculated and measured VFO for the investigated 15 samples is less than 5% except for one sample that revealed an absolute error of 5.98%. Results attest that the proposed CDD model equation has high reliability in quantifying the relation between the VFO and P, A, and T. Based on the statistical analysis, Eq. (6) can be approximated in (7).

Insulators of overhead power lines are expected to maintain reliable dielectric and mechanical properties over its service life. However, these insulators are operating under harsh environmental conditions that may degrade its insulation properties and accelerate its aging. Pollution, inclined angle of insulators with the cross arm, and surrounding temperature can influence the flashover voltage (VFO) of the insulator. So, it is necessary to investigate the effect of these parameters on VFO through regular experimental measurements. Due to the high cost of these experiments and the consumed time, a theoretical approach is introduced in this paper to correlate the insulator’s flashover voltage and these parameters. The central composite design is employed to develop a mathematical equation correlating VFO as a dependent variable with P, A, and T as independent variables through extensive experimental measurements of VFO for several insulators under different values of the independent variables. The developed correlation has been validated using another set of measurements. Results reveal a good agreement between the actual and predicted VFO as the absolute error for all investigated samples was less than 6%. The developed equation can pave the way for a reliable design of the transmission and distribution insulators that may be installed at different locations with extreme environmental conditions.

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

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The authors extend their appreciation to Taif University, Saudi Arabia, for supporting this work through the project number (TU-DSPP-2024-14).

This research was funded by Taif University, Taif, Saudi Arabia (TU-DSPP-2024-14).

Mininstry of Higher Education, Mataria Technical College, Cairo, 11718, Egypt

Ramy N. R. Ghaly & Ali Ibrahim

Electrical Engineering Department, College of Engineering, Taif University, P. O. Box 11099, Taif, 21944, Saudi Arabia

Sherif S. M. Ghoneim

Electrical and Computer Engineering Discipline, Curtin University, Bentley, WA6102, Australia

Ahmed Abu-Siada

Department of Electrical Engineering, Graphic Era (Deemed to be University), Dehradun, 248002, India

Mohit Bajaj

Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, Jordan

Mohit Bajaj

College of Engineering, University of Business and Technology, Jeddah, 21448, Saudi Arabia

Mohit Bajaj

Department of Theoretical Electrical Engineering and Diagnostics of Electrical Equipment, Institute of Electrodynamics, National Academy of Sciences of Ukraine, Peremogy, 56, , Kyiv-57, 03680, Ukraine

Ievgen Zaitsev

Center for Information-Analytical and Technical Support of Nuclear Power Facilities Monitoring, National Academy of Sciences of Ukraine, Akademika Palladina Avenue, 34-A, Kyiv, Ukraine

Ievgen Zaitsev

Department of Electrical Technology, Faculty of Technology and Education, Helwan University, Cairo, Egypt

Hilmy Awad

Chitkara Centre for Research and Development, Chitkara University, Baddi, Himachal Pradesh, 174103, India

Ramy N. R. Ghaly

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Ramy N. R. Ghaly, Ali Ibrahim, Sherif S. M. Ghoneim: Conceptualization, Methodology, Software, Visualization, Investigation, Writing- Original draft preparation. Ahmed Abu-Siada: Data curation, Validation, Supervision, Resources, Writing - Review & Editing. Hilmy Awad, Mohit Bajaj, Ievgen Zaitsev: Project administration, Supervision, Resources, Writing - Review & Editing.Data Availability Statement: The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Correspondence to Sherif S. M. Ghoneim, Mohit Bajaj or Ievgen Zaitsev.

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Ghaly, R.N.R., Ibrahim, A., Ghoneim, S.S.M. et al. Impact of atmospheric conditions on the flash-over voltage of the transmission line insulators using central composite design. Sci Rep 14, 22395 (2024). https://doi.org/10.1038/s41598-024-72815-z

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