# Flashover Voltage Prediction Models under Agricultural and Biological Contaminant Conditions on Insulators

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}SO

_{4}, NaHCO

_{3}, CaSO

_{4}, KHCO

_{3}, MgSO

_{4}, NH

_{4}), 2Fe(SO

_{4})

_{2}, and 6H

_{2}O (ferrous ammonium sulphate, dust, and urea) at different concentrations, and biological contaminants, such as algae and fungi, were taken as pollutants, and the AC flashover behavior of a porcelain-cap-and-pin-type insulator polluted with these two different pollutants was investigated. The experiment was carried out by a semi-natural method, wherein the insulator was first polluted artificially; thereafter, natural fog was applied to measure the wet flashover voltage. Test results indicated that the flashover voltages were affected by both soluble salts and non-soluble components deposited on the insulator surface. In the case of the thickly contaminated layers, non-soluble deposits greatly reduced the flashover voltage. Moreover, by using regression analysis, four empirical models based on different variables were developed. The empirical models developed in the present work represented a good degree of relation in predicting the flashover voltage of naturally contaminated insulators.

## 1. Introduction

## 2. Statistical Models

^{2}). The insoluble component of the contamination can be expressed as a non-soluble deposit density (in mg/cm

^{2}). These two approaches have been widely used to determine the severity of the contamination [21,22]. Flashover voltage (FOV) in kV is the response variable.

_{o}is the intercept, b

_{i}is the slope, x

_{i}is the regressor or independent variable, and e

_{i}is the error term (residuals).

- Normal distribution of errors. This aspect is inferred through the normal probability plot of residuals. Corresponding to the normal probability plot of residuals, the residual points should lie approximately in a straight line. If this is satisfied, then the data points can be assumed to be normally distributed [25,26].
- Zero mean and constant variance of errors. This is ensured through the plot of residuals and predicted data. If the plot between residuals and predicted values does not show any specific shape, the residual plot is assumed to be structured and the assumptions of constant variance to be satisfactory [25,26].

## 3. Samples, Experimental Details, and Test Procedure

#### 3.1. Test Samples

^{2}.

#### 3.2. Experimental Setup

#### 3.3. Test Procedure

#### 3.3.1. Sample Preparation and Polluting

_{2}SO

_{4}, NaHCO

_{3}, CaSO

_{4}, KHCO

_{3}, MgSO

_{4}, ferrous ammonium sulphate, cultivated field dust, and urea were selected as agricultural contaminants. Among the agricultural pollutants NaCl, K

_{2}SO

_{4}, NaHCO

_{3}, KHCO

_{3}, MgSO

_{4}, ferrous ammonium sulphate are soluble salts, while CaSO

_{4}and dust are partially soluble. The collected field dust is comprised of various sizes of particulate ranging from 10 microns to 100 microns (PM

_{10}to PM

_{100}). The biological group contained algae and fungi, as they contained inert particles, both of which are partially soluble. To pollute the sample insulators, one of the standard techniques used is the solid layer method of artificial pollution, which was used in this work. For this, a contamination slurry was prepared by adding a particular set of salts to two liters of demineralized water. Then the pre-treated insulator samples were dipped carefully into the slurry for about 6 h, so the samples received an approximate uniform pollution layer and conductivity up to a certain value, after which they were removed. The same procedure was applied to every group of salt.

#### 3.3.2. Wetting

## 4. Measurement System

#### 4.1. Flashover Voltage Measurement

#### 4.2. Pressure, Temperature, and Humidity Measurement

#### 4.3. Pollution Severity Measurement

^{2}; σ is the washed suspension conductivity in mS/cm; C

_{t}is the temperature coefficient, ~0.02/°C; and T is the solution temperature in °C.

- ${W}_{f}$ is the weight of filter paper with pollutants under the dry condition in mg;
- ${W}_{i}$ is the weight of filter paper without pollutants under the dry condition in mg; and
- A is the surface area of the insulator in cm
^{2}.

## 5. Experimental Results Analysis and Discussion

#### 5.1. Analysis of Experimental Results of AC-Contaminated Flashover Voltage

- Since the various international standard classifies the severity of pollution range on high voltage insulators in terms of ESDD between very-light to extremely-severe levels i.e., from 0.0 to 1.0 mg/cm
^{2}, the concentration of pollutants and their combination were taken as per the specified ESDD level. Due to strong winds and sand storms, the dust from agricultural fields are transported to the line insulators. Moreover, when agricultural fields have been plowed for cultivation, the field dust, with the help of air or wind, settles down on the line insulators that pass through these agricultural fields. Under dry conditions, these (dust plus other particles) deposited pollutants do not much affect the dielectric strength of the high-voltage insulators; but, if these pollutants get wet in any way, such as by fog, light rain, dew, etc., they can greatly reduce the insulating capacity of the insulator. As, in the literature. Various kinds of pollutants are described, including agricultural and biological pollution that can influence the FOV performance of high voltage insulators, agricultural salts and biological pollutants were chosen as insulator pollution, here. - The tested agricultural pollutants were primarily of conductive salts and soluble in water. However, the insulators polluted with these contaminants had lower conductivity. Whereas the existing research and theoretical analysis indicate that, if pollutants are soluble, they should have higher conductivity [4,28]. Other than this, as the concentration of the contaminant will increase, the conductivity should also increase and the flashover voltage should decrease. Despite this fact, in this work, the flashover of the insulators contaminated with agricultural pollutants (3 to 9 in Table 1) occurred at slightly higher values than those with partially soluble biological contaminants, because of the low level of NSDD measured on the insulators polluted with agricultural contaminants. The variations of FOV with ESDD for soluble agricultural pollutants are shown in Figure 3.
- Under wet conditions, the algae- and fungi-polluted (sets 1 and 2 of the contaminants in Table 1) insulators, at the same concentration, attained higher surface conductivity than agricultural pollutants, even though these are partially soluble in water and do not contain highly conductive constituents. The main reason behind this is that such types of contaminants have higher water-retaining capability. Due to this property of the non-soluble contaminants deposited on the insulator surface, a larger amount of leakage current could flow for long periods through the insulator surface. Thus, we can say that the higher values of NSDD could significantly lower the flashover voltages of the insulator. Flashover voltage variations with ESDD and NSDD for partially soluble pollutants are shown in Figure 4 and Figure 5 respectively. The soluble parts in these contaminants may be attributable to the environment in which they grew; that is, to the material and salts involved in growing these contaminants, and to pH, temperature, pressure, humidity, etc.
- Yet, both the agricultural and biological contaminants had a quite high degree of pollution, which is expressed in terms of the ESDD and NSDD, and presented in Table 1. Additionally, the FOV decreased with an increase in ESDD and NSDD. Thus, both types of pollutants could greatly affect the flashover performance of the insulators. For many years, the use of fertilizers over manure has been increasing to enhance the fertility of soil and grow increasingly more crops. Thus, to secure the insulators on lines crossing over agricultural fields from the negative impact of highly conductive fertilizer salts, condition monitoring of the insulators necessary.
- The standard deviation of all the test results was lower than 16%, which means that the dispersion degree of the data achieved by the tests was small and thus the method is acceptable.

#### 5.2. Flashover Voltage Model Based on ESDD

^{2}and were obtained experimentally by using the aforesaid contaminants. According to the correlation curve fitting analysis, the FOV and ESDD were shown to have a negative power function, so the logarithmic values of ESDD were used as regressors and FOV as a response. Based on these values, Minitab was used for statistical analysis and to develop model 1 to predict the flashover voltage. The details of the statistical model are given in Table 2.

- S—standard deviation
- R2—residual sum of squares
- R2 (adj)—the adjusted residual sum of squares
- R2 (pred)—predicted residual sum of squares
- SE Coef—standard error coefficient
- T-Value—standard ‘T’ statistic
- p-Value—probability of testing the significance of the null hypothesis
- F—standard ‘F’ statistic
- DF—degrees of freedom
- SS—sum of squares
- MS—mean-sum of squares

- Analyzing model coefficients, predicting values, and using prior experience and physical theory.
- Data splitting technique in which some of the original data was not used for model building but was used to investigate the predictive performance of the model [29].

#### 5.3. Flashover Voltage Model Based on NSDD

#### 5.4. Flashover Voltage Model Based on the Combined Effect of ESDD and NSDD

#### 5.5. Flashover Voltage Model Based on ESDD, NSDD, Atmospheric Pressure, and Relative Humidity

## 6. Conclusions

^{2}. The humidity and thickness of pollutants on the insulators are also important factors that determine the wet flashover voltage performance of the insulator. If the case where humidity on the insulator surface is found less, while the NSDD value on the insulator is high, it has been found that the insulator flashover performance falls at a higher rate than in the case where the humidity on the insulator surface is high and NSDD is low. It is due to the ambient air effect on the insulator; under high moisture and low humidity, it dries earlier, while the insulator surface with low moisture and high NSDD dries later because of the higher water retention capability of the inert particles (NSDD). Yet, due to the higher water retention capacity of the biological contaminants, they can more affect the insulator flashover performance than can agricultural contaminants. A relative humidity greater than 85% reduces the flashover voltage abruptly. It is also found that the conductivity of the contaminated insulator surface and ESDD have a non-linear relationship, in contrast to that with the amount of salt concentration. Similarly, the relationships of the ESDD, NSDD, temperature, and pressure with FOV are also found non-linear. By using regression analysis (simple and multiple) techniques, different models have been developed to widen the validity of theoretical models for evaluating and determining the flashover performance of porcelain insulators. The models evolved here are based on contamination severity approaches (ESDD and NSDD), temperature, atmospheric pressure, and relative humidity. For all the models developed, the model performance evaluation parameters i.e., the R-sq, multiple correction coefficients (R), and the p-values, determine the degree of relationship between the dependent and independent variables. The model based on ESDD only has R-sq = 0.1559, R (multiple) = 0.383, and p-value = 0.021; for the model that is based on NSDD, R-sq = 0.684, R (multiple) = 0.827, and p-value = 0.000; for the model based on the product of NSDD and ESDD, the values of the evaluation parameters are R-sq = 0.794, R (multiple) = 0.891, and p-value = 0.000; and, for last model, is R-sq = 0.965, R (multiple) = 0.953, and p-value = 0.000. Values of all these parameters for each developed model indicate that a good degree of relationship exists between experimental and predicted values for the given data set. As values of R-sq and R (multiple) are close to 1 and the p-value is less than 0.05 for all the models (which are the criteria for determining the accuracy and validity of the model), they fulfill, here, such criteria for the models developed in this study. It has been illustrated that the model equations developed for the selected pollutants can be used to estimate and predict the flashover voltage of insulators that are normally operating in tropical areas, where ambient humidity remains high throughout the year and such type of pollution is very common. This can be taken as an elementary reference value also with which to predict the flashover voltage of contaminated insulators.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Prepared polluted samples. (

**a**) Urea and dust; (

**b**) algae; (

**c**) fungus—bottom view; (

**d**) fungus—top view.

**Figure 3.**ESDD vs. FOV characteristics of the insulator contaminated with soluble agricultural pollutants.

**Figure 4.**ESDD vs. FOV characteristics of the insulator contaminated with partially soluble biological and agricultural pollutants.

**Figure 5.**NSDD vs. FOV characteristics of the insulator contaminated with different partially soluble pollutants.

Set of Contaminant | Con. of Pollutants (gm) | Conductivity (mS/cm) | ESDD (mg/cm ^{2}) | FOV (kV) | σ% | NSDD (mg/cm^{2}) | σ% |
---|---|---|---|---|---|---|---|

algae | 20 | 3.09 | 0.0822 | 69.0 | −10.11 | 2.2158 | 4.45 |

30 | 3.31 | 0.0881 | 63.0 | −10.64 | 2.2716 | 3.96 | |

40 | 4.85 | 0.1291 | 59.0 | −13.25 | 3.1071 | −1.75 | |

50 | 5.46 | 0.1453 | 56.0 | −13.96 | 3.5014 | −3.73 | |

fungi | 20 | 4.22 | 0.1104 | 64.0 | −9.94 | 2.4540 | 2.42 |

30 | 4.35 | 0.1138 | 63.0 | −10.24 | 2.4947 | 2.07 | |

40 | 4.50 | 0.1177 | 61.0 | −10.57 | 2.8352 | −0.59 | |

50 | 5.55 | 0.1446 | 58.0 | −12.43 | 3.0432 | −1.99 | |

dust | 20 | 1.40 | 0.0393 | 83.0 | −5.15 | 0.1573 | 5.91 |

30 | 1.44 | 0.0404 | 79.0 | −5.32 | 0.1604 | 5.55 | |

40 | 1.88 | 0.0528 | 76.0 | −6.90 | 0.2008 | 1.62 | |

50 | 1.92 | 0.0540 | 75.0 | −7.01 | 0.2047 | 1.29 | |

dust + urea | 10 + 10 | 1.48 | 0.0379 | 78.0 | −8.36 | 0.1483 | 3.50 |

10 + 20 | 2.48 | 0.0637 | 72.0 | −9.99 | 0.2290 | −5.15 | |

10 + 30 | 3.77 | 0.0969 | 65.0 | −11.02 | 0.2607 | −7.44 | |

10 + 40 | 3.80 | 0.0977 | 62.0 | −11.04 | 0.2688 | −7.96 | |

NaCl + K_{2}SO_{4} | 10 + 10 | 2.07 | 0.0823 | 86.0 | 9.35 | ||

10 + 20 | 2.78 | 0.1105 | 80.0 | 5.38 | |||

10 + 30 | 2.82 | 0.1121 | 78.0 | 5.20 | |||

10 + 40 | 3.50 | 0.1392 | 73.0 | 2.62 | |||

NaHCO_{3} + CaSO_{4} | 10 + 10 | 1.95 | 0.0775 | 91.0 | 14.26 | ||

10 + 20 | 2.41 | 0.0958 | 87.0 | 10.15 | |||

10 + 30 | 2.86 | 0.1137 | 81.0 | 7.13 | |||

10 + 40 | 2.91 | 0.1157 | 78.0 | 6.84 | |||

K_{2}SO_{4} + KHCO_{3} | 10 + 10 | 1.82 | 0.0705 | 95.0 | 15.65 | ||

10 + 20 | 1.93 | 0.0748 | 92.0 | 14.81 | |||

10 + 30 | 2.22 | 0.0860 | 90.0 | 12.89 | |||

10 + 40 | 2.50 | 0.0968 | 86.0 | 11.35 | |||

MgCl_{2} + NH_{4}Cl | 10 + 10 | 2.45 | 0.0862 | 89.0 | 13.30 | ||

10 + 20 | 3.04 | 0.1069 | 84.0 | 8.20 | |||

10 + 30 | 3.07 | 0.1080 | 82.0 | 7.98 | |||

10 + 40 | 3.21 | 0.1129 | 78.0 | 7.00 | |||

FAS + MgSO_{4} | 10 + 10 | 2.40 | 0.0826 | 87.0 | 10.49 | ||

10 + 20 | 2.85 | 0.0980 | 84.0 | 6.94 | |||

10 + 30 | 2.89 | 0.0994 | 80.0 | 6.67 | |||

10 + 40 | 3.05 | 0.1049 | 79.0 | 5.63 |

**Table 2.**Statistical results of ESDD-based model for both agricultural- and biological-polluted suspension insulators.

The Regression Equation Is$\mathrm{ln}\mathit{F}\mathit{O}\mathit{V}\left(\mathrm{kV}\right)=3.941-0.161\mathrm{ln}\left(\mathit{E}\mathit{S}\mathit{D}\mathit{D}\right)$ | |||||
---|---|---|---|---|---|

S = 13.7% | R-Sq = 14.69% | R-Sq(adj) = 12.19% | Multiple R = 0.383 | R-Sq(pred) = 5.13% | |

Regressor | Coef | SE Coef | T-Value | p-Value | |

Constant | 3.941 | 0.163 | 24.22 | 0.000 | |

ln ESDD | −0.1615 | 0.0667 | −2.42 | 0.021 | |

Analysis of Variance | |||||

Source | DF | SS | MS | F | P |

Regression | 1 | 0.109746 | 0.109746 | 5.86 | 0.021 |

Residual | 34 | 0.636840 | 0.018731 | ||

Total | 35 | 0.746586 |

**Table 3.**Statistical results of NSDD based model for both partially soluble agricultural- and biological-polluted suspension insulators.

The Regression Equation Is $\mathrm{ln}\mathit{F}\mathit{O}\mathit{V}\left(\mathrm{kV}\right)=4.185-0.074\mathrm{ln}\left(\mathit{N}\mathit{S}\mathit{D}\mathit{D}\right)$ | |||||
---|---|---|---|---|---|

S = 7.14% | R-Sq = 68.34% | R-Sq(adj) = 66.08% | Multiple R = 0.8266 | R-Sq(pred) = 59.56% | |

Regressor | Coef | SE Coef | T-Value | p-Value | |

Constant | 4.1848 | 0.0183 | 228.39 | 0.000 | |

ln NSDD | −0.0744 | 0.0135 | −5.50 | 0.000 | |

Analysis of Variance | |||||

Source | DF | SS | MS | F | P |

Regression | 1 | 0.15387 | 0.153870 | 30.22 | 0.000 |

Residual | 14 | 0.07129 | 0.005092 | ||

Total | 15 | 0.22516 |

The Regression Equation Is $\mathrm{ln}\mathit{F}\mathit{O}\mathit{V}\left(\mathrm{kV}\right)=4.034-0.061\mathrm{ln}\left(\mathit{E}\mathit{S}\mathit{D}\mathit{D}\ast \mathit{N}\mathit{S}\mathit{D}\mathit{D}\right)$ | |||||
---|---|---|---|---|---|

S = 5.76% | R-Sq = 79.36% | R-Sq(adj) = 77.88% | Multiple R = 0.8908 | R-Sq(pred) = 74.41% | |

Regressor | Coef | SE Coef | T-Value | p-Value | |

Constant | 4.0342 | 0.0277 | 145.59 | 0.000 | |

ln NSDD | −0.06135 | 0.0084 | −7.34 | 0.000 | |

Analysis of Variance | |||||

Source | DF | SS | MS | F | P |

Regression | 1 | 0.1786 | 0.1786 | 53.81 | 0.000 |

Residual | 14 | 0.0464 | 0.0033 | ||

Total | 15 | 0.2251 |

**Table 5.**Statistical results of ESDD-, NSDD-, AP-, and RH-based model for agricultural- and biological-pollution-contaminated insulators.

The Regression Equation Is $\mathit{F}\mathit{O}\mathit{V}=-598-233.3\mathit{E}\mathit{S}\mathit{D}\mathit{D}-0.140\mathit{N}\mathit{S}\mathit{D}\mathit{D}+0.930\mathit{A}\mathit{P}-0.1219\mathit{R}\mathit{H}\%$ R-Sq = 96.53% R-Sq(adj) = 95.27% R-Sq(pred) = 91.40% | |||||
---|---|---|---|---|---|

S = 1.8275 | R-Sq = 96.53% | R-Sq(adj) = 95.27% | R-Sq(pred) = 91.40% | ||

Regressor | Coef | SE Coef | T-Value | p-Value | |

Constant | −598 | 343 | -1.74 | 0.110 | |

ESDD | −233.3 | 27.0 | −8.63 | 0.000 | |

NSDD | −0.140 | 0.888 | −0.16 | 0.877 | |

Pressure | 0.930 | 0.460 | 2.02 | 0.068 | |

RH % | −0.1219 | 0.0610 | −2.00 | 0.071 | |

Analysis of Variance | |||||

Source | DF | SS | MS | F | P |

Regression | 4 | 1022.70 | 255.674 | 76.55 | 0.000 |

Residual | 11 | 36.74 | 3.340 | ||

Total | 15 | 1059.44 |

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**MDPI and ACS Style**

Khatoon, S.; Khan, A.A.; Tariq, M.; Alamri, B.; Mihet-Popa, L.
Flashover Voltage Prediction Models under Agricultural and Biological Contaminant Conditions on Insulators. *Energies* **2022**, *15*, 1297.
https://doi.org/10.3390/en15041297

**AMA Style**

Khatoon S, Khan AA, Tariq M, Alamri B, Mihet-Popa L.
Flashover Voltage Prediction Models under Agricultural and Biological Contaminant Conditions on Insulators. *Energies*. 2022; 15(4):1297.
https://doi.org/10.3390/en15041297

**Chicago/Turabian Style**

Khatoon, Shabana, Asfar Ali Khan, Mohd Tariq, Basem Alamri, and Lucian Mihet-Popa.
2022. "Flashover Voltage Prediction Models under Agricultural and Biological Contaminant Conditions on Insulators" *Energies* 15, no. 4: 1297.
https://doi.org/10.3390/en15041297