Modelling the Effect of Thermal Aging on Transformer Oil Electrical Characteristics Using a Regression Approach

Abstract

The effect of thermal aging on the electrical properties of the insulating oil used for transformers has been explored in this experimental work. In particular the dielectric dissipation factor, the resistivity and the breakdown voltage have been measured and correlated. The numerical results predicted by mathematical model and those measured in the laboratory have been compared by using a regression analysis. Experiments on thermal aging were performed on insulating oil (Borak 22, Nynas, Austria) during a period of time of 5000-h at three different temperatures. First, the transformer oil’s dielectric dissipation factor, the resistivity and the breakdown voltage are measured after every 500 h of aging. Then, polynomial and exponential regression expressions are proposed for modelling the oil’s electrical parameters variations with thermal ageing at different aging temperatures and periods. The results show that after thermal aging, the resistivity and the breakdown voltage decrease with thermal aging, however, the dielectric dissipation factor which increases. This trend is similar for all different aging temperatures. The numerical results show close agreement with the measured results for all the samples and all studied properties. The regression model presents strong correlation with high coefficients (>94%).

1. Introduction

Transformers are crucial apparatus of power networks, and the condition of their insulation strongly affects their reliability. The insulation usually consists of oil-impregnated paper for coil insulation and mineral insulating oils for both cooling and insulation [1,2]. Assessing the electrical, chemical, and physical characteristics of transformer oils forms the basis of transformers condition monitoring. This helps to minimize energy losses, identify insulation degradation and provide timely maintenance. Furthermore, it provides information on the condition of different transformer parts, the presence of contaminants and internal partial discharge [3,4,5].

Transformer oil degrades over time under the effect of electrical stress but this is accelerated by the presence of moisture in paper and dissolved oxygen in oil. The aging process is also accelerated by other factors such as temperature hot spots and high localised electric field. The temperature’s impact on oil-impregnated paper insulation’s characteristics has been reported by many researchers [6,7,8]. This effect appears in a modification in the physical and chemical characteristics of oil and a redistribution of moisture within the oil-paper insulation.

Aging and external factors are the most important elements that promote moisture infiltration in transformer which has a negative impact on oil and paper. These factors affect the transformer’s electrical characteristics by reducing the dielectric strength and the partial discharge inception voltage [9,10,11,12,13,14].

The thermal aging mechanism influences strongly the electrical and physico-chemical characteristics of transformer oils. It usually causes a reduction of dielectric strength, the breakdown voltage and the resistivity, and an increase in the dielectric dissipation factor. In addition, it contributes to the production of dissolved gases in oil which degrades the physico-chemical characteristics of the liquid. The deterioration of solid insulation is further precipitated by the reduction of the degree of polymerization (DP) and tensile strength (TS) of the paper. This interdependence between thermal aging and electrical parameters of transformer oils has been studied by many researchers [15,16,17,18,19,20,21,22,23].

Numerical methods have been used to explore the relationship between thermal aging and the electrical properties of transformer oils [24,25,26,27]. Other researchers have focused on regression models to correlate the transformer oil’s properties and the thermal aging [28,29]. However, in these studies, the temperature of thermal aging has been neglected which is a key factor determining the degree of deterioration.

In a recent study by the authors [30], regression models were developed and used to correlate between transformer oil electrical properties with water content. In this study, regression models are used to correlate the thermal aging of transformer oil at different temperatures with the oil’s electrical properties. Experiments were performed on different transformer oil samples for a period of 5000-h of accelerated thermal aging at three temperatures: 80, 120 and 140 °C. After every 500-h, the dielectric dissipation factor, the resistivity and the breakdown voltage are measured in accordance with the relevant standards. In second step, a regression approach is applied to determine a mathematical model correlating the experimental results with thermal aging. The results show that the operating aging temperature strongly influences the electrical characteristics of insulating oil. Furthermore, the regression model shows strong correlation between thermal aging and electrical properties with high coefficients.

2. Experimental Work

Experiments on thermal aging were conducted on transformer oil samples (Borak 22, Nynas, Graz, Austria) used by the Algerian Electricity and Gas Company, Sonelgaz, Algiers, Algeria. The oil’s properties are given in

Table 1. Transformer Oil properties.

Property	Standard	Unit	Value
tan $\delta$ (90 °C)	IEC 60247	—	5 × 10${}^{-4}$
Permittivity	IEC 60247	—	2.13
Resistivity (90 °C)	IEC 60247	$\mathrm{\Omega }$.cm	7.66 × 10${}^{13}$
Breakdown voltage	IEC 60156	kV	79.8
Acidity	IEC 62021	mg KOH/g	1.17 × 10${}^{-2}$
Water content	IEC 60814	ppm	8.2
Viscosity (40 °C)	ISO 3104	mm${}^2$/s	6.998
Density (20 °C)	ISO 3675	g/mL	0.680
Colour factor	ISO 2049	—	<0.5
Flash point	ISO 2719	°C	140

.

The method of sampling is conducted in accordance with the standard [31]. Glass bottles were cleaned, dried and heated in order to eliminate all traces of contamination and humidity. New oil is filled in the glass bottles and sealed with cork plugs surrounded with aluminium leaf. Four controlled ovens are used at different aging temperatures 80, 120, and 140 °C during a time of 5000-h.

The dielectric dissipation factor, the resistivity and the breakdown voltage are measured in accordance to the relevant standards [32,33] after every 500 h of aging for all aging temperatures.

The Automatic Dissipation Factor and Resistivity Test Equipment Dieltest DTL system (Baur, Austria), that employs the Schering Bridge principle, was used to measure the dielectric dissipation factor and the resistivity. According to the recommendations in [32], the apparatus includes a 45-mL measurement cell and an automatic screen module.

For the breakdown voltage, and in accordance to [33], the tests were measured at a temperature that was no more than 5 °C higher than the ambient air temperature. An Automatic Oil Test Sets OTS 100AF/2 apparatus (Megger Group, Baunach, Germany) that contains a measurement cell containing spherical electrodes was used for the measurement of the AC breakdown voltage.

3. Regression Methods and Correlation

The relationship between experimental values and statistical random variables is found by using regression analysis. This relationship can be identified by applying correlation analysis when the dependence between the tested variables is linear. When the values of the acquired random variables approach those of the experiment, the correlation becomes stronger and regression analysis can be used to examine the functional relationship between random variables. Moreover, a close relationship between variables and experiment factors can be established. In order to solve these diverse problems, numerical processes can then be used by presenting graphically the variables. This research is interested in finding the existence of a relationship between random variables and measured values [34,35].

The correlation between values normally takes the form of a nonlinear equation when the variation of the random variables is considered nonlinear. The sample of pairs of measured values presented graphically is used to find the mathematical expression, and then, the nonlinear regression shows a dispersion of the obtained results. Furthermore, a small coefficient of determination indicates that the nonlinear dependency between random variables is low. However, if the test results are centered at particular positions, the correlation is significant [36,37].

In this research, polynomial and exponential regression models are established to evaluate the dielectric dissipation factor, the resistivity and the breakdown voltage as a result of thermal aging of oil. The forms of the adopted polynomial regression model are given in Equations (1) and (2):

$$y_i=a\ast x_i+b$$

(1)

$$y_i=a\ast {x_i}^2+b{x}_i+c$$

(2)

For the exponential regression model, the expression is presented in Equation (3):

$$y_i=a\ast exp\left(b{x}_i\right)+c\ast exp\left(d{x}_i\right)$$

(3)

where,

• $x_i$ is the aging time and $y_i$ is the parameter defining the oil electrical characteristics.
• a, b, c and d are the parameters of the regression method.

The Y vector provided in Equation (4) represents the random variables resulting from the mathematical model. It represents the set of values of the oil’s dielectric parameters under consideration: the dielectric dissipation factor, the resistivity and the breakdown voltage.

$$Y=[y_1,y_2,y_3,...,y_n]$$

(4)

The values of the aging time of oil for the different aging temperatures define the X vector.

$$X=[x_1,x_2,x_3,...,x_n]$$

(5)

The difference between each individual value and the mean is defined as the variation. The sum of squares SS is the sum of the variations of the squares. It is determined by squaring and then adding the distances between each data value and the best model graph, as given in Equation (6).

$$SS=\sum _{i=1}^n[{(f(d\left(i\right),x\left(i\right))-y\left(i\right))}^2]$$

(6)

where,

• d(i): the vector which contains the parameters of the model a, b, c and d depending on the regression model
• x(i): the aging times
• y(i): the measurement values of the characteristics
• f(d(i),x(i)): the polynomial or exponential functions presented in Equations (1)–(3).

The coefficient of correlation named R-squared or R${}^2$ is used to measure the closeness of fit of the regression model to the experimental data [38,39]. Equation (7) presents the R${}^2$ coefficient calculated by utilising the sum of square SS.

$$R^2=1-\frac{{\sum }_{i=1}^n{(yi-\widehat{yi})}^2}{{\sum }_{i=1}^n{(yi-\overline{yi})}^2}$$

(7)

where,

• $y_i$: the measurement values of the characteristics,
• $\widehat{y_i}$: numerical values for each property,
• $\overline{y_i}$: the mean of the experimental values.

4. Results and Discussion

4.1. Dielectric Dissipation Factor

The results of the dielectric dissipation factor variation with aging time for the three aging temperatures 80, 120 and 140 °C are shown in Figure 1, Figure 2 and Figure 3.

Figure 1 shows that the dielectric dissipation factor increases with aging time for the temperature of 80 °C. It rises from 5 × 10${}^{-4}$ to 1.72 × 10${}^{-2}$ after 5000-h of aging but is considered acceptable [32]. This variation is identical to those obtained for the temperatures of aging of 120 and 140 °C. However, the variations in dielectric dissipation at the higher temperature are more significant than those measured at the aging temperature of 80 °C. The increase is not significant for for the time period under 2500-h, however, it is high between 2500-h to 5000-h aging time. In Figure 2 and Figure 3, the increase in dielectric dissipation factor is very important and reach high values reaching 6.15 × 10${}^{-2}$ and 24.98 × 10${}^{-2}$ after the aging period for the temperatures of aging of 120 and 140 °C respectively. These values indicate significant thermal degradation and are considered excessive if referring to the relevant standard [32]. Because the oil deteriorates quickly at the ageing temperature of 140 °C, the ageing test was stopped at 3000 h.

This rise of the dielectric dissipation factor is a result of the production of oxidation products increased by overheating during aging. Because of the increased ionic mobility at elevated temperatures, there are more ionic conduction losses, which increase the dielectric dissipation factor [40]. Furthermore, it is due to the rise of liquid’s ion content, the oxidization reactions, and the diminution of viscosity as an effect of aging at high temperatures and during prolonged time [41].

The regression expression used to represent the dielectric dissipation factor shows very good fit with the experimental results. The fit parameters and the R${}^2$ coefficients are shown in

Table 2. The regression results of dielectric dissipation factor for T = 80, 120 and 140 °C.

Aging Time (hours)	The Regression Model	The Model’s Parameters	R${}^2$	SS
T = 80 °C
[0–2500]	Polynomial	a = 2.714 × 10${}^{-8}$; b = 1.416 × 10${}^{-4}$; c = 0.04357	97.93%	5.9143 × 10${}^{-4}$
[2500–5000]	Exponential	a = 2.782 × 10${}^{-11}$; b = 4.857 × 10${}^{-11}$; c = 0.1063; d = 3.881 × 10${}^{-4}$	99.62%	5.10${}^{-3}$
T = 120 °C
[0–2500]	Polynomial	a = 3.2 × 10${}^{-4}$; b = 0.1533	94.29%	2.71 × 10${}^{-2}$
[2500–5000]	Exponential	a = 1.187 × 10${}^{13}$; b = −0.0105; c = 0.2094; d = 6.778 × 10${}^{-4}$	99.68%	4.05 × 10${}^{-2}$
T = 140 °C
[0–3000]	Exponential	a = 2.605 × 10${}^{-2}$; b = 2.29 × 10${}^{-3}$; c = 2.395 × 10${}^{-2}$; d = 10.02	99.56%	2.2048

tan $\delta$: dielectric dissipation factor, t: aging time [hours], R²: correlation coefficient, SS: sum of squares.

for the three aging temperatures.

The regression models for dielectric dissipation factor presented in Table 2 presents high correlation coefficients for all studied oil samples. For the thermal aging of 80 °C, the correlation coefficient is 97.73% between 0 to 2500 h of aging time interval with a polynomial equation, and 99.62% between 2500 to 5000 h of aging time interval with an exponential equation. For the thermal aging of 120 °C, the trend is similar to the other aging temperatures. The model is linear for the aging time interval between 0 to 2500 h with a high value of correlation coefficient corresponding to 94.29%. However, for the aging time interval between 2500 to 5000 h, the model is exponential and the value of correlation coefficient is very high (99.%). For the thermal aging of 120 °C, the regression model is exponential during all the aging time interval of 5000-h, and the correlation coefficient is 99.56% which indicates an excellent fit.

The regression model is therefore appropriate with high R${}^2$ coefficients (>94%). For the aging temperatures of 80 and 120 °C, the correlation coefficients are smaller for the aging time interval between 0 to 2500-h (94.29%, 97.73%) compared with those corresponding to the aging time interval between 2500 to 5000-h (99.62%, 99.68%), and with the value of correlation coefficient of the aging temperatures of 140 °C (99.56%). This is can be explained by the fact that the model is close to linear trend than exponential trend when the aging time is not too long. It was claimed by [20] that the rise of the dielectric dissipation factor with regard to the thermal aging time is relatively small between the interval time of 0 to 2500-h and thought to have a linear trend. However, for the interval time of 2500 to 5000-h, the increase occurs at a much higher rate, and the trend is exponential. Hence, the numerical model for the dielectric dissipation factor for the all the samples is strongly considerable.

4.2. Resistivity

Figure 4, Figure 5 and Figure 6 show the variation of resistivity with aging time for the three aging temperatures respectively.

The resistivity decreases as a result of thermal aging time for the three aging temperatures. It falls from 7.66 × 10${}^{13}$ Ω.cm down to 1.02 × 10${}^{13}$ Ω.cm at the end of aging period time for 80 °C, i.e., a decrease of 86%. However the value after thermal aging at this temperature is still appropriate and acceptable according to the standard [32]. For the aging temperature of 120 and 140 °C, the values of resistivity reach critical values after only 2500-h of aging period time, it takes values of 9.85 × 10${}^{11}$ Ω.cm and 8.75 × 10${}^{11}$ Ω.cm respectively decreasing by by 98% and 99% after only 2500-h and 2000-h of aging time respectively.

The decrease of resistivity is due to the increase of ionic mobility as a result of the oil deterioration caused by overheating during aging, especially for elevated aging temperatures of 120 and 140 °C as argued by [20]. Furthermore, this decrease can be explained by the fact that the aging phenomena especially at elevated temperatures promotes the presence of water in oil after overheating which leads to the generation of partial discharges causing an increase in conduction and hence, the decrease of resistivity [42].

Figure 4, Figure 5 and Figure 6 show that the adopted regression models give a very close representation of the test results. The parameters of regression and coefficients are given in

Table 3. The regression results of resistivity for T = 80, 120 and 140 °C.

Aging Temperature	The Regression Model	The Model’s Parameters	R${}^2$	SS
T = 80 °C	Exponential	a = 1.177 × 10${}^{13}$; b = 1.56 × 10${}^{-3}$; c = 5.981 × 10${}^{13}$ d = −3.055 × 10${}^{-4}$	98.61%	5.87 × 10${}^{25}$
T = 120 °C	Exponential	a = 5.866 × 10${}^{13}$; b = −5.622 × 10${}^{-2}$; c = 1.794 × 10${}^{13}$; d = −1.094 × 10${}^{-3}$	99.98%	6.909 × 10${}^{23}$
T = 140 °C	Exponential	a = 5.658 × 10${}^{13}$; b = −5.623 × 10${}^{-2}$; c = 2.002 × 10${}^{13}$; d = −1.34 × 10${}^{-3}$	99.9%	7.069 × 10${}^{23}$

$\rho$: resistivity in (GΩ.m), t: aging time [hours], R²: correlation coefficient, SS: sum of squares.

.

As presented in Table 3, the R${}^2$ coefficients after regression are 98.61%, 99.98% and 99.98% which indicate close correlation. The exponential model’s parameters a,b,c and d are closely similar for the three aging temperatures. The resistivity exponential model is extremely significant for all the samples, and reproduces quite well the sharp fall in resistivity with aging time especially at high aging temperatures.

4.3. Breakdown Voltage

The breakdown voltage variations versus time for the three aging temperatures are presented in Figure 7, Figure 8 and Figure 9, respectively.

The breakdown voltage of the aged transformer oil at 80 °C decreases from 79.8 kV to 27.4 kV, i.e., a decrease of 65% at the end of the 5000-h aging period time. This trend is similar for the aged transformer oil at 120 °C, its value reach 16.3 kV at the end of 5000-h aging period time, which means a decrease of 79%. However, for the aged transformer oil at 140 °C, the decrease in breakdown voltage is very fast, it reaches a value of 14.1 kV after only 3000-h of aging period time, which means it decreases by 82% during this short aging period time.

After long thermal aging, the transformer oil becomes contaminated and contains large amounts of water. This increase the partial discharges activity and the oil dielectric strength decreases, and as a consequence, the breakdown voltage decreases [43].

The regression results of the breakdown voltage for the all the samples reveals a non-linear trend versus thermal aging. The results of the regression are summarized in

Table 4. The regression results of breakdown voltage for T = 80, 120 and 140 °C.

Aging Temperature	The Regression Model	The Model’s Parameters	R${}^2$	SS
T = 80 °C	Exponential	a = 2.204 × 10${}^4$; b = 5.319 × 10${}^{-5}$; c = 2.196 × 10${}^4$; d = 5.374 × 10${}^{-5}$	94.77%	184.5883
T = 120 °C	Exponential	a = 38; b = −8.68 × 10${}^{-4}$; c = 44.54; d = −1.771 × 10${}^{-4}$	96.83%	135.489
T = 140 °C	Exponential	a = 43.65; b = −1.153 × 10${}^{-3}$; c = 37.08; d = −2.719 × 10${}^{-4}$	97.53%	77.324

BDV: breakdown voltage [kV], t: aging time [hours], R²: correlation coefficient, SS: sum of squares.

.

The regression model and experimental results as presented in Figure 7, Figure 8 and Figure 9 are very close for the three thermal aging tests. The values of the correlation coefficients presented in Table 4 are very acceptable. For the sample aged at 80 °C, the value is 94.77%, however for the samples aged at 120 and 140 °C, the coefficients take values of 96.83% and 97.53%, and the model’s parameters are closely similar. For the three aged samples, the exponential regression model is highly relevant for representing the variations of the breakdown voltage.

5. Conclusions

In this research, regression approach was conducted to find correlation between thermal aging and electrical characteristics of insulating oil, namely the dielectric dissipation factor, the resistivity and the breakdown voltage. This was realized by conducting experiments on oil thermal aging at different aging temperatures of 80, 120 and 140 °C during 5000-h time period. A regression approach using polynomial and exponential model was adopted to propose expressions for the trend of the oil’s electrical parameters versus time at different temperatures.

As expected, it is found that after thermal aging, the dielectric dissipation factor rises versus time of aging. However, the resistivity and the breakdown voltage decrease for all oil samples. The results showed that, for the thermal aging of 80 °C, the deterioration is not critical referring to the recommendations given in the standards. However, for thermal aging at high temperatures 120 and 140 °C, the deterioration is fast and critical compared to the standard. Furthermore, for these temperatures, the fall in characteristics is reached after only 2500-h time period.

For the representation of the dielectric dissipation factor, a polynomial model is used for the aging temperatures of 80 °C and 120 °C during time period between 0 and 2500-h with correlation coefficients equal to 97.73% and 94.29% respectively. However, for the thermal aging of 80 and 120 °C during time period between 3000 and 5000-h, and for the thermal aging of 140 °C during all the time period of 5000-ht, the regression model of the dielectric dissipation factor takes an exponential equation with very high correlation coefficients R${}^2$ = 99.62%, R${}^2$ = 99.68% and R${}^2$ = 99.56%. For the resistivity, the exponential model is proposed for three aging temperatures 80, 120 and 140 °C with very high correlation coefficients, respectively, R${}^2$ = 98.61%, R${}^2$ = 99.98% and R${}^2$ = 99.98%. For the breakdown voltage, the exponential model presents a strong correlation for the three aging temperatures 80, 120 and 140 °C, with high correlation coefficients, respectively, R${}^2$ = 94.77%, R${}^2$ = 96.83% and R${}^2$ = 97.53%.

The proposed polynomial and exponential models are strongly adequate because they provide excellent resemblance compared to the test results with elevated coefficients (>94%).

The combined effect of thermal aging and water content on the a physico-chemical properties of transformer oil will be considered for future work.