# Interaction of Transformer Oil Parameters on Each Other and on Transformer Health Index Using Curve Estimation Regression Method

Authors: Morteza Saeid; Hamed Zeinoddini-Meymand; Salah Kamel; Baseem Khan
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

Power transformers are one of the most significant and expensive equipment in power systems that are exposed to electrical, thermal, and chemical tensions. The transformer health index is a measure that uses test data and field inspections to assess the condition and determine the remaining life of the transformer. The purpose of this article as a new idea is to determine the relationships between electrical, physical, and chemical parameters of transformer oil, dissolved gases, and the transformer health index. One of the advantages of using the regression method in analyzing transformer data compared to the other methods to evaluate the transformer health index is determining the influence of the parameters that have the most impact on each other. Some achievements of this article are as follows: (1) introducing moisture content as the parameter that plays an effective role in reducing dielectric oil breakdown voltage and improving the transformer health index; (2) determining the inverse relationship between acidity and furfural components; (3) determining furfural as a parameter with the greatest role in reducing the Interfacial tension (IFT) of oil (molecular interconnection); (4) determining CO gas as the parameter with the most role in the production of furfural component; (5) determining C2H2 gas as the parameter with the most role in producing the acid component. For example, with a 1 ppm increase in the moisture component, the oil breakdown voltage decreases by 0.583 kV in the compound, growth, exponential, and logistic regressions, or with a 1 ppm increase in the furfural component, the oil interfacial tension decreases by 0.644 mN/m in power regression. In this article, the curve estimation regression method is used and the results are plotted by SPSS statistical software to analyze the interaction between different transformer parameters. To perform the simulations, test data related to 120 transformers have been considered.


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## Body

## 1. Introduction

By sampling from transformer oil and performing different tests, many faults in the transformer can be diagnosed, the remaining transformer life can be estimated and the condition assessment of the transformer can be specified. The transformer oil decays like most insulation and dielectric materials. This deterioration is due to resistance to electrical stresses and heat transfer from the core and coils to the oil. The condition of the dielectric oil is determined by contamination, type of dielectric oil, and the shape of the acid compounds, such as metal sulphide particles. In addition to contamination, dielectric oil decomposes by exposure to partial discharge, arc, and temperature rise. The oil decomposes into low molecular weight gases, oil-soluble gases, and carbon particles. The behaviour of each type of dielectric oil in converting to carbon particles is different. Dielectric oil analysis is the key to detecting the normal and abnormal behaviour of the transformer. The dielectric oil deteriorates due to physical and chemical contamination. Figure1 shows the stages of the transformer oil and paper insulation failure.Figure 1
Transformer oil and paper insulation failure process.There is always some oxygen in the transformer oil. The presence of oxygen produces CO, CO2 gases, and acid content. By increasing the temperature in the transformer, the moisture component with the acid component causes a hydrolysis reaction and decomposition of the paper insulation occurs. On the other hand, overheating causes the paper insulation molecules to break down. This is called the pyrolysis phenomenon. The products of the hydrolysis and pyrolysis phenomena combine to form furfural. Furfural is composed of oxygen, acid, moisture, CO, and CO2 gases. The acid, moisture, and oxygen components of furfural again result in the transformer oil and paper insulation deterioration cycle. Some of the transformer oil parameters are as follows: dissolved gases in transformer oil, oil interfacial tension (IFT), furfural, oil breakdown voltage, dissipation factor, moisture component, and acidity.Dissolved gases in transformer oil are classified as follows [1]. CO and CO2 gases in the transformer oil indicate the faults result in decomposition and degradation of paper insulation in the transformer oil. CH4, C2H4, and C2H6 gases indicate the transformer overload fault and the presence of C2H2 gas indicates the arcing fault in the transformer, which can be due to the failure of the tap changer contact short connections in the transformer. Producing CH4, C2H4, C2H6, CO2, and CO gases simultaneously in the dielectric oil indicate that there is a hot metal fault that burns the paper insulation of the transformer. H2 gas indicates a partial discharge fault and also, this gas is produced with most of fault types.The interfacial tension between water and oil is a measure of the molecular force between water and oil. The interfacial tension of the dielectric oil should be large enough to ensure that the oil oxidation or chemical contaminants do not form the particles in the oil [2]. Furans are a group of chemical components that include 2-furfuraldehyde and other dependent subsets, which are produced during the aging of the paper insulation. The furfural component can be used to determine the paper insulation degree of polymerization and estimate the remaining life of transformer paper insulation [3]. The degree of polymerization is about the molecular weight of the cellulosic insulation. Oil breakdown voltage should be large enough to ensure that the dielectric oil does not decompose under electrical tension [4]. The dissipation factor is one of the electrical tests of transformers, which is considered a tangent delta of the transformer winding [5]. The failure rate of paper insulation is doubled by a 1% increase in the moisture content in the amount of mass fraction greater than 0.5 [1]. The water distribution between oil and paper insulation is not constant and differs from the thermal cycle that occurs during the operation of the transformer [6]. The acidity of the oil destroys the insulating properties of the paper insulation and accelerates the oxidation process in the oil. Acid also causes iron to rust in the presence of moisture [7].Health index (HI) is a procedure of combining complex condition information to give a single numerical value as a comparative indication of the overall condition of the transformer. It helps the operator to make the distinction between degradation that needs maintenance and diagnosis plans and degradation that indicates approaching end of life. HI derives from database parameters in simple numerical values to support and direct asset management decisions and also provides a procedure of employing existing engineering knowledge and experience to predict future performance and failure probabilities and replace plans. HI quantifies the transformer condition based on multiple condition criteria related to the long-term degradation factors that cumulatively result in the transformer’s end of life. Several methods have been proposed to determine the transformer health index. In [8], the health index for each of the oil dissolved gases and the electrical, physical, and chemical parameters of the oil are calculated using the weight coefficients and the value of each of the parameters and the furfural component to determine the faults that occurred in the transformer. HI can be calculated using parameters such as tap changer contacts conditions, tap changer oil quality, bushing condition, winding frequency response analysis, transformer cooling condition, DGA (dissolved gas analysis) and oil quality indices, electrical current, and winding resistance [9]. In [10], weight coefficients and scores are used to calculate the DGA and oil quality indices, and the furfural component is used to determine the health condition of the transformer paper insulation. The DGA index indicates the dissolved gases in transformer oil that are produced due to the faults and temperature rise in the oil. Various methods have been proposed to determine the transformer health index [11]. In [12], the weighting coefficients and scores provided in the standards are used to calculate DGA and oil quality indices; then, the particle filter is used to determine the condition of paper insulation and estimates the insulation life by applying the uncertainties of current measurement error and oil temperature error in calculating the hot spot of the transformer winding. In addition to calculating DGA and oil quality indices, the transformer health index can also be calculated through other indicators such as economic index [13]. In [14], DGA and oil quality indices, along with paper insulation quality index, are classified and normalized in five groups, and a combination of fuzzy logic and support vector machine methods is used to determine the transformer health index. The DGA index is used to determine the faults that occurred in the transformer [15, 16] and the oil quality index is obtained by the electrical, physical, and chemical oil parameters [12, 13, 15]. One of the common methods for calculating the DGA index for fault detection in transformers is artificial neural networks [16]. Fault detection, loading, and evaluation of transformer conditions are one of the essential tasks in the operation of transformers [17, 18]. The furfural component in transformer oil is used to determine the transformer paper insulation health condition [19]. The furfural component also determines the transformer paper insulation degree of polymerization [20, 21]. The novelty of this article is that in previous works, the oil quality and DGA indices were calculated separately for a number of parameters to determine the health index or fault diagnosis, but the effect of electrical, physical, and chemical parameters of the transformer oil on each other are not considered.In [22], the relationship between health index and operation age is shown. The transformer health index value tends to decrease with a correlation coefficient (R2) of 0.631 with increasing operation age. In [23], the correlation coefficient for the correlation between operation age and transformer health index is presented with some linear and nonlinear models. In [24], support vector linear regression and fine tree decision-based regression model have been used to predict the transformer health index. In [25], artificial intelligence algorithms such as the Random Forest algorithm are used to evaluate the transformer health index. In [26], genetic algorithm and partial least squares regression are used to better determine the transformer oil samples and the attenuated Fourier transform infrared spectroscopy method is used to calculate the transformer oil breakdown voltage. Some new methods and algorithms have been used for fault detection in transformers with higher accuracy than traditional methods [27]. In [28], photoluminescence spectroscopy is used instead of visible ultraviolet spectroscopy for transformer condition assessment. In [29], DGA and partial discharge sensors are used in various modes for fault detection in the transformer. In [30], the Box–Behnken design (BBD) model is used to predict and evaluate the breakdown voltage of the transformer dielectric oil.In this article, the electrical, physical, and chemical parameters of transformer oil along with dissolved gases, which are produced due to the faults in the oil, are used to evaluate the transformer health index and also the effect of transformer parameters on each other. In previous works, the transformer health index is determined by different methods, such as using weight coefficients; however, the mathematical relationships between the transformer oil parameters and their effectiveness on each other are not specified. The novelty of this article is that in this article, using the mathematical relations of the curve estimation regression method, the changes in transformer oil parameters and their effects on each other can be determined. In other words, the effect of each of the oil quality parameters and dissolved gases on the transformer health index as a criterion for assessing the condition of the transformer has been determined.In this article, the effect of each of the dissolved gases on the electrical, physical, and chemical parameters of the oil is determined by curve estimation regression methods. Also, the effect of each of the oil quality parameters and dissolved gases on the transformer health index as a criterion for assessing the condition of the transformer has been determined. Some of the achievements of this article are as follows: (1) introducing the water content as a parameter with the greatest role in reducing the dielectric oil breakdown voltage and transformer health index; (2) finding the inverse relationship between the acid component and the furfural component; (3) determining furfural as the parameter with the greatest role in reducing the oil interfacial tension (molecular interconnection); (4) determining CO gas with the most role in the production of furfural component; (5) determining C2H2 gas with the most role in producing the acid component.


## 2. Curve Estimation Regression Method

Regression analysis is widely used for forecasting purposes. Regression analysis is also used to identify the relation between the independent and dependent variables and the type of these relations. In statistical models, regression analysis is a statistical process for estimating the relationships between different variables. This method includes many techniques for modelling and analyzing specific variables, focusing on the relationship between the dependent variable and one or more independent variables. Regression analysis describes how the value of a dependent variable changes with the change of the independent variables and remains constant with the other independent variables. In all cases, the purpose of the estimate is a function of independent variables called the regression function. Curve estimation regression methods include 11 types of regression function as follows and the best regression model that fits the data should be selected.Linear regression [31] is as follows:(1)Y=a+bX.Logarithmic regression is as follows:(2)Y=a+blnX.Inverse regression is as follows:(3)Y=a+bX.Quadratic regression [32] is as follows:(4)Y=a+b1X+b2X2.Cubic regression is as follows:(5)Y=a+b1X+b2X2+b3X3.Power regression is as follows:(6)Y=aXb1.Compound regression is as follows:(7)Y=a⋅b1X.Logistic regression is as follows, whereu is the high limit value.(8)Y=11/u+ab1X.Growth regression [33, 34] is as follows:(9)Y=ea+b1X.Exponential regression is as follows:(10)Y=a⋅eb1X.S-curve regression is as follows:(11)Y=ea+X/b1.In equations (1) to (11), the variables X to Xn are independent variables. The variable Y is a dependent variable. For example, if the water component in transformer oil is an independent variable and the acid component is a dependent variable, the purpose of the curve estimation regression method is to determine with a 1 ppm change in the water component (independent variable) and the acid component (dependent variable) changes in ppm. These changes are determined with the coefficient of determination (R-Square). The coefficients b1 to bn are the regression model coefficients for the corresponding variables. The parameter a is a constant value without considering any of the independent variables. The mathematical relationship between dependent and independent variables could be obtained using the curve estimation regression methods. By applying the regression method, for example, the relationship between the moisture component and the acid component in transformer oil could be found, or it could be determined the gas with the most role in the production of the acid component.


## 3. Simulation Results

The data of 120 transformers, including dissolved gases, oil quality parameters, and transformer health index, are used to determine parameter variations, for example, variation of the transformer health index relative to dissolved gases or oil quality parameters and variation of oil quality parameters relative to each other. The results were obtained using curve estimation regression methods with SPSS statistical software for different transformer parameters and the best results are selected from 50 different cases. In the results, the coefficient of determination (R-Square) expresses the percentage of data that is closest to the best fit line. In other words, for one unit of change in the independent variable, the dependent variable changes with the amount of R-Square. The parameter F is the statistical distribution, df1 and df2 are degrees of freedom referring to the maximum right to change the values of the variables in a sample data. The Sig parameter shows the statistical significance column of the regression analysis model. The model is a good predictor for the dependent variable if the Sig value is less than 0.05. The most important parameter determining the estimation of the relationship between two variables in regression methods is R-Square. Table 1 shows that the most variation in the transformer health index is due to variation of the dielectric oil breakdown voltage. In Table 1, the inverse regression method has the lowest and the cubic regression method provides the highest value of the R-Square. The cubic regression results are that if the transformer oil breakdown voltage (independent variable) changes by 1 kV, the transformer health index (dependent variable) changes by 0.314. Due to the presence of particles such as iron filings and impurities in the dielectric oil, the amount of breakdown voltage and the dielectric strength of oil are reduced.Table 1
Comparison of two regression methods to predict the relationship between transformer health index (HI) and oil breakdown voltage (BDV).
EquationModel summaryParameter estimatesR-SquareFdf1df2SigConstantb1b2b3Inverse0.25139.585111800.957−3.536——Cubic0.41327.216311600.5440.02103.62E-6Dependent variable: HI; independent variable: BDV.Figure2 shows the variation of the transformer health index relative to the breakdown voltage with two inverse and cubic regression methods. The cubic regression shows that the higher the transformer oil breakdown voltage, the higher the transformer health index. Reverse regression also indicates that the transformer health index decreases with the transformer oil breakdown voltage decreasing. Oil breakdown voltage is one of the electrical parameters of transformer oil, which indicates the amount of dielectric strength against tensions such as arcing.Figure 2
Variation of transformer health index (HI) relative to oil breakdown voltage (BDV).In Table2, the acid component is considered as the independent variable and the furfural component is considered as the dependent variable. The highest R-Square value is related to the inverse regression and the lowest R-Square value is related to the power regression method. In Table 2, the furfural component, which results from the degradation of the transformer paper insulation, is inversely related to the acid component. Thus, increasing the acid component by 1 ppm in transformer oil results in decreasing the furfural component by 0.569 ppm.Table 2
Comparison of two regression methods to predict the relationship between furfural and acidity components of the transformer.
EquationModel summaryParameter estimatesR-SquareFdf1df2SigConstantb1Inverse0.569155.864111800.1830.003Power0.0010.13611180.7130.189−0.031Dependent variable: furfural; independent variable: acidity.Oxygen and oxidation of oil are considered the main causes of acid production in transformer oil. Oxygen, hydrolysis (decomposition by water), and pyrolysis (heat decomposition) are introduced as three causes of degradation of transformer paper insulation and the production of furfural component [35]. Figure 3 clearly shows the inverse relationship between the acid and furfural components. The furfural component decreases with increasing the acid component in transformer oil.Figure 3
Variation the furfural relative to acidity component in the transformer oil.In Table3, the water content is considered as the independent variable and the furfural component is considered as the dependent variable. The R-Square value in this case is the same for exponential, growth, logistic, and compound regression methods. This means that by changing 1 ppm of the water content, the value of the furfural component changes 0.069 ppm. The lowest R-Square value is related to the power regression method.Table 3
Comparison of five regression methods to predict the relationship between furfural and water components of the transformer.
EquationModel summaryParameter estimatesR-SquareFdf1df2SigConstantb1Compound0.0698.69111180.0040.2490.976Power0.0364.45111180.0370.277-0.189Growth0.0698.69111180.004−1.390−0.025Exponential0.0698.69111180.0040.249−0.025Logistic0.0698.69111180.0044.0151.025Dependent variable: furfural; independent variable: water.Figure4 shows the variation of the furfural component relative to the water content. In addition to the moisture of the outside environment, the hydrolysis (decomposition with water) of the paper insulation also causes moisture production inside the transformer oil [35].Figure 4
Variation of furfural relative to water component in the transformer oil.The moisture inside the transformer oil turns into bubbles with increasing temperature and causes partial discharge and hydrogen production. Frequency response analysis and discrete wavelet transform can be used to detect this fault [36, 37]. Artificial neural network and fuzzy logic methods have been used in fault detection of transformers [38]. The parameter with the most effect on the transformer oil breakdown voltage is the water content. The oil conductivity increases with increasing the water content in transformer oil and the dielectric strength of the oil against electrical tensions decreases.In Table4, the water content is considered the independent variable and the oil breakdown voltage is considered the dependent variable. In this case, the highest value is for the exponential, compound, growth, and logistic regression methods. The oil breakdown voltage decreases by 0.58 kV with increasing the water content 1 ppm. The lowest value of R-Square is related to S-curve regression.Table 4
Comparison of five regression methods to predict the relationship between oil breakdown voltage (BDV) and water components of transformer.
EquationModel summaryParameter estimatesR-SquareFdf1df2SigConstantb1Compound0.583164.8781118073.0490.969S0.16523.343111803.8970.541Growth0.583164.878111804.291-0.031Exponential0.583164.8781118073.049-0.031Logistic0.583164.878111800.0141.032Dependent variable: BDV; independent variable: water.It can be seen from Figure5 that when the water content is low, the breakdown voltage of the transformer oil is at its highest value with the highest resistance against electrical stresses. The transformer oil breakdown voltage is reduced by increasing the water content. So, with occurring a fault, it could propagate rapidly.Figure 5
Variation of oil breakdown voltage (BDV) relative to water component in transformer oil.Moisture sensors can be used to determine the amount of moisture in the transformer oil. The amount of water in paper insulation can be estimated using the moisture relationship between oil and paper insulation [6].In Table5, the water content is the independent variable and the acid component is the dependent variable. The highest value of R-Square is related to the cubic regression. The acid component increases by 0.134 ppm with an increase of 1 ppm in the water content. The lowest R-Square value is related to the linear regression.Table 5
Comparison of two regression methods to predict the relationship between acidity and water components of the transformer.
EquationModel summaryParameter estimatesR-SquareFdf1df2SigConstantb1b2b3Linear0.0526.49511180.0120.076−0.001——Cubic0.1345.97831160.0010.0440.00907.674E − 6Dependent variable: acidity; independent variable: water.Figure6 shows the variation of the acid component relative to the water content with linear and cubic regressions. Water and acid components are related to the production of the furfural [18]. The variation of these two parameters is with a third-order relation. It is difficult to determine from Figure 5 the relation between water and acidity.Figure 6
Variation of acidity relative to water component in transformer oil.The parameter that has the greatest effect on the interfacial tension of transformer oil is the furfural component. In Table6, the highest value of R-Square is related to the power regression method and the lowest R-Square is related to S-curve regression. The interfacial tension of transformer oil changes 0.644 mN/m with a 1 ppm change in the furfural component.Table 6
Comparison of two regression methods to predict the relationship between IFT and furfural components of transformer.
EquationModel summaryParameter estimatesR-SquareFdf1df2SigConstantb1Power0.644213.5091118018.937−0.240S0.13918.988111803.2460.011Dependent variable: IFT; independent variable: furfural.It can be seen from Figure7 that the interfacial tension of the transformer oil increases when the furfural component decreases. Furfural has components such as oxygen, moisture, acid, and CO and CO2 gases, which causes degradation of the transformer oil [35].Figure 7
Variation of interfacial tension (IFT) of transformer oil compared to furfural component.Loss of interfacial tension of transformer oil reduces the cohesion of oil molecules, heat exchange in the windings, and the breakdown voltage of the transformer oil and limits loadability of the transformer.Gases produced by faults and thermal stresses in transformer oil also affect the transformer health index. The gas that has the greatest impact on the transformer health index is CO2 gas, which is produced by the decomposition of the paper insulation of the transformer and affects the furfural parameter [35]. In Table 7, the highest value of R-Square between transformer health index and CO2 gas is related to cubic regression and the lowest R-Square value is related to the S-curve regression. In this table, CO2 gas is the independent variable and the health index of the transformer is the dependent variable. The transformer health index decreases to 0.47 of its initial value by changing 1 ppm of CO2 gas.Table 7
Comparison of two regression methods to predict the relationship between HI and CO2 components of transformer.
EquationModel summaryParameter estimatesR-SquareFdf1df2SigConstantb1b2b3Cubic0.47034.334311600.983−3.790E − 51.033E − 102.319E − 13S0.14820.52411180-0.14337.202——Dependent variable: HI, independent variable: CO2.Figure8 shows that when the CO2 content is between 0 and 2000 ppm, the transformer health index is close to its final value. With increasing of faults in the transformer and decomposition of the paper insulation, the amount of CO2 gas increases and the transformer health index decreases gradually. CO2 gas is one of the components of furfural which indicates the deterioration of the paper insulation of the transformer [35].Figure 8
Variation of transformer health index (HI) relative to CO2 gas.The gas with the greatest effect on the breakdown voltage is CH4 gas. This gas is produced due to the overload fault in the transformer. In Table 8, the highest value of R-Square between CH4 gas and oil breakdown voltage is related to the cubic regression and the lowest of R-Square value is related to the S-curve regression. In this table the CH4 gas is the independent variable and oil breakdown voltage is the dependent variable. The oil breakdown voltage will change 0.216 kV if the CH4 gas changes 1 ppm.Table 8
Comparison of two regression methods to predict the relationship between BDV and CH4 parameters of the transformer.
EquationModel summaryParameter estimatesR-SquareFdf1df2SigConstantb1b2b3Cubic0.21610.6593116069.878−0.3350.001−5.171E − 7S0.0587.29911180.0084.0060.340——Dependent variable: BDV, independent variable: CH4The increase or decrease of the oil breakdown voltage due to CH4 gas variations is shown in Figure 9. In this case, when the amount of CH4 gas is low, the amount of oil breakdown voltage is high and by increasing the amount of CH4 gas with a cubic curve, the oil breakdown voltage decreases. Variables such as moisture content, acidity, metal particles, and decomposed materials from paper insulation reduce the breakdown voltage of transformer oil.Figure 9
Variation of transformer oil breakdown voltage (BDV) relative to CH4 gas.One of the gases produced by the decomposition of the transformer paper insulation is the CO gas. This gas has the greatest impact on the furfural component. In Table9, the highest value of R-Square between CO gas and furfural component is related to quadratic regression and the lowest R-Square value is related to the inverse regression. In Table 9, CO gas is the independent variable and furfural is the dependent variable. Furfural value changes to be 0.622 ppm with 1 ppm change in CO gas.Table 9
Comparison of two regression methods to predict the relationship between furfural and CO parameters of the transformer.
EquationModel summaryParameter estimatesR-SquareFdf1df2SigConstantb1b2b3Inverse0.0475.87611180.0170.423−16.118——Cubic0.62263.719311600.0020.002−5.126E − 63.591E − 9Dependent variable: furfural; independent variable: CO.According to Figure10, when the CO gas value in the transformer oil is low, the furfural component is also low. By decomposing the transformer paper insulation due to heat and increasing the CO gas, the furfural component also increases in the transformer oil. The furfural component is one of the parameters used to determine the degree of polymerization and to estimate the paper insulation life of the transformer.Figure 10
Variation of the furfural component relative to CO gas.Table 10
Comparison of five regression methods to predict the relationship between water and C2H6 parameters of transformer.
EquationModel summaryParameter estimatesR-SquareFdf1df2SigConstantb1b2b3Cubic0.20710.108311604.5910.08804.340E-8Compound0.0394.73411180.0324.2921——Growth0.0394.73411180.0321.4570——Exponential0.0394.73411180.0324.2920——Logistic0.0394.73411180.0320.2331——Dependent variable: water; independent variable: C2H6.Moisture in the transformer is produced through the degradation of the paper insulation, residual moisture in the wooden equipment, or moisture that leaks from the outside into the transformer tank. The C2H6 gas has the most effect on the moisture component of transformer oil. This gas has the most hydrogen atoms compared to the other dissolved gases in transformer oil. The highest value of R-Square is related to the cubic regression with the value of 0.207. As shown in Table 10, by changing 1 ppm of C2H6 gas, the moisture component changes to 0.207 ppm. The lowest R-Square value is related to compound, growth, logistic, and exponential regressions.The variation of the water content relative to the C2H6 gas is shown in Figure 11. In this figure, when the amount of C2H6 gas is low, the amount of water content is also low. The relation between the two independent and dependent variables is a cubic curve.Figure 11
Variation of water component of transformer oil relative to C2H6 gas.Water content values between 30 and 40 ppm are not selected with the degree of freedom criteria. For the water content values between 30 and 40 ppm, it will be difficult to determine the relationship between the two variables of C2H6 gas and water because when C2H6 gas is low, a large amount of water is produced in the transformer oil.Acid components and acid vapors cause corrosion of the transformer paper insulation and some other parts. The most important gas that affects the acid component is the C2H2 gas, which is generated by the electric arc in the transformer oil. According to Table 11, the highest value of R-Square between C2H2 gas and acid component is related to the cubic regression and the lowest R-Square value is related to the compound, growth, logistic, and exponential regressions. In Table 11, C2H2 gas is the independent variable and acidity is the dependent variable. According to the cubic regression with 1 ppm change in C2H2 gas, the acid component changes to 0.111 ppm.Table 11
Comparison of five regression methods to predict the relationship between acidity and C2H2 parameters of transformer.
EquationModel summaryParameter estimatesR-SquareFdf1df2SigConstantb1b2b3Cubic0.1114.83231160.0030.0640.0050.0050.000Compound0.0020.21011180.6480.0491.021——Growth0.0020.21011180.648-3.0190.021——Exponential0.0020.21011180.6480.0490.021——Logistic0.0020.21011180.64820.4730.980——Dependent variable: acidity; independent variable: C2H2.The variation of the acid component relative to the C2H2 gas is shown in Figure 12. When the amount of C2H2 gas is low, the acid component is in the range of 10 to 19 ppm. With the increase of C2H2 gas, the acid component also increases gradually. Oxygen and oxidation of oil are introduced as the cause of acid production in the transformer oil [35].Figure 12
Variation of acidity component of transformer oil relative to C2H2 gas.


## 4. Discussion

The values ofR-Square for some parameters of oil quality and dissolved gases in transformer oil as the independent or dependent variables calculated with the regression estimation curve are shown in Table 12. The type of regression given in this table is extracted according to the best solution of the previous tables. It can be seen that the type of regression for most of these parameters is the cubic regression.Table 12
Comparison the results of regression methods for independent and dependent variables.
Parameter (dependent)Parameter (independent)Regression typeR-squareHealth index (HI)Breakdown voltage (BDV)Cubic0.413BDVWaterCompound Growth Exponential Logistic0.583FurfuralAcidityInverse0.569IFTFurfuralPower0.644BDVCH4Cubic0.216HICO2Cubic0.470FurfuralCOCubic0.622WaterC2H6Cubic0.207AcidityC2H2Cubic0.111AcidityWaterCubic0.134


## 5. Conclusions

In this article, some of the electrical, physical, and chemical parameters of transformer oil with dissolved gases in transformer oil and the transformer health index (HI) are classified by different regression methods. For example, transformer health index for furfural, acidity, interfacial tension (IFT), breakdown voltage (BDV), dissipation factor (DF), and water component are compared with regression methods for 50 comparisons between the parameters of oil quality, oil dissolved gases, and transformer health index. The most important results are as follows.The most variation of the transformer health index is due to the change in the oil breakdown voltage. Due to the presence of particles and impurities in the transformer oil, the amount of breakdown voltage and the insulation strength of the dielectric oil are reduced.The parameter with the greatest effect on the breakdown voltage is the water component. Therefore, it can be concluded that the parameter that most reduces the health index of the transformer is the water content, which is consistent with the results of the references. The furfural component is inversely related to the acidity component, and as the acidity increases, the furfural value decreases. Most of the variations in the interfacial tension are due to the furfural component. As the furfural component increases, the cohesion of the transformer oil molecules decreases, the interfacial tension of the oil molecules decreases, and the heat exchange between the windings and the oil does not take place properly. The gas that has the greatest effect on the breakdown voltage of transformer oil is CH4. This gas is produced in transformer oil when the transformer is overloaded. The gas that has the greatest impact on the transformer health index is CO2. CO2 gas is produced by the decomposition of the transformer paper insulation in transformer oil. The gas that has the greatest impact on the furfural component is CO. The CO gas is also produced by the decomposition of transformer paper insulation in transformer oil. The gas that has the greatest effect on the water component of transformer oil is C2H6. Also, the gas that has the greatest effect on the acidity component is C2H2. One of the advantages of using the regression method for transformer oil parameters is that by measuring the moisture content inside the transformer oil, the oil failure voltage parameter can be estimated online. In oil, the oil breakdown voltage changes by 583 volts in the exponential and power regressions or by measuring the CO gas by the sensor. It can be estimated that by increasing the CO gas by 1 ppm, the furfural component changes by 0.622 ppm. Of course, using a combination of machine learning algorithms and the ANFIS method can play an important role in determining the health index and the effect of transformer parameters on each other.



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*Source: 7548533-2022-04-23.xml*