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

Interaction of Transformer Oil Parameters on Each Other and on Transformer Health Index Using... Hindawi International Transactions on Electrical Energy Systems Volume 2022, Article ID 7548533, 14 pages https://doi.org/10.1155/2022/7548533 Research Article Interaction of Transformer Oil Parameters on Each Other and on Transformer Health Index Using Curve Estimation Regression Method 1 1 2 3 Morteza Saeid, Hamed Zeinoddini-Meymand , Salah Kamel , and Baseem Khan Department of Electrical and Computer Engineering, Graduate University of Advanced Technology, Kerman, Iran Department of Electrical Engineering, Faculty of Engineering, Aswan University, Aswan 81542, Egypt Department of Electrical and Computer Engineering, Hawassa University, Hawassa, Ethiopia Correspondence should be addressed to Hamed Zeinoddini-Meymand; h.zeinoddini@kgut.ac.ir Received 10 November 2021; Revised 24 March 2022; Accepted 8 April 2022; Published 23 April 2022 Academic Editor: Tianqi Hong Copyright © 2022 Morteza Saeid et al. ,is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Power transformers are one of the most significant and expensive equipment in power systems that are exposed to electrical, thermal, and chemical tensions. ,e 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. ,e 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 C H gas as the parameter with the most role in producing the acid component. For example, 2 2 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. contamination, dielectric oil decomposes by exposure to 1. Introduction partial discharge, arc, and temperature rise. ,e oil de- By sampling from transformer oil and performing different composes into low molecular weight gases, oil-soluble gases, and carbon particles. ,e behaviour of each type of dielectric tests, many faults in the transformer can be diagnosed, the remaining transformer life can be estimated and the con- oil in converting to carbon particles is different. Dielectric oil dition assessment of the transformer can be specified. ,e analysis is the key to detecting the normal and abnormal transformer oil decays like most insulation and dielectric behaviour of the transformer. ,e dielectric oil deteriorates materials. ,is deterioration is due to resistance to electrical due to physical and chemical contamination. Figure 1 shows stresses and heat transfer from the core and coils to the oil. the stages of the transformer oil and paper insulation failure. ,e condition of the dielectric oil is determined by con- ,ere is always some oxygen in the transformer oil. ,e tamination, type of dielectric oil, and the shape of the acid presence of oxygen produces CO, CO gases, and acid compounds, such as metal sulphide particles. In addition to content. By increasing the temperature in the transformer, 2 International Transactions on Electrical Energy Systems CO CO H O Cellulose Oil oxidation oxidation Acids H O Temperature Hydrolysis Pyrolysis Division of Depolymerization molecule Chipping off levoglucosane Dehydration Levoglucosane fragmentation Furanoid compounds acids CO CO H O 2 Figure 1: Transformer oil and paper insulation failure process. the moisture component with the acid component causes a not form the particles in the oil [2]. Furans are a group of hydrolysis reaction and decomposition of the paper insu- chemical components that include 2-furfuraldehyde and lation occurs. On the other hand, overheating causes the other dependent subsets, which are produced during the paper insulation molecules to break down. ,is is called the aging of the paper insulation. ,e furfural component can be pyrolysis phenomenon. ,e products of the hydrolysis and used to determine the paper insulation degree of poly- pyrolysis phenomena combine to form furfural. Furfural is merization and estimate the remaining life of transformer composed of oxygen, acid, moisture, CO, and CO gases. ,e paper insulation [3]. ,e degree of polymerization is about acid, moisture, and oxygen components of furfural again the molecular weight of the cellulosic insulation. Oil result in the transformer oil and paper insulation deterio- breakdown voltage should be large enough to ensure that the ration cycle. Some of the transformer oil parameters are as dielectric oil does not decompose under electrical tension follows: dissolved gases in transformer oil, oil interfacial [4]. ,e dissipation factor is one of the electrical tests of tension (IFT), furfural, oil breakdown voltage, dissipation transformers, which is considered a tangent delta of the factor, moisture component, and acidity. transformer winding [5]. ,e failure rate of paper insulation Dissolved gases in transformer oil are classified as fol- is doubled by a 1% increase in the moisture content in the lows [1]. CO and CO gases in the transformer oil indicate amount of mass fraction greater than 0.5 [1]. ,e water the faults result in decomposition and degradation of paper distribution between oil and paper insulation is not constant insulation in the transformer oil. CH , C H , and C H gases and differs from the thermal cycle that occurs during the 4 2 4 2 6 indicate the transformer overload fault and the presence of operation of the transformer [6]. ,e acidity of the oil C H gas indicates the arcing fault in the transformer, which destroys the insulating properties of the paper insulation and 2 2 can be due to the failure of the tap changer contact short accelerates the oxidation process in the oil. Acid also causes connections in the transformer. Producing CH , C H , iron to rust in the presence of moisture [7]. 4 2 4 C H , CO , and CO gases simultaneously in the dielectric oil Health index (HI) is a procedure of combining complex 2 6 2 indicate that there is a hot metal fault that burns the paper condition information to give a single numerical value as a insulation of the transformer. H gas indicates a partial comparative indication of the overall condition of the transformer. It helps the operator to make the distinction discharge fault and also, this gas is produced with most of fault types. between degradation that needs maintenance and diagnosis plans and degradation that indicates approaching end of life. ,e interfacial tension between water and oil is a measure of the molecular force between water and oil. ,e HI derives from database parameters in simple numerical interfacial tension of the dielectric oil should be large enough values to support and direct asset management decisions and to ensure that the oil oxidation or chemical contaminants do also provides a procedure of employing existing engineering Residual and ingressed oxygen International Transactions on Electrical Energy Systems 3 knowledge and experience to predict future performance and nonlinear models. In [24], support vector linear regression failure probabilities and replace plans. HI quantifies the and fine tree decision-based regression model have been transformer condition based on multiple condition criteria used to predict the transformer health index. In [25], arti- related to the long-term degradation factors that cumulatively ficial intelligence algorithms such as the Random Forest result in the transformer’s end of life. Several methods have algorithm are used to evaluate the transformer health index. been proposed to determine the transformer health index. In In [26], genetic algorithm and partial least squares regression [8], the health index for each of the oil dissolved gases and the are used to better determine the transformer oil samples and electrical, physical, and chemical parameters of the oil are the attenuated Fourier transform infrared spectroscopy calculated using the weight coefficients and the value of each method is used to calculate the transformer oil breakdown of the parameters and the furfural component to determine voltage. Some new methods and algorithms have been used the faults that occurred in the transformer. HI can be cal- for fault detection in transformers with higher accuracy than culated using parameters such as tap changer contacts con- traditional methods [27]. In [28], photoluminescence ditions, tap changer oil quality, bushing condition, winding spectroscopy is used instead of visible ultraviolet spectros- frequency response analysis, transformer cooling condition, copy for transformer condition assessment. In [29], DGA DGA (dissolved gas analysis) and oil quality indices, electrical and partial discharge sensors are used in various modes for current, and winding resistance [9]. In [10], weight coeffi- fault detection in the transformer. In [30], the Box–Behnken cients and scores are used to calculate the DGA and oil quality design (BBD) model is used to predict and evaluate the indices, and the furfural component is used to determine the breakdown voltage of the transformer dielectric oil. health condition of the transformer paper insulation. ,e In this article, the electrical, physical, and chemical DGA index indicates the dissolved gases in transformer oil parameters of transformer oil along with dissolved gases, that are produced due to the faults and temperature rise in the which are produced due to the faults in the oil, are used to oil. Various methods have been proposed to determine the evaluate the transformer health index and also the effect of transformer health index [11]. In [12], the weighting coeffi- transformer parameters on each other. In previous works, cients and scores provided in the standards are used to the transformer health index is determined by different calculate DGA and oil quality indices; then, the particle filter methods, such as using weight coefficients; however, the is used to determine the condition of paper insulation and mathematical relationships between the transformer oil estimates the insulation life by applying the uncertainties of parameters and their effectiveness on each other are not current measurement error and oil temperature error in specified. ,e novelty of this article is that in this article, calculating the hot spot of the transformer winding. In ad- using the mathematical relations of the curve estimation dition to calculating DGA and oil quality indices, the regression method, the changes in transformer oil param- transformer health index can also be calculated through other eters and their effects on each other can be determined. In indicators such as economic index [13]. In [14], DGA and oil other words, the effect of each of the oil quality parameters quality indices, along with paper insulation quality index, are and dissolved gases on the transformer health index as a classified and normalized in five groups, and a combination of criterion for assessing the condition of the transformer has fuzzy logic and support vector machine methods is used to been determined. determine the transformer health index. ,e DGA index is In this article, the effect of each of the dissolved gases on used to determine the faults that occurred in the transformer the electrical, physical, and chemical parameters of the oil is [15, 16] and the oil quality index is obtained by the electrical, determined by curve estimation regression methods. Also, physical, and chemical oil parameters [12, 13, 15]. One of the the effect of each of the oil quality parameters and dissolved common methods for calculating the DGA index for fault gases on the transformer health index as a criterion for detection in transformers is artificial neural networks [16]. assessing the condition of the transformer has been deter- Fault detection, loading, and evaluation of transformer mined. Some of the achievements of this article are as conditions are one of the essential tasks in the operation of follows: (1) introducing the water content as a parameter transformers [17, 18]. ,e furfural component in transformer with the greatest role in reducing the dielectric oil break- oil is used to determine the transformer paper insulation down voltage and transformer health index; (2) finding the health condition [19]. ,e furfural component also deter- inverse relationship between the acid component and the mines the transformer paper insulation degree of polymer- furfural component; (3) determining furfural as the pa- ization [20, 21]. ,e novelty of this article is that in previous rameter with the greatest role in reducing the oil interfacial works, the oil quality and DGA indices were calculated tension (molecular interconnection); (4) determining CO separately for a number of parameters to determine the health gas with the most role in the production of furfural com- index or fault diagnosis, but the effect of electrical, physical, ponent; (5) determining C H gas with the most role in 2 2 and chemical parameters of the transformer oil on each other producing the acid component. are not considered. In [22], the relationship between health index and op- 2. Curve Estimation Regression Method eration age is shown. ,e transformer health index value tends to decrease with a correlation coefficient (R ) of 0.631 Regression analysis is widely used for forecasting purposes. with increasing operation age. In [23], the correlation co- Regression analysis is also used to identify the relation efficient for the correlation between operation age and between the independent and dependent variables and the transformer health index is presented with some linear and type of these relations. In statistical models, regression 4 International Transactions on Electrical Energy Systems analysis is a statistical process for estimating the relation- Growth regression [33, 34] is as follows: ships between different variables. ,is method includes many techniques for modelling and analyzing specific a+b X ( ) variables, focusing on the relationship between the depen- 1 (9) Y � e . dent variable and one or more independent variables. Re- gression analysis describes how the value of a dependent Exponential regression is as follows: variable changes with the change of the independent vari- ables and remains constant with the other independent variables. In all cases, the purpose of the estimate is a b X ( ) (10) Y � a · e . function of independent variables called the regression function. Curve estimation regression methods include 11 types of regression function as follows and the best re- S-curve regression is as follows: gression model that fits the data should be selected. Linear regression [31] is as follows: a+ X/b ( ( )) (11) Y � e . In equations (1) to (11), the variables X to X are in- Y � a + bX. (1) dependent variables. ,e variable Y is a dependent variable. For example, if the water component in transformer oil is an Logarithmic regression is as follows: 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 Y � a + b (ln X). (2) component (independent variable) and the acid component (dependent variable) changes in ppm. ,ese changes are determined with the coefficient of determination (R-Square). Inverse regression is as follows: ,e coefficients b to b are the regression model coefficients 1 n for the corresponding variables. ,e parameter a is a con- b stant value without considering any of the independent Y � a + 􏼠 􏼡. (3) variables. ,e mathematical relationship between dependent and independent variables could be obtained using the curve estimation regression methods. By applying the regression Quadratic regression [32] is as follows: 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 Y � a + b X􏼁 + 􏼐b X 􏼑. (4) 1 2 role in the production of the acid component. Cubic regression is as follows: 3. Simulation Results ,e data of 120 transformers, including dissolved gases, oil 2 3 Y � a + b X + b X + b X . (5) quality parameters, and transformer health index, are used to 􏼁 􏼐 􏼑 􏼐 􏼑 1 2 3 determine parameter variations, for example, variation of the transformer health index relative to dissolved gases or oil Power regression is as follows: quality parameters and variation of oil quality parameters relative to each other. ,e results were obtained using curve estimation regression methods with SPSS statistical software Y � aX . (6) for different transformer parameters and the best results are selected from 50 different cases. In the results, the coefficient of Compound regression is as follows: 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 Y � a · 􏼐b 􏼑. (7) changes with the amount of R-Square. ,e parameter F is the statistical distribution, df1 and df2 are degrees of freedom referring to the maximum right to change the values of the Logistic regression is as follows, where u is the high variables in a sample data. ,e Sig parameter shows the sta- limit value. tistical significance column of the regression analysis model. ,e model is a good predictor for the dependent variable if the Sig value is less than 0.05. ,e most important parameter Y � . (8) X determining the estimation of the relationship between two 􏼐(1/u) + ab 􏼑 variables in regression methods is R-Square. Table 1 shows that International Transactions on Electrical Energy Systems 5 Table 1: Comparison of two regression methods to predict the relationship between transformer health index (HI) and oil breakdown voltage (BDV). Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Inverse 0.251 39.585 1 118 0 0.957 −3.536 — — Cubic 0.413 27.216 3 116 0 0.544 0.021 0 3.62E-6 Dependent variable: HI; independent variable: BDV. the most variation in the transformer health index is due to the outside environment, the hydrolysis (decomposition with water) of the paper insulation also causes moisture variation of the dielectric oil breakdown voltage. In Table 1, the inverse regression method has the lowest and the cubic re- production inside the transformer oil [35]. ,e moisture inside the transformer oil turns into gression method provides the highest value of the R-Square. ,e cubic regression results are that if the transformer oil bubbles with increasing temperature and causes partial breakdown voltage (independent variable) changes by 1 kV, discharge and hydrogen production. Frequency response the transformer health index (dependent variable) changes by analysis and discrete wavelet transform can be used to detect 0.314. Due to the presence of particles such as iron filings and this fault [36, 37]. Artificial neural network and fuzzy logic impurities in the dielectric oil, the amount of breakdown methods have been used in fault detection of transformers voltage and the dielectric strength of oil are reduced. [38]. ,e parameter with the most effect on the transformer Figure 2 shows the variation of the transformer health oil breakdown voltage is the water content. ,e oil con- index relative to the breakdown voltage with two inverse and ductivity increases with increasing the water content in transformer oil and the dielectric strength of the oil against cubic regression methods. ,e cubic regression shows that the higher the transformer oil breakdown voltage, the higher electrical tensions decreases. In Table 4, the water content is considered the inde- the transformer health index. Reverse regression also in- dicates that the transformer health index decreases with the pendent variable and the oil breakdown voltage is consid- transformer oil breakdown voltage decreasing. Oil break- ered the dependent variable. In this case, the highest value is down voltage is one of the electrical parameters of trans- for the exponential, compound, growth, and logistic re- former oil, which indicates the amount of dielectric strength gression methods. ,e oil breakdown voltage decreases by against tensions such as arcing. 0.58 kV with increasing the water content 1 ppm. ,e lowest In Table 2, the acid component is considered as the value of R-Square is related to S-curve regression. independent variable and the furfural component is con- It can be seen from Figure 5 that when the water content sidered as the dependent variable. ,e highest R-Square is low, the breakdown voltage of the transformer oil is at its highest value with the highest resistance against electrical value is related to the inverse regression and the lowest R- Square value is related to the power regression method. In stresses. ,e transformer oil breakdown voltage is reduced by increasing the water content. So, with occurring a fault, it Table 2, the furfural component, which results from the degradation of the transformer paper insulation, is inversely could propagate rapidly. related to the acid component. ,us, increasing the acid Moisture sensors can be used to determine the amount component by 1 ppm in transformer oil results in decreasing of moisture in the transformer oil. ,e amount of water in the furfural component by 0.569 ppm. paper insulation can be estimated using the moisture rela- Oxygen and oxidation of oil are considered the main tionship between oil and paper insulation [6]. causes of acid production in transformer oil. Oxygen, hy- In Table 5, the water content is the independent variable drolysis (decomposition by water), and pyrolysis (heat de- and the acid component is the dependent variable. ,e composition) are introduced as three causes of degradation highest value of R-Square is related to the cubic regression. ,e acid component increases by 0.134 ppm with an increase of transformer paper insulation and the production of furfural component [35]. Figure 3 clearly shows the inverse of 1 ppm in the water content. ,e lowest R-Square value is related to the linear regression. relationship between the acid and furfural components. ,e furfural component decreases with increasing the acid Figure 6 shows the variation of the acid component component in transformer oil. relative to the water content with linear and cubic regres- In Table 3, the water content is considered as the in- sions. Water and acid components are related to the pro- dependent variable and the furfural component is consid- duction of the furfural [18]. ,e variation of these two ered as the dependent variable. ,e R-Square value in this parameters is with a third-order relation. It is difficult to case is the same for exponential, growth, logistic, and determine from Figure 5 the relation between water and acidity. compound regression methods. ,is means that by changing 1 ppm of the water content, the value of the furfural com- ,e parameter that has the greatest effect on the in- terfacial tension of transformer oil is the furfural compo- ponent changes 0.069 ppm. ,e lowest R-Square value is related to the power regression method. nent. In Table 6, the highest value of R-Square is related to Figure 4 shows the variation of the furfural component the power regression method and the lowest R-Square is relative to the water content. In addition to the moisture of related to S-curve regression. ,e interfacial tension of 6 International Transactions on Electrical Energy Systems 1.00 0.90 0.80 0.70 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 Oil Breakdown voltage Observed Inverse Cubic Figure 2: Variation of transformer health index (HI) relative to oil breakdown voltage (BDV). Table 2: Comparison of two regression methods to predict the relationship between furfural and acidity components of the transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b 1 2 1 Inverse 0.569 155.864 1 118 0 0.183 0.003 Power 0.001 0.136 1 118 0.713 0.189 −0.031 Dependent variable: furfural; independent variable: acidity. 4.00 3.00 2.00 1.00 0.00 0.00 0.10 0.20 0.30 0.40 Acidity Observed Inverse Power Figure 3: Variation the furfural relative to acidity component in the transformer oil. Table 3: Comparison of five regression methods to predict the relationship between furfural and water components of the transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b 1 2 1 Compound 0.069 8.691 1 118 0.004 0.249 0.976 Power 0.036 4.451 1 118 0.037 0.277 -0.189 Growth 0.069 8.691 1 118 0.004 −1.390 −0.025 Exponential 0.069 8.691 1 118 0.004 0.249 −0.025 Logistic 0.069 8.691 1 118 0.004 4.015 1.025 Dependent variable: furfural; independent variable: water. furfural Health Index International Transactions on Electrical Energy Systems 7 4.00 3.00 2.00 1.00 0.00 0.00 10.00 20.00 30.00 40.00 50.00 water Growth Observed Exponential Compound Logistic Power Figure 4: Variation of furfural relative to water component in the transformer oil. Table 4: Comparison of five regression methods to predict the relationship between oil breakdown voltage (BDV) and water components of transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b 1 2 1 Compound 0.583 164.878 1 118 0 73.049 0.969 S 0.165 23.343 1 118 0 3.897 0.541 Growth 0.583 164.878 1 118 0 4.291 -0.031 Exponential 0.583 164.878 1 118 0 73.049 -0.031 Logistic 0.583 164.878 1 118 0 0.014 1.032 Dependent variable: BDV; independent variable: water. 80.00 70.00 60.00 50.00 40.00 30.00 20.00 10.00 0.00 10.00 20.00 30.00 40.00 50.00 water Observed Growth Compound Exponential S Logistic Figure 5: Variation of oil breakdown voltage (BDV) relative to water component in transformer oil. transformer oil changes 0.644 mN/m with a 1 ppm change in Loss of interfacial tension of transformer oil reduces the the furfural component. cohesion of oil molecules, heat exchange in the windings, It can be seen from Figure 7 that the interfacial tension of and the breakdown voltage of the transformer oil and limits the transformer oil increases when the furfural component loadability of the transformer. decreases. Furfural has components such as oxygen, mois- Gases produced by faults and thermal stresses in ture, acid, and CO and CO gases, which causes degradation transformer oil also affect the transformer health index. ,e of the transformer oil [35]. gas that has the greatest impact on the transformer health Oil Breakdown voltage furfural 8 International Transactions on Electrical Energy Systems Table 5: Comparison of two regression methods to predict the relationship between acidity and water components of the transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Linear 0.052 6.495 1 118 0.012 0.076 −0.001 — — Cubic 0.134 5.978 3 116 0.001 0.044 0.009 0 7.674E − 6 Dependent variable: acidity; independent variable: water. 0.40 0.30 0.20 0.10 0.00 0.00 10.00 20.00 30.00 40.00 50.00 water Observed Linear Cubic Figure 6: Variation of acidity relative to water component in transformer oil. index is CO gas, which is produced by the decomposition of of CH gas with a cubic curve, the oil breakdown voltage 2 4 the paper insulation of the transformer and affects the decreases. Variables such as moisture content, acidity, furfural parameter [35]. In Table 7, the highest value of R- metal particles, and decomposed materials from paper Square between transformer health index and CO gas is insulation reduce the breakdown voltage of transformer related to cubic regression and the lowest R-Square value is oil. related to the S-curve regression. In this table, CO gas is the One of the gases produced by the decomposition of the independent variable and the health index of the trans- transformer paper insulation is the CO gas. ,is gas has the former is the dependent variable. ,e transformer health greatest impact on the furfural component. In Table 9, the index decreases to 0.47 of its initial value by changing 1 ppm highest value of R-Square between CO gas and furfural of CO2 gas. component is related to quadratic regression and the lowest Figure 8 shows that when the CO content is between 0 R-Square value is related to the inverse regression. In Table 9, CO gas is the independent variable and furfural is the de- and 2000 ppm, the transformer health index is close to its final value. With increasing of faults in the transformer and pendent variable. Furfural value changes to be 0.622 ppm decomposition of the paper insulation, the amount of CO with 1 ppm change in CO gas. gas increases and the transformer health index decreases According to Figure 10, when the CO gas value in the gradually. CO gas is one of the components of furfural transformer oil is low, the furfural component is also low. By which indicates the deterioration of the paper insulation of decomposing the transformer paper insulation due to heat the transformer [35]. and increasing the CO gas, the furfural component also ,e gas with the greatest effect on the breakdown voltage increases in the transformer oil. ,e furfural component is is CH gas. ,is gas is produced due to the overload fault in one of the parameters used to determine the degree of polymerization and to estimate the paper insulation life of the transformer. In Table 8, the highest value of R-Square between CH gas and oil breakdown voltage is related to the the transformer. Moisture in the transformer is produced through the cubic regression and the lowest of R-Square value is related to the S-curve regression. In this table the CH gas is the degradation of the paper insulation, residual moisture in the independent variable and oil breakdown voltage is the de- wooden equipment, or moisture that leaks from the outside pendent variable. ,e oil breakdown voltage will change into the transformer tank. ,e C H gas has the most effect 2 6 0.216 kV if the CH gas changes 1 ppm. on the moisture component of transformer oil. ,is gas has ,e increase or decrease of the oil breakdown voltage the most hydrogen atoms compared to the other dissolved due to CH gas variations is shown in Figure 9. In this case, gases in transformer oil. ,e highest value of R-Square is when the amount of CH gas is low, the amount of oil related to the cubic regression with the value of 0.207. As breakdown voltage is high and by increasing the amount shown in Table 10, by changing 1 ppm of C H gas, the 2 6 Acidity International Transactions on Electrical Energy Systems 9 Table 6: Comparison of two regression methods to predict the relationship between IFT and furfural components of transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b 1 2 1 Power 0.644 213.509 1 118 0 18.937 −0.240 S 0.139 18.988 1 118 0 3.246 0.011 Dependent variable: IFT; independent variable: furfural. 40.00 30.00 20.00 10.00 0.00 1.00 2.00 3.00 4.00 furfural Observed Power Figure 7: Variation of interfacial tension (IFT) of transformer oil compared to furfural component. Table 7: Comparison of two regression methods to predict the relationship between HI and CO components of transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Cubic 0.470 34.334 3 116 0 0.983 −3.790E − 5 1.033E − 10 2.319E − 13 S 0.148 20.524 1 118 0 -0.143 37.202 — — Dependent variable: HI, independent variable: CO . 1.00 0.90 0.80 0.70 0.00 2000.00 4000.00 6000.00 8000.00 10000.00 Carbon Dioxid Gas Observed Cubic Figure 8: Variation of transformer health index (HI) relative to CO gas. Oil Interfacial Tenssion Health Index 10 International Transactions on Electrical Energy Systems Table 8: Comparison of two regression methods to predict the relationship between BDV and CH parameters of the transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Cubic 0.216 10.659 3 116 0 69.878 −0.335 0.001 −5.171E − 7 S 0.058 7.299 1 118 0.008 4.006 0.340 — — Dependent variable: BDV, independent variable: CH 80.00 70.00 60.00 50.00 40.00 30.00 20.00 10.00 0.00 500.00 1000.00 1500.00 2000.00 Methan Gas Observed Cubic Figure 9: Variation of transformer oil breakdown voltage (BDV) relative to CH gas. Table 9: Comparison of two regression methods to predict the relationship between furfural and CO parameters of the transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Inverse 0.047 5.876 1 118 0.017 0.423 −16.118 — — Cubic 0.622 63.719 3 116 0 0.002 0.002 −5.126E − 6 3.591E − 9 Dependent variable: furfural; independent variable: CO. moisture component changes to 0.207 ppm. ,e lowest R- regressions. In Table 11, C H gas is the independent var- 2 2 Square value is related to compound, growth, logistic, and iable and acidity is the dependent variable. According to the exponential regressions. cubic regression with 1 ppm change in C H gas, the acid 2 2 ,e variation of the water content relative to the C H component changes to 0.111 ppm. 2 6 gas is shown in Figure 11. In this figure, when the amount of ,e variation of the acid component relative to the C H 2 2 C H gas is low, the amount of water content is also low. ,e gas is shown in Figure 12. When the amount of C H gas is 2 6 2 2 relation between the two independent and dependent var- low, the acid component is in the range of 10 to 19 ppm. iables is a cubic curve. With the increase of C H gas, the acid component also 2 2 Water content values between 30 and 40 ppm are not increases gradually. Oxygen and oxidation of oil are in- selected with the degree of freedom criteria. For the water troduced as the cause of acid production in the transformer content values between 30 and 40 ppm, it will be difficult to oil [35]. determine the relationship between the two variables of C H gas and water because when C H gas is low, a large 2 6 2 6 4. Discussion amount of water is produced in the transformer oil. Acid components and acid vapors cause corrosion of the ,e values of R-Square for some parameters of oil quality transformer paper insulation and some other parts. ,e and dissolved gases in transformer oil as the independent or most important gas that affects the acid component is the dependent variables calculated with the regression esti- C H gas, which is generated by the electric arc in the mation curve are shown in Table 12. ,e type of regression 2 2 transformer oil. According to Table 11, the highest value of given in this table is extracted according to the best solution R-Square between C H gas and acid component is related to of the previous tables. It can be seen that the type of re- 2 2 the cubic regression and the lowest R-Square value is related gression for most of these parameters is the cubic to the compound, growth, logistic, and exponential regression. Oil Breakdown voltage International Transactions on Electrical Energy Systems 11 4.00 3.00 2.00 1.00 0.00 0.00 250.00 500.00 750.00 1000.00 1250.00 Carbon Monoxid Gas Observed Inverse Cubic 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 C H parameters of transformer. 2 6 Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Cubic 0.207 10.108 3 116 0 4.591 0.088 0 4.340E-8 Compound 0.039 4.734 1 118 0.032 4.292 1 — — Growth 0.039 4.734 1 118 0.032 1.457 0 — — Exponential 0.039 4.734 1 118 0.032 4.292 0 — — Logistic 0.039 4.734 1 118 0.032 0.233 1 — — Dependent variable: water; independent variable: C H . 2 6 50.00 40.00 30.00 20.00 10.00 0.00 0.00 500.00 1000.00 1500.00 2000.00 Etahane Gas Growth Observed Exponential Cubic Logistic Compound Figure 11: Variation of water component of transformer oil relative to C H gas. 2 6 Table 11: Comparison of five regression methods to predict the relationship between acidity and C H parameters of transformer. 2 2 Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Cubic 0.111 4.832 3 116 0.003 0.064 0.005 0.005 0.000 Compound 0.002 0.210 1 118 0.648 0.049 1.021 — — Growth 0.002 0.210 1 118 0.648 -3.019 0.021 — — Exponential 0.002 0.210 1 118 0.648 0.049 0.021 — — Logistic 0.002 0.210 1 118 0.648 20.473 0.980 — — Dependent variable: acidity; independent variable: C H . 2 2 water furfural 12 International Transactions on Electrical Energy Systems 0.40 0.30 0.20 0.10 0.00 0.00 2.50 5.00 7.50 10.00 12.50 Acethylen Gas Growth Observed Exponential Cubic Logistic Compound Figure 12: Variation of acidity component of transformer oil relative to C H gas. 2 2 Table 12: Comparison the results of regression methods for independent and dependent variables. Parameter (dependent) Parameter (independent) Regression type R-square Health index (HI) Breakdown voltage (BDV) Cubic 0.413 BDV Water Compound Growth Exponential Logistic 0.583 Furfural Acidity Inverse 0.569 IFT Furfural Power 0.644 BDV CH Cubic 0.216 HI CO Cubic 0.470 Furfural CO Cubic 0.622 Water C H Cubic 0.207 2 6 Acidity C H Cubic 0.111 2 2 Acidity Water Cubic 0.134 the furfural component. As the furfural component in- 5. Conclusions creases, the cohesion of the transformer oil molecules In this article, some of the electrical, physical, and chemical decreases, the interfacial tension of the oil molecules de- parameters of transformer oil with dissolved gases in creases, and the heat exchange between the windings and transformer oil and the transformer health index (HI) are the oil does not take place properly. ,e gas that has the classified by different regression methods. For example, greatest effect on the breakdown voltage of transformer oil transformer health index for furfural, acidity, interfacial is CH . ,is gas is produced in transformer oil when the tension (IFT), breakdown voltage (BDV), dissipation factor transformer is overloaded. ,e gas that has the greatest (DF), and water component are compared with regression impact on the transformer health index is CO . CO gas is 2 2 methods for 50 comparisons between the parameters of oil produced by the decomposition of the transformer paper quality, oil dissolved gases, and transformer health index. insulation in transformer oil. ,e gas that has the greatest ,e most important results are as follows. impact on the furfural component is CO. ,e CO gas is also ,e most variation of the transformer health index is due produced by the decomposition of transformer paper to the change in the oil breakdown voltage. Due to the insulation in transformer oil. ,e gas that has the greatest presence of particles and impurities in the transformer oil, effect on the water component of transformer oil is C H . 2 6 the amount of breakdown voltage and the insulation Also, the gas that has the greatest effect on the acidity strength of the dielectric oil are reduced. component is C H . One of the advantages of using the 2 2 ,e parameter with the greatest effect on the break- regression method for transformer oil parameters is that by down voltage is the water component. ,erefore, it can be measuring the moisture content inside the transformer oil, concluded that the parameter that most reduces the health the oil failure voltage parameter can be estimated online. In index of the transformer is the water content, which is oil, the oil breakdown voltage changes by 583 volts in the consistent with the results of the references. ,e furfural exponential and power regressions or by measuring the CO component is inversely related to the acidity component, gas by the sensor. It can be estimated that by increasing the and as the acidity increases, the furfural value decreases. CO gas by 1 ppm, the furfural component changes by Most of the variations in the interfacial tension are due to 0.622 ppm. Of course, using a combination of machine Acidity International Transactions on Electrical Energy Systems 13 transformer oil,” in Proceedings of the IEEE 11th International learning algorithms and the ANFIS method can play an Conference on the Properties and Applications of Dielectric important role in determining the health index and the Materials, IEEE, Sydney, Australia, 2015. effect of transformer parameters on each other. [8] I. G. N. 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Interaction of Transformer Oil Parameters on Each Other and on Transformer Health Index Using Curve Estimation Regression Method

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Hindawi International Transactions on Electrical Energy Systems Volume 2022, Article ID 7548533, 14 pages https://doi.org/10.1155/2022/7548533 Research Article Interaction of Transformer Oil Parameters on Each Other and on Transformer Health Index Using Curve Estimation Regression Method 1 1 2 3 Morteza Saeid, Hamed Zeinoddini-Meymand , Salah Kamel , and Baseem Khan Department of Electrical and Computer Engineering, Graduate University of Advanced Technology, Kerman, Iran Department of Electrical Engineering, Faculty of Engineering, Aswan University, Aswan 81542, Egypt Department of Electrical and Computer Engineering, Hawassa University, Hawassa, Ethiopia Correspondence should be addressed to Hamed Zeinoddini-Meymand; h.zeinoddini@kgut.ac.ir Received 10 November 2021; Revised 24 March 2022; Accepted 8 April 2022; Published 23 April 2022 Academic Editor: Tianqi Hong Copyright © 2022 Morteza Saeid et al. ,is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Power transformers are one of the most significant and expensive equipment in power systems that are exposed to electrical, thermal, and chemical tensions. ,e 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. ,e 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 C H gas as the parameter with the most role in producing the acid component. For example, 2 2 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. contamination, dielectric oil decomposes by exposure to 1. Introduction partial discharge, arc, and temperature rise. ,e oil de- By sampling from transformer oil and performing different composes into low molecular weight gases, oil-soluble gases, and carbon particles. ,e behaviour of each type of dielectric tests, many faults in the transformer can be diagnosed, the remaining transformer life can be estimated and the con- oil in converting to carbon particles is different. Dielectric oil dition assessment of the transformer can be specified. ,e analysis is the key to detecting the normal and abnormal transformer oil decays like most insulation and dielectric behaviour of the transformer. ,e dielectric oil deteriorates materials. ,is deterioration is due to resistance to electrical due to physical and chemical contamination. Figure 1 shows stresses and heat transfer from the core and coils to the oil. the stages of the transformer oil and paper insulation failure. ,e condition of the dielectric oil is determined by con- ,ere is always some oxygen in the transformer oil. ,e tamination, type of dielectric oil, and the shape of the acid presence of oxygen produces CO, CO gases, and acid compounds, such as metal sulphide particles. In addition to content. By increasing the temperature in the transformer, 2 International Transactions on Electrical Energy Systems CO CO H O Cellulose Oil oxidation oxidation Acids H O Temperature Hydrolysis Pyrolysis Division of Depolymerization molecule Chipping off levoglucosane Dehydration Levoglucosane fragmentation Furanoid compounds acids CO CO H O 2 Figure 1: Transformer oil and paper insulation failure process. the moisture component with the acid component causes a not form the particles in the oil [2]. Furans are a group of hydrolysis reaction and decomposition of the paper insu- chemical components that include 2-furfuraldehyde and lation occurs. On the other hand, overheating causes the other dependent subsets, which are produced during the paper insulation molecules to break down. ,is is called the aging of the paper insulation. ,e furfural component can be pyrolysis phenomenon. ,e products of the hydrolysis and used to determine the paper insulation degree of poly- pyrolysis phenomena combine to form furfural. Furfural is merization and estimate the remaining life of transformer composed of oxygen, acid, moisture, CO, and CO gases. ,e paper insulation [3]. ,e degree of polymerization is about acid, moisture, and oxygen components of furfural again the molecular weight of the cellulosic insulation. Oil result in the transformer oil and paper insulation deterio- breakdown voltage should be large enough to ensure that the ration cycle. Some of the transformer oil parameters are as dielectric oil does not decompose under electrical tension follows: dissolved gases in transformer oil, oil interfacial [4]. ,e dissipation factor is one of the electrical tests of tension (IFT), furfural, oil breakdown voltage, dissipation transformers, which is considered a tangent delta of the factor, moisture component, and acidity. transformer winding [5]. ,e failure rate of paper insulation Dissolved gases in transformer oil are classified as fol- is doubled by a 1% increase in the moisture content in the lows [1]. CO and CO gases in the transformer oil indicate amount of mass fraction greater than 0.5 [1]. ,e water the faults result in decomposition and degradation of paper distribution between oil and paper insulation is not constant insulation in the transformer oil. CH , C H , and C H gases and differs from the thermal cycle that occurs during the 4 2 4 2 6 indicate the transformer overload fault and the presence of operation of the transformer [6]. ,e acidity of the oil C H gas indicates the arcing fault in the transformer, which destroys the insulating properties of the paper insulation and 2 2 can be due to the failure of the tap changer contact short accelerates the oxidation process in the oil. Acid also causes connections in the transformer. Producing CH , C H , iron to rust in the presence of moisture [7]. 4 2 4 C H , CO , and CO gases simultaneously in the dielectric oil Health index (HI) is a procedure of combining complex 2 6 2 indicate that there is a hot metal fault that burns the paper condition information to give a single numerical value as a insulation of the transformer. H gas indicates a partial comparative indication of the overall condition of the transformer. It helps the operator to make the distinction discharge fault and also, this gas is produced with most of fault types. between degradation that needs maintenance and diagnosis plans and degradation that indicates approaching end of life. ,e interfacial tension between water and oil is a measure of the molecular force between water and oil. ,e HI derives from database parameters in simple numerical interfacial tension of the dielectric oil should be large enough values to support and direct asset management decisions and to ensure that the oil oxidation or chemical contaminants do also provides a procedure of employing existing engineering Residual and ingressed oxygen International Transactions on Electrical Energy Systems 3 knowledge and experience to predict future performance and nonlinear models. In [24], support vector linear regression failure probabilities and replace plans. HI quantifies the and fine tree decision-based regression model have been transformer condition based on multiple condition criteria used to predict the transformer health index. In [25], arti- related to the long-term degradation factors that cumulatively ficial intelligence algorithms such as the Random Forest result in the transformer’s end of life. Several methods have algorithm are used to evaluate the transformer health index. been proposed to determine the transformer health index. In In [26], genetic algorithm and partial least squares regression [8], the health index for each of the oil dissolved gases and the are used to better determine the transformer oil samples and electrical, physical, and chemical parameters of the oil are the attenuated Fourier transform infrared spectroscopy calculated using the weight coefficients and the value of each method is used to calculate the transformer oil breakdown of the parameters and the furfural component to determine voltage. Some new methods and algorithms have been used the faults that occurred in the transformer. HI can be cal- for fault detection in transformers with higher accuracy than culated using parameters such as tap changer contacts con- traditional methods [27]. In [28], photoluminescence ditions, tap changer oil quality, bushing condition, winding spectroscopy is used instead of visible ultraviolet spectros- frequency response analysis, transformer cooling condition, copy for transformer condition assessment. In [29], DGA DGA (dissolved gas analysis) and oil quality indices, electrical and partial discharge sensors are used in various modes for current, and winding resistance [9]. In [10], weight coeffi- fault detection in the transformer. In [30], the Box–Behnken cients and scores are used to calculate the DGA and oil quality design (BBD) model is used to predict and evaluate the indices, and the furfural component is used to determine the breakdown voltage of the transformer dielectric oil. health condition of the transformer paper insulation. ,e In this article, the electrical, physical, and chemical DGA index indicates the dissolved gases in transformer oil parameters of transformer oil along with dissolved gases, that are produced due to the faults and temperature rise in the which are produced due to the faults in the oil, are used to oil. Various methods have been proposed to determine the evaluate the transformer health index and also the effect of transformer health index [11]. In [12], the weighting coeffi- transformer parameters on each other. In previous works, cients and scores provided in the standards are used to the transformer health index is determined by different calculate DGA and oil quality indices; then, the particle filter methods, such as using weight coefficients; however, the is used to determine the condition of paper insulation and mathematical relationships between the transformer oil estimates the insulation life by applying the uncertainties of parameters and their effectiveness on each other are not current measurement error and oil temperature error in specified. ,e novelty of this article is that in this article, calculating the hot spot of the transformer winding. In ad- using the mathematical relations of the curve estimation dition to calculating DGA and oil quality indices, the regression method, the changes in transformer oil param- transformer health index can also be calculated through other eters and their effects on each other can be determined. In indicators such as economic index [13]. In [14], DGA and oil other words, the effect of each of the oil quality parameters quality indices, along with paper insulation quality index, are and dissolved gases on the transformer health index as a classified and normalized in five groups, and a combination of criterion for assessing the condition of the transformer has fuzzy logic and support vector machine methods is used to been determined. determine the transformer health index. ,e DGA index is In this article, the effect of each of the dissolved gases on used to determine the faults that occurred in the transformer the electrical, physical, and chemical parameters of the oil is [15, 16] and the oil quality index is obtained by the electrical, determined by curve estimation regression methods. Also, physical, and chemical oil parameters [12, 13, 15]. One of the the effect of each of the oil quality parameters and dissolved common methods for calculating the DGA index for fault gases on the transformer health index as a criterion for detection in transformers is artificial neural networks [16]. assessing the condition of the transformer has been deter- Fault detection, loading, and evaluation of transformer mined. Some of the achievements of this article are as conditions are one of the essential tasks in the operation of follows: (1) introducing the water content as a parameter transformers [17, 18]. ,e furfural component in transformer with the greatest role in reducing the dielectric oil break- oil is used to determine the transformer paper insulation down voltage and transformer health index; (2) finding the health condition [19]. ,e furfural component also deter- inverse relationship between the acid component and the mines the transformer paper insulation degree of polymer- furfural component; (3) determining furfural as the pa- ization [20, 21]. ,e novelty of this article is that in previous rameter with the greatest role in reducing the oil interfacial works, the oil quality and DGA indices were calculated tension (molecular interconnection); (4) determining CO separately for a number of parameters to determine the health gas with the most role in the production of furfural com- index or fault diagnosis, but the effect of electrical, physical, ponent; (5) determining C H gas with the most role in 2 2 and chemical parameters of the transformer oil on each other producing the acid component. are not considered. In [22], the relationship between health index and op- 2. Curve Estimation Regression Method eration age is shown. ,e transformer health index value tends to decrease with a correlation coefficient (R ) of 0.631 Regression analysis is widely used for forecasting purposes. with increasing operation age. In [23], the correlation co- Regression analysis is also used to identify the relation efficient for the correlation between operation age and between the independent and dependent variables and the transformer health index is presented with some linear and type of these relations. In statistical models, regression 4 International Transactions on Electrical Energy Systems analysis is a statistical process for estimating the relation- Growth regression [33, 34] is as follows: ships between different variables. ,is method includes many techniques for modelling and analyzing specific a+b X ( ) variables, focusing on the relationship between the depen- 1 (9) Y � e . dent variable and one or more independent variables. Re- gression analysis describes how the value of a dependent Exponential regression is as follows: variable changes with the change of the independent vari- ables and remains constant with the other independent variables. In all cases, the purpose of the estimate is a b X ( ) (10) Y � a · e . function of independent variables called the regression function. Curve estimation regression methods include 11 types of regression function as follows and the best re- S-curve regression is as follows: gression model that fits the data should be selected. Linear regression [31] is as follows: a+ X/b ( ( )) (11) Y � e . In equations (1) to (11), the variables X to X are in- Y � a + bX. (1) dependent variables. ,e variable Y is a dependent variable. For example, if the water component in transformer oil is an Logarithmic regression is as follows: 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 Y � a + b (ln X). (2) component (independent variable) and the acid component (dependent variable) changes in ppm. ,ese changes are determined with the coefficient of determination (R-Square). Inverse regression is as follows: ,e coefficients b to b are the regression model coefficients 1 n for the corresponding variables. ,e parameter a is a con- b stant value without considering any of the independent Y � a + 􏼠 􏼡. (3) variables. ,e mathematical relationship between dependent and independent variables could be obtained using the curve estimation regression methods. By applying the regression Quadratic regression [32] is as follows: 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 Y � a + b X􏼁 + 􏼐b X 􏼑. (4) 1 2 role in the production of the acid component. Cubic regression is as follows: 3. Simulation Results ,e data of 120 transformers, including dissolved gases, oil 2 3 Y � a + b X + b X + b X . (5) quality parameters, and transformer health index, are used to 􏼁 􏼐 􏼑 􏼐 􏼑 1 2 3 determine parameter variations, for example, variation of the transformer health index relative to dissolved gases or oil Power regression is as follows: quality parameters and variation of oil quality parameters relative to each other. ,e results were obtained using curve estimation regression methods with SPSS statistical software Y � aX . (6) for different transformer parameters and the best results are selected from 50 different cases. In the results, the coefficient of Compound regression is as follows: 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 Y � a · 􏼐b 􏼑. (7) changes with the amount of R-Square. ,e parameter F is the statistical distribution, df1 and df2 are degrees of freedom referring to the maximum right to change the values of the Logistic regression is as follows, where u is the high variables in a sample data. ,e Sig parameter shows the sta- limit value. tistical significance column of the regression analysis model. ,e model is a good predictor for the dependent variable if the Sig value is less than 0.05. ,e most important parameter Y � . (8) X determining the estimation of the relationship between two 􏼐(1/u) + ab 􏼑 variables in regression methods is R-Square. Table 1 shows that International Transactions on Electrical Energy Systems 5 Table 1: Comparison of two regression methods to predict the relationship between transformer health index (HI) and oil breakdown voltage (BDV). Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Inverse 0.251 39.585 1 118 0 0.957 −3.536 — — Cubic 0.413 27.216 3 116 0 0.544 0.021 0 3.62E-6 Dependent variable: HI; independent variable: BDV. the most variation in the transformer health index is due to the outside environment, the hydrolysis (decomposition with water) of the paper insulation also causes moisture variation of the dielectric oil breakdown voltage. In Table 1, the inverse regression method has the lowest and the cubic re- production inside the transformer oil [35]. ,e moisture inside the transformer oil turns into gression method provides the highest value of the R-Square. ,e cubic regression results are that if the transformer oil bubbles with increasing temperature and causes partial breakdown voltage (independent variable) changes by 1 kV, discharge and hydrogen production. Frequency response the transformer health index (dependent variable) changes by analysis and discrete wavelet transform can be used to detect 0.314. Due to the presence of particles such as iron filings and this fault [36, 37]. Artificial neural network and fuzzy logic impurities in the dielectric oil, the amount of breakdown methods have been used in fault detection of transformers voltage and the dielectric strength of oil are reduced. [38]. ,e parameter with the most effect on the transformer Figure 2 shows the variation of the transformer health oil breakdown voltage is the water content. ,e oil con- index relative to the breakdown voltage with two inverse and ductivity increases with increasing the water content in transformer oil and the dielectric strength of the oil against cubic regression methods. ,e cubic regression shows that the higher the transformer oil breakdown voltage, the higher electrical tensions decreases. In Table 4, the water content is considered the inde- the transformer health index. Reverse regression also in- dicates that the transformer health index decreases with the pendent variable and the oil breakdown voltage is consid- transformer oil breakdown voltage decreasing. Oil break- ered the dependent variable. In this case, the highest value is down voltage is one of the electrical parameters of trans- for the exponential, compound, growth, and logistic re- former oil, which indicates the amount of dielectric strength gression methods. ,e oil breakdown voltage decreases by against tensions such as arcing. 0.58 kV with increasing the water content 1 ppm. ,e lowest In Table 2, the acid component is considered as the value of R-Square is related to S-curve regression. independent variable and the furfural component is con- It can be seen from Figure 5 that when the water content sidered as the dependent variable. ,e highest R-Square is low, the breakdown voltage of the transformer oil is at its highest value with the highest resistance against electrical value is related to the inverse regression and the lowest R- Square value is related to the power regression method. In stresses. ,e transformer oil breakdown voltage is reduced by increasing the water content. So, with occurring a fault, it Table 2, the furfural component, which results from the degradation of the transformer paper insulation, is inversely could propagate rapidly. related to the acid component. ,us, increasing the acid Moisture sensors can be used to determine the amount component by 1 ppm in transformer oil results in decreasing of moisture in the transformer oil. ,e amount of water in the furfural component by 0.569 ppm. paper insulation can be estimated using the moisture rela- Oxygen and oxidation of oil are considered the main tionship between oil and paper insulation [6]. causes of acid production in transformer oil. Oxygen, hy- In Table 5, the water content is the independent variable drolysis (decomposition by water), and pyrolysis (heat de- and the acid component is the dependent variable. ,e composition) are introduced as three causes of degradation highest value of R-Square is related to the cubic regression. ,e acid component increases by 0.134 ppm with an increase of transformer paper insulation and the production of furfural component [35]. Figure 3 clearly shows the inverse of 1 ppm in the water content. ,e lowest R-Square value is related to the linear regression. relationship between the acid and furfural components. ,e furfural component decreases with increasing the acid Figure 6 shows the variation of the acid component component in transformer oil. relative to the water content with linear and cubic regres- In Table 3, the water content is considered as the in- sions. Water and acid components are related to the pro- dependent variable and the furfural component is consid- duction of the furfural [18]. ,e variation of these two ered as the dependent variable. ,e R-Square value in this parameters is with a third-order relation. It is difficult to case is the same for exponential, growth, logistic, and determine from Figure 5 the relation between water and acidity. compound regression methods. ,is means that by changing 1 ppm of the water content, the value of the furfural com- ,e parameter that has the greatest effect on the in- terfacial tension of transformer oil is the furfural compo- ponent changes 0.069 ppm. ,e lowest R-Square value is related to the power regression method. nent. In Table 6, the highest value of R-Square is related to Figure 4 shows the variation of the furfural component the power regression method and the lowest R-Square is relative to the water content. In addition to the moisture of related to S-curve regression. ,e interfacial tension of 6 International Transactions on Electrical Energy Systems 1.00 0.90 0.80 0.70 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 Oil Breakdown voltage Observed Inverse Cubic Figure 2: Variation of transformer health index (HI) relative to oil breakdown voltage (BDV). Table 2: Comparison of two regression methods to predict the relationship between furfural and acidity components of the transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b 1 2 1 Inverse 0.569 155.864 1 118 0 0.183 0.003 Power 0.001 0.136 1 118 0.713 0.189 −0.031 Dependent variable: furfural; independent variable: acidity. 4.00 3.00 2.00 1.00 0.00 0.00 0.10 0.20 0.30 0.40 Acidity Observed Inverse Power Figure 3: Variation the furfural relative to acidity component in the transformer oil. Table 3: Comparison of five regression methods to predict the relationship between furfural and water components of the transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b 1 2 1 Compound 0.069 8.691 1 118 0.004 0.249 0.976 Power 0.036 4.451 1 118 0.037 0.277 -0.189 Growth 0.069 8.691 1 118 0.004 −1.390 −0.025 Exponential 0.069 8.691 1 118 0.004 0.249 −0.025 Logistic 0.069 8.691 1 118 0.004 4.015 1.025 Dependent variable: furfural; independent variable: water. furfural Health Index International Transactions on Electrical Energy Systems 7 4.00 3.00 2.00 1.00 0.00 0.00 10.00 20.00 30.00 40.00 50.00 water Growth Observed Exponential Compound Logistic Power Figure 4: Variation of furfural relative to water component in the transformer oil. Table 4: Comparison of five regression methods to predict the relationship between oil breakdown voltage (BDV) and water components of transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b 1 2 1 Compound 0.583 164.878 1 118 0 73.049 0.969 S 0.165 23.343 1 118 0 3.897 0.541 Growth 0.583 164.878 1 118 0 4.291 -0.031 Exponential 0.583 164.878 1 118 0 73.049 -0.031 Logistic 0.583 164.878 1 118 0 0.014 1.032 Dependent variable: BDV; independent variable: water. 80.00 70.00 60.00 50.00 40.00 30.00 20.00 10.00 0.00 10.00 20.00 30.00 40.00 50.00 water Observed Growth Compound Exponential S Logistic Figure 5: Variation of oil breakdown voltage (BDV) relative to water component in transformer oil. transformer oil changes 0.644 mN/m with a 1 ppm change in Loss of interfacial tension of transformer oil reduces the the furfural component. cohesion of oil molecules, heat exchange in the windings, It can be seen from Figure 7 that the interfacial tension of and the breakdown voltage of the transformer oil and limits the transformer oil increases when the furfural component loadability of the transformer. decreases. Furfural has components such as oxygen, mois- Gases produced by faults and thermal stresses in ture, acid, and CO and CO gases, which causes degradation transformer oil also affect the transformer health index. ,e of the transformer oil [35]. gas that has the greatest impact on the transformer health Oil Breakdown voltage furfural 8 International Transactions on Electrical Energy Systems Table 5: Comparison of two regression methods to predict the relationship between acidity and water components of the transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Linear 0.052 6.495 1 118 0.012 0.076 −0.001 — — Cubic 0.134 5.978 3 116 0.001 0.044 0.009 0 7.674E − 6 Dependent variable: acidity; independent variable: water. 0.40 0.30 0.20 0.10 0.00 0.00 10.00 20.00 30.00 40.00 50.00 water Observed Linear Cubic Figure 6: Variation of acidity relative to water component in transformer oil. index is CO gas, which is produced by the decomposition of of CH gas with a cubic curve, the oil breakdown voltage 2 4 the paper insulation of the transformer and affects the decreases. Variables such as moisture content, acidity, furfural parameter [35]. In Table 7, the highest value of R- metal particles, and decomposed materials from paper Square between transformer health index and CO gas is insulation reduce the breakdown voltage of transformer related to cubic regression and the lowest R-Square value is oil. related to the S-curve regression. In this table, CO gas is the One of the gases produced by the decomposition of the independent variable and the health index of the trans- transformer paper insulation is the CO gas. ,is gas has the former is the dependent variable. ,e transformer health greatest impact on the furfural component. In Table 9, the index decreases to 0.47 of its initial value by changing 1 ppm highest value of R-Square between CO gas and furfural of CO2 gas. component is related to quadratic regression and the lowest Figure 8 shows that when the CO content is between 0 R-Square value is related to the inverse regression. In Table 9, CO gas is the independent variable and furfural is the de- and 2000 ppm, the transformer health index is close to its final value. With increasing of faults in the transformer and pendent variable. Furfural value changes to be 0.622 ppm decomposition of the paper insulation, the amount of CO with 1 ppm change in CO gas. gas increases and the transformer health index decreases According to Figure 10, when the CO gas value in the gradually. CO gas is one of the components of furfural transformer oil is low, the furfural component is also low. By which indicates the deterioration of the paper insulation of decomposing the transformer paper insulation due to heat the transformer [35]. and increasing the CO gas, the furfural component also ,e gas with the greatest effect on the breakdown voltage increases in the transformer oil. ,e furfural component is is CH gas. ,is gas is produced due to the overload fault in one of the parameters used to determine the degree of polymerization and to estimate the paper insulation life of the transformer. In Table 8, the highest value of R-Square between CH gas and oil breakdown voltage is related to the the transformer. Moisture in the transformer is produced through the cubic regression and the lowest of R-Square value is related to the S-curve regression. In this table the CH gas is the degradation of the paper insulation, residual moisture in the independent variable and oil breakdown voltage is the de- wooden equipment, or moisture that leaks from the outside pendent variable. ,e oil breakdown voltage will change into the transformer tank. ,e C H gas has the most effect 2 6 0.216 kV if the CH gas changes 1 ppm. on the moisture component of transformer oil. ,is gas has ,e increase or decrease of the oil breakdown voltage the most hydrogen atoms compared to the other dissolved due to CH gas variations is shown in Figure 9. In this case, gases in transformer oil. ,e highest value of R-Square is when the amount of CH gas is low, the amount of oil related to the cubic regression with the value of 0.207. As breakdown voltage is high and by increasing the amount shown in Table 10, by changing 1 ppm of C H gas, the 2 6 Acidity International Transactions on Electrical Energy Systems 9 Table 6: Comparison of two regression methods to predict the relationship between IFT and furfural components of transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b 1 2 1 Power 0.644 213.509 1 118 0 18.937 −0.240 S 0.139 18.988 1 118 0 3.246 0.011 Dependent variable: IFT; independent variable: furfural. 40.00 30.00 20.00 10.00 0.00 1.00 2.00 3.00 4.00 furfural Observed Power Figure 7: Variation of interfacial tension (IFT) of transformer oil compared to furfural component. Table 7: Comparison of two regression methods to predict the relationship between HI and CO components of transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Cubic 0.470 34.334 3 116 0 0.983 −3.790E − 5 1.033E − 10 2.319E − 13 S 0.148 20.524 1 118 0 -0.143 37.202 — — Dependent variable: HI, independent variable: CO . 1.00 0.90 0.80 0.70 0.00 2000.00 4000.00 6000.00 8000.00 10000.00 Carbon Dioxid Gas Observed Cubic Figure 8: Variation of transformer health index (HI) relative to CO gas. Oil Interfacial Tenssion Health Index 10 International Transactions on Electrical Energy Systems Table 8: Comparison of two regression methods to predict the relationship between BDV and CH parameters of the transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Cubic 0.216 10.659 3 116 0 69.878 −0.335 0.001 −5.171E − 7 S 0.058 7.299 1 118 0.008 4.006 0.340 — — Dependent variable: BDV, independent variable: CH 80.00 70.00 60.00 50.00 40.00 30.00 20.00 10.00 0.00 500.00 1000.00 1500.00 2000.00 Methan Gas Observed Cubic Figure 9: Variation of transformer oil breakdown voltage (BDV) relative to CH gas. Table 9: Comparison of two regression methods to predict the relationship between furfural and CO parameters of the transformer. Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Inverse 0.047 5.876 1 118 0.017 0.423 −16.118 — — Cubic 0.622 63.719 3 116 0 0.002 0.002 −5.126E − 6 3.591E − 9 Dependent variable: furfural; independent variable: CO. moisture component changes to 0.207 ppm. ,e lowest R- regressions. In Table 11, C H gas is the independent var- 2 2 Square value is related to compound, growth, logistic, and iable and acidity is the dependent variable. According to the exponential regressions. cubic regression with 1 ppm change in C H gas, the acid 2 2 ,e variation of the water content relative to the C H component changes to 0.111 ppm. 2 6 gas is shown in Figure 11. In this figure, when the amount of ,e variation of the acid component relative to the C H 2 2 C H gas is low, the amount of water content is also low. ,e gas is shown in Figure 12. When the amount of C H gas is 2 6 2 2 relation between the two independent and dependent var- low, the acid component is in the range of 10 to 19 ppm. iables is a cubic curve. With the increase of C H gas, the acid component also 2 2 Water content values between 30 and 40 ppm are not increases gradually. Oxygen and oxidation of oil are in- selected with the degree of freedom criteria. For the water troduced as the cause of acid production in the transformer content values between 30 and 40 ppm, it will be difficult to oil [35]. determine the relationship between the two variables of C H gas and water because when C H gas is low, a large 2 6 2 6 4. Discussion amount of water is produced in the transformer oil. Acid components and acid vapors cause corrosion of the ,e values of R-Square for some parameters of oil quality transformer paper insulation and some other parts. ,e and dissolved gases in transformer oil as the independent or most important gas that affects the acid component is the dependent variables calculated with the regression esti- C H gas, which is generated by the electric arc in the mation curve are shown in Table 12. ,e type of regression 2 2 transformer oil. According to Table 11, the highest value of given in this table is extracted according to the best solution R-Square between C H gas and acid component is related to of the previous tables. It can be seen that the type of re- 2 2 the cubic regression and the lowest R-Square value is related gression for most of these parameters is the cubic to the compound, growth, logistic, and exponential regression. Oil Breakdown voltage International Transactions on Electrical Energy Systems 11 4.00 3.00 2.00 1.00 0.00 0.00 250.00 500.00 750.00 1000.00 1250.00 Carbon Monoxid Gas Observed Inverse Cubic 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 C H parameters of transformer. 2 6 Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Cubic 0.207 10.108 3 116 0 4.591 0.088 0 4.340E-8 Compound 0.039 4.734 1 118 0.032 4.292 1 — — Growth 0.039 4.734 1 118 0.032 1.457 0 — — Exponential 0.039 4.734 1 118 0.032 4.292 0 — — Logistic 0.039 4.734 1 118 0.032 0.233 1 — — Dependent variable: water; independent variable: C H . 2 6 50.00 40.00 30.00 20.00 10.00 0.00 0.00 500.00 1000.00 1500.00 2000.00 Etahane Gas Growth Observed Exponential Cubic Logistic Compound Figure 11: Variation of water component of transformer oil relative to C H gas. 2 6 Table 11: Comparison of five regression methods to predict the relationship between acidity and C H parameters of transformer. 2 2 Model summary Parameter estimates Equation R-Square F df df Sig Constant b b b 1 2 1 2 3 Cubic 0.111 4.832 3 116 0.003 0.064 0.005 0.005 0.000 Compound 0.002 0.210 1 118 0.648 0.049 1.021 — — Growth 0.002 0.210 1 118 0.648 -3.019 0.021 — — Exponential 0.002 0.210 1 118 0.648 0.049 0.021 — — Logistic 0.002 0.210 1 118 0.648 20.473 0.980 — — Dependent variable: acidity; independent variable: C H . 2 2 water furfural 12 International Transactions on Electrical Energy Systems 0.40 0.30 0.20 0.10 0.00 0.00 2.50 5.00 7.50 10.00 12.50 Acethylen Gas Growth Observed Exponential Cubic Logistic Compound Figure 12: Variation of acidity component of transformer oil relative to C H gas. 2 2 Table 12: Comparison the results of regression methods for independent and dependent variables. Parameter (dependent) Parameter (independent) Regression type R-square Health index (HI) Breakdown voltage (BDV) Cubic 0.413 BDV Water Compound Growth Exponential Logistic 0.583 Furfural Acidity Inverse 0.569 IFT Furfural Power 0.644 BDV CH Cubic 0.216 HI CO Cubic 0.470 Furfural CO Cubic 0.622 Water C H Cubic 0.207 2 6 Acidity C H Cubic 0.111 2 2 Acidity Water Cubic 0.134 the furfural component. As the furfural component in- 5. Conclusions creases, the cohesion of the transformer oil molecules In this article, some of the electrical, physical, and chemical decreases, the interfacial tension of the oil molecules de- parameters of transformer oil with dissolved gases in creases, and the heat exchange between the windings and transformer oil and the transformer health index (HI) are the oil does not take place properly. ,e gas that has the classified by different regression methods. For example, greatest effect on the breakdown voltage of transformer oil transformer health index for furfural, acidity, interfacial is CH . ,is gas is produced in transformer oil when the tension (IFT), breakdown voltage (BDV), dissipation factor transformer is overloaded. ,e gas that has the greatest (DF), and water component are compared with regression impact on the transformer health index is CO . CO gas is 2 2 methods for 50 comparisons between the parameters of oil produced by the decomposition of the transformer paper quality, oil dissolved gases, and transformer health index. insulation in transformer oil. ,e gas that has the greatest ,e most important results are as follows. impact on the furfural component is CO. ,e CO gas is also ,e most variation of the transformer health index is due produced by the decomposition of transformer paper to the change in the oil breakdown voltage. Due to the insulation in transformer oil. ,e gas that has the greatest presence of particles and impurities in the transformer oil, effect on the water component of transformer oil is C H . 2 6 the amount of breakdown voltage and the insulation Also, the gas that has the greatest effect on the acidity strength of the dielectric oil are reduced. component is C H . One of the advantages of using the 2 2 ,e parameter with the greatest effect on the break- regression method for transformer oil parameters is that by down voltage is the water component. ,erefore, it can be measuring the moisture content inside the transformer oil, concluded that the parameter that most reduces the health the oil failure voltage parameter can be estimated online. In index of the transformer is the water content, which is oil, the oil breakdown voltage changes by 583 volts in the consistent with the results of the references. ,e furfural exponential and power regressions or by measuring the CO component is inversely related to the acidity component, gas by the sensor. It can be estimated that by increasing the and as the acidity increases, the furfural value decreases. CO gas by 1 ppm, the furfural component changes by Most of the variations in the interfacial tension are due to 0.622 ppm. Of course, using a combination of machine Acidity International Transactions on Electrical Energy Systems 13 transformer oil,” in Proceedings of the IEEE 11th International learning algorithms and the ANFIS method can play an Conference on the Properties and Applications of Dielectric important role in determining the health index and the Materials, IEEE, Sydney, Australia, 2015. effect of transformer parameters on each other. [8] I. G. N. 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International Transactions on Electrical Energy SystemsHindawi Publishing Corporation

Published: Apr 23, 2022

References