energies Article
Transformer Paper Expected Life Estimation Using ANFIS Based on Oil Characteristics and Dissolved Gases (Case Study: Indonesian Transformers) Rahman Azis Prasojo 1, *, Karunika Diwyacitta 1 , Suwarno 1 1 2
*
ID
and Harry Gumilang 2
School of Electrical Engineering and Informatics, Institut Teknologi Bandung, Bandung 40132, Indonesia;
[email protected] (K.D.);
[email protected] (S.) PT. PLN (Persero) TJBT, Bandung 40243, Indonesia;
[email protected] Correspondence:
[email protected]; Tel.: +62-819-448-48246
Received: 7 June 2017; Accepted: 27 July 2017; Published: 2 August 2017
Abstract: This article presents an algorithm for modelling an Adaptive Neuro Fuzzy Inference System (ANFIS) for power transformer paper conditions in order to estimate the transformer’s expected life. The dielectric characteristics, dissolved gasses, and furfural of 108 running transformers were collected, which were divided into 76 training datasets and another 32 testing datasets. The degree of polymerization (DP) of the transformer paper was predicted using the ANFIS model based on using the dielectric characteristics and dissolved gases as input. These inputs were analyzed, and the best combination was selected, whereas CO + CO2 , acidity, interfacial tension, and color were correlated with the paper’s deterioration condition and were chosen as the input variables. The best combination of input variables and membership function was selected to build the optimal ANFIS model, which was then compared and evaluated. The proposed ANFIS model has 89.07% training accuracy and 85.75% testing accuracy and was applied to a transformer paper insulation assessment and an estimation of the expected life of four Indonesian transformers for which furfural data is unavailable. This proposed algorithm can be used as a furfural alternative for the general assessment of transformer paper conditions and the estimation of expected life and provides a helpful assistance for experts in transformer condition assessment. Keywords: ANFIS; furanic compounds; degree of polymerization; paper insulation; remaining life; dissolved gas analysis; dielectric characteristic
1. Introduction A power transformer is a piece of equipment that is designed for years of usage and generally has good reliability, with a life expectancy up to 40 years or more. The condition of the transformer naturally decreases as it is operated because of the processes of aging. However, it may become damaged faster than normal. During operation, transformers experience things that accelerate aging such as increased water content, temperature, and oxidation [1]. Without proper maintenance, the aging agents such as oxygen, heat, and moisture will cause acid formation and other materials that negatively impact cellulose insulation. Thus, these transformers may become unreliable and incapable of functioning as expected. The remaining life of a power transformer is an important aspect that the owner of the transformer needs to know. A good transformer assessment will give better insights on the condition of the transformer for maintenance purposes. This will result in better power transfer efficiency because of the smaller loss of opportunity resulting from power outages. Aging power transformers have become a great concern for providers of electric power around the world, along with the growing needs of the power system. The oil-cellulose insulation in transformers will continue aging over a lifetime, and the cellulose insulation cannot be replaced. The aging of Energies 2017, 10, 1135; doi:10.3390/en10081135
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oil-immersed cellulose insulation decreases the mechanical strength and further limits the operation of the transformer [2]. Many data confirm that most of the damage to the transformer is related to the failure of the insulation system, while the life of the cellulose insulation is the life of the transformer [3]. Failures of transformers that are operating are commonly dominated by events such as a short circuit or a lightning strike. Due to the aging on the transformer, the mechanical strength of the paper insulation will decrease, and short circuit events like this can cause the ultimate failure of the transformer. Due to their random occurrence, we cannot be certain when the final failure of the transformer is going to happen. However, if the strength of the latest paper insulation can be known, it is possible to make an estimation of when these events might occur [1]. Different methods of diagnosis have been used to estimate the insulation degradation rate, i.e., dissolved gas analysis (DGA) and the estimation of the aging based on the loading history. Furanic compounds have been a concern in the past 20 years because they offer measurement of specific chemical compounds that can be transformed directly into an indicator of the aging of the transformer’s paper insulation [4]. Furfural testing data of transformers in Indonesia is limited, unlike DGA and dielectric characteristics. Therefore, it is necessary to find an alternative way to do transformer paper insulation condition assessments using other test parameters. This study collected 108 transformer testing datasets, consisting of dielectric characteristics, Dissolved Gas Analysis (DGA), and furfural (2FAL). Several different approaches to paper insulation condition prediction have been reported such as a Fuzzy based method using interfacial tension and acidity as the input in [5], a Fuzzy Logic model using CO and CO2 as the input in [6], a ML (Machine Learning) approach using CO2 and acidity as the input in [7]. The research in [8,9] shows the possibility of using neural networks to predict the furfural level. Another study uses the loading and temperature history to calculate and predict the degree of polymerization of the transformer paper, as reported in [10]. ANFIS has been used as estimator in several studies for many purposes. For transformer diagnosis purposes, various studies report the use of ANFIS to do dissolved gas analysis and complement the existing methods as shown in [11–13]. For its good purpose as an ultimate estimator [14], this article presents the development of an ANFIS model to help the experts in transformer paper condition assessment using widely available data, dielectric characteristics, and dissolved gasses as the input variables when furfural data is unavailable. 2. Methodology This study used power transformer test data consisting of dielectric characteristics, dissolved gas analysis, and furfural. The transformers that were included in this study were 108 transformers with the nominal voltage of 150 and 500 kV and a capacity of 10 up to 100 MVA. There were 38 units under 30 MVA, 25 units between 30 and 60 MVA, and 45 units 60 MVA and more. All of the transformers used were mineral-oil immersed free breathing transformers with conservators. The transformers discussed in this article were already in operation for at least two years up to 53 years. These transformers underwent routine tests once a year and, if necessary, a few times a year. Dielectric characteristics and dissolved gas analysis tests are routinely performed, and the test datasets were collected. There are a lot of factors that influence transformer paper aging; the effects of nominal voltage, capacity, and the design of transformer on the aging of the paper are beyond the scope of this research and will further be ignored. Figure 1 shows one of the transformers included in the study. The ANFIS modelling process will be elaborated below.
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Figure 1. Example of 150/20 kV transformer with a capacity of 60 MVA.
Figure 1. Example of 150/20 kV transformer with a capacity of 60 MVA. 2.1. Transformer Paper Deterioration Indicator
2.1. Transformer Paper Deterioration Indicator
The degree of polymerization test is done in order to measure precisely the degradation of the paper insulation used in the transformer. Cellulose, which used as solid transformer insulation, is of the The degree of polymerization test is done in order toismeasure precisely the degradation a linear polymer molecule consisting of hundreds of glucose units. DP is the average number of paper insulation used in the transformer. Cellulose, which is used as solid transformer insulation, glucose molecules that make cellulose chains. The DP value decreases by the time proportional to is a linear polymer molecule consisting of hundreds of glucose units. DP is the average number of the broken cellulose molecule. The deterioration rate is highly dependent on the temperature. Based glucose molecules that make cellulose chains. The DP value decreases by the time proportional to the on IEEE C57 140 standard, DP values vary from about 1200 for new paper to at least 100 for aging brokenpaper. cellulose molecule. The deterioration rate is highly dependent on the temperature. Based on At DP 200, the paper has lost about 70% of the initial tensile strength. At this point, the paper IEEE C57 140 standard, vary from about 1200 paper to at least 100 for lost aging becomes brittle andDP thevalues transformer is considered at for the new end of its life because it has its paper. At DP mechanical 200, the paper has lost about 70% of the initial tensile strength. At this point, the paper becomes strength. concentration is a very important aging for the evaluation life assessment brittle and Furans the transformer is considered at the end of indicator its life because it has lost and its mechanical strength. of transformers in service [15,16]. Furanic compounds are easier to get than DP and TS (Tensile Furans concentration is a very important aging indicator for the evaluation and life assessment of Strength) only need to test an oil sample than taking paper of in service transformers inbecause servicewe [15,16]. Furanic compounds arerather easier to get than DP samples and TS (Tensile Strength) transformers. The furanic compound is one of the byproducts of the aging of oil-immersed cellulose because we only need to test an oil sample rather than taking paper samples of in service transformers. paper and can be directly correlated to the degree of polymerization. Furfural (2FAL) is a compound The furanic compound is one of the byproducts of the aging of oil-immersed cellulose paper and that is tested to determine the aging rate of transformer paper. For non-upgraded kraft paper can betransformers, directly correlated to the degree compound 2-Furaldehyde (2FAL), of orpolymerization. so-called furfural,Furfural can be (2FAL) linked is to athe degree ofthat is tested polymerization to determine the aging rate[17] of Equation transformer by Chendong (1). paper. For non-upgraded kraft paper transformers,
2-Furaldehyde (2FAL), or so-called furfural, can be linked to the degree of polymerization by Log 2FAL − 1.51 (1) Chendong [17] Equation (1). DP = −0.0035 Log10 2FALppm − 1.51 DPtransformer, = (1) For a thermally upgraded paper Stebbins − 0.0035 proposed that Equation (2), a modified Chendong equation, be used.
For a thermally upgraded paper transformer, Stebbins proposed that Equation (2), a modified Log 2FAL × 0.88 − 4.51 Chendong equation, be used. (2)
DP =
−0.0035 Log10 2FALppb × 0.88 − 4.51
DP =System 2.2. Adaptive Neuro-Fuzzy Inference
−0.0035
(2)
The architecture and learning procedure underlying ANFIS (adaptive neuro fuzzy inference
2.2. Adaptive Inference System system)Neuro-Fuzzy is a fuzzy inference system implemented in the framework of adaptive networks [13]. By using a hybrid learning procedure, the proposed ANFIS can construct an input-output mapping
The architecture and learning procedure underlying ANFIS (adaptive neuro fuzzy inference based on both human knowledge (in the form of fuzzy logic if-then rules) and stipulated system) is a fuzzy inference system implemented in the framework of adaptive networks [13]. By using input-output data pairs [18]. a hybrid learning procedure, thetheproposed can construct an input-output mapping and based on Two of the first parts of process ofANFIS fuzzy logic, the fuzzification of the input parameters both human knowledge (in the form of fuzzy logic the use of the use of membership functions (MF), areif-then used in rules) ANFIS.and The stipulated difference isinput-output in the output data pairs [18]. of the membership functions of Sugeno system, which can be either linear or constant. Two of the first parts of the process of fuzzy logic, the fuzzification of the input parameters and the use of the use of membership functions (MF), are used in ANFIS. The difference is in the output of the membership functions of Sugeno system, which can be either linear or constant. The structures of two input ANFIS models are shown in Figure 2. By using the input-output data sets, ANFIS makes a FIS (Fuzzy Inference System). The MF parameters are set by training using a
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The structures of two input ANFIS models are shown in Figure 2. By using the input-output data sets, ANFIS makes a FIS (Fuzzy Inference System). The MF parameters are set by training using hybrid algorithm, which is combination of backpropagation and least squares. This led to the ability of a hybrid algorithm, which is combination of backpropagation and least squares. This led to the the FIS system the training ability ofto thelearn FIS system to learn data. the training data.
Figure 2. Network structure of an Adaptive Neuro Fuzzy Inference System (ANFIS) model.
Figure 2. Network structure of an Adaptive Neuro Fuzzy Inference System (ANFIS) model. The training obtains as many rule numbers as does the training data as shown below.
The training obtains as many rule numbers does as shown below. Rule 1: IF x is A1as AND y isthe B1 training THEN f1 =data 1 Rule 2: IF x is A2 AND y is B1 THEN f2 = 2
Rule 1: IF x is A1 AND y is B1 THEN f 1 = 1 Rule 3: IF x is A1 AND y is B2 THEN f3 = 3 Rule 2:Rule IF x4: is y isy is B1B2THEN IF A2 x is AND A2 AND THEN ff42==4 2 Rule 3:….IFand x issoA1 on AND y is B2 THEN f 3 = 3 Rule 4: IF x is A2 AND y is B2 THEN f 4 = 4 where x and y are the input of the fuzzy logic, and fi is the output of a constant. . . . . and so on
At the first layer, all nodes are adaptive or the parameters can be changed by Equation (3). for = 1,2 or , =μ
where x and y are the input of the fuzzy logic, and fi is the output of a constant. (3) for = 3,4 μ , =or At the first layer, all nodes are adaptive the parameters can be changed by Equation (3). With x (or y) as the input from the first node, while Ai or Bi is a linguistic label (high, low, medium), μ and μ are the membership O1,i = µ Aifunctions =each 1, 2 node. or ( x ) for i of At the second layer, each node is labelled Π, which is non-adaptive. This is obtained by O1,i = µBi−2 (y) for i = 3, 4 multiplying each input signal to generate an output signal using Equation (4).
(3)
. μ Ai or forBi=is1,2 = node, = μ while With x (or y) as the input from the , first a linguistic label (high, low,(4)medium), µ Ai and µBi Each are the membership functions each node. output node represents the of degree of activation. In the third layer, each node is At non-adaptive, the second labelled layer, each is labelled Π, which is non-adaptive. is obtained by N, andnode its function is to normalize the degree of activation by This calculating the ratio of the input first node of the previous layer to all layers of using the previous output. multiplying each signal to generate an output signal Equation (4).Equation (5) is as follows.
O2,i ==wi = µ ( x ).µ i = 1, 2 (y), for = Ai =Bi for = 1,2 ,
+
∑
(5)
(4)
Each output node represents the degree of activation. In theEquation third layer, In the fourth layer, each node is adaptive, by the following (6). each node is non-adaptive, labelled N, and its function is to normalize the degree of activation by calculating the ratio (6) of the first for = 1,2 . = + + , = node of the previous layer to all layers of the previous output. Equation (5) is as follows. f1 and f2 are fuzzy logic if-then functions, is the output of the third layer, and + + is an adaptive parameter. w wi O3,i =w = layer1 is non-adaptive, = , forlabelled i = 1, 2Σ; this node generates the In the fifth layer, each node ini this w1 + w2 ∑ wi output function of the ANFIS system by Equation (7).
(5)
In the fourth layer, each node is adaptive, by the following Equation (6). O4,i = wi . f i = wi ( pi x + qi y + ri ) for i = 1, 2
(6)
f 1 and f 2 are fuzzy logic if-then functions, wi is the output of the third layer, and ( pi x + qi y + ri ) is an adaptive parameter. In the fifth layer, each node in this layer is non-adaptive, labelled Σ; this node generates the output function of the ANFIS system by Equation (7).
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O5,i = Σi wi . f i =
Σ i wi . f i Σ i wi
(7)
2.3. Potential Input Variables The dielectric characteristics and a dissolved gases test dataset of the transformers were collected and analyzed in this study. 2.3.1. Dielectric Characteristics Temperature, water, and oxygen are the main agents of cellulose degradation as well as the oxidation of the oil. Insulation decomposition is a chemical phenomenon. The three mechanisms of degradation, namely, hydrolysis, pyrolysis, and oxidation, act simultaneously. Hydrolysis is the decomposition of a chemical compound by reaction with water. Pyrolysis is the decomposition or transformation of a compound caused by heat. Oxidation is the combination of a substance with oxygen [1]. When the transformer insulation undergoes degradation, the dielectric characteristics of the oil will change from the initial value. The dielectric characteristics parameters used in this article consist of
• • • • •
Breakdown voltage in kV (IEC 60156-02) Water content in ppm (IEC 60814) Acidity in mg KOH/g (IEC 62021-1) Interfacial tension in dyne/cm (ASTM D 971-99a) Color (ISO 2049)
According to [19] acidity, has a relationship with the DP value through the oxidation of insulation oil that degrades the insulation paper through a hydrolysis process. In a transformer, we expect that paper aging is the main source of low molecular weight acids. Oil acidity is measured as the sum of all acids and expressed as the total acid number [2]. Paper aging decomposition is also related to interfacial tension, which is sensitive to the presence of soluble polar contaminants from solid insulating material [3]. The interfacial tension of oil in a transformer is the object of one of the tests done to assess the water content in solid insulation according to [1]. As the time elapsed, the degradation of the oil as well as the paper was indicated by the darker color of the aged oils [20]. 2.3.2. Dissolved Gas Analysis Dissolved gas analysis (DGA) was used to identify the gasses released in the paper-oil composite insulation as the results of the thermal aging process [20]. Normal operation will also result in the formation of some gases. In fact, it is possible for some transformers to operate throughout their useful life with substantial quantities of combustible gases present [21]. Operating a transformer with large quantities of combustible gas present is not a normal occurrence but it does happen, usually after some degree of investigation and an evaluation of the possible risk. The concentration of gasses detected by the DGA test used in this article are:
• • • • • • • •
H2 (hydrogen) CH4 (methane) N2 (nitrogen) O2 (oxygen) CO (carbon monoxide) CO2 (carbon dioxide) C2 H6 (ethane) C2 H4 (ethylene)
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• Tdcg (Total Dissolved Combustible Gas) CO and CO2 are a result of the thermal aging of paper insulation through an oxidation CO and CO 2 are a resultof of dissolved the thermalcarbon aging ofmonoxide paper insulation throughdioxide an oxidation process process [2,3,20]. The amount and carbon in oil could be [2,3,20]. The amount of dissolved carbon monoxide and carbon dioxide in oil could be correlated correlated with the degree of polymerization and the tensile strength of the paper. When insulating with degree of polymerization and the tensile strength of the paper. insulating papers are papers arethe degraded, their degree of polymerization decreases, andWhen CO and CO2 are generated. degraded, their degree of polymerization decreases, and CO and CO2 are generated. The higher the The higher the temperature, the more gasses are generated [22]. temperature, the more gasses are generated [22].
2.4. Modelling ANFIS for Transformer Paper Condition
2.4. Modelling ANFIS for Transformer Paper Condition
The proposed algorithm for building an ANFIS model for transformer paper condition estimation The proposed algorithm for building an ANFIS model for transformer paper condition is shown in Figure 3 estimation is shown in Figure 3
Figure 3. Adaptive neuro-fuzzy inference system (ANFIS) flowchart for modelling transformer
Figure 3. Adaptive neuro-fuzzy inference system (ANFIS) flowchart for modelling transformer paper paper condition estimations. condition estimations.
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(2)
(3)
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Data Preparation: In the first stage, DP is estimated from 2FAL using Equations (1) and (2). The correlation of estimated DP and potential variables consists of dielectric characteristics, and the dissolved gases of transformer oil are analysed. The best combination of input variables for predicting DP is selected. The data from 108 transformers are then divided into training and testing datasets. 76 datasets will be used for training, and 32 datasets will be used to evaluate the proposed model. ANFIS Modelling: The training dataset is used for building the ANFIS model. The next step is to find the optimal combination of the Membership Function (MF). The number and type of MF for each input variable is selected, the model of each combination is trained using the training dataset, and each model is tested to find the satisfactory combination. Accuracy Evaluation: The proposed model is tested using the testing datasets, and then the error is calculated both from training and testing.
2.5. Prediction Accuracy and Evaluation There are several criteria that can be used to do the performance evaluation of a transformer paper condition model. The accuracy of the proposed model has been evaluated using these different methods. 2.5.1. Mean Absolute Error (MAE) This error evaluation criterion measures the difference between the estimated DP and the target DP. 1 N (8) MAE = | f − ti | N ∑ i =1 i Equation (8) calculates MAE where fi and ti are respectively the average difference of the estimated and target DP values of the i transformer, whereas N is the amount of DP predicted [23]. 2.5.2. Symmetric Mean Absolute Percentage Error (SMAPE) This criterion evaluates the prediction error as a percentage of the actual or target DP value using Equation (9) [24,25]. 100% N | f i − ti | SMAPE = (9) ∑ i = 1 N (| f i | + | f i |)/2 Provided that the data are strictly positive, a better measure of relative accuracy can be obtained based on the log of the accuracy ratio, log (Ft/At). This measure is easier to analyze statistically and has valuable symmetry and unbiasedness properties [26]. 2.5.3. Root Mean Squared Error (RMSE) RMSE is a measure of accuracy to compare the forecasting errors of different models for a particular variable and not between variables, as it is scale-dependent [27]. This is a criterion that minimizes the variance of the error distribution. For a target sequence t and forecast sequence f with N time steps, it is calculated by Equation (10). r RMSE =
1 N
N
∑ i=1 ( t i − f i )2
(10)
2.6. Transformer Paper Expected Life Estimation The result of the ANFIS model is DP prediction. This DP value indicates the condition of the transformer paper. The life of the paper insulation is the life of the transformer [3]. Estimated percentage remaining life (%Eprl) can then be calculated using Equation (11).
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( %Eprl = 100 −
Log10 (DP) − 2.903 −0.00602
) (11)
The DP value of cellulose decreases from its initial value (DP0 ) due to cellulosic chain termination. The relationship between chain scission (η) and measured DP is calculated using Equation (12). η=
DP0 −1 DPt
(12)
The Arrhenius Equation (13) about the aging of paper is shown below. Ea 1 1 − = A . e− RT .t DPt DP0
(13)
R is the molar gas constant (8.314 J/mole/K), T is the absolute temperature in Kelvin, and Ea is the activation energy in kilojoules per mole. A is a constant that is dependent on the chemical conditions. The chemical degradation of cellulose can be described, as above, by the above equation, which can be reconstituted into the equation below to determine the residual life of the transformer. In order to calculate expected life estimation of the transformer in years, Equation (14) is used. Remnant Life =
1 DPt
−
1 DP0
A × 24 × 365
Ea
× e RT [years]
(14)
Equation (15) is completed with coefficients that are needed. Remnant Life =
1 200
−
1 DP0
A × 24 × 365
111×1000
× e 8.314∗30+HST+273 [years]
(15)
A is a constant using the results of [28,29], which are 2 × 108 for non-upgraded kraft paper and 0.67 × 108 for thermally upgraded paper. HST is the hot spot temperature rise from the hot spot of the winding. The standard HST in Indonesia is 68 K from IEC (International Electrotechnical Commission) 60076-2 [30] which set the HST of transformer at 78 K and was then corrected using Ka -10. Ea is the activation energy, which is uncertain depending on the presence of oxygen and water. Based on [31], which models the remaining lifetime of the power transformer derived from the result of previous research [28,29], the energy activation used for expected life estimation is 111 kJ/mol. 2.7. Transformer Dielectric Characteristics and Dissolved Gases Data The predicted DP from the ANFIS model can be used as an alternative expected life estimation calculation for the transformer paper insulation if the current furfural level is unknown. Tables 1–4 show the dielectric characteristics and dissolved gases data from the three transformers to be assessed in this paper. Table 1. Transformer #1. Voltage (kV)
Rated Power (MVA)
Phase
Running Time (Years)
150/20
20
3
25
Dielectric Characteristic
Value
DGA
Value (ppm)
Water (ppm) VBD (kV) Acidity (mg KOH/g) IFT (dyne/cm) Color (0–10) -
5.64 92.10 0.19 13.30 3.40 -
H2 CH4 C2 H4 C2 H6 C2 H2 CO CO2 TDCG
0 25 0 0 19 1628 1119 1673
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Table 2. Transformer #2. Voltage (kV)
Rated Power (MVA)
Phase
Running Time (Years)
150/70
100
3
21
Dielectric Characteristic
Value
DGA
Value (ppm)
Water (ppm) VBD (kV) Acidity IFT (dyne/cm) Color (0–10) -
3.93 66 0.06 30.60 2.30 -
H2 CH4 C2 H4 C2 H6 C2 H2 CO CO2 TDCG
40 0 0 0 0 96.05 2250.10 96.05
Table 3. Transformer #3. Voltage (kV)
Rated Power (MVA)
Phase
Running Time (Years)
150/20
60
3
4
Dielectric Characteristic
Value
DGA
Value (ppm)
Water VBD Acidity IFT Color -
2.86 65.90 0.019 30.20 0.50 -
H2 CH4 C2 H4 C2 H6 C2 H2 CO CO2 TDCG
0 30.37 0 57.67 0 167.84 2787.33 249.90
Table 4. Transformer #4. Voltage (kV)
Rated Power (MVA)
Phase
Running Time (Years)
150/20
60
3
20
Dielectric Characteristic
Value
DGA
Value (ppm)
Water VBD Acidity IFT Color -
2.80 80 0.02 19.89 4.80 -
H2 CH4 C2 H4 C2 H6 C2 H2 CO CO2 TDCG
23 0 0 0 0 910.62 7115.37 910.62
3. Results and Discussion From transformed DP based on furfural data collected, a correlation analysis was performed on each of the dielectric characteristics, as shown in the Table 1. Figure 4 shows the scatterplots of acidity, interfacial tension, and color. Those three parameters have higher correlation with the DP value than do water content and voltage breakdown, which is proven by r (correlation coefficient).
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(a)
(b)
(c)
(d)
Figure 4.4 Scatterplots ScatterplotsofofDP DP (Degree of Polymerization) estimated versus variables. DP Figure (Degree of Polymerization) estimated versus input input variables. (a) DP (a) versus 2. versus Acidity; (b) DP versus Interfacial Tension; (c) DP versus Color; (d) DP versus CO + CO Acidity; (b) DP versus Interfacial Tension; (c) DP versus Color; (d) DP versus CO + CO2 .
3.1. Input Selection 3.1. Input Selection 3.1.1. Correlation Correlation Analysis Analysis 3.1.1. Correlation analysis analysis is is aa highly highly general general and and therefore therefore very very flexible flexible data data analytic analytic system. system. Basic Basic Correlation linear regression may be used whenever a quantitative variable, the dependent variable is to be linear regression may be used whenever a quantitative variable, the dependent variable is to be studied studied as a function of, or in relationship to, any factors of interest, the independent variables [32]. as a function of, or in relationship to, any factors of interest, the independent variables [32]. Linear regression regression is is used used in in this this study study to to find find the the highly-correlated highly-correlated parameters parameters of of dielectric dielectric Linear characteristics and DGA to make a transformer paper condition assessment model. A correlation characteristics and DGA to make a transformer paper condition assessment model. A correlation coefficient is is aa number number that that quantifies quantifies aa type type of of correlation correlation and and dependence, dependence, meaning meaning statistical statistical coefficient relationships between two or more values in fundamental statistics. The correlation coefficient is in in relationships between two or more values in fundamental statistics. The correlation coefficient rr is the value range of −1 and +1. The closer ‘r’ is to −1 or +1, the more significant the correlation. If the the value range of −1 and +1. The closer ‘r’ is to −1 or +1, the more significant the correlation. If the value ofof‘r’‘r’is is closer to this +1, means this means that the correlation two is variables positive. value closer to +1, that the correlation betweenbetween two variables positive.isOtherwise, Otherwise, if the value of ‘r’ is closer to −1, this means that the correlation between two variables if the value of ‘r’ is closer to −1, this means that the correlation between two variables is negative. is negative. In this study, the correlation is verified by a t-test with α = 0.05. If the value of ‘P’ < α, this means In this study, the correlation by a t-test with α = 0.05. If the value of ‘P’ < α, this means that the result of linear regression is is verified significant. that the result of linear regression is significant. Table 5 shows that acidity, interfacial tension, and color are correlated with DP and are potential Table 5 shows that acidity, interfacial tension,to and withwith DPDP and are as transformer paper condition predictors. According [19], color acidityare hascorrelated a relationship value potential as transformer paper condition predictors. According to [19], acidity has a relationship through the oxidation of the insulation oil that degrades the insulation paper through a hydrolysis with DP value through the oxidation of the oil that degrades the contaminants insulation paper through process. Interfacial tension is sensitive to insulation the presence of soluble polar from solid a hydrolysis process. Interfacial tension is sensitive to the presence of soluble polar contaminants insulating material [3]. As the time elapsed, the degradation of the oil as well as the paper was from solidby insulating material the oils time[20]. elapsed, the degradation of the oil as well as the paper indicated the darker color of[3]. theAs aged was indicated by the darker color of the aged oils [20].values, which resulted in TDCG, CO, and CO Table 6 shows the correlation analysis of the DGA 2 Table 6 shows thecorrelation correlation analysis ofvalue. the DGA values, resulted in TDCG,Gasses) CO, and having relatively high with the DP TDCG (Totalwhich Dissolved Combustible is CO2used having high correlation the DP value. TDCG Dissolved Combustible not as arelatively potential predictor becausewith it is originally the sum of H(Total 2 , CH4 , CO, C2 H2 , C2 H4 , and Gasses) is not used as a potential predictor because it is originally the sum of H2, CH4, CO, C2H2, C2H4, and C2H6. The highest concentration of TDCG comes from CO, which makes a high multicollinearity of CO and TDCG.
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C2 H6 . The highest concentration of TDCG comes from CO, which makes a high multicollinearity of Table 5. The correlation coefficients of DP against the dielectric characteristics for oil-filled CO and TDCG. transformers. Table 5. The correlation coefficients of DP against the dielectric characteristics for oil-filled transformers.
Dielectric Characteristic Water Content (ppm) Dielectric Characteristic Voltage Breakdown (kV) Water Content (ppm) Acidity KOH/g) Voltage (mg Breakdown (kV) Interfacial Tension (dyne/cm) Acidity (mg KOH/g) Interfacial Tension (dyne/cm) Color (Scale 0–10)
r −0.244r 0.199 −0.244 −0.432 0.199 0.732 −0.432 0.732 −0.686 −0.686
Color (Scale 0–10)
p-Value 0.007 p-Value 0.029 0.007 0.000 0.029 0.000 0.000 0.000 0.000 0.000
Table 6. The correlation coefficients of DP against the dissolved gasses for oil-filled transformers. Table 6. The correlation coefficients of DP against the dissolved gasses for oil-filled transformers.
DGA
r
HDGA 2 (ppm)
r −0.069
CH 4 (ppm) H 2 (ppm) CH C2H 4 (ppm) 4 (ppm) CC 2H 4 2H6(ppm) (ppm) C2 H6 (ppm) C2H2 (ppm) C2 H2 (ppm) TDCG(ppm) (ppm) TDCG CO(ppm) (ppm) CO CO CO2 2(ppm) (ppm) CO 2 2(ppm) CO++CO CO (ppm)
−0.087 − 0.069 − 0.087 −0.242 − 0.242 −0.044 −0.044 −0.196 −0.196 −0.471 − 0.471 −0.511 − 0.511 − 0.536 −0.536 − 0.578 −0.578
p-Value p-Value 0.452 0.343 0.452 0.343 0.008 0.008 0.631 0.631 0.033 0.033 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
are aa result result of of thermal thermal aging aging of of paper paper insulation insulation through through oxidation oxidation process process [2,3,20]. [2,3,20]. CO and CO2 are Figure 5 shows the scatterplot as opposed opposed to to the the DP DP value. value. The The correlation correlation coefficient coefficient (r) scatterplot of of CO CO + CO22 as of CO + CO22 is is the the highest highest for for the the DGA DGA values, making it a better potential variable as a transformer paper condition predictor predictor than than other other forms forms of of DGA. DGA.
Figure 5. Root mean square error (RMSE) graph of 22 membership function combinations. Figure 5. Root mean square error (RMSE) graph of 22 membership function combinations.
Figure 4 shows the scatterplots of estimated DP versus potential independent variables. The Figure 4 shows the scatterplots of estimated DP versus potential independent variables. correlation of DP and acidity was statistically obtained with a correlation coefficient r of −0.432 and a The correlation of DP and acidity was statistically obtained with a correlation coefficient r of −0.432 p-value less than 0.05. This means that acidity has negative correlation with DP when the and a p-value less than 0.05. This means that acidity has negative correlation with DP when the transformer paper is getting worse, the DP value is going down, and the acidity of the oil insulation transformer paper is getting worse, the DP value is going down, and the acidity of the oil insulation is increasing. is increasing. The correlation of DP and interfacial tension was statistically obtained with a correlation coefficient r of 0.732 and a p-value less than 0.05. This means that interfacial tension has positive
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The correlation of DP and interfacial tension was statistically obtained with a correlation coefficient r of 0.732 and a p-value less than 0.05. This means that interfacial tension has positive correlation with DP; when the DP value decreased, the interfacial tension of the oil insulation decreased. The correlation of DP and color was statistically obtained by a correlation coefficient r of −0.686 and a p-value less than 0.05. This means that color has a negative correlation with DP; as the DP value decreases, the color of the oil insulation is getting darker. The correlation of DP and CO + CO2 was statistically obtained by a correlation coefficient r of −0.578 and a p-value less than 0.05. This means that CO + CO2 has a reversed correlation with DP; as the DP value decreases, the amount of CO + CO2 dissolved in the transformer oil is increased. From dielectric characteristics, after content and voltage breakdown have relatively low correlation with the estimated DP. In dissolved gases, H2 , CH4 , C2 H2 , C2 H4 , and C2 H6 have low correlation with the estimated DP [33]. Therefore, these parameters are not included as further potential input variables. 3.1.2. Various Combination of Input Variables From the correlation analysis, several independent variables were statistically obtained, including CO + CO2 , acidity, interfacial tension, and color. The various combinations of these independent variables were then tested to get the best predictors. Parameters such as R-Sq, R-Sq (adj), R-Sq (pred), and Mallows Cp are the specifications used in choosing the best predictor model. From Table 7, the best combination of variables is number 13, which consists of CO + CO2 , acidity, IFT (Interfacial Tension), and color with the highest R-Sq, while the R-Sq (pred) value is not far from R-Sq (adj), and the mallows Cp is close to the number of predictors plus one. Table 7. Various combinations of independent variables for DP prediction. Number of Combination
R-Sq
R-Sq (Adj)
R-Sq (Pred)
Mallows Cp
CO + CO2
1 2 3 4 5 6 7 8 9 10 11 12 13
33.6 18.6 53.6 46.9 61.7 53.9 47.9 60.4 51.2 50.0 64.6 63.0 68.0
33.0 17.9 53.3 46.4 60.7 53.1 47.0 59.4 50.4 49.1 63.2 61.5 66.9
31.3 16.2 51.9 45.3 58.7 51.6 45.5 57.4 48.9 47.9 61.3 59.4 65.6
33.2 66.8 50.7 75.0 7.8 3.0 3.0 10.6 3.0 3.0 3.6 7.1 5.0
x
Acidity
IFT
Color
x x
x x x
x x
x x x
x x x
x x
x x
x x x
x x x x x
3.2. Membership Functions Selection The MF number of each input into the ANFIS model influences the accuracy of DP prediction. To obtain the optimal ANFIS model, various combinations of membership functions have been tested. Table 8 shows various combinations of MF numbers used as considerations for selecting the MF number in creating the ANFIS model.
4 44 5 55 6 66 7 77 8 88 9 99 10 10 10 11 11 11 12 12 12 13 13 13 14 14 14 15 15 15 16 16 16
TrapMF 143.8 274.81 3 3 TrapMF 143.8 274.81 TrapMF 143.8 143.8 274.81274.81 44 33 333 333 333 222 222 TrapMF TrapMF 33 33 143.8 274.81 4 3 TrapMF 143.8 274.81 5 3 2 3 3 TrapMF 116.25 1114.95 3 2 TrapMF 116.25 1114.95 TrapMF 116.25116.25 1114.95 55 33 22 333 33 333 33 TrapMF TrapMF 1114.95 33 22 116.25 1114.95 TrapMF 116.25 1114.95 Energies 2017, 10, 1135 13 of 18 TrapMF 131.53 141.31 3 3 TrapMF 131.53 141.31 TrapMF 131.53131.53 141.31141.31 66 33 333 222 222 333 333 TrapMF TrapMF 33 33 131.53 141.31 6 3 TrapMF 131.53 141.31 TrapMF 117.58 169.15 3 3 TrapMF 117.58 169.15 TrapMF 117.58117.58 169.15169.15 77 33 333 333 33 333 333 TrapMF TrapMF 33 33 Table 117.58 169.15 7 3 TrapMF function 117.58 169.15 8. Various3 combinations of membership (MF) numbers. 8 4 3 3 3 TrapMF 94.08 639.51 4 3 TrapMF 94.08 639.51 TrapMF 94.08 94.08 639.51639.51 88 44 33 333 33 333 33 TrapMF TrapMF 44 33 94.08 639.51 TrapMF 94.08 639.51 No. CO + CO2 Acidity IFT Color MF Type RMSE Training RMSE Testing 4 4 3 3 3 3 TrapMF TrapMF 93.71 1431.84 4 4 93.71 1431.84 TrapMF 93.71 1431.84 99 TrapMF 93.71 1431.84 44 1 44 44 2 44 33 2 33 33 2 33 TrapMF 93.71 1431.84 9 TrapMF 93.71 1431.84 2 TrapMF 183.81 254.30 2 4 3 2 4 3 2 3 TrapMF 2 TrapMF 168.81 183.02 10 4 TrapMF 94.06 662.59 4 4 4 94.06 662.59 TrapMF 94.06 94.06 662.59662.59 10 TrapMF 44 3 44 44 3 44 33 2 33 TrapMF 94.06 662.59 10 44 3 44 TrapMF 94.06 662.59 2 TrapMF 161.06 296.70 4 3 3 3 2 TrapMF 143.8 274.81 11 4 3 4 4 TrapMF 83.31 1395.16 4 3 4 4 TrapMF 83.31 1395.16 TrapMF 83.31 83.31 1395.16 11 TrapMF 1395.16 33 3 33 44 2 44 44 3 44 TrapMF 83.31 1395.16 11 44 5 44 TrapMF 83.31 1395.16 3 TrapMF 116.25 1114.95 12 4 6 4 4 4 4 TrapMF 77.43 1886.97 3 TrapMF 131.53 141.31 43 4 3 4 2 TrapMF 77.43 1886.97 TrapMF 77.43 1886.97 12 TrapMF 77.43 1886.97 44 3 44 44 3 44 44 3 44 TrapMF 77.43 1886.97 12 44 7 44 TrapMF 77.43 1886.97 3 TrapMF 117.58 169.15 13 44 8 44 TrapMF 98.25 2089.57 3 TrapMF 94.08 639.51 2 4 2 3 3 3 3 3 3 TrapMF 98.25 2089.57 TrapMF 98.25 2089.57 13 TrapMF 98.25 2089.57 22 4 22 33 4 33 33 3 33 TrapMF 98.25 2089.57 13 4 9 4 TrapMF 98.25 3 TrapMF 93.71 1431.84 2089.57 14 44 10 44 TrapMF 107.09 110.55 2 4 22 33 4 33 33 4 33 TrapMF 107.09 110.55 3 TrapMF 94.06 662.59 TrapMF 107.09 110.55110.55 14 TrapMF 107.09 22 107.09 110.55 14 4 4 2 3 3 3 3 TrapMF TrapMF 107.09 110.55 11 4 3 4 4 TrapMF 83.31 1395.16 15 5 12 5 2 3 3 TrapMF 110.60 98.77 2 4 2 33 4 3 33 4 3 TrapMF 110.60 98.77 4 TrapMF 77.43 1886.97 TrapMF 110.60 98.77 98.77 15 55 TrapMF 110.60 22 110.60 98.77 15 55 2 3 3 3 3 TrapMF TrapMF 110.60 98.77 13 4 2 3 3 TrapMF 98.25 2089.57 16 55 14 55 TrapMF 53.17 569.61 55 4 55 55 2 55 55 3 55 TrapMF 53.17 569.61 3 TrapMF 107.09 110.55 TrapMF 53.17 569.61569.61 16 TrapMF 53.17 5 53.17 53.17 569.61 16 5 5 5 5 5 5 5 TrapMF TrapMF 569.61 15 16
5 5
2 5
3 5
3 5
TrapMF TrapMF
110.60 53.17
98.77 569.61
Arow redshows row shows shows high testing testing error even though though the training training error is small. very small. small. This shows shows A red a high testing error even though the training error is very This shows A red redA row shows highaaa testing testing error error even though though the training training error error is very very small. This shows shows red row high even the is very This A aa high error even the error is This Arow redshows row shows high testing error even though the training error is small. very small. This shows the overfitting overfitting oftraining the training training model, wherein, when given different transformer scenario, the the overfitting of the model, wherein, when given a different transformer scenario, the the overfitting overfitting of the training model, wherein, when given different transformer scenario, the the of the model, wherein, when aa different transformer scenario, Aof redthe row shows a high testing error even though thegiven training is very small. scenario, This shows the the the model, wherein, when given aa different transformer the the overfitting oftraining the training model, wherein, when given a error different transformer scenario, the tendency of error is very high. A combination of 15, the green line indicates a similarly low training tendency of error is very high. A combination of 15, the green line indicates a similarly low training tendency of error error isof very high. A model, combination ofwhen 15,of the green line indicates indicates similarly low training tendency of is very A 15, the green line indicates aa similarly low overfitting the training wherein, given a different transformer scenario, the training tendency tendency of is very A combination of 15, the green line aa similarly low tendency of error error is high. very high. high. A combination combination of 15, the green line indicates similarly low training training error and testing error. This suggests that, although training can produce fairly high accuracy, error and testing error. This suggests that, although training can produce fairly high accuracy, error error andoftesting testing error. ThisAsuggests suggests that, although training can produce produce fairly high high accuracy, errortesting is error. very high. combination of 15, thealthough green line training indicates acan similarly low fairly training erroraccuracy, and and error. This suggests that, produce error and This that, although training can fairly high accuracy, error and testing error. This suggests that, although training can produce fairly high accuracy, when given different transformer scenarios, the resulting predictions are quite good. when given different transformer scenarios, the resulting predictions are quite good. testing error. This transformer suggests that,scenarios, although training can produce fairly high accuracy, whenwhen given different transformer scenarios, the resulting resulting predictions are quite good. given different the predictions are quite good. when given different transformer scenarios, the predictions are quite good. when given different transformer scenarios, the resulting resulting predictions are quite good.when given The type of MF varies by shape. After the combination of variations in the number ofwith MFs with The type of MF varies by shape. After the combination of variations in the number of MFs different transformer scenarios, the resulting predictions are quite good. The type type of MFof varies by shape. shape. After After the combination combination of variations variations in the thein number of MFs MFs with The type MF by the of the of MFs The MF by After the of in number of Theof type ofvaries MF varies varies by shape. shape. After the combination combination of variations variations in the number number ofwith MFs with with the highest highest accuracy, MF type was with respect tointraining training andoftesting testing RMSE. Theaccuracy, typeMF of MF varies byselection shape. theperformed combination of variations theand number MFs with the highest accuracy, type selection was performed with respect to training testing RMSE. the highest highest accuracy, MF type selection wasAfter performed with respect respect to training training and testing RMSE. the MF type was with to and RMSE. the accuracy, MF type was performed with to and testing RMSE. the highest accuracy, MF selection type selection selection was performed performed with respect respect to training and testing RMSE. the9 highest accuracy, MF shapes type performed with respect to training and testing RMSE. Table shows the different and types types of MF. Table 9 shows the different shapes and types of MF. TableTable shows the different different shapes andselection types ofwas MF.of 99 shows the different shapes and MF. Table 99 shows the shapes and types of MF. Table shows thethe different shapes and types ofMF. MF. Table 9 shows different shapes and types of Table 10 shows shows the various various combinations oftype. MF type. type. Arow red shows row shows shows high testing testing error Table 10 shows the various combinations of MF A red aa high testing error TableTable 10 shows shows the various various combinations of MF MFof type. A red redA row shows highaa testing error error 10 the combinations MF red row high Table 10 the combinations of type. A shows ahigh high error Table 10 10 shows the various combinations of MF type. Arow redshows row shows a testing higherror testing error Table shows the various combinations of MF type. A red row a testing even even though the training error is very small. This shows the overfitting of the training model, even though the training error is very small. This shows the overfitting of the training model, even even though the training training error error is very very small.small. This shows shows the overfitting overfitting of the theof training model, though the training is very This shows the overfitting the training model, even though the error is small. This the of training model, even though the training error is very small. This shows the overfitting of the training model, though the training error is very small. This shows the overfitting of the training model, where, when where, when given different transformer scenario, the tendency tendency of error error can be high. very high. high. where, when given a different transformer scenario, the tendency of error can be very where, when given different transformer scenario, the tendency tendency ofbe error can becan very high. where, when given aaa different transformer scenario, of be very where, when given aa different transformer scenario, the of error be very where, when given different transformer scenario, the tendency of can error can be high. very high. given a different transformer scenario, the tendency ofthe error can very high. Table 9. Different Different MF and types and shapes. shapes. Table 9. Different MF types shapes. Table Table 9.Table Different MF types types and shapes. 9. MF types and Different MF and shapes. Table 9. Different MF and shapes. Table 9.9. Different MFtypes types and shapes.
MF Type Type MF Type MF Type Type MF MF MF Type MF Type
MF Shape Shape MF Shape MF Shape Shape MF MF MF MF Shape Shape
MF Type Type MF Type MFMF Type MF MF Type MF Type Type
TriMF TriMF TriMFTriMF TriMF TriMFTriMF
Gauss2MF Gauss2MF Gauss2MF Gauss2MF Gauss2MF Gauss2MF Gauss2MF
TrapMF TrapMF TrapMF TrapMF TrapMF TrapMF TrapMF
DsigMF DsigMF DsigMF DsigMF DsigMF DsigMF DsigMF
GbellMF GbellMF GbellMF GbellMF GbellMF GbellMF GbellMF
PsigMF PsigMF PsigMF PsigMF PsigMF PsigMF PsigMF
GaussMF GaussMF GaussMF GaussMF GaussMF GaussMF GaussMF
- - ---
MF Shape Shape MF Shape MF Shape MF MF MF Shape MF Shape Shape
---
---
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Table 10. Various combinations of MF types. No.
CO + CO2
Acidity
IFT
Color
MF Type
RMSE Training
RMSE Testing
15 17 18 19 20 21 22
5 5 5 5 5 5 5
2 2 5 2 2 2 2
3 3 5 3 3 3 3
3 3 5 3 3 3 3
TrapMF TriMF GbellMF GaussMF Gauss2MF DsigMF PsigMF
110.60 346.71 106.90 90.43 91.59 77.57 80.72
98.77 418.75 704.50 168.33 149.70 580.43 2893.2
From the selection of MF types, Table 10 shows that combination 15, with TrapMF (Trapezoid Membership Function), has the lowest RMSE training and testing values. Figure 6 shows the RMSE training and testing graph of various combinations of numbers and types of MF. The higher the graph, the greater the error that occurs. Combination 15 shows the lowest RMSE testing value, with a relatively low RMSE training value as well. 3.3. ANFIS Model Result and Evaluation The various parameter inputs to the ANFIS model (CO + CO2 , acidity, IFT, and color) has been developed based on the 76 transformers that were used as a training data set with the membership function selection shown in Table 11. Table 11. Membership function (MF) number and type of created ANFIS model. Input Variable
MF Number
MF Type
CO + CO2 Acidity Interfacial Tension Color
5 2 3 3
TrapMF TrapMF TrapMF TrapMF
Figure 6 shows the structure of the ANFIS model developed. The prediction result from the ANFIS model tested uses the testing data set that consists of 32 different transformers from the training data set. Figure 7 shows the DP value target and the prediction result made by the ANFIS model, following the error from training and testing dataset. Figure 7a,b show the estimated DP from the ANFIS model tested using the training dataset and the testing dataset. Blue dots show the targets of DP, and the red dots show the prediction results of the ANFIS model. Figure 7c,d show the residual value of the target and prediction results. It can be seen that the ANFIS is model able to predict the DP value using CO + CO2 , acidity, interfacial tension, and color as input variables. The performance indicators in Table 12 suggest that the ability of the ANFIS model to predict DP from multiple parameters has an accuracy of 89.07% for the training dataset and 85.75% for the testing dataset.
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DPest DPest
Figure 6. Proposed ANFIS model. Figure 6. Proposed ANFIS model.
(a) (a)
(b) (b)
(c) (c)
(d) (d)
Figure 7. Results of the ANFIS model. (a) Degree of Polymerization prediction results of 76 training Figure 7. Results ofResidual the ANFIS model. (a)target Degree of Polymerization prediction results of 76 training transformers; (b)of value of DP(a) and resultsprediction of 32 testing transformers; (c) Figure 7. Results the ANFIS model. Degree ofprediction Polymerization results of 76 training transformers; (b) Residual value of DP target and prediction results of 32 testing transformers; (c) Residual value of DP target and prediction results of 76 training transformers; (d) Residual value of transformers; (b) Residual value of DP target and prediction results of 32 testing transformers; Residual of DP target and prediction of 76 training transformers; (d) Residual value of DP targetvalue and prediction results 32 testingresults transformers. (c) Residual value of DP target andofprediction results of 76 training transformers; (d) Residual value of DP target and prediction results of 32 testing transformers. DP target and prediction results of 32 testing transformers. Table 12. Evaluation criteria of the model. Table 12. Evaluation criteria of the model. Table 12. Evaluation criteria of the model.Training Criteria Testing
Criteria Training Mean Absolute Error (MAE) 85.57 Criteria Training Mean Absolute 85.57 Root Mean SquareError Error(MAE) (RMSE) 110.60 Mean Absolute ErrorPercentage (MAE) Root Mean Square Error (RMSE) 110.60 Symmetrical Mean Absolute Error (SMAPE) 85.57 10.93% RootMean Mean Square Error (RMSE) Accuracy (100–% error) Error (SMAPE) 110.60 89.07% Symmetrical Absolute Percentage 10.93% Symmetrical Mean Absolute Percentage Error (SMAPE) 10.93% Accuracy (100–% error) 89.07% Accuracy (100–% error) 89.07%
Testing 85.52 Testing 85.52 98.77 85.52 98.77 14.25% 98.77 85.75% 14.25% 14.25% 85.75% 85.75%
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3.4. Expected Life Estimation of Transformer Paper Insulation In order to estimate the expected life of four transformers in Tables 1–4, dielectric characteristics and dissolved gases data are used to predict the condition of transformer paper based on degree of polymerization. The ANFIS model proposed in this article is used to predict the DP of transformer paper. This predicted DP is then used to estimate the expected life of transformer paper using Equation (13). The result of the DP prediction and the expected life estimation is shown in Table 13. Table 13. Expected life estimation. Transformer
Running Time
DP Predicted (ANFIS)
Interpretation
%Eprl
Expected Life Estimated (Years)
#1 #2 #3 #4
25 years 21 years 4 years 20 years
597.88 676.87 1044.46 369
Accelerated Aging Rate Normal Aging Rate Normal Aging Rate Accelerated Aging Rate
79.06% 90.79% 119.25% 44.25%
8.05 8.67 29.2 5.55
The results of expected life estimation from four Indonesian transformers show that Transformer #1 has 8.05 more years of life expectancy for transformer paper insulation. Transformer #2 is similar with 8.67 years, while Transformer #4 is in worse condition with 5.55 years of life expectancy. Transformer #3, on the other hand, has only been in use for four years and still has 29.2 years of life expectancy. Each estimated expected life span is result of the paper condition prediction using the ANFIS model based on using dielectric characteristics and dissolved gases as input variables. This expected life estimation result means that, as long as the hotspot temperature rise of the transformer is to be kept below 68 K (IEC 60076-2), the transformer paper life expectancy estimated should be more than that estimated in Table 13. 4. Conclusions An algorithm for building an Adaptive Neuro Fuzzy Inference System (ANFIS) model for power transformer paper condition and expected life estimation is presented in this article. The combination of CO + CO2 , acidity, interfacial tension, and color were used as input variables to estimate the transformer paper condition. The proposed ANFIS model has 89.07% training accuracy and 85.75% testing accuracy and was applied to transformer paper insulation assessment and an expected life estimation of four Indonesian transformers for which furfural data is unavailable. It can be seen that the proposed ANFIS model can be used to do a general estimation of the transformer paper condition and expected life when furfural data is unavailable. This algorithm acts as a helpful assistance for experts in transformer condition assessment. However, more confident engineering decisions on transformer paper condition assessment can be established when the transformers have furfural data as a main parameter. Author Contributions: The paper was a collaborative effort between the authors. The authors contributed collectively to the theoretical analysis, modeling, simulation, and manuscript preparation. Conflicts of Interest: The authors declare no conflict of interest.
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