Fuzzy Logic Expert System for Health Condition Assessment of Power Transformers

In the present chapter, a new fuzzy logic (FL) model is proposed to evaluate the overall health index (OHI) of power transformers. The most significant attributes such as dissolved gases, acidity, 2-furfuraldehyde, water content, breakdown voltage and dissipation factor that influence the health condition of transformers solid and liquid insulations are considered. These attributes are further divided into three different sets. Based on these sets, three different sub fuzzy models i.e. F 1 , F 2 and F 3 are designed in order to reduce the possible combinations of fuzzy rules. It results in reducing the complexity issues of the proposed OHI model. In addition, consideration of all significant testing parameters makes the model more reliable and accurate. Further, the proposed fuzzy model helps in initiating appropriate and early action on faulty conditions of the transformers. Conventional fuzzy logic models generally utilize large number of inputs and more number of rules in a single fuzzy model. It makes the models complex and inaccurate. Such shortcom-ings of existing conventional models are successfully overcame by the present proposed model. Furthermore, the results obtained from the proposed model are compared with the results obtained from expert model proposed by Abu-Elanien et al. This comparison ensures the reliability of the proposed method. Also, it is envisioned that the proposed model can be easily implemented by both the experi-enced and the inexperienced utility managers.


Introduction
Power transformers are vital components of power system. The total service life of power transformers is majorly depends on the life spans of their liquid and solid insulations [1]. The deterioration of the insulation is caused due to the various electrical and thermal stresses present inside the transformers. These stresses accumulate several dissolved gases within the transformer oil, and produce partial discharge, overheating and arcing [2,3]. Generally, the dissolved gases namely, hydrogen (H 2 ), acetylene (C 2 H 2 ), ethane (C 2 H 6 ), ethylene (C 2 H 4 ), methane (CH 4 ), carbon monoxide (CO) and carbon dioxide (CO 2 ) are induced in the transformer oil. The severity of these gas concentrations identifies the type of faults present in the transformer [4,5]. Moreover, these gas concentrations are employed to examine

Transformer diagnostic attributes
The major deterioration of transformer insulation is caused by attributes such as breakdown voltage, dissipation factor, water content, acidity, dissolved combustible gases and 2-furfuraldehyde. The brief introduction of these attributes is given in this section.
Breakdown voltage (BDV) is defined as voltage at which breakdown occurs between the two electrodes while oil is exposed to an electric field under critical conditions [11]. For insulation system of a transformer, electric strength is the basic parameter which indicates the presence of contaminants like perceptible sludge, moisture and sediment [12]. Dissipation factor (DF) is defined as the sine of loss angle. Also, it is important parameter to test the quality of insulation [13]. Some harmful contaminants such as oxidation products, water and de-polymerization of paper insulation are induced due to high value of DF [14].
The presence of dissolved water in the oil is termed as water content and it is expressed in parts per million (ppm) by weight [15]. The existence of moisture content in the oil is detrimental since it adversely affects the electrical characteristics of oil. Also, excess amount of moisture accelerates deterioration of insulating materials [16]. The measurement of free organic and inorganic acids accumulate in the transformer oil is defined as acidity, and is measured in milligrams of potassium hydroxide. It is required to neutralize the total free acid in one gram of oil [17].
When the influence of abnormal thermal and electrical stresses on transformer oil is not very high, the gases generated as a consequence of decomposition of insulating oil will get enough time to dissolve in the oil. In dissolved gas analysis, the percentage of gas concentrations present in oil is determined and analyzed [18]. These dissolved gas percentages helps in finding out the internal condition of transformer [19]. Solid dielectrics present in the two essential parts of transformer i.e. core and winding which is made of cellulose. Cellulose consists of long chain of molecule structure [20]. During the operation of transformer, these long chains are generally broken into several numbers of minute particles, as per the aging. These furan compounds belong to the fur-furaldehyde group. 2-Furfural is the most predominant among all furfurals compounds. The condition assessment and life estimation of paper insulation is done by using the rate of rise of furfural products with respect to time in oil. Damage in few grams of paper in oil is detected even for a large sized transformer. Therefore, fur-furaldehyde analysis is very sensitive [21]. When the transformer oil is soaked into solid dielectric, furan particles along with gases CO 2 and CO dissolved in the oil due to heat.

Proposed fuzzy logic model
Fuzzy logic is a very helpful tool in obtaining accurate output, and easy in implementation [22]. Also, it facilitates more effective and reasonable decision making for transformers in order to ensure maintainability and reliability [23,24]. The purpose of the proposed FL model is to integrate various diagnostic test results with the experience of transformer diagnosis experts [23]. Different stages of the FL models are discussed in the following sub-sections. The curve which converts the precise (crisp) inputs in to imprecise fuzzy sets with degrees of membership function (DOM) in the range 0 and 1. Generally, membership functions (MFs) have different shapes namely, triangular, sigmoidal or trapezoidal, Gaussian and Gauss2. Trapezoidal MF is widely used MF because of its simplicity [20,21]. It is shown in Figure 1, and given by Eq. (1). The trapezoidal MF consists of a truncated triangular curve and a flat top.

Fuzzy Systems
Where, input variable is denoted as 'x' , lower and upper limits are denoted as 'a' and 'b' , respectively. Similarly, 'c 1 ' and 'c 2 ' are the centers of the trapezoidal MF [21]. If the input value lies in between the range of'c 1 'and'c 2 'of the MFs, then the corresponding MF attains the maximum DOM of unity [25]. Whereas, input values lie between the range of 'a'and'c 1 'and between the range of'c 1 'and'b' , will have DOMs less than unity. Likewise, all the crisp input values (precise) are converted into fuzzy (imprecise) values in fuzzification stage. Where the fuzzy values range lie between 0 and 1.
In the present proposed model, fuzzy logic (FL) is used to determine the overall health index (OHI) of power transformers. The six parameters (Section 2) are considered as inputs in the present proposed model to determine the overall health index (OHI) of transformers. To make the model simple, three sub-fuzzy models viz. F 1 , F 2 and F 3 are designed separately. Two parameters namely, water content and acidity are assigned as inputs for F 1 , whereas BDV and DF are for F 2 . Similarly, DCG and 2-FAL are considered as inputs for F 3 . Furthermore, the outputs obtained from these three sub-models are considered as the inputs to a single fuzzy model called F 4 . The final output obtained from the model F 4 is OHI of transformers. All the inputs of F 1 , F 2 and F 3 used trapezoidal shaped MFs and their limits are assigned in accordance to [1]. These limits for MFs of water content input in F 1 are shown in Figure 2. Likewise, MFs are designed with trapezoidal shape for remaining sub models. The values of the six significant attributes have been listed in Table 1.
However, input 2-FAL in F 3 consists of 5 MFs as per [1].  10 10] respectively. In case of F 4 , the output MFs used in each of the three sub-models was used as input MFs. The corresponding input MFs of water content are same as described in Figure 2.
The block diagram consisting of the three sub fuzzy models and a main fuzzy model for transformer sample 12 is depicted in Figure 3. The lower and the upper limits along with the two centers of input MFs are specified in Table 2. Similarly, the output for each of the four models F 1 , F 2 , F 3 and F 4 was divided in to four MFs as specified in Figure 4.
In fuzzification stage, the input values are converted in to fuzzy values by using the Eq. (1) [26]. Consider transformer sample 12, where the value of acidity is 0.23 mgKOH/g. It lies in the range of Bad (Table 2). Therefore, the limits i.e. a, c 1 , c 2 and b  Table 3.
After fuzzification stage, the inputs are mapped with output by specially designed rules in the fuzzy inference stage. In the present work, a widely used Mamdani maximum-minimum fuzzy inference method is used [21,25]. Using the fuzzified set of inputs and the designed fuzzy rules, the output is determined in this method. Further, the method truncates the output MF at its minimum DOM value. Initially the inputs are fuzzified using Eq. (1). Further, the truncated output from each of the three models are obtained based on the specially designed expert fuzzy rules and fuzzified inputs. In the present work, the fuzzy rules possible between the inputs of F 1 are designed consisting two inputs each with three MFs generate a total of nine combinations. Similar combinations are also obtained for F 2 .
The rule base designed for sub fuzzy model, F 1 is given below:

Rule 1:
If Water content is Good and Acidity is Good then output is Excellent. Rule 3: If Water content is Good and Acidity is Bad then output is Poor. Rule 6: If Water content is Moderate and Acidity is Bad then output is Worst. Rule 9: If Water content is Bad and Acidity is Bad then output is Worst.
In case of F 3 , the three input MFs in DCG, and five MFs in 2-FAL make a total of fifteen fuzzy rules. The rule base designed for sub fuzzy model F 3 is given as below:      The rules are framed according to their severity level deteriorating transformer insulation. Since DCG and 2-FAL are very harmful attributes, the highest priority in determining OHI is given to B 3 (sub fuzzy model F 3 ). B 1 (sub fuzzy model F 1 ) has been considered as key factor next to B 3 . And, least priority has been given to B 2 (sub fuzzy model F 2 ) among all the three inputs.
Defuzzification is the last stage of this method where a precise quantitative value from the truncated output MF is determined [27]. Center of gravity is the most popular and efficient defuzzification method [20]. This method is used in the present work. It determines the center of gravity or the centroid (Z 0 ) of the area bounded by the truncated output MFs [20,21]. It is obtained by Where the output variable is denoted by 'z' and 'μ(z)' is the DOM of the truncated output MF. The crisp output is obtained by using Eq. (2). The centroid representation of the output value (sample 12) is depicted in Figure 5. Similarly, the outputs for remaining samples are obtained using the above equation.

Results and discussion
For an easy understanding of proposed method, consider sample 12 and its diagnostic values are detailed in Table 2. The data related to all diagnostic attributes has been collected from Himachal Pradesh State Electricity Board (HPSEB). In sample 12, 0.23 mgKOH/g of acidity, 0.43 of DF, 5.54 ppm of 2-FAL, 21.8 ppm of water content, 47.7 KV of BDV and 215 ppm of DCG were initially fuzzified in the fuzzification stage. Further, these values are converted into outputs depending upon rule base given in Section 4.
The outputs of sub fuzzy models F 1 , F 2 and F 3 are represented by B 1 , B 2 and B 3 , respectively. After the defuzzification stage, the outputs obtained from F 1 , F 2 and F 3 are 0.674, 0.35 and 0.6 using Eq. (2). These three outputs are utilized and converted to inputs for F 4 (i.e. B 4 or RHI). From the F 4 model, the final output for sample 12 is 0.788. Likewise, OHI for all the remaining transformer samples are determined and summarized in Table 4 (column 2). Also the health indices for each of these transformers were determined in accordance to [1], and are given in the same table (column 4).  Where in Table 4, E-Excellent, G-Good, P-Poor, W-worst, VG-Very good, M-Moderate, B-Bad and VB-Very bad.
Four output MFs have been designed in the proposed model, whereas five MFs were considered in Ref. model. The Excellent health condition of proposed model has been compared to the Very good and Good health conditions produced by the reference model [1]. Similarly, Good health condition of proposed model is compared with Moderate condition of reference model. And, comparison has been done Bad with Poor and Very bad with Worst. The overall comparison of all 20 transformer health index by the proposed model and model proposed in [1] is given in Table 5.
From Table 5, a curious difference has been found out while comparing the test results of proposed model with reference model [1]. It is noted that, out of total 20 test case transformers 11 test results of proposed model are matched with results obtained in [1]. From the comparison, it is observed that the proposed method has better results. To support the statement, consider test sample 12, the HC obtained using model proposed in [1] is Bad. But, the quantities of most influential parameters WC and DCG are 21 and 215 ppm, respectively. These quantities indicate that the transformer insulation is in critical condition and replacement is required. From the test results from proposed model, the HC of sample 12 is worst. It is most suitable condition for the health of transformer. It is proved that the results acquired from the proposed model provide accurate health condition. Also, all the fuzzy models in the proposed model are designed by analyzing the impact of significant diagnostic attributes on transformer insulation. These modifications make the proposed model efficient.

Author details
Teruvai Manoj and Chilaka Ranga* National Institute of Technology, Srinagar, Jammu and Kashmir, India *Address all correspondence to: chilakaranga@nitsri.ac.in

Conclusion
In the present chapter, a novel fuzzy logic model has been proposed to find the overall health index of oil-immersed transformers. Parameters that influence the health condition of transformer insulation such as acidity, BDV, DF, DCG, water content and 2-FAL are used to test the HC of transformer. Three sub fuzzy models are created namely, F 1 with water content and acidity as inputs, F 2 with BDV and DF as inputs, F 3 with DCG and 2-FAL as inputs. Further, the individual outputs of three fuzzy models are taken as inputs for the final fuzzy model F 4 . All the inputs of sub fuzzy models are designed with three MFs except for 2-FAL which has five. Also, the rule base is formed with nine, nine, and fifteen rules for F 1 , F 2 and F 3 subfuzzy models, respectively. And, sixty-four rules designed for main fuzzy model F 4 . The comparison has been done between the proposed model and fuzzy model designed in [1]. The fuzzy model designed in [1] consists of six inputs and thirty expert rules only. After comparing the two models, it is observed that the results of proposed model are more accurate. In addition, a complete rule base fulfilling all probable situations in determining HI is incorporated in the present model. Hence this model is most efficient, reliable and easily implemented by utilities and industries in order to obtain the health indices of their transformers which is a significant advantage. Total number of transformers 20 Table 5.
Comparison of the results obtained from both the methods.
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