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Multi‐criteria decision‐making methods for grading high‐performance transformer oil with antioxidants under accelerated ageing conditions

2017; Institution of Engineering and Technology; Volume: 11; Issue: 16 Linguagem: Inglês

10.1049/iet-gtd.2017.0350

1751-8695

R. Madavan, Sujatha Balaraman, S. Saroja,

High voltage insulation and dielectric phenomena

IET Generation, Transmission & DistributionVolume 11, Issue 16 p. 4051-4058 Research ArticleFree Access Multi-criteria decision-making methods for grading high-performance transformer oil with antioxidants under accelerated ageing conditions Madavan Rengaraj, Corresponding Author Madavan Rengaraj srmadavan@gmail.com Department of EEE, P.S.R. Engineering College, Sivakasi, IndiaSearch for more papers by this authorSujatha Balaraman, Sujatha Balaraman Department of EEE, Government College of Technology, Coimbatore, IndiaSearch for more papers by this authorSaroja Subbaraj, Saroja Subbaraj Department of Information Technology, Mepco Schlenk Engineering College, Sivakasi, IndiaSearch for more papers by this author Madavan Rengaraj, Corresponding Author Madavan Rengaraj srmadavan@gmail.com Department of EEE, P.S.R. Engineering College, Sivakasi, IndiaSearch for more papers by this authorSujatha Balaraman, Sujatha Balaraman Department of EEE, Government College of Technology, Coimbatore, IndiaSearch for more papers by this authorSaroja Subbaraj, Saroja Subbaraj Department of Information Technology, Mepco Schlenk Engineering College, Sivakasi, IndiaSearch for more papers by this author First published: 16 August 2017 https://doi.org/10.1049/iet-gtd.2017.0350Citations: 7AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In this study, different types of antioxidants (AO) such as natural and synthetic AOs are mixed with mineral oil (MO) at various individual and grouping concentrations to enhance the life of transformers. Water content in oil, water content in paper, breakdown voltage, acidity, 2-furaldehyde concentration, degree of polymerisation and tensile strength are the laboratory-based ageing-related performance characteristics considered in the proposed work to evaluate the degradation rate of MO samples. Multi-criteria decision-making methods such as analytic hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) are used to identify the sample concentration which gives maximum performance while considering all the characteristic performance of the MO samples precisely. Two different methods are employed to assess the performance characteristics of the MO samples. In first method, AHP is employed for both priority weight calculation and ranking of MO samples. In second method, AHP is used for weight calculation and TOPSIS is used for ranking. From the experimental results, it is found that, the MO sample S5 yields better performance when compared with other samples. Hence, it is suggested that MO sample S5 can be the best alternative for transformer oil. 1 Introduction The population of aged transformers are far above the ground and they are in operation beyond their designed life span, thus, the insulation degradation is the major concern over deciding the remaining life of transformers [1]. A fact revealed from numerous studies on transformers during the exploiting conditions is that, under higher operating temperature and voltage, the live components of transformer undergo chemical changes. This leads to oxidation process, decomposition of hydrocarbons and formation of gaseous (H2, CO, CO2, CH4, C2 H4, C2 H2 and C2 H6), liquid (H2 O) and chemical by-products in transformer oil. Due to the existence of impurities and oxidation by-products, the characteristics of oil are altered which in turn affects the safer operation and life of transformer [2, 3]. There must be an ample concern on the ageing-related degradation characteristics of oil and a method to inhibit the same is needed. For the purpose of enhancing the characteristics of oil and inhibiting the oxidation process, the feasible method used is addition of synthetic and natural AOs such as α -tocopherol (α -T), citric acid (CA), butylated hydroxy anisole (BHA) and butylated hydroxy toluene (BHT) at various concentrations [4]. Generally, AOs are added with transformer oil to reduce the effect of peroxy radical chain process. This chain process is responsible for degradation of insulation system, formation of oxidation by-products and production of acid contents [5]. Enhanced characteristic performance and degradation rate of blended oil samples are experimentally analysed by the life-determining properties such as water content in mineral oil (MO), water content in paper, breakdown voltage (BDV), acidity, furan, degree of polymerisation (DP) and tensile strength. From the above analysis by researchers, there is a lag in selecting the best sample which gives better performance and longer lifetime. Among the above-said properties, some need to be maximised and some need to be minimised. Moreover, it is impossible to find out the best blended sample which gives better performance and lower degradation rate by simply viewing the experimental results. Since choosing the best involves considering all the life-determining properties into account, in the proposed work the above issue is treated as multi-criteria decision-making (MCDM) problem. Further, water content in MO, water content in paper, BDV, acidity, furan, DP and tensile strength are considered and taken as multiple criteria for analysis. The various sample concentrations used for experimentation purpose are treated as alternatives. There exist many methods to solve MCDM problems [6–9]. The proposed work adapts analytic hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) as MCDM methods in order to choose the best sample concentration and also to rank the samples accordingly for the future purpose. TOPSIS is the only MCDM method which considers both positive as well as negative ideal solution in ranking [6]. The ranking result yielded by TOPSIS greatly depends on the priority weights assigned to the criteria. In order to determine the weights of the criteria, AHP is employed as in [7–10]. AHP calculates weights of the individual criterion by the construction of pair-wise comparison matrix [8]. Then, the subsequent steps of AHP process are continued to determine the weights. The survey was conducted among 68 subjects for matrix construction. It includes the distribution of questionnaire to the subjects, asking them to answer and collecting them back. The subjects involved in the process include academicians, researchers and assistant engineers and section engineers of Tamilnadu Electricity Board R&D division. Finally, the pair-wise comparison matrix is constructed by averaging the results obtained in the survey process. In the proposed work, an attempt has been made to find out the most excellent MO samples based on their performance characteristics using AHP and TOPSIS. 2 Sample preparation MO samples used for experimentation are prepared by following steps given below. The quantity of MO required for testing is purchased from commercial oil company. Initially, the MO is thermally treated at 100°C to remove the moisture content present in the MO. Thermally treated MO is brought down to room temperature and filtered with Whatman filter paper to remove the particles present in MO. Antioxidant (AO) blended samples are prepared by the blending of natural AO (α -T and CA) and synthetic AO (BHA and BHT) at various individual concentrations and different grouping concentrations. About 500 ml of MO is taken for preparation of samples and heated up to the temperature required to blend the AO. After that, the AOs are added in the heated MO at various individual concentrations and different grouping concentrations as shown in Table 1. As per IEC 296 (class 11) AO additives added with MO should not be beyond 0.30%, hence in this research work experimental works are carried out by adhering the standard. Table 1. Description about the samples Sample no. Concentration Sample no. Concentration Sample no. Concentration S1 MO S9 MO + 2 g of α -T S17 MO + 1 g of BHA + 1 g of CA S2 MO + 1 g of BHA S10 MO + 3 g of α -T S18 MO + 1 g of BHA + 2 g of CA S3 MO + 2 g of BHA S11 MO + 1 g of CA S19 MO + 2 g of BHA + 1 g of CA S4 MO + 3 g of BHA S12 MO + 2 g of CA S20 MO + 1 g of BHT + 1 g of α -T S5 MO + 1 g of BHT S13 MO + 3 g of CA S21 MO + 1 g of BHT + 2 g of α -T S6 MO + 2 g of BHT S14 MO + 1 g of BHA + 1 g of α -T S22 MO + 2 g of BHT + 1 g of α -T S7 MO + 3 g of BHT S15 MO + 1 g of BHA + 2 g of α -T S23 MO + 1 g of BHT + 1 g of CA S8 MO + 1 g of α -T S16 MO + 2 g of BHA + 1 g of α -T S24 MO + 1 g of BHT + 2 g of CA S25 MO + 2 g of BHT + 1 g of CA The temperature of the MO samples is maintained up to the melting point of AO and the AOs are blended with the MO using magnetic stirrer at required speed until the AOs are equally dispersed in the MO. To get proper blending in the MO samples, the temperature of the MO and the speed of the stirring process are maintained constantly. In the direction of removing the presence of moisture in paper insulation, the kraft paper is dried at 90°C, and the presence of moisture in paper is reduced to 0.2%. The dried paper insulation is impregnated with AOs blended MO samples by 10:1 ratio. In addition to that, 52 g of bare copper is added with MO samples in order to simulate the live operating condition in transformer, during controlled accelerated ageing. Then, the samples are kept in tightly closed glass container. Finally, the samples are placed into the thermal chamber, and accelerated ageing is carried out up to 500 h at 140°C. In order to simulate the ageing process of MO samples with the ageing process of live transformers, laboratory-based experiments are carried out at elevated temperatures for lesser time duration. 3 Results of oxidation inhibitor's degradation effect on MO To compare the degradation rate of inhibited MO with degradation rate of uninhibited MO, various life-determining characteristics such as water content in MO, water content in paper, BDV, acidity, 2-furaldehyde (2FAL), degree of polymerisation and tensile strength are observed by the laboratory-oriented accelerated ageing experimental tests. Moreover, individual inhibitory effects and different group inhibitors effects on MO samples are also measured as shown in Figs. 1–8. Fig. 1Open in figure viewerPowerPoint Variations in water content of aged MO samples Fig. 2Open in figure viewerPowerPoint Variations in water content of aged paper samples Fig. 3Open in figure viewerPowerPoint Variations in BDV of aged MO samples Fig. 4Open in figure viewerPowerPoint Variations in acidity of aged MO samples Fig. 5Open in figure viewerPowerPoint Variations in 2FAL concentration of aged MO samples Fig. 6Open in figure viewerPowerPoint DP of paper and relationship between 2FAL concentration and DP of paper (a) DP of aged paper samples, (b) Relationship between DP and 2FAL in aged condition Fig. 7Open in figure viewerPowerPoint Tensile strength of paper and relationship between tensile strength and DP (a) Tensile strength of aged paper samples, (b) Relationship between tensile strength and DP in aged condition Fig. 8Open in figure viewerPowerPoint Schematic diagram of the proposed work The water content in the MO samples and paper are maintained below 5 ppm and 0.2%, respectively, at the time of zero hours of ageing. It shows that MO samples are prepared to meet the basic requirements before starting the experiments. The total water content in MO samples is measured by Karl Fisher titration method as per ASTM D1533 [11]. It is noted that at the time of ageing, there is an increase in water content in all the MO samples. Particularly, in the case of uninhibited MO sample, water content reaches peak point as shown in Fig. 1. At the same time, inhibited MO samples have less amount of water content (<20 ppm). The water content in paper insulation samples is measured by measuring the weights of the paper samples when it is sampled first, then the paper samples are dried at 105°C and weighed. The weights of the two successive measurements are compared, and the water content is determined by the formula given below: (1) where m1 is the initial weight of the paper sample and m2 is the weight of the dried paper sample. It is observed from the experimental results that water content of all the paper insulation samples gets increased. In particular after ageing, the paper insulation which is impregnated in uninhibited MO sample has higher water content (around 1.6%) compared with the paper insulation impregnated with inhibited MO (below 1.2%) as shown in Fig. 2. The main source for generation of water in transformer is paper insulation. Through oxidation process, water is produced as a by-product from paper. Generally, both paper and oil carry the water which is present inside the transformer. The moisture equilibrium between oil–paper insulation gets distorted at elevated temperature. Thereby moisture moves between insulation paper and oil to maintain the equilibrium [12]. During ageing, the AOs present in MO samples involve chemical reaction which suppresses the auto-catalysing behaviour by means of consuming the water content [13]. The BDV of MO samples (S1–S25) is measured using a fully automatic megger oil BDV tester kit as per the IEC 60156 standard [14] using spherical electrode with 2.5 mm spacing. A step input voltage is applied on the electrodes at a uniform rate of 2 kV/s and the average of six successive measurements is taken as BDV of oil. The time delay between successive measurements is 2 min. At first (0 h of ageing), the BDV of both inhibited and uninhibited MO samples are from 52 kV/2.5 mm to 55 kV/2.5 mm. When the samples are aged, BDV of uninhibited sample (S1) is reduced about 53% (24 kV/2.5 mm), and the reduction range of inhibited samples lies between 19 and 28% (for samples S2–S25) as shown in Fig. 3. This shows that, degradation rate of inhibited samples is lesser compared with uninhibited samples since the decrease in BDV is mainly due to the increase in water content. When the water content is low about around 5 ppm, the BDV of both inhibited and uninhibited MO samples reaches a higher value. Further, with increase in water content, BDV of MO samples gets decreased. The increased water content weakens the dielectric properties of the MO samples and thus breakdown occurs in lesser voltages. This shows that the BDV has strong correlation with saturated water content level [15]. Acids are generated by the ageing of oil and paper insulation. These acids may also act as paper ageing accelerator and have closer relationship with transformer functionality. As per IEC 62021–1 [16], the change in acid content is measured for accelerated ageing conditions. Initially (0 h of ageing), the acid value is 0.0026 mgKOH/g for all the inhibited and uninhibited samples. When the samples are accelerated aged, uninhibited sample's acid value increased to 0.285 mgKOH/g, and acid values of the inhibited samples varied from 0.02 to 0.082 mgKOH/g. It is observed from the results that acid contents have a greater influence on ageing of MO samples with respect to the existence or non-existence of AO as shown in Fig. 4. Here, the acidity reaches the peak value in the case of non-existence of AO in MO samples. Looking over the inhibited MO samples acidity, there is an increase in acid content value, but it is not as much as of uninhibited MO sample. The increase in acid content of inhibited MO samples is partially neutralised by the existence of AO. Generally, AO has organic bases; it partially neutralises the acid contents present in MO [13]. Furan derivatives of MO samples are very important diagnostic indicators about the status of the transformers. It makes an impact on the DP and tensile strength of transformer insulation system. The development of furan derivatives depends on temperature, moisture, type of paper insulation and ageing time duration. During the thermal ageing process, due to the degradation of paper insulation, cellulose chains of paper insulation starts breakdown. The broken chain releases a glucose monomer; it further undergoes chemical reactions, turns into furanic components and produces by-products like water and gases. There are five furan derivatives such as 2FAL, 5-methyl-2-furaldehyde (5M2F), 5-hydroxymethyl-2-furaldehyde (5H2F), 2-acetyl furan (2ACF) and 2-furfurol (2FOL) [13] which are measured for analysis purpose. From these five furan derivatives, because of its higher production rate and stability, 2FAL is believed to be the major derivative for analysis [17]. In both inhibited and uninhibited MO samples, there is an absence of 2FAL component at initial ageing hours (0 h). Under thermally aged condition, 2FAL component of inhibited MO samples increases to 7 ppm whereas it is increases to 16.5 ppm for uninhibited MO sample as shown in Fig. 5. 2 FAL production rate of uninhibited MO sample is high compared with inhibited MO samples. It clearly indicates that increased 2FAL content affects the characteristic performance of MO samples. This degradation rate is also confirmed by DP values of paper. The AO which is present in MO samples provides protective effect to chemical process slows down the oxidation process and diminishes the production of 2FAL components. The DP is a key parameter that indicates the ageing degree of paper insulation in transformers. The DP of paper is decreased from its initial value since the molecular cellulose chains of paper are degraded by hydrolysis, oxidation and pyrolysis processes in transformer [18].The sampling of paper insulation from a service transformer is difficult to determine the condition of the transformer whereas sampling of oil is feasible from a service transformer, and it makes measurement of furan analysis easier. The concentration of furan derivatives provides the status of the paper by means of DP. Various indirect methods were proposed by researchers to determine the DP of paper by correlating the 2FAL concentration with DP. In this work, DP of paper insulation is determined by De Pablo equation [19]. In general, a brand new kraft paper has DP of 1000–1200. When DP of paper reaches about 200, the useful lifetime of the paper ends, hence it should be considered for replacement. The DP of paper is determined by De Pablo equation as mentioned earlier and shown in Fig. 6a. During the thermal ageing process, the DP of both inhibited and uninhibited paper samples gets decreased. However, the degradation rate of inhibited samples is high (around 500 DP) when compared with uninhibited sample (below 300 DP). The relationship between 2FAL concentration and DP of paper insulation is inversely proportional, and the two parameters are almost linear (R2 = 0.9952) as shown in Fig. 6b. The mechanical strength of paper insulation mainly depends on the connectivity between the cellulose fibres; it is measured by observing the tensile strength of paper insulation as per TAPPI standard [20]. As mentioned earlier, the existence of weak links in cellulose fibres of paper insulation gets easily split into smaller components due to the thermal stress at higher temperature, and it leads to rapid drop in tensile strength of paper. From Fig. 7a, it can be understood that the tensile strength of both inhibited and uninhibited oil–paper samples gets decreased with thermal ageing. However, the tensile strength of the inhibited samples is high (above 110) compared with uninhibited samples (below 70). AO present in MO slows down the auto-catalysing process. The polynomial regression analysis of tensile strength with DP of paper insulation shows that the two parameters are closer to linear (R2 = 0.91514) as shown in Fig. 7b. 4 MCDM methods for samples performance assessment In this study, two different methods were followed to assess the performance characteristics of various samples used in the proposed work and the schematic diagram is illustrated in Fig. 8. 4.1 Method 1: evaluation of the performance characteristics of samples using AHP Saaty [21] proposed AHP as decision-making tool. AHP has many applications [22–24] in most of the fields such as resource selection, strategic planning, supply chain management and power utility fields. The steps followed in AHP are as follows: (i) Identification of alternative options and evaluation criteria. In the proposed work, various chosen sample concentrations (S1–S13) are considered as alternatives and water content in oil, water content in paper, BDV, acidity, furan contents, DP and tensile strength are the different evaluation criteria. (ii) Construction of pair-wise comparison matrix by determining the relative importance of one criterion over another. Different scale values used in pair-wise matrix construction are given in Table 2. Table 3 shows an example pair-wise matrix constructed for the proposed work. (iii) Calculation of geometric mean for each criterion. For example, the geometric mean of BDV is calculated as follows: (2) The same calculation is repeated for calculating geometric mean of remaining criteria. Afterwards, the total geometric mean is calculated by summing up all geometric means. (iv) Calculation of weight for each criterion. For example, weight of BDV is calculated as (3) (v) Calculation of consistency ratio for consistency analysis. Consistency ratio = CI/RI, where CI = (λmax −n)/n −1 and RI = 1.35, where n is the number of criteria, and λmax is the largest eigen value of the matrix. If consistency ratio is <0.1, then the calculated weights are consistent, else AHP process needs to be repeated further. The results obtained for the above computations are shown in Table 4. (vi) The next step in AHP is to determine the overall performance of the alternatives in order to rank them. It is done by multiplying the normalised row average and criteria weight for each alternative. According to this calculated value, the alternatives are sorted, and the alternative which has the maximum value is chosen as the best one. Here sample S5 has higher overall performance score, and hence it is chosen as the best sample. The overall performance of the various samples is given in Table 5. Table 2. Values for pair-wise comparison matrix Value Description 1 equally important 3 moderately important 5 strongly important 7 very strongly important 9 extremely important Table 3. Pair-wise comparison matrix Factors Water content in oil Water content in paper BDV Acidity Furan DP Tensile strength water content in oil 1.00 1.00 5.00 1.00 0.14 0.2 0.33 water content in paper 1.00 1.00 5.00 1.00 0.14 0.14 0.2 BDV 0.20 0.20 1.00 0.33 0.11 0.11 0.33 acidity 1.00 1.00 3.00 1.00 0.14 0.14 0.33 furan 7.00 7.00 9.00 7.00 1.00 1.00 5.00 DP 5.00 7.00 9.00 7.00 1.00 1.00 7.00 tensile strength 3.00 5.00 3.00 3.00 0.20 0.14 1.00 Table 4. Results of AHP Factors Geometric mean Weight Total geometric mean λmax CI CR water content in oil 0.64 0.057 11.18 7.61 0.10 0.07 water content in paper 0.57 0.051 BDV 0.24 0.022 acidity 0.57 0.051 furan 3.96 0.354 DP 3.96 0.354 tensile strength 1.21 0.108 Table 5. Performance score obtained by method 1 Samples Overall performance score Samples Overall performance score Samples Overall performance score S1 0.464081 S9 0.872402 S17 0.868446 S2 0.861843 S10 0.93552 S18 0.905446 S3 0.911999 S11 0.98428 S19 0.849625 S4 0.85986 S12 0.914407 S20 0.882721 S5 0.988644 S13 0.893961 S21 0.833822 S6 0.791713 S14 0.939597 S22 0.938468 S7 0.848273 S15 0.91403 S23 0.900552 S8 0.836449 S16 0.88012 S24 0.862911 S25 0.895121 4.2 Method 2: evaluation of the performance characteristics of samples using AHP and TOPSIS This subsection presents the TOPSIS algorithm [7]. It is based on the idea that the best alternative must have the shortest distance from the positive ideal solution and must also have the farthest distance from the negative ideal solution. The positive ideal solution contains the highest value for the criteria in set 'J' and contains the least value for the criteria in the set 'J ''. The negative ideal solution contains the reverse of the positive ideal solution. In the proposed work, the number of criteria is declared as seven (water content in oil, water content in paper, BDV, acidity, furan contents, DP and tensile strength). Out of the seven criteria, set 'J' is assigned with three criteria (BDV, DP and tensile strength), which need to be maximised and the set 'J '' contains the remaining four criteria (water content in oil, water content in paper, acidity and furan), which need to be minimised. TOPSIS helps to select the best sample concentration among the available alternatives. Here, the number of alternatives is equal to 25 (S1–S25). The input to this algorithm is the decision matrix (experimental results for all sample concentrations) and the weights assigned for the criteria (obtained from AHP). The various steps involved in TOPSIS algorithm are given below. 1. Input: decision matrix (D), weight (w) 2. Output: best alternative 3. begin 4. m = number of alternatives; n = number of criteria 5. J = set containing criteria that need maximisation (i.e. BDV, DP and tensile strength); 6. J' = set containing criteria that need minimisation (i.e. water content in oil, water content in paper, acidity and furan) 7. Construct normalised decision matrix 'N d' 8. Construct weighted normalised decision matrix 'W nd' 9. Determine positive ideal Ap and negative ideal An solutions 10. Calculate separation measure from positive ideal solution Sp and from negative ideal solution Sn 11. Calculate relative closeness to the ideal solution Cp 12. Sort the alternatives according to relative closeness value in the decreasing order. 13. Return the alternative which has the highest relative closeness value as output. The first step of this algorithm involves the calculation of a normalised decision matrix from the decision matrix. It is calculated by the following equation: (4) From the normalised decision matrix, the weighted normalised decision matrix is calculated using (2) (5) The weighted normalised decision matrix is used to determine the positive and negative ideal solution for each criterion. The positive ideal solution is calculated using (5) (6) on the next page. Similarly, the negative ideal solution for each criterion is calculated by the following equation: (7) Now, the separation measures from the positive ideal solution and the negative ideal solution are calculated for each of the alternatives. The separation measure from the positive ideal solution is calculated using the following equation: (8) Similarly, the separation measure from the negative ideal solution is calculated using the following equation: (9) The next step is to calculate the relative closeness to the positive ideal solution, and it is calculated using the formula given below: (10) Finally, the relative closeness coefficient C [i]p is sorted in the decreasing order, and the alternative which has the highest relative closeness coefficient is declared as the best alternative. In this method, relative closeness coefficient of sample S5 is high and hence it is declared as the best sample. Samples used for experimentation and their relative closeness coefficient are given in Table 6. Table 6. Performance score obtained by method 2 Samples Relative closeness coefficient Samples Relative closeness coefficient Samples Relative closeness coefficient S1 0 S9 0.887673 S17 0.869232 S2 0.877254 S10 0.947832 S18 0.904207 S3 0.932603 S11 0.982064 S19 0.844109 S4 0.868464 S12 0.925028 S20 0.878857 S5 0.990161 S13 0.905043 S21 0.818073 S6 0.772006 S14 0.94479 S22 0.945223 S7 0.851758 S15 0.928978 S23 0.912409 S8 0.843459 S16 0.887974 S24 0.860485 S25 0.904522 If one compares the performance score obtained by the above two methods, the values pertaining to each sample is different, whereas if one rank the samples based on their performance score, the samples are possessing nearly the same rank. The sample S1 is ranked as first by both the methods. This shows that, sample S1 produces better performance when considering all the above parameters followed by sample S11 which is ranked as the second best. The sample S14 is ranked as third by method 1 and the sample S10 is ranked as third by method 2. When looking over the performance score of both the samples, there is a small deviation between those two samples and when comparing with fourth ranked sample S22, the performance scores of S14 and S10 are high. Hence, it is considered that both S14 and S10 samples are taken as third best samples. From this study, it is concluded that the above two methods (methods 1 and 2) of performance assessment yield almost close results, and hence any one of the above two methods can be used for performance assessment. Overall performance scores and the ranks obtained by the samples using the two methods are summarised in Table 7. In order to determine the best sample, any of the two methods (AHP and TOPSIS) can be employed whereas to rank the samples based on their performance, TOPSIS method is preferred since TOPSIS method has a speciality in choosing the best alternative by means of considering the shortest distance from the positive ideal solution and the longest solution from the negative ideal solution. This makes the rank of a particular sample as neutralised if it exhibits good result in one criterion and poor result in another criterion. This provides more realistic form of modelling when compared with other multi-criteria decision-making methods. Table 7. Overall evaluation results of the proposed work Samples Performance score Ranking index Method 1 Method 2 Method 1 Method 2 S1 0.464081 0 25 25 S2 0.861843 0.877254 18 16 S3 0.911999 0.932603 8 6 S4 0.85986 0.868464 19 18 S5 0.988644 0.990161 1 1 S6 0.791713 0.772006 24 24 S7 0.848273 0.851758 21 20 S8 0.836449 0.843459 22 22 S9 0.872402 0.887673 15 14 S10 0.93552 0.947832 5 3 S11 0.98428 0.982064 2 2 S12 0.914407 0.925028 6 8 S13 0.893961 0.905043 12 10 S14 0.939597 0.94479 3 5 S15 0.91403 0.928978 7 7 S16 0.88012 0.887974 14 13 S17 0.868446 0.869232 16 17 S18 0.905446 0.904207 9 12 S19 0.849625 0.844109 20 21 S20 0.882721 0.878857 13 15 S21 0.833822 0.818073 23 23 S22 0.938468 0.945223 4 4 S23 0.900552 0.912409 10 9 S24 0.862911 0.860485 17 19 S25 0.895121 0.904522 11 11 5 Conclusion In this work, MO is blended with different AOs at various individual and group concentrations, further ageing characteristics has been analysed and an attempt has been made to find out the AO concentration which produces better performance under accelerated ageing conditions using MCDM methods. The following conclusions are made from the laboratory-based experimental tests and also from the analysis of the experimental results using MCDM methods. The degradation rate of MO samples (S1–S25) decreased with accelerated thermal ageing process since due to the ageing process, increase in water content level and acidity values lead to decrease in BDV and increase in the formation of furan contents in oil. The increased furan content decreases the DP and tensile strength of paper insulation. When considering the degradation effect, uninhibited MO sample (S1) degradation rate is higher than that of inhibited MO samples (S2–S25). Moreover, the degradation rates of inhibited MO samples (S2–S25) are almost equal (i.e. small changes while comparing one over the other). Hence, it is difficult to select the best inhibited MO sample having lesser degradation rate by simply looking over the experimental test results. There is a necessity to choose the best sample (S2–S25) which gives the maximum performance. Hence, the proposed work employs two different evaluation methods for choosing the best sample. The evaluation results provide the valuable information for choosing the best sample, and also it provides ranking indices for all the samples used in experimentation. From these ranking indices, it is concluded that the inhibited MO sample S5 (as first) yields better performance followed by S11 (as second) and S10 and S14 (both as third) in the two methods. The uninhibited MO sample S1 holds the last position in the ranking. 6 Acknowledgments The corresponding author sincerely thank the Indian Academy of Sciences, Bangalore for providing the Summer Research Fellowship for doing this research work under the guidance of Professor S.V. Kulkarni, Insulation Diagnostics Lab, IIT Bombay. 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