Decision about criticality of power transformers using whitenization weight functions on DGA caution levels

Power transformers are the most significant as well as the major asset of any power system network. The condition monitoring and assessment is the main concern in transformer management activities. As a first information source, dissolved gases-in-oil analysis (DGA) is universally accepted. The assessment of dissolved gases is characteristically observed analogous to grey system analysis. Grey system theory is supportive to the cases, when less information about the system is available. The cluster of grey incidences and whitenization weight functions classifies the factors of same type, in order to simplify a complex system. Three caution levels of key gases specified in IEEE standards are utilized in this study, to whiten the weight functions. The whitenization weight function with lower measure is selected for caution level-1. However, whitenization weight functions with middle measure are preferred for level-2 and level-3. Several key gas samples of the equal rating transformers are collected from gas analyzer section and utilized in condition assessment computations. The test samples are verified with variable and equal weight clustering criteria. The criticality judgment of transformer with variable weight clustering successfully identifies the crucial elements amongst samples. *Corresponding author: Vikal R. Ingle, B.D. College of Engineering, Sevagram, Wardha, Maharashtra, India E-mail: Chin_vikal@yahoo.com Reviewing editor: Duc Pham, University of Birmingham, UK Additional information is available at the end of the article ABOUT THE AUTHOR Vikal R. Ingle was born on 1 January 1969. He received his BE (Electronics) and ME (Digital Electronics) degrees in 1996 and 2009, respectively. At present, he is an associate professor in Electronics engineering department of BDCE, Sevagram. He is a PhD researcher at PRMIT&R, Badnera. His major area of research includes electrical machines, Grey theory, and AI applications. He is a fellow of Institution of Engineers (India). PUBLIC INTEREST STATEMENT Power transformers are the most significant and the very expensive equipment of any electrical power supplying network. Reliable operation of this equipment is needed for uninterrupted power supply. Transformer outages can be catastrophic, and cause both direct and indirect costs to be incurred by industrial, commercial, and residential sectors. Direct costs include but are not limited to loss of production, idle facilities and labor, damaged or spoiled product, and damage to equipment. For commercial customers, the effects may include damage to electrical and electronic equipment, and in some cases, damage to goods. For residential customers, outages may cause food spoilage or damage to electrical equipment. In addition to direct costs, there are several types of indirect costs that may occur, such as accidental injuries, damage, legal costs, and increases in insurance rates. Therefore, vigilant management is the concern to extend their life, and to obtain the services for longer periods. Received: 28 March 2014 Accepted: 27 November 2014 Published: 09 January 2015 © 2015 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license.


PUBLIC INTEREST STATEMENT
Power transformers are the most significant and the very expensive equipment of any electrical power supplying network. Reliable operation of this equipment is needed for uninterrupted power supply. Transformer outages can be catastrophic, and cause both direct and indirect costs to be incurred by industrial, commercial, and residential sectors. Direct costs include but are not limited to loss of production, idle facilities and labor, damaged or spoiled product, and damage to equipment. For commercial customers, the effects may include damage to electrical and electronic equipment, and in some cases, damage to goods. For residential customers, outages may cause food spoilage or damage to electrical equipment. In addition to direct costs, there are several types of indirect costs that may occur, such as accidental injuries, damage, legal costs, and increases in insurance rates. Therefore, vigilant management is the concern to extend their life, and to obtain the services for longer periods.

Introduction
Power transformers play a key role in production and services, and in supplying the electricity to industrial and commercial sectors as well as to the domestic consumers. Maintaining the strength and reliability of the transformer has been a concern to avoid the power failure. There are several techniques for the maintenance, lifespan assessment, and condition evaluation of power system assets. Dealing with the problem of indicating and assessing the health of a transformer, several key measurements are available. The standards providing the guidance for use, analysis, and applications are included in ANSI/IEEE C57. 104™ (2009) andIEC 60599 (1992). These standards are commonly known as the gas guides, which include the safety ranges of dissolved gases-in-oil. The dominating gases consist of hydrogen (H 2 ), methane (CH 4 ), acetylene (C 2 H 2 ), ethylene (C 2 H 4 ), ethane (C 2 H 6 ), carbon monoxide (CO), and carbon dioxide (CO 2 ). These seven gases are referred as key gases in the literature. The IEC and IEEE specified that three caution levels of key gases are useful in condition judgments (Scatiggio & Pompili, 2013). In condition-based ranking, transformer's DGA data are evaluated against the established industry standards (Field, Cramer, & Antosz, 2002). Since the transformer condition was judged through health index or with criticality index, several groups assign scores as well (Jahromi, Piercy, Cress, Service, & Fan, 2009). These indices are vital in evaluating the state ranking of transformers (Abu-Siada, Arshad, & Islam, 2010). Researchers also attempt the different condition factors for every subsystem of transformer in preparing the concluding rank (Field et al., 2002;Hydroelectric Research and Technical Services Group, 2003;Toronto Hydro-Electric System Limited, 2010). However, condition-monitoring devices of power transformer are disseminated in nature and hardly interpret the inclusive and precise results for judgments about transformer health. As an immediate indicator, dissolved gas analysis is a simple and secured technique of power transformer testing. Significant weights are recommended in gas guide to main tank oil DGA. Furthermore, to draw a quantitative conclusion about the transformer reliability on numerical DGA data, appropriate assessment methods are desired.
Parametric data of transformer incorporated with soft-computing techniques are another kind of decision-making, applied in condition assessment of transformer. The several soft-computing methods are proposed and implemented based on DGA data intended for fault detection, criticality judgment, fault classifications, and state ranking. ANN with expert system (Wang, Liu, & Griffin, 1998), neuro-fuzzy inference system (Sun, Au, & Choi, 2007), fuzzy logic (Abu-Siada et al., 2010;Nemeth, Laboncz, & Kiss, 2009), and genetic algorithm (Zheng, Zhoa, & Wu, 2009) deduce the results effectively. However, these model-free methods necessitate massive data for precise analysis. Similarly, the existing parametric methods need large or reasonable samples with typical probability distributions. However, the conclusions drawn from quantitative analysis differ from that of qualitative results. In contrast, non-parametric test is competent in treating the distribution-free samples but applicable only to a continuous population distributions. Although in reality, the sample size may be prohibited from being large, either due to physical limitations or due to practical difficulties. Therefore, applying the statistical methods or model-free methods can hardly achieve useful solutions, when the system information becomes partially available. The solution to such problems with incomplete or non-deterministic information is always not unique. Whereas, the non-uniqueness is a basic law of the application of grey system theory and one can feel free to look at the problem with flexibility (Kuo, Yang, & Huang, 2008).
A system with partially known and partially unknown information is recognized as grey system. Grey system theory is useful in the condition, when less information about the system is available. It assists in determining the system's key factors and in identifying the factors' correlations. Grey numbers, grey relations, grey decision, grey predictions, and controls are the main subjects of grey system theory (Yang, 2008). The grey incidence analysis of grey theory is applied to the cases of different sample sizes and distributions. Relatively small computations are required and the conclusions drawn from quantitative analysis differ from that of qualitative results. The grey clusterings based on matrices of grey incidences or whitenization weight functions on grey numbers are useful in classifying the observational objects into predefined classes (Deng, 2005;Liu & Lin, 2006). Deng presented a grey whitenization weight function clustering method, wherein the weight of each index was calculated with the critical value of whitenization function (Deng, 2002). Zhang investigated the greyness of cluster result by establishing grey cluster on grey hazy set and combined the cluster result with cluster weight sequence (Zhang, 2002). Xiao et al. put forward grey optimal clustering, whitenization weight function constructed with the standard values of each class, and clustering performed with generalized weighted distance method (Xiao & Xiao, 1997). Liu et al. offered a grey fixed weight cluster decision analysis. The weight of each index has been determined by qualitative or quantitative analysis through Delphi method or analytic hierarchy process, and clustering carried out by whitenization function (Liu, Shen, Tan, & Guo, 2012). Liu and Xie proposed a grey cluster evaluation method based on triangle whitenization weight function; the method divides the values into a range of index "s" clusters so to fulfill the evaluation requirements. The calculation was conducted on grey fixed weight clustering (Liu & Xie, 2011). Qiu projected a grey correlation cluster analysis method (Qiu, 1995). Grey similarity matrices were calculated on the computation of grey correlation degree and clustering performed with maximal tree method or coding method.
The whitenization weight functions mainly classify the factors of same type in order to simplify the complex systems or phenomenon like DGA. This paper demonstrated the synthetic evaluation of DGA test samples, on both fixed and variable weight grey clustering decision. Three caution levels of key gases are utilized in whitening the three weight functions. The whitenization weight function with lower measure is selected for caution level-1. However, whitenization weight functions with middle measure are preferred for caution level-2 and level-3. While identifying the criticality of transformers, representative DGA samples are divided into three grey classes by means of grey clustering.

Grey clustering method
In classification of clustering method, grey clusters are divided into grey correlation cluster and grey whitenization weight function cluster. Among which, grey correlation cluster is mainly employed to incorporate the factors of same class for the simplification of a complex systems. However, grey whitenization weight function is majorly applied to inspect the presence of observational objectives in a predefined class. Grey clustering is also known as grey evaluation. The variable and fixed weight clustering is offered in whitenization weight functions. The fundamentals of both the methods are presented in next section, which covers a small part of grey incidence analysis but the conceptual framework is believed to be enough to realize the clustering methodology.

Grey clusters with variable weights
The grey clusterings based on matrices of grey incidences or whitenization weight functions of grey numbers are used in classifying the observational objects into predefined classes. In general, the whitenization weight function of the j-criterion and k-subclasses is determined by considering the objects of clustering or looking at all the same type of objects as a complete system. Assume that, there exist "n" objects to be clustered according to "m" cluster criteria into different grey classes. The clustering method based on the observational value of the ith objects, i = 1, 2, … , n with j-criterion, where j = 1, 2, … , m. Then the ith objects are classified into kth grey class, where, 1 ≤ k ≤ s. This process of computation is commonly known as grey clustering. Some of the imperative definitions are presented as follows: Definition 1: All the s grey classes formed by the n objects, defined by their observational values at criterion j, are called the j-criterion with subclasses of k .The whitenization weight function on k- Definition 2: Assuming that the whitenization weight function f k j (⋅) for k-subclass of the j-criterion is shown in Figure 1 and the points x k j (1), x k j (2), x k j (3) and x k j (4) are called turning points of f k j (⋅).
Definition 3: Whitenization weight functions: (a) If the whitenization weight function f k j (⋅) above does not have first x k j (1) and second x k j (2) turning points then f k j (⋅) is called whitenization weight function of lower measure as shown in Figure 2.
(b) If the second x k j (2) and third x k j (3) turning points of whitenization weight function f k j (⋅) coincide as shown in Figure 1 then the function f k j (⋅) is called a whitenization weight function of middle measure, shown in Figure 3. (b) The whitenization weight function of lower measure as shown in Figure 2 is given as:  The whitenization weights function in Figure 1 The whitenization weights function in Figure 2 The whitenization weights function in Figures 1 and 4 f k  Definition 5: Assuming the critical value k j for k-subclass of the j-criterion, then the weight of the j-criterion with respect to k-subclass is: Definition 6: Assume that Xij is the observation values of object "i" and criterion-j, the whitenization weight function f k j (⋅) of k-subclass of the j-criterion and the k j weight of the j-criterion with respect to k-subclass. Then is said to be the cluster coefficient of variable weight for object "i" that belongs to the kth grey class.
Definition 7: (a) The following is called the cluster coefficient vector of object "i".
(b) The matrix of such vector represented as: and is called the cluster coefficient matrix.

Definition 8: If
Then object i belong to the grey class k*.

Fixed weights clustering
A fixed weight clustering equally weights all criteria under consideration and also applicable to the situations, where observational data or dimensions are different.
Definition 10: Assuming that x ij (i = 1, 2, … , n; j = 1, 2, … , m) stands for the observational values of the object "i" with respect to criterion j, and f k j (⋅) is the whitenization weight function of the kth subclass of the j-criterion, then for any j = 1, 2, … , m, j = 1 m holds true and is called the equal weight cluster coefficient for object "i" belongs to kth grey class.

Configuration of whitenization weight functions
Several dissolved gas analysis (IEC, IEEE, CIGRE, and MSZ National standard's ratio codes and graphical techniques) schemes are developed on empirical assumptions and experts' knowledge in the interpretations (IEC 60599, 1992;Scatiggio & Pompili, 2013). These standards provide the threshold limits for guidance, investigation, and analysis. The IEEE Std. C.57.104 specified key gas values of three evaluation levels (Table 1) are considered for three cluster criteria.
Applying the whitenization weight function f k j (⋅), synthetic clustering performed on three different caution levels, where j = 1, 2, … , 7; for the criteria k = 1, 2, 3. The whitenization weight function of lower measure is used to figure out the caution level-1. However, whitenization weight functions with middle measure are preferred for caution level-2 and caution level-3 in experimentation. The chosen whitenization weight functions are configured with the equations to apprehend the three caution levels and displayed separately in the following in Tables 2-4.
The caution levels are used in tuning the preferred three whitenization weight functions. The critical values for k-subclass of the j-criterion with fixed weight clustering are given in Table 5. These critical values are used in computing the results of fixed weight clustering.

Identifying the criticality of transformers
This section presents execution of grey clustering on key gas data-set shown in Table 6. All seven key gases of every sample represent a characteristic of testing transformer. These key gas samples are the observational values represented as, x ij (i = 1, 2, … , 21; j = 1, 2, … , 7) of different transformers. The object "i" with respect to criterion "j" is chosen for the specific key gas concentration. These 21 specimens are used to find the cluster coefficient vectors. The configured whitenization weight functions are employed for observation values with fixed weight criteria. In fixed or equal weight criteria, the considered key gases are treated with a weight of (1/7) for every elements and employed in computing the clustering coefficients.
The critical values for variable weights clustering for three caution levels are obtained and displayed in Table 8. The ratio of specified safety concentration of a gas to the total concentration of all gases presented in a particular level is assigned for critical values. The observation values of object, whitenization weight function, and weights for variable clustering resulted into the cluster coefficient matrix as shown in Table 9.