**Fuzzy Logic Applied Duval Triangle for Fault Diagnosis in Power Transformers**

**The accuracy and uncertainties of diagnosis with dissolved gas analysis (DGA) is not satisfactory through conventional diagnostic techniques in power transformers. On other hand computer’ applications have found wide spread applications ‘human-like’ capabilities to make judgments, guesses, change of opinions.**

**- Sukhbir Singh and Dheeraj Joshi**

In this article, fuzzy logic approach on Duval triangle 1 for fault diagnosis besides the diverse gas content of transformer oil has been presented. For this simplified approach the numerical zone boundaries of seven fault coordinates of Duval triangle 1 are assigned with percentages of the gases methane, ethylene and acetylene. These percentage zone boundaries of faults are used to make the membership functions and fuzzy rules. Finally, conventional interpretations techniques’ fault diagnostic reports available from various organizations are compared with proposed fuzzy logic Duval triangle technique. Results reveal the increased in accuracy and reducing the uncertainties between the fault boundaries those can be improved further more and more by adding the experienced based fuzzy rules.

Transformer is one of the most important but complex component of electricity transmission and distribution system. The trend toward a deregulated global electricity market has put the electric utilities under severe stress to reduce operating costs, enhance the availability of the generation, transmission and distribution equipment and improve the supply of power and service to customers. Much attention is needed on maintenance of transformers in order to have fault free electric supply and to maximize the life and efficiency of a transformer. Thus, it is important to be aware of possible faults those may occur. It is equally important to know how to detect them early.

**Formation of Gases in Transformer Oil**

The faults that occur within the transformer protection zone are internal faults. Transformer internal faults can be divided into classification: internal short circuit faults and internal incipient faults. Incipient fault detection in power transformer can provide information to predict failures ahead of time so that the necessary corrective actions are taken to prevent outages and reduce downtime. Incipient faults can produce hydrocarbon molecules and carbon oxides due to the thermal decomposition of oil, cellulose, and other solid insulation.

Because the insulating oil used in power transformer is organic (i.e. composed primarily of hydrocarbons), certain fingerprint gases are generated at specific temperature ranges therefore, allowing the traditional methods to identity a possible fault temperature range and therefore the possible fault type. In the normal operation of the transformers, the released gases: Hydrogen (H2), methane (CH4), ethane (C2H6), ethylene (C2H4), acetylene (C2H2), carbon monoxide (CO), carbon dioxide (CO2) and so on are small in quantities as ageing effects. When there is an abnormal situation, as occurring a fault, some specific gases are produced more than in normal operation and the amount of them in transformer oil increases. This decreases the insulation properties of the transformer oil.

**Dissolved Gas Analysis**

The faults in power transformers can be detected and monitored for abnormal conditions with dissolved gas analysis (DGA). Throughout the world, different countries/utilities are using different fault interpretation techniques/tools to diagnose the faults; According to the pattern of the gases composition, their types and quantities, the conventional interpretation approaches below for dissolved gases are extensively followed as:

- IEEE Gas Guide C57.104TM- 2008
- IEC Standards 60599
- IS 10593: 1992 Standards.

At first a sample of transformer oil is taken and calculations for sampling intervals can be decided between typical and pre-failure values (e. g. every year for transmission transformer and every six months for nuclear transformers/power transformer), dissolved gases concentration requiring monthly, weekly, and daily sampling. Then the dissolved gases are extracted, separated and measured by means of chromatography. In order to interpret the results of experiment a data in suitable form to diagnose the faults is produced. The forming of the data is based on different standards.

**Duval Triangle 1 Fault Interpretations**

Conventional Duval triangle 1 technique used in fault diagnosis through dissolved gas analysis (DGA) in a power transformer is shown in Fig. 1. The faults have been divided in seven zones in an equilateral triangle. There are two different procedures to find the faults by the use of Duval triangles:

- By using total accumulated gas
- By using total increase between conjugative samples.

**Fig. 1: Duval Triangle 1 fault boundaries**

The following DGA interpretations are made in Duval triangle 1 for typical faults detected in power transformers given Table 1.

This Dissolved gas analysis involved percentage of these gases only in three dimensional arrangements: Methane (CH4), Ethylene (C2H4) and Acetylene (C2H2) in Duval triangle 1 where:

First calculate the sum of these three values: (CH4 + C2H4 + C2H2) = S, in ppm, then, calculate the relative proportion of the three gases, in %:

X = % CH4 = 100 (A/S),

Y = % C2H4 = 100 (B/S),

Z = % C2H2 = 100 (C/S).

X, Y and Z are necessarily between 0 and 100%, and (X + Y + Z) should always = 100%.

**Fuzzy Logic for Proposed Technique**

A fuzzy set F of a universe of discourse

X= (0, 1) is defined as a mapping, µF(x):

X → (0, α), by which each x is assigned a number in the range (0, α), indicating the extent to which x has the attribute F. if x is say ‘small’ a value of fuzzy variables from the range of ‘0 to ∞’, then µsmall (x) € (0, α) is called a ‘membership function’. A membership function is normalized (ie., α = 1), thus µF (x) : X→(0,1), fuzzy logic is called ‘normal’. The normalization of fuzzy set is expressed by F.

Where x € X, normalization of a set of numbers is achieved by dividing each number of the set by the largest one, the supermum. Where, X be a time-invariant set of objects x. a fuzzy set ¯ is X will be expressed by a set of ordered pairs:

Where, µ is the membership function that maps X to the membership space M (i.e. 0 to 1) and µ (x) is the grade of membership (degree of truth) x in .

**Methodology Used for Fuzzy Logic Approach**

**Step 1:** In this research work, firstly, polygon coordinates for the numerical zone boundaries of seven key faults of Duval Triangle 1 have been generated in terms of percentages of CH4, C2H4 and C2H2, from 0% to 100% respectively shown in Table 2.

** Step 2:** Fuzzy Diagnosis System, The fuzzy logic analysis involves three successive processes; namely fuzzification, fuzzy inference, and defuzzification. Fuzzzification converts the crisp the gas percentage into a fuzzy input membership. The fuzzy inference system (FIS) is responsible for creating the knowledge-based fuzzy rules set of If-Then linguistic statements. Defuzzification then converts the fuzzy output values back into crisp output actions.

**Fuzzy inputs-gas percentages**

In this diagnostic each crisp value of gas percentages (CH4, C2H4, C2H2) from Table 2 changed to triangular fuzzy-membership function ranges (i.e. A.......L, A1......G1 & A2......H2 respectively), given in Table 3. Fuzzy-membership function for %CH4 obtained in MATLAB fuzzy-box tool is illustrated in Fig. 2.

**Fuzzy-rule base**

The set of fuzzy inputs (% three gases) with their respective membership function form the integral part of fuzzy logic analysis. The fuzzy rule set (If-then linguistic statements) with AND operator for minimum and OR operator for maximum fault conditions is then used form ‘judgement’ on the fuzzy inputs derived from the 3 gas percentages, whose sum is always 100%. For example,**Rule 10: If (CH4 is E) and (C2H4 is E1) and (C2H2 is D2) then (FAULT is D24)**

**Fig. 2: %CH _{4 }membership-function in MATLAB toolbox**

All such 32 fuzzy rules just derived from Table 2 for mapping the fault types and screen shot of these rules is shown in Fig. 3 in MATLAB environment. Although these faults are defined strictly for the percentages of the zone boundaries of 7 faults in Duval triangle 1 coordinates. These 34 rules are just mapped on the joining points of the numerical zone boundaries of the faults in Duval triangle 1 coordinates. Membership function plot of the faults is also illustrated in Fig. 4 in MATLAB environment.

**Fig. 3: Fuzzy DGA rules**

**Fig. 4: Membership functions of faults**

**Fuzzy Inference System (FIS)**

FIS involves the operation between input fuzzy sets as shown in figure 5, known as ‘Mamdani’ type. This derives output fuzzy sets ‘judging’ all the possible fuzzy rules by finding the membership for the fault types as represented by 34 fuzzy output rules. The solution is reached by weighted average of the fuzzy inputs. The spikes in the figure denoting probabilities between 0 and 1 are the outputs from each fuzzy rule, which denotes the fault type. Thus each rule is a row of the plots and each column is variable.

**Fig. 5: Mamdani FIS analysis of fuzzy rules**

**Results and Discussions**

In order to evaluate the performance of the proposed fuzzy logic for fault diagnosis in power transforms through DGA, transformers’ fault analysis reports collected from different utilities and authorities are tested. Reported faults by different conventional diagnostic tools such as IEEE C-57, 104TM 2008, CIGRE, IEC Key gas ratios, Roger’s gas ratios, Doernenburg’ gas ratios and others are reconfirmed with fuzzy logic Duval triangle 1 based diagnosis. This fuzzy logic Duval triangle approach is also compared with other specifically generated MATLAB based Duval triangle 1 diagnostics tool. This has been achieved by forming different sets of fuzzy inputs and output rules on experiences (fault analysis reports) basis and by changing the FIS for inputs. Results are tabulated in Table 4. Results are found more specific & crisp. Result table has been prepared for integers (round up values) and nearer numerical values at the fault zones for three input gas percentages. Duval triangle 1 approach is cross . In some cases this DGA method could not provide the results, reasons are unclear fuzzy rules and the membership functions. This approach is more effective in case faults are ambiguous on zone boundaries. Table 5 has been tabulated to use these abbreviations/shorten forms in the result Table 4 only.

**Conclusions**

In this article, fuzzy logic Duval triangle 1 is applied for the interpretation of faults keeping in view that Duval Triangle 1 to Duval Triangle 5 needs three gases only. This approach can be explored to improve the incipient fault diagnosis technique by adding more and more fuzzy rules and adding membership functions. Fuzzy rules can be mapped for possible real number input percentages. Fuzzy logic is applied as the practical representation of the relationship between the fault type and the dissolved gases percentages with fuzzy membership function. To increase the accuracy of this method, more transformers fault reports should be analysed to compare the actual faults. In addition, appropriate membership functions and fuzzy rules are necessary to obtain the acceptable accuracy and to reduce the ambiguity between the faults.

**Authors **are from NIT Kurukshetra.

**If you want to share any thoughts or feedback on this article then please leave a comment below.**