Power Transformer Incipient Faults Diagnosis Using Dissolved Gas Analysis and Rough Set

Noor Akhmad Setiawan, Sarjiya and Zenith Adhiarga Electrical Engineering and Information Technology Department

Universitas Gadjah Mada Jalan Grafika 2 Yogyakarta 55281, Indonesia

noorwewe@ugm.ac.id

Abstract— Dissolved Gas Analysis (DGA) is standard technique to detect and diagnose power transformer incipient faults. Many methods based on DGA have been proposed such as Duval Triangle, IEC, Roger’s Ratio, Key Gases, etc. The relationship between gas and type of faults is difficult to model and highly non-linear. Knowledge Discovery from Data (KDD) based on Rough Set Theory (RST) can be used to find that relationship. Thus RST is used in this research. The objective of this research is to diagnose incipient fault of power transformer. The diagnosis method is using DGA and RST. All of possible gas ratios are used as input to determine types of fault. The value of gas ratios are discretized before being processed with Rough Set Theory (RST). The number of input attributes is reduced using RST. The knowledge is extracted in the form of IF-THEN rules. The extracted and reduced rules are used to diagnose the incipient faults of power transformer. The resulting rules have the accuracy of 81.25%.

Keywords- transformer; DGA; RST; incipient faults; diagnosis

I. INTRODUCTION Transformer is one of the most important equipment in

electrical power system that serves to convert the power with different level of voltage without changing the electrical frequency. One of the components of a transformer which need attention and regular maintenance is the insulation material, especially the liquid insulation (oil). Along with the operation of the transformer age, transformer oil will gradually undergo deterioration (decline of quality). As a result the oil contaminants will arise which may take the form of solid particles, gases, or liquids. Even for the flammable gases if accompanied by sufficient oxygen and temperature can cause the occurrence of a fire in a transformer.

One of the transformer oil monitoring is using Dissolved Gas Analysis (DGA) test. With the DGA test the dissolved gas content in a transformer will be obtained. Gas can be obtained from the DGA test is nitrogen (N2), oxygen (O2), carbon dioxide (CO2), carbon monoxide (CO), hydrogen (H2), ethane (C2H6), methane (CH4), ethylene (C2H4), and acetylene (C2H2) [1]. The resulting gas is translated by the amount of parts per million (ppm). The concentration of several types of gas produced depends on the type of incipient faults. But it can also be said that any type of faults will produce gas, known as key gases.

The incipient faults in a transformer occur with the development of dissolved gas pattern where the relationship with the faults is difficult to be mathematically modeled. So the patterns that can map the relationships between inputs in the form of DGA test results with the outputs which are types of incipient faults that occurred are needed. The pattern will be used to map the data resulting from other DGA in the future.

RST is a mathematical approximation method based on set theory, which deals with imprecision, and uncertainty. RST is based on association of some information [2]. In this case, rough set is used to diagnose abnormality or incipient faults of the transformer. The results of DGA are used to obtain the relationship between dissolved gas resulted from DGA with incipient faults of the transformer. RST is done through several stages, including the reduction of some attribute information (reduction) so it can be obtained a set of decision rule.

DGA method showed good result as shown in research works that have been conducted [3]. RST has been used to built diagnosis system for many areas such as medical field [4][5]. RST is also used to build diagnosis system for transformer incipient faults [6-9]. RST was used alone to diagnose incipient faults of transformer by applying of rule simplification method [6][10]. RST was also used with Artificial Neural Network (ANN) to diagnose the transformer faults where the accuracy was lower than single RST [6][7]. RST was combined with fuzzy and inclusion degree theory and with fuzzy and Bayesian for the incipient faults diagnosis of transformer [8][9]. Hybrid method is adding complexity to the diagnosis system.

This paper presents RST application to diagnose incipient faults of power transformer. RST is used to reduce input dimension and simplify generated rules before applying the rule to diagnose transformer incipient faults [5]. Unlike black box model such as ANN, the model generated by RST is transparent then the model can be understood easily.

II. METHODOLOGY

A. Data Data obtained from the New IEC Publication 60 599 [3].

This data is used as the learning data and testing data. The data is then processed into a decision table that consists of objects (rows) and attribute (column). Totally 159 objects and 6 units of attributes are used in the decision table. Attributes consist of

A-160 2012 IEEE International Conference on Condition Monitoring and Diagnosis23-27 September 2012, Bali, Indonesia

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five attributes as input attributes or conditions and one diagnosis attribute, which is an output or decision [3].

Inputs attributes are H2, CH4, C2H2, C2H4, and C2H6. Output attributes are:

1. Partial discharge (PD)

2. Low energy Discharge (D1)

3. High energy Discharge (D2)

4. Impaired thermal < 700° C (T1 and T2)

5. Impaired thermal > 700° C (T3)

6. Normal

B. Research Flow

Figure 1. Research flow diagram

C. Rough Set Theory RST is a method that is used to find the rules (knowledge)

from information or decision system (learning data). RST method uses a decision table to find knowledge which is rules from a learning database. A decision table is defined as follows:

(1) refers to decision . To and x expressing an object,

indiscernibility relation defined as follows:

(2)

Indiscernibility relation will induce U into sets based on the condition A. Every object in a set can not be distinguished from other objects in the same set. The objects that have been classified into sets called equivalence classes which are denoted by [x]A. Approximation of the set is used when a desicion (d) cannot be precisely defined. To approximation of which uses the information in A divided into lower-approximation ( ) and upper-approximation ( ) which is defined as follows :

(3)

(4)

The set which contains objects that cannot be precisely classified in the X or outside X called the boundary region of X:

(5)

D is a decision and is a condition, A-positive region from D is defined as follows:

(6)

is the partition from U to a decision D.

The condition attributes of a DS decision system is likely to contain redundancies so as attributes in DS need to be reduced. The result of the reduction is a reduct. Reduct is a minimal set of attributes so that . A reduct is a combination of conditions that can distinguish between objects. Reduct has an equivalent classification quality to DS. A reduct can be obtained using a matrix of discernibility and discernibility function [4].

Equation (1) is the definition of a decision table. A decision table is an object of the RST. Decision tables are also often referred to the information system or set of approximation.

TABLE I. AN EXAMPLE OF DECISION TABLE

No c1 c2 d 1 0 3 1 2 0 0 0 3 1 1 0 4 1 1 1 5 2 2 0 6 0 3 1 7 2 2 0

a

start

collecting data

creating temporary decision table

data discretisation

reduction of decision table attributes

a

creating new decision table

extraction of IF-THEN rule

reduction of rule

comparing with other methods

finish

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Table I is an example of a decision table with d = {D} and C = {c1, c2}. C defined as the set of attribute conditions or simply conditions.

Based on the Table I and (2) for A = {c2}. The partition is . The set that classified based on objects referred to equivalence classes by the notation [x]A.

The set of approximation is used when a decisions concept with d cannot be crisps or precise. It can be seen from an object x3 and x4 on the table. To , the approximation for using only the A information will be obtained the lower approximation , the upper approximation , and boundary regions

. The condition of a DC decision system is very likely to

contain redundancy, so it needs the reduction process. Reduction of the DS produces reduct. A reduct is a minimal set of attributes such as . A reduct is a combination of conditions which is distinguish that the object was equally good as a whole used condition. A reduct can be calculated using the discernibility matrix and discernibility function of the bias of DS decision system that defined M matrix n x n with elements:

(7) For i , j = 1.....n and d D.

Element of m is a condition that requires object differentiation i from a relative object j to a decision. A discernibility function fc for a DS decision system consists of variable k Boolean from the function of Boolean that is defined as:

(8)

where . All minimal reduct of decision systems may be calculated

by finding the set for all prime implicant of discernibility function. Discernibility function of DS decision systems is

after simplification is obtained.. If R = {Rule1, Rule2, ..., Rulej} was assumed as one set of rules that are generated from the decision table. If the number of objects in the decision table was i then one new decision table DSix (j+1) could be established. The value of Rulea attribute of an object xb is one if the Rulea could be applied to xb both antecedent and consequent of the rules. The value should be zero when the rule was inapplicable. A value of j+1 was equal to the value of the decision on the decision table on test data. With a = 1,... j and b = 1,... i. So the generated selected rule is the rule that will be implemented on testing data [5]. The research flow shown in Fig 1 then conducted to get the results.

III. RESULTS

A. Data Discretisation The data are used as much as 159 objects taken from the

New IEC Publiction 60 599 [3]. The data subjected to the discretization process through some stages:

1. Defining ratio of gases which are C2H2/C2H4 (C1), CH4/H2 (C2), C2H4/C2H6 (C3), C2H6/CH4 (C4), CH4/C2H4 (C5), C2H2/CH4 (C6), C2H2/C2H6 (C7), C2H6/H2 (C8), C2H4/H2 (C9), C2H2/H2 (C10), CH4/total hydrocarbons (C11) , C2H4/ total hydrocarbons (C12 ), C2H6/ total hydrocarbons (C13), C2H2/ total hydrocarbons (C14), and H2 / (total hydrocarbon + H2) (C15) [6 7].

2. Normalisation of ratio of gas between 0-10 . 3. Categorization of the normalized ratio in three

categories, namely low, med, and high using and the equal frequency binning methods. Limits of the value of each category are shown in Table II.

TABLE II. LIMITS OF LOW, MED , AND HIGH VALUES

low med high

C1 < 0,0989 0,0989 - 0,6877 > 0,6877 C2 < 0,0042 0,0042 - 0,014 > 0,0140 C3 < 0,0429 0,0429 - 0,2412 > 0,2412 C4 < 0,0854 0,0859 - 0,3818 > 0,3818 C5 < 0,0056 0,0056 - 0,0112 > 0,0112 C6 < 0,0989 0,0989 - 0,6877 > 0,6877 C7 < 0,0038 0,0038 - 0,2815 > 0,2815 C8 < 0,0001 0,0001 - 0,0005 > 0,0005 C9 < 0,0006 0,0006 - 0,0023 > 0,0023

C10 < 0,0726 0,0726 - 0,4357 > 0,4357 C11 < 1,9334 1,9334 - 3,4596 > 3,4596 C12 < 2,1857 2,1857 - 3,5737 > 3,5737 C13 < 0,4055 0,4055 - 1,7263 > 1,7263 C14 < 0,3517 0,3517 - 3,8769 > 3,8769 C15 < 2,2647 2,3670 - 4,8766 > 4,8766

B. Attributes Reduction Reduction of data is obtained using Johnson’s Algorithm,

resulting in 8 reducst which would then be used to extract the rules. Results of the reduct, i.e. C2 = CH4/H2; C4 = C2H6/CH4; C7 = C2H2/C2H6; C8 = C2H6/H2; C10 = C2H2/H2; C11 = CH4/Total hydrocarbon; C12 = C2H4/Total hydrocarbon; and C15 = H2/(Total hydrocarbon + H2).

C. Rules Extraction Eight attribute that has been generated is used to extract

the rules, thus obtained 485 rules with accuracy of 76.56%. The resulting rules are still too many. The rules can be reduced by eliminating the rule with certain support value without reducing accuracy. Here the rules with RHS support 2 removed. The rules reduced from 485 become 140 rules with accuracy of 78.25%. The results of the RHS reduction support

2 shown in Table III.

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TABLE III. EXTRACTION OF RHS SUPPORT RULES = 2

Rule RHS Support

1 c2(low) AND c4(low) AND c7(low) => Diag(PD) 4 2 c2(low) AND c4(high) AND c7(high) => Diag(Normal) 5 3 c4(low) AND c7(low) AND c8(low) => Diag(PD) 4 4 c4(low) AND c7(high) AND c8(med) => Diag(D2) 6 5 c4(high) AND c7(high) AND c8(low) => Diag(Normal) 4 6 c7(low) AND c8(low) AND c12(low) => Diag(PD) 6 7 c7(high) AND c8(med) AND c12(med) => Diag(D2) 4

…

…

…

134 c7(med) AND c8(high) AND c15(med) => Diag(Normal) 3 135 c2(med) AND c7(low) => Diag(Normal) 4 136 c2(low) AND c8(high) => Diag(Normal) 4

137 c4(med) AND c10(med) AND c11(med) AND c12(high) => Diag(T3) 3

138 c4(high) AND c15(med) => Diag(Normal) 12 139 c10(low) AND c11(low) => Diag(Normal) 8 140 c7(low) AND c11(low) => Diag(Normal) 4

Applying rule selection method in [5] results in 20 selected rules shown in Table IV.

TABLE IV. SELECTED RULES

No Selected rules No. rules

1 IF c4(high) AND c15(med) THEN Diag(Normal) Rule 1 2 IF c10(high) AND c12(med) THEN Diag(D2) Rule 2

3 IF c8(med) AND c12(med) AND c15(med) THEN Diag(D2) Rule 3

4 IF c8(med) AND c10(high) AND c11(med) THEN Diag(D2) Rule 5

5 IF c10(low) AND c11(low) THEN Diag(Normal) Rule 7

6 IF c2(low) AND c8(low) AND c11(high) AND c12(low) THEN Diag(PD) Rule 10

7 IF c8(med) AND c11(med) AND c15(med) THEN Diag(D2) Rule 12

8 IF c4(high) AND c8(high) AND c10(med) THEN Diag(Normal) Rule 27

9 IF c2(low) AND c8(low) AND c10(med) THEN Diag(D1) Rule 35

10 IF c4(low) AND c12(med) AND c15(high) THEN Diag(D2) Rule 52

11 IF c2(med) AND c10(high) AND c12(low) THEN Diag(D1) Rule 56

12 IF c2(low) AND c10(med) AND c12(low) THEN Diag(D1) Rule 57 13 IF c4(low) AND c12(high) AND c15(low) THEN Diag(T3) Rule 95

14 IF c4(med) AND c10(med) AND c12(low) THEN Diag(D1) Rule 96

15 IF c2(med) AND c4(low) AND c12(high) THEN Diag(D2) Rule 99

16 IF c2(med) AND c4(high) AND c12(high) THEN Diag(Normal) Rule 120

17 IF c4(high) AND c7(med) AND c12(low) THEN Diag(Normal) Rule 133

18 IF c8(high) AND c10(low) AND c11(high) AND c15(low) THEN Diag(T1 dan T2) Rule 135

19 IF c4(high) AND c8(med) THEN Diag(Normal) Rule138 20 IF c2(high) AND c4(med) AND c10(med) THEN Diag(T3) Rule 140

The 20 selected rules are implemented in testing data. The results of the implementation are producing accuracy of 81.25%. The accuracy is better than artificial intelligence method and machine learning methods such as MLP (75%), C4.5 (57%), k-NN (78%), RIPPER (67%) and conventional methods which are IEC (58%), Roger (41%) and Duval Triangle (48%).

IV. CONCLUSIONS The RST method with rule selection has successfully been

demonstrated to diagnose incipient faults of power transformer. The extracted knowledge is just 20 rules which will be easy to be understood. The diagnosis system that uses the rules has 81.25% accuracy which is better than MLP, C4.5, k-NN, RIPPER, IEC, Roger and Duval Triangle.

REFERENCES

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