�

Abstract—A genetic algorithm combined with theories of rough set is proposed in the process of fault diagnosis of power transformer .Then by the process of value reducing, the fault diagnosis rules are extracted from the minimal decision table obtained from the algorithm. Besides, the feasibility of the generalized rules for power transformer fault diagnosis and the efficiency of the algorithm are illustrated with two specific examples.

. INTRODUCTIONOWER transformer is the key equipment of power system, and its reliability is directly related to the security and reliability of power system[1]. For a long time, many

techniques have been introduced into the transformer fault diagnosis. In recent years, with the development and progress of the fuzzy theory, rough sets, artificial neural networks and theory of expert systems, many artificial intelligence algorithms, some of which are combined with theories of fuzzy set, rough set etc, have been applied in the Dissolved Gases Analysis (DGA) to establish failure tables, which are vital in the judgment mechanism of transformer fault, and have achieved good results. The characteristics and the structure of a large power transformer fault diagnosis expert system (TFDES), together with the functions of its each module are detailed introduced in [2]. A transformer fault diagnosis system based on BP neural network theory is designed in [3], and a transformer fault diagnosis based on artificial neural network method is introduced in [4].An application of the fuzzy theory to power transformer fault diagnosis is introduced in [5] and [6].

Dissolved Gas Analysis (DGA), as the routine method of monitoring oil-immersed power transformers in the current power system, has eliminated a lot of accidents of the operation and maintenance in the past years owing to its ability of detecting early faults in time that exist within the transformer. According to the statistics, more than 50% of the faults of the transformer are detected by this method. This detecting technology can be applied in the no-blackout case, not affected by all kinds of electromagnetic interference. Lots of experience has been accumulated from qualitative to quantitative analysis of this mature technology, and the relative data has high reliability. "The preventive

Manuscript received July 1, 2011. And this paper is supported by the Chinese Natural Science Fund (51007052).

Zhu Ji. Author, He is with the Department of Automation, Shanghai University, Shanghai 200072, China (e-mail: zhuji857441@163.com).

Yu Ying. Author, She is with the Department of Automation, Shanghai University, Shanghai 200072, China (e-mail: squarey@shu.edu.cn).

experimental procedures for power equipments ", which was promulgated in 1997, put the analysis of dissolved gases in oil in the first place.

Two kinds of methods, which are based on the absolute value and the ratio of the dissolved gases in oil respectively, with various preventive experiments, are currently primarily used DGA methods. On one hand the methods based on the absolute value of dissolved gases (e.g.: LCIE Judgment method and Gas Graphic method) do not take into account the links between the relevant gases, which may lead to inaccurate diagnosis; On the other hand, the drawback of the Gas Ratio methods (such as: Dornenburg four ratios method, Germany four Ratios method, Improved Roger method and GE two ratios method) is that the ratio may fall inside the range of failure with two rare gases compared, which may also leads to misjudgment. Literature [7] gives some examples for the above mentioned misjudgments, but the results of the diagnosis by the methods described above have errors more or less. Therefore, it is necessary for both the absolute value and the ratio of the dissolved gases in oil to be applied for the fault diagnosis.

Since uncertainty exists in the process of data collection, data for the diagnosis may be incomplete or be redundant. As rough set could make effective analysis from incomplete information, by methods of attribute/value reduction etc, the theories of rough set have gained much popularity in the process of transformer fault diagnosis.

Attribute reduction algorithm is the core of the rough set theory. The main methods of attribute reduction are the heuristic reduction algorithm based on the importance of attributes and the reduction algorithm based on discernible matrix. But the former may not obtain the global optimal reduction combination, while the latter is too complex to be suitable for mass data processing. As genetic algorithm has the advantages of global optimization and implicit parallelism etc, it could be used to get minimal or relative minimal attribute reduction with much less computational complexity. Therefore, a genetic algorithm is applied in this paper for attribute reducing, and hence a minimal decision table is formed. Then the procedure of value reduction presented in [8] is used for value reduction. Finally, decision rules, for power transformer fault diagnosis, are extracted from reduction tables.

.THE BASIC THEORY OF ROUGH SET

Definition 1(Information System): Any 4-tuple S = <U, R, V, f> is called an information system, where U is a non-null finite set of objects; R is a finite set of attributes, V= a Rva,

Application of Rough Set and Genetic Algorithm to Transformer Fault Diagnosis

Ji Zhu and Ying Yu

P

1

Fourth International Workshop on Advanced Computational Intelligence Wuhan, Hubei, China; October 19-21, 2011

978-1-61284-375-9/11/$26.00 @2011 IEEE

where va is a domain of the attributes; f: U×R → V is an information function by ρ(x,a)=a(x) va for every a R and x

U. An information system is denoted by S= (U, R)[9]. Definition 2(Decision Table): Let S= (U, R) be an infor

-mation system. If there are C, D � R such that C∩D= � and C D=R. Then S is called a decision table, which is denoted by S= (U, C, D). C, D are called condition and decision attributes, respectively [9].

Definition 3 (Indiscernibility Relation): Let S=(U,R) be an information system. Every B � R generates a binary relation on U, which is called an indiscernibility relation, and defined by IND (B) = {(x, y) | (x, y) U U, b (x) = b (y), � b B }, It is denoted by IND(B) or simply by B[9].

Definition 4(approximation space): Let S=(U, R) be an information system and B⊆R.The pair A=(U, IND(B)) is called approximation space[9].

Definition 5(Lower Approximated Set): Let A=(U, IND(B)) be an approximation space and X � U.The lower approximation of X in A is defined as

( ) { :[ ] }[9].BA x x U x X� � �Definition 6 (Positive Region): Suppose P and Q are two

equivalence relation clusters defined in U, if P positive region of Q is denoted by POSP(Q), then POSp(Q)={p_(X):X U/Q}.

Definition7 (Reduction): Let S=(U,R) be an information system and B � R. The least B’ that B’ � B such that IND(B’)=IND(B) is called a reduce in B. The set of all reduces in B is denoted by RED (B), and the reduce of a set is not unique[8].

Definition8(Core): Let S=(U,R) be an information system and B � R . Then the intersection of all reduces of B is called the core of B, i.e ( ) ( )Core B RED B� I .The core is a collection of the most significant attributes in the system[9].

. ATTRIBUTE REDUCTION BASED ON IMPROVED GENETIC ALGORITHM

A. Description Of The Genetic Algorithm For Attribute Reducing

A genetic algorithm is applied in this paper to obtain a minimal decision table containing rules for power transformer fault diagnosis. The genetic algorithm in this paper not only has the common advantages of traditional genetic algorithm, but also has its unique characteristics: an amendment operator is embedded in the algorithm to accelerate the convergent speed of the algorithm and to improve the accuracy of the results.

The general schema of the algorithm is that: Firstly ,in the population generation process of the algorithm, the code of each individual in the population is required to have the attribute core included, and then the population evolves through the processes of selection, crossover and mutation, amendment and reproduction. The best individual is kept and the bad one is eliminated in each iteration. After certain iterations, the optimal reduction (that is, the best individual

with the maximum fitness) could be obtained, and thus the minimum decision table is generated.

The detailed steps are described as follows: Step 1:Seek the core, and randomly generate the initial

population Pop(t) whose individuals are coded as containing the core ;

Step 2:Amend the initial population Pop (t); Step 3:Evaluate the fitness of Pop(t), and estimate whether the number of iterations has reached the maximum,

if reached , then go to Step 9, otherwise go to step 4; Step 4:Select the next generation of Pop (t+1) from Pop (t)

by the way of roulette ; Step5: Make cross-operation for the individuals in Pop (t+1)

according to the crossover probability; Step 6: Make mutation for the individuals in Pop (t+1)

according to the mutation probability ; Step 7: Amend the individuals in Pop (t +1); Step 8: Let t=t+1 Pop(t)=Pop(t+1), and go to Step 3. Step 9: Remove the duplicate records, and extract condition

attributes and attribute values based on the attribute reduction results generated by the algorithm, and then the minimal decision table is obtained.

B. Coding The length of chromosome is equal to the number of

condition attribute. Binary coding is used: 1 means that the condition attribute is selected as the key attribute , and 0 means the condition attribute is not selected. The attribute core is included in the encoding of the initial population . For example: Supposing that there are five condition attributes {a1, a2, a3, a4, a5}, the core of the decision table is {a2, a4}, and then *1*1* is chosen as the mode of chromosomes.

C. Fitness function The fitness function is defined as:

f(x)=card(C)-count(x) where card (C) is the number of all condition attributes, and

count (x) is the number of condition attributes included in the individual.

D .Selection Roulette wheel method is used in selection.

E. Crossover operator and mutation operator One-point crossover is used. Once a cross-point is selected

randomly, by exchanging the two substrings besides the cross-point of the parent individuals, two offspring individuals are generated.

Swap mutation is used. 0-1 swapping happens in the mutate-point once an individual is selected randomly to mutate.

F. Amendment operatorAmendment is used to ensure that each chromosome is a feasible reduction, and to keep the search range of genetic

algorithm in the feasible solution space. Amendment operator can reduce the number of iterations effectively. The detailed steps of amendment operator are as follows:

2

TABLE 1

Original decision table of transformer fault diagnosis

Remark:TH=total hydrocarbon;H=hydroca

TABLE 2 Discrete decision table of Transformer fault diagnosis

Remark:TH=total hydrocarbon=hydrocarbon

3

TABLE 3 Minimal attribute reduction decision table

TABLE 4 Result of value reduction

4

TABLE 5Chromatographic data of No.2 main transformer μL/ L

Date H2 CH4 C2H6 C2H4 C2H2 CO CO2 TH1997.12.17 279 41 9.7 42 34.0 378 1739 126.7

Remark hydrocarbon:TH=total

TABLE 6

Chromatographic data of No.1 main transformer in Panlong Substation μL/ L

Date H2 CH4 C2H6 C2H4 C2H2 CO CO2 TH2008.5.28 5.48 48.82 96.81 489.57 0.30 113.37 18795 635.50

Remark:TH=total hydrocarbon

Step 1: For an individual, replace 0 to 1 in the first gene whose value is 0. Then calculate the positive domain of the attribute set represented by the new genes, and estimate

MATLAB, and is used to obtain the attribute reduction for the discrete decision table shown in Table 2. The result of the attribute reduction is shown in Table 3 where C1 - C15 are used to represent the 15 condition attributes in Table 1/2, and

D is used to represent the decision attribute.So we obtain 6 groups of minimum condition attributes as: (C2,C7,C8),(C6,C7,C8), (C2,C7,C13), (C2,C7,C14), (C7,C8,C15),(C7,C14,C15).

The procedure of value reduction[8] is used to do value reducing and obtain the minimum decision table, and the result is shown in Table 4.

By techniques of information fusion, decision rules could be extracted from the results of value reduction shown in Table 4, and integrated into mixed strategies , which may be useful for a rule knowledge base for power transformer fault diagnosis. 1) (C2=2∩C14=2) (C2=0∩C14=1) (C14=2∩C15=0)

(C14=1∩C15=2), then the fault type is normalMixed strategy rule 2: If (C2=0∩C7=2∩C8=0) (C2=0

∩C7=1∩C8=2) (C6=0∩C7=2∩C8=0) (C6=0∩C7=1∩C8=2) (C8=0∩C15=2) (C7=1∩C15=2) (C2=0∩C7=2∩C13=0) (C2=0∩C7=1∩C13=2) (C2=0∩C7=2∩C14=0) (C2=0∩C7=1∩C14=2) (C14=0∩C15=2), then the fault type is low-energy discharging

Mixed strategy rule 3: If (C7=0∩C8=2) (C13=2) (C14=2) , then the fault type is high-energy discharging

Mixed strategy rule 4: If (C2=2∩C7=2) (C7=1∩C8=2)(C2=1∩C7=1) (C7=1∩C8=0) (C6=1∩C7=1) (C7=2

∩C15=0) (C7=1∩C15=1) (C7=1∩C13=0) (C7=1∩C14=0), then the fault type is medium low-temperatureoverheating;

Mixed strategy rule 5 If (C2=2∩C7=1∩C8=0) (C7=0∩C8=1) (C7=0∩C8=0) (C6=2∩C8=2) (C8=1) (C8=1∩C15=0) (C7=1∩C8=0∩C15=0) (C2=2∩C7=1∩C13=0)

(C7=0∩C13=1) (C2=2∩C7=1∩C14=0) (C7=0∩C14=1) (C14=1∩C15=0) (C7=0∩C14=0) (C7=1∩C14=0∩C15=0), then the fault type is high-temperature overheating.

VI. EXAMPLES AND RESULTS

Example 1 : The chromatographic analysis data of the No. 2 main transformer in Guangzhou Pumped Storage Power Plant is shown in Table 5(Sample data is from [11]).

The calculating result shows that :C2H4 / total hydrocarbon = 0.332; C2H6 / total hydrocarbon = 0.077; C2H2 / total hydrocarbon = 0.268. According to the methods adopted in this paper, the discretized code is 102 which is consistent with *02 in Table 4, and the corresponding fault type is 3 described as high-energy discharge, which is the same as that in [11].

Example 2: The chromatographic analysis data of the No.1 main transformer in YongChuan Panlong Substation is shown in Table 6(Sample data is from [12]).

Calculating result shows that :C2H4 / total hydrocarbon = 0.770; C2H6 / total hydrocarbon = 0.152; C2H2 / total hydrocarbon = 4.72×10-4. According to the methods adopted in this paper, the discretized code is 211 wh The ich is consistent with **1 in Table 4, and the corresponding fault type is 5. So the fault type is described as high-temperature overheating, which is the same as that in [12]

VII. CONCLUSION

Many problems exist in the current attribute reduction process of rough set application, such as, complexity of the reduction algorithm, difficulty to achieve the optimal reduction combination etc. So an improved attribute reduction algorithm based on the genetic algorithm is proposed to effectively avoid the above mentioned problems. By applying the proposed genetic algorithm and the improved value reduction algorithm into the decision table reduction process of the power transformer diagnosis, the optimal reduction combination could be quickly obtained. Besides, an idea of forming hybrid strategy, which is integrated into the reduction results, is presented in this paper, thus a comprehensive knowledge base model for fault diagnosis of power transformers could be established. Two specific examples are

5

given to illustrate the validity and practicality of the methods applied in this paper.

REFERENCES

[1] Q.Y. Sun,"Rough Set Theory and its Application in Power Industry,”. Beijing: Machinery Industry Press, 2009

[2] Q. P. Yang, W. D. Xue,Y. Fu and Z.D. Lan, "Expert System for Transformer Fault Diagnosis," Transformer, vol. 5, 35-38, 1996.

[3] H.M. Yang, J. Liu, and J. Zhang, "BP neural Network for Transformer fault Diagnosis," Transformer, vol. 46, pp. 67-70, 2009.

[4] Q. P. Yang, W. D. Xue, and Z.D. Lan, "Transformer Fault Diagnosis Based on Artificial Neural Network, "Transformer, vol. 37, pp. 33-36,2000.

[5] Q. Yang and W.K. Shi, "Fuzzy Control of Transformer Failure,".Transformer, vol.35, pp. 32-35, 1998.

[6] J.Y. Zhu, Y.B. Kang, and L.J. Shen, "Software Programming of Power Transformer Fault Diagnosis Based on Fuzzy Comprehensive Theory,"Transformer, vol. 47, pp. 41-44, .2010.

[7] Q.Y. Sun, H.G. Zhang, and X.R. Liu."Rough Sets and Genetic Algorithm in Fault Diagnosis of Transformer".Chinese Journal of Scientific Instrument, vol. 29, pp.2034-2040, 2008.

[8] Y. Y. Zhou, Q. Zhou, "Rough Set Theory Applied to Fault Diagnosis Rule Extraction for Distribution System," International Conference on High Voltage Engineering and Application, vol.9, pp. 750-753 , 2008.

[9] J.H.Nasiri and M.Mashinchi, "Rough Set and Data Analysis in Decision Tables,"Journal of Uncertain Systems, vol.3, pp. 232 -240, 2009.

[10] X. F. Qian, "The Research on Apply the Rough Set Theory to Transformer Fault Diagnosis," Nanjing:Power System and Automation of Nanjing University of Science, 2005.

[11] Y. P. Xiang and P. Liu." Oil Chromatographic Monitoring Found Transformer High Energy Discharge Fault". Transformer, vol.36, pp. 28-30, 1999.

[12] C. Hong and H. K. Shu," The Application of Chromatographic Analysis and Comprehensive Electrical Test Method to Transformer Fault Location",Transformer, vol. 45, pp. 38-40, 2008.

[13] D. R. Zhuang and X. Q. Li, "Transformer Fault Diagnosis Based on Attribute Reduction," Transformer, vol. 46, pp. 70 -73, 2009.

[14] N.Sun, "Research of Transformer Fault Diagnosis Methods Based on Rough Set", Guangdong Electric Power, vol. 23, pp.14-17, 2010.

[15] X. J. Li and Z. H. Jin "Development and Application Example Of Oil and Gas Analysis and Fault Diagnosis Technology For Transformer Equipment," Transformer, vol.48, pp.59-63, 2011.

[16] Q. P. Yang, W. D. Xue and Z. D. Lan, "Research of transformer Fault Diagnosis Technology," Transformer, vol. 39 2002.

[17] L. Y. Wei, and C. Xia "The Application of Comprehensive Artificial Intelligence Technology In Transformer Fault Offline Diagnosis ", Transformer, vol.46, pp.22-24, 2009.

[18] F. Wang "Attribute Reduction Method based On Improved Heuristic Genetic Algorithm " Dalian:Computer Application Technology ofDalian Jiaotong University,2007.

[19] J.M. Zhang and J.G. Liu "Rough Sets and BP Neural Network for Transformer Fault Diagnosis " Transformer, vol.46, pp.18-22, 2009.

[20] W.S. Li and Z. Yi."Rough Set Attribute Reduction Algorithm Based onGenetic Algorithm," Microelectronics and Computer, vol. 27,pp.71-74, 2010.

6