Fault Diagnosis of Power Transformer Based on Fuzzy Logic,

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					The Online Journal on Power and Energy Engineering (OJPEE)                                                    Vol. (1) – No. (2)



 Fault Diagnosis of Power Transformer Based on
  Fuzzy Logic, Rough Set theory and Inclusion
                 Degree Theory
                        Hossam A. Nabwey 3, E. A. Rady 1, A.M. Kozae 2, A. N. Ebady 3

                              (1) I.S.S.R, Cairo University, Cairo, Egypt.
          (2) Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.
    (3) Department of Engineering Basic science, Faculty of Engineering, Menofia University, Egypt.

Abstract- Power transformers are one of the most                 information, and these methods have different shortage. For
expensive components of electrical power plants and the          example, Petri network puts domain knowledge into a series
failures of such transformers can result in serious power        of producing rules; this can solve fault diagnosis problems.
system issues, so fault diagnosis for power transformer is       But when new fault or new information is coming, it will lead
very important to insure the whole power system run              to matching collision and combination blast because of the
normally. Due to information transmission mistakes as            slow speed of Petri network which resulted from vast rules.
well as arisen errors while processing data in surveying
and monitoring state information of transformer,                    In this paper, a new method aims to use fuzzy logic, rough
uncertain and incomplete information may be produced.            set theory and inclusion degree theory to infer useful rules for
Moreover, real time is another important characteristic so       power transformer fault diagnosis is presented. By using
as to meet high speed diagnosis requirements. Based on           fuzzy logic technique, the continuous attribute values are
these points, this paper presents an intelligent fault           transformed into the fuzzy values by automatically deriving
diagnosis method of power transformer based on fuzzy             membership functions from a set of data with similarity
logic Rough set theory and inclusion degree theory. By           clustering, then rough sets is applied to implement attributes
using a fuzzy logic technique, the continuous attribute          reduction and a simplified decision table is got, finally,
values are transformed into the fuzzy values by                  inclusion degree theory is used for extracting rules. The
automatically deriving membership functions from a set           application to fault diagnosis of transformer shows the
of data with similarity clustering, then rough sets is           proposed algorithm can find more objective and effective
applied to implement attributes reduction and a simplified       diagnostic rules from the quantitative data and has yielded
decision table is got, finally, inclusion degree theory is       promising results.
used for inducing logical rules from quantitative data. The
practical results show that the method is an effective                    II. REVIEW OF ROUGH SET THEORY
method for fault diagnosis of transformer and has yielded
promising results.
                                                                   The Rough Set Theory is a new mathematical tool
  Keywords- Transformer, Fuzzy logic, inclusion degree           presented to dispose incomplete and uncertainty problem by
theory, rule induction, fault diagnosis, Rough Set theory        Pawlak [3] in 1982. He defined the knowledge according to
                                                                 new point of view, and regarded it as partition of universe.
                    I. INTRODUCTION                              The concept of a rough set can be defined quite generally by
                                                                 means of topological operation, interior and closure, called
   Power transformers are one of the most expensive              approximations. Rough set theory can discover implicit
components of electrical power plants and are vital to make      knowledge and open out potentially useful rule by efficiently
the whole power system run normally. The failures of such        analyzing and dealing with all kinds of imprecise, incomplete
transformers can result in serious power system issues,          and disaccord information.
particularly those come without warning, cause service
disruptions and severe economic losses [4]. A diagnostic         A. Decision system
technique is needed to assess any degradation of the               Definition 1): In rough set theory, an information system
insulation materials on power transformer. Many artificial       can be considered as system S =(U, A, V, f) , where U is the
intelligence technologies such as neural network [11],           universe; A  C  D is the sets of fault attribute, the subset
Wavelet Analysis [2], gray clustering [7], decision tree [6],    C and D are disjoint sets of fault symptoms attribute and fault
Petri network [8], information fusion [5] have been applied to
                                                                 decision attributes respectively; V   Va ,where Va is the
transformer diagnosis and produced some results. But                                                   rR
transformers are complex system with uncertainty factors and     value set of fault symptoms attribute a ,is named the domain



Reference Number: W09-0011                                                                                                    45
The Online Journal on Power and Energy Engineering (OJPEE)                                                           Vol. (1) – No. (2)




of attribute a .Each attribute a  A ; f is an information                           
                                                                        If D Bx /A x p 1 and i  k the rule “if Ai then B j ” can
                              f  x,a   Va
function f : UxA  V , and                   , in which x  U .       be obtained on condition that B ji can be found to meet the

                                                                                                    1                
B. Equivalent relations
   Definition 2): In decision system S = (U, A, V, f), every                                    
                                                                      requirement of D B ji /A i    D B j /Ai
                                                                                                   
                                                                                                    j 1
                                                                                                                     .
                                                                                                                      
                                                                                                                      
attributes subset, an indiscernible relation (or equivalence
relation) IND(B) defined in the following way:
            x,y   Ux U a  B, f  x, a   f  y, a 
                                                                                  IV. FUZZIFICATION OF ATTRIBUTES
IND(B) =                                                       (1)
The family of all equivalence relation of IND(B), a partition           The fuzzy logic theory was first proposed by Zade in
determined by B, denoted by U/IND(B),[x]B can be                      1965[12]. It is primarily concerned with quantifying and
considered as equivalence classes, and defined as follows:            reasoning using natural language in which words can have
           x B = y  U a  B, f  x, a   f  y, a      (2)
                                                                      ambiguous meanings. This can be thought of as an extension
                                                                      of traditional crisp sets in which each element must either be
And                                                                   in or not in a set. Fuzzy set concepts are often used to
           x  IND ( B ) =   x B                           (3)    represent quantitative data expressed in linguistic terms and
                                                                      membership functions in intelligent systems because of its
                                                                      simplicity and similarity to human reasoning. They have been
C. Reduction and Core                                                 applied to many fields such as manufacturing, engineering,
   Definition 3): In decision system S=(U, A, V ,f), Let              diagnosis, and economics. In this paper, a fuzzy discretization
 b  B and B  A , if posB(D) = posB −{b}(D), attribute b is          method is proposed. A learning method is given for
redundant to B, which relatives to D, otherwise the attribute b       automatically deriving membership functions from a set of
is indispensable.                                                     data with similarity clustering [1].
If IND(B) = IND(A) and POSB (D) ≠ POSB −{b} (D) , then B                For a m-dimensional attribute, the jth attribute value can be
is called a reduction for information system S , are denoted as       describes as (x1j, x2j…xnj), where n is the number of objects.
RED( A) ; the intersection of these reduction sets is called          The fuzzification method of continuous attributes proceeds as
core, denoted as CORE =  RED( A) .                                   follows:
                                                                        Step1: Sort the attribute values in an ascending order. The
                                                                      modified order after sorting is then x1j, x2j…xnj.
          III. THE INCLUSION DEGREE THEORY
                                                                         Step2: Find the difference between adjacent data. The
  The inclusion degree theory was proposed by Zhang                   difference between adjacent data provides the information
Wenxiu, a professor of Xi’an Jiaotong University, in 1995. It         about the similarity between them. for each pair xij and x(i+1)j
has been applied to several fields in recent years [9, 10].           ,(i = 1,2,…, n-1), the differences is diffij = (x(i+1)j- xij ).
  Suppose X is an object set, Ai  X (i  k ) is the partition
                                                                        Step3: Find the value of similarity between adjacent data.
                                               k                      In order to obtain the value of similarity between adjacent
of X. That is, Ai I A j = (i  j ) , and U Ai  X . Ax is a
                                             i 1                     data, we convert each distance diffij to a real number sij
                                                                      between 0 and 1 according to the following formula:
partition of X, Ax   Ai : i  k  and D is the total partition of
                                                                               diffij
X. x and x are two partitions of X, Ax   Ai : i  k  and
   A           B                                                              1 
                                                                                             diffij  C . ij
                                                                        sij   C . ij                                           (8)
Bx   Bi : j 1 . Bx depends on Ax  Ax  Bx  if Ai  B j .                
                                                                              0            diffij f C . ij
                                
  D B j /Ai and D Bx /A x are the inclusion degree of X
                                                                              
                                                                        Where sij represents the similarity between xij and x(i+1)j,
and D respectively. The definition of inclusion is:                    ij is the standard derivation of diff’s, and C is a control
               k  1                    
             
  D Bx /A x     D B j /Ai
             i 1  j 1
                                      
                                        
                                                              (4)     parameter deciding the shape of the membership functions of
                                                                      similarity. A large C causes a grater similarity.
                                       
  A x  Bx , D  Bx /A x   1                                (5)       Step4: Cluster the data according to similarity. Here we use

                  
  A x x Bx = Ai I B j : i  k , j  1                        (6)
                                                                                                                      
                                                                      the cut of similarity to cluster the data. If sij then divide the
                                                                      two adjacent data into the same groups; else put them into
   Ax x Bx  Ax , Ax x Bx  B x                               (7)     different groups. After the above operation, the data will be


Reference Number: W09-0011                                                                                                          46
The Online Journal on Power and Energy Engineering (OJPEE)                                                                            Vol. (1) – No. (2)




clustered into the l j , where l j means the jth produced fuzzy                         from quantitative data for the power transformer. According
                                                                                        to the historical fault data of the power transformer, the fault
region.                                                                                 decision table is shown in Table1. Here, the condition
                                                                                        attributes are concentrations (ppm by volume) of dissolved
   Step5: Determine membership functions. For simplicity,                               gases in the insulation oil, such as H2, CH4, C2H6, C2H4, and
triangle membership functions are used here for each                                    C2H2. The decision attribute (D) is the fault class of the
linguistic variable. A triangle membership function can be                              transformer, where “0” represents the fault of local discharge,
defined by a triad (b,a,c). For the hth fuzzy region, the                               “1” represents the fault of low-energy discharge, “2”
parameters {bh, ah, ch} can be defined as:                                              represents the fault of high-energy discharge, “3” represents
                                                                                        the fault of low-temperature superheat, “4” represents the
                g 2             sij  s(i 1) j                                        fault of medium-temperature superheat and “5” represents the
     xij .sij   x(i 1) j .                     x gj .s( g 1) j                     fault of high-temperature superheat.
bh              i 1                  2                             (9)
                      g  2 sij  s(i 1) j                                                    Table 1. A decision table for the transformer fault
               sij                         s( g 1) j
                      i 1         2                                                      U        H2      CH4    C2H6      C2H4      C2H2           D
                                  bh  xij
                                                                                          X1
                  ah  bh                                                                         68       8       3         8         11           2

                                                
                                                                    (10)
                               1   h xij                                                X2     49.7      18.5   4.4         60        12           1
                                                                                          X3     33.9      36.7   31.5      39.2        0            5
                                          x gj  bh                                       X4       47      75.6   47.1      190.6       0            3
                   ch  bh 
                                                
                                                                                (11)      X5     18.7      7.5    1.2       1.7         0            0
                                    1   h x gj
                                                                                          X6       24      27.9   24.3        30        0            5
  Where                                                                                   X7       80      95.4   33.1      150         0            3

                                  
 h xij   h x gj  min sij , s i 1 j , ...., s g -1 j , for 1th                   X8
                                                                                          X9
                                                                                                   34
                                                                                                   42
                                                                                                           60.5
                                                                                                            62
                                                                                                                  24.3
                                                                                                                    5
                                                                                                                            69.3
                                                                                                                              63
                                                                                                                                        0
                                                                                                                                        73
                                                                                                                                                     4
                                                                                                                                                     1
fuzzy    region,              
                          h x  b1  1 ;             for   the       l j th   fuzzy    X10       55       57      37       90         0            3


            
region,  h x  bij  1 .                                                                 The membership functions for each condition attribute are
                                                                                        given according to previous algorithm. Take the attribute H 2
                                                                                        and C2H4 as an example, the membership functions are shown
  Step6: Find the membership value. The attribute value                                 in Fig.1 and Fig.2.
vij (i=1, 2, …., n; j=1, 2, …., m) can be described as :
                                                   l
                   1
                    ij
                               2
                              ij                 ijj
           vij                     .......                                  (12)
                   F1
                    j
                               2
                              Fj                   l
                                                  Fj j
          h                                      h
  Where F j is the hth fuzzy region of is c j , ij is the
                                                                   h
                                          F
membership value of xi  U in fuzzy region j .                                                      Fig.1 The membership functions of H2

      V. POWER TRANSFORMER FAULT DIAGNOSIS

   In the normal operation of the transformer, the released
gases are methane (CH4), ethane (C2H6), Hydrogen (H2),
ethylene (C2H4), and acetylene (C2H2) and so on. When there
is an abnormal situation such as occurring a fault, some
specific gases are produced more than in the normal operation
and the amount of them in the transformer oil increase. The
increase in the amount of gases results in saturation of the
transformer oil and no more gas can be dissolved in oil.                                            Fig.2 The membership functions of C2H
  In this section, an example is given to show how the                                    So the quantitative values of each object are transformed
proposed method can be used to generate diagnostic rules                                into fuzzy sets. Take the attribute H2 in x3 as an example. The


Reference Number: W09-0011                                                                                                                               47
The Online Journal on Power and Energy Engineering (OJPEE)                                                         Vol. (1) – No. (2)




value “33.9” is converted into a fuzzy set (0.28/L+0.42/M)                      Table 3. Simplified fuzzy decision table
using the given membership functions. Results for all the
objects are shown in Table2.                                               U            CH4               C2H6              D

                                                                           X1              1/L            0.99/L            2
               Table 2. Fuzzy decision table                               X2          0.55/L             0.91/L            1
                                                                           X3          0.55/L             0.07/M            1
         U      H2      CH4     C2H6     C2H4     C2H2   D
                                                                           X4          0.07/M             0.91/L            1
         X1   0.81/H    1/L     0.99/L   0.99/L   1/M    2                 X5          0.07/M             0.07/M            1
         X2   0.71/M   0.55/L   0.91/L   0.98/M   1/M    1                 X6          0.68/M             0.28/M            5
         X3   0.71/M   0.55/L   0.07/M   0.98/M   1/M    1                 X8          0.68/M             0.35/H            5
         X4   0.71/M   0.07/M   0.91/L   0.98/M   1/M    1                X14              1/H             1/H              3
         X5   0.71/M   0.07/M   0.07/M   0.98/M   1/M    1                X15              1/L             1/L              0
         X6   0.28/L   0.68/M   0.28/M   0.09/L   1/L    5                X16          0.04/L             0.93/M            5
         X7   0.28/L   0.68/M   0.28/M   0.57/M   1/L    5                X18          0.41/M             0.93/M            5
         X8   0.28/L   0.68/M   0.35/H   0.09/L   1/L    5                X20              1/H            0.07/M            3
         X9   0.28/L   0.68/M   0.35/H   0.57/M   1/L    5                X21              1/H            0.51/H            3
        X10   0.42/M   0.68/M   0.28/M   0.09/L   1/L    5                X22          0.22/M             0.93/M            4
        X11   0.42/M   0.68/M   0.28/M   0.57/M   1/L    5                X23          0.03/H             0.93/M            4
        X12   0.42/M   0.68/M   0.35/H   0.09/L   1/L    5                X26          0.13/M             0.88/L            1
        X13   0.42/M   0.68/M   0.35/H   0.57/M   1/L    5                X27          0.13/M             0.1/M             1
        X14   0.87/M    1/H      1/H      1/H     1/L    3                X28          0.15/H             0.88/L            1
        X15   0.87/L    1/L      1/L      1/L     1/L    0                X29          0.15/H             0.1/M             1
        X16   0.66/L   0.04/L   0.93/M   0.36/L   1/L    5                X30          0.42/M             0.9/H             3
        X17   0.66/L   0.04/L   0.93/M   0.48/M   1/L    5
        X18   0.66/L   0.41/M   0.93/M   0.36/L   1/L    5             By application of the inclusion degree theory to the
        X19   0.66/L   0.41/M   0.93/M   0.48/M   1/L    5           Simplified fuzzy decision table shown in table 2,
        X20     1/H     1/H     0.07/M    1/H     1/L    3
                                                                     The results of partitions of U divided by CH4 are as follows:
        X21     1/H     1/H     0.51/H    1/H     1/L    3
        X22   0.27/L   0.22/M   0.93/M   0.82/M   1/L    4
        X23   0.27/L   0.03/H   0.93/M   0.82/M   1/L    4                 * 
                                                                              {1, 9},{2, 3},{4, 5},{6, 7},{11},{14},{15}
                                                                                                                         
                                                                       CH 4                                            ,
        X24   0.42/M   0.22/M   0.93/M   0.82/M   1/L    4
                                                                              {8, 12, 13},{10},{16, 17},{18, 19},{20} 
                                                                                                                        
        X25   0.42/M   0.03/H   0.93/M   0.82/M   1/L    4
        X26   0.86/M   0.13/M   0.88/L   0.95/M   1/H    1
                                                                     The results of partitions of U divided by C2H6 are as follows:
        X27   0.86/M   0.13/M   0.1/M    0.95/M   1/H    1

                                                                                {1},{2, 4},{3, 5, 12},{6},{7},{8},{9},{13}
        X28   0.86/M   0.15/H   0.88/L   0.95/M   1/H    1
                                                                             *                                            
        X29   0.86/M   0.15/H   0.1/M    0.95/M   1/H    1             C2 H 6                                            
        X30   0.42/M   0.42/M   0.9/H    0.39/M   1/L    3                      {10, 11, 14, 15},{17, 19},{16, 18},{20} 
                                                                                                                          
        X31   0.05/H   0.42/M   0.9/H    0.39/M   1/L    3

                                                                       The results of partitions of U divided by D are as follows:
   In order to simplify the fuzzy decision table it is required to
find the insignificant conditional attributes in the diagnoses,                  {1},{2, 3, 4, 5, 16, 17, 18, 19},{9}, 
                                                                                                                        
i.e. it is required to find a minimum number of conditional                 D*                                         
attributes, but, are still able to diagnose the problem. This is                 {8, 12, 13, 20},{14, 15},{6, 7, 10, 11}
                                                                                                                        
done by number of conditional attributes should be removed
each time and the decision table should be checked to make           Then, all kinds of partitions of U divided by different
sure any contradiction has not occurred. In this paper               attributes are as follows:

                                                                                                                       
computing the reduct is done by using software called                                         *     *       *      *
ROSETTA (a Rough Set tool kit for analysis of data). The                           U  CH 4 , C2 H 6 , CH 4 xC2 H 6
GA is adopted in Reduction process. The simplified fuzzy
                                                                                    *      *     *     *
decision table is shown in table 3.                                     Since CH 4 f D , C2 H 6 f D then It is impossible to
                                                                     form decision rules only according to one of CH4 or C2H6.



Reference Number: W09-0011                                                                                                        48
The Online Journal on Power and Energy Engineering (OJPEE)                                                  Vol. (1) – No. (2)




But   CH 4*xC2H6*  D*      shows that it is possible to
                                                                                       REFERENCES

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                    VI. CONCLUSION
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Reference Number: W09-0011                                                                                                 49