chen_fault section estimation using fuzzy matrix-based reasoning methods_2011

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 26, NO. 1, JANUARY 2011 205

Fault Section Estimation Using FuzzyMatrix-Based Reasoning Methods

Wen-Hui Chen, Member, IEEE

AbstractA technique of fuzzy reasoning via rule matrix trans-formations has been developed to estimate fault sections for dis-tribution substations. This study extended the application of faultdiagnosis from binary reasoning to fuzzy reasoning. In the infer-ence procedures, the causalities of fault sections and the actions ofprotective devices were first represented by the fuzzy cause-effectnetworks (FCE-Nets). After performing some simple matrix oper-ations, the possible fault sections were estimated. This proposedapproach offers a clear framework, rapid reasoning, the ability tohandleuncertainty, and it has no problem with convergence duringthe diagnosis procedure.

Index TermsBoolean rule matrix, cause-effect networks, fault

diagnosis, fuzzy reasoning.

I. INTRODUCTION

THESE DAYS, most power systems are equipped with

supervisory-control-and- data-acquisition (SCADA)

systems for operational improvement applications. When a

fault occurs, it is imperative to limit the impact of outages to

the minimum and to restore the fault area as soon as possible.

This requires that the fault segment be identified from informa-

tion provided by protective devices. Various approaches have

been proposed to address fault diagnosis problems for powersystems. Among those techniques, rule-based expert systems,

artificial neural networks (ANNs), genetic algorithms (GAs),

and their hybrid models are commonly used. Although many

works have been performed for power system fault diagnosis,

recent research interests are especially focused on how to deal

with uncertainty inherent in the operation of protective devices.

In [1] and [2], the authors used fuzzy relations represented by

sagittal diagrams to deal with uncertainty for power transmis-

sion networks, and good results were obtained even in device

malfunctions. In order to apply an approach adaptive to network

topology change, the authors in [2] extended their work by in-

tegrating time-sequence information, protective schemes, and

network topology to a 3-D matrix. In [3], the authors presenteda hybrid fuzzy rule-based expert system for transmission-level

fault diagnosis. The fuzzy concept in this paper is to assign each

rule a subjective assigned possibility for the expert system to

Manuscript received March 26, 2010; revised July 10, 2010; accepted July13, 2010. Date of publication September 07, 2010; date of current version De-cember 27, 2010. This work was supported by the National Science Councilof Taiwan (NSC98-2221-E-027-072 and NSC98-2218-E-002-012). Paper no.TPWRD-00222-2010.

The author is withthe Graduate Institute of Automation Technology, NationalTaipei Universityof Technology, Taipei, Taiwan (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRD.2010.2061873

perform reasoning. The fuzzy reasoning process was carried out

by performing max-product composition.

Petri nets are a useful tool for event modeling in a concur-

rent structure. However, it lacks the ability to handle uncer-

tainty in information. As such, the authors in [4] applied fuzzy

Petri nets approach for fault diagnosis in transmission networks.

They combined fuzzy logical reasoning with Petri nets to deal

with uncertainty existing in the operation of protective devices.

The analysis of cause-and-effect relationships for fault diag-

nosis has been a favorite application in [5] and [6]. In [7] and [8],

a fast fault diagnosis algorithm based on cause-effect networks

(CE-Nets) was proposed for distribution substations. Fault diag-

nosis can be considered as a classification task. The authors in

[9] have successfully applied a data-mining-based fuzzy classi-

fication algorithm to handle fault cause identification problems

and demonstrated good results.

To summarize, previous research tended to use a fuzzy re-

lation to deal with the uncertainty in the operation of protec-

tive devices. In addition, they preferred using subjective pos-

sibility given by the operators as a certainty factor in a rule.

Note that many previous works assumed that there is no uncer-

tainty between the operations of the relays and circuit breakers

(CBs). Fault diagnosis problems for power systems range from

power equipment [10], [11]; substations [12], [13]; distributionnetworks [14]; and transmission networks [15] to power plants

[16]. For different applications, the characteristics of a problem,

domain knowledge, and concerns would vary accordingly. To

endow CE-Nets with inexact reasoning ability, in this paper, a

new technique using the fuzzy rule matrix transformation was

proposed for fault diagnosis in distribution substations.

II. FUZZY CAUSE-EFFECT NETWORKS (FCE-NETS)

A. Review of Cause-Effect Networks (CE-Nets)

CE-Nets are graphic-modeling methods for representing the

causalities between faults and the actions of protective devices[7], [8]. They consist of three kinds of nodes: 1) fault section

node, 2) relay node, and 3) CB node. If two nodes and

are related, a directed arc is placed on the graph from node

to node , indicating the relation. There are three kinds of di-

rected arcs: protected-by arc, cause arc, and backup-by arc, that

describe different connections between two nodes.

A CE-Net can be represented by a binary matrix. The trans-

pose of the matrix is equivalent to the reversal of all arrows

in the associated CE-Net. Therefore, we can use this property

to achieve backward reasoning to estimate the possible fault

causes. A CE-Net can be easily derived from the system con-

figuration.

0885-8977/$26.00 2010 IEEE


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206 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 26, NO. 1, JANUARY 2011

Fig. 1. Simple model distribution system.

Fig. 2. CE-Net that represents the model system.

A simple model distribution system, as shown in Fig. 1, is em-ployed to illustrate the concept. The model system is protected

by overcurrent (CO) relays, low-energy over current (LCO) re-

lays, and CBs. Suppose that a fault occurs at the feeder F1

and causes the action of the relay CO1, which trips the circuit

breaker CB1. If CB1 fails to open at this moment, the backup

protective relay CO3 will operate to trip the circuit breaker CB3.

This event is described in the portion of the dotted outline in

Fig. 2. After considering all possible fault sections, the CE-Net

that represents the model system can then be derived.

B. Concept of FCE-Nets

Since human knowledge can contain linguistic terms withsome degree of uncertainty, it is desired to express the degree

of certainty of a rule as a real number between 0 and 1, and in-

corporate such an expression in the inference.

A rule consists of an antecedent part and a consequence part,

with the antecedent parts describing causes and the consequent

parts describing effects. For example, a rule could be IF (relay

CO1 operates) THEN (circuit breaker CB1 tripped). However,

in some situations, CB1cannot be asserted to have tripped, when

CO1 operates due to incorrect settings or equipment malfunc-

tion. In the classic (nonfuzzy) inference, when the condition in

the antecedent part matches the effect, its consequent part is as-

serted. This is not necessarily true for protective device opera-

tion. This uncertainty regarding the operation of protective de-vices should be considered for practical applications.

Fig. 3. Trapezoidal fuzzy number.

Fig. 4. Membership functions for the linguistic term set.

The certainty factor refers to the degree of confidence thatthe event will occur. As operators knowledge may contain lin-

guistic terms with some degree of uncertainty, the use of cer-

tainty factor is a good way to describe the uncertainty in nu-

merical expression. In this study, the certainty factor is used to

represent the uncertain characteristic in conditions and rules.

The assignment of a certainty factor can be intuitively given

by experts using a linguistic term set [17] or based on some

mathematical operations, such as the frequency of occurrences

from historical data. For example, the operators may say that a

fault causing the main protective relay to operate is extremely

true or that the CB that will be tripped is very true. They cannot

precisely tell you how true it is in a quantitative way. Table Ilists the linguistic terms and their corresponding fuzzy num-

bers. A fuzzy number can be characterized as a four-tuple

, where denotes the interval in which the mem-

bership value is equal to 1, and and indicate the left and

right width of the trapezoidal distribution. Fig. 3 shows a trape-

zoidal fuzzy number parameterized by . The cor-

responding membership functions are given in Fig. 4.

The other way to decide the certainty factor is based on the

frequency of occurrences from historical data. For example,

from historical data, the frequency of occurrences of a fault

hitting the feeder F1 was up to 20 times, and only in 19 times,

the fault has caused the operation of relay CO1. According to

the statistical data, we can calculate the certainty factor of therule as 19/20 or 0.95. With the certainty factor, the rule can


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CHEN: FAULT SECTION ESTIMATION USING FUZZY MATRIX-BASED REASONING METHODS 207

TABLE IA NINE-MEMBER LINGUISTIC TERM SET

Fig. 5. Associated graph for fuzzy implication rules.

Fig. 6. Basic node-arc relations in FCE-Nets.

be expressed as IF (a fault at F1) THEN (relay CO1 operates)

0.95)

Suppose that and are node conditions in a given FCE-

Net. The general formulation of a fuzzy implication rule can be

denoted as

(1)

This infers that the truth of condition implies the truth of

condition with a certainty factor . The value of a certainty

factor is between 0 and 1, which indicates the strength of thebelief in the rule. The larger the value is, the more reliable the

rule is. The associated graph for (1) is shown in Fig. 5.

There are three basic node-arc relations of FCE-Nets, as

shown in Fig. 6.

Generally, the choice of a good certainty factor needs some

expertise. In order to avoid a bias in assigning the certainty fac-

tors, it is suggested to determine the value based on experts or

senior operators experience and historical data.

Since operators knowledge can contain some degree of un-

certainty, a rule expressed for the linguistic knowledge can be

described as

IF (a fault at F1) THEN (relay CO1 operates)

For different occasions, the same rule may change to

IF (a fault at F1) THEN (relay CO1 operates)

or we can express it in a general form:

IF (a fault at F1) THEN (relay CO1 operates) (

or ET or VT or T, )

The determination of which linguistic terms

to be used is based on oper-

ator experience and the frequency of occurrences. In otherwords, according to confirmed cases and operator experience,

the value of a certainty factor can be different in a rule.

Examples of node-arc relations are given below.

IF (a fault at F1) THEN (CO1 operates)

IF (CO1 operates) THEN (CB1 tripped) .

A SCADA system typically consists of a master station,

communication networks, remote terminal units (RTUs), and a

number of transducers. A transducer is a device which provides

a transformed output in response to a specific quantity, such

as feeder currents and bus voltages. For example, a current

transducer provides the RTU with current information by con-

verting current transformer (CT) signals to the value that can be

handled by a RTU, and then the RTU transmits this information

to the control center through communication networks.

In the signal transmission process, there may be a data mis-

match between the measured quantity of a substation and the

SCADA computer of the control center due to transducer im-

perfection or software conversion errors. For example, if a fault

occurs at feeder F1 in a substation, the circuit breaker connected

to feeder F1 will be tripped, which leads to the current of feeder

F1 reaching zero. In normal situation, this zero value will be dis-

played in the control center. When the current transducer asso-

ciated with feeder F1 has improper installation or ill-calibration,

the practical feeder current could not correctly be displayed in

the SCADA computer. As a result, it may show a very small

value instead of zero.

Conventional rule-based approaches do not allow linguistic

variables to appear in the condition of a rule, and have very

little power in dealing with imprecise information. In order to

deal with this situation, the proposed approach utilizes fuzzy

membership functions to represent measured quantities derived

from SCADA systems instead of specifying a fixed value, and

use fuzzy inference techniques to perform inexact reasoning in

the proposed inference algorithm.

As an opened CB leads to no current passing through it, the

degree of truth in the condition circuit breaker CB1 is tripped

can be determined by the degree of truth that the value of currentpassing through CB1 is near zero. A membership function deter-

mining the degree of CB in open status is shown in Fig. 7. For

example, suppose the value of a current passing through CB1

is 150 A. One can therefore infer that the degree where CB1

tripped is 0.

The certainty factor can be viewed as the degree of confidence

that the event will occur. The assignment of a certainty factor

can be intuitively given by experts or based on some mathematic

operations, such as the frequency of occurrences from historical

data. Generally, the choice of a good certainty factor needs some

expertise. In order to avoid a bias in assigning the certainty fac-

tors, it is suggested to determine the value based on experts or

senior operators experience and historical data.


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Fig. 7. The membership function for CB in open status.

Fig. 8. The associated FCE-Net for the model system.

C. Matrix Representation of FCE-Nets

The rules with linguistic certainty factors can be represented

as the fuzzy rule matrix . This matrix describes the relations

between causes and effects of FCE-Nets. Once the fuzzy rule

matrix is established, the diagnosis algorithm can then be per-

formed by matrix operations.

A fuzzy rule matrix associated with conditions is a -by-

matrix with all ones on the diagonal by reflexivity because each

condition implies itself. The entry means that con-

dition implies condition with the certainty factor , and

indicates that there is no implication between

and . A fuzzy value in the entry of the fuzzy rule matrix givesthe degree of confidence in how condition implies the truth

of condition . The simplemodelsystem inFig. 1 isused again

as an example to illustrate the concept of matrix representation

of FCE-Nets. The associated FCE-Net for the model system is

shown in Fig. 8. The set of conditions is listed in Table II.

According to the connectivity of each node in Fig. 8, the fuzzy

rule matrix that represents the FCE-Net can be built as: see equa-

tion at the bottom of the page

TABLE IITHE SET OF CONDITIONS AND THEIR DESCRIPTIONS

III. REASONING WITH FUZZY RULE MATRICES

In this section, an inexact reasoning algorithm via fuzzy rule

matrix transformation for FCE-Nets is presented. Assume that

a FCE-Net contains a set of conditions. Each condition con-

tains a high level of linguistic expression for humans to use (e.g.,

relay CO1 operates). However, this string expression is in-

convenient and inefficient for computers to process. Therefore,

we defined some vectors to transform string based conditions

into numerical vectors for reasoning and computation. The fol-

lowing vectors and matrix operations are defined to develop the

inference procedures.

1) Truth State Vector : The truth state vector is em-

ployed to represent the fault symptom with the status of protec-

tive devices. This vector contains the truth values for a set of

conditions, . Each component is defined by

, where is the truth value of condition .

2) Fault Node Vector : The fault node vector is de-

fined to represent the fault section nodes in a given FCE-Net.

This vector contains Boolean valued components for a set of

conditions. If node condition is associated with a fault sec-

tion node, the value of is assigned to 1, otherwise is 0

if

otherwise

This vector is defined for extracting the nodes that belong to

the fault section node through fuzzy intersection operation.

3) Backup Node Vector : The backup node vector is

employed to represent the backup relay nodes in a given FCE-

Net. This vector contains Boolean valued components for a


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set of conditions. If node condition is associated with a

backup relay node, the value of is assigned to 1, otherwise

is 0.

if

otherwise

This vector is defined for extracting operated backup relaysthrough fuzzy intersection operation.

4) Fuzzy Min-Operator : The fuzzy min-operator for two

column vectors and on the corresponding entry is written

as . For example,

In the inference procedures, there is a process to remove the

status of operated backup relays in the truth state vector if the

action of the backup relay is caused by a main relay failure.

This process is used to discriminate the source that activatesbackup relays. This discrimination can be carried out by using

the intersection operation. As such, we introduced this operator

to perform the required computation for deriving a systematic

inference algorithm.

5) Fuzzy Multiplication Operator : The fuzzy multipli-

cation operator for two matrices and is written as

The row-by-column matrix product is perfromed by replacing

multiplication and addition with the min and max operations,

repectively. For example,

The fuzzy multiplication operator is used for performing truth

state transformation on the transpose of the fuzzy rule matrix

and a truth state vector that contains the degree of truth in its en-

tries. The entry of a fuzzy rule matrix represents an implication

between two conditions. As truth state contains in-

formation of fault symptoms, the function of this operator is to

perform a composition transformation that propagates the truth

state leading backward into the fault cause. In this study, we

adopted max-min operation to replace real multiplication and

addition in arithmetic matrix multiplication. The inference pro-cedures are summarized as below.

At first, we built a -by- fuzzy rule matrix according to

the given FCE-Nets, with rows and columns indexed by nodes.

If an arc presented, we put the certainty factor in cell

; otherwise we left as zero. denotes a

directed arc from node to node . According to fault symp-

toms, we put the truth value of each condition in the entry

to derive the truth state vector. Calculate transformation vector,

using (2). The meaning of this transformation is to propa-

gate the truth state of given fault symptoms leading backward

into the fault cause. The vector contains information that

causes the fault symptoms.

(2)

Then, wecompared with . The step ofcomparing

with with was to check if there was a device failure. If

equaled with , this means that there was no failure operation

at feeder protection; otherwise, failures did occur. If did

not equal with , the process went to update and assign it

to using (3); otherwise, assigned to .

(3)

Fuzzy min-operator in (3) is used to remove the status of op-

erated backup relays in the truth state vector when the action of

the backup relays is caused by a main relay failure. The fuzzy

multiplication operator is used for performing truth state trans-

formation on the transpose of the fuzzy rule matrix and the truth

state vector operated on a backup relay node by fuzzy min-op-

erator. As such, the updated transformation vector using (3) is

to remove the status of backup relays from fault section candi-

dates.

As the vector contained information about fault causes,

we selected only fault section nodes with the entry value greaterthan a threshold as estimated fault sections. The selection

of fault section nodes from can be achieved by computing

. As suggested in [3], the possibility of a solution below

0.8 would be meaningless. The threshold value for selecting

fault sections was set to 0.5 in this study. This value was suit-

able after testing on many runs. The flow chart of the inference

procedures is shown in Fig. 9.

IV. CASE STUDY

A typical Taipowers secondary substation, as shown in Fig.

10, is employed to illustrate the reasoning process of the pro-

posed approach. The substation is composed of three sub-trans-mission lines, three main transformers, two tie circuit breakers,

one 69 kV primary bus bar, and three 11.4 kV secondary bus

bars. Each secondary bus bar contains five radial distribution

feeders. Each feeder is protected by three CO relays and one

LCO relay. For example, feeder F1 is protected by three CO

relays: CO1-A, CO1-B, and CO1-C as well as one LCO relay:

LCO1. The protective relays for 11 kV bus bars also serve as the

back-up protection for their connected feeders. This study case

is the same as case 2 in [8] except there is missing information

in this case.

Operated relays: CO3-A, CO3-B, CO3-C, COM1-A,

COM1-B, COM1-C, CO8-B, CO8-C

Tripped circuit breakers: CB-M1, CB-8

Failure devices: LCO8, CB-3

Missing information: the status of LCO8, CO8-B, CO8-C

A. Fault Diagnosis by FCE-Nets Approach

In this example, transformer TR #2 has de-energized for

maintenance and CB Tie-1 is in closing status. A three-phase

fault occurs at the feeder F3. Relays CO3-A, CO3-B and

CO3-C operate correctly while the circuit breaker CB-3 fails

to trip. Owing to the tripping failure of CB-3, the backup

breaker CB-M1 is tripped by the relays COM1-A, COM1-B

and COM1-C. Meanwhile, a double-line to ground fault at

phases B and C happens at feeder F8, which causes CO8-B andCO8-C operating to trip CB-8. However, the status of relays,


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Fig. 9. The flow chart of the proposed inference procedures.

Fig. 10. The distribution substation for the study case.

LCO8, CO8-B and CO8-C, is missing. The set of conditions is

listed in Table III.

The certainty factor is determined by operators according to

their knowledge and the frequency of occurrences from con-

firmed events of historical data, given in Table IV. It is assumed

that the event in the same category has the same occurrence fre-quency.

TABLE IIITHE SET OF NODE CONDITIONS

TABLE IVCONFIRMED EVENTS FROM SCADA SYSTEM DATABASE

The corresponding FCE-Net associated with this fault case is

shown in Fig. 11. The inference procedures are described step

by step as follows.

Step 1: Step 1 At first, we build the fuzzy rule matrix

according to Fig. 11. As the dimension of the matrix

is 51-by-51, only nonzero entries of the matrix are

listed in Table V.

Step 2: Step 2 The currents for the related devices are listed

in Table VI.

The possibility of a condition that a relay operates

is evaluated according to the device current and

the membership value that the device is in its open

status, set in Fig. 7. The nonzero entries of truthstate vector are listed in Table VII.


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Fig. 11. The associated FCE-Net of the study case.

Step 3: Step 3 The fuzzy truth state transformation can be

obtained using (2), and the results are listed in

Table VIII.

Step 4: Step 4 As these two vectors, and , are not

equal, the inference procedure goes to update the

fuzzy truth state transformation using (3). Then, we

assign the updated values to . The value of vector

is listed in Table IX.

Step 5: Step 5 As the vector contains information about

fault causes, the fault sections can be retrieved by

selecting fault section nodes from with entryvalue greater than 0.5. This can be achieved by first

performing , and then selecting the entry

value greater than 0.5 as estimated fault sections.

The nonzero entries of the fault node vector are

listed in Table X.

The results after selecting the fault section nodes by

performing are listed in Table XI

From Table XI, the estimated fault sections can be

obtained by selecting the entry value greater than

0.5. Therefore, feeders F3 and F8 are selected as

fault sections, i.e., multiple faults at F3 and F8 are

estimated. The inference results are summarized in

Table XII.

B. Fault Diagnosis by CE-Nets Approach

In order to make comparisons with CE-Nets based approach,

the method presented in [8] was applied to this fault case. The

associated CE-Nets and the rule matrix are the same as those of

case 2 in [8]. The inference results using CE-Nets approach are

summarized in Table XIII.

Note that the fault situation has missing signals, which is dif-

ferent and more complicated than that in case 2 of [8]. From

the experimental results, as shown in Tables XII and XIII, the

proposed FCE-Nets can correctly identify the fault sections, F3

and F8, while the approach using CE-Nets fails to find the faultsection F8 due to incomplete information.

TABLE VNONZERO ENTRIES OF FUZZY RULE MATRIX

TABLE VIDEVICE CURRENTS OF THE STUDY CASE

TABLE VIINONZERO ENTRIES OF TRUTH STATE VECTOR

TABLE VIIIENTRY VALUES OF TV


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TABLE IXENTRY VALUES OF T

TABLE XNONZERO ENTRIES OF FAULT NODE VECTOR

TABLE XIENTRY VALUES OF T F

In general, CE-Nets approach has some advantages in fault

diagnosis but only work well when the fault information iscomplete and certain. FCE-Nets approach is an extension of

TABLE XIIESTIMATED RESULTS USING FCE-NETS APPROACH

TABLE XIIIESTIMATED RESULTS USING CE-NETS APPROACH

CE-Nets approach with the ability of handling uncertain and

incomplete information that may happen in power system oper-

ation. This example demonstrates that the proposed FCE-Nets

approach outperforms the method presented in [8].

When the information is complete, both fuzzy (FCE-Nets)

and non-fuzzy (CE-Nets) approach can obtain the correct re-sults. In the situation where a status signal is missing, CE-Nets

approach fails to find the fault sections. From this study, it is ob-

served that the proposed algorithm has the ability to infer mul-

tiple faults even when a failure device and incomplete informa-

tion or missing signals occur. The merits of the proposed ap-

proach compared to the approach in [8] are summarized below.

1) The proposed approach can handle linguistic terms in con-

ditions and rules. It is more flexible than that in [8] as it al-

lows the use of certainty factors in a rule rather than crisp

numerical values.

2) The proposed approach provides the results with quantita-

tive confidence level for all estimated fault sections, which

makes the results more conclusive.3) The proposed approach successfully integrates fuzzy rea-

soning with graphical model representation. Therefore, the

proposed approach has the ability to handle incomplete and

uncertain information in practical problems with fast com-

putation speed.

V. CONCLUSION

In this study, we developed fuzzy CE-Nets and presented a

new reasoning algorithm for fault diagnosis in distribution sub-

stations. The proposed approach is capable of representing un-

certain knowledge and performing fuzzy reasoning through ma-

trix based transformation. Since knowledge representation withthe fuzzy CE-Nets model is based on graphical methodology, it


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is easy to understand the relationship between the rules and con-

ditions. Also, it is possible to predict the inference results in ad-

vance by observing the flow of truth state in the FCE-Nets when

some conditions are specified. Since the proposed reasoning al-

gorithm requires only simple matrix operations, it is well suited

for integration with existing SCADA systems for on-line appli-

cations.ACKNOWLEDGMENT

The author would like to thank Prof. C.-W. Liu of National

Taiwan University for his guidance and Prof. C.-J. Chou of

National Taipei University of Technology for his insightful

conversations.

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[17] S. H. Wei and S. M. Chen, A new approach for fuzzy risk analysisbased on similarity measures of generalized fuzzy numbers, ExpertSyst. Appl., vol. 36, pp. 589598, 2009.

Wen-Hui Chen (M04) was born in Taiwan in 1965.He received his B.S. degree from National TaiwanUniversity of Science and Technology, and the M.S.and Ph.D. degrees from National Taiwan University,all in electrical engineering. From year 1992 to2000, he held the position as a senior engineer andreceived numerous employee outstanding awards atTaiwan Power Company (Taipower Co.), Taiwanslargest power utility company. He is currently an

associate professor at the Graduate Institute ofAutomation Technology, National Taipei University

of Technology.

chen_fault section estimation using fuzzy matrix-based reasoning methods_2011

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